PageSourceSearch

https://maths-angel.com/lessons

html maths-angel.com collected 2026-10-09 22:36:35 UTC 438,964 bytes, 3 lines download raw bytes

1<!DOCTYPE html><html lang="en"><head><meta charSet="utf-8"/><meta name="viewport" content="width=device-width, initial-scale=1"/><link rel="preload" href="/_next/static/media/5c8bbc89ca099f34-s.p.2qijkc4_gtkq0.woff2" as="font" crossorigin="" type="font/woff2"/><link rel="preload" href="/_next/static/media/fed68dff3ca987ed-s.p.3e08ior5wrhci.woff2" as="font" crossorigin="" type="font/woff2"/><link rel="preload" as="image" href="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/number-line-inequality-symbols/number-line-and-comparing-numbers-math-angel.webp"/><link rel="preload" as="image" href="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/place-value-chart-rounding/place-value-and-rounding-numbers-math-angel.webp"/><link rel="preload" as="image" href="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/natural-numbers-whole-numbers-and-integers-math-angel.webp"/><link rel="preload" as="image" href="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/rational-numbers/rational-numbers-and-their-location-on-a-number-line-math-angel.webp"/><link rel="stylesheet" href="/_next/static/chunks/3_f885ikmu7vm.css" data-precedence="next"/><link rel="stylesheet" href="/_next/static/chunks/1_oj-8fpiwx0n.css" data-precedence="next"/><link rel="stylesheet" href="/_next/static/chunks/0zrd7rd7ow0gg.css" data-precedence="next"/><link rel="stylesheet" href="/_next/static/chunks/1etrw9bfctihn.css" data-precedence="next"/><link rel="preload" as="script" fetchPriority="low" href="/_next/static/chunks/2epzldmiz9i3c.js"/>
1<script src="/_next/static/chunks/2-urkx3cuhmdn.js" async=""></script>
1<script src="/_next/static/chunks/37vyuzuaigr6t.js" async=""></script>
1<script src="/_next/static/chunks/3bw0iio86plvw.js" async=""></script>
1<script src="/_next/static/chunks/26g4tn5b226u5.js" async=""></script>
1<script src="/_next/static/chunks/turbopack-36a_noq--0_5p.js" async=""></script>
1<script src="/_next/static/chunks/3ne1-gn2awz9c.js" async=""></script>
1<script src="/_next/static/chunks/19lc_9yhbdjne.js" async=""></script>
1<script src="/_next/static/chunks/33iayyub0472u.js" async=""></script>
1<script src="/_next/static/chunks/1t7rb6j7892t6.js" async=""></script>
1<script src="/_next/static/chunks/2zxltq5qa7_bl.js" async=""></script>
1<script src="/_next/static/chunks/2lmepge7i28qd.js" async=""></script>
1<script src="/_next/static/chunks/09g_5jf_1uhqn.js" async=""></script>
1<script src="/_next/static/chunks/0nbze1qbdcyos.js" async=""></script>
1<script src="/_next/static/chunks/3-hayde213ruy.js" async=""></script>
1<script src="/_next/static/chunks/00twfinmahjsm.js" async=""></script>
1<script src="/_next/static/chunks/19za4y212u0u3.js" async=""></script>
1<script src="/_next/static/chunks/1rug5xx3k1d2p.js" async=""></script>
1<script src="/_next/static/chunks/3hiv2moa078xj.js" async=""></script>
1<script src="/_next/static/chunks/10qmdweo5dkwv.js" async=""></script>
1<script src="/_next/static/chunks/2rv5xxhy5fe63.js" async=""></script>
1<script src="/_next/static/chunks/349nks73i4b-b.js" async=""></script>
1<script src="/_next/static/chunks/3y_s5s_a6rtf2.js" async=""></script>
1<script src="/_next/static/chunks/17hw6cj44vit3.js" async=""></script>
1<script src="/_next/static/chunks/0noi9m_o50fzl.js" async=""></script>
1<script src="/_next/static/chunks/2oz-5926v45re.js" async=""></script>
1<script src="/_next/static/chunks/146ib6hwvnpj6.js" async=""></script>
1<script src="/_next/static/chunks/1jgvs1y9ykbgi.js" async=""></script>
1<script src="/_next/static/chunks/442n0v4gb2bin.js" async=""></script>
1<script src="/_next/static/chunks/1yiixfgw446ng.js" async=""></script>
1<script src="https://clerk.maths-angel.com/npm/@clerk/[email protected]/dist/clerk.browser.js" data-clerk-js-script="true" async="" crossorigin="anonymous" data-clerk-publishable-key="pk_live_Y2xlcmsubWF0aHMtYW5nZWwuY29tJA"></script>
1<link rel="preload" href="https://www.googletagmanager.com/gtag/js?id=G-CDKJFVYDT4" as="script"/><meta name="next-size-adjust" content=""/><link rel="preconnect" href="https://mathangelwebsitestorage.blob.core.windows.net" crossorigin="anonymous"/><link rel="preconnect" href="https://x.maths-angel.com"/><link rel="preconnect" href="https://api.ipinfo.io"/><link rel="preconnect" href="https://clerk.maths-angel.com"/><link rel="preconnect" href="https://mathangel-website-backend.azurewebsites.net/api"/><link rel="preload" as="script" href="https://clerk.maths-angel.com/npm/@clerk/[email protected]/dist/clerk.browser.js" crossorigin="anonymous" fetchPriority="high"/><title>Bite-sized Video Lessons for Year 6 to GCSE &amp; IGCSE | Maths Angel</title><meta name="description" content="Browse all Maths Angel lessons for ages 10 to 16: short videos, flashcards, quizzes and AI help across algebra, geometry, fractions and statistics. Start free."/><meta name="keywords" content="maths lessons,KS3 maths lessons,KS4 maths lessons,GCSE maths lessons,maths video lessons,algebra lessons,geometry lessons,fractions lessons,statistics lessons,maths curriculum"/><link rel="canonical" href="https://maths-angel.com/lessons"/><meta property="og:title" content="Bite-sized Video Lessons for Year 6 to GCSE &amp; IGCSE | Maths Angel"/><meta property="og:description" content="Browse all Maths Angel lessons for ages 10 to 16: short videos, flashcards, quizzes and AI help across algebra, geometry, fractions and statistics. Start free."/><meta property="og:url" content="https://maths-angel.com/lessons"/><meta property="og:site_name" content="Maths Angel"/><meta property="og:locale" content="en_GB"/><meta property="og:image" content="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-website-images/og-images/og_course_overview.png"/><meta property="og:image:width" content="1200"/><meta property="og:image:height" content="630"/><meta property="og:image:alt" content="Bite-sized Video Lessons for Year 6 to GCSE &amp; IGCSE | Maths Angel"/><meta property="og:type" content="website"/><meta name="twitter:card" content="summary_large_image"/><meta name="twitter:title" content="Bite-sized Video Lessons for Year 6 to GCSE &amp; IGCSE | Maths Angel"/><meta name="twitter:description" content="Browse all Maths Angel lessons for ages 10 to 16: short videos, flashcards, quizzes and AI help across algebra, geometry, fractions and statistics. Start free."/><meta name="twitter:image" content="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-website-images/og-images/og_course_overview.png"/><meta name="twitter:image:alt" content="Bite-sized Video Lessons for Year 6 to GCSE &amp; IGCSE | Maths Angel"/><link rel="icon" href="/favicon.ico?favicon.3du3gu3vpsoqm.ico" sizes="48x48" type="image/x-icon"/>
1<script>(function(){var p=location.pathname;document.documentElement.setAttribute('data-b2b-pupil-links-document',p==='/missioncontrol/pupil-links'||p==='/missioncontrol/pupil-links/'?'private':'ordinary');})();</script>
1<script>(function(){try{var g={"cookieSuffix":"ywXlGdM0","frontendApi":"clerk.maths-angel.com","instanceType":"production"},c=document.cookie.split(';'),m=Object.create(null),i,p,x,k,v;for(i=0;i<c.length;i++){p=c[i].trim();x=p.indexOf('=');if(x<1)continue;k=p.slice(0,x);if(m[k]!==undefined)continue;v=p.slice(x+1);try{v=decodeURIComponent(v);}catch(e){}m[k]=v;}var q='_'+g.cookieSuffix,u=m.__client_uat,s=m.__session,su=m['__client_uat'+q],ss=m['__session'+q];function d(t){try{var a=t.split('.')[1];if(!a)return null;a=a.replace(/-/g,'+').replace(/_/g,'/');while(a.length%4)a+='=';return JSON.parse(atob(a));}catch(e){return null;}}function f(j){return j&&typeof j.iss==='string'&&j.iss.replace(/^https?:\/\//i,'')===g.frontendApi;}var sd=d(s||''),ssd=d(ss||''),z=false;if(s&&(!sd||!sd.iss)){z=false;}else if(s&&!f(sd)){z=true;}else if(!su&&!ss){z=false;}else{var si=sd&&Number(sd.iat)||0,ssi=ssd&&Number(ssd.iat)||0;if(su!=='0'&&u!=='0'&&si>ssi){z=false;}else if(su==='0'&&u!=='0'){z=false;}else if(g.instanceType!=='production'&&su!=='0'&&u==='0'&&ssd&&Number(ssd.exp)<=Math.floor(Date.now()/1000)){z=false;}else if(!su&&ss){z=false;}else{z=true;}}var au=z?su:u,as=z?ss:s,aj=z?ssd:sd;if(/^[1-9][0-9]*$/.test(au||'')&&as&&f(aj)){document.documentElement.dataset.authHint='signed-in';}}catch(e){}})();</script>
1<script src="/_next/static/chunks/0cz1d0mv5g_q7.js" noModule=""></script>
1</head><body class="geist_mono_c932d54b-module__LyTxPG__variable mulish_69dbb4a9-module__HhoaQW__variable urbanist_ad9e5074-module__oipyna__variable antialiased font-sans"><div hidden=""><!--$--><!--/$--></div><header class="fixed left-0 right-0 top-0 z-[60] bg-[#ffffff] shadow-[0_1px_2px_rgba(30,10,60,0.04),0_12px_32px_-20px_rgba(30,10,60,0.2)]"><div class="mx-auto px-4 md:px-6 xl:px-[40px]"><div class="flex h-16 items-center gap-3 md:gap-4"><div class="flex-1 min-w-0 flex justify-start items-center"><a class="flex-shrink-0 flex items-center gap-2 hover:opacity-80 transition-opacity" href="/"><div class="relative shrink-0 size-[40px] rounded-full overflow-hidden bg-white flex items-center justify-center"><img alt="Maths Angel" loading="lazy" width="40" height="40" decoding="async" data-nimg="1" class="w-full h-full object-cover" style="color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-website-images/jimmy_avatar.webp"/></div><span class="font-urbanist font-semibold text-xl text-[#1e0a3c]">Maths Angel</span></a></div><nav class="relative h-16 hidden min-[700px]:flex items-center gap-3 min-[1150px]:gap-6 flex-shrink-0"><div data-bar-menu="true" class="h-16 flex items-center"><button type="button" aria-expanded="false" aria-haspopup="true" class="flex items-center gap-1 text-[18px] font-urbanist font-semibold px-3 py-1.5 rounded-lg transition-colors cursor-pointer whitespace-nowrap text-[#6960d9]">Learn<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-chevron-down w-4 h-4 transition-transform" aria-hidden="true"><path d="m6 9 6 6 6-6"></path></svg></button><div class="absolute top-full left-1/2 -translate-x-1/2 z-50 w-[min(840px,calc(100vw-24px))] transition-[opacity,visibility] duration-100 ease-out motion-reduce:transition-none invisible opacity-0 pointer-events-none"><div class="bg-white border-x border-b border-gray-200 rounded-b-xl shadow-[0_16px_40px_-8px_rgba(30,10,60,0.25)] max-h-[calc(100dvh-4rem)] overflow-y-auto overscroll-contain "><div class="grid grid-cols-1 md:grid-cols-[1fr_1.05fr_1fr] gap-x-6 gap-y-5 px-6 pt-5 pb-5"><div><p class="mb-5 font-urbanist text-[16px] font-bold text-[#1e0a3c]">By topic</p><a class="mb-3 flex items-start gap-3 rounded-xl border border-[#6960d9]/20 bg-[#f7f5ff] px-3 py-3 transition-colors hover:border-[#6960d9]/40 hover:bg-[#f0eeff]" href="/lessons"><span class="flex h-9 w-9 shrink-0 items-center justify-center rounded-lg bg-[#f0eeff] text-[#6960d9]" aria-hidden="true"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-book-open h-[18px] w-[18px]" aria-hidden="true"><path d="M12 7v14"></path><path d="M3 18a1 1 0 0 1-1-1V4a1 1 0 0 1 1-1h5a4 4 0 0 1 4 4 4 4 0 0 1 4-4h5a1 1 0 0 1 1 1v13a1 1 0 0 1-1 1h-6a3 3 0 0 0-3 3 3 3 0 0 0-3-3z"></path></svg></span><span class="min-w-0"><span class="block font-urbanist text-[17px] font-bold text-[#1e0a3c]">All lessons</span><span class="block font-urbanist text-[13px] leading-snug text-gray-500">Full curriculum<span class="block">Videos · Flashcards · Quizzes</span></span></span></a><div class="mt-1 flex flex-col gap-0.5"><a class="rounded-lg px-3 py-2 font-urbanist text-[15px] font-bold text-gray-600 transition-colors hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?category=numbers">Number</a><a class="rounded-lg px-3 py-2 font-urbanist text-[15px] font-bold text-gray-600 transition-colors hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?category=algebra">Algebra</a><a class="rounded-lg px-3 py-2 font-urbanist text-[15px] font-bold text-gray-600 transition-colors hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?category=ratio-proportion-rates-of-change">Ratio and Proportion</a><a class="rounded-lg px-3 py-2 font-urbanist text-[15px] font-bold text-gray-600 transition-colors hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?category=geometry-measures">Geometry and Measures</a><a class="rounded-lg px-3 py-2 font-urbanist text-[15px] font-bold text-gray-600 transition-colors hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?category=probability-statistics">Probability and Statistics</a></div></div><div class="md:border-l md:border-gray-100 md:pl-6"><p class="mb-5 font-urbanist text-[16px] font-bold text-[#1e0a3c]">By year or grade</p><div class="grid gap-2 transition-opacity duration-300 grid-cols-1 pointer-events-none opacity-0"><a class="rounded-full border border-gray-300 bg-white px-3 py-2 text-center font-urbanist text-[13.5px] font-bold text-gray-600 whitespace-nowrap transition-colors hover:border-[#6960d9]/60 hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?years=6">Year 6 · Grade 5</a><a class="rounded-full border border-gray-300 bg-white px-3 py-2 text-center font-urbanist text-[13.5px] font-bold text-gray-600 whitespace-nowrap transition-colors hover:border-[#6960d9]/60 hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?years=7">Year 7 · Grade 6</a><a class="rounded-full border border-gray-300 bg-white px-3 py-2 text-center font-urbanist text-[13.5px] font-bold text-gray-600 whitespace-nowrap transition-colors hover:border-[#6960d9]/60 hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?years=8">Year 8 · Grade 7</a><a class="rounded-full border border-gray-300 bg-white px-3 py-2 text-center font-urbanist text-[13.5px] font-bold text-gray-600 whitespace-nowrap transition-colors hover:border-[#6960d9]/60 hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?years=9">Year 9 · Grade 8</a><a class="rounded-full border border-gray-300 bg-white px-3 py-2 text-center font-urbanist text-[13.5px] font-bold text-gray-600 whitespace-nowrap transition-colors hover:border-[#6960d9]/60 hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?years=10">Year 10 · Grade 9</a><a class="rounded-full border border-gray-300 bg-white px-3 py-2 text-center font-urbanist text-[13.5px] font-bold text-gray-600 whitespace-nowrap transition-colors hover:border-[#6960d9]/60 hover:bg-[#f7f5ff] hover:text-[#6960d9]" href="/lessons?years=11">Year 11 · Grade 10</a></div></div><div class="md:border-l md:border-gray-100 md:pl-6"><p class="mb-5 font-urbanist text-[16px] font-bold text-[#1e0a3c]">Not sure where to start?</p><a class="relative flex flex-col gap-1.5 overflow-hidden rounded-xl border border-[#6960d9]/20 bg-[#f7f5ff] p-4 transition-colors hover:border-[#6960d9]/40 hover:bg-[#f0eeff]" href="/maths-check"><span class="flex flex-wrap items-center gap-2 font-urbanist text-[15px] font-semibold text-[#1e0a3c]">Take the Maths Check<span class="inline-flex items-center rounded-full bg-[#6960d9] px-2 py-0.5 text-[10.5px] font-extrabold leading-none tracking-wide text-white">FREE</span></span><span class="pr-[68px] font-urbanist text-[13px] leading-snug text-gray-500">5 mins. Find your strengths and gaps. Colour your<!-- --> <span class="whitespace-nowrap">Skills Map.</span></span><span class="mt-1 font-urbanist text-[13px] font-extrabold text-[#6960d9]">Start now ›</span><img alt="" loading="lazy" width="480" height="480" decoding="async" data-nimg="1" class="pointer-events-none absolute -bottom-1 -right-1 h-[76px] w-[76px] select-none" style="color:transparent" src="/mascots/jimmy-standing.webp"/></a></div></div></div></div></div><a class="text-[18px] font-urbanist font-semibold px-3 py-1.5 rounded-lg transition-colors whitespace-nowrap text-[#0a0a0a] hover:text-[#6960d9]" href="/chatcat">ChatCat (AI)</a><div data-bar-menu="true" class="relative h-16 hidden min-[1150px]:flex items-center"><button type="button" aria-expanded="false" aria-haspopup="true" class="flex items-center gap-1 text-[18px] font-urbanist font-semibold px-3 py-1.5 rounded-lg transition-colors cursor-pointer whitespace-nowrap text-[#0a0a0a] hover:text-[#6960d9]">Exam Prep<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-chevron-down w-4 h-4 transition-transform" aria-hidden="true"><path d="m6 9 6 6 6-6"></path></svg></button><div class="absolute top-full left-1/2 -translate-x-1/2 w-[720px] z-50 transition-[opacity,visibility] duration-100 ease-out motion-reduce:transition-none invisible opacity-0 pointer-events-none"><div class="bg-white border-x border-b border-gray-200 rounded-b-xl shadow-[0_16px_40px_-8px_rgba(30,10,60,0.25)] max-h-[calc(100dvh-4rem)] overflow-y-auto overscroll-contain "><div class="grid grid-cols-2 gap-x-6 px-6 pt-5 pb-5"><div class=""><p class="mb-5 font-urbanist text-[16px] font-bold text-[#1e0a3c]">Practice</p><div class="-mx-2.5 flex flex-col gap-2"><a class="flex items-start gap-3 rounded-lg px-2.5 py-3.5 transition-colors hover:bg-[#f7f5ff]" href="/gcse-maths-questions"><span class="flex h-9 w-9 shrink-0 items-center justify-center rounded-lg bg-[#f0eeff] text-[#6960d9]" aria-hidden="true"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-chart-column h-[18px] w-[18px]" aria-hidden="true"><path d="M3 3v16a2 2 0 0 0 2 2h16"></path><path d="M18 17V9"></path><path d="M13 17V5"></path><path d="M8 17v-3"></path></svg></span><span class="min-w-0"><span class="flex flex-wrap items-center gap-2 font-urbanist text-[16px] font-semibold text-[#1e0a3c]"><span>GCSE Maths Questions</span></span><span class="mt-1 block font-urbanist text-[13px] leading-snug text-gray-500">Real past paper questions. AQA, Edexcel, OCR.</span></span></a><a class="flex items-start gap-3 rounded-lg px-2.5 py-3.5 transition-colors hover:bg-[#f7f5ff]" href="/gcse-boost"><span class="flex h-9 w-9 shrink-0 items-center justify-center rounded-lg bg-[#f0eeff] text-[#6960d9]" aria-hidden="true"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-zap h-[18px] w-[18px]" aria-hidden="true"><path d="M4 14a1 1 0 0 1-.78-1.63l9.9-10.2a.5.5 0 0 1 .86.46l-1.92 6.02A1 1 0 0 0 13 10h7a1 1 0 0 1 .78 1.63l-9.9 10.2a.5.5 0 0 1-.86-.46l1.92-6.02A1 1 0 0 0 11 14z"></path></svg></span><span class="min-w-0"><span class="flex flex-wrap items-center gap-2 font-urbanist text-[16px] font-semibold text-[#1e0a3c]"><span>GCSE Boost</span></span><span class="mt-1 block font-urbanist text-[13px] leading-snug text-gray-500">Practice by topic. Exam methods marked by AI.</span></span></a></div></div><div class="border-l border-gray-100 pl-6"><p class="mb-5 font-urbanist text-[16px] font-bold text-[#1e0a3c]">Revision</p><div class="-mx-2.5 flex flex-col gap-2"><a class="flex items-start gap-3 rounded-lg px-2.5 py-3.5 transition-colors hover:bg-[#f7f5ff]" href="/gcse-revision"><span class="flex h-9 w-9 shrink-0 items-center justify-center rounded-lg bg-[#f0eeff] text-[#6960d9]" aria-hidden="true"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-graduation-cap h-[18px] w-[18px]" aria-hidden="true"><path d="M21.42 10.922a1 1 0 0 0-.019-1.838L12.83 5.18a2 2 0 0 0-1.66 0L2.6 9.08a1 1 0 0 0 0 1.832l8.57 3.908a2 2 0 0 0 1.66 0z"></path><path d="M22 10v6"></path><path d="M6 12.5V16a6 3 0 0 0 12 0v-3.5"></path></svg></span><span class="min-w-0"><span class="flex flex-wrap items-center gap-2 font-urbanist text-[16px] font-semibold text-[#1e0a3c]"><span>GCSE Maths Revision</span></span><span class="mt-1 block font-urbanist text-[13px] leading-snug text-gray-500">
1AQA, Edexcel, OCR. Foundation and Higher.</span></span></a><a class="flex items-start gap-3 rounded-lg px-2.5 py-3.5 transition-colors hover:bg-[#f7f5ff]" href="/igcse-revision"><span class="flex h-9 w-9 shrink-0 items-center justify-center rounded-lg bg-[#f0eeff] text-[#6960d9]" aria-hidden="true"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-globe h-[18px] w-[18px]" aria-hidden="true"><circle cx="12" cy="12" r="10"></circle><path d="M12 2a14.5 14.5 0 0 0 0 20 14.5 14.5 0 0 0 0-20"></path><path d="M2 12h20"></path></svg></span><span class="min-w-0"><span class="flex flex-wrap items-center gap-2 font-urbanist text-[16px] font-semibold text-[#1e0a3c]"><span>IGCSE Maths Revision</span></span><span class="mt-1 block font-urbanist text-[13px] leading-snug text-gray-500">Edexcel: Foundation and Higher. Cambridge (CIE): Core and Extended.</span></span></a></div></div></div></div></div></div><div data-bar-menu="true" class="relative h-16 hidden lg:flex items-center"><button type="button" aria-expanded="false" aria-haspopup="true" class="flex items-center gap-1 text-[18px] font-urbanist font-semibold px-3 py-1.5 rounded-lg transition-colors cursor-pointer whitespace-nowrap text-[#0a0a0a] hover:text-[#6960d9]">Why Us<svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-chevron-down w-4 h-4 transition-transform" aria-hidden="true"><path d="m6 9 6 6 6-6"></path></svg></button><div class="absolute top-full left-0 w-[460px] z-50 transition-[opacity,visibility] duration-100 ease-out motion-reduce:transition-none invisible opacity-0 pointer-events-none"><div class="bg-white border-x border-b border-gray-200 rounded-b-xl shadow-[0_16px_40px_-8px_rgba(30,10,60,0.25)] max-h-[calc(100dvh-4rem)] overflow-y-auto overscroll-contain "><div class=""><a class="flex items-start gap-3 px-5 py-4 transition-colors hover:bg-[#f0eeff]" href="/about-us"><span class="flex h-9 w-9 shrink-0 items-center justify-center rounded-lg bg-[#f0eeff] text-[#6960d9]" aria-hidden="true"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-users h-[18px] w-[18px]" aria-hidden="true"><path d="M16 21v-2a4 4 0 0 0-4-4H6a4 4 0 0 0-4 4v2"></path><path d="M16 3.128a4 4 0 0 1 0 7.744"></path><path d="M22 21v-2a4 4 0 0 0-3-3.87"></path><circle cx="9" cy="7" r="4"></circle></svg></span><span class="min-w-0"><span class="flex items-center gap-2 font-urbanist font-semibold text-[16px] text-[#1e0a3c]"><span>About Us</span></span><span class="block text-[13px] text-gray-500 mt-1 font-urbanist leading-snug">Our mission and team</span></span></a></div><div class="border-t border-gray-100"><a class="flex items-start gap-3 px-5 py-4 transition-colors hover:bg-[#f0eeff]" href="/how-we-teach"><span class="flex h-9 w-9 shrink-0 items-center justify-center rounded-lg bg-[#f0eeff] text-[#6960d9]" aria-hidden="true"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-lightbulb h-[18px] w-[18px]" aria-hidden="true"><path d="M15 14c.2-1 .7-1.7 1.5-2.5 1-.9 1.5-2.2 1.5-3.5A6 6 0 0 0 6 8c0 1 .2 2.2 1.5 3.5.7.7 1.3 1.5 1.5 2.5"></path><path d="M9 18h6"></path><path d="M10 22h4"></path></svg></span><span class="min-w-0"><span class="flex items-center gap-2 font-urbanist font-semibold text-[16px] text-[#1e0a3c]"><span>How We Teach</span></span><span class="block text-[13px] text-gray-500 mt-1 font-urbanist leading-snug">What makes Maths Angel different</span></span></a><div class="flex flex-wrap gap-1.5 px-5 pt-2.5 pb-4"><a class="inline-flex items-center gap-1.5 rounded-full border px-2.5 py-1 text-[12.5px] font-urbanist font-semibold transition-colors border-gray-200 bg-white text-[#4a5565] hover:border-[#6960d9]/50 hover:bg-[#f0eeff] hover:text-[#6960d9]" href="/how-we-teach/videos"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-play h-3.5 w-3.5" aria-hidden="true"><path d="M5 5a2 2 0 0 1 3.008-1.728l11.997 6.998a2 2 0 0 1 .003 3.458l-12 7A2 2 0 0 1 5 19z"></path></svg>Video lessons</a><a class="inline-flex items-center gap-1.5 rounded-full border px-2.5 py-1 text-[12.5px] font-urbanist font-semibold transition-colors border-gray-200 bg-white text-[#4a5565] hover:border-[#6960d9]/50 hover:bg-[#f0eeff] hover:text-[#6960d9]" href="/how-we-teach/flashcards"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-layers h-3.5 w-3.5" aria-hidden="true"><path d="M12.83 2.18a2 2 0 0 0-1.66 0L2.6 6.08a1 1 0 0 0 0 1.83l8.58 3.91a2 2 0 0 0 1.66 0l8.58-3.9a1 1 0 0 0 0-1.83z"></path><path d="M2 12a1 1 0 0 0 .58.91l8.6 3.91a2 2 0 0 0 1.65 0l8.58-3.9A1 1 0 0 0 22 12"></path><path d="M2 17a1 1 0 0 0 .58.91l8.6 3.91a2 2 0 0 0 1.65 0l8.58-3.9A1 1 0 0 0 22 17"></path></svg>
1Flashcards</a><a class="inline-flex items-center gap-1.5 rounded-full border px-2.5 py-1 text-[12.5px] font-urbanist font-semibold transition-colors border-gray-200 bg-white text-[#4a5565] hover:border-[#6960d9]/50 hover:bg-[#f0eeff] hover:text-[#6960d9]" href="/how-we-teach/interactive-practice"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-hand h-3.5 w-3.5" aria-hidden="true"><path d="M18 11V6a2 2 0 0 0-2-2a2 2 0 0 0-2 2"></path><path d="M14 10V4a2 2 0 0 0-2-2a2 2 0 0 0-2 2v2"></path><path d="M10 10.5V6a2 2 0 0 0-2-2a2 2 0 0 0-2 2v8"></path><path d="M18 8a2 2 0 1 1 4 0v6a8 8 0 0 1-8 8h-2c-2.8 0-4.5-.86-5.99-2.34l-3.6-3.6a2 2 0 0 1 2.83-2.82L7 15"></path></svg>Interactive practice</a></div></div><div class="border-t border-gray-100"><a class="flex items-start gap-3 px-5 py-4 transition-colors hover:bg-[#f0eeff]" href="/ai-maths-tutor"><span class="flex h-9 w-9 shrink-0 items-center justify-center rounded-lg bg-[#f0eeff] text-[#6960d9]" aria-hidden="true"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-message-circle h-[18px] w-[18px]" aria-hidden="true"><path d="M2.992 16.342a2 2 0 0 1 .094 1.167l-1.065 3.29a1 1 0 0 0 1.236 1.168l3.413-.998a2 2 0 0 1 1.099.092 10 10 0 1 0-4.777-4.719"></path></svg></span><span class="min-w-0"><span class="flex items-center gap-2 font-urbanist font-semibold text-[16px] text-[#1e0a3c]"><span>ChatCat, AI Maths Tutor</span><span class="inline-flex items-center rounded-full bg-gradient-to-r from-cyan-400 to-violet-300 px-2.5 py-1 text-[11px] font-bold leading-none tracking-wide text-[#1a1a2e]">NEW</span></span><span class="block text-[13px] text-gray-500 mt-1 font-urbanist leading-snug">Help the moment your child is stuck</span></span></a></div><div class="border-t border-gray-100"><a class="flex items-start gap-3 px-5 py-4 transition-colors hover:bg-[#f0eeff]" href="/safeguarding"><span class="flex h-9 w-9 shrink-0 items-center justify-center rounded-lg bg-[#f0eeff] text-[#6960d9]" aria-hidden="true"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-shield-check h-[18px] w-[18px]" aria-hidden="true"><path d="M20 13c0 5-3.5 7.5-7.66 8.95a1 1 0 0 1-.67-.01C7.5 20.5 4 18 4 13V6a1 1 0 0 1 1-1c2 0 4.5-1.2 6.24-2.72a1.17 1.17 0 0 1 1.52 0C14.51 3.81 17 5 19 5a1 1 0 0 1 1 1z"></path><path d="m9 12 2 2 4-4"></path></svg></span><span class="min-w-0"><span class="flex items-center gap-2 font-urbanist font-semibold text-[16px] text-[#1e0a3c]"><span>Safeguarding</span></span><span class="block text-[13px] text-gray-500 mt-1 font-urbanist leading-snug">How we keep your child safe</span></span></a></div><div class="border-t border-gray-100"><a class="flex items-start gap-3 px-5 py-4 transition-colors hover:bg-[#f0eeff]" href="/for-schools"><span class="flex h-9 w-9 shrink-0 items-center justify-center rounded-lg bg-[#f0eeff] text-[#6960d9]" aria-hidden="true"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-school h-[18px] w-[18px]" aria-hidden="true"><path d="M14 21v-3a2 2 0 0 0-4 0v3"></path><path d="M18 5v16"></path><path d="m4 6 7.106-3.79a2 2 0 0 1 1.788 0L20 6"></path><path d="m6 11-3.52 2.147a1 1 0 0 0-.48.854V19a2 2 0 0 0 2 2h16a2 2 0 0 0 2-2v-5a1 1 0 0 0-.48-.853L18 11"></path><path d="M6 5v16"></path><circle cx="12" cy="9" r="2"></circle></svg></span><span class="min-w-0"><span class="flex items-center gap-2 font-urbanist font-semibold text-[16px] text-[#1e0a3c]"><span>For Schools</span><span class="inline-flex items-center rounded-full bg-gradient-to-r from-cyan-400 to-violet-300 px-2.5 py-1 text-[11px] font-bold leading-none tracking-wide text-[#1a1a2e]">NEW</span></span><span class="block text-[13px] text-gray-500 mt-1 font-urbanist leading-snug">Free five-week class pilot for teachers</span></span></a></div></div></div></div><a class="hidden min-[760px]:flex text-[18px] font-urbanist font-semibold px-3 py-1.5 rounded-lg transition-colors whitespace-nowrap text-[#0a0a0a] hover:text-[#6960d9]" href="/pricing">Pricing</a></nav><div class="flex-1 min-w-fit flex justify-end items-center gap-2 min-[1150px]:gap-4"><div class="relative flex items-center"><button type="button" aria-label="Search lessons" aria-expanded="false" aria-controls="header-lesson-search-panel" class="inline-flex items-center justify-center h-10 w-10 rounded-lg text-[#1e0a3c] hover:text-[#6960d9] transition-colors cursor-pointer focus-visible:outline-none focus-visible:ring-2 focus-visible:ring-[#6960d9] focus-visible:ring-offset-2"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-search w-5 h-5" aria-hidden="true"><path d="m21 21-4.34-4.34"></path><circle cx="11" cy="11" r="8"></circle></svg></button></div><div class="header-auth-loading-avatar h-9 w-9 shrink-0 items-center justify-center overflow-hidden rounded-full bg-[#6c47ff]" aria-hidden="true" data-header-auth-placeholder="avatar"><svg viewBox="0 0 36 36" class="h-9 w-9 text-white" fill="currentColor" focusable="false"><circle cx="18" cy="13" r="6"></circle><path d="M7 31c.6-6.4 4.3-9.7 11-9.7S28.4 24.6 29 31H7Z"></path></svg></div><span class="header-auth-loading-signed-out"><!--$?--><template id="B:0"></template><button type="button" class="text-[18px] font-urbanist font-semibold text-[#0a0a0a] hover:text-[#6960d9] px-3 py-1.5 rounded-lg transition-colors hidden min-[900px]:inline-block cursor-pointer whitespace-nowrap">Log in</button><button type="button" class="px-3 sm:px-4 lg:px-6 py-2 lg:py-2.5 text-[14px] sm:text-[15px] lg:text-[18px] font-urbanist font-semibold bg-[#1E0A3C] text-white rounded-[10px] shadow-[0_10px_24px_-10px_rgba(30,10,60,0.55)] transition-[transform,box-shadow] duration-[420ms] ease-[cubic-bezier(0.2,0.8,0.2,1)] will-change-transform hover:-translate-y-0.5 hover:shadow-[0_14px_28px_-10px_rgba(30,10,60,0.6)] cursor-pointer whitespace-nowrap ">Join Free</button><!--/$--></span><button aria-label="Open menu" aria-controls="landing-header-mobile-menu" class="group min-[1150px]:hidden inline-flex items-center justify-center h-10 w-10 sm:h-11 sm:w-11 rounded-md hover:bg-[#f0eeff] transition-colors cursor-pointer" type="button" aria-haspopup="dialog" aria-expanded="false" data-state="closed" data-slot="sheet-trigger"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-menu w-6 h-6 sm:w-7 sm:h-7 text-[#1E0A3C] group-hover:text-[#6960d9] transition-colors" aria-hidden="true"><path d="M4 5h16"></path><path d="M4 12h16"></path><path d="M4 19h16"></path></svg></button></div></div></div></header><main class="w-full">
1<script type="application/ld+json">{"@context":"https://schema.org","@graph":[{"@type":"CollectionPage","@id":"https://maths-angel.com/lessons#webpage","name":"Maths Lessons","description":"Explore six maths topic categories with video lessons, flashcards and practice questions.","url":"https://maths-angel.com/lessons","isPartOf":{"@id":"https://maths-angel.com/#website"},"mainEntity":{"@type":"ItemList","name":"Maths lesson categories","numberOfItems":6,"itemListElement":[{"@type":"ListItem","position":1,"name":"Number","url":"https://maths-angel.com/lessons/number","item":{"@type":"CollectionPage","@id":"https://maths-angel.com/lessons/number#webpage","name":"Number","description":"Video lessons on place value, fractions, decimals, powers, roots and standard form.","url":"https://maths-angel.com/lessons/number"}},{"@type":"ListItem","position":2,"name":"Algebra","url":"https://maths-angel.com/lessons/algebra","item":{"@type":"CollectionPage","@id":"https://maths-angel.com/lessons/algebra#webpage","name":"Algebra","description":"Video lessons on expressions, equations, sequences, graphs, quadratics and simultaneous equations.","url":"https://maths-angel.com/lessons/algebra"}},{"@type":"ListItem","position":3,"name":"Ratio, Proportion and Rates of Change","url":"https://maths-angel.com/lessons/ratio-proportion-and-rates-of-change","item":{"@type":"CollectionPage","@id":"https://maths-angel.com/lessons/ratio-proportion-and-rates-of-change#webpage","name":"Ratio, Proportion and Rates of Change","description":"Video lessons on ratios, proportion, percentages, interest and compound measures.","url":"https://maths-angel.com/lessons/ratio-proportion-and-rates-of-change"}},{"@type":"ListItem","position":4,"name":"Geometry and Measures","url":"https://maths-angel.com/lessons/geometry-and-measures","item":{"@type":"CollectionPage","@id":"https://maths-angel.com/lessons/geometry-and-measures#webpage","name":"Geometry and Measures","description":"Video lessons on angles, shapes, area, volume, transformations, Pythagoras and trigonometry.","url":"https://maths-angel.com/lessons/geometry-and-measures"}},{"@type":"ListItem","position":5,"name":"Probability","url":"https://maths-angel.com/lessons/probability","item":{"@type":"CollectionPage","@id":"https://maths-angel.com/lessons/probability#webpage","name":"Probability","description":"Video lessons on calculating probability, the addition rule, tree diagrams and Venn diagrams.","url":"https://maths-angel.com/lessons/probability"}},{"@type":"ListItem","position":6,"name":"Statistics","url":"https://maths-angel.com/lessons/statistics","item":{"@type":"CollectionPage","@id":"https://maths-angel.com/lessons/statistics#webpage","name":"Statistics","description":"Video lessons on charts, averages, spread, box plots and interpreting data.","url":"https://maths-angel.com/lessons/statistics"}}]}},{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https://maths-angel.com"},{"@type":"ListItem","position":2,"name":"Lessons","item":"https://maths-angel.com/lessons"}]}]}</script>
1<div class="min-h-screen bg-white pt-16"><div class="relative overflow-hidden bg-[#EAEBFF] pt-12 pb-8 md:pt-16 md:pb-10"><div class="absolute inset-0 pointer-events-none" style="background-image:linear-gradient(to right, rgba(255, 255, 255, 0.6) 1px, transparent 1px),
2            linear-gradient(to bottom, rgba(255, 255, 255, 0.6) 1px, transparent 1px);background-size:40px 40px;opacity:0.6"></div><div class="absolute left-0 top-0 bottom-0 w-1/3 hidden md:block pointer-events-none overflow-hidden"><div class="absolute top-[20%] left-[10%] opacity-40" style="opacity:0;transform:scale(0.8)"><svg width="40" height="60" viewBox="0 0 40 60" fill="none"><path d="M10 10L35 30L10 50" stroke="#6960d9" stroke-width="1.5" stroke-linecap="round"></path><circle cx="10" cy="10" r="2" fill="#6960d9"></circle><circle cx="35" cy="30" r="2" fill="#52FFEB"></circle><circle cx="10" cy="50" r="2" fill="#6960d9"></circle></svg></div><div class="absolute top-[45%] left-[5%] opacity-20 scale-75 blur-[0.5px]" style="opacity:0;transform:scale(0.6)">
2<svg width="40" height="60" viewBox="0 0 40 60" fill="none"><path d="M30 10L5 30L30 50" stroke="#6960d9" stroke-width="1.5" stroke-linecap="round"></path><circle cx="30" cy="10" r="2" fill="#6960d9"></circle><circle cx="5" cy="30" r="2" fill="#52FFEB"></circle><circle cx="30" cy="50" r="2" fill="#6960d9"></circle></svg></div><div class="absolute top-[65%] left-[15%] opacity-30 rotate-12" style="opacity:0;transform:translateY(20px)"><svg width="60" height="80" viewBox="0 0 60 80" fill="none"><path d="M10 10H50V70H10V10Z" stroke="#6960d9" stroke-width="1.5" stroke-linecap="round"></path><rect x="15" y="15" width="30" height="15" stroke="#6960d9" stroke-width="1.5"></rect><circle cx="20" cy="40" r="1.5" fill="#52FFEB"></circle><circle cx="30" cy="40" r="1.5" fill="#6960d9"></circle><circle cx="40" cy="40" r="1.5" fill="#6960d9"></circle><circle cx="20" cy="50" r="1.5" fill="#6960d9"></circle><circle cx="30" cy="50" r="1.5" fill="#52FFEB"></circle><circle cx="40" cy="50" r="1.5" fill="#6960d9"></circle><circle cx="20" cy="60" r="1.5" fill="#6960d9"></circle><circle cx="30" cy="60" r="1.5" fill="#6960d9"></circle><circle cx="40" cy="60" r="1.5" fill="#52FFEB"></circle><circle cx="10" cy="10" r="2" fill="#52FFEB"></circle><circle cx="50" cy="10" r="2" fill="#6960d9"></circle><circle cx="50" cy="70" r="2" fill="#52FFEB"></circle><circle cx="10" cy="70" r="2" fill="#6960d9"></circle></svg></div></div><div class="absolute right-0 top-0 bottom-0 w-1/3 hidden md:block pointer-events-none overflow-hidden"><div class="absolute top-[20%] right-[10%] opacity-40" style="opacity:0;transform:scale(0.8)">
2<svg width="60" height="60" viewBox="0 0 60 60" fill="none"><line x1="50" y1="10" x2="10" y2="50" stroke="#6960d9" stroke-width="1.5" stroke-linecap="round"></line><circle cx="15" cy="15" r="4" stroke="#6960d9" stroke-width="1.5"></circle><circle cx="15" cy="15" r="2" fill="#52FFEB"></circle><circle cx="45" cy="45" r="4" stroke="#6960d9" stroke-width="1.5"></circle><circle cx="45" cy="45" r="2" fill="#52FFEB"></circle><circle cx="50" cy="10" r="2" fill="#6960d9"></circle><circle cx="10" cy="50" r="2" fill="#6960d9"></circle></svg></div><div class="absolute top-[50%] right-[5%] opacity-20 scale-75 blur-[0.5px] -rotate-12" style="opacity:0;transform:scale(0.6)"><svg width="120" height="40" viewBox="0 0 120 40" fill="none"><rect x="0" y="0" width="120" height="40" stroke="#6960d9" stroke-width="1.5"></rect><line x1="10" y1="0" x2="10" y2="15" stroke="#6960d9" stroke-width="1.5"></line><line x1="20" y1="0" x2="20" y2="10" stroke="#6960d9" stroke-width="1"></line><line x1="30" y1="0" x2="30" y2="15" stroke="#6960d9" stroke-width="1.5"></line><line x1="40" y1="0" x2="40" y2="10" stroke="#6960d9" stroke-width="1"></line><line x1="50" y1="0" x2="50" y2="15" stroke="#6960d9" stroke-width="1.5"></line><line x1="60" y1="0" x2="60" y2="10" stroke="#6960d9" stroke-width="1"></line><line x1="70" y1="0" x2="70" y2="15" stroke="#6960d9" stroke-width="1.5"></line><line x1="80" y1="0" x2="80" y2="10" stroke="#6960d9" stroke-width="1"></line><line x1="90" y1="0" x2="90" y2="15" stroke="#6960d9" stroke-width="1.5"></line><line x1="100" y1="0" x2="100" y2="10" stroke="#6960d9" stroke-width="1"></line><line x1="110" y1="0" x2="110" y2="15" stroke="#6960d9" stroke-width="1.5"></line><circle cx="0" cy="0" r="2" fill="#52FFEB"></circle><circle cx="120" cy="0" r="2" fill="#6960d9"></circle><circle cx="120" cy="40" r="2" fill="#52FFEB"></circle><circle cx="0" cy="40" r="2" fill="#6960d9"></circle></svg></div><div class="absolute top-[80%] right-[10%] opacity-30" style="opacity:0;transform:translateY(20px)">
