[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"content-index":3,"content-layer:magnets:extend":1434},{"release":4,"domains":9,"concepts":110,"edges":1322,"journeys":1431,"sources":1432,"glossary":1433,"lean":147},{"releaseId":5,"mode":6,"createdAt":7,"manifestHash":8},"remote-muarqumu","approved","2026-09-21T04:52:24.342Z","efdbdc0e58f4c54e74ab5330ffe7aa73dd8184fc4b473a83b828fd400c1b6143",[10,40,62,76,86,100],{"id":11,"title":12,"description":13,"order":14,"areas":15},"mathematics","Mathematics","Numbers, shapes, patterns and data — and the reasoning that connects them.",0,[16,20,24,28,32,36],{"id":17,"title":18,"description":19},"math-number","Numbers","Reading, writing and comparing large numbers, their properties, the four operations and the order we do them in.",{"id":21,"title":22,"description":23},"math-factors","Factors and multiples","Prime and composite numbers, twin primes and co-primes, HCF and LCM.",{"id":25,"title":26,"description":27},"math-patterns","Patterns","Finding the rule behind number and shape patterns, and using it to predict.",{"id":29,"title":30,"description":31},"math-geometry","Geometry","Shapes and solids, lines and rays, and the angles they make.",{"id":33,"title":34,"description":35},"math-measurement","Measurement","Measuring and constructing angles with a protractor, ruler and compass.",{"id":37,"title":38,"description":39},"math-data","Data handling","Collecting and organising data, and summarising it with mean, median, mode and range.",{"id":41,"title":42,"description":43,"order":44,"areas":45},"matter-energy","Physics","Light, sound, forces, energy and electricity — how the physical world behaves.",1,[46,50,54,58],{"id":47,"title":48,"description":49},"phys-light","Light","How light travels, what it does when it meets things, and why we see colour.",{"id":51,"title":52,"description":53},"phys-sound","Sound","Vibrations that travel through materials, and how we hear them.",{"id":55,"title":56,"description":57},"phys-forces","Forces and motion","Pushes, pulls and the force that holds moons, planets and falling apples.",{"id":59,"title":60,"description":61},"phys-electricity","Electricity and magnetism","Charge, circuits, power and magnets.",{"id":63,"title":64,"description":65,"order":66,"areas":67},"earth-space","Earth and space","Our planet, its oceans and skies, and the Sun and Moon that move them.",2,[68,72],{"id":69,"title":70,"description":71},"earth-space-astro","Sun, Moon and sky","What we see in the sky, why it changes, and what is really moving.",{"id":73,"title":74,"description":75},"earth-oceans","Oceans","Seas, coasts and the daily rise and fall of the tide.",{"id":77,"title":78,"description":79,"order":80,"areas":81},"living-world","Living world","Bodies, plants, animals and the systems that keep them alive.",3,[82],{"id":83,"title":84,"description":85},"bio-body","The human body","What is inside you, where it sits, and how the parts work together.",{"id":87,"title":88,"description":89,"order":90,"areas":91},"people-society","People and society","How people organise themselves, and what happens when they travel, trade and rule.",4,[92,96],{"id":93,"title":94,"description":95},"soc-government","Government and citizenship","Who makes the rules, who carries them out, and how people have a say.",{"id":97,"title":98,"description":99},"soc-exploration","Exploration and encounter","Why people set out into the unknown, and what followed for everyone involved.",{"id":101,"title":102,"description":103,"order":104,"areas":105},"technology","Technology","How tools, machines and computers are designed and used.",5,[106],{"id":107,"title":108,"description":109},"tech-engineering","Engineering and power","Designing machines, structures and energy systems.",[111,179,239,286,339,389,438,488,540,587,637,689,738,788,827,876,928,979,1029,1076,1125,1177,1227,1275],{"id":112,"slug":112,"title":113,"question":114,"promise":115,"domains":116,"areas":117,"keywords":118,"status":139,"layers":140,"questionBank":172},"human-body-anatomy","Anatomy of the human body","What is inside you, and where exactly does it all sit?","A guided tour of the body: bones that hold you up, muscles that move you, and the organs packed inside — what each one is, where it sits, and how big it really is.",[77],[83],[119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138],"anatomy","organ","skeleton","bone","muscle","heart","lungs","brain","stomach","liver","kidney","intestine","skin","joint","ribcage","spine","diaphragm","cell","tissue","body systems","available",[141,149,155,161,167],{"depth":142,"revision":44,"title":143,"subtitle":144,"summary":145,"estimatedMinutes":146,"reviewed":147,"reviewMethod":148},"discover","A guided tour of the body you live in","What is inside you, where it sits, and how big it really is","Climb the ladder from cells to organ systems, learn the words anatomists use for where things are, meet the 206 bones and their joints, find out why a muscle can only ever pull, and take an organ-by-organ tour with real sizes and positions — then measure your own body.",38,true,"owner_bulk",{"depth":150,"revision":44,"title":151,"subtitle":152,"summary":153,"estimatedMinutes":154,"reviewed":147,"reviewMethod":148},"understand","How the body is put together","Tissues, bone, joints, muscle and the cavities that hold the organs","Go one level below the organs to the four tissue types they are built from, learn the direction words and the standard pose they are measured from, see why bone is a living composite, count the skeleton to 206, and place every major organ in its cavity with its mass.",42,{"depth":156,"revision":44,"title":157,"subtitle":158,"summary":159,"estimatedMinutes":160,"reviewed":147,"reviewMethod":148},"investigate","Predict it, then test it","Seven claims about your body, tested with paper, a tape measure and real class data","Guess before you look: does a hollow tube beat a solid rod, does height equal arm span for everyone, can a bone reveal a stranger’s height, does exercise raise every pulse equally, are you really symmetric, and does your shoulder really out-move your hip? Seven hands-on tests against real evidence.",36,{"depth":162,"revision":44,"title":163,"subtitle":164,"summary":165,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"deepen","Why it works: levers, remodelling and a history of being corrected","Lever mechanics in every joint, bone that rebuilds under load, and how anatomy overturned a thousand years of error","Treat every muscle-moved bone as a lever and see why the body favours the class that trades force for speed. Meet bone that rebuilds along its real loads, the genuine edge cases in \"206 bones\", and how Vesalius corrected centuries of Galen’s animal-based errors.",40,{"depth":168,"revision":44,"title":169,"subtitle":170,"summary":171,"estimatedMinutes":146,"reviewed":147,"reviewMethod":148},"extend","Beyond the syllabus: animals, projects, puzzles and careers","Other body plans, three things to build, puzzles worth reasoning through, and where this knowledge earns a living","Compare your body plan with a giraffe, a bird, a snake and a boneless octopus; build a working paper hand and a life-size organ map; solve puzzles spanning the whole topic; meet seven careers built on this knowledge; finish with open questions.",{"count":173,"sections":174,"levels":175},79,10,{"foundation":176,"core":177,"stretch":178,"challenge":174},22,32,15,{"id":180,"slug":180,"title":181,"question":182,"promise":183,"domains":184,"areas":185,"keywords":186,"status":139,"layers":207,"questionBank":231},"angles","Angles","How much does a door turn when it opens — and how do we measure a turn?","What an angle is, types of angles, angle pairs (complementary, supplementary, linear pairs, vertically opposite) and how to use them to find missing angles.",[11],[29],[187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206],"angle","vertex","arm","degrees","acute","right angle","obtuse","straight angle","reflex","complete angle","complementary","supplementary","linear pair","vertically opposite","adjacent angles","angles at a point","clock angles","transversal","parallel lines","angle sum of a triangle",[208,213,218,222,227],{"depth":142,"revision":44,"title":209,"subtitle":210,"summary":211,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Angles are turns","Doors, clocks, scissors and compass directions: meet the angle and learn to name its size","See an angle as a turn and as two arms meeting at a vertex. Measure turns in degrees (full 360°, half 180°, quarter 90°), sort angles into seven types, turn through N, E, S, W, read angles on a clock and meet angle partners.",35,{"depth":150,"revision":44,"title":214,"subtitle":215,"summary":216,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Naming, sorting and pairing angles","Precise definitions, the seven types, and the angle pairs that let you find what you cannot measure","Define an angle as two rays with a common vertex, name it with ∠ABC, and use degrees and landmark angles. Pin down the seven types, clock and compass angles, then adjacent, complementary, supplementary, linear-pair, vertically opposite and around-a-point angles.",45,{"depth":156,"revision":44,"title":219,"subtitle":220,"summary":221,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Is it always true? Testing angle ideas","Predict, test with labs and numbers, hunt counterexamples and find the reasons behind angle patterns","Investigate angle estimation, sums of angle types, complement and supplement patterns, linear pairs and their bisectors, crossing lines, clock-hand puzzles, turning walks around shapes and the tear-the-corners experiment, sorting claims into always, sometimes and never.",{"depth":162,"revision":44,"title":223,"subtitle":224,"summary":225,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Why angles behave: proofs, parallels and polygons","From Babylonian 360 to Euclid's proofs: transversals, triangle and polygon angle sums, and hard missing-angle problems","Why a full turn is 360°, how to write a proof with reasons, why vertically opposite angles are equal, the angles made by a transversal on parallel lines and their converses, the triangle and polygon angle sums, bends and zigzags between parallels, and where 180° fails.",55,{"depth":168,"revision":44,"title":228,"subtitle":229,"summary":230,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Angles at work and play","Clock formulas, exterior angles, bearings, radians, real-world angles, olympiad puzzles and projects","Use |30h − 5.5m| for any clock time, prove and use the exterior angle property, navigate with bearings and runway numbers, meet the radian, see angles in ramps, ladders, bowling and pie charts, and tackle olympiad-style angle chases, projects and open questions.",{"count":232,"sections":233,"levels":234},80,9,{"foundation":235,"core":236,"stretch":237,"challenge":238},20,28,21,11,{"id":240,"slug":240,"title":241,"question":242,"promise":243,"domains":244,"areas":245,"keywords":246,"status":139,"layers":261,"questionBank":281},"body-systems","Body systems and how they connect","No organ works alone — so how does a mouthful of roti reach your toes as energy?","Digestive, circulatory, respiratory, nervous, muscular, skeletal and excretory systems, and the handovers between them that keep you alive every second.",[77],[83],[247,248,249,250,251,252,253,254,255,256,257,195,258,259,260],"digestive system","circulatory system","respiratory system","nervous system","excretory system","muscular system","skeletal system","blood","oxygen","nutrients","homeostasis","heart rate","breathing","interconnected",[262,266,270,273,277],{"depth":142,"revision":44,"title":263,"subtitle":264,"summary":265,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Seven teams, one body","What each system does, and where it hands the work to the next one","Meet the organ systems one at a time — digestive, respiratory, circulatory, excretory, nervous, muscular and skeletal — then follow a roti and a breath across the hand-over points where each system passes its work to the next.",{"depth":150,"revision":44,"title":267,"subtitle":268,"summary":269,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"How the systems work, and how they hand over","One design used six times: thin wall, huge surface, steep difference","Go inside each system: enzymes and the chemical works, the pressure trick that moves air, two circuits through a four-chambered heart, filter-and-reclaim kidneys, the reflex arc and the nerve-to-muscle gap — then follow a breath all the way to a working cell.",{"depth":156,"revision":44,"title":157,"subtitle":271,"summary":272,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Reaction time, a real enzyme test, exercise data and a fever that is not a malfunction","Turn the claims from earlier layers into experiments you can actually run: a ruler-drop reaction test, an iodine test for digested starch, pulse and breathing data before and after exercise, and a look at why a fever is a controlled response rather than a failure.",{"depth":162,"revision":44,"title":274,"subtitle":275,"summary":276,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Where the tidy rule bends","The mathematics of a thin wall, bone's double life, the lymphatic system, and why some hand-overs must be prevented","Quantify why hand-over barriers must be thin, meet the lymphatic system that returns leaked fluid and carries digested fat, see bone as a blood factory and calcium bank, and look at clotting and the blood-brain barrier as hand-overs the body deliberately controls or resists.",{"depth":168,"revision":44,"title":278,"subtitle":279,"summary":280,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"History, machines and weightlessness","Harvey's arithmetic, the stethoscope and ECG, three ways to image the body, artificial hand-overs, and bodies in orbit","Meet the arithmetic that proved blood circulates, the instruments that let doctors listen to and image a living body without cutting it, machines that rebuild a failed hand-over, what microgravity does to every system at once, and a few careers and open questions this topic leads to.",{"count":173,"sections":233,"levels":282},{"foundation":176,"core":283,"stretch":284,"challenge":285},25,19,13,{"id":287,"slug":287,"title":38,"question":288,"promise":289,"domains":290,"areas":291,"keywords":292,"status":139,"layers":313,"questionBank":335},"data-handling","What is a typical value — and how can one number summarise a whole class?","Collecting and organising data, tally marks and frequency tables, bar graphs, and summarising data with mean, median, mode and range.",[11],[37],[293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312],"data","mean","median","mode","range","average","tally","frequency table","bar graph","pictograph","pie chart","double bar graph","grouped data","outlier","survey","probability","census","rainfall","batting average","raw data",[314,318,322,326,330],{"depth":142,"revision":44,"title":315,"subtitle":316,"summary":317,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Counting what matters: meeting data","From a messy list of answers to one number that tells the story","Ask a question, collect answers, and turn a jumble of raw data into tally marks, tables, pictographs and bar graphs. Then meet four friendly numbers that sum up a whole group: the fair share (mean), the middle (median), the most common (mode) and the spread (range).",{"depth":150,"revision":44,"title":319,"subtitle":320,"summary":321,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Organise, picture, summarise: how the methods work","Kinds of data, tables and graphs done properly, and exact methods for mean, median, mode and range","Tell categorical from numerical data, build self-checking frequency tables, choose a key or scale for pictographs and bar graphs, and use exact methods for mean, median (odd and even counts), mode (two modes or none) and range, even from a frequency table.",{"depth":156,"revision":44,"title":323,"subtitle":324,"summary":325,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"What happens if…? Experiments with averages","Predict, change the data, and test: outliers, shifts, missing values and datasets built to order","Treat averages like a science experiment. Predict what adding a value, an outlier, or a change to every value does to the mean, median, mode and range, then test it in the labs. Build data sets to order, hunt missing values and compare real Indian data.",{"depth":162,"revision":44,"title":327,"subtitle":328,"summary":329,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Why averages work, and which one to trust","Balance points, proofs, grouped data, combined groups and the art of choosing an average","Prove the mean is a balance point and how it reacts to shifts and scaling. Combine groups correctly, handle grouped data with class intervals, read double bar graphs, and choose between mean, median and mode with outliers, cricket averages and average speeds. Plus a history of statistics in India.",{"depth":168,"revision":44,"title":331,"subtitle":332,"summary":333,"estimatedMinutes":334,"reviewed":147,"reviewMethod":148},"Data in the wild: pie charts, tricks, chance and projects","Draw pie charts, catch misleading graphs, talk about chance, and investigate real Indian data","Turn data into pie charts with angles, spot graphs that mislead, describe chance from impossible to certain, and run real projects on electricity bills, the census and monsoon rain. Think about privacy and fairness in data, meet careers built on data, and try olympiad-style puzzles.",60,{"count":232,"sections":233,"levels":336},{"foundation":337,"core":338,"stretch":176,"challenge":174},18,30,{"id":340,"slug":340,"title":341,"question":342,"promise":343,"domains":344,"areas":345,"keywords":346,"status":139,"layers":362,"questionBank":383},"eclipses","Eclipses","If the Moon goes round Earth every month, why isn't there an eclipse every month?","An eclipse is a shadow falling exactly where it can be seen. Learn the geometry of umbra and penumbra, why the Moon's tilted orbit makes eclipses rare, and how to watch one safely.",[63],[69],[347,348,349,350,351,352,353,354,355,356,357,358,359,360,361],"eclipse","solar eclipse","lunar eclipse","umbra","penumbra","annular","totality","syzygy","nodes","orbit tilt","Saros","corona","blood moon","eye safety","shadow",[363,367,371,375,379],{"depth":142,"revision":44,"title":364,"subtitle":365,"summary":366,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"An eclipse is a shadow that finds you","Two shadows, two kinds of eclipse, and how to watch one without hurting your eyes","Meet eclipses as what they really are: shadows. Learn whose shadow falls on what in solar and lunar eclipses, why the eclipsed Moon turns red, why we don't get one every month, and the safe ways to watch the Sun.",{"depth":150,"revision":44,"title":368,"subtitle":369,"summary":370,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"The geometry of a shadow in space","Umbra and penumbra, apparent sizes, nodes and seasons — and the reasons behind every safety rule","Work out the actual geometry: how long each shadow cone is, why the Moon's only just reaches us, why the discs match to 3%, how far from a node an eclipse can happen, why the Moon turns red, and the physics behind every solar viewing rule.",{"depth":156,"revision":44,"title":372,"subtitle":373,"summary":374,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Build it, test it, try to break it","A lamp-and-balls model, hands-on measurements, and predictions checked against real eclipses","Hands-on layer: build a scale model of the Earth-Moon-Sun system, test the new-moon\u002Ffull-moon rule and the shadow-width formula for yourself, find the tilt's hidden threshold, build a pinhole projector and check its numbers, and plan around three real upcoming eclipses.",{"depth":162,"revision":44,"title":376,"subtitle":377,"summary":378,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"The Saros cycle, and two eclipses that changed physics","The Saros arithmetic, the astronomers who computed it, and how a belief should really be tested","Deeper reasoning: rebuild the 1.474° eclipse limit term by term, derive the Saros and exeligmos cycles from three different lunar months, see how Aryabhata and Brahmagupta actually computed eclipses, and examine the two solar eclipses that discovered helium and tested general relativity.",{"depth":168,"revision":44,"title":380,"subtitle":381,"summary":382,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"The same shadow rule, everywhere in the Solar System","Moons too small to eclipse, a moon that eclipses constantly, transits at home, and other worlds' planets","Take the eclipse geometry beyond Earth: why Phobos and Deimos only ever transit the Sun from Mars, why Io causes true eclipses on Jupiter routinely, how Mercury and Venus transit the Sun from Earth, Venus's 243-year transit rhythm, and how the same trick finds other stars' planets.",{"count":384,"sections":385,"levels":386},68,8,{"foundation":235,"core":387,"stretch":388,"challenge":385},24,16,{"id":390,"slug":390,"title":391,"question":392,"promise":393,"domains":394,"areas":395,"keywords":396,"status":139,"layers":416,"questionBank":437},"electricity","Electricity","What actually happens between the power station and the switch under your finger?","Electricity is charge on the move. Learn what pushes it, what resists it, how it is made and delivered, what it costs, and how to stay safe around it.",[41,101],[59,107],[390,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415],"voltage","current","resistance","Ohm's law","circuit","AC","DC","generator","power station","grid","transformer","kWh","electricity bill","safety","MCB","earth wire","battery","conductor","insulator",[417,421,425,429,433],{"depth":142,"revision":44,"title":418,"subtitle":419,"summary":420,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Electricity is charge on the move","From a balloon on your hair to a day that runs on it","Meet the charges hiding in every atom, see why a doorknob spark and lightning are the same idea, discover why slow electrons still light a bulb instantly, build circuits that break, and learn the first rules for staying safe.",{"depth":150,"revision":44,"title":422,"subtitle":423,"summary":424,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"The big three: voltage, current, resistance","The push, the flow and the pushback, and the one rule that ties them together","Build the pump-and-pipe picture of a circuit, then meet voltage (the push), current (the flow) and resistance (the pushback) with real numbers from AA cells to lightning. Finish with Ohm's law, V = I × R, and the mix-ups it clears up.",{"depth":156,"revision":44,"title":426,"subtitle":427,"summary":428,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Circuits