2<svg width="80" height="60" viewBox="0 0 80 60" fill="none"><line x1="10" y1="50" x2="70" y2="50" stroke="#6960d9" stroke-width="1.5" stroke-linecap="round"></line><line x1="10" y1="50" x2="60" y2="20" stroke="#6960d9" stroke-width="1.5" stroke-linecap="round"></line><path d="M25 50 Q 25 45 23 42" stroke="#52FFEB" stroke-width="1"></path><circle cx="10" cy="50" r="2" fill="#6960d9"></circle><circle cx="70" cy="50" r="2" fill="#52FFEB"></circle><circle cx="60" cy="20" r="2" fill="#52FFEB"></circle></svg></div></div><div class="relative mx-auto max-w-2xl md:max-w-3xl lg:max-w-4xl px-8 text-center z-10"><h1 class="mb-6 mt-[10px] text-[34px] md:text-[48px] lg:text-[56px] font-urbanist font-extrabold leading-tight text-[#1e0a3c]">Bite-sized Video Lessons for<!-- --> <span class="text-[#6960d9] transition-opacity duration-300 opacity-0">Year 6 to GCSE &amp; IGCSE</span></h1><p class="text-balance text-[16px] md:text-[17px] lg:text-[20px] font-urbanist font-medium text-[#414b5a]">10-minute lessons with videos, flashcards, quizzes, interactive practice, and AI help.</p></div></div><div class="scroll-mt-[72px]"><div class="relative bg-[#EAEBFF] pt-0 pb-4 overflow-hidden"><div class="absolute inset-0 pointer-events-none opacity-60 z-0" style="background-image:url(https://mathangelwebsitestorage.blob.core.windows.net/mathangel-website-images/cloud-decorations.webp);background-size:100% auto;background-position:top center;background-repeat:no-repeat"></div><div class="relative z-10 mx-auto max-w-7xl 2xl:max-w-[1600px] px-4 md:px-8"><div class="mx-auto max-w-2xl"><div class="relative"><svg xmlns="http://www.w3.org/2000/svg" width="20" height="20" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-search absolute left-4 top-1/2 -translate-y-1/2 text-[#6960d9] z-10 pointer-events-none" aria-hidden="true"><path d="m21 21-4.34-4.34"></path><circle cx="11" cy="11" r="8"></circle></svg><input type="text" placeholder="Search any maths topic…" class="w-full rounded-[16px] border-2 border-[#6960d9]/20 bg-white/80 backdrop-blur-sm py-3.5 pl-12 pr-12 text-[#1e0a3c] placeholder:text-[#6a7282] focus:border-[#6960d9] focus:outline-none focus:ring-2 focus:ring-[#6960d9]/20 hover:shadow-[0_0_16px_rgba(105,96,217,0.15)] font-urbanist text-[16px] font-medium transition-all shadow-sm relative z-0" value=""/></div><div class="mt-3 flex min-h-[44px] flex-col items-center justify-center gap-2 px-2"></div></div></div></div><div class="bg-white"><div class="mx-auto max-w-7xl 2xl:max-w-[1600px] px-8"><div class="relative pt-12 transition-opacity duration-300 pointer-events-none opacity-0"><div class="flex flex-wrap items-center gap-3"><span class="font-urbanist text-sm font-bold text-gray-500">Choose your country:</span><div class="static sm:relative"><button type="button" disabled="" aria-expanded="false" aria-haspopup="dialog" class="flex cursor-pointer items-center gap-2 rounded-xl border border-[#6960d9]/30 bg-white px-4 py-2 font-urbanist text-sm font-bold text-gray-900 transition-colors hover:border-[#6960d9]/60 disabled:cursor-wait disabled:opacity-60"><span aria-hidden="true">🌐</span><span>Other</span><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-chevron-down text-gray-500 transition-transform duration-200" aria-hidden="true"><path d="m6 9 6 6 6-6"></path></svg></button></div></div></div></div></div><div class="bg-white"><div class="mx-auto max-w-7xl 2xl:max-w-[1600px] px-8"><div class="flex flex-wrap gap-2.5 pt-5 pb-8"><button type="button" aria-pressed="true" class="shrink-0 rounded-full border font-bold transition-colors duration-200 whitespace-nowrap font-urbanist px-4 py-2 text-sm md:px-6 md:py-2.5 md:text-[15px] cursor-pointer border-transparent bg-[#6960d9] text-white">All years</button><button type="button" data-year="6" aria-pressed="false" class="shrink-0 rounded-full border font-bold transition-colors duration-200 whitespace-nowrap font-urbanist px-4 py-2 text-sm md:px-6 md:py-2.5 md:text-[15px] cursor-pointer border-gray-300 bg-white text-gray-600 hover:border-[#6960d9]/60 hover:text-[#6960d9]">Year 6 · Grade 5</button><button type="button" data-year="7" aria-pressed="false" class="shrink-0 rounded-full border font-bold transition-colors duration-200 whitespace-nowrap font-urbanist px-4 py-2 text-sm md:px-6 md:py-2.5 md:text-[15px] cursor-pointer border-gray-300 bg-white text-gray-600 hover:border-[#6960d9]/60 hover:text-[#6960d9]">Year 7 · Grade 6</button><button type="button" data-year="8" aria-pressed="false" class="shrink-0 rounded-full border font-bold transition-colors duration-200 whitespace-nowrap font-urbanist px-4 py-2 text-sm md:px-6 md:py-2.5 md:text-[15px] cursor-pointer border-gray-300 bg-white text-gray-600 hover:border-[#6960d9]/60 hover:text-[#6960d9]">Year 8 · Grade 7</button><button type="button" data-year="9" aria-pressed="false" class="shrink-0 rounded-full border font-bold transition-colors duration-200 whitespace-nowrap font-urbanist px-4 py-2 text-sm md:px-6 md:py-2.5 md:text-[15px] cursor-pointer border-gray-300 bg-white text-gray-600 hover:border-[#6960d9]/60 hover:text-[#6960d9]">Year 9 · Grade 8</button><button type="button" data-year="10" aria-pressed="false" class="shrink-0 rounded-full border font-bold transition-colors duration-200 whitespace-nowrap font-urbanist px-4 py-2 text-sm md:px-6 md:py-2.5 md:text-[15px] cursor-pointer border-gray-300 bg-white text-gray-600 hover:border-[#6960d9]/60 hover:text-[#6960d9]">Year 10 · Grade 9</button><button type="button" data-year="11" aria-pressed="false" class="shrink-0 rounded-full border font-bold transition-colors duration-200 whitespace-nowrap font-urbanist px-4 py-2 text-sm md:px-6 md:py-2.5 md:text-[15px] cursor-pointer border-gray-300 bg-white text-gray-600 hover:border-[#6960d9]/60 hover:text-[#6960d9]">Year 11 · Grade 10</button><button type="button" class="ml-auto shrink-0 cursor-pointer self-center whitespace-nowrap font-urbanist text-[15px] font-bold text-[#6960d9] transition-colors hover:text-[#5850c4]">Clear filters</button></div></div></div><div class="bg-white pb-0"><div class="mx-auto max-w-7xl 2xl:max-w-[1600px] px-4 md:px-8"><div class="flex flex-wrap gap-0 border-b-2 border-[#6960d9]/10"><div class="relative group min-w-0 basis-1/2 md:basis-0 md:grow"><button class="relative w-full flex flex-col items-center gap-2 py-4 md:py-5 transition-all font-urbanist font-bold text-[#6960d9]"><svg xmlns="http://www.w3.org/2000/svg" width="26" height="26" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-calculator" aria-hidden="true"><rect width="16" height="20" x="4" y="2" rx="2"></rect><line x1="8" x2="16" y1="6" y2="6"></line><line x1="16" x2="16" y1="14" y2="18"></line><path d="M16 10h.01"></path><path d="M12 10h.01"></path><path d="M8 10h.01"></path><path d="M12 14h.01"></path><path d="M8 14h.01"></path><path d="M12 18h.01"></path><path d="M8 18h.01"></path></svg><span class="text-[14px] md:text-[15px] leading-tight">Number</span><div class="absolute bottom-0 left-0 right-0 h-1 bg-[#6960d9] rounded-t-sm"></div></button></div><div class="relative group min-w-0 basis-1/2 md:basis-0 md:grow"><button class="relative w-full flex flex-col items-center gap-2 py-4 md:py-5 transition-all font-urbanist font-bold text-gray-600 hover:text-[#6960d9] cursor-pointer"><svg xmlns="http://www.w3.org/2000/svg" width="26" height="26" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-superscript" aria-hidden="true"><path d="m4 19 8-8"></path><path d="m12 19-8-8"></path><path d="M20 12h-4c0-1.5.442-2 1.5-2.5S20 8.334 20 7.002c0-.472-.17-.93-.484-1.29a2.105 2.105 0 0 0-2.617-.436c-.42.239-.738.614-.899 1.06"></path></svg><span class="text-[14px] md:text-[15px] leading-tight">Algebra</span><div class="absolute bottom-0 left-0 right-0 h-1 bg-[#6960d9] opacity-0 group-hover:opacity-50 transition-opacity rounded-t-sm"></div></button></div><div class="relative group min-w-0 basis-1/2 md:basis-0 md:grow"><button class="relative w-full flex flex-col items-center gap-2 py-4 md:py-5 transition-all font-urbanist font-bold text-gray-600 hover:text-[#6960d9] cursor-pointer"><svg xmlns="http://www.w3.org/2000/svg" width="26" height="26" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-percent" aria-hidden="true">
2<line x1="19" x2="5" y1="5" y2="19"></line><circle cx="6.5" cy="6.5" r="2.5"></circle><circle cx="17.5" cy="17.5" r="2.5"></circle></svg><span class="text-[14px] md:text-[15px] leading-tight">Ratio and Proportion</span><div class="absolute bottom-0 left-0 right-0 h-1 bg-[#6960d9] opacity-0 group-hover:opacity-50 transition-opacity rounded-t-sm"></div></button></div><div class="relative group min-w-0 basis-1/2 md:basis-0 md:grow"><button class="relative w-full flex flex-col items-center gap-2 py-4 md:py-5 transition-all font-urbanist font-bold text-gray-600 hover:text-[#6960d9] cursor-pointer"><svg xmlns="http://www.w3.org/2000/svg" width="26" height="26" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-shapes" aria-hidden="true"><path d="M8.3 10a.7.7 0 0 1-.626-1.079L11.4 3a.7.7 0 0 1 1.198-.043L16.3 8.9a.7.7 0 0 1-.572 1.1Z"></path><rect x="3" y="14" width="7" height="7" rx="1"></rect><circle cx="17.5" cy="17.5" r="3.5"></circle></svg><span class="text-[14px] md:text-[15px] leading-tight">Geometry and Measures</span><div class="absolute bottom-0 left-0 right-0 h-1 bg-[#6960d9] opacity-0 group-hover:opacity-50 transition-opacity rounded-t-sm"></div></button></div><div class="relative group min-w-0 basis-1/2 md:basis-0 md:grow"><button class="relative w-full flex flex-col items-center gap-2 py-4 md:py-5 transition-all font-urbanist font-bold text-gray-600 hover:text-[#6960d9] cursor-pointer"><svg xmlns="http://www.w3.org/2000/svg" width="26" height="26" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2.5" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-chart-pie" aria-hidden="true"><path d="M21 12c.552 0 1.005-.449.95-.998a10 10 0 0 0-8.953-8.951c-.55-.055-.998.398-.998.95v8a1 1 0 0 0 1 1z"></path><path d="M21.21 15.89A10 10 0 1 1 8 2.83"></path></svg><span class="text-[14px] md:text-[15px] leading-tight">Probability and Statistics</span><div class="absolute bottom-0 left-0 right-0 h-1 bg-[#6960d9] opacity-0 group-hover:opacity-50 transition-opacity rounded-t-sm"></div></button></div></div></div></div></div><div class="bg-white py-12"><div class="mx-auto max-w-7xl 2xl:max-w-[1600px] px-8"><div class="grid grid-cols-1 gap-6 sm:grid-cols-2 lg:grid-cols-3 2xl:grid-cols-4"><a data-testid="maths-check-grid-card" class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg hover:ring-2 hover:ring-[#6960d9]/40 focu
2s:outline-none focus-visible:ring-2 focus-visible:ring-[#6960d9]/50 focus-visible:ring-offset-2" href="/maths-check"><div class="relative aspect-video overflow-hidden bg-[#EAEBFF] p-3 sm:p-3.5"><div aria-hidden="true" class="flex h-full gap-2"><div class="flex flex-1 flex-col gap-2"><div class="flex min-h-0 flex-col rounded-xl px-2.5 pt-2 pb-2.5 basis-[52%]" style="background-color:#D8EBFC"><span class="block min-w-0 pb-2 font-urbanist text-[11px] font-bold leading-tight tracking-tight" style="color:#1668B5">Number</span><span class="mt-auto block h-1.5 w-full overflow-hidden rounded-full bg-white/80"><span class="block h-full rounded-full" style="width:86%;background-color:#78ABE0"></span></span></div><div class="flex min-h-0 flex-col rounded-xl px-2.5 pt-2 pb-2.5 flex-1" style="background-color:#D7F2E9"><span class="block min-w-0 pb-2 font-urbanist text-[11px] font-bold leading-tight tracking-tight" style="color:#0E7A64">Geometry</span><span class="mt-auto block h-1.5 w-full overflow-hidden rounded-full bg-white/80"><span class="block h-full rounded-full" style="width:58%;background-color:#5FB3A4"></span></span></div></div><div class="flex flex-1 flex-col gap-2"><div class="flex min-h-0 flex-col rounded-xl px-2.5 pt-2 pb-2.5 basis-[36%]" style="background-color:#EAE1FB"><span class="block min-w-0 pb-2 font-urbanist text-[11px] font-bold leading-tight tracking-tight" style="color:#6A3BC4">Algebra</span><span class="mt-auto block h-1.5 w-full overflow-hidden rounded-full bg-white/80"><span class="block h-full rounded-full" style="width:72%;background-color:#AC93E9"></span></span></div><div class="flex min-h-0 flex-col rounded-xl px-2.5 pt-2 pb-2.5 flex-1" style="background-color:#F7E9CF"><span class="block min-w-0 pb-2 font-urbanist text-[11px] font-bold leading-tight tracking-tight" style="color:#A76909">Ratio &amp; Proportion</span><span class="mt-auto block h-1.5 w-full overflow-hidden rounded-full bg-white/80"><span class="block h-full rounded-full" style="width:41%;background-color:#DCA779"></span></span></div></div><div class="flex flex-1 flex-col gap-2"><div class="flex min-h-0 flex-col rounded-xl px-2.5 pt-2 pb-2.5 basis-[58%]" style="background-color:#FAE3EA"><span class="block min-w-0 pb-2 font-urbanist text-[11px] font-bold leading-tight tracking-tight" style="color:#B23A62">Probability &amp; Statistics</span><span class="mt-auto block h-1.5 w-full overflow-hidden rounded-full bg-white/80"><span class="block h-full rounded-full" style="width:63%;background-color:#EDA2BB"></span></span></div><div class="flex flex-1 items-end justify-center"><img alt="" loading="lazy" width="280" height="280" decoding="async" data-nimg="1" class="pointer-events-none h-auto w-[92%] max-w-[96px] translate-y-[6%] select-none transition-transform group-hover:translate-y-0" style="color:transparent" src="/mascots/jimmy-standing.webp"/></div></div></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-2"><span class="inline-flex items-center rounded-full bg-[#6960d9] px-2.5 py-0.5 text-[11px] font-bold leading-snug text-white">Free Maths Check</span><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">5 mins</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Not sure where to start?</h3><p class="text-sm text-gray-600">Answer 16 quick questions. Find your strengths and gaps. Colour your Skills Map.</p><div class="mt-3 flex justify-end"><span class="inline-flex items-center font-urbanist text-[14px] font-extrabold text-[#6960d9] transition-transform group-hover:translate-x-0.5">Start now ›</span></div></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/number-line-inequality-symbols"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Number line from −5 to 5 showing negative numbers, the origin, and positive numbers at equal intervals" loading="eager" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/number-line-inequality-symbol
2s/number-line-and-comparing-numbers-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:10</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Number Types and Place Values lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#DBEAFE;color:#1E40AF"><span class="truncate">Number Types and Place Values</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Number Line and Comparing Numbers</h3><p class="text-sm text-gray-600 line-clamp-2">A number line places numbers in order on a straight line. Interactive practice to try, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/place-value-chart-rounding"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Place value chart and rounding rules for whole numbers with worked examples" loading="eager" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/place-value-chart-rounding/place-value-and-rounding-numbers-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">
22:34</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Number Types and Place Values lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#DBEAFE;color:#1E40AF"><span class="truncate">Number Types and Place Values</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Place Value and Rounding Numbers</h3><p class="text-sm text-gray-600 line-clamp-2">Place value is what each digit is worth: in 3482 the 4 means 400. To round, look at the next digit; 5 or more rounds up. Download the flashcards to revise.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/natural-numbers-whole-numbers-integers"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Definition of Natural numbers, whole numbers, and integers." loading="eager" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/natural-numbers-whole-numbers-and-integers-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:52</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Number Types and Place Values lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#DBEAFE;color:#1E40AF"><span class="truncate">Number Types and Place Values</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Natural Numbers, Whole Numbers, and Integers</h3><p class="text-sm text-gray-600 line-clamp-2">Natural numbers start at 1, whole numbers include 0, and integers add negatives. Worked examples, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/rational-numbers"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Rational numbers lesson showing fractions, terminating decimals, and recurring decimals." loading="eager" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/rational-numbers/rational-numbers-and-their-location-on-a-number-line-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:03</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Number Types and Place Values lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#DBEAFE;color:#1E40AF"><span class="truncate">Number Types and Place Values</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 9–10 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Rational Numbers and Their Location on a Number Line</h3><p class="text-sm text-gray-600 line-clamp-2">A rational number is one integer over another, like 3/4, −2 or 0.75; √2 and π are not. Worked examples, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/absolute-value"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Absolute value is always non-negative: |x| ≥ 0, with examples |5| = 5, |0| = 0, and |−3| = 3" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/absolute-value/absolute-value-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:37</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Number Types and Place Values lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#DBEAFE;color:#1E40AF"><span class="truncate">Number Types and Place Values</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Absolute Value</h3><p class="text-sm text-gray-600 line-clamp-2">Absolute value is the distance from zero, so |−5| = 5 and |5| = 5; it is never negative. Worked examples, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/basic-arithmetic-inverse-operations"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Basic arithmetic operations and inverse operations diagram with examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basic-arithmetic-inverse-operations/basic-arithmetic-and-inverse-operations-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:02</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Basic Calculations lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FFEDD5;color:#C2410C"><span class="truncate">Basic Calculations</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Basic Arithmetic and Inverse Operations</h3><p class="text-sm text-gray-600 line-clamp-2">Basic arithmetic covers addition, subtraction, multiplication and division; inverse operations undo each other. Worked examples, plus flashcards.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/bidmas-order-of-operations"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="BIDMAS order of operations lesson covering brackets, indices, division, multiplication, addition, subtraction" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/bidmas-order-of-operations/bidmas-order-of-operations-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">2:52</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Basic Calculations lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FFEDD5;color:#C2410C"><span class="truncate">Basic Calculations</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">BIDMAS - Order of Operations</h3><p class="text-sm text-gray-600 line-clamp-2">BIDMAS is the order of operations: Brackets, Indices, Divide, Multiply, Add, Subtract. Flashcards to download, plus a quiz to test yourself.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/commutative-and-associative-laws"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Commutative and associative property lesson showing how to swap and regroup numbers in maths" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/commutative-property-associative-property/commutative-property-and-associative-property-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:16</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Basic Calculations lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FFEDD5;color:#C2410C"><span class="truncate">Basic Calculations</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Commutative and Associative Laws</h3><p class="text-sm text-gray-600 line-clamp-2">Commutative: a + b = b + a. Associative: (a + b) + c = a + (b + c). Same for multiplying. Flashcards to download to revise both laws.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/column-addition-and-subtraction"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Column addition and subtraction worked examples showing carrying and borrowing with multi-digit numbers" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/column-addition-and-subtraction/column-addition-and-column-subtraction-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:10</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Basic Calculations lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FFEDD5;color:#C2410C"><span class="truncate">Basic Calculations</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Column Addition and Column Subtraction</h3><p class="text-sm text-gray-600 line-clamp-2">Column addition and subtraction are used to add and subtract multi-digit numbers vertically. Interactive practice to try, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/long-multiplication"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Long multiplication method showing step-by-step partial products for multiplying multi-digit numbers" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-multiplication/long-multiplication-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:18</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Basic Calculations lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FFEDD5;color:#C2410C"><span class="truncate">Basic Calculations</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Long Multiplication</h3><p class="text-sm text-gray-600 line-clamp-2">Long multiplication splits large calculations into smaller digit-by-digit steps. Interactive practice to try, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/long-division"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Long division worked example showing dividend, divisor, quotient and remainder step by step" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-division/long-division-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:10</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Basic Calculations lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FFEDD5;color:#C2410C"><span class="truncate">Basic Calculations</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Long Division</h3><p class="text-sm text-gray-600 line-clamp-2">Long division goes one digit at a time: divide, multiply, subtract, bring down, repeat. Worked examples, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/decimal-point-movement"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Decimal point shifting right for multiplication and left for division by powers of 10" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimal-point-movement/movement-of-the-decimal-point-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:08</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Basic Calculations lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FFEDD5;color:#C2410C"><span class="truncate">Basic Calculations</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Movement of the Decimal Point</h3><p class="text-sm text-gray-600 line-clamp-2">Moving the decimal point right multiplies a number by 10, 100 or 1000; moving it left divides. Free 3-minute video, plus a quiz to test yourself.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/adding-and-subtracting-negative-numbers"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Adding and subtracting negative numbers with sign rules and number line examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-negative-numbers/adding-and-subtracting-negative-numbers-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:40</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Basic Calculations lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FFEDD5;color:#C2410C"><span class="truncate">Basic Calculations</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Adding and Subtracting Negative Numbers</h3><p class="text-sm text-gray-600 line-clamp-2">Adding and subtracting negatives: two signs the same make a plus, two different make a minus. Flashcards to download to revise the rules.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/multiplying-and-dividing-negative-numbers"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Sign rules for multiplying and dividing negative numbers with worked examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-and-dividing-negative-numbers/multiplying-and-dividing-negative-numbers-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:04</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Basic Calculations lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FFEDD5;color:#C2410C"><span class="truncate">Basic Calculations</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Multiplying and Dividing Negative Numbers</h3><p class="text-sm text-gray-600 line-clamp-2">Multiplying or dividing negatives: same signs give a plus, different signs give a minus. Interactive practice to try, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/calculating-money"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Step-by-step guide to calculating money with pounds and pence examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-money/calculating-money-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:23</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Units, Money and Time lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#DCFCE7;color:#166534"><span class="truncate">Units, Money and Time</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Calculating Money</h3><p class="text-sm text-gray-600 line-clamp-2">Calculating money involves separating pounds and pence for each operation. Interactive practice to try, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/units-of-length"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Metric units of length conversion chart showing km, m, cm, and mm with examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-length/converting-and-calculating-units-of-length-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:47</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Units, Money and Time lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#DCFCE7;color:#166534"><span class="truncate">Units, Money and Time</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Converting and Calculating Units of Length</h3><p class="text-sm text-gray-600 line-clamp-2">1 km = 1000 m, 1 m = 100 cm and 1 cm = 10 mm. Convert between them and add or subtract lengths. Free 4-minute video, plus a quiz to test yourself.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/units-of-mass"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Metric units of mass conversion chart showing tonnes, kilograms, grams, and milligrams" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-mass/converting-and-calculating-units-of-mass-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:33</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Units, Money and Time lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#DCFCE7;color:#166534"><span class="truncate">Units, Money and Time</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Converting and Calculating Units of Mass</h3><p class="text-sm text-gray-600 line-clamp-2">1 tonne = 1000 kg, 1 kg = 1000 g and 1 g = 1000 mg: multiply going down, divide going up. Flashcards to download, plus a quiz to test yourself.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/converting-time"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Converting time and calculating time lesson covering hours, minutes, and seconds" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/converting-time/converting-time-and-calculating-time-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:00</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Units, Money and Time lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#DCFCE7;color:#166534"><span class="truncate">Units, Money and Time</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Converting Time and Calculating Time</h3><p class="text-sm text-gray-600 line-clamp-2">1 hour = 60 minutes and 1 minute = 60 seconds, so 2 h 15 min is 135 minutes. Quiz to test yourself, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/divisibility-rules"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Divisibility rules for 2, 4, and 8 using last-digit checks, with worked examples for 26, 328, and 6160" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/divisibility-rules/divisibility-and-divisibility-rules-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:22</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Factors, Multiples and Primes lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FCE7F3;color:#9D174D"><span class="truncate">Factors, Multiples and Primes</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Divisibility and Divisibility Rules</h3><p class="text-sm text-gray-600 line-clamp-2">Divisibility rules for 2 to 10 are simple digit checks to test if a number divides evenly. Interactive practice to try, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/prime-numbers-prime-factorisation"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Prime numbers under 20 and prime factorisation of 126 = 2 × 3² × 7 using a factor tree" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/prime-numbers-prime-factorisation/prime-numbers-and-prime-factorisation-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:23</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Factors, Multiples and Primes lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FCE7F3;color:#9D174D"><span class="truncate">Factors, Multiples and Primes</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Prime Numbers and Prime Factorisation</h3><p class="text-sm text-gray-600 line-clamp-2">A prime number has exactly two factors: 1 and itself. Interactive practice to try, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/hcf-and-lcm"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Step-by-step guide showing how to find HCF and LCM using prime factorisation with worked examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/hcf-and-lcm/how-to-find-hcf-and-lcm-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">4:01</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Factors, Multiples and Primes lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FCE7F3;color:#9D174D"><span class="truncate">Factors, Multiples and Primes</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">How to Find HCF and LCM</h3><p class="text-sm text-gray-600 line-clamp-2">The HCF is the largest factor two numbers share; the LCM is their smallest common multiple. Free 4-minute video, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/introduction-to-fractions"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Introduction to fractions showing numerator and denominator with pizza slice examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/introduction-to-fractions/introduction-to-fractions-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:34</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#EDE9FE;color:#5B21B6"><span class="truncate">Fractions</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Introduction to Fractions</h3><p class="text-sm text-gray-600 line-clamp-2">Fractions show parts of a whole with a numerator and denominator, like 3/4. Find a fraction of an amount too. Worked examples, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/equivalent-fractions"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Equivalent fractions: simplifying 18/63 to 2/7 and expanding 2/7 to 18/63" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/equivalent-fractions/equivalent-fractions-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:22</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#EDE9FE;color:#5B21B6"><span class="truncate">Fractions</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Equivalent Fractions</h3><p class="text-sm text-gray-600 line-clamp-2">Equivalent fractions look different but have the same value, like 1/2 = 2/4 = 3/6. Free 3-minute video, plus a quiz to test yourself.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/comparing-fractions"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Comparing fractions with same denominator (5/8 &gt; 3/8) and same numerator (4/5 &gt; 4/9) using chocolate bar and pizza visuals" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-fractions/comparing-fractions-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:02</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#EDE9FE;color:#5B21B6"><span class="truncate">Fractions</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Comparing Fractions</h3><p class="text-sm text-gray-600 line-clamp-2">To compare fractions, use the same denominator: 2/3 = 8/12 and 3/4 = 9/12, so 3/4 is bigger. Worked examples, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/adding-and-subtracting-fractions"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Adding and subtracting like and unlike fractions with common denominators and worked examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-fractions/adding-and-subtracting-fractions-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:27</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#EDE9FE;color:#5B21B6"><span class="truncate">Fractions</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Adding and Subtracting Fractions</h3><p class="text-sm text-gray-600 line-clamp-2">Adding and subtracting fractions requires a common denominator when fractions are unlike. Worked examples, plus a 3-minute video.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/multiplying-fractions"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Multiplying fractions lesson covering cross-cancelling, whole numbers, and mixed number examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-fractions/multiplying-fractions-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">2:55</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#EDE9FE;color:#5B21B6"><span class="truncate">Fractions</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Multiplying Fractions</h3><p class="text-sm text-gray-600 line-clamp-2">Multiply the tops, multiply the bottoms, then simplify, or cross-cancel first. Whole and mixed numbers are covered. Download the flashcards to revise.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/dividing-fractions"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Dividing fractions lesson showing reciprocal method with whole numbers and mixed number examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/dividing-fractions/dividing-fractions-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">2:39</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#EDE9FE;color:#5B21B6"><span class="truncate">Fractions</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Dividing Fractions</h3><p class="text-sm text-gray-600 line-clamp-2">Dividing fractions means keeping the first fraction, flipping the second, and multiplying. Quiz to test yourself, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/decimals-and-fractions"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Decimal place value chart and step-by-step decimal to fraction conversion with examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimals-and-fractions/decimals-and-fractions-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:04</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions and Decimals lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#E2E8F0;color:#334155"><span class="truncate">Fractions and Decimals</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Decimals and Fractions</h3><p class="text-sm text-gray-600 line-clamp-2">Decimals and fractions are two ways to show parts of a number. Quiz to test yourself, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/comparing-and-rounding-decimals"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Decimal place value of 12.348 showing 1st, 2nd, and 3rd decimal places as tenths, hundredths, and thousandths" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-and-rounding-decimals/comparing-and-rounding-decimals-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">2:31</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions and Decimals lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#E2E8F0;color:#334155"><span class="truncate">Fractions and Decimals</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Comparing and Rounding Decimals</h3><p class="text-sm text-gray-600 line-clamp-2">Compare decimals digit by digit from the left; to round, 5 or more in the next digit rounds up. Worked examples, plus a 3-minute video.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/convert-fraction-to-decimal"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Step-by-step long division converting fraction 21/16 to terminating decimal 1.3125" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/convert-fraction-to-decimal/convert-fraction-to-decimal-using-long-division-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">2:55</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions and Decimals lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#E2E8F0;color:#334155"><span class="truncate">Fractions and Decimals</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 6–7 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Convert Fraction to Decimal Using Long Division</h3><p class="text-sm text-gray-600 line-clamp-2">A fraction converts to a decimal by dividing the numerator by the denominator. Interactive practice to try, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/adding-subtracting-fractions-and-decimals"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Adding and subtracting fractions and decimals using both decimal and fraction conversion methods" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-subtracting-fractions-and-decimals/adding-and-subtracting-fractions-and-decimals-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">2:55</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions and Decimals lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#E2E8F0;color:#334155"><span class="truncate">Fractions and Decimals</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Adding and Subtracting Fractions and Decimals</h3><p class="text-sm text-gray-600 line-clamp-2">To add or subtract fractions and decimals, convert them to one form first. Worked examples of both methods, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/multiplying-decimals"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Multiplying decimals lesson showing the three-step method with worked examples and decimal point placement" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-decimals/multiplying-decimals-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:13</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions and Decimals lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#E2E8F0;color:#334155"><span class="truncate">Fractions and Decimals</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Multiplying Decimals</h3><p class="text-sm text-gray-600 line-clamp-2">To multiply decimals, ignore the points, multiply as whole numbers, then put the point back. Worked examples, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/calculating-fractions-and-decimals"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Worked example: calculating fractions and decimals by rearranging 1.1 + ³⁄₇ + 0.4 + ⁴⁄₇ with commutative and associative laws" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-fractions-and-decimals/calculating-fractions-and-decimals-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:42</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions and Decimals lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#E2E8F0;color:#334155"><span class="truncate">Fractions and Decimals</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Calculating Fractions and Decimals</h3><p class="text-sm text-gray-600 line-clamp-2">The commutative, associative and distributive laws make fraction and decimal sums quicker. Worked examples, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/recurring-decimals-to-fractions"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Step-by-step method for converting recurring decimals to fractions with worked examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/recurring-decimals-to-fractions/convert-recurring-decimals-to-fractions-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">2:36</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Fractions and Decimals lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#E2E8F0;color:#334155"><span class="truncate">Fractions and Decimals</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 10–11 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Convert Recurring Decimals to Fractions</h3><p class="text-sm text-gray-600 line-clamp-2">Recurring decimal to fraction: let x = 0.333…, so 10x = 3.333…, then 9x = 3 and x = 1/3. Worked examples for GCSE and IGCSE, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/powers-indices"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Powers and indices: 3⁴ with base and index labelled, expanded as 3 × 3 × 3 × 3 to show repeated multiplication" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/powers-indices/powers-and-indices-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:20</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Powers, Roots and Standard Form lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FEF3C7;color:#92400E"><span class="truncate">Powers, Roots and Standard Form</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Powers and Indices</h3><p class="text-sm text-gray-600 line-clamp-2">Powers and indices mean repeated multiplication, for example, 5³ = 5 × 5 × 5. Interactive practice to try, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/standard-form"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Standard form (scientific notation): expressing numbers as A × 10ⁿ where 1 ≤ A &lt; 10, with example 26,000 = 2.6 × 10⁴" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/standard-form/standard-form-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:08</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Powers, Roots and Standard Form lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FEF3C7;color:#92400E"><span class="truncate">Powers, Roots and Standard Form</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 9–10 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Standard Form</h3><p class="text-sm text-gray-600 line-clamp-2">Standard form writes a big or small number as A × 10ⁿ, with A between 1 and 10. So 26000 = 2.6 × 10⁴. Download the flashcards for GCSE and IGCSE revision.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/basics-of-square-roots"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Square roots lesson thumbnail with definition and examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basics-of-square-roots/basics-of-square-roots-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">2:50</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Powers, Roots and Standard Form lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FEF3C7;color:#92400E"><span class="truncate">Powers, Roots and Standard Form</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 7–8 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Basics of Square Roots</h3><p class="text-sm text-gray-600 line-clamp-2">A square root is a non-negative value that, when squared, gives the original number, so √49 = 7. Worked examples, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/multiplying-dividing-square-roots"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Multiplying and dividing square roots lesson with step-by-step formulas and examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-dividing-square-roots/multiplying-and-dividing-square-roots-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:37</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Powers, Roots and Standard Form lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FEF3C7;color:#92400E"><span class="truncate">Powers, Roots and Standard Form</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 10–11 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Multiplying and Dividing Square Roots</h3><p class="text-sm text-gray-600 line-clamp-2">Multiplying square roots follows √a × √b = √(ab), and dividing follows √a ÷ √b = √(a/b). Flashcards to download for GCSE and IGCSE.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/laws-of-indices-same-base-or-index"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Laws of indices lesson covering same base and same index rules with worked examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/laws-of-indices-same-base-or-index/laws-of-indices-(same-base-or-same-indices)-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:51</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Powers, Roots and Standard Form lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FEF3C7;color:#92400E"><span class="truncate">Powers, Roots and Standard Form</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 10–11 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Laws of Indices (Same Base, Same Indices)</h3><p class="text-sm text-gray-600 line-clamp-2">Laws of indices: with the same base, add the exponents to multiply and subtract to divide. Worked examples for GCSE and IGCSE, plus flashcards to download.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/negative-indices-and-power-of-a-power"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="Negative exponents and power of a power lesson with reciprocal and exponent rules" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/negative-exponents-power-of-a-power/negative-exponents-and-power-of-a-power-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:33</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Powers, Roots and Standard Form lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FEF3C7;color:#92400E"><span class="truncate">Powers, Roots and Standard Form</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#
2E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 10–11 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">Negative Indices and Power of a Power</h3><p class="text-sm text-gray-600 line-clamp-2">Negative indices flip the base to a reciprocal, and power of a power multiplies the exponents. Worked examples for GCSE and IGCSE, plus a 4-minute video.</p></div></a><a class="group block overflow-hidden rounded-2xl bg-gray-50 transition-all hover:shadow-lg cursor-pointer hover:ring-2 hover:ring-[#6960d9]/40" href="/lessons/nth-root-fractional-indices"><div class="relative aspect-video overflow-hidden bg-gray-200"><div class="absolute inset-0 bg-gradient-to-r from-gray-200 via-gray-100 to-gray-200 animate-shimmer bg-[length:200%_100%]"></div><img alt="nth root and fractional indices lesson with cube root and fourth root worked examples" loading="lazy" decoding="async" data-nimg="fill" class="object-cover transition-transform group-hover:scale-105 opacity-0" style="position:absolute;height:100%;width:100%;left:0;top:0;right:0;bottom:0;color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/nth-root-fractional-indices/the-nth-root-and-fractional-indices-math-angel.webp"/><div class="absolute bottom-3 right-3 flex items-center gap-1 px-2.5 py-1 rounded-full" style="background:rgba(0, 0, 0, 0.65);backdrop-filter:blur(8px);z-index:3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-clock text-white" aria-hidden="true" style="width:10px;height:10px;opacity:0.85"><path d="M12 6v6l4 2"></path><circle cx="12" cy="12" r="10"></circle></svg><span class="text-white" style="font-size:0.68rem;font-weight:600;letter-spacing:0.02em">3:51</span></div></div><div class="p-4 sm:p-5"><div class="mb-2 flex flex-wrap items-center gap-x-2 gap-y-1"><button type="button" title="Show only Powers, Roots and Standard Form lessons" class="inline-flex max-w-full cursor-pointer items-center rounded-full px-2.5 py-0.5 text-[11px] font-semibold leading-snug transition-opacity hover:opacity-75" style="background-color:#FEF3C7;color:#92400E"><span class="truncate">Powers, Roots and Standard Form</span></button><span class="inline-block whitespace-nowrap rounded-full border border-[#E2DCFF] bg-[#F3F1FF] px-2.5 py-0.5 text-[11px] font-semibold leading-snug text-[#6D28D9]">Year 10–11 (UK)</span></div><h3 class="mb-2 text-[#1f2937]" style="font-weight:600">The nth Root and Fractional Indices</h3><p class="text-sm text-gray-600 line-clamp-2">A fractional index is a root: x^(1/2) = √x and x^(1/3) = ∛x, so 8^(1/3) = 2 and 8^(2/3) = 4. Flashcards to download for GCSE and IGCSE.</p></div></a></div></div></div></div><nav aria-hidden="true" class="sr-only"><a href="/lessons/distributive-law">Distributive Law - Video, Quiz and Flashcards</a><a href="/lessons/perpendicular-and-parallel-lines">Perpendicular and Parallel Lines - Free Video and Quiz</a><a href="/lessons/number-line-inequality-symbols">Number Line and Inequality Symbols - Compare Numbers</a><a href="/lessons/tally-marks-bar-chart">Tally Marks, Bar Charts and Tables - Video and Quiz</a><a href="/lessons/ratios">Introduction to Ratios - Video, Quiz and Flashcards</a><a href="/lessons/expressions-with-one-variable">Expressions with One Variable - Video and Quiz</a><a href="/lessons/measurement-and-types-of-angles">Types of Angles - Free Video and Interactive Practice</a><a href="/lessons/place-value-chart-rounding">Place Value and Rounding - Free Video and Quiz</a><a href="/lessons/absolute-relative-frequency">Absolute and Relative Frequency - Video and Quiz</a><a href="/lessons/how-to-combine-ratios">How to Combine Ratios - Video and Interactive Practice</a><a href="/lessons/simplifying-expressions">Simplifying Expressions - Video and Quiz</a><a href="/lessons/angle-relationships">Angle Relationships in Parallel Lines - Video and Quiz</a><a href="/lessons/natural-numbers-whole-numbers-integers">Natural Numbers, Whole Numbers and Integers - Video and Quiz</a><a href="/lessons/pie-chart">Pie Charts - Video and Interactive Practice</a><a href="/lessons/fractions-and-percentages">Fractions and Percentages - Video and Quiz</a><a href="/lessons/simplifying-expressions-multiple-variables">Simplifying Expressions with Multiple Variables - Examples</a><a href="/lessons/polygons-quadrilaterals">Polygons and Types of Quadrilaterals - Video and Quiz</a><a href="/lessons/rational-numbers">Rational Numbers on a Number Line - Video and Quiz</a><a href="/lessons/line-graphs-curve-graphs">Line Graphs and Curve Graphs - Video and Quiz</a><a href="/lessons/percentage-of-a-number">How to Find a Percentage of a Number - Video and Quiz</a><a href="/lessons/expanding-double-brackets">Expanding Double Brackets - Video and Quiz</a><a href="/lessons/properties-of-circles">Properties of Circles - Diameter, Chord, Sector, Tangent</a><a href="/lessons/absolute-value">Absolute Value - Video and Interactive Practice</a><a href="/lessons/mean-median-mode-range">Mean, Median, Mode and Range - Free Video and Quiz</a><a href="/lessons/interest-rate-calculation">Interest Rate Calculation - Video and Interactive Practice</a><a href="/lessons/square-of-a-binomial">Square of a Binomial - Flashcards and Quiz</a><a href="/lessons/thales-theorem">Thales&#x27; Theorem - Video and Interactive Practice</a><a href="/lessons/basic-arithmetic-inverse-operations">Basic Arithmetic and Inverse Operations - Video and Quiz</a><a href="/lessons/median-mean-mode-frequency-table">Mean, Median, Mode and Range from a Frequency Table</a><a href="/lessons/simple-interest-and-compound-interest">Simple and Compound Interest - Video and Quiz</a><a href="/lessons/introduction-to-mapping">Introduction to Mapping - Video and Quiz</a><a href="/lessons/units-of-area">
2Units of Area - Converting between mm², cm², m², km²</a><a href="/lessons/bidmas-order-of-operations">BIDMAS - Order of Operations Rules &amp; Worked Examples</a><a href="/lessons/box-plot">Box Plot - How to Draw, Read, and Find Interquartile Range</a><a href="/lessons/percentage-increase-and-decrease">Percentage Increase and Decrease - Free Video and Quiz</a><a href="/lessons/introduction-to-formulas">Introduction to Formulas - Video and Quiz</a><a href="/lessons/area-of-a-triangle">How to Find the Area of a Triangle - Free Video and Quiz</a><a href="/lessons/commutative-and-associative-laws">Commutative and Associative Laws - Video and Quiz</a><a href="/lessons/grouped-frequency-table">Grouped Frequency Table - Video and Quiz</a><a href="/lessons/percentage-change">How to Calculate Percentage Change - Video and Quiz</a><a href="/lessons/introduction-to-functions-and-graphs">Introduction to Functions and Graphs - f(x) Explained</a><a href="/lessons/perimeter-of-a-polygon">Perimeter of a Polygon - Rectangles, Triangles, Compound Shapes</a><a href="/lessons/column-addition-and-subtraction">Column Addition and Subtraction - Carrying and Borrowing</a><a href="/lessons/calculating-probability">Calculating Probability - Video and Quiz</a><a href="/lessons/directly-proportional-inversely-proportional">Directly and Inversely Proportional - Video and Quiz</a><a href="/lessons/solving-equations">Solving Equations Step by Step - Video and Quiz</a><a href="/lessons/area-of-a-trapezium">Area of a Trapezium - Free Video and Quiz</a><a href="/lessons/long-multiplication">Long Multiplication - How to Multiply Large Numbers</a><a href="/lessons/addition-rule-of-probability-expected-frequency">Addition Rule of Probability and Expected Frequency</a><a href="/lessons/direct-proportion">Direct Proportion - Formula y = kx with Worked Examples</a><a href="/lessons/solving-rational-equations">Solving Rational Equations - Video and Quiz</a><a href="/lessons/area-parallelograms-triangles">Area of Parallelograms and Triangles - Flashcards and Quiz</a><a href="/lessons/long-division">Long Division - Video and Interactive Practice</a><a href="/lessons/probability-tree-diagrams">Probability Tree Diagrams - How to Draw and Interpret</a><a href="/lessons/inverse-proportion">Inverse Proportion - Formula y = k/x with Worked Examples</a><a href="/lessons/m-and-c-in-linear-equations">Gradient and Y-Intercept in Linear Equations - y = mx + c</a><a href="/lessons/area-of-compound-shapes">Area of Compound Shapes - Flashcards and Quiz</a><a href="/lessons/decimal-point-movement">Decimal Point Movement - Multiply &amp; Divide by Powers of 10</a><a href="/lessons/sets-and-venn-diagrams">Sets and Venn Diagrams - Video and Interactive Practice</a><a href="/lessons/speed-distance-time">Speed, Distance and Time - Flashcards and Quiz</a><a href="/lessons/equation-of-a-straight-line">Equation of a Straight Line - Video and Quiz</a><a href="/lessons/circumference-area-circle-sector">Circumference and Area of a Circle and a Sector</a><a href="/lessons/adding-and-subtracting-negative-numbers">Adding and Subtracting Negative Numbers - Video and Quiz</a><a href="/lessons/density-mass-volume">Density, Mass and Volume - Free Video and Quiz</a><a href="/lessons/x-intercept-y-intercept-intersection">How to Find X-Intercept, Y-Intercept and Line Intersections</a><a href="/lessons/line-of-symmetry">Lines of Symmetry and Reflection - Free Video and Quiz</a><a href="/lessons/multiplying-and-dividing-negative-numbers">Multiplying &amp; Dividing Negative Numbers - Sign Rules</a><a href="/lessons/pressure-force-area">Pressure, Force and Area - Video and Interactive Practice</a><a href="/lessons/nth-term-of-a-linear-sequence">Finding the nth Term of a Linear Sequence - Rule &amp; Examples</a><a href="/lessons/rotational-symmetry">Rotational Symmetry - Flashcards and Quiz</a><a href="/lessons/calculating-money">Calculating Money - Add, Subtract, Multiply, Divide</a><a href="/lessons/quadratic-and-geometric-sequences">Quadratic and Geometric Sequences - nth Term and Examples</a><a href="/lessons/reflecting-points-coordinate-plane">Reflecting Points on the Coordinate Plane - Video and Quiz</a><a href="/lessons/units-of-length">Units of Length - Convert and Calculate km, m, cm, mm</a><a href="/lessons/fibonacci-sequence">Fibonacci Sequence - Find Terms, Rule &amp; Examples</a><a href="/lessons/translating-shapes">Translating Shapes - Translation with Column Vectors</a><a href="/lessons/units-of-mass">Units of Mass - Convert and Calculate t, kg, g, mg</a><a href="/lessons/simple-quadratic-equations">Simple Quadratic Equations - Effect of a on the Parabola</a><a href="/lessons/rotating-shapes">Rotating Shapes - Video and Interactive Practice</a><a href="/lessons/converting-time">Converting &amp; Calculating Time - Hours, Minutes, Seconds</a><a href="/lessons/vertex-form">Vertex Form and Parabola Transformations - h, k, and Shifts</a><a href="/lessons/enlargement">Enlargement and Scale Factors - Video and Quiz</a><a href="/lessons/divisibility-rules">Divisibility Rules for 2 to 10 - Tests with Examples</a><a href="/lessons/converting-standard-form-and-vertex-form">Converting Quadratics Between Standard and Vertex Form</a><a href="/lessons/constructing-triangles">Constructing Triangles - Video and Interactive Practice</a><a href="/lessons/prime-numbers-prime-factorisation">Prime Numbers and Prime Factorisation - Factor Tree Method</a><a href="/lessons/quadratic-equations-in-vertex-form-standard-form">Writing Quadratic Equations in Vertex Form and Standard Form</a><a href="/lessons/congruent-triangles">Congruent Triangles - SSS, SAS, ASA, and RHS</a><a href="/lessons/hcf-and-lcm">HCF and LCM - Prime Factorisation &amp; Worked Examples</a><a href="/lessons/solving-simple-quadratic-equations">Solving Simple Quadratic Equations - Video and Quiz</a><a href="/lessons/perpendicular-bisectors-and-circumcircle">Perpendicular Bisectors and Circumcircle - How to Construct</a><a href="/lessons/introduction-to-fractions">Introduction to Fractions - Video and Quiz</a><a href="/lessons/solving-quadratic-equations-factorising">Solving Quadratic Equations by Factorising - Video and Quiz</a><a href="/lessons/angle-bisectors-and-incircle">Angle Bisectors and Incircle - Video and Quiz</a><a href="/lessons/equivalent-fractions">Equivalent Fractions - Simplify and Expand Fractions</a><a href="/lessons/quadratic-formula">Quadratic Formula - Solve Quadratic Equations Step by Step</a><a href="/lessons/medians-and-centroid-of-a-triangle">Medians and Centroid of a Triangle - Video and Quiz</a><a href="/lessons/comparing-fractions">Comparing Fractions - Video and Interactive Practice</a><a href="/lessons/equations-with-2-variables">Solving Equations with 2 Variables - Video and Quiz</a><a href="/lessons/solids-units-of-volume">Solids and Units of Volume - mm³, cm³, ml, L</a><a href="/lessons/adding-and-subtracting-fractions">Adding and Subtracting Fractions - Flashcards and Quiz</a><a href="/lessons/solving-simultaneous-equations-graphically">Solving Simultaneous Equations Graphically - Video and Quiz</a><a href="/lessons/volume-of-a-cuboid">Volume of a Cuboid and Cube - Free Video and Quiz</a><a href="/lessons/multiplying-fractions">How to Multiply Fractions - Free Video and Quiz</a><a href="/lessons/equal-values-and-substitution-method">Simultaneous Equations: Equal Values and Substitution Method</a><a href="/lessons/surface-area">Surface Area of Solids - Cuboid, Cube, Prism</a><a href="/lessons/dividing-fractions">Dividing Fractions - Reciprocals, Whole &amp; Mixed Numbers</a><a href="/lessons/elimination-method">Elimination Method for Simultaneous Equations - Examples</a><a href="/lessons/volume-prisms-cylinders">Volume of Prisms and Cylinders - Video and Quiz</a><a href="/lessons/decimals-and-fractions">Decimals and Fractions - Place Value &amp; How to Convert</a><a href="/lessons/cavalieris-principle">Cavalieri&#x27;s Principle - Video, Quiz and Flashcards</a><a href="/lessons/comparing-and-rounding-decimals">Comparing and Rounding Decimals - Flashcards and Quiz</a>
2<a href="/lessons/volume-surface-area-pyramids-cones-spheres">Volume and Surface Area of Pyramids, Cones, and Spheres</a><a href="/lessons/convert-fraction-to-decimal">Convert Fraction to Decimal - Long Division Method</a><a href="/lessons/pythagoras-theorem">Pythagoras&#x27; Theorem - Free Video and Quiz</a><a href="/lessons/adding-subtracting-fractions-and-decimals">Add and Subtract Fractions and Decimals - Video and Quiz</a><a href="/lessons/trigonometry-sine-cosine-tangent">Trigonometry: Sine, Cosine, and Tangent - SOH CAH TOA</a><a href="/lessons/multiplying-decimals">Multiplying Decimals - Video and Interactive Practice</a><a href="/lessons/cosine-rule">Cosine Rule - Find Missing Sides and Angles in Triangles</a><a href="/lessons/calculating-fractions-and-decimals">Calculating Fractions and Decimals - Video and Quiz</a><a href="/lessons/sine-rule">Sine Rule - How to Use the Formula to Find Sides or Angles</a><a href="/lessons/recurring-decimals-to-fractions">Recurring Decimals to Fractions - Video and Quiz</a><a href="/lessons/powers-indices">Powers and Indices - Base, Exponent, Square and Cube Numbers</a><a href="/lessons/standard-form">Standard Form (Scientific Notation) - Free Video and Quiz</a><a href="/lessons/basics-of-square-roots">Square Roots - Video and Interactive Practice</a><a href="/lessons/multiplying-dividing-square-roots">Multiplying and Dividing Square Roots - Video and Quiz</a><a href="/lessons/laws-of-indices-same-base-or-index">Laws of Indices - Video and Interactive Practice</a><a href="/lessons/negative-indices-and-power-of-a-power">Negative Indices and Power of a Power - Flashcards and Quiz</a><a href="/lessons/nth-root-fractional-indices">Fractional Indices and nth Roots - Video and Quiz</a></nav></main><footer class="bg-black w-full relative "><div data-nosnippet="" class="mx-auto px-4 md:px-6 xl:px-[40px] py-[48px]"><div class="flex flex-col md:flex-row md:items-start md:justify-between w-full gap-10 md:gap-y-0 md:gap-x-10 lg:gap-x-12"><div class="flex flex-col gap-[36px] items-start w-full md:w-[300px]"><a class="flex gap-2 items-center hover:opacity-80 transition-opacity" href="/"><div class="relative shrink-0 size-[40px] rounded-full overflow-hidden bg-white flex items-center justify-center"><img alt="" loading="lazy" width="40" height="40" decoding="async" data-nimg="1" class="w-full h-full object-cover" style="color:transparent" src="https://mathangelwebsitestorage.blob.core.windows.net/mathangel-website-images/jimmy_avatar.webp"/></div><span class="font-urbanist font-semibold text-xl text-white">Maths Angel</span></a><div class="flex gap-[13.5px]"><a href="https://www.instagram.com/mathsangel_global/" target="_blank" rel="noopener noreferrer" aria-label="Instagram" class="bg-[#1e2939] border border-[#2a3749] rounded-full size-[40.5px] flex items-center justify-center transition-transform duration-150 cursor-pointer group hover:scale-105 hover:bg-gradient-to-br hover:from-[#833AB4] hover:via-[#E1306C] hover:to-[#F77737] hover:border-transparent"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-instagram size-[18px] text-[#c3cad6] group-hover:text-white transition-colors" aria-hidden="true"><rect width="20" height="20" x="2" y="2" rx="5" ry="5"></rect><path d="M16 11.37A4 4 0 1 1 12.63 8 4 4 0 0 1 16 11.37z"></path><line x1="17.5" x2="17.51" y1="6.5" y2="6.5"></line></svg></a><a href="https://www.tiktok.com/@mathsangel_official" target="_blank" rel="noopener noreferrer" aria-label="Tiktok" class="bg-[#1e2939] border border-[#2a3749] rounded-full size-[40.5px] flex items-center justify-center transition-transform duration-150 cursor-pointer group hover:scale-105 hover:bg-[#25F4EE] hover:border-transparent"><svg class="size-[18px] text-[#c3cad6] group-hover:text-black transition-colors" fill="currentColor" viewBox="0 0 24 24"><path d="M19.59 6.69a4.83 4.83 0 0 1-3.77-4.25V2h-3.45v13.67a2.89 2.89 0 0 1-5.2 1.74 2.89 2.89 0 0 1 2.31-4.64 2.93 2.93 0 0 1 .88.13V9.4a6.84 6.84 0 0 0-1-.05A6.33 6.33 0 0 0 5 20.1a6.34 
26.34 0 0 0 10.86-4.43v-7a8.16 8.16 0 0 0 4.77 1.52v-3.4a4.85 4.85 0 0 1-1-.1z"></path></svg></a><a href="https://www.youtube.com/@Math-Angel-global" target="_blank" rel="noopener noreferrer" aria-label="Youtube" class="bg-[#1e2939] border border-[#2a3749] rounded-full size-[40.5px] flex items-center justify-center transition-transform duration-150 cursor-pointer group hover:scale-105 hover:bg-[#FF0000] hover:border-transparent"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-youtube size-[18px] text-[#c3cad6] group-hover:text-white transition-colors" aria-hidden="true"><path d="M2.5 17a24.12 24.12 0 0 1 0-10 2 2 0 0 1 1.4-1.4 49.56 49.56 0 0 1 16.2 0A2 2 0 0 1 21.5 7a24.12 24.12 0 0 1 0 10 2 2 0 0 1-1.4 1.4 49.55 49.55 0 0 1-16.2 0A2 2 0 0 1 2.5 17"></path><path d="m10 15 5-3-5-3z"></path></svg></a></div><div class="flex flex-col gap-3"><div class="flex items-start gap-3"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-map-pin size-4 shrink-0 mt-[3px] text-[#99a1af]" aria-hidden="true"><path d="M20 10c0 4.993-5.539 10.193-7.399 11.799a1 1 0 0 1-1.202 0C9.539 20.193 4 14.993 4 10a8 8 0 0 1 16 0"></path><circle cx="12" cy="10" r="3"></circle></svg><p class="font-urbanist font-semibold text-[16px] text-[#99a1af] leading-[23.625px]"><span class="block">71-75 Shelton St, Covent Garden, </span><span class="block">London, WC2H 9JQ, </span><span class="block">United Kingdom</span></p></div><a href="mailto:[email protected]" class="flex items-center gap-3 w-fit font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]"><svg xmlns="http://www.w3.org/2000/svg" width="24" height="24" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-mail size-4 shrink-0" aria-hidden="true"><path d="m22 7-8.991 5.727a2 2 0 0 1-2.009 0L2 7"></path><rect x="2" y="4" width="20" height="16" rx="2"></rect></svg><span>[email protected]</span></a></div></div><div class="grid grid-cols-2 lg:grid-cols-3 gap-y-10 gap-x-6 md:gap-x-10 lg:gap-x-12 md:mt-[7px] 2xl:flex 2xl:gap-x-12 md:mr-[60px]"><div class="flex flex-col gap-4 md:gap-[18px] min-w-[140px] md:min-w-[106px]"><p class="font-urbanist font-semibold text-[16px] md:text-[18px] text-white leading-tight md:leading-[27px]">Maths Curriculum</p><div class="flex flex-col gap-2 md:gap-[9px]"><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/lessons">All Lessons</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/lessons/number">Number</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/lessons/algebra">Algebra</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/lessons/ratio-proportion-and-rates-of-change">Ratio and Proportion</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/lessons/geometry-and-measures">Geometry and Measures</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/lessons/probability">Probability</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/lessons/statistics">Statistics</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/maths-check">Maths Check</a></div></div><div class="flex flex-col gap-4 md:gap-[18px] min-w-[140px] md:min-w-[106px]"><p class="font-urbanist font-semibold text-[16px] md:text-[18px] text-white leading-tight md:leading-[27px]">Why Maths Angel</p><div class="flex flex-col gap-2 md:gap-[9px]"><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/how-we-teach">How We Teach</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/how-we-teach/videos">Video Lessons</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/how-we-teach/flashcards">Flashcards</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/how-we-teach/interactive-practice">Interactive Practice</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/ai-maths-tutor">ChatCat, AI Maths Tutor</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/compare">Compare Maths Angel</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/safeguarding">Safeguarding</a></div></div><div class="flex flex-col gap-4 md:gap-[18px] min-w-[140px] md:min-w-[106px]"><p class="font-urbanist font-semibold text-[16px] md:text-[18px] text-white leading-tight md:leading-[27px]">Exam Prep</p><div class="flex flex-col gap-2 md:gap-[9px]"><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/gcse-boost">GCSE Boost</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/gcse-maths-questions">GCSE Maths Questions</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/gcse-revision">GCSE Revision</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/igcse-revision">IGCSE Revision</a></div></div><div class="flex flex-col gap-4 md:gap-[18px] min-w-[140px] md:min-w-[106px]"><p class="font-urbanist font-semibold text-[16px] md:text-[18px] text-white leading-tight md:leading-[27px]">For Parents</p><div class="flex flex-col gap-2 md:gap-[9px]"><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/year-7-maths-help">Year <!-- -->7<!-- --> Maths Help</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/year-8-maths-help">Year <!-- -->8<!-- --> Maths Help</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/year-9-maths-help">Year <!-- -->9<!-- --> Maths Help</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/year-10-maths-help">Year <!-- -->10<!-- --> Maths Help</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/year-11-maths-help">Year <!-- -->11<!-- --> Maths Help</a></div></div><div class="flex flex-col gap-4 md:gap-[18px] min-w-[140px] md:min-w-[106px]"><a href="/tools"><p class="font-urbanist font-semibold text-[16px] md:text-[18px] text-white leading-tight md:leading-[27px] hover:opacity-80 transition-opacity">Free Maths Tools</p></a><div class="flex flex-col gap-2 md:gap-[9px]"><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/tools/percentage-calculator">Percentage Calculator</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/tools/fractions-calculator">Fractions Calculator</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/tools/rounding-calculator">Rounding Calculator</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/tools/unit-converter">Unit Converter</a></div></div><div class="flex flex-col gap-4 md:gap-[18px] min-w-[140px] md:min-w-[81px]"><p class="font-urbanist font-semibold text-[16px] md:text-[18px] text-white leading-tight md:leading-[27px]">Company</p><div class="flex flex-col gap-2 md:gap-[9px]"><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/about-us">About Us</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/for-schools">For Schools</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/newsroom">Newsroom</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/pricing">Pricing</a><a class="text-left font-urbanist font-semibold text-[16px] text-[#99a1af] hover:text-white transition-colors leading-[23.625px]" href="/pricing#contact">Contact Us</a></div></div></div></div><div class="flex flex-col md:flex-row justify-between items-center h-auto md:h-[106px] border-t border-[#1e2939] w-full py-6 md:py-0 gap-4 md:gap-0 mt-[54px]"><p class="font-urbanist font-normal text-[13.5px] text-[#99a1af] leading-[20.25px]">© 2026 Maths Angel. All rights reserved.</p><div class="flex gap-[27px]"><a class="text-left font-urbanist font-normal text-[13.5px] text-[#99a1af] hover:text-white transition-colors leading-[20.25px]" href="/privacy-policy">Privacy Policy</a><a class="text-left font-urbanist font-normal text-[13.5px] text-[#99a1af] hover:text-white transition-colors leading-[20.25px]" href="/terms-of-service">Terms of Service</a><a class="text-left font-urbanist font-normal text-[13.5px] text-[#99a1af] hover:text-white transition-colors leading-[20.25px]" href="/cookies">Cookies</a><button type="button" class="text-left font-urbanist font-normal text-[13.5px] text-[#99a1af] hover:text-white transition-colors leading-[20.25px]">Manage Cookies</button></div></div></div></footer><!--$--><!--/$-->
2<script>(function(){try{var o=document.createElement('div');o.style.cssText='position:absolute;top:-9999px;width:100px;height:100px;overflow:scroll';document.body.appendChild(o);document.documentElement.style.setProperty('--app-sbw',(o.offsetWidth-o.clientWidth)+'px');document.body.removeChild(o);}catch(e){}})();</script>
2<script>requestAnimationFrame(function(){$RT=performance.now()});</script>
2<script src="/_next/static/chunks/2epzldmiz9i3c.js" id="_R_" async=""></script>
2<div hidden id="S:0"><button type="button" class="text-[18px] font-urbanist font-semibold text-[#0a0a0a] hover:text-[#6960d9] px-3 py-1.5 rounded-lg transition-colors hidden min-[900px]:inline-block cursor-pointer whitespace-nowrap">Log in</button><button type="button" class="px-3 sm:px-4 lg:px-6 py-2 lg:py-2.5 text-[14px] sm:text-[15px] lg:text-[18px] font-urbanist font-semibold bg-[#1E0A3C] text-white rounded-[10px] shadow-[0_10px_24px_-10px_rgba(30,10,60,0.55)] transition-[transform,box-shadow] duration-[420ms] ease-[cubic-bezier(0.2,0.8,0.2,1)] will-change-transform hover:-translate-y-0.5 hover:shadow-[0_14px_28px_-10px_rgba(30,10,60,0.6)] cursor-pointer whitespace-nowrap ">Join Free</button></div>
2<script>$RB=[];$RV=function(a){$RT=performance.now();for(var b=0;b<a.length;b+=2){var c=a[b],e=a[b+1];null!==e.parentNode&&e.parentNode.removeChild(e);var f=c.parentNode;if(f){var g=c.previousSibling,h=0;do{if(c&&8===c.nodeType){var d=c.data;if("/$"===d||"/&"===d)if(0===h)break;else h--;else"$"!==d&&"$?"!==d&&"$~"!==d&&"$!"!==d&&"&"!==d||h++}d=c.nextSibling;f.removeChild(c);c=d}while(c);for(;e.firstChild;)f.insertBefore(e.firstChild,c);g.data="$";g._reactRetry&&requestAnimationFrame(g._reactRetry)}}a.length=0};
3$RC=function(a,b){if(b=document.getElementById(b))(a=document.getElementById(a))?(a.previousSibling.data="$~",$RB.push(a,b),2===$RB.length&&("number"!==typeof $RT?requestAnimationFrame($RV.bind(null,$RB)):(a=performance.now(),setTimeout($RV.bind(null,$RB),2300>a&&2E3<a?2300-a:$RT+300-a)))):b.parentNode.removeChild(b)};$RC("B:0","S:0")</script>
3<script>(self.__next_f=self.__next_f||[]).push([0])</script>
3<script>self.__next_f.push([1,"1:\"$Sreact.fragment\"\n3:I[731362,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\"],\"GoogleAnalytics\"]\n9:I[563491,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\",\"/_next/static/chunks/3hiv2moa078xj.js\"],\"default\"]\n:HL[\"/_next/static/chunks/3_f885ikmu7vm.css\",\"style\"]\n:HL[\"/_next/static/chunks/1_oj-8fpiwx0n.css\",\"style\"]\n:HL[\"/_next/static/chunks/0zrd7rd7ow0gg.css\",\"style\"]\n:HL[\"/_next/static/chunks/1etrw9bfctihn.css\",\"style\"]\n:HL[\"/_next/static/media/5c8bbc89ca099f34-s.p.2qijkc4_gtkq0.woff2\",\"font\",{\"crossOrigin\":\"\",\"type\":\"font/woff2\"}]\n:HL[\"/_next/static/media/fed68dff3ca987ed-s.p.3e08ior5wrhci.woff2\",\"font\",{\"crossOrigin\":\"\",\"type\":\"font/woff2\"}]\n2:T50f,(function(){try{var g={\"cookieSuffix\":\"ywXlGdM0\",\"frontendApi\":\"clerk.maths-angel.com\",\"instanceType\":\"production\"},c=document.cookie.split(';'),m=Object.create(null),i,p,x,k,v;for(i=0;i\u003cc.length;i++){p=c[i].trim();x=p.indexOf('=');if(x\u003c1)continue;k=p.slice(0,x);if(m[k]!==undefined)continue;v=p.slice(x+1);try{v=decodeURIComponent(v);}catch(e){}m[k]=v;}var q='_'+g.cookieSuffix,u=m.__client_uat,s=m.__session,su=m['__client_uat'+q],ss=m['__session'+q];function d(t){try{var a=t.split('.')[1];if(!a)return null;a=a.replace(/-/g,'+').replace(/_/g,'/');while(a.length%4)a+='=';return JSON.parse(atob(a));}catch(e){return null;}}function f(j){return j\u0026\u0026typeof j.iss==='string'\u0026\u0026j.iss.replace(/^https?:\\/\\//i,'')===g.frontendApi;}var sd=d(s||''),ssd=d(ss||''),z=false;if(s\u0026\u0026(!sd||!sd.iss)){z=false;}else if(s\u0026\u0026!f(sd)){z=true;}else if(!su\u0026\u0026!ss){z=false;}else{var si=sd\u0026\u0026Number(sd.iat)||0,ssi=ssd\u0026\u0026Number(ssd.iat)||0;if(su!=='0'\u0026\u0026u!=='0'\u0026\u0026si\u003essi){z=false;}else if(su==='0'\u0026\u0026u!=='0'){z=false;}else if(g.instanceType!=='production'\u0026\u0026su!=='0'\u0026\u0026u==='0'\u0026\u0026ssd\u0026\u0026Number(ssd.exp)\u003c=Math.floor(Date.now()/1000)){z=false;}else if(!su\u0026\u0026ss){z=false;}else{z=true;}}var au=z?su:u,as=z?ss:s,aj=z?ssd:sd;if(/^[1-9][0-9]*$/.test(au||'')\u0026\u0026as\u0026\u0026f(aj)){document.documentElement.dataset.authHint='signed-in';}}catch(e){}})();7:X\n0:{\"P\":null,\"c\":[\"\",\"lessons\"],\"q\":\"\",\"i\":false,\"f\":[[[\"\",{\"children\":[\"lessons\",{\"children\":[\"__PAGE__\",{},\"$undefined\",\"$undefined\",4608]},\"$undefined\",\"$undefined\",4608]},\"$undefined\",\"$undefined\",4624],[[\"$\",\"$1\",\"c\",{\"children\":[[[\"$\",\"link\",\"0\",{\"rel\":\"stylesheet\",\"href\":\"/_next/static/chunks/3_f885ikmu7vm.css\",\"precedence\":\"next\",\"crossOrigin\":\"$undefined\",\"nonce\":\"$undefined\"}],[\"$\",\"link\",\"1\",{\"rel\":\"stylesheet\",\"href\":\"/_next/static/chunks/1_oj-8fpiwx0n.css\",\"precedence\":\"next\",\"crossOrigin\":\"$undefined\",\"nonce\":\"$undefined\"}],[\"$\",\"link\",\"2\",{\"rel\":\"stylesheet\",\"href\":\"/_next/static/chunks/0zrd7rd7ow0gg.css\",\"precedence\":\"next\",\"crossOrigin\":\"$undefined\",\"nonce\":\"$undefined\"}],[\"$\",\"link\",\"3\",{\"rel\":\"stylesheet\",\"href\":\"/_next/static/chunks/1etrw9bfctihn.css\",\"precedence\":\"next\",\"crossOrigin\":\"$undefined\",\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-0\",{\"src\":\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-1\",{\"src\":\"/_next/static/chunks/19lc_9yhbdjne.js\",\"async\":true,\"nonce\":\"$undefined\"}