you can test","Fair tests, meters, series and parallel, Ohm's law, fuses and fruit batteries","Design fair circuit tests, place ammeters and voltmeters correctly, compare series and parallel bulbs, test Ohm's law and see a filament bulb break it, work out when an MCB trips, and build a safe lemon battery.",{"depth":162,"revision":44,"title":430,"subtitle":431,"summary":432,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"How it's made and how it reaches you","From Faraday's spinning magnets to the socket on your wall","Follow electricity from a spinning magnet in a power station, through transformers and 765 kV lines, down to the 230 V socket in your room. Learn why the grid runs on AC at 50 Hz, why it transmits at high voltage, and why supply must match demand every second.",{"depth":168,"revision":44,"title":434,"subtitle":435,"summary":436,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Power, bills, safety and the future","From watts on a rating plate to units on your bill, the milliamps that matter, and the grid that is coming","Use P = V × I and E = P × t to read rating plates and work out a real electricity bill in units (kWh). Learn why current through the body is what injures, how earth pins, MCBs and RCCBs protect you, what to do in a shock emergency, and how solar, storage and smart meters are changing the grid.",null,{"id":439,"slug":439,"title":440,"question":441,"promise":442,"domains":443,"areas":444,"keywords":445,"status":139,"layers":463,"questionBank":485},"exploration","Exploration: reasons and consequences","What made people sail into oceans they could not map — and who paid for it?","Curiosity, trade, faith, gold and rivalry sent people across oceans. Follow the voyages, the technology that made them possible, and the consequences — for those who travelled and for those already there.",[87],[97],[439,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462],"voyage","navigation","trade route","spices","Vasco da Gama","Columbus","Zheng He","Silk Road","colonisation","Columbian exchange","monsoon winds","astrolabe","compass","cartography","empire","consequences","indigenous peoples",[464,468,473,477,481],{"depth":142,"revision":44,"title":465,"subtitle":466,"summary":467,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Why sail into an ocean nobody has mapped?","Reasons, routes and results, told from both ends of the voyage","Meet exploration honestly: what the word means and why 'discovery' misleads, six reasons people set out, the busy Indian Ocean world before European ships, how sailors found their way, four voyages worth knowing, and what followed - new foods, new maps, disease, slavery and empire.",{"depth":150,"revision":44,"title":469,"subtitle":470,"summary":471,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"How the navigator's toolkit actually works","Mechanisms behind the voyages: instruments, sails, clocks, charts and the economics of a monopoly","Go under Discover's story to the mechanisms: how a compass, kamal, astrolabe, lateen sail and sternpost rudder actually work, why longitude needed a clock and took decades to solve, how flat maps must distort a round Earth, and why a royal charter let a trading company become a ruler.",50,{"depth":156,"revision":44,"title":474,"subtitle":475,"summary":476,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Predict it, try it, compare it, test it","Lab-heavy investigations that check what the Discover layer told you","Compare stated reasons with actual results for Columbus and Zheng He, run a monsoon 'what if', judge whether one number sums up a disputed history, sort evidence against a claim about da Gama, read a paraphrased passage from two sides, and test sweeping generalisations against real voyages.",{"depth":162,"revision":44,"title":478,"subtitle":479,"summary":480,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Mechanism, harder numbers, and how historians know","Why the monsoon reverses, how clock drift compounds, and the method behind contested figures","Go beneath Discover's facts into mechanism and method: why the monsoon reverses, how clock drift compounds over a long voyage, an edge case in kamal readings, how historians back-project contested figures, how to weigh one account against another, and what shipwreck years teach about mean vs median.",{"depth":168,"revision":44,"title":482,"subtitle":483,"summary":484,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Beyond the horizon: exploration to today","Cook, the poles, space, the deep sea, and the questions nobody has answered yet","Carries exploration from Cook's Pacific voyage to today: the race to the poles and the treaty that followed, leaving Earth's gravity for the Moon and beyond, the deepest ocean trench, and the hardest open questions - who owns what nobody lives on, and who decides.",{"count":486,"sections":233,"levels":487},75,{"foundation":178,"core":236,"stretch":176,"challenge":174},{"id":489,"slug":489,"title":490,"question":491,"promise":492,"domains":493,"areas":494,"keywords":495,"status":139,"layers":515,"questionBank":536},"four-operations","Four operations","When should you add, subtract, multiply or divide — and how do you know your answer makes sense?","Addition, subtraction, multiplication and division with large numbers, choosing the right operation in real problems, and checking answers by estimating and by inverse operations.",[11],[17],[496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514],"addition","subtraction","multiplication","division","word problems","estimation","inverse operations","quotient","remainder","dividend","divisor","product","sum","difference","regrouping","long division","long multiplication","unitary method","word problems in rupees",[516,520,524,528,532],{"depth":142,"revision":44,"title":517,"subtitle":518,"summary":519,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Four ways to change a number","Adding, subtracting, multiplying and dividing: what each one means and when to use it","Meet the four operations through a kirana-shop trip, cricket scores, egg trays and shared laddoos. Learn what each operation means, how they undo each other, how to pick the right one from a story, and how to check that an answer is sensible.",{"depth":150,"revision":44,"title":521,"subtitle":522,"summary":523,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"How the column methods work","Carrying, borrowing, long multiplication and long division, and why every step is allowed","Learn the exact name for every part of a calculation, then master column addition and subtraction up to crores, long multiplication, long division with remainders and zeros in the quotient, checking with inverse operations, and working with money and units.",{"depth":156,"revision":44,"title":525,"subtitle":526,"summary":527,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Predict, test, check","Estimating first, changing the numbers, making sense of remainders and catching keyword traps","Predict before you calculate and test with labs and tables: estimate sums and products, see what happens when numbers change, decide what a remainder means in a story, catch misleading keywords and check answers by undoing them.",{"depth":162,"revision":44,"title":529,"subtitle":530,"summary":531,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Why the methods work","Regrouping, the distributive property, the division algorithm, checks, proportion and the history behind them","Prove why carrying, borrowing, long multiplication and long division work, meet the division algorithm and why dividing by zero is impossible, check with casting out nines, use the unitary method wisely, and solve India-sized multi-step problems.",{"depth":168,"revision":44,"title":533,"subtitle":534,"summary":535,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Other ways to calculate, and harder puzzles","Lattices, Vedic-style shortcuts, doubling, binary, classic puzzles, olympiad problems and real projects","Try the lattice, Napier's bones, Vedic-style shortcuts and Russian peasant multiplication and see why each works. Crack classic puzzles and olympiad problems, then plan real projects: a trip budget, a kirana bill, a harvest and a run chase.",{"count":537,"sections":385,"levels":538},74,{"foundation":178,"core":539,"stretch":176,"challenge":385},29,{"id":541,"slug":541,"title":542,"question":543,"promise":544,"domains":545,"areas":546,"keywords":547,"status":139,"layers":563,"questionBank":584},"gravity","Gravity","Why does everything fall down — and what is the Moon falling towards?","The force that pulls an apple to the ground is the same one that keeps the Moon circling Earth. Meet mass and weight, free fall, orbits and why astronauts float.",[41],[55],[541,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562],"mass","weight","free fall","orbit","force","Newton","air resistance","g","acceleration","satellite","weightlessness","planet","tides","escape velocity","centre of mass",[564,568,572,576,580],{"depth":142,"revision":44,"title":565,"subtitle":566,"summary":567,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Why does everything fall down?","Meet the pull that drops a pencil, bends the Moon’s path and holds the sky together","Start with a dropped pencil and end with galaxies. Discover what a force is, why heavy things do not fall faster, how air changes everything, the real difference between mass and weight, and the true reason astronauts float.",{"depth":150,"revision":44,"title":569,"subtitle":570,"summary":571,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"How gravity works: weight, falling and orbits","Mass against weight, g against speed, drag against gravity — and why an orbit is a permanent miss","Turn the story into rules you can use: weight = mass × g, distance = ½ g t², why mass cancels in free fall, how drag sets terminal velocity, Newton’s universal law in words, and the real reason astronauts float.",{"depth":156,"revision":44,"title":573,"subtitle":574,"summary":575,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Test it: predictions, ramps, pendulums and Newton’s own proof","Predict, try, compare and ask \"is it always true?\" — with a ramp, a pendulum, a leaking cup and a spacecraft","Turn gravity into hands-on science: rebuild Galileo’s ramp, design fair tests for mass and shape, weigh the Earth with a pendulum, check whether Newton’s law survives the trip to the Moon, hunt for orbital speed by binary search, and see how ISRO climbs to the Moon and Mars one burn at a time.",{"depth":162,"revision":44,"title":577,"subtitle":578,"summary":579,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"The mathematics behind every number in this topic","G, orbits derived from first principles, Newton’s Moon test in full, and the coincidence Einstein could not ignore","Meet Newton’s law with its constant G, derive orbital and escape speed from scratch, redo Newton’s Moon test in full, explore why gravitational and inertial mass are equal, see why g is not uniform on Earth, and look at the mechanics behind ISRO’s orbit-raising missions.",{"depth":168,"revision":44,"title":581,"subtitle":582,"summary":583,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Curved spacetime, black holes and the questions nobody has answered yet","Einstein’s radical idea, tested and confirmed — and an honest look at where gravity’s biggest mysteries still are","Go beyond Newton to Einstein: gravity as curved spacetime, the rubber-sheet picture and its flaws, the tests that confirmed general relativity, black holes, gravitational waves, orbital puzzles from tidal locking to dark matter, and open questions with real projects.",{"count":585,"sections":233,"levels":586},70,{"foundation":388,"core":387,"stretch":235,"challenge":174},{"id":588,"slug":588,"title":589,"question":590,"promise":591,"domains":592,"areas":593,"keywords":594,"status":139,"layers":613,"questionBank":634},"hcf-and-lcm","HCF and LCM","When will two blinking lights flash together again — and what is the biggest tile that fits a floor exactly?","Highest common factor and lowest common multiple by listing, prime factorisation and division, their link HCF × LCM = product, and real problems that need them.",[11],[21],[595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,500,611,612],"HCF","LCM","GCD","GCF","highest common factor","lowest common multiple","least common multiple","common factors","common multiples","prime factorisation","Venn diagram","long division method","Euclid's algorithm","common division method","co-prime","HCF × LCM","remainder problems","fractions",[614,618,622,626,630],{"depth":142,"revision":44,"title":615,"subtitle":616,"summary":617,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Sharing and meeting: meet the HCF and LCM","The biggest equal pieces and the next time things line up","Start from two puzzles, the biggest tile for a courtyard and the next time two lights flash together, and discover factors, multiples, common factors, common multiples, the HCF and the LCM, and how to tell which one a problem needs.",{"depth":150,"revision":44,"title":619,"subtitle":620,"summary":621,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Four ways to find the HCF and LCM","Listing, prime factors, long division and the ladder, and why they work","Precise definitions, then four methods: listing, prime factorisation with a Venn picture, long (continued) division for the HCF and common division for the LCM. Three numbers, the rule HCF × LCM = product, co-primes, fractions and the classic mix-ups.",{"depth":156,"revision":44,"title":623,"subtitle":624,"summary":625,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Predict, test and explain: HCF and LCM patterns","Always, sometimes or never? Find out with your own experiments","Make predictions and test them: when the LCM equals the product, why neighbours are co-prime, how HCF × LCM = a × b holds for two numbers but not three, what scaling does, how remainder puzzles work, and how changing a word problem changes the answer.",{"depth":162,"revision":44,"title":627,"subtitle":628,"summary":629,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Why it works: proofs, Euclid and the edges","Unique prime recipes, the product rule, Euclid’s algorithm and Bézout","Proofs in plain language: unique prime factorisation, why HCF takes smallest powers and LCM largest, why HCF × LCM = a × b (and why not for three numbers), why Euclid’s method works and how fast it is, Bézout’s identity, edge cases, harder problems and history.",{"depth":168,"revision":44,"title":631,"subtitle":632,"summary":633,"estimatedMinutes":334,"reviewed":147,"reviewMethod":148},"Cycles, gears and puzzles: HCF and LCM in the wild","Calendars, cicadas, tabla, bicycles, jugs, screens and olympiad problems","Expeditions beyond the textbook: cycles with head starts, calendars and planetary alignments (and why they are not LCMs), prime-cycle cicadas, gears and bicycle chains, tala rhythms, water jugs, ancient remainder puzzles, screen ratios, fractions, olympiad problems, careers and open questions.",{"count":173,"sections":385,"levels":635},{"foundation":235,"core":636,"stretch":337,"challenge":174},31,{"id":638,"slug":638,"title":639,"question":640,"promise":641,"domains":642,"areas":643,"keywords":644,"status":139,"layers":665,"questionBank":686},"government-india","How government works in India","Who decides what a country does — and where does a citizen fit in?","Parliament, the President and the Prime Minister, states and panchayats, courts and elections: how India makes its laws, carries them out and settles disputes, and how people have a say.",[87],[93],[645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664],"government","democracy","Parliament","Lok Sabha","Rajya Sabha","President","Prime Minister","Supreme Court","election","vote","constitution","panchayat","municipality","state","federal","law","rights","duties","citizen","judiciary",[666,670,674,678,682],{"depth":142,"revision":44,"title":667,"subtitle":668,"summary":669,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Who decides the rules?","From an hour in the school hall to a republic of a hundred and forty crore people","Start with thirty children, one football and no rules, and discover the three jobs every group has to invent: making rules, carrying them out and settling disputes. Then meet India's version — the Constitution, three organs, three levels, and the vote.",{"depth":150,"revision":44,"title":671,"subtitle":672,"summary":673,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"How each part actually works","Parliament's machinery, a bill's journey, the courts' ladder, and the levels beneath the Union","Go inside the institutions Discover introduced: how Parliament questions ministers, how a bill becomes an Act, what a President does that a Prime Minister does not, how courts check Parliament, and how the Union, States, Union Territories and local bodies share the work.",{"depth":156,"revision":44,"title":675,"subtitle":676,"summary":677,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Test it yourself: does the arithmetic hold up?","Seat share against vote share, real turnout data, and edge cases in how a bill becomes an Act","Put the rules from Understand under pressure: work through seat-versus-vote-share examples, test what happens when the two Houses disagree over a money bill, analyse real turnout data with mean, median and range, and sort everyday problems by the level of government actually responsible.",{"depth":162,"revision":44,"title":679,"subtitle":680,"summary":681,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Why it is built this way","The amendment procedure's arithmetic, the basic structure doctrine, and the freedom movement's fingerprints","Go after the reasoning: the arithmetic of amending the Constitution, the basic structure doctrine, how judges come to be chosen, the freedom movement's own arguments becoming institutions, and a few genuine edge cases put under pressure.",{"depth":168,"revision":44,"title":683,"subtitle":684,"summary":685,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Build it, test it, take it further","A mini-constitution, a mock Parliament, coalition puzzles, other countries' choices, and where this knowledge leads","Put the whole topic to work: draft and stress-test a mini-constitution, run a mock Parliament, prove a coalition-counting puzzle, compare India's design with other countries', research your own representatives, and meet real careers and open questions this knowledge connects to.",{"count":687,"sections":385,"levels":688},76,{"foundation":176,"core":636,"stretch":178,"challenge":385},{"id":690,"slug":690,"title":48,"question":691,"promise":692,"domains":693,"areas":694,"keywords":695,"status":139,"layers":713,"questionBank":735},"light","What is light, how does it travel, and why can you see this page at all?","Light travels in straight lines at extraordinary speed, bounces, bends, splits into colours and lets you see. Find out how, and why shadows, mirrors and rainbows behave as they do.",[41],[47],[690,696,697,698,361,699,700,701,702,703,704,705,706,707,708,709,710,350,711,712],"luminous","reflection","refraction","mirror","spectrum","colour","transparent","opaque","translucent","ray","speed of light","rainbow","prism","lens","eye","scattering","laser",[714,718,722,726,730],{"depth":142,"revision":44,"title":715,"subtitle":716,"summary":717,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Light: how you can see anything at all","Sources, straight lines, shadows, mirrors, bent straws and the colours hiding inside white","Meet light as the messenger that carries the world to your eyes: what makes its own light and what only reflects it, why light travels dead straight, how that one fact explains shadows, and first looks at mirrors, bending and the colours inside white light.",{"depth":150,"revision":44,"title":719,"subtitle":720,"summary":721,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"How light behaves: rays, angles and rules you can use","Shadow arithmetic, the law of reflection, what refraction really is, and the two kinds of colour mixing","Turn the facts of Discover into rules that predict. Work out shadow sizes with similar triangles, meet umbra and penumbra, apply the law of reflection to mirrors and periscopes, see why light bends when its speed changes, and separate the two opposite kinds of colour mixing.",{"depth":156,"revision":44,"title":723,"subtitle":724,"summary":725,"estimatedMinutes":154,"reviewed":147,"reviewMethod":148},"Chasing light: measuring, mirroring and bending it on purpose","How fast is light, and how would you find out? Predict and test curved mirrors, lenses, TIR and rainbows.","Step into the shoes of Rømer and Fizeau to measure something that seemed instant, then turn detective on curved mirrors, lenses pushed to a magnifier, total internal reflection in a diamond and a fibre-optic cable, and finally the exact geometry that puts a rainbow at 42 degrees from the Sun.",{"depth":162,"revision":44,"title":727,"subtitle":728,"summary":729,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Precise light: derivations, corrective lenses and the shape of a rainbow","Beyond the syllabus: derive the mirror formula, correct short and long sight, and see why a rainbow sits at 42 degrees.","Follow the speed of light to its modern exact definition, derive the mirror\u002Flens formula from similar triangles, work out lens powers for short and long sight, put numbers on fibre-optic latency, and see why the rainbow's angle is a genuine minimum.",{"depth":168,"revision":44,"title":731,"subtitle":732,"summary":733,"estimatedMinutes":734,"reviewed":147,"reviewMethod":148},"Waves, particles and the light you cannot see","Beyond visible light: wave versus particle, a real chocolate-bar experiment, and looking into the past with light-years.","Step past visible light into the wider spectrum, meet the wave-versus-particle debate (light is genuinely both), measure light's speed with a microwave and a chocolate bar, see how bending stretches every day, and use light-years to look into the past.",44,{"count":232,"sections":233,"levels":736},{"foundation":284,"core":737,"stretch":284,"challenge":178},27,{"id":739,"slug":739,"title":740,"question":741,"promise":742,"domains":743,"areas":744,"keywords":745,"status":139,"layers":763,"questionBank":784},"lines","Lines, rays and line segments","What is the difference between a line, a ray and a segment — and why do railway tracks never meet?","Points, lines, rays and line segments, intersecting, parallel and perpendicular lines, and where we see them in the world.",[11],[29],[746,747,705,748,749,750,751,752,205,753,754,204,755,756,757,758,759,760,761,762],"point","line","line