3],[\"$\",\"script\",\"script-2\",{\"src\":\"/_next/static/chunks/33iayyub0472u.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-3\",{\"src\":\"/_next/static/chunks/1t7rb6j7892t6.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-4\",{\"src\":\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-5\",{\"src\":\"/_next/static/chunks/2lmepge7i28qd.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-6\",{\"src\":\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-7\",{\"src\":\"/_next/static/chunks/0nbze1qbdcyos.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-8\",{\"src\":\"/_next/static/chunks/3-hayde213ruy.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-9\",{\"src\":\"/_next/static/chunks/00twfinmahjsm.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-10\",{\"src\":\"/_next/static/chunks/19za4y212u0u3.js\",\"async\":true,\"nonce\":\"$undefined\"}],[\"$\",\"script\",\"script-11\",{\"src\":\"/_next/static/chunks/1rug5xx3k1d2p.js\",\"async\":true,\"nonce\":\"$undefined\"}]],[\"$\",\"html\",null,{\"lang\":\"en\",\"suppressHydrationWarning\":true,\"children\":[[\"$\",\"head\",null,{\"children\":[[\"$\",\"script\",null,{\"dangerouslySetInnerHTML\":{\"__html\":\"(function(){var p=location.pathname;document.documentElement.setAttribute('data-b2b-pupil-links-document',p==='/missioncontrol/pupil-links'||p==='/missioncontrol/pupil-links/'?'private':'ordinary');})();\"}}],[\"$\",\"script\",null,{\"dangerouslySetInnerHTML\":{\"__html\":\"$2\"}}],[\"$\",\"$L3\",null,{}],[\"$\",\"link\",null,{\"rel\":\"preconnect\",\"href\":\"https://mathangelwebsitestorage.blob.core.windows.net\",\"crossOrigin\":\"anonymous\"}],[[\"$\",\"link\",null,{\"rel\":\"preconnect\",\"href\":\"https://x.maths-angel.com\"}],[\"$\",\"link\",null,{\"rel\":\"preconnect\",\"href\":\"https://api.ipinfo.io\"}]],[\"$\",\"link\",null,{\"rel\":\"preconnect\",\"href\":\"https://clerk.maths-angel.com\"}],[\"$\",\"link\",null,{\"rel\":\"preconnect\",\"href\":\"https://mathangel-website-backend.azurewebsites.net/api\"}]]}],\"$L4\"]}]]}],{\"children\":[\"$L5\",{\"children\":[\"$L6\",{},null,false,null]},null,false,\"$7\"]},null,false,null],\"$L8\",false]],\"m\":\"$undefined\",\"G\":[\"$9\",[\"$La\",\"$Lb\",\"$Lc\",\"$Ld\"]],\"S\":true,\"h\":null,\"r\":\"$undefined\",\"s\":\"$undefined\",\"a\":\"$undefined\",\"l\":\"$undefined\",\"p\":\"$undefined\",\"d\":\"$undefined\",\"b\":\"pdT8kYIA379aQJAe6omiC\"}\ne:I[155516,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\"],\"B2bJoiningPrivacyGuard\"]\nf:I[530824,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\"],\"Providers\"]\n10:I[339756,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\"],\"default\"]\n11:I[758298,[\"/_
3next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\",\"/_next/static/chunks/10qmdweo5dkwv.js\"],\"default\"]\n12:I[837457,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\"],\"default\"]\n13:I[605500,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\",\"/_next/static/chunks/2rv5xxhy5fe63.js\"],\"Image\"]\n14:I[522016,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\",\"/_next/static/chunks/2rv5xxhy5fe63.js\"],\"\"]\n15:I[880071,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\",\"/_next/static/chunks/2rv5xxhy5fe63.js\"],\"NotFoundAnalytics\"]\n16:I[246301,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\",\"/_next/static/chunks/349nks73i4b-b.js\",\"/_next/static/chunks/3y_s5s_a6rtf2.js\",\"/_next/static/chunks/17hw6cj44vit3.js\",\"/_next/static/chunks/0noi9m_o50fzl.js\",\"/_next/static/chunks/2oz-5926v45re.js\",\"/_next/static/chunks/146ib6hwvnpj6.js\",\"/_next/static/chunks/1jgvs1y9ykbgi.js\",\"/_next/static/chunks/442n0v4gb2bin.js\",\"/_next/static/chunks/1yiixfgw446ng.js\"],\"ConditionalLayout\"]\n18:I[86224,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\",\"/_next/static/chunks/349nks73i4b-b.js\",\"/_next/static/chunks/3
3y_s5s_a6rtf2.js\",\"/_next/static/chunks/17hw6cj44vit3.js\",\"/_next/static/chunks/0noi9m_o50fzl.js\",\"/_next/static/chunks/2oz-5926v45re.js\",\"/_next/static/chunks/146ib6hwvnpj6.js\",\"/_next/static/chunks/1jgvs1y9ykbgi.js\",\"/_next/static/chunks/442n0v4gb2bin.js\",\"/_next/static/chunks/1yiixfgw446ng.js\"],\"CoursesPageClient\"]\n24:I[897367,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\"],\"ViewportBoundary\"]\n26:I[897367,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\"],\"MetadataBoundary\"]\n27:\"$Sreact.suspense\"\n4:[\"$\",\"body\",null,{\"className\":\"geist_mono_c932d54b-module__LyTxPG__variable mulish_69dbb4a9-module__HhoaQW__variable urbanist_ad9e5074-module__oipyna__variable antialiased font-sans\",\"suppressHydrationWarning\":true,\"children\":[false,[\"$\",\"$Le\",null,{}],[\"$\",\"$Lf\",null,{\"clerkScriptUrl\":\"https://clerk.maths-angel.com/npm/@clerk/[email protected]/dist/clerk.browser.js\",\"children\":[\"$\",\"$L10\",null,{\"parallelRouterKey\":\"children\",\"error\":\"$11\",\"errorStyles\":[],\"errorScripts\":[[\"$\",\"script\",\"script-0\",{\"src\":\"/_next/static/chunks/10qmdweo5dkwv.js\",\"async\":true,\"nonce\":\"$undefined\"}]],\"template\":[\"$\",\"$L12\",null,{}],\"templateStyles\":\"$undefined\",\"templateScripts\":\"$undefined\",\"notFound\":[[\"$\",\"div\",null,{\"className\":\"flex min-h-[80vh] items-center justify-center px-4 py-12 font-urbanist\",\"children\":[[\"$\",\"div\",null,{\"className\":\"mx-auto flex max-w-3xl flex-col items-center gap-6 text-center sm:flex-row sm:gap-10 sm:text-left\",\"children\":[[\"$\",\"$L13\",null,{\"src\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-website-images/jimmy_404.webp\",\"alt\":\"Jimmy the Maths Angel mascot looking sad\",\"width\":240,\"height\":240,\"className\":\"h-auto w-40 shrink-0 sm:w-48 md:w-56\",\"priority\":true}],[\"$\",\"div\",null,{\"className\":\"max-w-md\",\"children\":[[\"$\",\"h1\",null,{\"className\":\"mb-8 text-4xl font-bold text-[#2d1b69] sm:text-5xl\",\"children\":\"Error 404\"}],[\"$\",\"p\",null,{\"className\":\"mb-6 text-base font-medium leading-relaxed text-[#4A5565] sm:text-lg\",\"children\":[\"Sorry, the page you were looking for doesn't exist. Try going to\",\" \",[\"$\",\"$L14\",null,{\"href\":\"/\",\"className\":\"font-bold text-[#6c3ecf] hover:underline\",\"children\":\"maths-angel.com\"}],\", or follow us on\",\" \",[\"$\",\"a\",null,{\"href\":\"https://www.instagram.com/mathsangel_global/\",\"target\":\"_blank\",\"rel\":\"noopener noreferrer\",\"className\":\"font-bold text-[#6c3ecf] hover:underline\",\"children\":\"Instagram\"}],\".\"]}],[\"$\",\"$L14\",null,{\"href\":\"/\",\"className\":\"inline-block rounded-xl bg-[#7C3AED] px-7 py-3 font-semibold text-white transition-colors hover:bg-[#6D28D9]\",\"children\":\"Go to Homepage\"}]]}]]}],[\"$\",\"$L15\",null,{}]]}],[]],\"forbidden\":\"$undefined\",\"unauthorized\":\"$undefined\"}]}],[\"$\",\"script\",null,{\"dangerouslySetInnerHTML\":{\"__html\":\"(function(){try{var o=document.createElement('div');o.style.cssText='position:absolute;top:-9999px;width:100px;height:100px;overflow:scroll';document.body.appendChild(o);document.documentElement.style.setProperty('--app-sbw',(o.offsetWidth-o.clientWidth)+'px');document.body.removeChild(o);}catch(e){}})();\"}}]]}]\n5:[\"$\",\"$1\",\"c\",{\"children\":[null,[\"$\",\"$L10\",null,{\"parallelRouterKey\":\"children\",\"error\":\"$undefined\",\"errorStyles\":\"$undefined\",\"errorScripts\":\"$undefined\",\"template\":[\"$\",\"$L12\",null,{}],\"templateStyles\":\"$undefined\",\"templateScripts\":\"$undefined\",\"notFound\":\"$undefined\",\"forbidden\":\"$undefined\",\"unauthorized\":\"$undefined\"}]]}]\n17:Tbf6,{\"@context\":\"https://schema.org\",\"@graph\":[{\"@type\":\"CollectionPage\",\"@id\":\"https://maths-angel.com/lessons#webpage\",\"name\":\"Maths Lessons\",\"description\":\"Explore six maths topic categories with video lessons, flashcards and practice questions.\",\"url\":\"https://maths-angel.com/lessons\",\"isPartOf\":{\"@id\":\"https://maths-angel.com/#website\"},\"mainEntity\":{\"@type\":\"ItemList\",\"name\":\"Maths lesson categories\",\"numberOfItems\":6,\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Number\",\"url\":\"https://maths-angel.com/lessons/number\",\"item\":{\"@type\":\"CollectionPage\",\"@id\":\"https://maths-angel.com/lessons/number#webpage\",\"name\":\"Number\",\"description\":\"Video lessons on place value, fractions, decimals, powers, roots and standard form.\",\"url\":\"https://maths-angel.com/lessons/number\"}},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Algebra\",\"url\":\"https://maths-angel.com/lessons/algebra\",\"item\":{\"@type\":\"CollectionPage\",\"@id\":\"https://maths-angel.com/lessons/algebra#webpage\",\"name\":\"Algebra\",\"description\":\"Video lessons on expressions, equations, sequences, graphs, quadratics and simultaneous equations.\",\"url\":\"https://maths-angel.com/lessons/algebra\"}},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Ratio, Proportion and Rates of Change\",\"url\":\"https://maths-angel.com/lessons/ratio-prop
3ortion-and-rates-of-change\",\"item\":{\"@type\":\"CollectionPage\",\"@id\":\"https://maths-angel.com/lessons/ratio-proportion-and-rates-of-change#webpage\",\"name\":\"Ratio, Proportion and Rates of Change\",\"description\":\"Video lessons on ratios, proportion, percentages, interest and compound measures.\",\"url\":\"https://maths-angel.com/lessons/ratio-proportion-and-rates-of-change\"}},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"Geometry and Measures\",\"url\":\"https://maths-angel.com/lessons/geometry-and-measures\",\"item\":{\"@type\":\"CollectionPage\",\"@id\":\"https://maths-angel.com/lessons/geometry-and-measures#webpage\",\"name\":\"Geometry and Measures\",\"description\":\"Video lessons on angles, shapes, area, volume, transformations, Pythagoras and trigonometry.\",\"url\":\"https://maths-angel.com/lessons/geometry-and-measures\"}},{\"@type\":\"ListItem\",\"position\":5,\"name\":\"Probability\",\"url\":\"https://maths-angel.com/lessons/probability\",\"item\":{\"@type\":\"CollectionPage\",\"@id\":\"https://maths-angel.com/lessons/probability#webpage\",\"name\":\"Probability\",\"description\":\"Video lessons on calculating probability, the addition rule, tree diagrams and Venn diagrams.\",\"url\":\"https://maths-angel.com/lessons/probability\"}},{\"@type\":\"ListItem\",\"position\":6,\"name\":\"Statistics\",\"url\":\"https://maths-angel.com/lessons/statistics\",\"item\":{\"@type\":\"CollectionPage\",\"@id\":\"https://maths-angel.com/lessons/statistics#webpage\",\"name\":\"Statistics\",\"description\":\"Video lessons on charts, averages, spread, box plots and interpreting data.\",\"url\":\"https://maths-angel.com/lessons/statistics\"}}]}},{\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://maths-angel.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Lessons\",\"item\":\"https://maths-angel.com/lessons\"}]}]}6:[\"$\",\"$1\",\"c\",{\"children\":[[\"$\",\"$L16\",null,{\"children\":[[\"$\",\"script\",null,{\"type\":\"application/ld+json\",\"dangerouslySetInnerHTML\":{\"__html\":\"$17\"}}],[\"$\",\"$L18\",null,{\"lessons\":[{\"id\":\"distributive-law\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Distributive Law\",\"title\":\"Distributive Law - Video, Quiz and Flashcards\",\"description\":\"The distributive law lets you multiply a number across a sum or difference: a(b + c) = ab + ac. Worked examples expand and factorise brackets.\",\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and Simplifying\",\"category\":\"$undefined\",\"intro\":\"**The distributive law** (or **distributive property**) means multiplying the number outside the brackets by each term inside, so **a × (b + c) = a × b + a × c** and **a × (b − c) = a × b − a × c**. It works both ways to **expand brackets** or **factorise**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"distributive law\",\"distributive property\",\"expanding brackets\",\"expand brackets\",\"factorise\",\"factoring\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/distributive-property/distributive-property-math-angel.webp\",\"lesson_image_alt\":\"Distributive law illustrated with coloured balls showing 3 times (4 + 2) equals 3 times 4 + 3 times 2\",\"videoDuration\":181,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and Simplifying\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"perpendicular-and-parallel-lines\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Perpendicular and Parallel Lines\",\"title\":\"Perpendicular and Parallel Lines - Free Video and Quiz\",\"description\":\"Perpendicular lines meet at 90°. Parallel lines never meet and have the same gradient. Spot each type in the examples, plus flashcards to download.\",\"subtopicId\":\"angles-lines\",\"subtopicName\":\"Angles and Lines\",\"category\":\"$undefined\",\"intro\":\"**Perpendicular lines** cross at a **right angle** of exactly **90°**. Where they meet, they form a square corner, like the corner of a book. **Parallel lines** stay the **same distance ap
3art** and **never meet**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"perpendicular lines\",\"parallel lines\"],\"searchAliases\":[\"ray\",\"line segment\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-and-parallel-lines/perpendicular-and-parallel-lines-math-angel.webp\",\"lesson_image_alt\":\"Lesson preview showing perpendicular and parallel lines.\",\"videoDuration\":178,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"angles-lines\",\"subtopicName\":\"Angles and Lines\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"number-line-inequality-symbols\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Number Line and Comparing Numbers\",\"title\":\"Number Line and Inequality Symbols - Compare Numbers\",\"description\":\"A number line places numbers in order on a straight line. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"number-types-place-value\",\"subtopicName\":\"Number Types and Place Values\",\"category\":\"$undefined\",\"intro\":\"**A number line** places numbers in order, getting bigger as you move right. So −3 sits to the left of 2, which means **−3 is smaller**. **Inequality symbols** compare values: **\u003e means greater than** and **\u003c means less than**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"number line\",\"inequality symbols\",\"comparing numbers\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/number-line-inequality-symbols/number-line-and-comparing-numbers-math-angel.webp\",\"lesson_image_alt\":\"Number line from −5 to 5 showing negative numbers, the origin, and positive numbers at equal intervals\",\"videoDuration\":190,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"number-types-place-value\",\"subtopicName\":\"Number Types and Place Values\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"tally-marks-bar-chart\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"Tally Marks, Bar Charts, Tables\",\"title\":\"Tally Marks, Bar Charts and Tables - Video and Quiz\",\"description\":\"Tally marks count in fives, bar charts compare amounts and tables keep data tidy. Flashcards to download to revise all three.\",\"subtopicId\":\"charts-data-display\",\"subtopicName\":\"Charts and Data Display\",\"category\":\"$undefined\",\"intro\":\"**Tally marks** count data as you collect it, **grouped in fives**. **Bar charts** then compare the groups, where each **bar's height** shows its value. **Tables** tidy the counts into rows, pairing each category with its **total count**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"tally marks\",\"bar charts\",\"frequency tables\",\"data representation\"],\"searchAliases\":[\"tally chart\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/tally-marks-bar-chart/tally-mark-charts-bar-charts-tables-math-angel.webp\",\"lesson_image_alt\":\"Tally marks, bar charts, and tables lesson thumbnail with colourful data display examples\",\"videoDuration\":189,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"charts-data-display\",\"subtopicName\":\"Charts and Data Display\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"ratios\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Introduction to Ratios\",\"title\":\"Introduction to Ratios - Video, Quiz and Flashcards\",\"description\":\"A ratio compares quantities, written as a:b. Simplify ratios and share an amount in a given ratio, with worked examples for each.\",\"subtopicId\":\"ratios\",\"subtopicName\":\"Ratios\",\"category\":\"$undefined\",\"intro\":\"**A ratio** compares quantities to show their relative sizes, written as **a : b**. For example, 2 apples to 3 bananas is **2 : 3**. To **simplify**, divide both parts by the same number, so **24 : 40 becomes 3 : 5**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"ratios\",\"ratio calculation\",\"ratio simplification\",\"simplify ratios\",\"ratio expansion\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-prop
3ortion-rates-of-change/ratios/introduction-to-ratios-math-angel.webp\",\"lesson_image_alt\":\"Introduction to ratios lesson thumbnail with examples of ratio notation\",\"videoDuration\":210,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"ratios\",\"subtopicName\":\"Ratios\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"expressions-with-one-variable\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Deriving and Evaluating Expressions with One Variable\",\"title\":\"Expressions with One Variable - Video and Quiz\",\"description\":\"An expression uses a letter for a number you do not know yet: 3x + 2 is 11 when x = 3. Worked examples, plus flashcards to download.\",\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and Simplifying\",\"category\":\"$undefined\",\"intro\":\"**Expressions with one variable** combine numbers with a letter, like **20 + 5x**. Here 20 is the starting amount and 5x adds 5 for each x. To **evaluate** it, replace the letter with a number: when x = 8, **20 + 5 × 8 = 60**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"expressions with one variable\",\"evaluating expressions\",\"deriving expressions\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expressions-with-one-variable/deriving-and-evaluating-expressions-with-one-variable-math-angel.webp\",\"lesson_image_alt\":\"Worked examples of deriving and evaluating the one-variable expression 20 + 5x for different x values\",\"videoDuration\":184,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and Simplifying\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"measurement-and-types-of-angles\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Measurement and Types of Angles\",\"title\":\"Types of Angles - Free Video and Interactive Practice\",\"description\":\"Acute, right, obtuse, straight and reflex: the five types of angle. Measure any angle with a protractor and have a go yourself. Flashcards to download too.\",\"subtopicId\":\"angles-lines\",\"subtopicName\":\"Angles and Lines\",\"category\":\"$undefined\",\"intro\":\"**Types of angles** are grouped by their size in degrees. An **acute angle** is under 90°, an **obtuse angle** is 90° to 180°, and a **reflex angle** is over 180°. You **measure** them with a **protractor**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"measurement of angles\",\"types of angles\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/measurement-and-types-of-angles/measurement-and-types-of-angles-math-angel.webp\",\"lesson_image_alt\":\"Types of angles lesson preview showing acute, right, obtuse, straight, reflex, and full angles\",\"videoDuration\":232,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"angles-lines\",\"subtopicName\":\"Angles and Lines\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":6,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"place-value-chart-rounding\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Place Value and Rounding Numbers\",\"title\":\"Place Value and Rounding - Free Video and Quiz\",\"description\":\"Place value is what each digit is worth: in 3482 the 4 means 400. To round, look at the next digit; 5 or more rounds up. Download the flashcards to revise.\",\"subtopicId\":\"number-types-place-value\",\"subtopicName\":\"Number Types and Place Values\",\"category\":\"$undefined\",\"intro\":\"**Place value** is the value of each digit in a number, so in 321 **the 3 is worth 300**. Each column is worth **ten times** the one on its right. **Rounding numbers** makes them simpler: **5 or more rounds up, 4 or less rounds down**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"place value\",\"rounding numbers\",\"place value chart\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/place-value-chart-rounding/place-value-and-rounding-numbers-math-angel.webp\",\"lesson_image_alt\":\"Place value chart and rounding rules for whole numbers with worked examples\",\"videoDuration\":154,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"number-types-place-value\",\"subtopicName\":\"Number Types and Place Values\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"absolute-relative-frequency\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"Absolute Frequency and Relative Frequency\",\"t
3itle\":\"Absolute and Relative Frequency - Video and Quiz\",\"description\":\"Relative frequency is the absolute frequency divided by the total, so 12 out of 40 is 0.3. Flashcards to download to revise both formulas.\",\"subtopicId\":\"charts-data-display\",\"subtopicName\":\"Charts and Data Display\",\"category\":\"$undefined\",\"intro\":\"**Absolute frequency** is how often something happens, and **relative frequency** is that count divided by the total: **count ÷ total**. The relative frequencies always add up to **1**, or **100%**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"relative frequency\",\"absolute frequency\",\"frequency table\",\"relative frequency formula\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/absolute-relative-frequency/absolute-and-relative-frequency-math-angel.webp\",\"lesson_image_alt\":\"Absolute and relative frequency lesson thumbnail with a data table and percentage values\",\"videoDuration\":181,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"charts-data-display\",\"subtopicName\":\"Charts and Data Display\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"how-to-combine-ratios\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"How to Combine Ratios\",\"title\":\"How to Combine Ratios - Video and Interactive Practice\",\"description\":\"Combine two ratios into one three-part ratio by matching the common term. Worked examples for GCSE and IGCSE, plus flashcards to download.\",\"subtopicId\":\"ratios\",\"subtopicName\":\"Ratios\",\"category\":\"$undefined\",\"intro\":\"**Combining ratios** joins two ratios into one **three-part ratio** by matching the number they share. If a:b = 2:3 and b:c = 3:5, the shared 3 gives **a:b:c = 2:3:5**. If the shared numbers differ, scale them to their **LCM** first.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"combining ratios\",\"ratio combination\",\"ratio simplification\",\"ratio expansion\",\"three-part ratio\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/how-to-combine-ratios/how-to-combine-ratios-math-angel.webp\",\"lesson_image_alt\":\"How to combine ratios lesson thumbnail showing two-part ratios merging into a three-part ratio\",\"videoDuration\":221,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"ratios\",\"subtopicName\":\"Ratios\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"simplifying-expressions\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Simplifying Expressions\",\"title\":\"Simplifying Expressions - Video and Quiz\",\"description\":\"Simplify an expression by collecting like terms: 3x + 2y + 4x − y = 7x + y. Worked examples, plus flashcards to download.\",\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and Simplifying\",\"category\":\"$undefined\",\"intro\":\"**Simplifying expressions** means rewriting them in their shortest equal form. First **expand brackets**, like **2(3 + x) = 6 + 2x**, then **collect like terms**. Only terms with the same letter and power can be collected.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"simplifying expressions\",\"expanding brackets\",\"collecting like terms\",\"expand brackets\",\"collect like terms\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions/simplifying-expressions-math-angel.webp\",\"lesson_image_alt\":\"Simplifying expressions lesson showing how to expand brackets and collect like terms step by step\",\"videoDuration\":206,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and 
3Simplifying\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"angle-relationships\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Angle Relationships in Intersecting and Parallel Lines\",\"title\":\"Angle Relationships in Parallel Lines - Video and Quiz\",\"description\":\"Angle relationships form when a line crosses two parallel lines: corresponding, alternate and co-interior. Flashcards to download to learn the names.\",\"subtopicId\":\"angles-lines\",\"subtopicName\":\"Angles and Lines\",\"category\":\"$undefined\",\"intro\":\"**Angle relationships** are the rules that link angles when lines cross. Across **parallel lines**, **corresponding and alternate angles are equal**, while **co-interior angles sum to 180°**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"angle relationships\",\"co-interior angles\",\"vertically opposite angles\",\"corresponding angles\",\"alternate angles\"],\"searchAliases\":[\"supplementary angles\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-relationships/angle-relationships-in-intersecting-and-parallel-lines-math-angel.webp\",\"lesson_image_alt\":\"Angle relationships in parallel lines showing corresponding, alternate, and co-interior angles\",\"videoDuration\":207,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"angles-lines\",\"subtopicName\":\"Angles and Lines\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"natural-numbers-whole-numbers-integers\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Natural Numbers, Whole Numbers, and Integers\",\"title\":\"Natural Numbers, Whole Numbers and Integers - Video and Quiz\",\"description\":\"Natural numbers start at 1, whole numbers include 0, and integers add negatives. Worked examples, plus flashcards to download.\",\"subtopicId\":\"number-types-place-value\",\"subtopicName\":\"Number Types and Place Values\",\"category\":\"$undefined\",\"intro\":\"**Natural numbers** are the counting numbers that start at 1, like **1, 2, 3, 4, 5**. **Whole numbers** add **0**, while **integers** also include negatives like **−1, −2, −3**. Each set fits inside the next, so every whole number is an integer.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"natural numbers\",\"whole numbers\",\"integers\",\"types of numbers maths\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/natural-numbers-whole-numbers-integers/natural-numbers-whole-numbers-and-integers-math-angel.webp\",\"lesson_image_alt\":\"Definition of Natural numbers, whole numbers, and integers.\",\"videoDuration\":232,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"number-types-place-value\",\"subtopicName\":\"Number Types and Place Values\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":7,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"pie-chart\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"Pie Chart\",\"title\":\"Pie Charts - Video and Interactive Practice\",\"description\":\"A pie chart shows data as slices of a circle. Each slice is its share of 360°, so a quarter of the data gets 90°. Flashcards to download.\",\"subtopicId\":\"charts-data-display\",\"subtopicName\":\"Charts and Data Display\",\"category\":\"$undefined\",\"intro\":\"**A pie chart** shows data as slices of a circle, each slice a **part of the whole**. To draw one, find each **central angle** using **frequency ÷ total × 360°**, so 25 of 100 gives **90°**. Together the slices fill the whole circle of **360°**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"pie chart\",\"central angle formula\",\"how to draw a pie chart\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/pie-chart/pie-chart-math-angel.webp\",\"lesson_image_alt\":\"Pie chart lesson thumbnail showing a colourful circle divided into percentage slices\",\"videoDuration\":234,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"charts-data-display\",\"subtopicName\":\"Charts and Data Dis
3play\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"fractions-and-percentages\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Fractions and Percentages\",\"title\":\"Fractions and Percentages - Video and Quiz\",\"description\":\"A percentage is a fraction out of 100: 3/4 = 75/100 = 75%, and 40% = 40/100 = 2/5. Worked examples, plus flashcards to download.\",\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"category\":\"$undefined\",\"intro\":\"**Fractions and percentages** are two ways to write the same amount. To turn a fraction into a percentage, make the **denominator 100**. A **percentage** always means out of 100.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"fractions and percentages\",\"percentage\",\"fraction\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/fractions-and-percentages/fractions-and-percentages-math-angel.webp\",\"lesson_image_alt\":\"Fractions and percentages: 70% written as 70/100 and simplified to 7/10, showing percent means out of 100\",\"videoDuration\":172,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"simplifying-expressions-multiple-variables\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Simplifying Expressions with Multiple Variables\",\"title\":\"Simplifying Expressions with Multiple Variables - Examples\",\"description\":\"Simplify expressions with multiple variables by collecting like terms and using the index laws. Flashcards to download, plus a 4-minute video.\",\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and Simplifying\",\"category\":\"$undefined\",\"intro\":\"**Simplifying expressions with multiple variables** means writing them in their shortest form. You **collect like terms** with the same letters, so 2a + 3b + 5a - b becomes **7a + 2b**. You also use **exponents**, writing x × y × y as **xy²**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"simplifying expressions with multiple variables\",\"exponents\",\"collecting like terms\",\"collect like terms\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simplifying-expressions-multiple-variables/simplifying-expressions-with-multiple-variables-math-angel.webp\",\"lesson_image_alt\":\"Simplifying algebraic expressions with multiple variables using exponents and collecting like terms\",\"videoDuration\":222,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and Simplifying\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"polygons-quadrilaterals\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Polygons and Types of Quadrilaterals\",\"title\":\"Polygons and Types of Quadrilaterals - Video and Quiz\",\"description\":\"Polygons are shapes with straight sides. Quadrilaterals have four: squares, rectangles, parallelograms, rhombuses and trapeziums. Flashcards to download.\",\"subtopicId\":\"shapes-properties\",\"subtopicName\":\"Shapes and Properties\",\"category\":\"$undefined\",\"intro\":\"**Polygons** are 2D closed shapes made from **straight line segments**. They are named by their number of sides, like a **triangle (3)** or **pentagon (5)**. A polygon with **n sides** has interior angles adding up to **(n − 2) × 180°**, so a **quadrilateral (4)** totals **360°**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"polygons\",\"quadrilaterals\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/polygons-quadrilaterals/polygons-and-types-of-quadrilaterals-math-angel.webp\",\"lesson_image_alt\":\"Polygons and quadrilaterals lesson preview showing different shapes with their names and properties\",\"videoDuration\":185,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"shapes-properties\",\"subtopicName\":\"Shapes and Properties\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"rational-numbers\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Rational Numbers and Their Location on a Number Line\",\"title\":\"Rational Numbers on a Number Line - Video and Quiz\",\"description\":\"A rational number is one integer over another, like 3/4, −2 or 0.75; √2 and π are not. Worked examples, plus flashcards to download.\",\"subtopicId\":\"number-types-place-value\",\"subtopicName\":\"Number Types and Place Values\",\"category\":\"$undefined\",\"intro\":\"**Rational numbers** can be written as a **fraction of two integers**. This covers all fractions, integers and decimals that end or repeat. **Irrational numbers** cannot: their decimals **never end or repeat**, like π.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"rational numbers\",\"irrational numbers\",\"number line\",\"fractions\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/rational-numbers/rational-numbers-and-their-location-on-a-number-line-math-angel.webp\",\"lesson_image_alt\":\"Rational numbers lesson showing fractions, terminating decimals, and recurring decimals.\",\"videoDuration\":183,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"number-types-place-value\",\"subtopicName\":\"Number Types and Place Values\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"line-graphs-curve-graphs\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"Line Graphs and Curve Graphs\",\"title\":\"Line Graphs and Curve Graphs - Video and Quiz\",\"description\":\"Line graphs connect points with straight lines, curve graphs use smooth curves. Read, draw and compare both kinds. Flashcards to download.\",\"subtopicId\":\"charts-data-display\",\"subtopicName\":\"Charts and Data Dis
3play\",\"category\":\"$undefined\",\"intro\":\"**A line graph** joins data points with **straight lines** to show how a value changes over time. You read up from the x-axis, then across to the y-axis. **A curve graph** instead uses **one smooth curve** when the relationship is not linear.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"line graphs\",\"curve graphs\",\"how to read a line graph\",\"data representation\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/line-graphs-curve-graphs/line-graphs-and-curve-graphs-math-angel.webp\",\"lesson_image_alt\":\"Line graphs and curve graphs lesson thumbnail comparing straight-line and smooth-curve data plots\",\"videoDuration\":197,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"charts-data-display\",\"subtopicName\":\"Charts and Data Display\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"percentage-of-a-number\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"How to Find Percentage of a Number\",\"title\":\"How to Find a Percentage of a Number - Video and Quiz\",\"description\":\"Find a percentage of a number by multiplying it by the rate, so 20% of 60 is 0.2 × 60 = 12. Flashcards to download to revise the method.\",\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"category\":\"$undefined\",\"intro\":\"**Percentage of a number** is a part of it out of 100. To find it, change the percent to a **decimal** and multiply, so 20% of 180 is **0.2 × 180 = 36**. As a shortcut, **10%** of a number is just that number **÷ 10**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"percentage of a number\",\"finding percentage\",\"percentage formula\",\"percentage calculation\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-of-a-number/how-to-find-percentage-of-a-number-math-angel.webp\",\"lesson_image_alt\":\"How to find percentage of a number lesson thumbnail with formula and worked percentage examples\",\"videoDuration\":238,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"expanding-double-brackets\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Expanding Double Brackets\",\"title\":\"Expanding Double Brackets - Video and Quiz\",\"description\":\"Expand double brackets term by term: (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6. Worked examples, plus flashcards to download.\",\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and Simplifying\",\"category\":\"$undefined\",\"intro\":\"**Expanding double brackets** means multiplying every term in one bracket by each term in the other. This **binomial product** uses **(a+b)(c+d) = ac+ad+bc+bd** to give four terms. You then **collect like terms**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"expanding double brackets\",\"binomial products\",\"FOIL method\",\"simplifying algebraic expressions\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/expanding-double-brackets/expanding-double-brackets-math-angel.webp\",\"lesson_image_alt\":\"Expanding double brackets formula (a+b)(c+d) = ac+ad+bc+bd shown with coloured rectangles\",\"videoDuration\":225,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and 
3Simplifying\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"properties-of-circles\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Properties of Circles\",\"title\":\"Properties of Circles - Diameter, Chord, Sector, Tangent\",\"description\":\"All points on a circle are equidistant from the centre. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"shapes-properties\",\"subtopicName\":\"Shapes and Properties\",\"category\":\"$undefined\",\"intro\":\"**The properties of a circle** are its key parts. The **radius** is the fixed distance from the **centre** to any point on the edge. The **diameter** goes through the centre, so it is **twice the radius** (a 16 cm diameter has an 8 cm radius).\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"properties of circles\",\"radius and diameter\",\"chord\",\"sector\",\"tangent\",\"properties of a circle\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/properties-of-circles/properties-of-circles-math-angel.webp\",\"lesson_image_alt\":\"Properties of circles lesson preview showing labelled radius, diameter, chord, sector, arc, and tangent\",\"videoDuration\":158,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"shapes-properties\",\"subtopicName\":\"Shapes and Properties\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":2,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"absolute-value\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Absolute Value\",\"title\":\"Absolute Value - Video and Interactive Practice\",\"description\":\"Absolute value is the distance from zero, so |−5| = 5 and |5| = 5; it is never negative. Worked examples, plus flashcards to download.\",\"subtopicId\":\"number-types-place-value\",\"subtopicName\":\"Number Types and Place Values\",\"category\":\"$undefined\",\"intro\":\"**Absolute value** is the **distance from zero** on the number line. Because distance is never negative, the answer is always **positive or zero**. A **positive number** stays as it is, while a **negative number** drops its minus sign, so **|−3| = 3**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"absolute value\",\"negative numbers\",\"simplify absolute value\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/absolute-value/absolute-value-math-angel.webp\",\"lesson_image_alt\":\"Absolute value is always non-negative: |x| ≥ 0, with examples |5| = 5, |0| = 0, and |−3| = 3\",\"videoDuration\":217,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"number-types-place-value\",\"subtopicName\":\"Number Types and Place Values\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"mean-median-mode-range\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"How to Calculate the Mean, Median, Mode and Range\",\"title\":\"Mean, Median, Mode and Range - Free Video and Quiz\",\"description\":\"The range is the biggest value minus the smallest. Mean, median and mode are the three averages. Download the flashcards to revise.\",\"subtopicId\":\"averages-spread\",\"subtopicName\":\"Averages and Spread\",\"category\":\"$undefined\",\"intro\":\"**Mean, median, mode and range** are four ways to describe data. The **mean** is the average, the **median** is the middle value once sorted, and the **mode** is the most common. The **range** is largest − smallest.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"mean median mode and range\",\"how to calculate the mean\",\"median and mode\",\"range\"],\"searchAliases\":[\"most frequent value\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/mean-median-mode-range/how-to-calculate-the-mean-median-mode-and-range-math-angel.webp\",\"lesson_image_alt\":\"Mean, median, mode and range lesson thumbnail with formulas and example calculations\",\"videoDuration\":209,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"averages-spread\",\"subtopicName\":\"Averages and Spread\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"interest-rate-calculation\",\"courseId\":\"ratio-prop
3ortion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Interest and Interest Rate Calculation\",\"title\":\"Interest Rate Calculation - Video and Interactive Practice\",\"description\":\"Interest = principal × rate × time, so £200 at 5% for a year earns £10. Flashcards to download to revise the formula.\",\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"category\":\"$undefined\",\"intro\":\"**Calculate interest** by multiplying the **principal**, your starting amount, by the **interest rate**: **interest = principal × rate**. So **5% of £200 is £10**, growing the £200 to **£210**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"interest rate calculation\",\"interest formula\",\"calculate interest\",\"principal and interest\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/interest-rate-calculation/interest-and-interest-rate-calculation-math-angel.webp\",\"lesson_image_alt\":\"Interest and interest rate calculation lesson thumbnail with formula and worked examples\",\"videoDuration\":216,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"square-of-a-binomial\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Square of a Binomial\",\"title\":\"Square of a Binomial - Flashcards and Quiz\",\"description\":\"(a + b)² = a² + 2ab + b². The middle term, 2ab, is the one people forget. Worked examples, plus a 4-minute video.\",\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and Simplifying\",\"category\":\"$undefined\",\"intro\":\"**The square of a binomial** means multiplying a bracket by itself, giving **(a + b)² = a² + 2ab + b²**. The middle **2ab** appears because the product **ab** turns up twice. The **difference of squares** rule gives **(a + b)(a − b) = a² − b²**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"square of a binomial\",\"(a + b) squared\",\"(a - b) squared\",\"difference of squares\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/square-of-a-binomial/square-of-a-binomial-math-angel.webp\",\"lesson_image_alt\":\"Three binomial formulas: (a+b) squared, (a-b) squared, and (a+b)(a-b) = a squared minus b squared\",\"videoDuration\":258,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"expressions-simplifying\",\"subtopicName\":\"Expressions and Simplifying\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":6}],\"flashcardCount\":6,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"thales-theorem\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Thales' Theorem\",\"title\":\"Thales' Theorem - Video and Interactive Practice\",\"description\":\"Thales' Theorem states that any triangle drawn on a semicircle's diameter has a 90° angle. Worked examples, plus flashcards to download.\",\"subtopicId\":\"shapes-properties\",\"subtopicName\":\"Shapes and Properties\",\"category\":\"$undefined\",\"intro\":\"**Thales' Theorem** says a triangle formed by the **diameter** and **any other point** on the circle is always a **right-angled triangle**. Since a triangle's angles add to **180°**, subtract the **90°** and the known angle to find the **missing angle**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"Thales Theorem\",\"Right-angled Triangle\",\"Circle\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/thales-theorem/thales-theorem-math-angel.webp\",\"lesson_image_alt\":\"Thales' Theorem lesson preview showing a right-angled triangle inscribed in a semicircle\",\"videoDuration\":178,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"shapes-properties\",\"subtopicName\":\"Shapes and Properties\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"basic-arithmetic-inverse-operations\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Basic Arithmetic and Inverse Operations\",\"t
3itle\":\"Basic Arithmetic and Inverse Operations - Video and Quiz\",\"description\":\"Basic arithmetic covers addition, subtraction, multiplication and division; inverse operations undo each other. Worked examples, plus flashcards.\",\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"category\":\"$undefined\",\"intro\":\"**Basic arithmetic** covers all four operations: **addition**, **subtraction**, **multiplication** and **division**. **Inverse operations** are two operations that undo each other. For example, addition is reversed by subtraction.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"basic arithmetic\",\"inverse operations\",\"four operations maths\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basic-arithmetic-inverse-operations/basic-arithmetic-and-inverse-operations-math-angel.webp\",\"lesson_image_alt\":\"Basic arithmetic operations and inverse operations diagram with examples\",\"videoDuration\":182,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"median-mean-mode-frequency-table\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"Median, Mean, Mode and Range from a Frequency Table\",\"title\":\"Mean, Median, Mode and Range from a Frequency Table\",\"description\":\"Mean from a frequency table: multiply each value by its frequency, add up, divide by the total. Flashcards to download, plus a quiz to test yourself.\",\"subtopicId\":\"averages-spread\",\"subtopicName\":\"Averages and Spread\",\"category\":\"$undefined\",\"intro\":\"**A frequency table** shows how often each value appears. To find the **mean**, multiply each value by its frequency, add the results, then divide by the **total frequency**. The **mode** is the value with the highest frequency, and the **median** sits at position **(n + 1) ÷ 2**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"mean from a frequency table\",\"median from a frequency table\",\"mode\",\"range\",\"frequency table\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/median-mean-mode-frequency-table/median-mean-mode-range-from-a-frequency-table-math-angel.webp\",\"lesson_image_alt\":\"Mean, median, mode and range from a frequency table lesson thumbnail with worked calculations\",\"videoDuration\":215,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"averages-spread\",\"subtopicName\":\"Averages and Spread\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"simple-interest-and-compound-interest\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Simple Interest and Compound Interest\",\"title\":\"Simple and Compound Interest - Video and Quiz\",\"description\":\"Simple interest earns a fixed amount each year; compound interest earns on the interest too. Flashcards to download for GCSE and IGCSE.\",\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"category\":\"$undefined\",\"intro\":\"**Simple interest** is worked out only on the original amount, so **£100 at 5%** earns **£5 a year**. **Compound interest** also pays interest on the **interest already added**, so your money grows faster: the compound interest formula 
3is **total = principal × (1 + rate)ᵗ**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"simple interest\",\"compound interest\",\"interest formulas\",\"interest calculations\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/simple-interest-and-compound-interest/simple-interest-and-compound-interest-math-angel.webp\",\"lesson_image_alt\":\"Simple and compound interest lesson thumbnail comparing both formulas and how they grow over time\",\"videoDuration\":223,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"introduction-to-mapping\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Introduction to Mapping\",\"title\":\"Introduction to Mapping - Video and Quiz\",\"description\":\"Mapping in maths shows the relationship between two quantities, like time and speed. Worked examples, plus flashcards to download.\",\"subtopicId\":\"formulas-functions\",\"subtopicName\":\"Formulas and Functions\",\"category\":\"$undefined\",\"intro\":\"**Mapping in maths** links each **input** to one **output**, describing how two quantities relate, and is often drawn as a function machine. For example, **time is mapped to speed**, so each hour has a matching speed value.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"mapping in maths\",\"tables and graphs\",\"input and output\",\"quantities\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-mapping/introduction-to-mapping-math-angel.webp\",\"lesson_image_alt\":\"Mapping of time to speed shown with a table and graph, illustrating how one quantity relates to another\",\"videoDuration\":171,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"formulas-functions\",\"subtopicName\":\"Formulas and Functions\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"units-of-area\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Units of Area\",\"title\":\"Units of Area - Converting between mm², cm², m², km²\",\"description\":\"Area measures how much space a surface covers, in units like mm², cm², and m². Flashcards to download, plus a quiz to test yourself.\",\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"category\":\"$undefined\",\"intro\":\"**Units of area** are square units that measure the space a shape covers, like **mm², cm², m², and km²**. To **convert between units of area**, square the length conversion, so **1 cm² = 100 mm²**. Multiply for smaller units, divide for larger.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"units of area\",\"mm² to cm²\",\"cm² to m²\",\"m² to km²\",\"convert between units of area\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/units-of-area/units-of-area-math-angel.webp\",\"lesson_image_alt\":\"Units of area table comparing mm², cm², m², and km² with edge lengths and scale examples: pencil, calculator, window, city\",\"videoDuration\":189,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"bidmas-order-of-operations\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"BIDMAS - Order of Operations\",\"t
3itle\":\"BIDMAS - Order of Operations Rules \u0026 Worked Examples\",\"description\":\"BIDMAS is the order of operations: Brackets, Indices, Divide, Multiply, Add, Subtract. Flashcards to download, plus a quiz to test yourself.\",\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"category\":\"$undefined\",\"intro\":\"**BIDMAS** tells you the correct **order of operations**. It stands for **Brackets**, **Indices**, **Division**, **Multiplication**, **Addition**, **Subtraction**. When two operations are on the same level, work from **left to right**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"BIDMAS\",\"order of operations\",\"BODMAS\",\"BIDMAS rules\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/bidmas-order-of-operations/bidmas-order-of-operations-math-angel.webp\",\"lesson_image_alt\":\"BIDMAS order of operations lesson covering brackets, indices, division, multiplication, addition, subtraction\",\"videoDuration\":172,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"box-plot\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"How to Draw and Read a Box Plot\",\"title\":\"Box Plot - How to Draw, Read, and Find Interquartile Range\",\"description\":\"A box plot shows data distribution using minimum, Q1, median, Q3, and maximum. GCSE quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"averages-spread\",\"subtopicName\":\"Averages and Spread\",\"category\":\"$undefined\",\"intro\":\"**A box plot** shows how a data set is spread out using five values: the **minimum, Q1, median, Q3, and maximum**. The box runs from **Q1 to Q3**, with a line at the **median**. The **interquartile range (IQR)** is **Q3 − Q1**, the middle **50%**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"box plot\",\"interquartile range\",\"quartiles\",\"how to draw a box plot\"],\"searchAliases\":[\"box and whisker plot\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/box-plot/how-to-draw-and-read-a-box-plot-math-angel.webp\",\"lesson_image_alt\":\"Box plot lesson thumbnail showing minimum, quartiles, median, and maximum on a number line\",\"videoDuration\":198,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"averages-spread\",\"subtopicName\":\"Averages and Spread\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"percentage-increase-and-decrease\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Percentage Increase and Decrease\",\"title\":\"Percentage Increase and Decrease - Free Video and Quiz\",\"description\":\"Percentage increase and decrease use one formula: original × (1 ± change). Reverse percentages are covered too. Download the flashcards to revise.\",\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"category\":\"$undefined\",\"intro\":\"**Percentage increase and decrease** use one formula: **new value = original × (1 ± percentage change)**. Add to increase, subtract to decrease. A **reverse percentage** divides to find the original value.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"percentage increase\",\"percentage decrease\",\"percentage increase and decrease formula\",\"reverse percentage\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-prop
3ortion-rates-of-change/percentage-increase-and-decrease/percentage-increase-and-decrease-math-angel.webp\",\"lesson_image_alt\":\"Percentage increase and decrease lesson thumbnail showing the formula and worked examples of price changes\",\"videoDuration\":203,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"introduction-to-formulas\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Introduction to Formulas\",\"title\":\"Introduction to Formulas - Video and Quiz\",\"description\":\"A formula links quantities with letters: A = l × w, so a 5 by 3 rectangle has area 15. Worked examples, plus flashcards to download.\",\"subtopicId\":\"formulas-functions\",\"subtopicName\":\"Formulas and Functions\",\"category\":\"$undefined\",\"intro\":\"**A formula** is a maths rule that links two **variables**, like **y = 2x + 3**. Whichever value you pick for x, the rule gives one matching y. To find it, **substitute** your value in place of x and work it out: if x = 1, then y = 2 × 1 + 3, so **y = 5**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"formulas\",\"variables\",\"substitution\",\"tables\",\"graphs\",\"substitute\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-formulas/introduction-to-formulas-math-angel.webp\",\"lesson_image_alt\":\"Definition of a formula with y = 2x + 3 and substitution examples for x = 1, 2, and 3 giving y = 5, 7, and 9\",\"videoDuration\":160,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"formulas-functions\",\"subtopicName\":\"Formulas and Functions\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"area-of-a-triangle\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Area of a Triangle\",\"title\":\"How to Find the Area of a Triangle - Free Video and Quiz\",\"description\":\"Find the area of any triangle with ½ × base × height. The height must be at right angles to the base. Download the flashcards to see the worked examples.\",\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"category\":\"$undefined\",\"intro\":\"**The area of a triangle** = **½ × base × height**. Multiply the base by the height, then divide by 2, so a base of 6 and height of 5 gives **½ × 6 × 5 = 15**. The height must be **perpendicular**, meeting the base at a right angle.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"area of a triangle\",\"triangle area formula\"],\"searchAliases\":[\"triangle altitude\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-triangle/area-of-a-triangle-math-angel.webp\",\"lesson_image_alt\":\"Area of a triangle lesson preview showing the formula ½ × base × height with a labelled triangle\",\"videoDuration\":202,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"commutative-and-associative-laws\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Commutative and Associative Laws\",\"title\":\"Commutative and Associative Laws - Video and Quiz\",\"description\":\"Commutative: a + b = b + a. Associative: (a + b) + c = a + (b + c). Same for multiplying. Flashcards to download to revise both laws.\",\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"category\":\"$undefined\",\"intro\":\"**The commutative law** lets you swap the order of numbers, like **3 + 5 = 5 + 3**. **The associative law** lets you regroup them, like **(2 × 5) × 4 = 2 × (5 × 4)**. Both keep the answer the same when you add or multiply.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"commutative law\",\"associative law\",\"commutative property\",\"associative property\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/commutative-property-associative-property/commutative-property-and-associative-property-math-angel.webp\",\"lesson_image_alt\":\"Commutative and associative property lesson showing how to swap and regroup numbers in maths\",\"videoDuration\":196,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"grouped-frequency-table\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"Averages from a Grouped Frequency Table\",\"title\":\"Grouped Frequency Table - Video and Quiz\",\"description\":\"A grouped frequency table puts data into class intervals. Find the modal class, median class and estimated mean. Flashcards for GCSE and IGCSE.\",\"subtopicId\":\"averages-spread\",\"subtopicName\":\"Averages and Spread\",\"category\":\"$undefined\",\"intro\":\"**A grouped frequency table** sorts data into **class intervals** and lists their **frequencies**. A frequency of 8 for 20-30 means 8 values fall in that range. From it you find the **modal class, median class,** and **estimate the mean**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"grouped frequency table\",\"modal class\",\"median class\",\"estimated mean\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/grouped-frequency-table/averages-from-grouped-frequency-table-math-angel.webp\",\"lesson_image_alt\":\"Grouped frequency table with class intervals 10 \u003c x ≤ 20 to 40 \u003c x ≤ 50 showing delivery time frequencies\",\"videoDuration\":194,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"averages-spread\",\"subtopicName\":\"Averages and Spread\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0}
3,{\"id\":\"percentage-change\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"How to Calculate Percentage Change\",\"title\":\"How to Calculate Percentage Change - Video and Quiz\",\"description\":\"Percentage change = (new − original) ÷ original × 100, so £40 rising to £50 is a 25% increase. Worked examples, plus flashcards to download.\",\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"category\":\"$undefined\",\"intro\":\"**Percentage change** shows how much a value has risen or fallen. Find it with **(change ÷ original) × 100**, so £20 rising to £25 gives **25%**. A positive answer is a **percentage increase**, a negative one a **percentage decrease**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"percentage change\",\"percentage increase\",\"percentage decrease\",\"percentage formula\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/percentage-change/how-to-calculate-percentage-change-math-angel.webp\",\"lesson_image_alt\":\"Percentage change lesson thumbnail showing the formula with worked increase and decrease examples\",\"videoDuration\":239,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"percentages-interest\",\"subtopicName\":\"Percentages and Interest\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":6}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"introduction-to-functions-and-graphs\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Introduction to Functions and Graphs\",\"title\":\"Introduction to Functions and Graphs - f(x) Explained\",\"description\":\"A function maps each input to exactly one output, like f(x) = 2x + 1. GCSE quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"formulas-functions\",\"subtopicName\":\"Formulas and Functions\",\"category\":\"$undefined\",\"intro\":\"**A function** takes each input and turns it into exactly one output. Put x = 3 into the rule **f(x) = 2x + 1** to get **f(3) = 7**. Show it with a table of values, then plot the points as a **graph**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"functions and graphs\",\"function notation\",\"graphing functions\",\"f(x)\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/introduction-to-functions-and-graphs/introduction-to-functions-and-graphs-math-angel.webp\",\"lesson_image_alt\":\"Function f(x) = 2x + 1 with a table of values and plotted graph showing input-output pairs\",\"videoDuration\":219,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"formulas-functions\",\"subtopicName\":\"Formulas and Functions\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"perimeter-of-a-polygon\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Perimeter of a Polygon\",\"title\":\"Perimeter of a Polygon - Rectangles, Triangles, Compound Shapes\",\"description\":\"The perimeter of a polygon is the total length of all its sides. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"category\":\"$undefined\",\"intro\":\"**The perimeter of a polygon** is the **total length of all its sides**. To find the perimeter, add up the length of every side: a triangle with sides of 5, 4 and 3 cm has a perimeter of 12 cm. For a **rectangle**, use the shortcut **2 × (length + width)**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"perimeter of a polygon\",\"rectangles\",\"triangles\",\"compound shapes\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perimeter-of-a-polygon/perimeter-of-a-polygon-math-angel.webp\",\"lesson_image_alt\":\"Perimeter of a polygon formulas for rectangles, squares, isosceles and equilateral triangles with labelled diagrams\",\"videoDuration\":181,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"column-addition-and-subtraction\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Column Addition and Column Subtraction\",\"title\":\"Column Addition and Subtraction - Carrying and Borrowing\",\"description\":\"Column addition and subtraction are used to add and subtract multi-digit numbers vertically. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"category\":\"$undefined\",\"intro\":\"**Column addition and subtraction** line up 
3numbers by **place value** and work from the right. If a column makes 10 or more, you **carry 1**. If the top digit is too small, you **borrow 1** from the left.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"column addition and subtraction\",\"column addition\",\"column subtraction\",\"carrying and borrowing\"],\"searchAliases\":[\"regrouping\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/column-addition-and-subtraction/column-addition-and-column-subtraction-math-angel.webp\",\"lesson_image_alt\":\"Column addition and subtraction worked examples showing carrying and borrowing with multi-digit numbers\",\"videoDuration\":190,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":2,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"calculating-probability\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"Calculating Probability\",\"title\":\"Calculating Probability - Video and Quiz\",\"description\":\"Probability = favourable outcomes ÷ total outcomes. Rolling a 6 on a dice is 1/6; an even number is 3/6 = 1/2. Worked examples, plus flashcards.\",\"subtopicId\":\"probability\",\"subtopicName\":\"Probability\",\"category\":\"$undefined\",\"intro\":\"**Calculating probability** means working out how likely an event is. Divide the **desired outcomes** by the **total outcomes**, so 3 red balls out of 10 gives **3/10**. **Experimental probability** estimates it by repeating an experiment.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"calculating probability\",\"probability formula\",\"experimental probability\",\"probability examples\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/calculating-probability/calculating-probability-math-angel.webp\",\"lesson_image_alt\":\"Calculating probability lesson thumbnail with a probability scale from impossible to certain\",\"videoDuration\":186,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"probability\",\"subtopicName\":\"Probability\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"directly-proportional-inversely-proportional\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Directly Proportional and Inversely Proportional\",\"title\":\"Directly and Inversely Proportional - Video and Quiz\",\"description\":\"Direct: y = kx, both grow together. Inverse: xy = k, one grows as the other shrinks. Worked examples, plus flashcards to download.\",\"subtopicId\":\"proportion\",\"subtopicName\":\"Proportion\",\"category\":\"$undefined\",\"intro\":\"**Directly proportional** means two amounts rise at the same rate, so doubling one **doubles** the other. For example, if 1 watermelon costs **£4**, then 2 cost **£8**. **Inversely proportional** is the opposite: doubling one **halves** the other.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"directly proportional\",\"inversely proportional\",\"direct proportion\",\"inverse proportion\"],\"searchAliases\":[\"unit rates\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/directly-proportional-inversely-proportional/directly-proportional-and-inversely-proportional-math-angel.webp\",\"lesson_image_alt\":\"Directly and inversely proportional lesson thumbnail comparing both relationship types with examples\",\"videoDuration\":205,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"proportion\",\"subtopicName\":\"Proportion\",\"topicId\":\"ratio-prop
3ortion-rates-of-change\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"solving-equations\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Solving Equations\",\"title\":\"Solving Equations Step by Step - Video and Quiz\",\"description\":\"Solving equations means finding the value that makes the equation true, like x = 3 in 3x + 2 = 11. Worked examples, plus flashcards to download.\",\"subtopicId\":\"linear-equations-graphs\",\"subtopicName\":\"Linear Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**Solving equations** means finding the value of **x** that makes the equation true. To solve **3x + 2 = 11**, subtract 2 from both sides to get 3x = 9, then divide both sides by 3, so **x = 3**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"solving equations\",\"algebraic equations\",\"equation solving\",\"algebra equations\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-equations/solving-equations-math-angel.webp\",\"lesson_image_alt\":\"Step-by-step solving of a linear equation showing simplification, rearrangement, and finding x\",\"videoDuration\":212,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"linear-equations-graphs\",\"subtopicName\":\"Linear Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"area-of-a-trapezium\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Area of a Trapezium\",\"title\":\"Area of a Trapezium - Free Video and Quiz\",\"description\":\"Find the area of a trapezium with ½ × (a + b) × h. Add the parallel sides, halve, then multiply by the height. Download the flashcards to see each step.\",\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"category\":\"$undefined\",\"intro\":\"**The trapezium area formula** is **(a + b) ÷ 2 × h**, where a and b are the **parallel sides** and h is the **perpendicular height**, not the slanted side. With bases 8 cm and 12 cm and height 6 cm: (8 + 12) ÷ 2 × 6 = 10 × 6 = 60 cm².\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"area of a trapezium\",\"trapezium area formula\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-a-trapezium/area-of-a-trapezium-math-angel.webp\",\"lesson_image_alt\":\"Area of a trapezium formula (a + b) ÷ 2 × h with labelled diagram and worked example showing 60 cm²\",\"videoDuration\":244,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"long-multiplication\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Long Multiplication\",\"title\":\"Long Multiplication - How to Multiply Large Numbers\",\"description\":\"Long multiplication splits large calculations into smaller digit-by-digit steps. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"category\":\"$undefined\",\"intro\":\"**Long multiplication** splits a large calculation into **digit-by-digit steps**. You multiply the top number by each bottom digit and add the partial products. This lets you **multiply large numbers**, like **352 × 24 = 8448**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"long multiplication\",\"long multiplication method\",\"multiply large numbers\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-multiplication/long-multiplication-math-angel.webp\",\"lesson_image_alt\":\"Long multiplication method showing step-by-step partial products for multiplying multi-digit numbers\",\"videoDuration\":198,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":2,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"addition-rule-of-probability-expected-frequency\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"Addition Rule of Probability and Expected Frequency\",\"t
3itle\":\"Addition Rule of Probability and Expected Frequency\",\"description\":\"For mutually exclusive events, P(A or B) = P(A) + P(B). GCSE quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"probability\",\"subtopicName\":\"Probability\",\"category\":\"$undefined\",\"intro\":\"**The addition rule of probability** finds the chance of A or B when they are **mutually exclusive** (cannot both happen). Just add: **P(A or B) = P(A) + P(B)**. **Expected frequency** is how often it happens: **probability × number of trials**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"addition rule of probability\",\"expected frequency\",\"P(A or B)\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/addition-rule-of-probability-expected-frequency/addition-rule-of-probability-and-expected-frequency-math-angel.webp\",\"lesson_image_alt\":\"Addition rule of probability lesson thumbnail showing P(A or B) = P(A) + P(B) formula\",\"videoDuration\":215,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"probability\",\"subtopicName\":\"Probability\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"direct-proportion\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Direct Proportion Formula and Examples\",\"title\":\"Direct Proportion - Formula y = kx with Worked Examples\",\"description\":\"Direct proportion means both values increase together using y = kx. GCSE quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"proportion\",\"subtopicName\":\"Proportion\",\"category\":\"$undefined\",\"intro\":\"**Direct proportion** means two amounts change together by the same factor, so if x doubles, y doubles too. The **direct proportion formula** is **y = kx**. First find the constant **k** by dividing y by x, such as **k = 20 ÷ 4 = 5**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"direct proportion\",\"direct proportion formula\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/direct-proportion/direct-proportion-formula-and-examples-math-angel.webp\",\"lesson_image_alt\":\"Direct proportion definition, notation y ∝ x, and formula y = kx where k is a constant\",\"videoDuration\":213,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"proportion\",\"subtopicName\":\"Proportion\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"solving-rational-equations\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Solving Rational Equations\",\"title\":\"Solving Rational Equations - Video and Quiz\",\"description\":\"Rational equations have x in a denominator, like 6/x = 2. Multiply both sides by x to clear the fraction, then solve: x = 3. Worked examples included.\",\"subtopicId\":\"linear-equations-graphs\",\"subtopicName\":\"Linear Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**Solving rational equations** means finding x when it lies in the **denominator**. Multiply both sides to clear the fraction, then solve. Always check your answer, and never let the denominator be zero.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"rational equations\",\"solving rational equations\",\"equation solving\",\"algebra equations\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-rational-equations/solving-rational-equations-math-angel.webp\",\"lesson_image_alt\":\"Steps to solve a rational equation with x in the denominator, clearing fractions and checking the answer\",\"videoDuration\":237,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"linear-equations-graphs\",\"subtopicName\":\"Linear Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":2,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"area-parallelograms-triangles\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Area of Parallelograms and Triangles\",\"title\":\"Area of Parallelograms and Triangles - Flashcards and Quiz\",\"description\":\"Area of a parallelogram = base × height, and a triangle is half of that: ½ × base × height. Worked examples, plus a 3-minute video.\",\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"category\":\"$undefined\",\"intro\":\"**The area of a parallelogram** is **base × height**. The height must be **perpendicular** to the base, not the slanted side. The **area of a triangle** is exactly half of this: **½ × base × height**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"area of a parallelogram\",\"area of a triangle\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-parallelograms-triangles/area-of-parallelograms-and-triangles-math-angel.webp\",\"lesson_image_alt\":\"Area of a parallelogram formula A = b × h with two diagrams showing perpendicular height h inside and outside the shape\",\"videoDuration\":180,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"long-division\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Long Division\",\"title\":\"Long Division - Video and Interactive Practice\",\"description\":\"Long division goes one digit at a time: divide, multiply, subtract, bring down, repeat. Worked examples, plus flashcards to download.\",\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"category\":\"$undefined\",\"intro\":\"**Long division** is a method for dividing large numbers in small steps. You repeat **divide, multiply, subtract, bring down** until no digits are left. Anything left over is the **remainder**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"long division\",\"long division method\",\"long division 
3with remainders\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/long-division/long-division-math-angel.webp\",\"lesson_image_alt\":\"Long division worked example showing dividend, divisor, quotient and remainder step by step\",\"videoDuration\":190,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":6}],\"flashcardCount\":2,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"probability-tree-diagrams\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"Probability Tree Diagrams\",\"title\":\"Probability Tree Diagrams - How to Draw and Interpret\",\"description\":\"Probability tree diagrams show all outcomes step by step. Interactive practice to try, plus flashcards for GCSE and IGCSE.\",\"subtopicId\":\"probability\",\"subtopicName\":\"Probability\",\"category\":\"$undefined\",\"intro\":\"**A probability tree diagram** shows **all possible outcomes** of a two-stage event step by step. You **multiply along the branches** to find one path. Then **add** the paths for a **combined event**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"probability tree diagrams\",\"dependent probability\",\"combined events\",\"multiply along branches\"],\"searchAliases\":[\"conditional probability\",\"without replacement\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/probability-tree-diagrams/probability-tree-diagrams-math-angel.webp\",\"lesson_image_alt\":\"Probability tree diagrams lesson thumbnail with branching outcomes for two-stage events\",\"videoDuration\":231,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"probability\",\"subtopicName\":\"Probability\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"inverse-proportion\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Inverse Proportion Formula and Examples\",\"title\":\"Inverse Proportion - Formula y = k/x with Worked Examples\",\"description\":\"Inverse proportion means one value increases as the other decreases, keeping xy = k constant. GCSE quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"proportion\",\"subtopicName\":\"Proportion\",\"category\":\"$undefined\",\"intro\":\"**Inverse proportion** means as one value goes up, the other goes down, so their product **xy = k** stays constant. Multiply a known pair like **6 × 8 = 48** to find the constant **k**. Then write **y = k ÷ x** to work out any missing value.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"inverse proportion\",\"inverse proportion formula\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/inverse-proportion/inverse-proportion-formula-and-examples-math-angel.webp\",\"lesson_image_alt\":\"Inverse proportion definition, notation y ∝ 1/x, and formula y = k/x where xy = k and k is a constant\",\"videoDuration\":212,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"proportion\",\"subtopicName\":\"Proportion\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"m-and-c-in-linear-equations\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Gradient and Y-Intercept in Linear Equations\",\"title\":\"Gradient and Y-Intercept in Linear Equations - y = mx + c\",\"description\":\"In y = mx + c, m is the gradient and c is the y-intercept. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"linear-equations-graphs\",\"subtopicName\":\"Linear Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**Gradient (m)** and **y-intercept (c)** are the two parts of a straight line **y = mx + c**. The gradient shows how steep the line is, so **m = 2** means y rises 2 as x rises 1. The y-intercept is where the line crosses the y-axis, at **x = 0**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"linear equations\",\"gradient\",\"y-intercept\",\"graphs\"],\"searchAliases\":[\"slope\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/m-and-c-in-linear-equations/gradient-and-y-intercept-in-linear-equations-math-angel.webp\",\"lesson_image_alt\":\"Linear equation y = mx + c on a graph showing gradient m and y-intercept c where the line crosses the y-axis\",\"videoDuration\":221,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"linear-equations-graphs\",\"subtopicName\":\"Linear Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"area-of-compound-shapes\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Area of Compound Shapes\",\"title\":\"Area of Compound Shapes - Flashcards and Quiz\",\"description\":\"Split a compound shape into rectangles and triangles, find each area, then add them up. Worked examples, plus a 3-minute video.\",\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"category\":\"$undefined\",\"intro\":\"**The area of a compound shape** is found by splitting it into simpler shapes like **rectangles and triangles**. Find each area, such as **length × width**, then **add** them for the **total area**. You **subtract** instead when a part is cut out.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"area of a compound shape\",\"compound shape area formula\"],\"searchAliases\":[\"composite shapes\",\"area of irregular shapes\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/area-of-compound-shapes/area-of-compound-shapes-math-angel.webp\",\"lesson_image_alt\":\"Area of compound shapes lesson preview showing an L-shape split into rectangles\",\"videoDuration\":181,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":6}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"decimal-point-movement\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Movement of the Decimal Point\",\"title\":\"Decimal Point Movement - Multiply \u0026 Divide by Powers of 10\",\"description\":\"Moving the decimal point right multiplies a number by 10, 100 or 1000;