segment","plane","collinear","concurrent","intersecting lines","perpendicular lines","perpendicular bisector","skew lines","horizontal and vertical","measuring segments","parallax error","Euclid's postulates","parallel postulate","vanishing point","railway tracks",[764,768,772,776,780],{"depth":142,"revision":44,"title":765,"subtitle":766,"summary":767,"estimatedMinutes":283,"reviewed":147,"reviewMethod":148},"Straight paths: points, lines, rays and segments","Meet the alphabet of geometry in torch beams, railway tracks and cricket creases","Meet points, line segments, rays and lines through everyday things, then see how two lines can cross, meet at square corners or run side by side forever.",{"depth":150,"revision":44,"title":769,"subtitle":770,"summary":771,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Names, notation and rules for lines","Precise definitions, careful measuring and the mix-ups they clear up","Pin down point, line and plane; name lines, rays and segments correctly; measure without parallax error; and define collinear, concurrent, parallel and perpendicular lines precisely.",{"depth":156,"revision":44,"title":773,"subtitle":774,"summary":775,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Test it: predictions about points and lines","Count, fold, measure and hunt for counterexamples","Predict and count how many lines, segments, rays and crossing points some points and lines can make; run a measuring experiment; beat optical illusions; and sort claims into always, sometimes and never true.",{"depth":162,"revision":44,"title":777,"subtitle":778,"summary":779,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Why it must be so: reasoning about lines","Euclid's rules, proofs, counting arguments and the puzzle of parallels","Build geometry from Euclid's postulates, prove key facts about intersecting, parallel and perpendicular lines, count with pairs, and follow the 2,000-year story of the parallel postulate from Alexandria to curved space.",{"depth":168,"revision":44,"title":781,"subtitle":782,"summary":783,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Lines in the wider world","Perspective, skew lines, maps, sport, careers, puzzles and open questions","See parallel lines meet in perspective drawings, find skew lines in rooms and solids, read lines on maps and sports grounds, meet people who use lines at work, and tackle puzzles from pizza cuts to string art.",{"count":232,"sections":233,"levels":785},{"foundation":786,"core":539,"stretch":176,"challenge":787},17,12,{"id":789,"slug":789,"title":790,"question":790,"promise":791,"domains":792,"areas":793,"keywords":794,"status":139,"layers":800,"questionBank":823},"magnets","Magnets: why do some things stick to a magnet and others do not?","A new science topic for learners aged 10 to 12 (Class 5-6, India). Cover: what a magnet is; poles, attraction and repulsion; which materials are magnetic (iron, nickel, cobalt, steel) and which are not (wood, plastic, copper, aluminium); th",[41],[59],[789,795,796,797,798,799],"some","things","stick","magnet","others",[801,807,811,815,819],{"depth":142,"revision":44,"title":802,"subtitle":803,"summary":804,"estimatedMinutes":805,"reviewed":147,"reviewMethod":806},"The Invisible Grip: How Magnets Pull and Push","A journey from fridge magnets to Earth's hidden force — why some things stick and others slip away","This lesson introduces magnets through everyday objects, explains how poles attract and repel, and shows how to test materials for magnetism. Readers will map invisible magnetic fields, make a simple compass, and connect it all to Earth acting as a giant magnet.",90,"per_lesson",{"depth":150,"revision":44,"title":808,"subtitle":809,"summary":810,"estimatedMinutes":805,"reviewed":147,"reviewMethod":806},"The Hidden Army Inside a Magnet","How tiny atomic teams line up to pull, stick or snap — and why heat or a hard knock sends them tumbling","This lesson reveals the invisible world of magnetic domains: why iron sticks but copper slips, how stroking or electricity organises atoms into a magnet, and why heat or hammering destroys that order. It also covers common mix-ups like 'all metals attract' and how to test unknown",{"depth":156,"revision":44,"title":812,"subtitle":813,"summary":814,"estimatedMinutes":805,"reviewed":147,"reviewMethod":806},"The Magnet Investigation Lab","How changing conditions, careful measurement and fair tests reveal what magnets really do","This lesson puts every magnet claim to the test. Learners plan fair comparisons, predict outcomes, gather evidence and use it to decide how magnets behave, how they weaken, and how an electromagnet's design changes its power.",{"depth":162,"revision":44,"title":816,"subtitle":817,"summary":818,"estimatedMinutes":805,"reviewed":147,"reviewMethod":806},"The Invisible Architecture of Magnetism","How atoms, domains, and field lines explain why some materials obey the magnet and others refuse","This lesson traces magnetism from everyday fridge magnets to atomic arrangements and magnetic domains, explaining why iron rushes to a magnet while copper stays still. Readers learn to predict magnetic behaviour, interpret field-line patterns, and calculate simple field relations",{"depth":168,"revision":44,"title":820,"subtitle":821,"summary":822,"estimatedMinutes":805,"reviewed":147,"reviewMethod":806},"The Invisible Push: Magnets at Work and at Scale","From iron filings to maglev trains — how hidden fields, domains and electromagnets shape our world","This lesson explores how magnetic domains explain why some materials become magnets and others do not, then builds to electromagnets, real engineering uses, and how to test magnetism fairly at home. It closes with open questions about magnetic storage and levitation that learners",{"count":824,"sections":66,"levels":825},52,{"foundation":826,"core":337,"stretch":787,"challenge":385},14,{"id":828,"slug":828,"title":829,"question":830,"promise":831,"domains":832,"areas":833,"keywords":834,"status":139,"layers":853,"questionBank":874},"constructing-angles","Measuring and constructing angles","How do you draw an exact 60° angle with only a compass and a ruler?","Reading a protractor correctly, measuring and drawing angles, and constructing 60°, 120°, 90°, 30° and 45° angles and bisectors with a ruler and compass.",[11],[33,29],[835,458,836,837,754,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852],"protractor","construction","angle bisector","60 degrees","90 degrees","120 degrees","45 degrees","30 degrees","geometry box","set square","divider","measuring angles","drawing angles","reflex angle","inner and outer scale","ruler and compass","trisection","constructing triangles",[854,858,862,866,870],{"depth":142,"revision":44,"title":855,"subtitle":856,"summary":857,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Angles you can measure and make","The geometry box, the protractor and the compass trick for an exact 60°","Open the geometry box, learn what a degree is, estimate angles by eye, measure and draw angles with a protractor, and discover how a compass alone can make an exact 60° angle.",{"depth":150,"revision":44,"title":859,"subtitle":860,"summary":861,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Reading the protractor and the compass constructions","Why the two scales exist, how to measure and draw any angle, and why 60°, 90°, 30° and 45° constructions work","Learn the precise protractor method (and the wrong-scale trap), measure and draw reflex angles, copy lengths with a compass, and construct 60°, 120°, 90°, 30° and 45° angles and perpendicular bisectors with the reason each one works.",{"depth":156,"revision":44,"title":863,"subtitle":864,"summary":865,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Test it: estimates, radii and angle recipes","Predict, try and check: what really changes an angle, and what never does","Predict and test: does arm length matter, what does a wrong-scale reading look like, how good is your eye, does the compass radius matter, which angles can bisecting and set squares reach, how accurate can a check be, and why bisectors always work.",{"depth":162,"revision":44,"title":867,"subtitle":868,"summary":869,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Why the constructions work","Proofs behind the recipes, edge cases, accuracy and the problems the Greeks could not solve","Find out why each compass construction is exact: equilateral triangles for 60°, congruent triangles for bisectors, equidistant points for perpendiculars. Then test edge cases, measure reflex angles, analyse errors and meet the impossible trisection problem.",{"depth":168,"revision":44,"title":871,"subtitle":872,"summary":873,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Triangles, polygons and the impossible angle","Build triangles and regular polygons, meet Gauss's 17-gon, and find out why 20° can never be constructed","Construct triangles from SSS, SAS and ASA, draw regular polygons from a circle, discover which polygons and whole-degree angles are constructible (multiples of 3°), meet the trisection problem, and use angles in projects, puzzles and careers.",{"count":537,"sections":233,"levels":875},{"foundation":178,"core":338,"stretch":284,"challenge":174},{"id":877,"slug":877,"title":878,"question":879,"promise":880,"domains":881,"areas":882,"keywords":883,"status":139,"layers":903,"questionBank":924},"patterns","Number and shape patterns","How can you predict the 100th term without drawing 100 pictures?","Spotting rules in number sequences and growing shape patterns, describing them in words and symbols, and using the rule to predict.",[11],[25],[877,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902],"sequence","rule","term","nth term","repeating patterns","growing patterns","arithmetic sequence","geometric sequence","square numbers","cube numbers","triangular numbers","Fibonacci","Pascal's triangle","matchstick patterns","odd numbers","even numbers","magic squares","kolam","algebra",[904,908,912,916,920],{"depth":142,"revision":44,"title":905,"subtitle":906,"summary":907,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"What comes next? Meeting patterns","Bangles, kolam borders, calendars, matchsticks and the rules that make them","Meet repeating and growing patterns in beads, rangoli, calendars and the hundred square. Find the unit, find the difference, describe the rule in words, and use jumps to predict terms far ahead.",{"depth":150,"revision":44,"title":909,"subtitle":910,"summary":911,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Rules, terms and sequences","Arithmetic and geometric sequences, special numbers, digit patterns and shape rules","Learn the precise language of sequences, the difference method for finding rules, arithmetic and geometric sequences, square, cube, triangular and Fibonacci numbers, digit patterns, and the rules behind growing matchstick and dot patterns.",{"depth":156,"revision":44,"title":913,"subtitle":914,"summary":915,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Pattern detectives: predict, test, explain","Matchstick challenges, Gauss’s trick, calendar magic, growth races and patterns that fool you","Investigate growing patterns like a detective: predict first, collect small cases, find the rule, test it and explain why it works. Includes far predictions, working backwards, odd sums, Gauss’s pairing, grid tricks and always-sometimes-never reasoning.",{"depth":162,"revision":44,"title":917,"subtitle":918,"summary":919,"estimatedMinutes":334,"reviewed":147,"reviewMethod":148},"Why patterns work: rules, algebra and proof","nth terms, equivalent expressions, picture proofs, Pingala’s rhythms, Meru Prastara and patterns that break","Turn rules into algebra and prove them: why the step becomes the coefficient of n, why odd numbers make squares, sums of powers and cubes, the Indian discovery of the Fibonacci numbers and Meru Prastara, why digit patterns stop, and why patterns that look certain can break.",{"depth":168,"revision":44,"title":921,"subtitle":922,"summary":923,"estimatedMinutes":334,"reviewed":147,"reviewMethod":148},"Pattern hunters: puzzles, projects and open questions","Magic squares from Khajuraho, tessellations, figurate numbers, cycles, olympiad problems and unsolved mysteries","Take patterns into the wider world: Lo Shu, Khajuraho and Ramanujan magic squares, tessellations and symmetry, figurate numbers, cycles of last digits and weekdays, the chessboard legend and binary, olympiad problems, patterns in music and careers, projects, and open questions like Collatz.",{"count":925,"sections":233,"levels":926},81,{"foundation":178,"core":927,"stretch":387,"challenge":233},33,{"id":929,"slug":929,"title":930,"question":931,"promise":932,"domains":933,"areas":934,"keywords":935,"status":139,"layers":955,"questionBank":976},"number-system","Number system","How do we read, write and compare really big numbers — and why do Indians and the rest of the world put commas in different places?","Place value, number names, expanded form, predecessors and successors, the Indian and International systems, and rounding — the toolkit for every large number you will ever meet.",[11],[17],[936,937,938,939,940,941,942,943,944,945,946,947,501,948,949,950,951,952,953,954],"place value","number names","expanded form","predecessor","successor","Indian number system","International number system","lakh","crore","million","billion","rounding","comparing numbers","face value","Roman numerals","arab and kharab","Hindu-Arabic numerals","binary","expanded form with powers of ten",[956,960,964,968,972],{"depth":142,"revision":44,"title":957,"subtitle":958,"summary":959,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Big numbers all around us","Ten digits, a few clever places, and every number you will ever need","Meet place value through bundles of sticks, cricket crowds and rupee notes. Learn to read and write big numbers the Indian way (lakh, crore) and the international way (million, billion), find the number just before and after, compare, round and even read Roman numerals.",{"depth":150,"revision":44,"title":961,"subtitle":962,"summary":963,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"How place value works, and how to use it","Precise rules for names, commas, comparing, forming, rounding and estimating","Exact rules for place and face value, expanded form, number names and both comma systems, with many worked examples. Then reliable methods for converting, comparing, ordering, forming numbers, rounding, estimating and Roman numerals, plus the mix-ups to avoid.",{"depth":156,"revision":44,"title":965,"subtitle":966,"summary":967,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Testing big-number ideas","Predict first, then try it: shifting digits, rollovers, rounding traps and estimation errors","Make predictions about place value and then test them: what moving a digit does, how many numbers of each size exist, when a successor gains a digit, which numbers round to the same value, how far off an estimate can be, and why 6174 keeps appearing.",{"depth":162,"revision":44,"title":969,"subtitle":970,"summary":971,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Why place value works","Powers of ten, proofs of the rules, error bounds and the Indian story of zero","Powers of ten, and proofs that the rules for comparing, rounding and forming numbers always work. Bound estimate errors, meet Sanskrit names for powers of ten, follow our digits from Brahmi to Aryabhata to Baghdad to Europe, and see metric units as place value.",{"depth":168,"revision":44,"title":973,"subtitle":974,"summary":975,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Beyond a billion, and beyond base ten","Arab, kharab and trillion; ISRO distances; binary and other bases; puzzles and projects","Stretch the number system in every direction: bigger names in both systems, real Indian large numbers from elections to Mars, number systems of the Babylonians, Maya and Egyptians, binary as a place-value system, olympiad-style puzzles, Fermi estimates, projects and open questions.",{"count":977,"sections":233,"levels":978},83,{"foundation":235,"core":338,"stretch":176,"challenge":238},{"id":980,"slug":980,"title":981,"question":982,"promise":983,"domains":984,"areas":985,"keywords":986,"status":139,"layers":1006,"questionBank":1027},"order-of-operations","Order of operations","Is 2 + 3 × 4 equal to 20 or 14 — and who decides?","Why we need an agreed order, the DMAS \u002F BODMAS rule, brackets, and how the distributive property explains it all.",[11],[17],[987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,500,1003,1004,1005],"DMAS","BODMAS","BIDMAS","PEMDAS","order of operations","brackets","simplify","expression","terms","left to right","precedence","vinculum","of","implied multiplication","four fours","24 game","calculator","distributive property","nested brackets",[1007,1011,1015,1019,1023],{"depth":142,"revision":44,"title":1008,"subtitle":1009,"summary":1010,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"One line of maths, one answer","Why 2 + 3 × 4 is 14 everywhere in the world, and the simple rules that make it so","Meet the puzzle 2 + 3 × 4 through a shopping bill, learn why everyone needs one agreed order, and practise the three rules: brackets first, then × and ÷, then + and −, with partners going left to right.",{"depth":150,"revision":44,"title":1012,"subtitle":1013,"summary":1014,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"The rule, precisely","Terms, memory words, three kinds of brackets, “of”, word problems and error-spotting","Make the order of operations precise: split expressions into terms, see why DMAS, BODMAS and PEMDAS all mean one rule, handle nested brackets and \"of\", write expressions from word problems and find mistakes in working.",{"depth":156,"revision":44,"title":1016,"subtitle":1017,"summary":1018,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Brackets under the microscope","Predict, test and explain: moving brackets, missing signs, calculators and targets","Experiment with the order of operations: count how many values brackets can make, find when brackets change nothing, test always\u002Fsometimes\u002Fnever statements, fill in missing signs, compare calculators and hit targets.",{"depth":162,"revision":44,"title":1020,"subtitle":1021,"summary":1022,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Why the rule is the rule","Repeated addition, the distributive property, powers, the vinculum, history and how machines read maths","Justify the order of operations: why × comes before + (repeated addition, the distributive property), why partners go left to right (negatives and reciprocals), where powers fit, the vinculum and history of brackets, expression trees, RPN and edge cases.",{"depth":168,"revision":44,"title":1024,"subtitle":1025,"summary":1026,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Puzzles, arguments and the wider world","Viral puzzles, four fours, the 24 game, olympiad problems, code and open questions","Take the order of operations further: why 8 ÷ 2(2 + 2) starts arguments, the four fours and 24 puzzles, olympiad problems, how code and spreadsheets differ, other notations, projects and open questions.",{"count":486,"sections":385,"levels":1028},{"foundation":284,"core":636,"stretch":786,"challenge":385},{"id":1030,"slug":1030,"title":1031,"question":1032,"promise":1033,"domains":1034,"areas":1035,"keywords":1036,"status":139,"layers":1053,"questionBank":1074},"phases-of-the-moon","Phases of the Moon","Why does the Moon change shape — and why is it never really a different shape at all?","Half the Moon is always lit. What changes is how much of the lit half faces us. Follow the monthly cycle, learn the names, and find out why the Moon is up in the daytime too.",[63],[69],[1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,551,1047,1048,1049,1050,1051,1052],"moon","phases","new moon","full moon","crescent","gibbous","waxing","waning","lunar month","synodic","tithi","Purnima","Amavasya","terminator","earthshine","far side",[1054,1058,1062,1066,1070],{"depth":142,"revision":44,"title":1055,"subtitle":1056,"summary":1057,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"The shape that changes — except it never does","Why the Moon looks different every night, and what is really going on","Meet the Moon's monthly cycle: borrowed sunlight, a ball that is always half lit, and eight named phases. Learn to tell waxing from waning tonight, find out why the Moon is up in the daytime, and kill the biggest myth in astronomy — that the phases are Earth's shadow.",{"depth":150,"revision":44,"title":1059,"subtitle":1060,"summary":1061,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Reading the Moon: one angle explains everything","Elongation, lit fraction, rise times, the terminator and why one face always faces us","Turn the phase picture into a tool. Learn to go from the Sun-Earth-Moon angle to the shape, the fraction lit and the rise and set times; find out why craters show best at quarter moon, what earthshine is, and why the Moon keeps one face towards Earth.",{"depth":156,"revision":44,"title":1063,"subtitle":1064,"summary":1065,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Put the Moon on trial","Eight investigations, from an orange and a lamp to a month-long diary","Stop reading and start checking. Build a working model of the phases with a ball and a lamp, keep a month-long moon diary, measure the fifty-minute daily lag against your own rooftop, hunt earthshine, and predict a festival moonrise well enough to announce it.",{"depth":162,"revision":44,"title":1067,"subtitle":1068,"summary":1069,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"The chase, the wobble and the brake","Deriving 29.53 days, the elastic tithi, adhik maas, eclipse rarity and the recession, from first principles","Go past the rules to the reasoning: derive the synodic month from two orbital speeds, see why a tithi stretches and shrinks, work out how often adhik maas is needed, derive eclipse rarity from the 5.1-degree tilt, and follow the torque that locked the Moon and is now pushing it away.",{"depth":168,"revision":44,"title":1071,"subtitle":1072,"summary":1073,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"To the wobble, the far side and the far future","Libration, Chandrayaan-3 and the south pole, deep time, other calendars, puzzles and open questions","Push past the settled parts of the topic: measure libration for yourself, trace the far side from Luna 3 to Chandrayaan-3, work out why total eclipses have an expiry date, compare world calendars, and take on puzzles and open questions nobody has fully answered.",{"count":486,"sections":233,"levels":1075},{"foundation":284,"core":387,"stretch":337,"challenge":826},{"id":1077,"slug":1077,"title":1078,"question":1079,"promise":1080,"domains":1081,"areas":1082,"keywords":1083,"status":139,"layers":1102,"questionBank":1123},"prime-and-composite","Prime and composite numbers","Why are some numbers impossible to split into equal groups?","Factors and multiples, prime and composite numbers, the Sieve of Eratosthenes, divisibility tests, twin primes and co-primes.",[11],[21],[1084,1085,1086,1087,1088,609,1089,1090,604,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101],"prime number","composite number","factor","multiple","twin primes","sieve of Eratosthenes","divisibility rules","factor tree","1 is neither","relatively prime","prime triplet","trial division","fundamental theorem of arithmetic","Euclid","Goldbach conjecture","Mersenne prime","perfect number","periodical cicadas",[1103,1107,1111,1115,1119],{"depth":142,"revision":44,"title":1104,"subtitle":1105,"summary":1106,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Numbers that will not make rectangles","Factors, multiples and the numbers that can only stand in a single line","Share laddoos, set out chairs and build rectangles from tiles to meet factors and multiples. Discover prime numbers, composite numbers, the odd case of 1, the Sieve of Eratosthenes, twin primes and co-primes.",{"depth":150,"revision":44,"title":1108,"subtitle":1109,"summary":1110,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Factors, primes and how to test them","Precise definitions, reliable methods and the mix-ups to avoid","Find every factor with the factor-pair method, sieve to 100 and see why you can stop at 7, test any number for primality by trial division up to its square root, use divisibility rules, and meet twin primes, co-primes and factor trees.",{"depth":156,"revision":44,"title":1112,"subtitle":1113,"summary":1114,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Hunting patterns among the primes","Predict, test and decide: which prime patterns are real, and which ones fool you?","Test claims about primes like a mathematician: how fast primes thin out, the 6-column grid, last digits, twin prime hunts, why 3, 5, 7 stands alone, co-prime experiments, patterns that break, prime deserts and numbers with the most factors.",{"depth":162,"revision":44,"title":1116,"subtitle":1117,"summary":1118,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Why it all works: proofs about primes","Unique factorisation, the square-root rule, the reasons behind divisibility tests, and Euclid’s endless primes","Prove that every number is built from primes in exactly one way, see a world where that fails, count factors from a factorisation, explain the square-root rule and every divisibility test, follow Euclid’s proof that primes never end, and prove facts about co-primes and twin primes.",{"depth":168,"revision":44,"title":1120,"subtitle":1121,"summary":1122,"estimatedMinutes":334,"reviewed":147,"reviewMethod":148},"Primes in the wild: cicadas, codes and unsolved puzzles","From insect life cycles and online banking to record primes, perfect numbers and problems nobody has solved","Take primes into the world: prime cicada cycles, the prime-based codes behind online payments, Mersenne primes and perfect numbers, Goldbach’s and the twin prime conjectures, Indian mathematicians, other number bases, olympiad puzzles and projects.",{"count":173,"sections":233,"levels":1124},{"foundation":235,"core":236,"stretch":176,"challenge":233},{"id":1126,"slug":1126,"title":1127,"question":1128,"promise":1129,"domains":1130,"areas":1131,"keywords":1132,"status":139,"layers":1153,"questionBank":1174},"properties-of-numbers","Properties of numbers","Why does 7 × 8 equal 8 × 7, and how can such rules make mental maths easy?","The closure, commutative, associative and distributive properties, the special roles of 0 and 1, and how they turn hard calculations into easy ones.",[11],[17],[1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152],"commutative","associative","distributive","closure","identity","additive identity","multiplicative identity","natural numbers","whole numbers","number line","mental maths","properties of zero","properties of one","division by zero","even and odd","counterexample","always sometimes never","area model","integers","clock arithmetic",[1154,1158,1162,1166,1170],{"depth":142,"revision":44,"title":1155,"subtitle":1156,"summary":1157,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Rules that numbers always follow","Turn-around facts, friendly groups, breaking apart and the magic of 0 and 1","Meet the properties of numbers through chairs, laddoos, kirana bills and socks: why 4 × 6 = 6 × 4, why you can add in any order, how breaking numbers apart makes sums easy, and what 0 and 1 do.",{"depth":150,"revision":44,"title":1159,"subtitle":1160,"summary":1161,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"The properties, precisely","Closure, commutative, associative and distributive laws, and the special numbers 0 and 1","State each property of whole numbers exactly, in words and with letters; see why it holds for + and × but fails for − and ÷; learn why division by zero is undefined; and use the properties for fast, reliable mental maths.",{"depth":156,"revision":44,"title":1163,"subtitle":1164,"summary":1165,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Always, sometimes or never?","Predict, test and explain: counterexamples, grouping gaps, parity patterns and shortcut showdowns","Test claims about whole numbers the way mathematicians do: predict, hunt for counterexamples, measure how badly subtraction and division fail to swap or regroup, discover patterns and shortcuts, and explain why the true ones must be true.",{"depth":162,"revision":44,"title":1167,"subtitle":1168,"summary":1169,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Why the rules must be true","Proofs with arrays and boxes, the distributive law behind every method, zero through history, and the road to algebra","Prove the commutative, associative and distributive laws for every whole number, see why long multiplication and divisibility tests work, show why division by zero would make 0 = 1, prove parity facts with letters, and meet the properties as the rules of algebra.",{"depth":168,"revision":44,"title":1171,"subtitle":1172,"summary":1173,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Properties beyond the whole numbers","Integers, fractions, clocks, computers, puzzles and the problems nobody has solved","Take the properties into new worlds: integers and fractions that repair closure, clock arithmetic, non-commutative everyday actions, rounding inside computers, olympiad puzzles built on parity and the distributive law, projects to try and open questions like Goldbach.",{"count":1175,"sections":385,"levels":1176},85,{"foundation":237,"core":212,"stretch":284,"challenge":174},{"id":1178,"slug":1178,"title":1179,"question":1180,"promise":1181,"domains":1182,"areas":1183,"keywords":1184,"status":139,"layers":1204,"questionBank":1225},"shape-and-space","Shape and space","What makes a square a square, and how many edges does a cube really have?","2D shapes and their properties, 3D solids and their faces, edges and vertices, nets, views from different sides, and symmetry.",[11],[29],[1185,1186,1187,1188,1189,1190,1191,708,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203],"polygon","triangle","quadrilateral","circle","diagonals","cube","cuboid","pyramid","faces edges vertices","net","views","line symmetry","rotational symmetry","Euler","Platonic solids","tangram","tessellation","2D","3D",[1205,1209,1213,1217,1221],{"depth":142,"revision":44,"title":1206,"subtitle":1207,"summary":1208,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Shapes all around us","Flat shapes, solid shapes, and how to count, fold, view and mirror them","Meet 2D and 3D shapes through things you know: carrom boards, dice, laddoos, honeycombs, the Ashoka Chakra and the Taj Mahal. Learn to name polygons, count faces, edges and corners, unfold a box into a net, and find lines of symmetry.",{"depth":150,"revision":44,"title":1210,"subtitle":1211,"summary":1212,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Naming shapes precisely","Definitions, properties and the mix-ups they clear up","Give every shape an exact definition: polygons and diagonals, triangles by sides and angles, the quadrilateral family tree, the parts of a circle, perimeter, prisms and pyramids, nets, views and line symmetry, with worked examples and common mix-ups.",{"depth":156,"revision":44,"title":1214,"subtitle":1215,"summary":1216,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Test it, fold it, count it","Predictions and experiments with diagonals, triangles, nets, views, symmetry and π","Predict, then test: how fast diagonals multiply, which three sticks make a triangle, what polygon angles add up to, which statements are always true, the F + V − E pattern, which six-square shapes fold into a cube, symmetry in letters, measuring π and which shapes tile a floor.",{"depth":162,"revision":44,"title":1218,"subtitle":1219,"summary":1220,"estimatedMinutes":472,"reviewed":147,"reviewMethod":148},"Why shapes behave as they do","Proofs, edge cases and history: diagonals, angle sums, inequality, Euler and symmetry","Turn patterns into proofs: the diagonal formula, why angles add to 180° and (n − 2) × 180°, the triangle inequality, quadrilateral inheritance, why wheels are round, a sketch proof of Euler’s formula and where it fails, cube-net rules, symmetry orders, and the history of π.",{"depth":168,"revision":44,"title":1222,"subtitle":1223,"summary":1224,"estimatedMinutes":226,"reviewed":147,"reviewMethod":148},"Projects, puzzles and the wider world of shape","Platonic solids, all 11 cube nets, rotational symmetry, tilings, olympiad problems and open questions","Build the five Platonic solids and hunt all 11 cube nets, design rangoli with rotational symmetry, explore tangram paradoxes and semi-regular tilings, count a football, see geometry in Indian monuments and nature, solve olympiad-style problems, and meet questions still unsolved.",{"count":232,"sections":233,"levels":1226},{"foundation":284,"core":636,"stretch":284,"challenge":238},{"id":1228,"slug":1228,"title":52,"question":1229,"promise":1230,"domains":1231,"areas":1232,"keywords":1233,"status":139,"layers":1252,"questionBank":1273},"sound","Why does a drum you cannot touch still reach your ears?","Sound is a vibration travelling through air, water and solids. Learn what makes a sound high or low, loud or soft, why space is silent, and how your ears turn shaking air into music.",[41],[51],[1228,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251],"vibration","wave","pitch","frequency","amplitude","loudness","decibel","echo","medium","ultrasound","hertz","eardrum","resonance","speed of sound","noise","music","sonar","vacuum",[1253,1257,1261,1265,1269],{"depth":142,"revision":44,"title":1254,"subtitle":1255,"summary":1256,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Everything that sounds is shaking","Find the vibration behind every sound, follow it to your ear, and learn why space is silent","Feel your own throat buzz, watch a tuning fork throw water, and follow the shaking from a tabla skin across the room to the hair cells in your ear. Meet pitch, loudness, echoes and the thunder rule, and find out why nothing at all can be heard in space.",{"depth":150,"revision":44,"title":1258,"subtitle":1259,"summary":1260,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"Compressions, rarefactions and the wave equation","What is really travelling, how fast, and how the ear turns it into a signal","See what a sound wave actually is: a train of squashed and stretched air marching outwards. Meet longitudinal waves on a slinky, the equation v = f × λ, why steel beats air by seventeen times, how decibels multiply, and the engineering of the human ear.",{"depth":156,"revision":44,"title":1262,"subtitle":1263,"summary":1264,"estimatedMinutes":212,"reviewed":147,"reviewMethod":148},"Predict it, try it: resonance, echoes and everyday sound technology","Test resonance with a swing and a singing glass, then use echoes the way sonar, ultrasound, bats and dolphins do","Push a swing at the wrong rhythm, make a wine glass sing, and find the sympathetic strings that ring inside a sitar untouched. Time an echo the way sonar and a hospital scanner do, compare a bat's call with a dolphin's, and see why India's noise rules are stricter near a hospital than in a market.",{"depth":162,"revision":44,"title":1266,"subtitle":1267,"summary":1268,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Why resonance, harmonics and reverberation work the way they do","Damping, aeroelastic flutter, singing granite pillars, harmonics and a physicist with 300 cushions","Find out why resonance cannot grow forever, why two famous bridge wobbles had different causes, and why 56 granite pillars at Hampi ring with different notes. Meet Wallace Sabine, who found the reverberation formula with borrowed cushions, and the arithmetic of combining decibels.",{"depth":168,"revision":44,"title":1270,"subtitle":1271,"summary":1272,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Doppler shifts, digital recording and listening to the Earth","The physics of a passing siren, why your recorded voice sounds strange, and how earthquakes get located","Work out how much a siren's pitch shifts as it passes, find out why your recorded voice sounds strange (a real anatomical reason), and see why 44,100 Hz was not an arbitrary choice. Try two projects, solve combined puzzles, and use sound's own reasoning to locate an earthquake.",{"count":687,"sections":233,"levels":1274},{"foundation":388,"core":927,"stretch":337,"challenge":233},{"id":560,"slug":560,"title":1276,"question":1277,"promise":1278,"domains":1279,"areas":1280,"keywords":1281,"status":139,"layers":1298,"questionBank":1319},"Tides","Why does the sea climb up the beach and slide back, twice a day, forever?","The Moon's pull stretches the ocean into two bulges and Earth turns through them. Learn why there are two high tides a day, why they arrive later each day, and what makes a spring tide.",[63],[73],[1282,1283,1284,1285,1286,1287,1288,541,1289,1290,1291,1292,1293,1294,1295,1296,1297],"tide","high tide","low tide","spring tide","neap tide","tidal range","bulge","Moon","Sun","tidal bore","estuary","tide table","coast","fishing","Chandipur","Hooghly",[1299,1303,1307,1311,1315],{"depth":142,"revision":44,"title":1300,"subtitle":1301,"summary":1302,"estimatedMinutes":338,"reviewed":147,"reviewMethod":148},"Tides: the sea's daily rise and fall","Why the whole ocean leans towards the Moon, twice a day, forever","Meet the tide: not a wave but the whole sea rising and falling. Find out how the Moon's pull makes two bulges, why most coasts get two high tides a day, why the tide is 50 minutes later each day, and what spring and neap tides are.",{"depth":150,"revision":44,"title":1304,"subtitle":1305,"summary":1306,"estimatedMinutes":166,"reviewed":147,"reviewMethod":148},"How the Moon builds two bulges","Difference, not strength: the mechanism behind every tide","Work out why a pull towards the Moon makes a bulge away from it, where 24 h 50 min comes from, why the Sun's tide is only 46% of the Moon's, and why the same Moon gives Kochi one metre and Bhavnagar ten.",{"depth":156,"revision":44,"title":1308,"subtitle":1309,"summary":1310,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Investigate: predicting, classifying and staying safe","Test the ideas from Understand against a real tide table, real coasts and real disasters","Predict and check a day of tide heights, learn to tell semidiurnal, diurnal and mixed tides apart, meet the Hooghly bore and storm surges, see how tidal power and INCOIS's predictions work, and test the funnelling and resonance ideas with real numbers.",{"depth":162,"revision":44,"title":1312,"subtitle":1313,"summary":1314,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Deepen: the mathematics and history behind a tide table","Newton, Laplace, harmonic waves, closed-pipe resonance, and the physics of a bore","Trace the two-hundred-year path from Newton's equilibrium theory to Laplace's ocean waves and Kelvin's tide-predicting machine, meet the harmonic constituents that a real tide is built from, derive why a bay resonates at a quarter wavelength, and quantify Earth's own solid and atmospheric tides.",{"depth":168,"revision":44,"title":1316,"subtitle":1317,"summary":1318,"estimatedMinutes":217,"reviewed":147,"reviewMethod":148},"Extend: deep time, deep space, and open questions","Tidal friction across hundreds of millions of years, tides on other worlds, and what is still unknown","Follow tidal friction from a subtle offset in Earth's bulge to a shorter Cretaceous day, a measurably receding Moon, tidal heating on Io, Europa and Enceladus, and a set of open questions and careers built on this one idea.",{"count":1320,"sections":385,"levels":1321},71,{"foundation":786,"core":283,"stretch":284,"challenge":174},[1323,1326,1328,1331,1333,1335,1337,1339,1341,1343,1345,1347,1350,1353,1355,1357,1359,1361,1363,1365,1367,1369,1371,1373,1375,1377,1379,1381,1383,1385,1387,1389,1391,1393,1395,1397,1399,1401,1403,1405,1407,1409,1411,1413,1415,1417,1419,1421,1423,1425,1427,1429],{"from":929,"to":489,"relation":1324,"reason":1325},"helps_understand","Place value is what makes column addition, carrying and long division work.",{"from":929,"to":287,"relation":1324,"reason":1327},"Reading, comparing and rounding numbers comes first when you sort data and round a mean.",{"from":929,"to":877,"relation":1329,"reason":1330},"related_to","Place-value charts are full of patterns: each place is ten times the one to its right.",{"from":1126,"to":489,"relation":1324,"reason":1332},"Commutative, associative and distributive properties are the shortcuts behind fast, accurate calculation.",{"from":1126,"to":980,"relation":1324,"reason":1334},"The distributive property explains why multiplication is done before addition and how brackets change a result.",{"from":1126,"to":877,"relation":1329,"reason":1336},"Many number patterns — like the sum of consecutive odd numbers — are properties of numbers in disguise.",{"from":489,"to":980,"relation":1324,"reason":1338},"Once each operation is reliable, the next question is which one to do first when several appear together.",{"from":489,"to":1077,"relation":1324,"reason":1340},"Testing whether a number is prime is just careful division: does anything divide it exactly?",{"from":489,"to":287,"relation":1324,"reason":1342},"Finding a mean means adding every value and dividing by how many there are.",{"from":980,"to":877,"relation":1329,"reason":1344},"A pattern rule such as 3 × n + 1 is an expression — you need the order of operations to use it.",{"from":1077,"to":588,"relation":1324,"reason":1346},"Prime factorisation is the fastest route to both the HCF and the LCM.",{"from":1077,"to":877,"relation":1348,"reason":1349},"contrasts_with","Primes famously refuse to follow a simple pattern, unlike even numbers, squares or multiples.",{"from":588,"to":877,"relation":1351,"reason":1352},"applied_in","Two repeating cycles line up again after their LCM — the pattern behind blinking lights and bus timetables.",{"from":588,"to":1178,"relation":1351,"reason":1354},"The largest square tile that fits a rectangular floor exactly has a side equal to the HCF of its length and width.",{"from":877,"to":1178,"relation":1329,"reason":1356},"Growing shape patterns — matchstick squares, dot triangles — are geometry and number at the same time.",{"from":1178,"to":739,"relation":1329,"reason":1358},"Every polygon is built from line segments, and its sides can be parallel or perpendicular.",{"from":1178,"to":180,"relation":1329,"reason":1360},"The corners of shapes are angles: a square has four right angles and a triangle's angles add to 180°.",{"from":739,"to":180,"relation":1324,"reason":1362},"An angle is two rays that share an end point; intersecting lines make angle pairs.",{"from":739,"to":828,"relation":1324,"reason":1364},"Constructions rely on drawing straight lines, perpendiculars and bisectors accurately.",{"from":180,"to":828,"relation":1324,"reason":1366},"Knowing angle types and pairs tells you what you are measuring and checks if your construction is sensible.",{"from":180,"to":287,"relation":1351,"reason":1368},"In a pie chart each slice's angle shows a share of the data: 360° stands for the whole.",{"from":828,"to":1178,"relation":1351,"reason":1370},"Drawing accurate triangles, squares and regular polygons needs measured or constructed angles.",{"from":287,"to":390,"relation":1351,"reason":1372},"A family's monthly electricity use varies; the mean, median and range of a year of bills show what is typical.",{"from":929,"to":390,"relation":1351,"reason":1374},"Power stations are rated in megawatts and India uses lakhs of crores of units a year: reading such numbers needs place value and the Indian system.",{"from":489,"to":390,"relation":1351,"reason":1376},"An electricity bill is units × rate per unit, plus fixed charges, minus subsidies — all four operations in one sheet of paper.",{"from":180,"to":390,"relation":1351,"reason":1378},"A generator's coil turns through 360° every cycle — 50 full turns a second on India's 50 Hz supply.",{"from":1077,"to":390,"relation":1351,"reason":1380},"The encryption that protects smart meters and grid control systems relies on the difficulty of factorising huge numbers into primes.",{"from":690,"to":340,"relation":1324,"reason":1382},"An eclipse is a shadow, and shadows need light that travels in straight lines.",{"from":690,"to":1030,"relation":1324,"reason":1384},"The Moon has no light of its own: we see the half of it the Sun is lighting.",{"from":690,"to":112,"relation":1351,"reason":1386},"The eye is a lens, a screen and a shutter — optics built out of living tissue.",{"from":690,"to":1228,"relation":1348,"reason":1388},"Both travel as waves and carry energy, but light needs no material and races a million times faster than sound.",{"from":1228,"to":112,"relation":1351,"reason":1390},"The ear turns shaking air into signals a nerve can carry: a drum, three tiny bones and a spiral of fluid.",{"from":541,"to":1030,"relation":1324,"reason":1392},"Gravity is what keeps the Moon in the orbit that produces the monthly cycle of phases.",{"from":541,"to":560,"relation":1324,"reason":1394},"Tides are gravity made visible: the Moon pulls the near ocean harder than the far ocean.",{"from":541,"to":340,"relation":1324,"reason":1396},"Eclipses happen only because the Sun, Earth and Moon move on fixed gravitational paths we can predict.",{"from":1030,"to":340,"relation":1324,"reason":1398},"Eclipses can only happen at new moon or full moon — the two phases where the three bodies line up.",{"from":1030,"to":560,"relation":1329,"reason":1400},"Spring and neap tides