3 moving it left divides. Free 3-minute video, plus a quiz to test yourself.\",\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"category\":\"$undefined\",\"intro\":\"**Decimal point movement** multiplies or divides a number by **powers of 10** like 10, 100 or 1000. Multiplying shifts the point **right**, making the number **bigger**. Dividing shifts it **left**, making the number **smaller**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"decimal point movement\",\"multiply by 10 100 1000\",\"divide by powers of 10\",\"moving the decimal point\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimal-point-movement/movement-of-the-decimal-point-math-angel.webp\",\"lesson_image_alt\":\"Decimal point shifting right for multiplication and left for division by powers of 10\",\"videoDuration\":188,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":7}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"sets-and-venn-diagrams\",\"courseId\":\"probability-statistics\",\"courseName\":\"Probability and Statistics\",\"lesson_title\":\"Sets and Venn Diagrams\",\"title\":\"Sets and Venn Diagrams - Video and Interactive Practice\",\"description\":\"A Venn diagram shows how sets overlap: the middle is in both, the outside in neither. Worked examples, plus flashcards to download.\",\"subtopicId\":\"probability\",\"subtopicName\":\"Probability\",\"category\":\"$undefined\",\"intro\":\"**A Venn diagram** uses **overlapping circles** to show how **sets** are related. Draw circles for football and tennis players: the overlap is the **intersection (∩)**, the players who do both (**AND**). Everything inside either circle is the **union (∪)**, all who play a sport (**OR**).\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"Venn diagrams\",\"sets\",\"set notation\",\"union and intersection\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/probability-statistics/sets-and-venn-diagrams/sets-and-venn-diagrams-math-angel.webp\",\"lesson_image_alt\":\"Sets and Venn diagrams lesson thumbnail with overlapping circles showing union and intersection\",\"videoDuration\":237,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"probability\",\"subtopicName\":\"Probability\",\"topicId\":\"probability-statistics\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"speed-distance-time\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Speed, Distance and Time\",\"title\":\"Speed, Distance and Time - Flashcards and Quiz\",\"description\":\"Speed = distance ÷ time, so 120 miles in 2 hours is 60 mph. Cover the one you want on the formula triangle to find it. Worked examples included.\",\"subtopicId\":\"compound-measures\",\"subtopicName\":\"Compound Measures\",\"category\":\"$undefined\",\"intro\":\"**Speed, distance and time** are linked by the speed distance time formula **speed = distance ÷ time**, so a car going 100 miles in 2 hours travels at 50 mph. The speed distance time triangle gives the other two: **distance = speed × time** and **time = distance ÷ speed**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"speed distance time\",\"speed formula\",\"formula triangle\",\"compound measures\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/speed-distance-time/speed-distance-time-maths-angel.webp\",\"lesson_image_alt\":\"The speed triangle with Distance on top and Speed and Time below, alongside the three formulas: distance = speed × time, speed = distance ÷ time, and time = distance ÷ speed\",\"videoDuration\":249,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"compound-measures\",\"subtopicName\":\"Compound Measures\",\"topicId\":\"ratio-prop
3ortion-rates-of-change\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":6,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"equation-of-a-straight-line\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Finding the Equation of a Straight Line\",\"title\":\"Equation of a Straight Line - Video and Quiz\",\"description\":\"A straight line is y = mx + c, where m is the gradient and c is where it crosses the y-axis. Worked examples, plus flashcards to download.\",\"subtopicId\":\"linear-equations-graphs\",\"subtopicName\":\"Linear Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**The equation of a straight line** is **y = mx + c**. The **gradient** m shows how steep the line is, found from two points using **m = (y₂ − y₁) ÷ (x₂ − x₁)**. The **y-intercept** c is where the line crosses the y-axis, when x = 0.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"equation of a straight line\",\"gradient\",\"y-intercept\",\"y = mx + c\"],\"searchAliases\":[\"slope\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equation-of-a-straight-line/finding-the-equation-of-a-straight-line-math-angel.webp\",\"lesson_image_alt\":\"Graph of the linear equation y = mx + c showing gradient and y-intercept labelled on a straight line\",\"videoDuration\":204,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"linear-equations-graphs\",\"subtopicName\":\"Linear Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"circumference-area-circle-sector\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Circumference and Area of a Circle and a Sector\",\"title\":\"Circumference and Area of a Circle and a Sector\",\"description\":\"The circumference of a circle is C = 2πr and the area is A = πr². GCSE quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"category\":\"$undefined\",\"intro\":\"**Circumference of a circle** is the distance around its edge, found with **C = 2πr**, where r is the radius. A circle with radius 5 has C = 10π. The **area of a circle** is the space inside it, found with **A = πr²**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"circumference of a circle\",\"area of a circle\",\"circle sector\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/circumference-area-circle-sector/circumference-and-area-of-a-circle-and-a-sector-math-angel.webp\",\"lesson_image_alt\":\"Circle with radius r labelled, showing circumference formula C = πd = 2πr and area formula A = πr²\",\"videoDuration\":191,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"area-perimeter\",\"subtopicName\":\"Area and Perimeter\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":7}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"adding-and-subtracting-negative-numbers\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Adding and Subtracting Negative Numbers\",\"title\":\"Adding and Subtracting Negative Numbers - Video and Quiz\",\"description\":\"Adding and subtracting negatives: two signs the same make a plus, two different make a minus. Flashcards to download to revise the rules.\",\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"category\":\"$undefined\",\"intro\":\"**Adding and subtracting negative numbers** follows two sign rules: **same signs become a plus** and **different signs become a minus**. On a **number line**, adding moves right and subtracting moves left.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"adding and subtracting negative numbers\",\"negative numbers rules\",\"number line\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-negative-numbers/adding-and-subtracting-negative-numbers-math-angel.webp\",\"lesson_image_alt\":\"Adding and subtracting negative numbers with sign rules and number line examples\",\"videoDuration\":220,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":8}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0}
3,{\"id\":\"density-mass-volume\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Density, Mass and Volume\",\"title\":\"Density, Mass and Volume - Free Video and Quiz\",\"description\":\"Density = mass ÷ volume, in g/cm³ or kg/m³. Cover the one you want on the formula triangle to find it. Download the flashcards for GCSE and IGCSE revision.\",\"subtopicId\":\"compound-measures\",\"subtopicName\":\"Compound Measures\",\"category\":\"$undefined\",\"intro\":\"**The density formula** is **density = mass ÷ volume**: 100 g in 50 cm³ gives 2 g/cm³. The density triangle puts mass on top, density and volume underneath, so you can rearrange it to **mass = density × volume**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"density mass volume\",\"density formula\",\"formula triangle\",\"compound measures\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/density-mass-volume/density-mass-volume-maths-angel.webp\",\"lesson_image_alt\":\"The density triangle with Mass on top and Density and Volume below, showing the three rearrangements: Mass = Density × Volume, Volume = Mass ÷ Density, and Density = Mass ÷ Volume.\",\"videoDuration\":247,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"compound-measures\",\"subtopicName\":\"Compound Measures\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":6,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"x-intercept-y-intercept-intersection\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"How to Find X-Intercept, Y-Intercept and Intersections\",\"title\":\"How to Find X-Intercept, Y-Intercept and Line Intersections\",\"description\":\"x-intercept: set y = 0. y-intercept: set x = 0. Two lines cross where their equations match. GCSE quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"linear-equations-graphs\",\"subtopicName\":\"Linear Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**The x-intercept** is found by setting **y = 0**, and the **y-intercept** by setting **x = 0**. For y = 200 − 50x, this gives an x-intercept of **4** and a y-intercept of **200**. Two lines **intersect** where they share the same x and y values.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"x-intercept\",\"y-intercept\",\"intersection of linear equations\",\"linear equations\",\"intersect\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/x-intercept-y-intercept-intersection/how-to-find-x-intercept-y-intercept-and-intersections-math-angel.webp\",\"lesson_image_alt\":\"Linear equation y = 200 - 50x showing where the line crosses the x-axis and y-axis with intercepts labelled\",\"videoDuration\":186,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"linear-equations-graphs\",\"subtopicName\":\"Linear Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"line-of-symmetry\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Line of Symmetry and Reflection Symmetry\",\"title\":\"Lines of Symmetry and Reflection - Free Video and Quiz\",\"description\":\"A line of symmetry splits a shape into two mirror-image halves. A square has 4, a rectangle 2, a regular pentagon 5. Download the flashcards to revise.\",\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"category\":\"$undefined\",\"intro\":\"**A line of symmetry** splits a shape into **two identical halves**. If you fold the shape along this line, both sides **match exactly**. A shape has **reflection symmetry** if it has **at least** one line of symmetry.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"line of symmetry\",\"what is a line of symmetry\",\"reflection symmetry\",\"how many lines of symmetry\",\"lines of symmetry in shapes\",\"symmetry in shapes\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/line-of-symmetry/line-of-symmetry-and-reflection-symmetry-math-angel.webp\",\"lesson_image_alt\":\"Line of symmetry lesson preview showing shapes with marked lines of symmetry\",\"videoDuration\":230,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"multiplying-and-dividing-negative-numbers\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Multiplying and Dividing Negative Numbers\",\"title\":\"Multiplying \u0026 Dividing Negative Numbers - Sign Rules\",\"description\":\"Multiplying or dividing negatives: same signs give a plus, different signs give a minus. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"category\":\"$undefined\",\"intro\":\"**Multiplying and divi
3ding negative numbers** follows **sign rules**. An **odd number of negatives** gives a negative answer, while an even number gives a positive answer, like **(−12) ÷ (−3) = +4**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"multiplying and dividing negative numbers\",\"negative numbers sign rules\",\"sign rules\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-and-dividing-negative-numbers/multiplying-and-dividing-negative-numbers-math-angel.webp\",\"lesson_image_alt\":\"Sign rules for multiplying and dividing negative numbers with worked examples\",\"videoDuration\":184,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"basic-calculations\",\"subtopicName\":\"Basic Calculations\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":9}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"pressure-force-area\",\"courseId\":\"ratio-proportion-rates-of-change\",\"courseName\":\"Ratio, Proportion and Rates of Change\",\"lesson_title\":\"Pressure, Force and Area\",\"title\":\"Pressure, Force and Area - Video and Interactive Practice\",\"description\":\"Pressure = force ÷ area, in N/m² (pascals), so 50 N on 2 m² is 25 N/m². Cover the one you want on the triangle to find it. Flashcards to download.\",\"subtopicId\":\"compound-measures\",\"subtopicName\":\"Compound Measures\",\"category\":\"$undefined\",\"intro\":\"**Pressure, force and area** are linked by **pressure = force ÷ area**. It shows how concentrated a force is, so 100 N spread over 2 m² gives 50 N/m². Rearrange it to get **force = pressure × area**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"pressure force area\",\"pressure formula\",\"formula triangle\",\"compound measures\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/ratio-proportion-rates-of-change/pressure-force-area/pressure-force-area-maths-angel.webp\",\"lesson_image_alt\":\"The pressure triangle with force on top, pressure and area below, showing force = pressure × area, pressure = force ÷ area, and area = force ÷ pressure\",\"videoDuration\":240,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"compound-measures\",\"subtopicName\":\"Compound Measures\",\"topicId\":\"ratio-proportion-rates-of-change\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"nth-term-of-a-linear-sequence\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Finding the nth Term of a Linear Sequence\",\"title\":\"Finding the nth Term of a Linear Sequence - Rule \u0026 Examples\",\"description\":\"In 2, 5, 8, 11 the terms go up by 3 each time, so the nth term is 3n − 1. Flashcards to download, plus a 4-minute video.\",\"subtopicId\":\"sequences\",\"subtopicName\":\"Sequences\",\"category\":\"$undefined\",\"intro\":\"**The nth term of a linear sequence** is the rule **an + b**. To find the nth term, take a as the **common difference** (how much it goes up each time) and b as **first term − a**, so 2, 5, 8, 11 has rule 3n − 1.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"nth term of a linear sequence\",\"nth term\",\"linear sequences\",\"arithmetic sequence\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/nth-term-of-a-linear-sequence/nth-term-of-a-linear-sequence-maths-angel.webp\",\"lesson_image_alt\":\"Finding the nth Term of a Linear Sequence\",\"videoDuration\":258,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"sequences\",\"subtopicName\":\"Sequences\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"rotational-symmetry\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Rotational Symmetry\",\"title\":\"Rotational Symmetry - Flashcards and Quiz\",\"description\":\"A shape has rotational symmetry if it looks the same after turning less than 360°. Worked examples, plus a 4-minute video.\",\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"category\":\"$undefined\",\"intro\":\"**Rotational symmetry** means a 
3shape looks the same after a turn of less than **360°** about its **centre**. The **order of rotational symmetry** counts how many times it matches in one full turn. For example, a square has order **4**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"rotational symmetry\",\"order of rotation\",\"angle of rotation\",\"order of rotational symmetry\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotational-symmetry/rotational-symmetry-math-angel.webp\",\"lesson_image_alt\":\"Rotational symmetry lesson preview showing shapes with different orders of rotational symmetry\",\"videoDuration\":217,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"calculating-money\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Calculating Money\",\"title\":\"Calculating Money - Add, Subtract, Multiply, Divide\",\"description\":\"Calculating money involves separating pounds and pence for each operation. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"units-money-time\",\"subtopicName\":\"Units, Money and Time\",\"category\":\"$undefined\",\"intro\":\"**Calculating money** means splitting each price into **pounds and pence**, since **£1 = 100p**, so **£3.68 = £3 + 68p**. This lets you **add, subtract, multiply, and divide** any prices, converting extra pence back into pounds.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"calculating money\",\"adding money\",\"subtracting money\",\"multiplying money\",\"dividing money\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-money/calculating-money-math-angel.webp\",\"lesson_image_alt\":\"Step-by-step guide to calculating money with pounds and pence examples\",\"videoDuration\":203,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"units-money-time\",\"subtopicName\":\"Units, Money and Time\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"quadratic-and-geometric-sequences\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Quadratic Sequence and Geometric Sequence\",\"title\":\"Quadratic and Geometric Sequences - nth Term and Examples\",\"description\":\"Quadratic sequences have a constant second difference. GCSE quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"sequences\",\"subtopicName\":\"Sequences\",\"category\":\"$undefined\",\"intro\":\"**Quadratic sequences** have a **constant second difference**. In 3, 9, 19, 33, 51 the gaps +6, +10, +14 climb by **+4**. **Geometric sequences** instead multiply by a fixed **common ratio**, like 2, 6, 18 with **r = 3**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"quadratic sequences\",\"geometric sequences\",\"nth term of a quadratic sequence\",\"sequences\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-and-geometric-sequences/quadratic-and-geometric-sequences-maths-angel.webp\",\"lesson_image_alt\":\"Quadratic sequence 3, 9, 19, 33, 51 with a constant second difference of 4, and geometric sequence 2, 6, 18, 54, 162 multiplying by 3 each time\",\"videoDuration\":244,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"sequences\",\"subtopicName\":\"Sequences\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"reflecting-points-coordinate-plane\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Plotting and Reflecting Points on the Coordinate Plane\",\"title\":\"Reflecting Points on the Coordinate Plane - Video and Quiz\",\"description\":\"Reflecting in the x-axis changes (x, y) to (
3x, −y); in the y-axis to (−x, y). Worked examples, plus flashcards to download.\",\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"category\":\"$undefined\",\"intro\":\"The **coordinate plane** locates every point with a pair **(x, y)**: x tells you how far left or right, y how far up or down, so **(3, 2)** is 3 right and 2 up from the **origin**. **Reflecting a point** over the **x-axis** or **y-axis** changes the sign of one coordinate, while reflecting it in the **origin** changes the sign of both.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"plotting points\",\"reflecting points\",\"coordinate plane\"],\"searchAliases\":[\"Cartesian plane\",\"coordinate system\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/reflecting-points-coordinate-plane/plotting-and-reflecting-points-on-the-coordinate-plane-math-angel.webp\",\"lesson_image_alt\":\"Coordinate plane with points (−3, 2) and (3, 2) reflected across the y-axis, showing how to locate, read, and reflect points\",\"videoDuration\":214,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":6,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"units-of-length\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Converting and Calculating Units of Length\",\"title\":\"Units of Length - Convert and Calculate km, m, cm, mm\",\"description\":\"1 km = 1000 m, 1 m = 100 cm and 1 cm = 10 mm. Convert between them and add or subtract lengths. Free 4-minute video, plus a quiz to test yourself.\",\"subtopicId\":\"units-money-time\",\"subtopicName\":\"Units, Money and Time\",\"category\":\"$undefined\",\"intro\":\"**Units of length** measure distance using **mm, cm, m, and km**. To **convert**, multiply for a smaller unit or divide for a larger one, so **47 m = 4700 cm**. To add or subtract lengths, first convert them to the **same unit**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"units of length\",\"km to m\",\"m to cm\",\"cm to mm\",\"cm to km\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-length/converting-and-calculating-units-of-length-math-angel.webp\",\"lesson_image_alt\":\"Metric units of length conversion chart showing km, m, cm, and mm with examples\",\"videoDuration\":227,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"units-money-time\",\"subtopicName\":\"Units, Money and Time\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"fibonacci-sequence\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Fibonacci Sequence and Fibonacci-Type Sequences\",\"title\":\"Fibonacci Sequence - Find Terms, Rule \u0026 Examples\",\"description\":\"A Fibonacci sequence adds the two previous terms to get the next, like 1, 1, 2, 3, 5. Quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"sequences\",\"subtopicName\":\"Sequences\",\"category\":\"$undefined\",\"intro\":\"**A Fibonacci sequence** starts **1, 1** and makes each new term by adding the two terms before it. This gives **1, 1, 2, 3, 5** and so on. A **Fibonacci-type sequence** follows the same rule but can start with **any two numbers**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"fibonacci sequence\",\"fibonacci-type sequences\",\"finding the next term\",\"sequences\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/fibonacci-sequence/fibonacci-sequence-maths-angel.webp\",\"lesson_image_alt\":\"Fibonacci sequence 1, 1, 2, 3, 5, 8, 13 and Fibonacci-type sequence 2, 5, 7, 12, 19, with arrows adding each pair of terms\",\"videoDuration\":251,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"sequences\",\"subtopicName\":\"Sequences\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"translating-shapes\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Translating Shapes\",\"title\":\"Translating Shapes - Translation with Column Vectors\",\"description\":\"Translation slides a shape on a grid without changing size or orientation. Quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"category\":\"$undefined\",\"intro\":\"**Translating a shape** slides it across a grid, 
3keeping its **size and orientation** the same. All vertices move the same way. A **column vector** like **(3, 2)** describes the translation: 3 right, then 2 up.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"translating shapes\",\"column vectors\",\"translation transformation\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/translating-shapes/translating-shapes-math-angel.webp\",\"lesson_image_alt\":\"Translating shapes lesson preview showing a shape moved on a grid using a column vector\",\"videoDuration\":204,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"units-of-mass\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Converting and Calculating Units of Mass\",\"title\":\"Units of Mass - Convert and Calculate t, kg, g, mg\",\"description\":\"1 tonne = 1000 kg, 1 kg = 1000 g and 1 g = 1000 mg: multiply going down, divide going up. Flashcards to download, plus a quiz to test yourself.\",\"subtopicId\":\"units-money-time\",\"subtopicName\":\"Units, Money and Time\",\"category\":\"$undefined\",\"intro\":\"**Units of mass** are measured in **milligrams (mg)**, **grams (g)**, **kilograms (kg)**, and **tonnes (t)**. Each unit is **1000 times** the one below it, so **1 kg = 1000 g**. To **convert**, multiply for a smaller unit and divide for a larger one.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"units of mass\",\"t to kg\",\"kg to g\",\"g to mg\",\"mg to t\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/units-of-mass/converting-and-calculating-units-of-mass-math-angel.webp\",\"lesson_image_alt\":\"Metric units of mass conversion chart showing tonnes, kilograms, grams, and milligrams\",\"videoDuration\":213,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"units-money-time\",\"subtopicName\":\"Units, Money and Time\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"simple-quadratic-equations\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Simple Quadratic Equations\",\"title\":\"Simple Quadratic Equations - Effect of a on the Parabola\",\"description\":\"The coefficient a in y = ax² controls whether a parabola opens up or down and how wide it is. Quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**A quadratic equation** has an **x² term**, and its graph is a U-shaped curve called a **parabola**. In y = ax² (a ≠ 0), the **sign of a** decides if it opens up or down. The **size of a** sets the width.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"quadratic equations\",\"parabola transformations\",\"graph transformations\",\"quadratic equation coefficients\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/simple-quadratic-equations/simple-quadratic-equations-math-angel.webp\",\"lesson_image_alt\":\"Quadratic equation y = ax² with parabolas showing how the coefficient a affects direction and width\",\"videoDuration\":221,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"rotating-shapes\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Rotating Shapes\",\"title\":\"Rotating Shapes - Video and Interactive Practice\",\"description\":\"Rotation turns a shape around a fixed point called the centre of rotation. Worked examples for GCSE and IGCSE, plus flashcards to download.\",\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"category\":\"$undefined\",\"intro\":\"**Rotating shapes** means turning a shape around a fixed point called the **centre of rotation**. The shape keeps its size and shape; only its position changes. To describe a rotation, give the **angle and direction**, like **90° clockwise**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"rotating shapes\",\"rotation transformation\",\"centre of rotation\",\"angle of rotation\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/rotating-shapes/rotating-shapes-math-angel.webp\",\"lesson_image_alt\":\"Rotating shapes lesson preview showing a shape rotated around a centre of rotation on a grid\",\"videoDuration\":212,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0}
3,{\"id\":\"converting-time\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Converting Time and Calculating Time\",\"title\":\"Converting \u0026 Calculating Time - Hours, Minutes, Seconds\",\"description\":\"1 hour = 60 minutes and 1 minute = 60 seconds, so 2 h 15 min is 135 minutes. Quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"units-money-time\",\"subtopicName\":\"Units, Money and Time\",\"category\":\"$undefined\",\"intro\":\"**Converting time** swaps between **hours**, **minutes** and **seconds**. You multiply for a smaller unit and divide for a larger one, so **1 h = 60 min**. **Calculating time** means adding or subtracting minutes and seconds separately.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"converting time\",\"calculating time\",\"time conversion\",\"hours to minutes\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/converting-time/converting-time-and-calculating-time-math-angel.webp\",\"lesson_image_alt\":\"Converting time and calculating time lesson covering hours, minutes, and seconds\",\"videoDuration\":180,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"units-money-time\",\"subtopicName\":\"Units, Money and Time\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"vertex-form\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Vertex Form and Parabola Transformations\",\"title\":\"Vertex Form and Parabola Transformations - h, k, and Shifts\",\"description\":\"Vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**Vertex form** writes a quadratic as **y = a(x − h)² + k**, where **(h, k)** is the vertex, so y = 2(x − 3)² − 1 has vertex (3, −1). In **parabola transformations**, h moves the graph **left or right** and k **up or down**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"vertex form\",\"parabola transformations\",\"vertex form definition\"],\"searchAliases\":[\"shifting parabola\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/vertex-form/vertex-form-and-parabola-transformations-math-angel.webp\",\"lesson_image_alt\":\"Vertex form y = a(x - h)² + k showing the vertex point (h, k) on a parabola graph\",\"videoDuration\":224,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"enlargement\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Introduction to Enlargement\",\"title\":\"Enlargement and Scale Factors - Video and Quiz\",\"description\":\"Enlargement changes a shape's size using a scale factor from a fixed centre. Worked examples, plus flashcards to download.\",\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"category\":\"$undefined\",\"intro\":\"**Enlargement** is a transformation that changes a shape's **size**. You multiply every length by a **scale factor**, so a factor of 2 turns a **4 cm side into 8 cm**. It grows or shrinks from a fixed point called the **centre of enlargement**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"enlargement\",\"scale factor\",\"centre of enlargement\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/enlargement/introduction-to-enlargement-math-angel.webp\",\"lesson_image_alt\":\"Enlargement lesson preview showing a shape scaled by different factors from a centre of enlargement\",\"videoDuration\":206,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"symmetry-transformations\",\"subtopicName\":\"Symmetry and Transformations\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":6}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"divisibility-rules\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Divisibility and Divisibility Rules\",\"title\":\"Divisibility Rules for 2 to 10 - Tests with Examples\",\"description\":\"Divisibility rules for 2 to 10 are simple digit checks to test if a number divides evenly. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"factors-multiples-primes\",\"subtopicName\":\"Factors, Multiples and Primes\",\"category\":\"$undefined\",\"intro\":\"**Divisibility rules** are quick digit checks that tell you whether a number is **divisible** by another, meaning it divides exactly with **no remainder**: a number is **divisible by 2** when its last digit is even.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"divisibility rules\",\"divisible by 2\",\"divisible by 3\",\"divisibility test\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/divisibility-rules/divisibility-and-divisibility-rules-math-angel.webp\",\"lesson_image_alt\":\"Divisibility rules for 2, 4, and 8 using last-digit checks, with worked examples for 26, 328, and 6160\",\"videoDuration\":202,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"factors-multiples-primes\",\"subtopicName\":\"Factors, Multiples and Primes\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0}
3,{\"id\":\"converting-standard-form-and-vertex-form\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Converting Quadratics: Standard Form and Vertex Form\",\"title\":\"Converting Quadratics Between Standard and Vertex Form\",\"description\":\"Convert quadratic equations between standard form and vertex form. Quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**Completing the square** turns **standard form**, **y = ax² + bx + c**, into **vertex form**, **y = a(x − h)² + k**: two ways of writing the same quadratic. Expanding the brackets changes it back.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"converting quadratics\",\"standard form\",\"vertex form\",\"completing the square\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/converting-standard-form-and-vertex-form/converting-quadratics-standard-form-and-vertex-form-math-angel.webp\",\"lesson_image_alt\":\"Converting a quadratic from general form y = ax² + bx + c to vertex form y = a(x-h)² + k\",\"videoDuration\":213,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"constructing-triangles\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Constructing Triangles\",\"title\":\"Constructing Triangles - Video and Interactive Practice\",\"description\":\"Construct a triangle from three sides, two sides and an angle, or two angles and a side, with ruler, compasses and protractor. Flashcards to download.\",\"subtopicId\":\"triangles-constructions\",\"subtopicName\":\"Triangles and Constructions\",\"category\":\"$undefined\",\"intro\":\"**Constructing triangles** means drawing them accurately with a **compass, ruler, and protractor**. You measure and copy each given side and angle exactly. Use **SSS, SAS, or ASA** to match the sides and angles given.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"constructing triangles\",\"triangle construction methods\",\"triangle construction examples\",\"sss, sas, or asa\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/constructing-triangles/constructing-triangles-math-angel.webp\",\"lesson_image_alt\":\"Constructing triangles lesson preview showing ASA, SAS, and SSS methods with compass and ruler\",\"videoDuration\":244,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"triangles-constructions\",\"subtopicName\":\"Triangles and Constructions\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"prime-numbers-prime-factorisation\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Prime Numbers and Prime Factorisation\",\"title\":\"Prime Numbers and Prime Factorisation - Factor Tree Method\",\"description\":\"A prime number has exactly two factors: 1 and itself. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"factors-multiples-primes\",\"subtopicName\":\"Factors, Multiples and Primes\",\"category\":\"$undefined\",\"intro\":\"**A prime number** is a whole number above 1 with **exactly two factors**: 1 and itself. So **7 is prime**, but 6 is not because it also divides by 2 and 3. **Prime factorisation** writes a number as a product of primes, like **90 = 2 × 3² × 5**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"prime numbers\",\"prime factorisation\",\"factor tree\",\"prime factors\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/prime-numbers-prime-factorisation/prime-numbers-and-prime-factorisation-math-angel.webp\",\"lesson_image_alt\":\"Prime numbers under 20 and prime factorisation of 126 = 2 × 3² × 7 using a factor tree\",\"videoDuration\":203,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"factors-multiples-primes\",\"subtopicName\":\"Factors, Multiples and Primes\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"quadratic-equations-in-vertex-form-standard-form\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"How to Write Quadratic Equations in Vertex Form and Standard Form\",\"title\":\"Writing Quadratic Equations in Vertex Form and Standard Form\",\"description\":\"Vertex form y = a(x − h)² + k needs the vertex and one point; standard form needs three points. Quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**Vertex form** writes a quadratic as **y = a(x − h)² + k**, where (h, k) is the **vertex**. Once you know the vertex, substitute one more point to find **a**. **Standard form**, **y = ax² + bx + c**, is used instead when you know three points.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"vertex form\",\"standard form\",\"quadratic equations\",\"quadratic equation coefficients\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-equations-in-vertex-form-standard-form/how-to-write-quadratic-equations-in-vertex-form-and-standard-form-math-angel.webp\",\"lesson_image_alt\":\"Quadratic equations in vertex form y = a(x-h)² + k and standard form y = ax² + bx + c\",\"videoDuration\":225,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"congruent-triangles\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Congruent Triangles\",\"title\":\"Congruent Triangles - SSS, SAS, ASA, and RHS\",\"description\":\"Congruent means identical in shape and size. Four tests prove it: SSS, SAS, ASA and RHS (right angle, hypotenuse, side). Interactive practice to try.\",\"subtopicId\":\"triangles-constructions\",\"subtopicName\":\"Tr