follow the phases: the biggest tides come at new and full moon.",{"from":112,"to":240,"relation":1324,"reason":1402},"Once you know where each organ sits, you can follow how they pass work to each other.",{"from":240,"to":541,"relation":1329,"reason":1404},"Bones, muscles and blood pressure are all built for a life spent pulling against Earth's gravity — which is why astronauts weaken in orbit.",{"from":439,"to":638,"relation":1324,"reason":1406},"The empires that grew out of the voyages shaped the constitution and the freedoms India wrote for itself afterwards.",{"from":439,"to":560,"relation":1351,"reason":1408},"Sailing ships left harbour on the tide, and monsoon winds and currents set the whole calendar of Indian Ocean trade.",{"from":439,"to":1030,"relation":1351,"reason":1410},"Before clocks and satellites, the Moon and stars were how a navigator knew where they were.",{"from":638,"to":287,"relation":1351,"reason":1412},"A census, an election result and a budget are all data: counted, summarised and argued over.",{"from":638,"to":929,"relation":1351,"reason":1414},"Election results and budgets are read in lakhs and crores — place value with real consequences.",{"from":690,"to":390,"relation":1329,"reason":1416},"A bulb, an LED and a solar panel are all conversions between electricity and light.",{"from":1228,"to":390,"relation":1329,"reason":1418},"Microphones and speakers turn sound into current and current back into sound.",{"from":439,"to":1178,"relation":1351,"reason":1420},"Maps, globes and navigation are geometry: a round Earth flattened onto paper without lying too much.",{"from":340,"to":180,"relation":1351,"reason":1422},"Whether an eclipse is total or partial comes down to angles: the Moon's tilted orbit and the apparent size of two discs.",{"from":560,"to":287,"relation":1351,"reason":1424},"A tide table is a data set: measure the water twice a day for years, and the pattern lets you predict it.",{"from":112,"to":287,"relation":1351,"reason":1426},"Heart rate, height and lung capacity across a class are real data to collect, average and compare.",{"from":541,"to":489,"relation":1351,"reason":1428},"Weight on another world is your mass times that world's gravity — multiplication with an astonishing answer.",{"from":240,"to":287,"relation":1351,"reason":1430},"Pulse and breathing rate before and after exercise are real class data to average, compare and graph.",[],[],[],{"layer":1435,"contentHash":2487,"dependencyHashes":2488,"approval":2489,"releaseId":2493,"sources":2494},{"schemaVersion":44,"conceptId":789,"locale":1436,"depth":168,"revision":44,"title":820,"subtitle":821,"summary":822,"objectives":1437,"estimatedMinutes":805,"plate":1441,"blocks":1467,"sourceIds":2482,"reviewStatus":2483,"authoring":2484},"en",[1438,1439,1440],"Learners can explain how magnetic domains create stronger or weaker magnetism using a labelled model.","Learners can design a fair-test home investigation comparing methods of making and destroying magnetism.","Learners can analyse why copper and aluminium are non-magnetic despite being metals.",{"title":1442,"rows":1443},"Extend",[1444,1446,1449,1452,1455,1458,1461,1464],{"label":1445,"value":1442},"Depth",{"label":1447,"value":1448},"Reading time","About 90 minutes",{"label":1450,"value":1451},"Chapters","11",{"label":1453,"value":1454},"Prior knowledge","Poles, field lines, compass, Earth as magnet",{"label":1456,"value":1457},"Units used","Ampere (A), Tesla (T), degree (°), metre (m), rupee (₹)",{"label":1459,"value":1460},"Time needed","35-40 minutes of reading, plus two home activities",{"label":1462,"value":1463},"Safety note","Neodymium magnets can pinch skin; never swallow",{"label":1465,"value":1466},"Key model","Magnetic domains as aligned regions",[1468,1472,1478,1481,1487,1497,1515,1520,1523,1528,1531,1552,1556,1559,1570,1574,1588,1621,1626,1629,1640,1644,1682,1693,1696,1722,1727,1730,1747,1751,1764,1767,1789,1794,1797,1812,1816,1836,1846,1879,1884,1909,1912,1922,1927,1930,1959,1963,1966,1969,1974,1977,2000,2010,2015,2034,2047,2069,2072,2077,2080,2092,2112,2116,2119,2132,2154,2159,2162,2166,2186,2193,2196,2205,2216,2221,2224,2246,2250,2260,2289,2294,2297,2366,2396,2405,2409,2412,2476],{"id":1469,"type":1470,"markdown":1471},"prose-1","prose","You have held a magnet, watched it pull a pin across a table, or used a compass to find north. But have you ever asked why a steel spoon becomes magnetic while a copper coin stays indifferent, or why heating a magnet in a tandoor can ruin it?\n\nThis lesson takes you inside the material: the tiny magnetic domains that act like miniature compass needles locked inside iron and steel. You will learn how to make and destroy a magnet deliberately, build your own electromagnet with a nail and wire, and see why MRI machines and maglev trains depend on magnetism that can be switched on and off. The ideas build on what you have already explored — poles, fields, attraction and repulsion — and stretch toward the physics and engineering that await in higher classes.",{"id":1473,"type":1474,"title":1475,"eyebrow":1476,"navLabel":1477},"chapter-2","chapter","The Weightlifter and the Nail: Why Strength Varies","Chapter 01","Strong and weak magnets",{"id":1479,"type":1470,"markdown":1480},"prose-3","Walk into any kitchen in India during summer and you will probably see a fridge magnet holding up a Kirana bill, a school timetable or a reminder about mango pickle delivery. That magnet is small — often smaller than a two-rupee coin — yet it clings on through door slams, power cuts and the vibrations of the water filter. Now visit a scrap yard near an industrial area. An electromagnet the size of a small car picks up crushed cars and drops them into a shredder. Both objects are \"magnets,\" but their strength differs by thousands of times. What decides how strong a magnet is? Size helps, but it is not the full story. A thin neodymium disc no wider than your thumbnail can lift fifty paper clips, while a chunky ceramic fridge magnet of the same diameter may manage only five. In this chapter we set up a puzzle: two identical-looking steel bars sit on a table. One lifts nails; the other does nothing. They are the same material, the same mass, the same shape. Something inside must be arranged differently. We will measure strength in a simple way, compare surprising examples, and leave you with a question that the next chapter answers.\n\n## Measuring strength with everyday objects\n\nScientists measure magnetic force in newtons, but at home or in a school lab you can use a fair comparison: count how many identical iron objects a magnet lifts before one falls. A \"paper-clip test\" is crude, but it is honest. You must use the same batch of clips, the same surface, and the same person placing them. We will call this a **lift count**. It is a model — a simplified stand-in for real magnetic force — and like all models it has limits. A very strong magnet may twist the clips together so they hang as a chain, which changes the rules. For now, accept the model and notice what it reveals.",{"id":1482,"type":1483,"variant":1484,"title":1485,"markdown":1486},"callout-4","callout","misconception","Bigger is always stronger","Many students assume a larger magnet is automatically stronger. The table above shows a neodymium disc two-thirds the width of the ceramic magnet yet roughly ten times stronger. Strength depends on the **material** the magnet is made from and how its internal structure is aligned, not merely on how much space it occupies. A large block of unmagnetised iron is weaker than a tiny neodymium disc.",{"id":1488,"type":1489,"title":1490,"problem":1491,"steps":1492},"worked-example-5","worked_example","Why the Two Steel Bars Behave Differently","Ravi finds two steel bars in his grandfather's toolbox. They look identical: 150 mm long, 12 mm diameter, same weight, same silvery colour. Bar A picks up ten small iron nails. Bar B picks up none. Both are steel. Why does only one act as a magnet?",[1493,1494,1495,1496],"Check for external clues: Bar A has a small painted dot near one end; Bar B does not. Marks often show that someone deliberately magnetised an object.","Test with a compass needle: Bring each bar near a compass. Bar A deflects the needle sharply; Bar B causes only mild disturbance, no stronger than an unmagnetised steel rod would.","Suspend each bar on a string: Bar A turns to align roughly north-south. Bar B drifts randomly. A freely rotating magnet aligns with Earth's magnetic field; ordinary steel does not.","Conclusion: Both bars are *magnetic materials* (steel contains iron), but only Bar A has its internal magnetic regions aligned so that their effects add up. Bar B's regions cancel out. We call these regions **domains**; they are the subject of the next chapter.",{"id":1498,"type":1499,"prompt":1500,"options":1501,"explanation":1514},"prediction-6","prediction","You have three mystery objects: a solid iron nail, a solid aluminium rod of the same size, and a steel sewing needle. You touch each to a strong permanent magnet for ten seconds, then lift it away and try to pick up iron filings. What do you predict will happen?",[1502,1505,1508,1511],{"id":1503,"label":1504},"a","Only the steel needle picks up filings; the others do nothing.",{"id":1506,"label":1507},"b","The iron nail and steel needle pick up filings; the aluminium rod does nothing.",{"id":1509,"label":1510},"c","All three pick up filings because they are all metals.",{"id":1512,"label":1513},"d","None pick up filings because only the original magnet attracts filings.","The correct answer is (b). Both iron and steel are magnetic materials: they contain iron and can be temporarily magnetised by the permanent magnet's field. Aluminium is a metal but not a magnetic material; its internal structure does not respond this way. The steel needle, being harder, may retain some magnetism longer. The iron nail is soft iron: it magnetises easily but loses it quickly. This is a first hint that *material type* and *internal arrangement* both matter.",{"id":1516,"type":1483,"variant":1517,"title":1518,"markdown":1519},"callout-7","model_limit","The \"lift count\" is only a model","Counting paper clips gives a useful comparison between similar magnets, but it is not a direct measure of magnetic field strength. Field strength (or magnetic flux density) is measured in teslas (T) with specialised instruments. A small neodymium magnet may have a surface field of 1.2 T, while a large ceramic magnet might reach only 0.3 T. The lift-count model fails when magnets have very different shapes: a thin, wide magnet spreads its field differently from a thick, narrow one, even at the same tesla rating. Use lift counts for rough classroom comparisons, not for engineering decisions.",{"id":1521,"type":1470,"markdown":1522},"prose-8","## The puzzle that remains\n\nWe have seen that magnet strength varies enormously for reasons invisible from the outside. We have seen that identical steel bars can behave like opposites. The next step is to look inside the material. What could be arranged differently in Bar A and Bar B? Early scientists imagined tiny compass needles locked inside iron. Modern physics replaces \"needles\" with **magnetic domains** — regions where billions of atomic magnets line up together. In an unmagnetised bar, these domains point every which way; their effects cancel. In a magnet, they point together. The following chapters will build this picture step by step, add the idea of electromagnets, and show how magnetism shapes technology from ISRO's torque rods to the maglev trains engineers dream of for India.",{"id":1524,"type":1474,"title":1525,"eyebrow":1526,"navLabel":1527},"chapter-9","Magnetic Domains: The Hidden Compass Needles","Chapter 02","Inside the metal",{"id":1529,"type":1470,"markdown":1530},"prose-10","If you break a bar magnet in half, you do not get one north piece and one south piece. You get two smaller magnets, each with its own north and south pole. Break one of those again, and the same thing happens. This continues down to tiny scales — as if every bit of iron carries something inside it that wants to point like a compass needle. Physicists call these invisible regions **magnetic domains**: clusters of atoms that behave like miniature magnets. In this chapter we will see how domains explain why an iron nail sticks to a magnet while a copper coin does not, why some steel retains magnetism and soft iron does not, and why heating or hammering can destroy what stroking built.\n\nAn **atom** is the smallest unit of a chemical element; it has a central nucleus and electrons moving around it. In iron, nickel, cobalt and some alloys, the electrons in the outer shells of certain atoms spin in a way that makes each atom act like a tiny magnet. A **domain** is a region inside the material where billions of these atomic magnets point the same way. In an unmagnetised nail, these domains point every which way — their tiny fields cancel one another, so the nail does not attract anything. When an external magnetic field is applied, domains that point along the field grow; others shrink or rotate. Once most domains align, their fields add up and the nail becomes a magnet itself. This is the **domain model**, a simplified picture accepted in school-level physics. Real domains are smaller and more complex, but the principle is sound.",{"id":1532,"type":1533,"tone":1534,"items":1535},"spec-11","spec","copper",[1536,1540,1544,1548],{"label":1537,"big":1538,"value":1539},"Atoms per domain","~10¹⁷","About one hundred million billion atoms in a typical iron domain, each acting as a tiny magnet.",{"label":1541,"big":1542,"value":1543},"Domain width","~0.01 mm","Small enough to need a microscope, large enough to contain vast numbers of atoms.",{"label":1545,"big":1546,"value":1547},"Elements with domains","3","Iron, nickel and cobalt are the common ferromagnetic elements; some alloys and rare-earth compounds also qualify.",{"label":1549,"big":1550,"value":1551},"Electron spin","½ ℏ","A quantum property; we treat it here as an internal rotation that gives each electron a tiny magnetic field.",{"id":1553,"type":1483,"variant":1517,"title":1554,"markdown":1555},"callout-12","A labelled simplification","The domain model is not a photograph. You cannot look inside iron with an ordinary microscope and see little arrows. Scientists infer domains from how materials behave and from special imaging techniques. The model is useful because it predicts and explains: why magnetisation can be partial, why magnets have poles, and why heat destroys magnetism. We use it as a **model** — a deliberate simplification — not as literal truth.",{"id":1557,"type":1470,"markdown":1558},"prose-13","**Soft iron** loses magnetism quickly because its domains return toward random orientations once the external field disappears. **Hard steel**, **alnico** and **neodymium alloys** hold their alignment because crystal structure and impurities pin domain walls in place. This difference matters for engineering: transformer cores use soft iron so magnetism switches with the alternating current, while loudspeaker magnets use hard materials so the field stays constant. The ease with which domains align is called **permeability**; the tendency to stay aligned is called **retentivity** or **remanence**.",{"id":1560,"type":1489,"title":1561,"problem":1562,"steps":1563},"worked-example-14","Why does a steel spoon keep magnetism and a soft-iron nail does not?","A student strokes both a steel spoon and a soft-iron nail with the same bar magnet, twenty times in the same direction. The nail lifts more paper clips immediately after stroking, but after ten minutes the nail has lost most of its strength while the spoon still attracts small objects. Use the domain model to explain.",[1564,1565,1566,1567,1568,1569],"In the soft-iron nail, domains align easily under the bar magnet's field. The nail becomes strongly magnetised quickly.","Soft iron has low retentivity: domain walls are mobile and internal stresses are few, so thermal motion randomises domains again once the external field is gone.","In the steel spoon, domains also align during stroking, but carbon atoms and crystal defects in steel trap domain walls in their new positions.","Because steel has higher retentivity, most domains remain aligned after the bar magnet is removed. The spoon keeps a weaker but stable magnetic field.","The nail's immediate strength was higher because more domains aligned under the same external field — soft iron has higher permeability — but this same mobility causes rapid loss.","The spoon wins for permanence; the nail wins for temporary, switchable magnetism. Both behaviours are useful in different devices.",{"id":1571,"type":1483,"variant":1484,"title":1572,"markdown":1573},"callout-15","All metals are magnetic","Many students assume metals and magnetism go together because iron is both metallic and magnetic. In fact, **copper, aluminium, gold and silver are not ferromagnetic**: their electrons do not form domains that can align this way. A strong magnet will not stick to a copper pipe or an aluminium window frame. Magnetism is a property of specific electron configurations, not of the metallic state itself.",{"id":1575,"type":1499,"prompt":1576,"options":1577,"explanation":1587},"prediction-16","You heat an iron magnet to 800 °C and then cool it. What do you predict about its magnetism, and why?",[1578,1581,1584],{"id":1579,"label":1580},"stronger","It becomes stronger because heat lets domains move more freely into alignment.",{"id":1582,"label":1583},"weaker","It becomes weaker because thermal vibration randomises domains above a critical temperature.",{"id":1585,"label":1586},"unchanged","It stays the same because cooling restores the original domain pattern.","Correct: weaker (and likely demagnetised). Every ferromagnetic material has a **Curie temperature** — 770 °C for pure iron — above which thermal vibration overwhelms the forces keeping domains aligned. The material becomes paramagnetic: individual atoms still respond to fields, but domains do not persist. Cooling without an external field does not restore the old pattern; domains form randomly. This is why blacksmiths can accidentally demagnetise tools, and why industrial demagnetisers sometimes use heating.",{"id":1589,"type":1590,"title":1591,"questions":1592},"quiz-17","quiz","Check your understanding of domains",[1593,1607],{"itemId":1594,"prompt":1595,"options":1596,"correct":1601,"why":1606},"magnets.q001","In an unmagnetised iron bar, what is true about the magnetic domains?",[1597,1600,1603],{"id":1598,"label":1599},"all-north","They all point north.",{"id":1601,"label":1602},"random","They point in random directions.",{"id":1604,"label":1605},"absent","They do not exist until the bar is magnetised.","Domains always exist in ferromagnetic materials. In the unmagnetised state their directions are random, so net magnetism is zero. Curiosity: Textbook of Science for Grade 6, Chapter 4 calls this the natural state before magnetisation.",{"itemId":1608,"prompt":1609,"options":1610,"correct":1615,"why":1620},"magnets.q002","Which material property describes how easily domains align with an external field?",[1611,1614,1617],{"id":1612,"label":1613},"retentivity","Retentivity",{"id":1615,"label":1616},"permeability","Permeability",{"id":1618,"label":1619},"conductivity","Conductivity","Permeability measures how readily magnetic flux passes through a material — equivalent to how easily domains align. Retentivity measures how well they stay aligned afterwards. Conductivity is about electric current, not magnetism.",{"id":1622,"type":1474,"title":1623,"eyebrow":1624,"navLabel":1625},"chapter-18","A Worked Case: Why the Spoon Sticks and the Coin Does Not","Chapter 03","Steel versus copper",{"id":1627,"type":1470,"markdown":1628},"prose-19","Open your kitchen drawer. You will find a steel spoon, a copper-bottomed pan, an aluminium foil roll, and some coins. If you hold a refrigerator magnet near each one, only the spoon jumps up to greet it. The foil and the coins simply sit there, indifferent. This is not because the magnet is \"tired\" or because the spoon is heavier. The difference lies deep inside the metal, in how its atoms organise their tiny magnetic selves—what we now call **magnetic domains**. In this chapter we will work through one careful case, step by step, so you can see exactly why the spoon sticks and the coin does not, and why copper and aluminium behave so differently from iron even though they are all shiny metals.",{"id":1630,"type":1489,"title":1631,"problem":1632,"steps":1633},"worked-example-20","The Spoon, the Coin and the Copper Wire","Riya has a strong neodymium magnet, a steel spoon, a copper wire, an aluminium foil strip, and a ₹5 coin (nickel-brass). She tests each object. Only the spoon is attracted. Explain why, using the domain model and the electron behaviour of each metal.",[1634,1635,1636,1637,1638,1639],"Identify the metals present. The spoon is **steel**, an alloy of iron with a small amount of carbon. The copper wire is pure **copper**. The foil is **aluminium**. The coin is a **nickel-brass alloy** (mostly copper and zinc, with a thin nickel layer for appearance).","Recall the domain rule: a material is strongly attracted to a magnet only if it contains atoms that can form **magnetic domains**—regions where billions of atomic magnets line up together.","Steel contains **iron**. Iron atoms have unpaired electrons whose spins create tiny atomic magnets. In steel, large domains can form and align with an external magnetic field. The magnet pulls on these aligned domains, so the spoon sticks.","Copper atoms have electron spins that pair up neatly. There are no unpaired spins to create atomic magnets, and therefore **no domains can form**. Copper is **diamagnetic**—it actually weakly resists a magnetic field, though the effect is far too small to feel.","Aluminium has one unpaired electron, but the atomic arrangement is such that aluminium does not form lasting domains either. It is **paramagnetic**—it very weakly aligns with a field, but the attraction is about a hundred thousand times weaker than iron. You cannot feel it with a fridge magnet.","The ₹5 coin is mainly copper and zinc (brass) with a thin nickel coating. The bulk material cannot form domains, and the nickel layer is too thin to give a noticeable pull against a small magnet.",{"id":1641,"type":1483,"variant":1484,"title":1642,"markdown":1643},"callout-21","\"All metals stick to magnets\"","Many children predict that copper wires should be attracted because copper is used in electrical wiring and \"electricity and magnetism go together.\" This mixes up two different ideas. Copper is an excellent **electrical conductor**, meaning electrons move freely *between* atoms. But for magnetic attraction, we need unpaired electron spins *within* atoms that can form domains. Conductivity and ferromagnetism are separate properties. Silver and gold are also non-magnetic conductors.",{"id":1645,"type":1646,"caption":1647,"columns":1648,"rows":1653},"table-22","table","Kitchen metals: magnetic response and why",[1649,1650,1651,1652],"Object","Main metal(s)","Domains can form?","Your fridge magnet",[1654,1659,1664,1668,1673,1677],[1655,1656,1657,1658],"Steel spoon","Iron + carbon","Yes — iron atoms align","Strong attraction",[1660,1661,1662,1663],"Copper wire","Copper","No — paired electron spins","No attraction",[1665,1666,1667,1663],"Aluminium foil","Aluminium","No — no lasting domain structure",[1669,1670,1671,1672],"₹5 coin","Brass (Cu + Zn), thin Ni","Only in thick nickel layers","Usually none",[1674,1675,1676,1658],"Iron kadai (if available)","Iron","Yes",[1678,1679,1680,1681],"Stainless steel plate","Iron + chromium + nickel","Depends on recipe","Often weak or none",{"id":1683,"type":1499,"prompt":1684,"options":1685,"explanation":1692},"prediction-23","Riya drops her strong neodymium magnet through a vertical copper pipe and a plastic pipe of the same size. What happens in each case?",[1686,1688,1690],{"id":1503,"label":1687},"The magnet falls at the same speed through both pipes.",{"id":1506,"label":1689},"The magnet falls slower through the copper pipe, even though copper is not attracted to magnets.",{"id":1509,"label":1691},"The magnet sticks to the inside of the copper pipe and does not fall.","The correct answer is **(b)**. Copper is not ferromagnetic, so the magnet is never attracted to it. However, as the moving magnet's field passes through the copper, it induces tiny electric currents called **eddy currents** in the pipe wall. By Lenz's law, these currents create their own magnetic field that opposes the change—pushing back on the falling magnet and slowing it down. This is a beautiful demonstration that copper responds to *changing* magnetic fields even though it has no domains and does not respond to *steady* ones. Through the plastic pipe, the magnet falls normally.",{"id":1694,"type":1470,"markdown":1695},"prose-24","This copper-pipe experiment is worth trying at home if you can find a thick copper pipe and a strong neodymium magnet (handle carefully—pinch hazard). The magnet takes several seconds to fall through 30 cm of copper, seeming to defy gravity. It does not stick, it does not stop, but it *lingers*. The phenomenon is called **electromagnetic induction**, and it will appear again when we study electromagnets in Chapter 7. For now, notice what it proves: a material can be dramatically affected by a magnet without ever being attracted to it. The domain model predicts no attraction for copper, and the experiment confirms this while revealing a deeper, different interaction.\n\nLet us also address stainless steel, which confuses many home tests. Stainless steel is an alloy—iron mixed with chromium and often nickel. Some recipes keep the iron's domain-forming ability; others, especially those high in chromium, rearrange the crystal structure so domains cannot grow freely. Your kitchen sink may be magnetic or not depending on its exact recipe, not on whether it is \"good\" steel. This is a useful reminder that our domain model is a simplified picture. It predicts the main pattern, but real materials contain engineering subtleties.",{"id":1697,"type":1590,"title":1698,"questions":1699},"quiz-25","Check your reasoning",[1700,1711],{"itemId":1701,"prompt":1702,"options":1703,"correct":1503,"why":1710},"magnets.q003","A student says, \"Copper conducts electricity, so it must be magnetic.\" What is the flaw?",[1704,1706,1708],{"id":1503,"label":1705},"Copper does conduct, but its electrons are paired so domains cannot form.",{"id":1506,"label":1707},"Copper actually is magnetic, but only on Mondays.",{"id":1509,"label":1709},"Copper would be magnetic if we used AC instead of a permanent magnet.","Conductivity depends on free electrons moving between atoms. Magnetism in the domain model depends on unpaired electron spins that can line up within atoms. Copper lacks these.",{"itemId":1712,"prompt":1713,"options":1714,"correct":1506,"why":1721},"magnets.q004","You bring a strong magnet near a thick block of aluminium. What should happen?",[1715,1717,1719],{"id":1503,"label":1716},"It sticks firmly because aluminium is a light metal.",{"id":1506,"label":1718},"Nothing visible, because aluminium does not form lasting magnetic domains.",{"id":1509,"label":1720},"It heats up and melts because aluminium has low melting point.","Aluminium is paramagnetic at best, with no domain structure. The force is far too weak to see or feel with ordinary magnets.",{"id":1723,"type":1474,"title":1724,"eyebrow":1725,"navLabel":1726},"chapter-26","Making a Magnet: Stroking, Stacking and Current","Chapter 04","Creating magnetism",{"id":1728,"type":1470,"markdown":1729},"prose-27","If you have ever watched a blacksmith at work in an old film, you have seen iron turn red-hot and then get hammered into shape. What the film rarely shows is that the blacksmith's tools themselves can become magnetic, simply from being struck again and again while pointing north-south. Magnetism is not a gift that only factories can give. You can make a magnet on your kitchen table with a steel spoon and a bar magnet, or with a battery, some wire and an iron nail. In this chapter we study three ways to turn an ordinary piece of iron or steel into a magnet: stroking, stacking (or hammering), and electric current. Each method works because it nudges the tiny magnetic domains inside the metal to line up and stay that way. The method you choose depends on how strong you need the magnet to be, and whether you want to switch it off later.",{"id":1731,"type":1732,"title":1733,"items":1734},"steps-28","steps","Three ways to make a magnet",[1735,1739,1743],{"title":1736,"tag":1737,"text":1738},"Stroking","Strongest for home","Drag one pole of a strong magnet along a steel needle or spoon, always in the same direction, many times. The domains swing into alignment with the magnet's field and stay lined up.",{"title":1740,"tag":1741,"text":1742},"Hammering in Earth's field","Weak but real","Place a steel rod pointing along Earth's magnetic north-south direction and strike one end sharply. The vibrations let domains settle parallel to Earth's field.",{"title":1744,"tag":1745,"text":1746},"Electric current in a coil","Most powerful","Wind insulated copper wire around an iron nail and connect to a battery. The current creates a magnetic field that forces domains into strong alignment.",{"id":1748,"type":1483,"variant":1484,"title":1749,"markdown":1750},"callout-29","Rubbing back and forth makes it stronger?","Many learners think that rubbing a magnet back and forth over a needle dozens of times will make it more magnetic. It does not. Each back-and-forth stroke undoes the alignment from the previous pass. The domains swing one way, then the opposite way, and end up nearly random again. Always stroke in one direction only, lifting the magnet away between strokes so the last pass is the one that matters.",{"id":1752,"type":1489,"title":1753,"problem":1754,"steps":1755},"worked-example-30","Making a compass needle by stroking: a worked sequence","You have a rusty sewing needle, a bar magnet, and a bowl of water. You want to make a floating compass. How do you stroke the needle so it becomes a magnet and points north?",[1756,1757,1758,1759,1760,1761,1762,1763],"Test the needle before you start: hold it near iron filings or a small staple. It should not attract them. This confirms it is not already magnetised.","Identify the poles of your bar magnet. The pole that points north when you hang the magnet is the north-seeking pole (N). You may use either pole for stroking, but you must use the same pole throughout.","Hold the needle flat on the table. Place the N pole of the bar magnet at one end of the needle.","Drag the N pole smoothly along the full length of the needle towards the other end. Lift the magnet well away from the needle, move it back to the starting end without touching, and repeat. Do this 20–30 times.","Do not rub back and forth. Each return journey must be through the air, not along the needle. Back-and-forth contact would randomise the domains again.","Stroke in the same direction every time. The domains gradually rotate so their north poles all point towards the end where you finish each stroke.","Test the needle again near iron filings. It should now lift them. Mark the end that was the last to be touched by the N pole of the bar magnet: this becomes the needle's own south pole (because opposite poles attract, the N pole of the bar magnet leaves the far end of the needle as a south pole).","Push the needle through a small cork or piece of foam and float it in still water. Once it settles, the marked S pole of the needle points towards Earth's magnetic north.",{"id":1765,"type":1470,"markdown":1766},"prose-31","The hammering method is older and weaker, but it shows beautifully that Earth itself is a magnet. A steel rod held lengthwise along the magnetic meridian — the imaginary line on the ground that runs towards magnetic north — already feels Earth's field pull faintly on its domains. The sharp blow from a hammer gives the domains enough energy to move, and Earth's field guides them to settle pointing north-south. Blacksmiths noticed this accidentally for centuries: their hammers and tongs, left lying on the forge aligned north-south, slowly became magnetic from repeated strikes. The magnetism is weak, enough to lift a small nail perhaps, but it proves that any steady magnetic field, even Earth's, can organise domains if the material is given a mechanical shake.",{"id":1768,"type":1769,"itemId":1770,"prompt":1771,"check":1772,"hints":1784,"feedback":1786},"practice-32","practice","magnets.p005","A student wraps 80 turns of copper wire around an iron nail, connects it to a 1.5 V cell, and finds it lifts 12 paper clips. She then replaces the iron nail with an aluminium rod of the same size, using the same wire and battery. How many paper clips does the coil with aluminium lift?",{"kind":1773,"options":1774,"correct":1783},"choice",[1775,1777,1779,1781],{"id":1503,"label":1776},"About 12, because aluminium is also a metal",{"id":1506,"label":1778},"Zero or almost zero, because aluminium is non-magnetic",{"id":1509,"label":1780},"More than 12, because aluminium is lighter than iron",{"id":1512,"label":1782},"None of the above",[1506],[1785],"Think about whether aluminium has magnetic domains that can align.",{"correct":1787,"incorrect":1788},"Correct. Aluminium is not a ferromagnetic material. It has no magnetic domains that can align with the coil's field, so the coil with aluminium behaves like an empty coil and lifts no paper clips.","Think again: the coil creates a magnetic field, but aluminium has no magnetic domains to concentrate that field. Without iron inside, the field is too weak to lift clips.",{"id":1790,"type":1474,"title":1791,"eyebrow":1792,"navLabel":1793},"chapter-33","Destroying Magnetism: Heat, Drop and Hammer","Chapter 05","Losing magnetism",{"id":1795,"type":1470,"markdown":1796},"prose-34","A permanent magnet seems like a solid promise: once it attracts, it should attract forever. But anyone who has left a magnet on a hot kitchen stove, or seen an old speaker magnet after years of rough handling, knows that promise can break. Magnetism is not locked in place like a carved stone; it is more like a carefully stacked pile of plates that can tumble if shaken hard enough. In this chapter we explore three ways to knock that stack over — heat, dropping and hammering — and we design a fair test to see which method works fastest. The key idea is the magnetic domain, a model we treat as clusters of tiny atomic magnets inside the material. When these domains all point the same way, the material is strongly magnetised. disturb them, and the magnet weakens or dies.",{"id":1798,"type":1533,"tone":1534,"items":1799},"spec-35",[1800,1804,1808],{"label":1801,"big":1802,"value":1803},"Curie temperature of iron","770 °C","Above this, iron loses ferromagnetism and domains randomise. A charcoal tandoor or village forge can reach this.",{"label":1805,"big":1806,"value":1807},"Mechanical shock count","~20–50","Repeated drops from table height can measurably weaken a cheap ferrite magnet over days.",{"label":1809,"big":1810,"value":1811},"Soft iron vs alnico","Very different","Soft iron domains shift easily; alnico domains are 'pinned' by the metal's crystal structure and need far more energy to randomise.",{"id":1813,"type":1483,"variant":1517,"title":1814,"markdown":1815},"callout-36","The domain model is a useful fiction","We draw domains as neat arrows inside boxes, but a real crystal is far messier. Domains are boundaries between regions where electron spins align; the boundaries themselves move and wobble. We use the model because it predicts behaviour well, not because we can photograph a single domain with a school microscope.",{"id":1817,"type":1732,"title":1818,"items":1819},"steps-37","How heat destroys magnetism",[1820,1824,1828,1832],{"title":1821,"tag":1822,"text":1823},"Thermal energy rises","molecular","As temperature increases, atoms in the magnet vibrate more vigorously.",{"title":1825,"tag":1826,"text":1827},"Domain walls wobble","domain level","The boundaries between aligned regions start to shift randomly as vibrations knock electrons out of their preferred spin directions.",{"title":1829,"tag":1830,"text":1831},"Alignment scrambles","bulk effect","Above the Curie temperature, thermal energy overwhelms the exchange force that keeps spins parallel; domains point every which way.",{"title":1833,"tag":1834,"text":1835},"Cooling in no field","critical step","If the magnet cools without an external magnetic field, domains freeze in random directions. The magnet is demagnetised.",{"id":1837,"type":1489,"title":1838,"problem":1839,"steps":1840},"worked-example-38","Designing a fair test: which kills a magnet fastest?","You have four identical bar magnets, a kitchen gas stove, a wooden table, a hammer, and a box of identical paper clips. You want to compare how heat, drops, and hammer blows affect magnet strength. How do you make the test fair, and what do you measure?",[1841,1842,1843,1844,1845],"Label magnets A (control), B (heat), C (drop), D (hammer). Test each first by seeing how many paper clips it can lift in a chain from a flat surface; record the number.","Decide fixed treatments: B is held in the hottest part of a blue gas flame (about 800 °C) for 60 seconds, then cooled to room temperature on a brick. C is dropped from exactly 75 cm onto the wooden table, 30 times in a row. D is struck on its pole face with the hammer, 30 times, on the same wooden table.","Keep B, C, and D away from other magnets and iron objects during treatment. This is a control variable: stray fields could remagnetise or confuse the result.","After all treatments, repeat the paper-clip lift test with each magnet, using the same surface and clip box. Record maximum clips lifted in one chain.","Compare: A should lift the original number, B probably lifts zero, C and D lift fewer than A but more than zero. The fair-test logic is 'one changed variable, many fixed variables, one clear measurement.'",{"id":1847,"type":1646,"caption":1848,"columns":1849,"rows":1854},"table-39","Comparison of three demagnetisation methods in a home or school lab",[1850,1851,1852,1853,1462],"Method","Energy type","Typical result","Why it works",[1855,1861,1867,1873],[1856,1857,1858,1859,1860],"Heat on gas flame","Thermal","Complete loss if above Curie temp","Thermal vibration randomises domains; cooling without a field locks in disorder","Use tongs; magnet and brick will be extremely hot",[1862,1863,1864,1865,1866],"Repeated dropping","Mechanical\u002Fkinetic","Partial loss after many drops","Impacts send shock waves through crystal, jolting domain walls past pinning defects","Do not drop on tile; magnet may chip or shatter",[1868,1869,1870,1871,1872],"Hammer blows","Mechanical\u002Fpressure","Strong partial to complete loss","Rapid compression and rarefaction create local heating plus mechanical disorder","Wear eye protection; fragments can fly",[1874,1875,1876,1877,1878],"Control (left alone)","None","No change","Domains stay aligned in their current state","None needed",{"id":1880,"type":1483,"variant":1881,"title":1882,"markdown":1883},"callout-40","nuance","Not all magnets die equally","A soft-iron nail magnetised by stroking loses most of its strength after a few drops. An alnico loudspeaker magnet survives oven temperatures that would kill a simple iron magnet, because aluminium-nickel-cobalt crystals 'pin' domain walls with extra energy barriers. This is why refrigerator magnets (usually ferrite) and MRI machine magnets (superconducting coils, not permanent) are chosen for how they resist change. The Curie temperature is still the absolute ceiling, but the path to get there varies in steepness.",{"id":1885,"type":1769,"itemId":1886,"prompt":1887,"check":1888,"hints":1902,"feedback":1906},"practice-41","magnets.p006","You heat a bar magnet red-hot and let it cool while lying east-west on a table, far from other magnets. After cooling, you test its strength. What do you predict?",{"kind":1773,"options":1889,"correct":1901},[1890,1892,1895,1898],{"id":1579,"label":1891},"It becomes stronger than before",{"id":1893,"label":1894},"same","It stays about the same",{"id":1896,"label":1897},"weaker-aligned","It becomes weaker and points north-south when free to rotate",{"id":1899,"label":1900},"zero","It lifts no paper clips at all",[1899],[1903,1904,1905],"Think about what happens to domains above the Curie temperature, and whether the cooling environment provides any aligning field.","The table is wooden and east-west: does that provide a magnetic field to organise domains?","What is the Earth's magnetic field strength compared to the magnet's own field?",{"correct":1907,"incorrect":1908},"Correct. Above 770 °C the domains randomise. Cooling without a strong aligning field leaves them random, so the bulk magnetism is effectively zero. The weak Earth's field is far too faint to realign a hot iron bar cooling on a table.","Reconsider. The Curie temperature destroys the ordered alignment. Cooling on a table — with no strong external field — lets domains freeze randomly. The Earth's field is only about 25–65 microtesla at India's latitude, far too weak to re-magnetise cooling iron.",{"id":1910,"type":1470,"markdown":1911},"prose-42","The hammer and the drop teach us that magnetism is a state of order, not a substance you can pour out. Imagine a classroom where every student faces the blackboard: that is a magnetised material. Now toss a cricket ball through the room: a few students turn to watch. Toss twenty balls, or blast loud music, and the neat rows collapse into chaos. Heat is the music, the hammer is the cricket ball, and the students are domains. The control room — the untreated magnet — keeps its order because no energy arrives to disturb it. This is why ancient compass needles were stroked into alignment but stored in padded boxes; the padding was not just care, it was physics.\n\nIn the next chapter we step back in time to see how this understanding grew from lumps of lodestone found in the earth to the careful experiments of William Gilbert, who first proved that Earth itself is the great magnet that orients our needles.",{"id":1913,"type":1914,"title":1915,"points":1916},"summary-43","summary","Key takeaways: destroying magnetism",[1917,1918,1919,1920,1921],"Magnetism depends on aligned magnetic domains; disorder the alignment and the magnet weakens or dies.","Heating past the Curie temperature (770 °C for iron) randomises domains through thermal vibration; cooling without a strong field leaves them random.","Mechanical shocks from dropping or hammering jostle domain walls past crystal defects, gradually or suddenly scrambling alignment.","A fair test compares treatments on identical magnets with one changed variable, controlled conditions, and a repeatable measurement like paper-clip lift count.","Some materials resist demagnetisation better than others because their crystal structure pins domain walls more strongly; this is a materials-science choice in engineering.",{"id":1923,"type":1474,"title":1924,"eyebrow":1925,"navLabel":1926},"chapter-44","From Lodestone to Gilbert: A Brief History","Chapter 06","History of magnetism",{"id":1928,"type":1470,"markdown":1929},"prose-45","If you dip a magnet into a box of iron filings today, you know exactly what will happen. But imagine being the first person to see a dark, heavy stone pull iron chips toward itself with no thread, no glue, no wind. That stone was magnetite, a naturally magnetic iron oxide found in places like Tamil Nadu and Karnataka. Ancient sailors called it *lodestone* — the \"leading stone\" — because it could lead a ship across open water when stars were hidden by cloud. For centuries, lodestone sat at the border between magic and machinery. This chapter follows how patience, careful measurement, and clever models turned that mystery into the science you now control in your own experiments.