3iangles and Constructions\",\"category\":\"$undefined\",\"intro\":\"**Congruent triangles** are the **same size and shape**, so their **corresponding sides and angles are equal**. One triangle can be slid, turned, or flipped to fit onto the other. You can prove this using **SSS, SAS, ASA, and RHS**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"congruent triangles\",\"SSS\",\"SAS\",\"ASA\",\"RHS\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/congruent-triangles/congruent-triangles-math-angel.webp\",\"lesson_image_alt\":\"Congruent triangles lesson preview showing SSS, SAS, ASA, and RHS rules with labelled triangle pairs\",\"videoDuration\":226,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"triangles-constructions\",\"subtopicName\":\"Triangles and Constructions\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":7,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"hcf-and-lcm\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"How to Find HCF and LCM\",\"title\":\"HCF and LCM - Prime Factorisation \u0026 Worked Examples\",\"description\":\"The HCF is the largest factor two numbers share; the LCM is their smallest common multiple. Free 4-minute video, plus flashcards to download.\",\"subtopicId\":\"factors-multiples-primes\",\"subtopicName\":\"Factors, Multiples and Primes\",\"category\":\"$undefined\",\"intro\":\"**HCF and LCM**: **the highest common factor (HCF)** is the **biggest factor** two numbers share, and **the lowest common multiple (LCM)** is the **smallest multiple** they share. Find either by listing or prime factorisation.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"hcf and lcm\",\"highest common factor\",\"lowest common multiple\",\"prime factorisation\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/hcf-and-lcm/how-to-find-hcf-and-lcm-math-angel.webp\",\"lesson_image_alt\":\"Step-by-step guide showing how to find HCF and LCM using prime factorisation with worked examples\",\"videoDuration\":241,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"factors-multiples-primes\",\"subtopicName\":\"Factors, Multiples and Primes\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"solving-simple-quadratic-equations\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Solving Simple Quadratic Equations\",\"title\":\"Solving Simple Quadratic Equations - Video and Quiz\",\"description\":\"Solve x² = 25 by taking the square root (x = ±5) and x² − 4x = 0 by factorising: x(x − 4) = 0. Worked examples for GCSE and IGCSE, plus flashcards.\",\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**Solving simple quadratic equations** means finding the x values that make them true. For **x² = k**, take the **square root** to get x = ±√k, so x² = 9 gives x = 3 or −3. For x² − dx = 0, **factorise** to x(x − d) = 0, so x = 0 or x = d.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"simple quadratic equations\",\"solving quadratic equations\",\"equation solving\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simple-quadratic-equations/solving-simple-quadratic-equations-math-angel.webp\",\"lesson_image_alt\":\"Solving simple quadratic equations showing x² = k with solutions x = ±√k\",\"videoDuration\":229,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":6,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"perpendicular-bisectors-and-circumcircle\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Perpendicular Bisectors and Circumcircle\",\"title\":\"Perpendicular Bisectors and Circumcircle - How to Construct\",\"description\":\"A perpendicular bisector divides a line segment in half at 90°. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"triangles-constructions\",\"subtopicName\":\"Tr
3iangles and Constructions\",\"category\":\"$undefined\",\"intro\":\"**A perpendicular bisector** cuts a line segment in half at a **right angle (90°)**. Every point on it is the **same distance** from both ends. In a triangle, the three bisectors meet at the **circumcentre**, the centre of its **circumcircle**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"perpendicular bisector\",\"circumcircle construction\",\"circumcircle properties\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/perpendicular-bisectors-and-circumcircle/perpendicular-bisectors-and-circumcircle-math-angel.webp\",\"lesson_image_alt\":\"Perpendicular bisector dividing a line segment in half at a 90° angle, with the midpoint labelled\",\"videoDuration\":197,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"triangles-constructions\",\"subtopicName\":\"Triangles and Constructions\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"introduction-to-fractions\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Introduction to Fractions\",\"title\":\"Introduction to Fractions - Video and Quiz\",\"description\":\"Fractions show parts of a whole with a numerator and denominator, like 3/4. Find a fraction of an amount too. Worked examples, plus flashcards to download.\",\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"category\":\"$undefined\",\"intro\":\"**Fractions** show part of a whole split into equal parts, like a pizza cut into 9 equal slices where taking 4 gives **4/9**. The **numerator** (4) counts the parts taken; the **denominator** (9) counts the total equal parts.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"fractions\",\"introduction to fractions\",\"numerator and denominator\",\"fraction of an amount\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/introduction-to-fractions/introduction-to-fractions-math-angel.webp\",\"lesson_image_alt\":\"Introduction to fractions showing numerator and denominator with pizza slice examples\",\"videoDuration\":214,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"solving-quadratic-equations-factorising\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Solving Quadratic Equations by Factorising\",\"title\":\"Solving Quadratic Equations by Factorising - Video and Quiz\",\"description\":\"x² + 5x + 6 = 0 factorises to (x + 2)(x + 3) = 0, so x = −2 or x = −3. Worked examples for GCSE and IGCSE, plus flashcards to download.\",\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**Solving quadratic equations by factorising** means writing **x² + 5x + 6 = 0** as **(x + 2)(x + 3) = 0**. You find two numbers that **multiply to 6** and **add to 5**. Then set **each bracket to zero** to get x = -2 and x = -3.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"factorising quadratic equations\",\"solving quadratic equations\",\"factorisation\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-quadratic-equations-factorising/solving-quadratic-equations-by-factorising-math-angel.webp\",\"lesson_image_alt\":\"Factorising x² + 5x + 6 = 0 into (x + 2)(x + 3) = 0, finding factors that multiply to 6 and add to 5\",\"videoDuration\":226,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":6}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"angle-bisectors-and-incircle\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Angle Bisectors and Incircle\",\"title\":\"Angle Bisectors and Incircle - Video and Quiz\",\"description\":\"An angle bisector cuts an angle in half. A triangle's three bisectors meet at the centre of its incircle. Flas
3hcards to download to revise.\",\"subtopicId\":\"triangles-constructions\",\"subtopicName\":\"Triangles and Constructions\",\"category\":\"$undefined\",\"intro\":\"**An angle bisector** cuts an angle into **two equal halves**. In a triangle, the three bisectors meet at the **incentre**. That point is the centre of the **incircle**: the circle inside the triangle that touches all three sides.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"angle bisectors\",\"incircles\",\"incentres\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/angle-bisectors-and-incircle/angle-bisectors-and-incircle-math-angel.webp\",\"lesson_image_alt\":\"Constructing an angle bisector two ways: with a protractor splitting 40 degrees into 20-degree halves, and with a compass using arcs\",\"videoDuration\":185,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"triangles-constructions\",\"subtopicName\":\"Triangles and Constructions\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"equivalent-fractions\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Equivalent Fractions\",\"title\":\"Equivalent Fractions - Simplify and Expand Fractions\",\"description\":\"Equivalent fractions look different but have the same value, like 1/2 = 2/4 = 3/6. Free 3-minute video, plus a quiz to test yourself.\",\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"category\":\"$undefined\",\"intro\":\"**Equivalent fractions** look different but have the same value, like **1/2 = 8/16**. To find them, multiply top and bottom by the same number to **expand**, or divide to **simplify**. Either way, **the value stays the same**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"equivalent fractions\",\"simplify fractions\",\"expand fractions\",\"simplest form\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/equivalent-fractions/equivalent-fractions-math-angel.webp\",\"lesson_image_alt\":\"Equivalent fractions: simplifying 18/63 to 2/7 and expanding 2/7 to 18/63\",\"videoDuration\":202,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"quadratic-formula\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Solving Quadratic Equations: Quadratic Formula\",\"title\":\"Quadratic Formula - Solve Quadratic Equations Step by Step\",\"description\":\"The quadratic formula solves equations in the form ax² + bx + c = 0. Interactive practice to try, plus flashcards for GCSE and IGCSE.\",\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"category\":\"$undefined\",\"intro\":\"**The quadratic formula** solves any equation written as **ax² + bx + c = 0**, even when it won't factorise. Put a, b and c into **x = (−b ± √(b² − 4ac)) ÷ 2a** to find the **roots**. Its **discriminant**, **b² − 4ac**, gives the number of solutions.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"quadratic formula\",\"solving quadratic equations\",\"discriminant\",\"roots of a quadratic\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/quadratic-formula/solving-quadratic-equations-quadratic-formula-math-angel.webp\",\"lesson_image_alt\":\"Quadratic formula applied to 3x² − 5x + 2 = 0 with step-by-step substitution, discriminant = 1, roots x = 1 and x = ⅔\",\"videoDuration\":204,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"quadratic-equations-graphs\",\"subtopicName\":\"Quadratic Equations and Graphs\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":7}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"medians-and-centroid-of-a-triangle\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Medians and Centroid of a Triangle\",\"title\":\"Medians and Centroid of a Triangle - Video and Quiz\",\"description\":\"A median joins a vertex to the midpoint of the opposite side; the three meet at the centroid. Flashcards to download to revise the properties.\",\"subtopicId\":\"triangles-constructions\",\"subtopicName\":\"Tr
3iangles and Constructions\",\"category\":\"$undefined\",\"intro\":\"**A median of a triangle** joins a **vertex** to the **midpoint** of the opposite side. The three medians meet at a single point called the **centroid**, which divides each median in a **2:1 ratio**, with the longer part next to the vertex.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"centroid of a triangle\",\"medians of a triangle\",\"median of a triangle\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/medians-and-centroid-of-a-triangle/medians-and-centroid-of-a-triangle-math-angel.webp\",\"lesson_image_alt\":\"Medians and centroid of a triangle lesson preview showing three medians meeting at the centroid\",\"videoDuration\":191,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"triangles-constructions\",\"subtopicName\":\"Triangles and Constructions\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"comparing-fractions\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Comparing Fractions\",\"title\":\"Comparing Fractions - Video and Interactive Practice\",\"description\":\"To compare fractions, use the same denominator: 2/3 = 8/12 and 3/4 = 9/12, so 3/4 is bigger. Worked examples, plus flashcards to download.\",\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"category\":\"$undefined\",\"intro\":\"**Comparing fractions** means finding which one is larger or smaller. If the denominators match, the **larger numerator** wins, so **5/8 \u003e 3/8**. If they differ, convert both to a **common denominator**, then compare.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"comparing fractions\",\"common denominator\",\"lowest common multiple\",\"compare fractions\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-fractions/comparing-fractions-math-angel.webp\",\"lesson_image_alt\":\"Comparing fractions with same denominator (5/8 \u003e 3/8) and same numerator (4/5 \u003e 4/9) using chocolate bar and pizza visuals\",\"videoDuration\":182,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"equations-with-2-variables\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Solving Equations with 2 Variables\",\"title\":\"Solving Equations with 2 Variables - Video and Quiz\",\"description\":\"x + 2y = 20 has many solutions: x = 2 gives y = 9, x = 4 gives y = 8. Plotted, they make a straight line. Worked examples, plus flashcards to download.\",\"subtopicId\":\"simultaneous-equations\",\"subtopicName\":\"Simultaneous Equations\",\"category\":\"$undefined\",\"intro\":\"**Equations with two variables** have two unknowns in one equation, like **x + 2y = 20**. You solve it by **substituting** a value for one variable to find the other, so **x = 10 gives y = 5**. They have **many solution pairs**, not just one.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"2 variable equations\",\"solving equations\",\"algebra equations\",\"substitution method\",\"graphing method\",\"equations with two variables\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equations-with-2-variables/solving-equations-with-two-variables-math-angel.webp\",\"lesson_image_alt\":\"Solving the equation x + 2y = 20 with multiple solutions showing different pairs of x and y values\",\"videoDuration\":183,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"simultaneous-equations\",\"subtopicName\":\"Simultaneous Equations\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"solids-units-of-volume\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Solids and Units of Volume\",\"title\":\"Solids and Units of Volume - mm³, cm³, ml, L\",\"description\":\"1 cm³ = 1 ml and 1000 cm³ = 1 litre, so a 10 by 10 by 10 cm box holds a litre. Quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"category\":\"$undefined\",\"intro\":\"**Units of volume** are the **cubic units** used to measure the space inside a **solid**, such as **mm³**, **cm³** and **ml**. O
3ne cm³ is a cube 1 cm on each side, like a dice. To reach a smaller unit, multiply by 1000, so **1 cm³ = 1000 mm³**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"solids and units of volume\",\"mm³ to cm³\",\"cm³ to ml\",\"ml to L\",\"L to m³\"],\"searchAliases\":[\"litres\",\"liters\",\"millilitres\",\"milliliters\",\"liquid volume\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/solids-units-of-volume/solids-and-units-of-volume-math-angel.webp\",\"lesson_image_alt\":\"Units of volume chart comparing mm³, cm³, mL, L, and m³ with edge lengths and real-life examples like a dice and milk carton.\",\"videoDuration\":207,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"adding-and-subtracting-fractions\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Adding and Subtracting Fractions\",\"title\":\"Adding and Subtracting Fractions - Flashcards and Quiz\",\"description\":\"Adding and subtracting fractions requires a common denominator when fractions are unlike. Worked examples, plus a 3-minute video.\",\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"category\":\"$undefined\",\"intro\":\"**Adding and subtracting fractions** is easy when the **denominators** are the same. Just add or subtract the **numerators** and keep the denominator. If the fractions are unlike, first find a **common denominator**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"adding and subtracting fractions\",\"common denominator\",\"improper and mixed fractions\",\"like and unlike fractions\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-and-subtracting-fractions/adding-and-subtracting-fractions-math-angel.webp\",\"lesson_image_alt\":\"Adding and subtracting like and unlike fractions with common denominators and worked examples\",\"videoDuration\":207,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"solving-simultaneous-equations-graphically\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Solving Simultaneous Equations Graphically\",\"title\":\"Solving Simultaneous Equations Graphically - Video and Quiz\",\"description\":\"Simultaneous equations can be solved by plotting both lines and reading off where they cross. Flashcards to download to revise the method.\",\"subtopicId\":\"simultaneous-equations\",\"subtopicName\":\"Simultaneous Equations\",\"category\":\"$undefined\",\"intro\":\"**Solving simultaneous equations graphically** means drawing both equations as lines. The **crossing point** solves both equations. There is **one solution** if lines cross, **no solution** if parallel, and **infinite solutions** if they overlap.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"simultaneous equations\",\"solving equations graphically\",\"intersection of lines\",\"simultaneous equations graphically\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/solving-simultaneous-equations-graphically/solving-simultaneous-equations-graphically-math-angel.webp\",\"lesson_image_alt\":\"Simultaneous equations x + y = 20 and x − y = 10 modelling Sebastian's and Sarah's ages as simultaneous linear equations\",\"videoDuration\":199,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"simultaneous-equations\",\"subtopicName\":\"Simultaneous Equations\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"volume-of-a-cuboid\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Volume of a Cuboid and Cube\",\"title\":\"Volume of a Cuboid and Cube - Free Video and Quiz\",\"description\":\"Find the volume of a cuboid with length × width × height, and a cube with side³. Download the flashcards to revise.\",\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"category\":\"$undefined\",\"intro\":\"**Volume of a cuboid** is the space inside it, found by **length × width × height**. For example, a 5 × 3 × 2 box holds 30 cm³, given in **cubic units**. A **cube** is a special cuboid with equal edges, so its volume is **side × side × side**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"volume of a cuboid\",\"volume of a cube\"],\"searchAliases\":[\"container capacity\",\"liquid capacity\",\"rectangular prism\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-of-a-cuboid/volume-of-a-cuboid-and-cube-math-angel.webp\",\"lesson_image_alt\":\"Volume of a cuboid and cube lesson preview showing 3D shapes with labelled length, width, and height\",\"videoDuration\":184,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"multiplying-fractions\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Multiplying Fractions\",\"t
3itle\":\"How to Multiply Fractions - Free Video and Quiz\",\"description\":\"Multiply the tops, multiply the bottoms, then simplify, or cross-cancel first. Whole and mixed numbers are covered. Download the flashcards to revise.\",\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"category\":\"$undefined\",\"intro\":\"**Multiplying fractions** means multiplying the **numerators**, then the **denominators**. Then simplify if you can. **Cross-cancelling** divides a top and bottom by a common factor first to keep numbers smaller.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"multiplying fractions\",\"cross-cancelling fractions\",\"multiplying mixed numbers\",\"fraction multiplication\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-fractions/multiplying-fractions-math-angel.webp\",\"lesson_image_alt\":\"Multiplying fractions lesson covering cross-cancelling, whole numbers, and mixed number examples\",\"videoDuration\":175,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"equal-values-and-substitution-method\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Simultaneous Equations: Equal Values and Substitution Method\",\"title\":\"Simultaneous Equations: Equal Values and Substitution Method\",\"description\":\"Solve simultaneous equations with the equal values method or the substitution method. Free 4-minute video, plus a GCSE quiz to test yourself.\",\"subtopicId\":\"simultaneous-equations\",\"subtopicName\":\"Simultaneous Equations\",\"category\":\"$undefined\",\"intro\":\"**Simultaneous equations** are two equations that share one solution. To solve, the **equal values method** rearranges both to **y = x − 1** and **y = 8 − 2x**, then sets them equal. The **substitution method** puts **x = y + 1** into the other equation.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"simultaneous equations\",\"solving equations\",\"algebra equations\",\"equal values method\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/equal-values-and-substitution-method/simultaneous-equations-equal-values-and-substitution-method-math-angel.webp\",\"lesson_image_alt\":\"Equal values method solving 2x + y = 8 and x - y = 1, showing steps to find x = 3 and y = 2\",\"videoDuration\":217,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"simultaneous-equations\",\"subtopicName\":\"Simultaneous Equations\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"surface-area\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Surface Area of Solids\",\"title\":\"Surface Area of Solids - Cuboid, Cube, Prism\",\"description\":\"Surface area is the total area of all faces of a 3D shape. Quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"category\":\"$undefined\",\"intro\":\"**The surface area of a cuboid** is **2lw + 2lh + 2hw** and **the surface area of a cube** is **6 × a × a**. **Surface area** is the **total area of all the faces** of a 3D shape: 3 matching pairs for a cuboid, 6 identical squares for a cube.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"surface area of a cuboid\",\"surface area of a cube\",\"surface area of a prism\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/surface-area/surface-area-of-solids-math-angel.webp\",\"lesson_image_alt\":\"Surface area of solids lesson preview showing a cuboid with labelled faces and dimensions\",\"videoDuration\":214,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"dividing-fractions\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Dividing Fractions\",\"t
3itle\":\"Dividing Fractions - Reciprocals, Whole \u0026 Mixed Numbers\",\"description\":\"Dividing fractions means keeping the first fraction, flipping the second, and multiplying. Quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"category\":\"$undefined\",\"intro\":\"**Dividing fractions** means keep the first, flip the second to its **reciprocal**, then multiply. The same rule handles a **whole number** (write it over 1) and a **mixed number** (make it improper).\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"dividing fractions\",\"divide fractions by whole number\",\"dividing mixed numbers\",\"fraction division reciprocal\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/dividing-fractions/dividing-fractions-math-angel.webp\",\"lesson_image_alt\":\"Dividing fractions lesson showing reciprocal method with whole numbers and mixed number examples\",\"videoDuration\":159,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"fractions\",\"subtopicName\":\"Fractions\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":6}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"elimination-method\",\"courseId\":\"algebra\",\"courseName\":\"Algebra\",\"lesson_title\":\"Elimination Method for Solving Simultaneous Equations\",\"title\":\"Elimination Method for Simultaneous Equations - Examples\",\"description\":\"Elimination adds or subtracts two simultaneous equations to remove one letter, then solves. Flashcards for GCSE and IGCSE, plus a 4-minute video.\",\"subtopicId\":\"simultaneous-equations\",\"subtopicName\":\"Simultaneous Equations\",\"category\":\"$undefined\",\"intro\":\"**The elimination method** removes one variable from **simultaneous equations** by **adding** or **subtracting** the two equations. The goal is to **cancel** one variable, leaving a single equation like **2x = 12** to solve.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"elimination method\",\"simultaneous equations\",\"solving equations\",\"algebra equations\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/algebra/elimination-method/elimination-method-for-solving-simultaneous-equations-math-angel.webp\",\"lesson_image_alt\":\"Elimination method steps: adding simultaneous equations to remove one variable\",\"videoDuration\":227,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"simultaneous-equations\",\"subtopicName\":\"Simultaneous Equations\",\"topicId\":\"algebra\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"volume-prisms-cylinders\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Volume of Prisms and Cylinders\",\"title\":\"Volume of Prisms and Cylinders - Video and Quiz\",\"description\":\"Volume of a prism = cross-section area × length; for a cylinder that is πr²h. Flashcards to download to revise both formulas.\",\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"category\":\"$undefined\",\"intro\":\"**Volume of prisms and cylinders** equals **base area × height**. Find the flat base area, then multiply by the height; a 20 cm² base 3 cm tall gives **60 cm³**. A **cylinder** has a circular base of area πr², so **V = πr²h**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"volume of prisms\",\"volume of cylinders\"],\"searchAliases\":[\"triangular prism\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-prisms-cylinders/volume-of-prisms-and-cylinders-math-angel.webp\",\"lesson_image_alt\":\"Volume of prisms and cylinders lesson preview showing the formula V = base area × height\",\"videoDuration\":182,\"ukYear\":8,\"placements\":[{\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"decimals-and-fractions\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Decimals and Fractions\",\"t
3itle\":\"Decimals and Fractions - Place Value \u0026 How to Convert\",\"description\":\"Decimals and fractions are two ways to show parts of a number. Quiz to test yourself, plus flashcards to download.\",\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"category\":\"$undefined\",\"intro\":\"**Decimals and fractions** are two ways to show the same value. To **convert a decimal to a fraction**, count the decimal places to set the denominator **10, 100 or 1000**, then simplify if you can. So **0.01 = 1/100**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"decimals and fractions\",\"decimal place value\",\"convert decimal to fraction\",\"decimal to fraction\",\"convert a decimal to a fraction\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/decimals-and-fractions/decimals-and-fractions-math-angel.webp\",\"lesson_image_alt\":\"Decimal place value chart and step-by-step decimal to fraction conversion with examples\",\"videoDuration\":184,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"cavalieris-principle\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Cavalieri's Principle\",\"title\":\"Cavalieri's Principle - Video, Quiz and Flashcards\",\"description\":\"Cavalieri's principle: solids with equal heights and equal cross-sections have equal volumes. Worked examples compare the volumes of different solids.\",\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"category\":\"$undefined\",\"intro\":\"**Cavalieri's Principle** says two solids have **equal volume** if they share the **same height** and **cross-sectional area** at every level. Slanting a stack of slices keeps its volume. So you can find each volume with **V = base area × height**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"cavalieri's principle\",\"equal volume\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cavalieris-principle/principle-of-cavalieri-math-angel.webp\",\"lesson_image_alt\":\"Cavalieri's Principle lesson preview showing two solids with equal cross-sections and volumes\",\"videoDuration\":135,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"comparing-and-rounding-decimals\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Comparing and Rounding Decimals\",\"title\":\"Comparing and Rounding Decimals - Flashcards and Quiz\",\"description\":\"Compare decimals digit by digit from the left; to round, 5 or more in the next digit rounds up. Worked examples, plus a 3-minute video.\",\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"category\":\"$undefined\",\"intro\":\"**Rounding decimals** keeps a set number of decimal places. Look at the **next digit**. If it is 5 or more, **round up**. If it is less, **round down**. **Comparing decimals** lines up the points, then reads left to right.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"comparing and rounding decimals\",\"rounding decimals\",\"comparing decimals\",\"decimal place value\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/comparing-and-rounding-decimals/comparing-and-rounding-decimals-math-angel.webp\",\"lesson_image_alt\":\"Decimal place value of 12.348 showing 1st, 2nd, and 3rd decimal places as tenths, hundredths, and thousandths\",\"videoDuration\":151,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0}
3,{\"id\":\"volume-surface-area-pyramids-cones-spheres\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Volume and Surface Area of Pyramids, Cones, Spheres\",\"title\":\"Volume and Surface Area of Pyramids, Cones, and Spheres\",\"description\":\"Pyramids and cones share the formula V = ⅓ × base area × height. Flashcards to download, plus a GCSE quiz to test yourself.\",\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"category\":\"$undefined\",\"intro\":\"**The volume of a pyramid** is **V = ⅓ × base area × height**, the same formula a cone uses. A base of 30 cm² and height 10 cm gives 100 cm³. Its **surface area** is **A = B + L**, the base area plus all its triangular faces.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"volume of a pyramid\",\"surface area of a cone\",\"surface area of a sphere\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/volume-surface-area-pyramids-cones-spheres/volume-and-surface-area-of-pyramids-cones-spheres-math-angel.webp\",\"lesson_image_alt\":\"Volume of a pyramid V = ⅓ × B × h and surface area A = B + L, with labelled 3D diagram and net\",\"videoDuration\":226,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"3d-shapes-volume\",\"subtopicName\":\"3D Shapes and Volume\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":6}],\"flashcardCount\":6,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"convert-fraction-to-decimal\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Convert Fraction to Decimal Using Long Division\",\"title\":\"Convert Fraction to Decimal - Long Division Method\",\"description\":\"A fraction converts to a decimal by dividing the numerator by the denominator. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"category\":\"$undefined\",\"intro\":\"**Convert a fraction to a decimal** by dividing the **numerator** by the **denominator**, e.g. 21 ÷ 16 = 1.3125. It either ends as a **terminating decimal** or repeats forever as a **recurring decimal**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"convert fraction to decimal\",\"fraction to decimal long division\",\"terminating decimal\",\"recurring decimal\",\"convert a fraction to a decimal\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/convert-fraction-to-decimal/convert-fraction-to-decimal-using-long-division-math-angel.webp\",\"lesson_image_alt\":\"Step-by-step long division converting fraction 21/16 to terminating decimal 1.3125\",\"videoDuration\":175,\"ukYear\":6,\"placements\":[{\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"pythagoras-theorem\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Pythagoras' Theorem\",\"title\":\"Pythagoras' Theorem - Free Video and Quiz\",\"description\":\"Find a missing side of a right-angled triangle with a² + b² = c², in 2D or 3D. Worked examples show each step. Download the flashcards to revise.\",\"subtopicId\":\"pythagoras-trigonometry\",\"subtopicName\":\"Pythagoras and Trigonometry\",\"category\":\"$undefined\",\"intro\":\"**Pythagoras' theorem** says that in a **right-angled triangle**, **a² + b² = c²**. The two shorter sides squared add up to the longest side squared, so **3² + 4² = 5²**. That longest side, c, is the **hypotenuse**, opposite the right angle.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"Pythagoras Theorem\",\"Right-angled Triangle\",\"3D Pythagoras\",\"hypotenuse\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/pythagoras-theorem/pythagoras-theorem-math-angel.webp\",\"lesson_image_alt\":\"Pythagoras' Theorem lesson preview showing a² + b² = c² with a labelled right-angled triangle\",\"videoDuration\":197,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"pythagoras-trigonometry\",\"subtopicName\":\"Pythagoras and Trigonometry\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"adding-subtracting-fractions-and-decimals\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Adding and Subtracting Fractions and Decimals\",\"title\":\"Add and Subtract Fractions and Decimals - Video and Quiz\",\"description\":\"To add or subtract fractions and decimals, convert them to one form first. Worked examples of both methods, plus flashcards to download.\",\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"category\":\"$undefined\",\"intro\":\"**Adding and subtracting fractions and decimals** means changing them into the same form. For example, **0.75 + 3/5 = 0.75 + 0.6 = 1.35**. The **decimal method** is faster, while the **fraction method** gives an exact answer.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"adding and subtracting fractions and decimals\",\"fractions and decimals\",\"decimal method\",\"fraction method\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/adding-subtracting-fractions-and-decimals/adding-and-subtracting-fractions-and-decimals-math-angel.webp\",\"lesson_image_alt\":\"Adding and subtracting fractions and decimals using both decimal and fraction conversion methods\",\"videoDuration\":175,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"trigonometry-sine-cosine-tangent\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Tr
3igonometry: Sine, Cosine, Tangent\",\"title\":\"Trigonometry: Sine, Cosine, and Tangent - SOH CAH TOA\",\"description\":\"Trigonometry ratios (sin, cos, tan) find missing sides and angles in right-angled triangles. Free 3-minute video, plus a GCSE quiz to test yourself.\",\"subtopicId\":\"pythagoras-trigonometry\",\"subtopicName\":\"Pythagoras and Trigonometry\",\"category\":\"$undefined\",\"intro\":\"**Trigonometry** uses **sine, cosine and tangent** to find missing sides and angles in right-angled triangles. **SOH CAH TOA** picks the right ratio, such as **sin θ = opposite ÷ hypotenuse**. For a given angle the ratio never changes.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"trigonometry\",\"sine\",\"cosine\",\"tangent\"],\"searchAliases\":[\"SOHCAHTOA\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/trigonometry-sine-cosine-tangent/trigonometry-sine-cosine-tangent-math-angel.webp\",\"lesson_image_alt\":\"Trigonometry lesson preview showing sine, cosine, and tangent ratios in a right-angled triangle\",\"videoDuration\":202,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"pythagoras-trigonometry\",\"subtopicName\":\"Pythagoras and Trigonometry\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"multiplying-decimals\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Multiplying Decimals\",\"title\":\"Multiplying Decimals - Video and Interactive Practice\",\"description\":\"To multiply decimals, ignore the points, multiply as whole numbers, then put the point back. Worked examples, plus flashcards to download.\",\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"category\":\"$undefined\",\"intro\":\"**Multiplying decimals** means ignoring the points and multiplying the digits as whole numbers. So 0.34 × 2.5 becomes **34 × 25 = 850**. Then count the **decimal places** and move the point 3 places left to get 0.85.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"multiplying decimals\",\"multiply decimals method\",\"decimal places multiplication\",\"multiplying decimals by whole numbers\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-decimals/multiplying-decimals-math-angel.webp\",\"lesson_image_alt\":\"Multiplying decimals lesson showing the three-step method with worked examples and decimal point placement\",\"videoDuration\":193,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"cosine-rule\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Cosine Rule\",\"title\":\"Cosine Rule - Find Missing Sides and Angles in Triangles\",\"description\":\"The cosine rule finds missing sides and angles in triangles without a right angle. Free 3-minute video, plus a GCSE quiz to test yourself.\",\"subtopicId\":\"pythagoras-trigonometry\",\"subtopicName\":\"Pythagoras and Trigonometry\",\"category\":\"$undefined\",\"intro\":\"**The cosine rule** finds a **missing side or angle**. If you know two sides and the angle between them, or all three sides, use **a² = b² + c² − 2bc cos A**. Use it in **non-right-angled triangles**; right-angled ones use **Pythagoras**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"cosine rule\",\"non-right-angled triangles\",\"missing sides and angles\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/cosine-rule/cosine-rule-math-angel.webp\",\"lesson_image_alt\":\"Cosine rule lesson preview showing the formula and a labelled non-right-angled triangle\",\"videoDuration\":164,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"pythagoras-trigonometry\",\"subtopicName\":\"Pythagoras and Trigonometry\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"calculating-fractions-and-decimals\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Calculating Fractions and Decimals\",\"title\":\"Calculating Fractions and Decimals - Video and Quiz\",\"description\":\"The commutative, associative and distributive laws make fraction and decimal sums quicker. Worked examples, plus flashcards to download.\",\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"category\":\"$undefined\",\"intro\":\"**Calculating fractions and decimals** is easier when you **group** the fractions and decimals **separately**. You work out each group first, then combine the results. The **commutative law** lets you swap the order when adding or multiplying.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"calculating fractions and decimals\",\"commutative law maths\",\"associative law examples\",\"distributive law fractions\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/calculating-fractions-and-decimals/calculating-fractions-and-decimals-math-angel.webp\",\"lesson_image_alt\":\"Worked example: calculating fractions and decimals by rearranging 1.1 + ³⁄₇ + 0.4 + ⁴⁄₇ with commutative and associative laws\",\"videoDuration\":222,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":6}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"sine-rule\",\"courseId\":\"geometry-measures\",\"courseName\":\"Geometry and Measures\",\"lesson_title\":\"Sine Rule\",\"title\":\"Sine Rule - How to Use the Formula to Find Sides or Angles\",\"description\":\"The sine rule, a/sin A = b/sin B = c/sin C, finds a side from a side and two angles. Flashcards to download, plus a GCSE quiz to test yourself.\",\"subtopicId\":\"pythagoras-trigonometry\",\"subtopicName\":\"Pythagoras and Trigonometry\",\"category\":\"$undefined\",\"intro\":\"**The sine rule formula** is **a/sin A = b/sin B = c/sin C**. It finds a **missing side or angle** in a **non-right-angled triangle**, linking each side to its opposite angle. You just need one angle and its opposite side as a **matching pair**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"sine rule formula\",\"non-right-angled triangles\",\"missing sides and angles\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/geometry-measures/sine-rule/sine-rule-math-angel.webp\",\"lesson_image_alt\":\"Sine Rule lesson preview showing the formula a/sin A = b/sin B with a labelled triangle\",\"videoDuration\":155,\"ukYear\":11,\"placements\":[{\"subtopicId\":\"pythagoras-trigonometry\",\"subtopicName\":\"Pythagoras and Trigonometry\",\"topicId\":\"geometry-measures\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"recurring-decimals-to-fractions\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Convert Recurring Decimals to Fractions\",\"t