\n\nThe name \"magnet\" itself comes from Magnesia, a region in Greece where rich deposits of magnetite were mined. But the knowledge was never limited to one place. Indian shipwrights in the port of Lothal (in what is now Gujarat) used iron-rich compasses or directional indicators by around 2000 BCE, and Chinese scholars described south-pointing spoons made of lodestone by the Han dynasty. What all these cultures shared was a practical puzzle: a rock that behaved as if it had invisible, reaching hands.",{"id":1931,"type":1932,"title":1933,"items":1934},"timeline-46","timeline","From Lodestone to Laboratory: Key Moments",[1935,1939,1943,1947,1951,1955],{"time":1936,"title":1937,"text":1938},"~600 BCE","Greek sailors note lodestone","Thales of Miletus and others record that magnetite attracts iron. The effect is filed alongside amber attracting straw — both seen as \"alive\" or magical, not yet mechanical.",{"time":1940,"title":1941,"text":1942},"~200 BCE","Chinese south-pointer","A Han-dynasty text describes a lodestone spoon on a bronze plate; the handle turns south. This is the first known compass-like device, used for divination as much as navigation.",{"time":1944,"title":1945,"text":1946},"~1000 CE","Needle compasses at sea","Chinese navigators float a magnetised iron needle on water or mount it on a pivot. Knowledge spreads via trade routes to the Arab world and eventually to Europe.",{"time":1948,"title":1949,"text":1950},"1600","Gilbert publishes 'De Magnete'","William Gilbert tests magnetism systematically. His key claim: Earth itself is a giant magnet. He demonstrates this with a shaped lodestone sphere he calls a terrella.",{"time":1952,"title":1953,"text":1954},"1820","Øersted's lecture surprise","During a demonstration, Hans Christian Øersted notices a compass needle twitch when a nearby wire is connected to a voltaic pile. Electricity and magnetism are revealed as one force.",{"time":1956,"title":1957,"text":1958},"1831","Faraday's induction","Michael Faraday shows that a changing magnetic field can create an electric current in a nearby coil. This principle now drives every thermal power station in India.",{"id":1960,"type":1483,"variant":1517,"title":1961,"markdown":1962},"callout-47","The Terrella Was a Model, Not Proof","Gilbert's *terrella* — a polished lodestone sphere — was a brilliant **model**. When he moved a tiny compass needle over its surface, the needle tilted and turned just as real compasses do on Earth. But the terrella did not *prove* Earth is magnetised; it showed only that a magnetic sphere *could* produce such patterns. Gilbert inferred the rest from global data on compass variation. Treat the terrella as an early analogue computer: it helped him think, not settle the debate forever.",{"id":1964,"type":1470,"markdown":1965},"prose-48","What unites these three choices is not genius alone, but the habit of *fair testing*. The ancient sailor varied how she stroked the needle. Gilbert checked multiple locations on his terrella and matched them to ship logs from around the world. Øersted repeated his lecture demonstration privately, trying different wire positions and current directions. Each accepted that a single strange event meant little until it could be reproduced and measured. This is the same discipline you use when you ask: does a magnet lift more paper clips at 5 cm or at 2 cm? History is not a parade of magical insights; it is a chain of ordinary people refusing to ignore odd results.\n\nThere is a deeper lesson too. Before Gilbert, many scholars believed magnetism came from a star, from garlic (yes, garlic!), or from a magical mountain at the North Pole. These ideas survived because they were hard to disprove without travel and measurement. Gilbert's terrella and global compass data replaced myth with a testable model. Science often advances not by proving a new idea right, but by showing that old ideas make wrong predictions. If your magnet stops working after heating, you do not need to know about domains to reject the \"permanent magic\" theory. You just need a thermometer, a flame, and patience.",{"id":1967,"type":697,"prompt":1968},"reflection-49","Think about a time you saw something unexpected — a toy rolling uphill, a shadow bending, water refusing to spill from an upside-down glass. Did you dismiss it, repeat it, or try to change one thing at a time to understand it? What would Gilbert or Øersted have done in your place, and what do you need to do your own small \"De Magnete\" at home?",{"id":1970,"type":1474,"title":1971,"eyebrow":1972,"navLabel":1973},"chapter-50","Electromagnets: Magnetism You Can Switch","Chapter 07","Electromagnets explained",{"id":1975,"type":1470,"markdown":1976},"prose-51","Imagine you are a scrapyard worker in Jamshedpur. A truck dumps a pile of crushed metal: iron sheets, aluminium cans, steel pipes and splintered wood. You need to lift only the iron and steel, leaving everything else behind. A permanent magnet would grab the iron, yes, but it would also cling to the scrap pile and refuse to let go when you want to drop the load. You need a magnet you can switch on to lift, then switch off to release. That is exactly what an electromagnet does. It is not forged from lodestone or cut from a bar of alnico. It is built from ordinary copper wire, an iron bolt and a battery, yet it can lift thousands of kilograms when the current flows and become completely inert the instant the current stops. In this chapter we will see how moving electrons create a magnetic field, how coiling the wire concentrates that field, and why stuffing an iron core inside the coil turns a feeble tug into an industrial grip.",{"id":1978,"type":1732,"title":1979,"items":1980},"steps-52","From Battery Bolt to Magnetic lift",[1981,1985,1989,1992,1996],{"title":1982,"tag":1983,"text":1984},"A single wire","weak field","When electric current flows through a straight wire, it creates a circular magnetic field around the wire. You can detect it with a small compass, but the field is too weak to lift a paper clip.",{"title":1986,"tag":1987,"text":1988},"Make a coil","concentration","Wrap the same wire into a tight spiral, called a solenoid. Each loop adds its field along the same axis. The fields stack up, producing a stronger, straight magnetic field through the centre.",{"title":1990,"tag":498,"text":1991},"Add an iron core","Slide an iron nail or bolt inside the coil. The iron contains magnetic domains that line up with the coil's field, amplifying the strength many times over. This assembly is the electromagnet.",{"title":1993,"tag":1994,"text":1995},"Apply current","On","Connect to a battery or power supply. Current flows, domains align, and the iron end becomes a strong north or south pole. The electromagnet can now attract ferromagnetic objects.",{"title":1997,"tag":1998,"text":1999},"Cut the current","Off","Open the switch. Current drops to zero, the coil's field collapses, the iron domains randomise, and the magnetic grip vanishes. The scrap falls away instantly.",{"id":2001,"type":1489,"title":2002,"problem":2003,"steps":2004},"worked-example-53","The Junkyard Crane Electromagnet","A scrapyard crane electromagnet uses a copper coil of 1200 turns wrapped around a cylindrical iron core 0.30 m long. When connected to a 240 V industrial supply, the coil draws 15 A of current. A student builds a small model using 200 turns of the same wire, a 0.05 m iron bolt, and a 12 V battery delivering 2 A. Roughly how many times stronger is the industrial electromagnet's field compared to the student's model?",[2005,2006,2007,2008,2009],"For a solenoid, the magnetic field strength inside is proportional to (number of turns × current) \u002F length of coil. This is a model that ignores core saturation and edge effects, but it gives the correct comparison.","Calculate the 'ampere-turns per metre' for the industrial magnet: (1200 turns × 15 A) \u002F 0.30 m = 18000 \u002F 0.30 = 60000 A-turns\u002Fm.","Calculate the same quantity for the student's model: (200 turns × 2 A) \u002F 0.05 m = 400 \u002F 0.05 = 8000 A-turns\u002Fm.","Divide the industrial value by the student value: 60000 \u002F 8000 = 7.5. The industrial field is roughly 7–8 times stronger by this measure.","In practice the industrial core is also much larger and made of better iron, so the actual lifting force is hundreds of times greater. The student model might lift a few nails; the crane magnet lifts a tonne of scrap steel.",{"id":2011,"type":1483,"variant":2012,"title":2013,"markdown":2014},"callout-54","careful","The Right-Hand Rule Gives Direction, Not Strength","To find which end of your coil is the north pole, grasp the coil with your right hand so that your fingers curl in the direction of conventional current (positive to negative). Your thumb points toward the north pole. This rule only tells you the **direction** of the field. It does **not** tell you how strong the field is. Strength comes from current, turns and core material, not from how firmly you grip an imaginary coil in the air. Also note: if you use the left hand by mistake, you will get the wrong pole. The right-hand rule works because it matches the actual relationship between moving positive charges and magnetic field direction in the standard model.",{"id":2016,"type":1533,"tone":1534,"items":2017},"spec-55",[2018,2022,2026,2030],{"label":2019,"big":2020,"value":2021},"Crane electromagnet coil turns","1,000–5,000","Typical industrial lifting magnets use thousands of turns of heavy-gauge copper wire to carry high current without overheating.",{"label":2023,"big":2024,"value":2025},"Typical crane current","20–100 A","High current creates strong fields, but thick copper cables are needed to resist overheating. Cooling systems are often built in.",{"label":2027,"big":2028,"value":2029},"Core material","Soft iron","Soft iron magnetises quickly and demagnetises instantly when current stops. Hard steel would retain some magnetism, making release difficult.",{"label":2031,"big":2032,"value":2033},"Switch-off time","\u003C 1 s","Magnetic field collapses almost instantly when current ceases, allowing rapid 'drop and grab' cycles in scrap sorting.",{"id":2035,"type":1499,"prompt":2036,"options":2037,"explanation":2046},"prediction-56","You have two electromagnet coils of identical copper wire. Coil A has 100 turns wound around a hollow cardboard tube. Coil B has 100 turns wound around an iron bolt of the same size. Both carry the same current. Which will lift more paper clips?",[2038,2040,2042,2044],{"id":1503,"label":2039},"Coil A, because cardboard is lighter and lets the magnet move faster",{"id":1506,"label":2041},"Coil B, because the iron core aligns its domains and strengthens the field",{"id":1509,"label":2043},"Both the same, because turns and current are identical",{"id":1512,"label":2045},"Coil A, because iron would block the magnetic field","The correct choice is **Coil B**. The iron core does not block the field; it **amplifies** it. Inside the iron, countless magnetic domains rotate to align with the coil's field, producing a much stronger combined field than the coil alone could create. This is why nearly every practical electromagnet contains an iron or steel core. Cardboard, being non-magnetic, offers no such amplification.",{"id":2048,"type":1769,"itemId":2049,"prompt":2050,"check":2051,"hints":2062,"feedback":2066},"practice-57","magnets.p007","A student wants to build the strongest possible electromagnet using a 9 V battery, a nail, and insulated copper wire. She can either: (1) wrap 50 turns in a single layer along most of the nail, or (2) wrap 200 turns in many tight layers near the nail's head. Which design is likely stronger, and what else could she do to increase strength further?",{"kind":1773,"options":2052,"correct":2061},[2053,2056,2059],{"id":2054,"label":2055},"single","50 turns spread out; it prevents overheating",{"id":2057,"label":2058},"tight","200 tight turns; concentration boosts field strength",{"id":1893,"label":2060},"Both equal; only battery voltage matters",[2057],[2063,2064,2065],"Think about what the formula B ∝ N × I \u002F L tells you about turns and coil length.","Consider whether spreading turns out or bunching them changes the turns-per-metre value.","What other variable besides turns could she adjust without buying new parts?",{"correct":2067,"incorrect":2068},"Correct. 200 tight turns give a higher turns-per-metre ratio, concentrating the field. She could also increase current by using a fresh battery, shortening the wire (less resistance), or connecting batteries in parallel. Adding more iron mass to the core helps too.","Not quite. Tight, concentrated turns raise the turns-per-metre ratio, which increases field strength for the same current. Spreading turns out weakens the field, and voltage alone does not determine strength—current does.",{"id":2070,"type":1470,"markdown":2071},"prose-58","The true power of electromagnets lies not merely in their strength but in their obedience. A permanent magnet is always 'on'; it cannot be commanded to release at a precise moment. An electromagnet follows the switch. This simple difference transforms entire industries. In a recycling plant, the operator flips a switch to hoist a crushed car body, then flips it off to drop the steel precisely into a furnace hopper while aluminium and copper fall elsewhere. In a hospital MRI machine, superconducting electromagnets create fields thousands of times stronger than Earth's, then hold that field perfectly steady for imaging, yet can be ramped down for maintenance. Even the tiny relay that clicks your geyser on when the temperature drops contains an electromagnet: current flows, a small iron armature snaps into the coil, and mechanical contacts close. No current, no magnetism, no contact. The electromagnet is the bridge between the world of electrons we cannot see and the mechanical world we can control.",{"id":2073,"type":1474,"title":2074,"eyebrow":2075,"navLabel":2076},"chapter-59","Magnets in Engineering: Speakers, Motors, MRI and Maglev","Chapter 08","Real-world magnets",{"id":2078,"type":1470,"markdown":2079},"prose-60","Think of the last time you heard music from a phone speaker, watched a mixer-grinder spin, or saw a doctor on television explain an MRI scan. None of these would work without magnets doing heavy engineering behind the scenes. In this chapter we look at four very different machines — a loudspeaker, an electric motor, a hospital scanner, and a levitating train — to see how engineers choose between permanent magnets and electromagnets to solve very different problems. What all four share is the same invisible push we have studied: a magnetic field producing force without touching anything.\n\nThe key engineering question is always the same: do you need a magnet that is always on, or one you can switch on and off? Permanent magnets keep their field forever (unless heated or hammered), which makes them simple and reliable. Electromagnets need current, which means they can be controlled — changed in strength, reversed, or turned off completely. A loudspeaker needs rapid, tiny changes, so it uses both kinds together. A recycling crane needs to grab scrap iron and then release it cleanly, so it uses an electromagnet. Matching magnet type to job is what makes modern technology possible.",{"id":2081,"type":1489,"title":2082,"problem":2083,"steps":2084},"worked-example-61","Inside a Loudspeaker: How a Magnet Makes Sound","A loudspeaker must turn an electrical music signal into moving air that your ear detects as sound. The music signal is an alternating current — it flows back and forth, changing direction up to 20,000 times per second for high notes. How does a magnet help?",[2085,2086,2087,2088,2089,2090,2091],"A permanent magnet is fixed in a ring shape around a central pole. This creates a steady magnetic field in the narrow gap between the ring and the centre.","A lightweight coil of wire, called the voice coil, sits in that gap and is glued to a paper or plastic cone.","When current from the amplifier flows through the voice coil, the coil becomes an electromagnet with a north and south pole.","The voice coil's poles are either attracted to or repelled by the fixed permanent magnet, depending on which way the current flows.","Because the current alternates, the coil is pushed in and out rapidly. It never fully escapes the gap; it just vibrates back and forth.","The cone moves with the coil, pushing and pulling air. Those pressure waves travel to your ear as sound.","For a loud note, the current is large, so the electromagnetic force is strong and the cone moves far. For a soft note, the current is small and the cone barely moves.",{"id":2093,"type":1533,"tone":2094,"items":2095},"spec-62","blue",[2096,2100,2104,2108],{"label":2097,"big":2098,"value":2099},"Typical MRI field","1.5–3 T","Tesla, the SI unit of magnetic flux density. A fridge magnet is about 0.005 T. Earth's field is about 0.00005 T.",{"label":2101,"big":2102,"value":2103},"Superconducting temperature","4 K","= −269 °C, the working temperature of MRI electromagnets cooled by liquid helium.",{"label":2105,"big":2106,"value":2107},"Maglev test speed","603 km\u002Fh","Japan's SCMaglev holds the rail speed record (2015), using superconducting electromagnets in guideway coils.",{"label":2109,"big":2110,"value":2111},"Voice coil travel","±2–10 mm","Typical maximum movement of a loudspeaker cone for full-volume music. Some subwoofers reach 30 mm.",{"id":2113,"type":1483,"variant":1517,"title":2114,"markdown":2115},"callout-63","The MRI 'Tunnel' Simplification","Popular descriptions say an MRI machine 'takes a photograph of your insides.' This is a useful analogy, but it is not accurate. What actually happens: the superconducting electromagnet aligns hydrogen nuclei (protons) in the water inside your body. Radio pulses then knock those protons slightly out of alignment. When the protons relax back, they emit tiny radio signals. Computers map those signals to build an image. The magnet does not 'see' anything; it prepares atoms so their radio whispers can be detected. Calling it a camera is a model, not the mechanism.",{"id":2117,"type":1470,"markdown":2118},"prose-64","Electric motors show the double-magnet idea in rotating form. Whether in a ₹ 800 mixer-grinder or a ₹ 2 lakh electric scooter, the layout is similar. Permanent magnets are fixed to the outer case, creating stationary north and south poles. Inside, coils of wire are wound on a central shaft called the rotor. A commutator — a split metal ring — reverses the current in the coils every half-turn. Just as the rotor poles are about to line up with and stick to the fixed poles, the commutator flips the current. The electromagnet poles swap, and the rotor is now repelled where it was attracted, so it keeps spinning. Without that timed reversal, the motor would lock in place. Modern brushless motors replace the mechanical commutator with electronic sensors and switches, but the magnetic dance remains the same.\n\nMaglev trains extend this dance to tonnes of moving steel. Electromagnets beneath the train are switched on to push against coils or magnets in the track. One set of magnets levitates the train a few centimetres above the concrete guideway, eliminating wheel friction entirely. Another set acts as a linear motor: instead of spinning a shaft, the magnetic field travels like a wave along the track, pulling the train forward without anything touching. Because there is no contact, there is almost no wear, no noise from wheels, and no speed limit from wheel friction. The trade-off is enormous electrical complexity: computers must adjust thousands of amperes every millisecond to keep the train stable.",{"id":2120,"type":1499,"prompt":2121,"options":2122,"explanation":2131},"prediction-65","A recycling plant crane must pick up a car body made mostly of steel, move it 20 metres, and drop it precisely into a shredding machine. Which magnet design is safest and most practical? Think about what happens after the lift.",[2123,2125,2127,2129],{"id":1503,"label":2124},"A huge permanent magnet, because it never needs power and cannot fail electrically.",{"id":1506,"label":2126},"A small permanent magnet on a rope, because it is cheap and easy to replace.",{"id":1509,"label":2128},"An electromagnet that can be switched on to lift and switched off to drop.",{"id":1512,"label":2130},"No magnet at all; use a giant mechanical claw like a crane game.","Option c is correct. An electromagnet solves two problems at once. While current flows, the magnetic field grips the steel car body firmly. When the car is over the shredder, the operator opens the switch. Current stops, the field collapses, and the car drops cleanly. A permanent magnet would never let go — you would have to pry the car off mechanically, which is dangerous and slow. A mechanical claw would work, but gripping odd-shaped crushed cars is unreliable and slow compared to a flat magnetic face. Many real scrap yards in India and worldwide use exactly this electromagnetic crane design.",{"id":2133,"type":1769,"itemId":2134,"prompt":2135,"check":2136,"hints":2147,"feedback":2151},"practice-66","magnets.p008","A maglev train engineer wants to reduce energy use. She considers replacing all track-side electromagnets with permanent magnets, keeping only the train's electromagnets. Why will this plan fail? Choose the best reason.",{"kind":1773,"options":2137,"correct":2146},[2138,2140,2142,2144],{"id":1503,"label":2139},"Permanent magnets cannot create a magnetic field.",{"id":1506,"label":2141},"With permanent magnets in the track, the train could not slow down or stop using magnetic braking.",{"id":1509,"label":2143},"Permanent magnets would attract each other and lock the train to the track with no way to release it.",{"id":1512,"label":2145},"Permanent magnets lose strength at high speeds.",[1506],[2148,2149,2150],"Think about control. What does 'permanent' mean for adjustability?","Consider how magnetic braking works in maglev systems: does it require changing fields?","If track magnets are fixed, can their strength or polarity be varied to push, pull, or resist motion?",{"correct":2152,"incorrect":2153},"Correct. Permanent track magnets would provide a fixed field with no way to vary, reverse, or switch off. Maglev systems need active control for levitation height, propulsion, and especially electromagnetic braking. Without adjustable track fields, the train could not be controlled precisely or slowed safely.","Look again at what 'permanent' implies. Permanent magnets do create fields, so option a is wrong. They do not necessarily lock together if arranged in alternating patterns, so c is not the best answer. High speed does not weaken permanent magnets, so d is wrong. The core problem is loss of control: fixed fields cannot brake or adjust.",{"id":2155,"type":1474,"title":2156,"eyebrow":2157,"navLabel":2158},"chapter-67","The Limits of Magnetism: What Magnets Cannot Do","Chapter 09","What magnets cannot do",{"id":2160,"type":1470,"markdown":2161},"prose-68","Every time you use a fridge magnet, you feel an invisible pull. It is easy to start believing magnets can do anything: pull any metal, work through metres of air, maybe even power a car forever. That feeling grows when you see videos of powerful neodymium magnets lifting huge weights or shaping iron filings into beautiful arcs. But magnets have strict limits, and ignoring them can lead to broken bones, cut fingers, or worse. In this chapter we separate what magnets really do from what they only seem to do, and we explain why some \"magnetic\" stunts are clever camera tricks rather than physics. The boundaries matter because some of the strongest magnets you can buy online are small enough to swallow and powerful enough to crush skin.",{"id":2163,"type":1483,"variant":1484,"title":2164,"markdown":2165},"callout-69","\"Magnets attract all metals\"","This is one of the most common wrong ideas in school science. Metals are a huge family. Only three — iron, nickel and cobalt — are ferromagnetic, meaning they line up their magnetic domains inside a field. Copper, aluminium, brass, gold and silver are metals too, but their electrons arrange themselves so that any magnetic response cancels out. A simple test: try dropping a magnet down a copper pipe. It falls *slowly* because of eddy currents, not because copper is attracted. The magnet never sticks.",{"id":2167,"type":1533,"tone":2168,"items":2169},"spec-70","amber",[2170,2174,2178,2182],{"label":2171,"big":2172,"value":2173},"Field