3itle\":\"Recurring Decimals to Fractions - Video and Quiz\",\"description\":\"Recurring decimal to fraction: let x = 0.333…, so 10x = 3.333…, then 9x = 3 and x = 1/3. Worked examples for GCSE and IGCSE, plus flashcards to download.\",\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"category\":\"$undefined\",\"intro\":\"**Convert recurring decimals to fractions** by letting x equal the decimal, then multiplying by a **power of 10** so the repeating digits line up. Subtracting cancels them: if x = 0.333…, then 10x = 3.333…, so **10x − x = 3** and **x = 1/3**, which is 0.3 recurring as a fraction.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"recurring decimals to fractions\",\"convert recurring decimals\",\"repeating decimals\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/recurring-decimals-to-fractions/convert-recurring-decimals-to-fractions-math-angel.webp\",\"lesson_image_alt\":\"Step-by-step method for converting recurring decimals to fractions with worked examples\",\"videoDuration\":156,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"fractions-decimals\",\"subtopicName\":\"Fractions and Decimals\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":7}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"powers-indices\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Powers and Indices\",\"title\":\"Powers and Indices - Base, Exponent, Square and Cube Numbers\",\"description\":\"Powers and indices mean repeated multiplication, for example, 5³ = 5 × 5 × 5. Interactive practice to try, plus flashcards to download.\",\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"category\":\"$undefined\",\"intro\":\"**Powers and indices** are a short way to write repeated multiplication, so **2³ = 2 × 2 × 2 = 8** makes 8 a cube number. Each power has a **base** and an **exponent** showing how many times it is multiplied.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"powers and indices\",\"exponents\",\"square numbers\",\"cube numbers\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/powers-indices/powers-and-indices-math-angel.webp\",\"lesson_image_alt\":\"Powers and indices: 3⁴ with base and index labelled, expanded as 3 × 3 × 3 × 3 to show repeated multiplication\",\"videoDuration\":200,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":1}],\"flashcardCount\":6,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"standard-form\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Standard Form\",\"title\":\"Standard Form (Scientific Notation) - Free Video and Quiz\",\"description\":\"Standard form writes a big or small number as A 
3× 10ⁿ, with A between 1 and 10. So 26000 = 2.6 × 10⁴. Download the flashcards for GCSE and IGCSE revision.\",\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"category\":\"$undefined\",\"intro\":\"**Standard form** (or **scientific notation**) writes very large or very small numbers as **A × 10ⁿ**, where **A is between 1 and 10**. The power n counts how many places the decimal point moves. So 0.007 becomes **7 × 10⁻³**, a negative power.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"standard form\",\"scientific notation\",\"standard form maths\",\"convert to standard form\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/standard-form/standard-form-math-angel.webp\",\"lesson_image_alt\":\"Standard form (scientific notation): expressing numbers as A × 10ⁿ where 1 ≤ A \u003c 10, with example 26,000 = 2.6 × 10⁴\",\"videoDuration\":188,\"ukYear\":9,\"placements\":[{\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":2}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"basics-of-square-roots\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Basics of Square Roots\",\"title\":\"Square Roots - Video and Interactive Practice\",\"description\":\"A square root is a non-negative value that, when squared, gives the original number, so √49 = 7. Worked examples, plus flashcards to download.\",\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"category\":\"$undefined\",\"intro\":\"**A square root** of a number is the **non-negative** value you multiply by itself to get that number. For example, **√400 = 20** because 20 × 20 = 400. Whole numbers like 1, 4, 9 and 16 are **perfect squares**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"square roots\",\"perfect squares\",\"square root properties\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/basics-of-square-roots/basics-of-square-roots-math-angel.webp\",\"lesson_image_alt\":\"Square roots lesson thumbnail with definition and examples\",\"videoDuration\":170,\"ukYear\":7,\"placements\":[{\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":3}],\"flashcardCount\":4,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"multiplying-dividing-square-roots\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Multiplying and Dividing Square Roots\",\"title\":\"Multiplying and Dividing Square Roots - Video and Quiz\",\"description\":\"Multiplying square roots follows √a × √b = √(ab), and dividing follows √a ÷ √b = √(a/b). Flashcards to download for GCSE and IGCSE.\",\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"category\":\"$undefined\",\"intro\":\"**Multiplying square roots**, or surds, uses **√a × √b = √(ab)**, so you multiply the numbers under one root sign. **Dividing square roots** works the same way using **√a ÷ √b = √(a/b)**. Both rules let you **simplify square roots** in a calculation.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"multiplying square roots\",\"dividing square roots\",\"simplify square roots\"],\"searchAliases\":[\"simplifying surds\"],\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/multiplying-dividing-square-roots/multiplying-and-dividing-square-roots-math-angel.webp\",\"lesson_image_alt\":\"Multiplying and divi
3ding square roots lesson with step-by-step formulas and examples\",\"videoDuration\":217,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":4}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"laws-of-indices-same-base-or-index\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Laws of Indices (Same Base, Same Indices)\",\"title\":\"Laws of Indices - Video and Interactive Practice\",\"description\":\"Laws of indices: with the same base, add the exponents to multiply and subtract to divide. Worked examples for GCSE and IGCSE, plus flashcards to download.\",\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"category\":\"$undefined\",\"intro\":\"**The laws of indices** are shortcut rules for simplifying powers. With the **same base**, you add the indices, e.g. **2³ × 2⁴ = 2³⁺⁴ = 2⁷**. With the **same index**, you multiply the bases, e.g. **2³ × 5³ = (2 × 5)³ = 10³**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"laws of indices\",\"index laws same base\",\"multiplying dividing indices\",\"same index\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/laws-of-indices-same-base-or-index/laws-of-indices-(same-base-or-same-indices)-math-angel.webp\",\"lesson_image_alt\":\"Laws of indices lesson covering same base and same index rules with worked examples\",\"videoDuration\":231,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":5}],\"flashcardCount\":3,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"negative-indices-and-power-of-a-power\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"Negative Indices and Power of a Power\",\"title\":\"Negative Indices and Power of a Power - Flashcards and Quiz\",\"description\":\"Negative indices flip the base to a reciprocal, and power of a power multiplies the exponents. Worked examples for GCSE and IGCSE, plus a 4-minute video.\",\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"category\":\"$undefined\",\"intro\":\"**Negative indices** tell you to take the **reciprocal**, so the base flips into a fraction with a positive power. For example, **2⁻³ = 1/2³ = 1/8**. A **power of a power** means you multiply the indices, giving **(2³)⁵ = 2¹⁵**.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"negative indices\",\"power of a power\",\"negative exponents\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/negative-exponents-power-of-a-power/negative-exponents-and-power-of-a-power-math-angel.webp\",\"lesson_image_alt\":\"Negative exponents and power of a power lesson with reciprocal and exponent rules\",\"videoDuration\":213,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":6}],\"flashcardCount\":5,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0},{\"id\":\"nth-root-fractional-indices\",\"courseId\":\"numbers\",\"courseName\":\"Number\",\"lesson_title\":\"The nth Root and Fractional Indices\",\"title\":\"Fractional Indices and nth Roots - Video and Quiz\",\"description\":\"A fractional index is a root: x^(1/2) = √x and x^(1/3) = ∛x, so 8^(1/3) = 2 and 8^(2/3) = 4. Flashcards to download for GCSE and IGCSE.\",\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"category\":\"$undefined\",\"intro\":\"**Fractional indices** write a root as a power. Raising 125 to the power 1/3 gives the **cube root of 125**, which is 5. The bottom of the fraction says which **root** to take, and the top says what **power** to raise it to.\\n\",\"interactiveTitle\":\"$undefined\",\"interactiveDescription\":\"$undefined\",\"keywords\":[\"fractional indices\",\"nth root\",\"roots and powers\"],\"searchAliases\":\"$undefined\",\"lesson_image\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-lesson-images/numbers/nth-root-fractional-indices/the-nth-root-and-fractional-indices-math-angel.webp\",\"lesson_image_alt\":\"nth root and fractional indices lesson with cube root and fourth root worked examples\",\"videoDuration\":231,\"ukYear\":10,\"placements\":[{\"subtopicId\":\"powers-roots-standard-form\",\"subtopicName\":\"Powers, Roots and Standard Form\",\"topicId\":\"numbers\",\"isMain\":true,\"sortOrder\":7}],\"flashcardCount\":6,\"practiceQuestionCount\":6,\"hasInteractiveActivity\":true,\"status\":\"$undefined\",\"progress\":0}]}],\"$L19\"]}],[\"$L1a\",\"$L1b\",\"$L1c\",\"$L1d\",\"$L1e\",\"$L1f\",\"$L20\",\"$L21\",\"$L22\"],\"$L23\"]}]\n90:I[897367,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\"],\"OutletBoundary\"]\n92:I[27201,[\"/_next/static/chunks/3ne1-gn2awz9c.js\",\"/_next/static/chunks/19lc_9yhbdjne.js\",\"/_next/static/chunks/33iayyub0472u.js\",\"/_next/static/chunks/1t7rb6j7892t6.js\",\"/_next/static/chunks/2zxltq5qa7_bl.js\",\"/_next/static/chunks/2lmepge7i28qd.js\",\"/_next/static/chunks/09g_5jf_1uhqn.js\",\"/_next/static/chunks/0nbze1qbdcyos.js\",\"/_next/static/chunks/3-hayde213ruy.js\",\"/_next/static/chunks/00twfinmahjsm.js\",\"/_next/static/chunks/19za4y212u0u3.js\",\"/_next/static/chunks/1rug5xx3k1d2p.js\"],\"IconMark\"]\n8:[\"$\",\"$1\",\"h\",{\"children\":[null,[\"$\",\"$L24\",null,{\"children\":\"$L25\"}],[\"$\",\"div\",null,{\"hidden\":true,\"children\":[\"$\",\"$L26\",null,{\"children\":[\"$\",\"$27\",null,{\"name\":\"Next.Metadata\",\"children\":\"$L28\"}]}]}],[\"$\",\"meta\",null,{\"name\":\"next-size-adjust\",\"content\":\"\"}]]}]\na:[\"$\",\"link\",\"0\",{\"rel\":\"stylesheet\",\"href\":\"/_next/static/chunks/3_f885ikmu7vm.css\",\"precedence\":\"next\",\"crossOrigin\":\"$undefined\",\"nonce\":\"$undefined\"}]\nb:[\"$\",\"link\",\"1\",{\"rel\":\"stylesheet\",\"href\":\"/_next/static/chunks/1_oj-8fpiwx0n.css\",\"precedence\":\"next\",\"crossOrigin\":\"$undefined\",\"nonce\":\"$undefined\"}]\nc:[\"$\",\"link\",\"2\",{\"rel\":\"stylesheet\",\"href\":\"/_next/static/chunks/0zrd7rd7ow0gg.css\",\"precedence\":\"next\",\"crossOrigin\":\"$undefined\",\"nonce\":\"$undefined\"}]\nd:[\"$\",\"link\",\"3\",{\"rel\":\"stylesheet\",\"href\":\"/_next/static/chunks/1etrw9bfctihn.css\",\"precedence\":\"next\",\"crossOrigin\":\"$undefined\",\"nonce\":\"$undefined\"}]\n7:C\n"])</script>
3<script>self.__next_f.push([1,"19:[\"$\",\"nav\",null,{\"aria-hidden\":\"true\",\"className\":\"sr-only\",\"children\":[[\"$\",\"a\",\"distributive-law\",{\"href\":\"/lessons/distributive-law\",\"children\":\"Distributive Law - Video, Quiz and Flashcards\"}],[\"$\",\"a\",\"perpendicular-and-parallel-lines\",{\"href\":\"/lessons/perpendicular-and-parallel-lines\",\"children\":\"Perpendicular and Parallel Lines - Free Video and Quiz\"}],[\"$\",\"a\",\"number-line-inequality-symbols\",{\"href\":\"/lessons/number-line-inequality-symbols\",\"children\":\"Number Line and Inequality Symbols - Compare Numbers\"}],[\"$\",\"a\",\"tally-marks-bar-chart\",{\"href\":\"/lessons/tally-marks-bar-chart\",\"children\":\"Tally Marks, Bar Charts and Tables - Video and Quiz\"}],[\"$\",\"a\",\"ratios\",{\"href\":\"/lessons/ratios\",\"children\":\"Introduction to Ratios - Video, Quiz and Flashcards\"}],[\"$\",\"a\",\"expressions-with-one-variable\",{\"href\":\"/lessons/expressions-with-one-variable\",\"children\":\"Expressions with One Variable - Video and Quiz\"}],[\"$\",\"a\",\"measurement-and-types-of-angles\",{\"href\":\"/lessons/measurement-and-types-of-angles\",\"children\":\"Types of Angles - Free Video and Interactive Practice\"}],[\"$\",\"a\",\"place-value-chart-rounding\",{\"href\":\"/lessons/place-value-chart-rounding\",\"children\":\"Place Value and Rounding - Free Video and Quiz\"}],[\"$\",\"a\",\"absolute-relative-frequency\",{\"href\":\"/lessons/absolute-relative-frequency\",\"children\":\"Absolute and Relative Frequency - Video and Quiz\"}],[\"$\",\"a\",\"how-to-combine-ratios\",{\"href\":\"/lessons/how-to-combine-ratios\",\"children\":\"How to Combine Ratios - Video and Interactive Practice\"}],[\"$\",\"a\",\"simplifying-expressions\",{\"href\":\"/lessons/simplifying-expressions\",\"children\":\"Simplifying Expressions - Video and Quiz\"}],[\"$\",\"a\",\"angle-relationships\",{\"href\":\"/lessons/angle-relationships\",\"children\":\"Angle Relationships in Parallel Lines - Video and Quiz\"}],[\"$\",\"a\",\"natural-numbers-whole-numbers-integers\",{\"href\":\"/lessons/natural-numbers-whole-numbers-integers\",\"children\":\"Natural Numbers, Whole Numbers and Integers - Video and Quiz\"}],[\"$\",\"a\",\"pie-chart\",{\"href\":\"/lessons/pie-chart\",\"children\":\"Pie Charts - Video and Interactive Practice\"}],[\"$\",\"a\",\"fractions-and-percentages\",{\"href\":\"/lessons/fractions-and-percentages\",\"children\":\"Fractions and Percentages - Video and Quiz\"}],[\"$\",\"a\",\"simplifying-expressions-multiple-variables\",{\"href\":\"/lessons/simplifying-expressions-multiple-variables\",\"children\":\"Simplifying Expressions with Multiple Variables - Examples\"}],[\"$\",\"a\",\"polygons-quadrilaterals\",{\"href\":\"/lessons/polygons-quadrilaterals\",\"children\":\"Polygons and Types of Quadrilaterals - Video and Quiz\"}],[\"$\",\"a\",\"rational-numbers\",{\"href\":\"/lessons/rational-numbers\",\"children\":\"Rational Numbers on a Number Line - Video and Quiz\"}],[\"$\",\"a\",\"line-graphs-curve-graphs\",{\"href\":\"/lessons/line-graphs-curve-graphs\",\"children\":\"Line Graphs and Curve Graphs - Video and Quiz\"}],[\"$\",\"a\",\"percentage-of-a-number\",{\"href\":\"/lessons/percentage-of-a-number\",\"children\":\"How to Find a Percentage of a Number - Video and Quiz\"}],[\"$\",\"a\",\"expanding-double-brackets\",{\"href\":\"/lessons/expanding-double-brackets\",\"children\":\"Expanding Double Brackets - Video and Quiz\"}],[\"$\",\"a\",\"properties-of-circles\",{\"href\":\"/lessons/properties-of-circles\",\"children\":\"Properties of Circles - Diameter, Chord, Sector, Tangent\"}],[\"$\",\"a\",\"absolute-value\",{\"href\":\"/lessons/absolute-value\",\"children\":\"Absolute Value - Video and Interactive Practice\"}],[\"$\",\"a\",\"mean-median-mode-range\",{\"href\":\"/lessons/mean-median-mode-range\",\"children\":\"Mean, Median, Mode and Range - Free Video and Quiz\"}],[\"$\",\"a\",\"interest-rate-calculation\",{\"href\":\"/lessons/interest-rate-calculation\",\"children\":\"Interest Rate Calculation - Video and Interactive Practice\"}],[\"$\",\"a\",\"square-of-a-binomial\",{\"href\":\"/lessons/square-of-a-binomial\",\"children\":\"Square of a Binomial - Flashcards and Quiz\"}],\"$L29\",\"$L2a\",\"$L2b\",\"$L2c\",\"$L2d\",\"$L2e\",\"$L2f\",\"$L30\",\"$L31\",\"$L32\",\"$L33\",\"$L34\",\"$L35\",\"$L36\",\"$L37\",\"$L38\",\"$L39\",\"$L3a\",\"$L3b\",\"$L3c\",\"$L3d\",\"$L3e\",\"$L3f\",\"$L40\",\"$L41\",\"$L42\",\"$L43\",\"$L44\",\"$L45\",\"$L46\",\"$L47\",\"$L48\",\"$L49\",\"$L4a\",\"$L4b\",\"$L4c\",\"$L4d\",\"$L4e\",\"$L4f\",\"$L50\",\"$L51\",\"$L52\",\"$L53\",\"$L54\",\"$L55\",\"$L56\",\"$L57\",\"$L58\",\"$L59\",\"$L5a\",\"$L5b\",\"$L5c\",\"$L5d\",\"$L5e\",\"$L5f\",\"$L60\",\"$L61\",\"$L62\",\"$L63\",\"$L64\",\"$L65\",\"$L66\",\"$L67\",\"$L68\",\"$L69\",\"$L6a\",\"$L6b\",\"$L6c\",\"$L6d\",\"$L6e\",\"$L6f\",\"$L70\",\"$L71\",\"$L72\",\"$L73\",\"$L74\",\"$L75\",\"$L76\",\"$L77\",\"$L78\",\"$L79\",\"$L7a\",\"$L7b\",\"$L7c\",\"$L7d\",\"$L7e\",\"$L7f\",\"$L80\",\"$L81\",\"$L82\",\"$L83\",\"$L84\",\"$L85\",\"$L86\",\"$L87\",\"$L88\",\"$L89\",\"$L8a\",\"$L8b\",\"$L8c\",\"$L8d\",\"$L8e\",\"$L8f\"]}]\n1a:[\"$\",\"script\",\"script-0\",{\"src\":\"/_next/static/chunks/349nks73i4b-b.js\",\"async\":true,\"nonce\":\"$undefined\"}]\n1b:[\"$\",\"script\",\"script-1\",{\"src\":\"/_next/static/chunks/3
3y_s5s_a6rtf2.js\",\"async\":true,\"nonce\":\"$undefined\"}]\n1c:[\"$\",\"script\",\"script-2\",{\"src\":\"/_next/static/chunks/17hw6cj44vit3.js\",\"async\":true,\"nonce\":\"$undefined\"}]\n1d:[\"$\",\"script\",\"script-3\",{\"src\":\"/_next/static/chunks/0noi9m_o50fzl.js\",\"async\":true,\"nonce\":\"$undefined\"}]\n1e:[\"$\",\"script\",\"script-4\",{\"src\":\"/_next/static/chunks/2oz-5926v45re.js\",\"async\":true,\"nonce\":\"$undefined\"}]\n1f:[\"$\",\"script\",\"script-5\",{\"src\":\"/_next/static/chunks/146ib6hwvnpj6.js\",\"async\":true,\"nonce\":\"$undefined\"}]\n20:[\"$\",\"script\",\"script-6\",{\"src\":\"/_next/static/chunks/1jgvs1y9ykbgi.js\",\"async\":true,\"nonce\":\"$undefined\"}]\n21:[\"$\",\"script\",\"script-7\",{\"src\":\"/_next/static/chunks/442n0v4gb2bin.js\",\"async\":true,\"nonce\":\"$undefined\"}]\n22:[\"$\",\"script\",\"script-8\",{\"src\":\"/_next/static/chunks/1yiixfgw446ng.js\",\"async\":true,\"nonce\":\"$undefined\"}]\n23:[\"$\",\"$L90\",null,{\"children\":[\"$\",\"$27\",null,{\"name\":\"Next.MetadataOutlet\",\"children\":\"$@91\"}]}]\n29:[\"$\",\"a\",\"thales-theorem\",{\"href\":\"/lessons/thales-theorem\",\"children\":\"Thales' Theorem - Video and Interactive Practice\"}]\n2a:[\"$\",\"a\",\"basic-arithmetic-inverse-operations\",{\"href\":\"/lessons/basic-arithmetic-inverse-operations\",\"children\":\"Basic Arithmetic and Inverse Operations - Video and Quiz\"}]\n2b:[\"$\",\"a\",\"median-mean-mode-frequency-table\",{\"href\":\"/lessons/median-mean-mode-frequency-table\",\"children\":\"Mean, Median, Mode and Range from a Frequency Table\"}]\n2c:[\"$\",\"a\",\"simple-interest-and-compound-interest\",{\"href\":\"/lessons/simple-interest-and-compound-interest\",\"children\":\"Simple and Compound Interest - Video and Quiz\"}]\n2d:[\"$\",\"a\",\"introduction-to-mapping\",{\"href\":\"/lessons/introduction-to-mapping\",\"children\":\"Introduction to Mapping - Video and Quiz\"}]\n2e:[\"$\",\"a\",\"units-of-area\",{\"href\":\"/lessons/units-of-area\",\"children\":\"Units of Area - Converting between mm², cm², m², km²\"}]\n2f:[\"$\",\"a\",\"bidmas-order-of-operations\",{\"href\":\"/lessons/bidmas-order-of-operations\",\"children\":\"BIDMAS - Order of Operations Rules \u0026 Worked Examples\"}]\n30:[\"$\",\"a\",\"box-plot\",{\"href\":\"/lessons/box-plot\",\"children\":\"Box Plot - How to Draw, Read, and Find Interquartile Range\"}]\n31:[\"$\",\"a\",\"percentage-increase-and-decrease\",{\"href\":\"/lessons/percentage-increase-and-decrease\",\"children\":\"Percentage Increase and Decrease - Free Video and Quiz\"}]\n32:[\"$\",\"a\",\"introduction-to-formulas\",{\"href\":\"/lessons/introduction-to-formulas\",\"children\":\"Introduction to Formulas - Video and Quiz\"}]\n33:[\"$\",\"a\",\"area-of-a-triangle\",{\"href\":\"/lessons/area-of-a-triangle\",\"children\":\"How to Find the Area of a Triangle - Free Video and Quiz\"}]\n34:[\"$\",\"a\",\"commutative-and-associative-laws\",{\"href\":\"/lessons/commutative-and-associative-laws\",\"children\":\"Commutative and Associative Laws - Video and Quiz\"}]\n35:[\"$\",\"a\",\"grouped-frequency-table\",{\"href\":\"/lessons/grouped-frequency-table\",\"children\":\"Grouped Frequency Table - Video and Quiz\"}]\n36:[\"$\",\"a\",\"percentage-change\",{\"href\":\"/lessons/percentage-change\",\"children\":\"How to Calculate Percentage Change - Video and Quiz\"}]\n37:[\"$\",\"a\",\"introduction-to-functions-and-graphs\",{\"href\":\"/lessons/introduction-to-functions-and-graphs\",\"children\":\"Introduction to Functions and Graphs - f(x) Explained\"}]\n38:[\"$\",\"a\",\"perimeter-of-a-polygon\",{\"href\":\"/lessons/perimeter-of-a-polygon\",\"children\":\"Perimeter of a Polygon - Rectangles, Triangles, Compound Shapes\"}]\n39:[\"$\",\"a\",\"column-addition-and-subtraction\",{\"href\":\"/lessons/column-addition-and-subtraction\",\"children\":\"Column Addition and Subtraction - Carrying and Borrowing\"}]\n3a:[\"$\",\"a\",\"calculating-probability\",{\"href\":\"/lessons/calculating-probability\",\"children\":\"Calculating Probability - Video and Quiz\"}]\n3b:[\"$\",\"a\",\"directly-proportional-inversely-proportional\",{\"href\":\"/lessons/directly-proportional-inversely-proportional\",\"children\":\"Directly and Inversely Proportional - Video and Quiz\"}]\n3c:[\"$\",\"a\",\"solving-equations\",{\"href\":\"/lessons/solving-equations\",\"children\":\"Solving Equations Step by Step - Video and Quiz\"}]\n3d:[\"$\",\"a\",\"area-of-a-trapezium\",{\"href\":\"/lessons/area-of-a-trapezium\",\"children\":\"Area of a Trapezium - Free Video and Quiz\"}]\n3e:[\"$\",\"a\",\"long-multiplication\",{\"href\":\"/lessons/long-multiplication\",\"children\":\"Long Multiplication - How to Multiply Large Numbers\"}]\n3f:[\"$\",\"a\",\"addition-rule-of-probability-expected-frequency\",{\"href\":\"/lessons/addition-rule-of-probability-expected-frequency\",\"children\":\"Addition Rule of Probability and Expected Frequency\"}]\n40:[\"$\",\"a\",\"direct-proportion\",{\"href\":\"/lessons/direct-proportion\",\"children\":\"Direct Proportion - Formula y = kx with Worked Examples\"}]\n41:[\"$\",\"a\",\"solving-rational-equations\",{\"href\":\"/lessons/solving-rational-equations\",\"children\":\"Solving Rational Equations - Video and Quiz\"}]\n42:[\"$\",\"a\",\"area-parallelograms-triangles\",{\"href\":\"/lessons/area-parallelograms-triangles\",\"children\":\"Area of Parallelograms and Triangles - Flashcards and Quiz\"}]\n43:[\"$\",\"a\",\"long-division\",{\"href\":\"/lessons/long-division\",\"children\":\"Long Division - Video and Interactive Practice\"}]\n44:[\"$\",\"a\",\"probability-tree-diagrams\",{\"href\":\"/lessons/probability-tree-diagrams\",\"children\":\"Probability Tree Diagrams - How to Draw and Interpret\"}]\n45:[\"$\",\"a\",\"inverse-proportion\",{\"href\":\"/lessons/inverse-proportion\",\"children\":\"Inverse Proportion - Formula y = k/x with Worked Examples\"}]\n46:[\"$\",\"a\",\"m-and-c-in-linear-equations\",{\"href\":\"/lessons/m-and-c-in-linear-equations\",\"children\":\"Gradient and Y-Intercept in Linear Equations - y = mx + c\"}]\n47:[\"$\",\"a\",\"area-of-compound-shapes\",{\"href\":\"/lessons/area-of-compound-shapes\",\"children\":\"Area of Compound Shapes - Flashcards and Quiz\"}]\n48:[\"$\",\"a\",\"decimal-point-movement\",{\"href\":\"/lessons/decimal-point-movement\",\"children\":\"Decimal Point Movement - Multiply \u0026 Divide by Powers of 10\"}]\n49:[\"$\",\"a\",\"sets-and-venn-diagrams\",{\"href\":\"/lessons/sets-and-venn-diagrams\",\"children\":\"Sets and Venn Diagrams - Video and Interactive Practice\"}]\n4a:[\"$\",\"a\",\"speed-distance-time\",{\"href\":\"/lessons/speed-distance-time\",\"children\":\"Speed, Distance and Time - Flashcards and Quiz\"}]\n4b:[\"$\",\"a\",\"equation-of-a-straight-line\",{\"href\":\"/lessons/equation-of-a-straight-line\",\"children\":\"Equation of a Straight Line - Video and Quiz\"}]\n4c:[\"$\",\"a\",\"circumference-area-circle-sector\",{\"href\":\"/lessons/circumference-area-circle-sector\",\"children\":\"Circumference and Area of a Circle and a Sector\"}]\n4d:[\"$\",\"a\",\"adding-and-subtracting-negative-numbers\",{\"href\":\"/lessons/adding-and-subtracting-negative-numbers\",\"children\":\"Adding and Subtracting Negative Numbers - Video and Quiz\"}]\n4e:[\"$\",\"a\",\"density-mass-volume\",{\"href\":\"/lessons/density-mass-volume\",\"children\":\"Density, Mass and Volume - Free Video and Quiz\"}]\n4f:[\"$\",\"a\",\"x-intercept-y-intercept-intersection\",{\"href\":\"/lessons/x-intercept-y-intercept-intersection\",\"children\":\"How to Find X-Intercept, Y-Intercept and Line Intersections\"}]\n50:[\"$\",\"a\",\"line-of-symmetry\",{\"href\":\"/lessons/line-of-symmetry\",\"children\":\"Lines of Symmetry and Reflection - Free Video and Quiz\"}]\n51:[\"$\",\"a\",\"multiplying-and-dividing-negative-numbers\",{\"href\":\"/lessons/multiplying-and-dividing-negative-numbers\",\"children\":\"Multiplying \u0026 Dividing Negative Numbers - Sign Rules\"}]\n52:[\"$\",\"a\",\"pressure-force-area\",{\"href\":\"/lessons/pressure-force-area\",\"children\":\"Pressure, Force and Area - Video and Interactive Practice\"}]\n53:[\"$\",\"a\",\"nth-term-of-a-linear-sequence\",{\"href\":\"/lessons/nth-term-of-a-linear-sequence\",\"children\":\"Finding the nth Term of a Linear Sequence - Rule \u0026 Examples\"}]\n54:[\"$\",\"a\",\"rotational-symmetry\",{\"href\":\"/lessons/rotational-symmetry\",\"children\":\"Rotational Symmetry - Flashcards and Quiz\"}]\n55:[\"$\",\"a\",\"calculating-money\",{\"href\":\"/lessons/calculating-money\",\"children\":\"Calculating Money - Add, Subtract, Multiply, Divide\"}]\n56:[\"$\",\"a\",\"quadratic-and-geometric-sequences\",{\"href\":\"/lessons/quadratic-and-geometric-sequences\",\"children\":\"Quadratic and Geometric Sequences - nth Term and Examples\"}]\n57:[\"$\",\"a\",\"reflecting-points-coordinate-plane\",{\"href\":\"/lessons/reflecting-points-coordinate-plane\",\"children\":\"Reflecting Points on the Coordinate Plane - Video and Quiz\"}]\n58:[\"$\",\"a\",\"units-of-length\",{\"href\":\"/lessons/units-of-length\",\"children\":\"Units of Length - Convert and Calculate km, m, cm, mm\"}]\n59:[\"$\",\"a\",\"fibonacci-sequence\",{\"href\":\"/lessons/fibonacci-sequence\",\"children\":\"Fibonacci Sequence - Find Terms, Rule \u0026 Examples\"}]\n5a:[\"$\",\"a\",\"translating-shapes\",{\"href\":\"/lessons/translating-shapes\",\"children\":\"Translating Shapes - Translation with Column Vectors\"}]\n5b:[\"$\",\"a\",\"units-of-mass\",{\"href\":\"/lessons/units-of-mass\",\"children\":\"Units of Mass - Convert and Calculate t, kg, g, mg\"}]\n5c:[\"$\",\"a\",\"simple-quadratic-equations\",{\"href\":\"/lessons/simple-quadratic-equations\",\"children\":\"Simple Quadratic Equations - Effect of a on the Parabola\"}]\n5d:[\"$\",\"a\",\"rotating-shapes\",{\"href\":\"/lessons/rotating-shapes\",\"children\":\"Rotating Shapes - Video and Interactive Practice\"}
3]\n5e:[\"$\",\"a\",\"converting-time\",{\"href\":\"/lessons/converting-time\",\"children\":\"Converting \u0026 Calculating Time - Hours, Minutes, Seconds\"}]\n5f:[\"$\",\"a\",\"vertex-form\",{\"href\":\"/lessons/vertex-form\",\"children\":\"Vertex Form and Parabola Transformations - h, k, and Shifts\"}]\n60:[\"$\",\"a\",\"enlargement\",{\"href\":\"/lessons/enlargement\",\"children\":\"Enlargement and Scale Factors - Video and Quiz\"}]\n61:[\"$\",\"a\",\"divisibility-rules\",{\"href\":\"/lessons/divisibility-rules\",\"children\":\"Divisibility Rules for 2 to 10 - Tests with Examples\"}]\n62:[\"$\",\"a\",\"converting-standard-form-and-vertex-form\",{\"href\":\"/lessons/converting-standard-form-and-vertex-form\",\"children\":\"Converting Quadratics Between Standard and Vertex Form\"}]\n63:[\"$\",\"a\",\"constructing-triangles\",{\"href\":\"/lessons/constructing-triangles\",\"children\":\"Constructing Triangles - Video and Interactive Practice\"}]\n64:[\"$\",\"a\",\"prime-numbers-prime-factorisation\",{\"href\":\"/lessons/prime-numbers-prime-factorisation\",\"children\":\"Prime Numbers and Prime Factorisation - Factor Tree Method\"}]\n65:[\"$\",\"a\",\"quadratic-equations-in-vertex-form-standard-form\",{\"href\":\"/lessons/quadratic-equations-in-vertex-form-standard-form\",\"children\":\"Writing Quadratic Equations in Vertex Form and Standard Form\"}]\n66:[\"$\",\"a\",\"congruent-triangles\",{\"href\":\"/lessons/congruent-triangles\",\"children\":\"Congruent Triangles - SSS, SAS, ASA, and RHS\"}]\n67:[\"$\",\"a\",\"hcf-and-lcm\",{\"href\":\"/lessons/hcf-and-lcm\",\"children\":\"HCF and LCM - Prime Factorisation \u0026 Worked Examples\"}]\n68:[\"$\",\"a\",\"solving-simple-quadratic-equations\",{\"href\":\"/lessons/solving-simple-quadratic-equations\",\"children\":\"Solving Simple Quadratic Equations - Video and Quiz\"}]\n69:[\"$\",\"a\",\"perpendicular-bisectors-and-circumcircle\",{\"href\":\"/lessons/perpendicular-bisectors-and-circumcircle\",\"children\":\"Perpendicular Bisectors and Circumcircle - How to Construct\"}]\n6a:[\"$\",\"a\",\"introduction-to-fractions\",{\"href\":\"/lessons/introduction-to-fractions\",\"children\":\"Introduction to Fractions - Video and Quiz\"}]\n6b:[\"$\",\"a\",\"solving-quadratic-equations-factorising\",{\"href\":\"/lessons/solving-quadratic-equations-factorising\",\"children\":\"Solving Quadratic Equations by Factorising - Video and Quiz\"}]\n6c:[\"$\",\"a\",\"angle-bisectors-and-incircle\",{\"href\":\"/lessons/angle-bisectors-and-incircle\",\"children\":\"Angle Bisectors and Incircle - Video and Quiz\"}]\n6d:[\"$\",\"a\",\"equivalent-fractions\",{\"href\":\"/lessons/equivalent-fractions\",\"children\":\"Equivalent Fractions - Simplify and Expand Fractions\"}]\n6e:[\"$\",\"a\",\"quadratic-formula\",{\"href\":\"/lessons/quadratic-formula\",\"children\":\"Quadratic Formula - Solve Quadratic Equations Step by Step\"}]\n6f:[\"$\",\"a\",\"medians-and-centroid-of-a-triangle\",{\"href\":\"/lessons/medians-and-centroid-of-a-triangle\",\"children\":\"Medians and Centroid of a Triangle - Video and Quiz\"}]\n70:[\"$\",\"a\",\"comparing-fractions\",{\"href\":\"/lessons/comparing-fractions\",\"children\":\"Comparing Fractions - Video and Interactive Practice\"}]\n71:[\"$\",\"a\",\"equations-with-2-variables\",{\"href\":\"/lessons/equations-with-2-variables\",\"children\":\"Solving Equations with 2 Variables - Video and Quiz\"}]\n72:[\"$\",\"a\",\"solids-units-of-volume\",{\"href\":\"/lessons/solids-units-of-volume\",\"children\":\"Solids and Units of Volume - mm³, cm³, ml, L\"}]\n73:[\"$\",\"a\",\"adding-and-subtracting-fractions\",{\"href\":\"/lessons/adding-and-subtracting-fractions\",\"children\":\"Adding and Subtracting Fractions - Flashcards and Quiz\"}]\n74:[\"$\",\"a\",\"solving-simultaneous-equations-graphically\",{\"href\":\"/lessons/solving-simultaneous-equations-graphically\",\"children\":\"Solving Simultaneous Equations Graphically - Video and Quiz\"}]\n75:[\"$\",\"a\",\"volume-of-a-cuboid\",{\"href\":\"/lessons/volume-of-a-cuboid\",\"children\":\"Volume of a Cuboid and Cube - Free Video and Quiz\"}]\n76:[\"$\",\"a\",\"multiplying-fractions\",{\"href\":\"/lessons/multiplying-fractions\",\"children\":\"How to Multiply Fractions - Free Video and Quiz\"}]\n77:[\"$\",\"a\",\"equal-values-and-substitution-method\",{\"href\":\"/lessons/equal-values-and-substitution-method\",\"children\":\"Simultaneous Equations: Equal Values and Substitution Method\"}]\n78:[\"$\",\"a\",\"surface-area\",{\"href\":\"/lessons/surface-area\",\"children\":\"Surface Area of Solids - Cuboid, Cube, Prism\"}]\n79:[\"$\",\"a\",\"dividing-fractions\",{\"href\":\"/lessons/dividing-fractions\",\"children\":\"Dividing Fractions - Reciprocals, Whole \u0026 Mixed Numbers\"}]\n7a:[\"$\",\"a\",\"elimination-method\",{\"href\":\"/lessons/elimination-method\",\"children\":\"Elimination Method for Simultaneous Equations - Examples\"}]\n7b:[\"$\",\"a\",\"volume-prisms-cylinders\",{\"href\":\"/lessons/volume-prisms-cylinders\",\"children\":\"Volume of Prisms and Cylinders - Video and Quiz\"}]\n7c:[\"$\",\"a\",\"decimals-and-fractions\",{\"href\":\"/lessons/decimals-and-fractions\",\"children\":\"Decimals and Fractions - Place Value \u0026 How to Convert\"}]\n7d:[\"$\",\"a\",\"cavalieris-principle\",{\"href\":\"/lessons/cavalieris-principle\",\"children\":\"Cavalieri's Principle - Video, Quiz and Flashcards\"}]\n7e:[\"$\",\"a\",\"comparing-and-rounding-decimals\",{\"href\":\"/lessons/comparing-and-rounding-decimals\",\"children\":\"Comparing and Rounding Decimals - Flashcards and Quiz\"}
3]\n7f:[\"$\",\"a\",\"volume-surface-area-pyramids-cones-spheres\",{\"href\":\"/lessons/volume-surface-area-pyramids-cones-spheres\",\"children\":\"Volume and Surface Area of Pyramids, Cones, and Spheres\"}]\n80:[\"$\",\"a\",\"convert-fraction-to-decimal\",{\"href\":\"/lessons/convert-fraction-to-decimal\",\"children\":\"Convert Fraction to Decimal - Long Division Method\"}]\n81:[\"$\",\"a\",\"pythagoras-theorem\",{\"href\":\"/lessons/pythagoras-theorem\",\"children\":\"Pythagoras' Theorem - Free Video and Quiz\"}]\n82:[\"$\",\"a\",\"adding-subtracting-fractions-and-decimals\",{\"href\":\"/lessons/adding-subtracting-fractions-and-decimals\",\"children\":\"Add and Subtract Fractions and Decimals - Video and Quiz\"}]\n83:[\"$\",\"a\",\"trigonometry-sine-cosine-tangent\",{\"href\":\"/lessons/trigonometry-sine-cosine-tangent\",\"children\":\"Trigonometry: Sine, Cosine, and Tangent - SOH CAH TOA\"}]\n84:[\"$\",\"a\",\"multiplying-decimals\",{\"href\":\"/lessons/multiplying-decimals\",\"children\":\"Multiplying Decimals - Video and Interactive Practice\"}]\n85:[\"$\",\"a\",\"cosine-rule\",{\"href\":\"/lessons/cosine-rule\",\"children\":\"Cosine Rule - Find Missing Sides and Angles in Triangles\"}]\n86:[\"$\",\"a\",\"calculating-fractions-and-decimals\",{\"href\":\"/lessons/calculating-fractions-and-decimals\",\"children\":\"Calculating Fractions and Decimals - Video and Quiz\"}]\n87:[\"$\",\"a\",\"sine-rule\",{\"href\":\"/lessons/sine-rule\",\"children\":\"Sine Rule - How to Use the Formula to Find Sides or Angles\"}]\n88:[\"$\",\"a\",\"recurring-decimals-to-fractions\",{\"href\":\"/lessons/recurring-decimals-to-fractions\",\"children\":\"Recurring Decimals to Fractions - Video and Quiz\"}]\n89:[\"$\",\"a\",\"powers-indices\",{\"href\":\"/lessons/powers-indices\",\"children\":\"Powers and Indices - Base, Exponent, Square and Cube Numbers\"}]\n8a:[\"$\",\"a\",\"standard-form\",{\"href\":\"/lessons/standard-form\",\"children\":\"Standard Form (Scientific Notation) - Free Video and Quiz\"}]\n8b:[\"$\",\"a\",\"basics-of-square-roots\",{\"href\":\"/lessons/basics-of-square-roots\",\"children\":\"Square Roots - Video and Interactive Practice\"}]\n8c:[\"$\",\"a\",\"multiplying-dividing-square-roots\",{\"href\":\"/lessons/multiplying-dividing-square-roots\",\"children\":\"Multiplying and Dividing Square Roots - Video and Quiz\"}]\n8d:[\"$\",\"a\",\"laws-of-indices-same-base-or-index\",{\"href\":\"/lessons/laws-of-indices-same-base-or-index\",\"children\":\"Laws of Indices - Video and Interactive Practice\"}]\n8e:[\"$\",\"a\",\"negative-indices-and-power-of-a-power\",{\"href\":\"/lessons/negative-indices-and-power-of-a-power\",\"children\":\"Negative Indices and Power of a Power - Flashcards and Quiz\"}]\n8f:[\"$\",\"a\",\"nth-root-fractional-indices\",{\"href\":\"/lessons/nth-root-fractional-indices\",\"children\":\"Fractional Indices and nth Roots - Video and Quiz\"}]\n25:[[\"$\",\"meta\",\"0\",{\"charSet\":\"utf-8\"}],[\"$\",\"meta\",\"1\",{\"name\":\"viewport\",\"content\":\"width=device-width, initial-scale=1\"}]]\n28:[[\"$\",\"title\",\"0\",{\"children\":\"Bite-sized Video Lessons for Year 6 to GCSE \u0026 IGCSE | Maths Angel\"}],[\"$\",\"meta\",\"1\",{\"name\":\"description\",\"content\":\"Browse all Maths Angel lessons for ages 10 to 16: short videos, flashcards, quizzes and AI help across algebra, geometry, fractions and statistics. Start free.\"}],[\"$\",\"meta\",\"2\",{\"name\":\"keywords\",\"content\":\"maths lessons,KS3 maths lessons,KS4 maths lessons,GCSE maths lessons,maths video lessons,algebra lessons,geometry lessons,fractions lessons,statistics lessons,maths curriculum\"}],[\"$\",\"link\",\"3\",{\"rel\":\"canonical\",\"href\":\"https://maths-angel.com/lessons\"}],[\"$\",\"meta\",\"4\",{\"property\":\"og:title\",\"content\":\"Bite-sized Video Lessons for Year 6 to GCSE \u0026 IGCSE | Maths Angel\"}],[\"$\",\"meta\",\"5\",{\"property\":\"og:description\",\"content\":\"Browse all Maths Angel lessons for ages 10 to 16: short videos, flashcards, quizzes and AI help across algebra, geometry, fractions and statistics. Start free.\"}],[\"$\",\"meta\",\"6\",{\"property\":\"og:url\",\"content\":\"https://maths-angel.com/lessons\"}],[\"$\",\"meta\",\"7\",{\"property\":\"og:site_name\",\"content\":\"Maths Angel\"}],[\"$\",\"meta\",\"8\",{\"property\":\"og:locale\",\"content\":\"en_GB\"}],[\"$\",\"meta\",\"9\",{\"property\":\"og:image\",\"content\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-website-images/og-images/og_c
3ourse_overview.png\"}],[\"$\",\"meta\",\"10\",{\"property\":\"og:image:width\",\"content\":\"1200\"}],[\"$\",\"meta\",\"11\",{\"property\":\"og:image:height\",\"content\":\"630\"}],[\"$\",\"meta\",\"12\",{\"property\":\"og:image:alt\",\"content\":\"Bite-sized Video Lessons for Year 6 to GCSE \u0026 IGCSE | Maths Angel\"}],[\"$\",\"meta\",\"13\",{\"property\":\"og:type\",\"content\":\"website\"}],[\"$\",\"meta\",\"14\",{\"name\":\"twitter:card\",\"content\":\"summary_large_image\"}],[\"$\",\"meta\",\"15\",{\"name\":\"twitter:title\",\"content\":\"Bite-sized Video Lessons for Year 6 to GCSE \u0026 IGCSE | Maths Angel\"}],[\"$\",\"meta\",\"16\",{\"name\":\"twitter:description\",\"content\":\"Browse all Maths Angel lessons for ages 10 to 16: short videos, flashcards, quizzes and AI help across algebra, geometry, fractions and statistics. Start free.\"}],[\"$\",\"meta\",\"17\",{\"name\":\"twitter:image\",\"content\":\"https://mathangelwebsitestorage.blob.core.windows.net/mathangel-website-images/og-images/og_course_overview.png\"}],[\"$\",\"meta\",\"18\",{\"name\":\"twitter:image:alt\",\"content\":\"Bite-sized Video Lessons for Year 6 to GCSE \u0026 IGCSE | Maths Angel\"}],[\"$\",\"link\",\"19\",{\"rel\":\"icon\",\"href\":\"/favicon.ico?favicon.3du3gu3vpsoqm.ico\",\"sizes\":\"48x48\",\"type\":\"image/x-icon\"}],[\"$\",\"$L92\",\"20\",{}]]\n91:null\n"])</script>
3</body></html>

Line numbers count LF bytes from the start of the resource, as the search results do. Vendor segments are library code the classifier recognised; they are stored but not indexed. Bytes are shown as Latin1 characters, one per byte.