at 1 cm","~100 mT","Typical pull force of a small neodymium disc on iron",{"label":2175,"big":2176,"value":2177},"Field at 5 cm","~2 mT","Same magnet; force drops to roughly 1\u002F125 of the 1 cm value",{"label":2179,"big":2180,"value":2181},"Field at 10 cm","~0.3 mT","Barely stronger than Earth's field; cannot lift a paper clip",{"label":2183,"big":2184,"value":2185},"Earth's field","~0.05 mT","Strong enough to align a compass needle, nothing more",{"id":2187,"type":2188,"items":2189},"formulas-71","formulas",[2190],{"expression":2191,"caption":2192},"F ∝ 1\u002Fr³ (small magnet, short distances)","For a small bar magnet near iron, pull force drops roughly with the cube of distance",{"id":2194,"type":1470,"markdown":2195},"prose-72","The inverse-cube rule is a *model*: it works when the magnet is small compared to the distance, and when you are measuring pull on a flat piece of iron. For two magnets facing each other pole-to-pole, the drop is closer to inverse-fourth power. The key point is not the exact exponent — it is that field strength collapses quickly. A magnet that lifts one kilogram at one centimetre cannot lift ten grams at ten centimetres. This is why magnetic levitation trains need huge electromagnets and active control systems, not simple fridge magnets scaled up.",{"id":2197,"type":1489,"title":2198,"problem":2199,"steps":2200},"worked-example-73","Could a pocket magnet pull a steel key through 10 cm of air?","Rohan has a neodymium disc magnet (10 mm diameter, 5 mm thick) rated to lift 2 kg of steel when in direct contact. He holds it 10 cm from his house key and expects it to slide across the table. It does not move. Why?",[2201,2202,2203,2204],"At contact (0.5 cm air gap plus surface roughness), the magnet can apply roughly 20 newtons of force. This equals the weight of a 2 kg mass.","At 10 cm distance, using the inverse-cube model, the field strength falls by a factor of (10 \u002F 0.5)³ ≈ 8000. The force drops to about 20 N ÷ 8000 ≈ 0.0025 N.","The key weighs about 0.01 kg, so its weight is 0.1 N. The magnetic pull at 10 cm is only 2.5% of the force needed to overcome friction, let alone lift the key.","Result: the key stays still. The magnet's field at 10 cm is weaker than a whisper. Magicians who appear to move objects across a table use hidden magnets glued underneath, not forces through the air.",{"id":2206,"type":1499,"prompt":2207,"options":2208,"explanation":2215},"prediction-74","You have two identical neodymium magnets. You place one on a table and hold the other 30 cm above it, same pole facing down. What happens?",[2209,2211,2213],{"id":1503,"label":2210},"The top magnet hovers in mid-air, unsupported",{"id":1506,"label":2212},"The top magnet slowly rises toward your hand",{"id":1509,"label":2214},"Nothing visible happens; the force is far too weak to feel at 30 cm","Option c is correct. At 30 cm, the repulsive force between two small magnets is microscopic — less than the weight of a grain of rice. You would need active electromagnets with position sensors (like in a maglev train) or a spinning top (like a Levitron toy) to achieve stable levitation. Permanent magnets alone cannot hover stably; this is called Earnshaw's theorem, first proved mathematically in 1842.",{"id":2217,"type":1474,"title":2218,"eyebrow":2219,"navLabel":2220},"chapter-75","Home Investigation: Fair Test — What Affects Magnet Strength?","Chapter 10","Design your test",{"id":2222,"type":1470,"markdown":2223},"prose-76","Every day you test magnets without thinking: you check if the fridge magnet still holds your drawing, or if two magnets push apart when flipped. But how do you know *why* one magnet seems stronger than another? Guessing is not enough. Scientists use a **fair test**—an experiment where only one thing changes at a time, everything else stays the same, and you repeat the test to be sure. In this chapter, you will design and run a fair test to answer a real question: *Does adding more coils of wire to an electromagnet make it lift more paper clips?* You will use only household materials: an iron nail, insulated copper wire from an old phone charger, a 1.5 V cell, and standard paper clips. By the end, you will have data, a graph, and a taste of what ISRO engineers do when they test a motor before launch.",{"id":2225,"type":1732,"title":2226,"items":2227},"steps-77","What You Need for the Fair Test",[2228,2231,2234,2237,2240,2243],{"title":2229,"text":2230},"Iron nail","About 8–10 cm long, not rusted. The nail is the core that becomes magnetised.",{"title":2232,"text":2233},"Insulated copper wire","About 2 m salvaged from an old charger or adapter. Strip 1 cm at each end with adult help.",{"title":2235,"text":2236},"1.5 V cell","A new AA or AAA cell. A fresh cell gives steady current; a weak cell ruins fairness.",{"title":2238,"text":2239},"Switch or tape","A simple tape switch: press the wire ends to the cell to close the circuit, lift to open.",{"title":2241,"text":2242},"Paper clips","Ten identical standard-size clips. They are your ‘weightlifter’s weights’.",{"title":2244,"text":2245},"Ruler","To measure 20, 40 and 60 turns consistently around the nail.",{"id":2247,"type":1483,"variant":2012,"title":2248,"markdown":2249},"callout-78","A fair test needs control","In a fair test, **only the independent variable changes**—here, the number of coil turns (20, 40, 60). Everything you keep the same is called a **controlled variable**: same nail, same cell, same clips, same room temperature, same waiting time before lifting. If you change the cell halfway through, you cannot tell whether turns or tiredness caused the difference.",{"id":2251,"type":1489,"title":2252,"problem":2253,"steps":2254},"worked-example-79","Sample Data from One Trial","Sneha wraps 20 turns, closes the circuit, and the nail lifts 2 paper clips. She repeats twice more and gets 2 and 3 clips. For 40 turns she gets 4, 5, 4. For 60 turns she gets 6, 6, 7. What pattern do you see, and what should she report?",[2255,2256,2257,2258,2259],"List raw results neatly: 20-turn trials = 2, 2, 3 clips; 40-turn = 4, 5, 4; 60-turn = 6, 6, 7.","Calculate the mean (average) for each set: 20 turns = (2+2+3)\u002F3 = 2.3 ≈ 2 clips; 40 turns = (4+5+4)\u002F3 = 4.3 ≈ 4 clips; 60 turns = (6+6+7)\u002F3 = 6.3 ≈ 6 clips.","Look for a pattern: the mean roughly doubles from 20 to 40 turns, and again from 40 to 60. More turns → stronger electromagnet.","Note the plateau warning: real cores eventually saturate. Sneha’s nail may not lift 8 clips at 80 turns; the gain would slow down.","Report with honesty: write the raw data, the mean, and note that clip size varied slightly (a limitation, not a failure).",{"id":2261,"type":1646,"caption":2262,"columns":2263,"rows":2267},"table-80","Planning your fair test: variables and how to control them",[2264,2265,2266],"Variable type","What it is","How we control it",[2268,2272,2276,2280,2283,2286],[2269,2270,2271],"Independent","Number of coil turns","Deliberately set to 20, 40, 60 turns using ruler marks",[2273,2274,2275],"Dependent","Number of paper clips lifted","Count carefully; same size clips only",[2277,2278,2279],"Controlled","Same iron nail","Use one nail, same position, same orientation",[2277,2281,2282],"Same current source","Same 1.5 V cell, same temperature, same connection time",[2277,2284,2285],"Same paper clips","Identical brand new standard clips; reject bent ones",[2277,2287,2288],"Same procedure","Lift slowly, count at first break of contact with table",{"id":2290,"type":1474,"title":2291,"eyebrow":2292,"navLabel":2293},"chapter-81","Check Yourself, and What Comes Next","Chapter 11","Quiz and next steps",{"id":2295,"type":1470,"markdown":2296},"prose-82","You have travelled from the first lodestone pulled from the earth to the electromagnets that lift scrap in a recycling yard, from invisible magnetic fields traced by iron filings to the spinning domains that explain why iron behaves so differently from copper. Along the way you stroked a needle to make a compass, saw magnetism vanish in a red-hot iron rod, and designed a fair test to find what weakens a magnet fastest. This chapter is your checkpoint. Work through the questions honestly — they are not for marks, but for you to see which ideas have stuck and which deserve another walk through the earlier chapters. After the quiz, you will glimpse where magnetism leads next: the quantum world inside the atom, the storage of every digital photograph, and the motors that drive India's metro trains.",{"id":2298,"type":1590,"title":2299,"questions":2300},"quiz-83","Check Yourself",[2301,2314,2327,2340,2353],{"itemId":2302,"prompt":2303,"options":2304,"correct":1509,"why":2313},"magnets.q009","Inside a piece of unmagnetised iron, thousands of tiny magnetic domains point in random directions. What happens to these domains when the iron is stroked repeatedly with a strong permanent magnet?",[2305,2307,2309,2311],{"id":1503,"label":2306},"The domains shrink until they disappear.",{"id":1506,"label":2308},"The domains grow larger and merge into one giant domain.",{"id":1509,"label":2310},"Most domains rotate and align their north-south directions with the stroking magnet's field.",{"id":1512,"label":2312},"The iron atoms turn into a different element with magnetic properties.","Each domain is already a tiny magnet. Stroking applies an external magnetic field that exerts a torque on these domains, causing them to rotate and align. Once aligned, their individual fields add up, and the iron behaves as one large magnet. The domains do not disappear, change element, or necessarily merge into a single physical region.",{"itemId":2315,"prompt":2316,"options":2317,"correct":1506,"why":2326},"magnets.q010","A student tests whether a material is magnetic by holding a bar magnet near a copper wire. The wire does not move toward the magnet. Which explanation is correct?",[2318,2320,2322,2324],{"id":1503,"label":2319},"Copper atoms have no electrons, so no magnetic effect is possible.",{"id":1506,"label":2321},"Copper atoms have paired electrons whose magnetic moments cancel out, and copper's crystal structure does not allow domain formation.",{"id":1509,"label":2323},"Copper is magnetic but too weak for a small bar magnet to detect.",{"id":1512,"label":2325},"The copper wire is too heavy compared to the magnet's pull.","Copper atoms do have electrons, but in copper the relevant electron spins are paired and their magnetic moments cancel. Additionally, copper does not form magnetic domains. Therefore copper shows no attraction to a magnet. Weight is irrelevant: even a tiny copper filing will not stick.",{"itemId":2328,"prompt":2329,"options":2330,"correct":1506,"why":2339},"magnets.q011","An electromagnet is built by wrapping 200 turns of insulated copper wire around an iron nail and passing a current. Which change would most increase its strength?",[2331,2333,2335,2337],{"id":1503,"label":2332},"Replacing the iron nail with an identical-sized wooden rod.",{"id":1506,"label":2334},"Increasing the number of turns to 400 while keeping the same current.",{"id":1509,"label":2336},"Using uninsulated wire so the current flows more easily.",{"id":1512,"label":2338},"Warming the nail with a candle before turning on the current.","Doubling the turns doubles the magnetising force (ampere-turns) if current is constant. Wood cannot form domains, so it would eliminate magnetism. Uninsulated wire would short-circuit between turns. Heating the nail would reduce domain alignment and weaken the electromagnet.",{"itemId":2341,"prompt":2342,"options":2343,"correct":1506,"why":2352},"magnets.q012","The Curie temperature of iron is about 770 °C. What does this temperature mean for a permanent magnet made of iron?",[2344,2346,2348,2350],{"id":1503,"label":2345},"Above this temperature, iron permanently loses its ability to ever be magnetised again.",{"id":1506,"label":2347},"Above this temperature, thermal vibration randomises domain alignment and the magnet temporarily loses its strength until cooled.",{"id":1509,"label":2349},"Iron melts at 770 °C, destroying the magnet's shape.",{"id":1512,"label":2351},"This is the temperature at which iron becomes a superconductor.","The Curie temperature is not the melting point (iron melts near 1,538 °C). Above the Curie point, thermal energy overcomes the exchange interaction that keeps domains aligned, so domains randomise and ferromagnetism disappears. Upon slow cooling in the absence of an external field, iron can regain some magnetism from Earth's field, though not necessarily its original strength.",{"itemId":2354,"prompt":2355,"options":2356,"correct":1509,"why":2365},"magnets.q013","A student records how many paper clips a magnet can lift after different treatments. Which table shows a fair test of whether 'number of drops from 1 metre' affects magnet strength?",[2357,2359,2361,2363],{"id":1503,"label":2358},"10 drops, 20 drops, 30 drops — each tested with a different size magnet.",{"id":1506,"label":2360},"10 drops, 20 drops, 30 drops — same magnet, same height, same clips, tested in a different room for each trial.",{"id":1509,"label":2362},"10 drops, 20 drops, 30 drops — same magnet, same height, same clips, same room temperature, tested on the same surface.",{"id":1512,"label":2364},"10 drops, 20 drops, 30 drops — magnet heated with a hair dryer for the 30-drop trial only.","A fair test changes only the independent variable (number of drops) while keeping all other variables constant: same magnet, same height, same clips, same environment. Changing magnet size, room, or adding heat introduces extra variables and invalidates the conclusion.",{"id":2367,"type":2368,"title":2369,"note":2370,"scale":2371,"rungs":2372},"ladder-84","ladder","From Classroom Magnets to the Technology Around You","A scale of magnetic field strength in tesla (T), showing how the devices you have studied compare.","log",[2373,2377,2381,2385,2388,2391,2393],{"label":2374,"value":2375,"display":2376},"Earth's magnetic field at the surface",0.00005,"~50 µT",{"label":2378,"value":2379,"display":2380},"Refrigerator magnet",0.005,"~5 mT",{"label":2382,"value":2383,"display":2384},"Small laboratory electromagnet",0.1,"0.1 T",{"label":2386,"value":44,"display":2387},"Loudspeaker voice-coil gap","~1 T",{"label":2389,"value":104,"display":2390},"Maglev train levitation magnet","~5 T",{"label":2392,"value":80,"display":2098},"Hospital MRI scanner",{"label":2394,"value":174,"display":2395},"ISRO's special test electromagnets","up to ~10 T",{"id":2397,"type":1489,"title":2398,"problem":2399,"steps":2400},"worked-example-85","Predict and Explain: The Hammered Horseshoe Magnet","A blacksmith finds an old horseshoe magnet in a scrap heap. It can lift 15 iron nails. He heats it to 900 °C, drops it on an anvil, and hammers it flat. After cooling to room temperature, it lifts only 2 nails. Explain what happened at each step, using the domain model.",[2401,2402,2403,2404],"Heating above the Curie temperature (770 °C for iron): thermal energy causes violent atomic vibration. The exchange interaction that keeps domains aligned is overcome; domains randomise. While hot, the iron is paramagnetic, not ferromagnetic — the magnet temporarily loses nearly all its organised field.","Dropping and hammering while hot: mechanical shocks help already-randomised domains stay random by introducing crystal defects and internal stress. These defects pin domain walls, making it harder for domains to realign later.","Cooling without an external field: as temperature falls below the Curie point, domains could reform, but with no strong external field to guide them and with internal stress from hammering, they settle into a complicated patchwork. Earth's weak field aligns only a small fraction.","Result: only a few regions align coherently. The net magnetic field is weak. The horseshoe now lifts 2 nails instead of 15. To restore it, one would need to stroke or place it inside a strong electromagnet's field while cooling — essentially remagnetising from scratch.",{"id":2406,"type":1483,"variant":1881,"title":2407,"markdown":2408},"callout-86","Fair Tests Have Limits Too","In Chapter 10 you designed a fair test for magnet strength. Remember that your model assumed 'strength' equals 'number of paper clips lifted.' This is a practical model, not the full physics. A magnet might have a strong field close to its pole but a narrow reach, lifting few large clips yet many small ones. Scientists use a gaussmeter to measure field strength in millitesla. At home, your clip test is valid for comparing *the same magnet before and after treatment*, but be cautious comparing different magnet shapes or sizes. Always state your model's limits when you report results.",{"id":2410,"type":1470,"markdown":2411},"prose-87","Where does magnetism lead after this? The next depth — 'Advanced' — opens three doors. First, the quantum origin: the magnetic moment of a single electron, spinning like a tiny charged sphere, is the ultimate source of every domain. Physicists use quantum mechanics to calculate why iron, cobalt, and nickel are ferromagnetic while their neighbours in the periodic table are not. Second, magnetic storage: in a hard disk drive, tiny regions of a cobalt alloy are magnetised 'up' or 'down' to store the 1s and 0s of your photographs and documents. Reading them back requires a sensor that detects the fringing field at each bit's edge — the same field pattern you traced with iron filings around a bar magnet. Third, the AC induction motor that powers metro trains and factory machines: here a changing magnetic field from the stator induces currents in the rotor, and those currents create their own magnetism that the stator then pushes against. No brushes, no permanent magnets in the rotor, just the dance of changing fields and induced currents. This is the physics that drives India's urban transport and much of its industry.",{"id":2413,"type":2414,"title":2415,"terms":2416},"glossary-88","glossary","Key Terms from This Lesson",[2417,2421,2425,2429,2433,2437,2441,2445,2449,2453,2457,2461,2465,2469,2473],{"term":2418,"meaning":2419,"example":2420},"Magnetic domain","A microscopic region within a ferromagnetic material where the magnetic moments of atoms are aligned parallel to one another. Each domain acts like a tiny magnet.","In an unmagnetised iron bar, domains point in all directions; their fields cancel out.",{"term":2422,"meaning":2423,"example":2424},"Ferromagnetic material","A material, such as iron, nickel, or cobalt, that can form magnetic domains and be strongly magnetised by an external field.","Steel paper clips are ferromagnetic; they stick to a fridge magnet.",{"term":2426,"meaning":2427,"example":2428},"Paramagnetic material","A material with unpaired electrons that weakly aligns with an external magnetic field but does not form domains or retain magnetisation.","Aluminium foil is weakly attracted to a very strong magnet but shows no permanent effect.",{"term":2430,"meaning":2431,"example":2432},"Diamagnetic material","A material whose electrons are all paired; it weakly opposes an external magnetic field and is repelled by very strong fields.","Bismuth and copper are diamagnetic; they are not attracted to ordinary magnets.",{"term":2434,"meaning":2435,"example":2436},"Magnetic pole","The region of a magnet where the magnetic field is strongest and field lines emerge (north pole) or enter (south pole).","A compass needle's north-seeking end is its north pole.",{"term":2438,"meaning":2439,"example":2440},"Magnetic field","The region around a magnet or current-carrying wire where magnetic forces act on other magnets or moving charges.","Iron filings sprinkled near a bar magnet trace out the field's curved pattern.",{"term":2442,"meaning":2443,"example":2444},"Electromagnet","A magnet created by passing electric current through a coil of wire, often with a ferromagnetic core to enhance the field.","Scrapyard cranes use electromagnets to lift cars and drop them when current stops.",{"term":2446,"meaning":2447,"example":2448},"Curie temperature","The temperature above which a ferromagnetic material loses its domain alignment and becomes paramagnetic.","Iron's Curie temperature is about 770 °C; above this, a permanent iron magnet loses its strength.",{"term":2450,"meaning":2451,"example":2452},"Solenoid","A coil of wire that produces a magnetic field when electric current passes through it.","A solenoid with an iron nail inside becomes a powerful electromagnet.",{"term":2454,"meaning":2455,"example":2456},"Ampere-turn","A unit of magnetomotive force; the product of current in amperes and number of turns in a coil.","2 amperes through 100 turns gives 200 ampere-turns of magnetising force.",{"term":2458,"meaning":2459,"example":2460},"Fair test","An investigation in which only the independent variable is changed, while all other variables are kept constant.","Testing magnet strength by counting clips lifted, using the same clips and magnet size each time.",{"term":2462,"meaning":2463,"example":2464},"Maglev","Magnetic levitation; a transport system where strong magnetic fields lift and propel a vehicle without wheel-rail contact.","Shanghai's airport maglev train reaches 430 km\u002Fh using electromagnets.",{"term":2466,"meaning":2467,"example":2468},"MRI","Magnetic Resonance Imaging; a medical scan that uses powerful electromagnets and radio waves to create images of organs and tissues.","A 3 tesla MRI scanner uses superconducting electromagnets cooled by liquid helium.",{"term":2470,"meaning":2471,"example":2472},"Lodestone","A naturally magnetised piece of the mineral magnetite (Fe₃O₄), used as an early compass.","Indian sailors of the Chola period used lodestone to navigate across the Bay of Bengal.",{"term":1613,"meaning":2474,"example":2475},"The ability of a ferromagnetic material to retain magnetisation after the external field is removed.","Steel has high retentivity, making good permanent magnets; soft iron has low retentivity, making good electromagnet cores.",{"id":2477,"type":2478,"sourceIds":2479},"sources-89","sources",[2480,2481],"magnets-ncert-curiosity-6-ch4","angles-wiki-degree",[2480,2481],"needs_review",{"generatedBy":2485,"notes":2486},"claude-code","generated from work item wi-61bfa1ee (11 chapters)","75378a7c64338031b06a4a377548f88625347facc35214515925aae1ce2e225c",{},{"state":6,"reviewer":2490,"selfReview":2491,"reviewedAt":2492,"method":806},"curator",false,"2026-09-21T04:52:13.354622+00:00","generation-19f885ad-fe89-48be-9528-20ae7eee520b",[2495,2503],{"id":2481,"title":2496,"publisher":2497,"url":2498,"kind":2499,"accessed":2500,"usage":2501,"verification":2502},"Degree (angle)","Wikipedia","https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FDegree_(angle)","reference","2026-09-20","Supports the history of dividing a full turn into 360 parts (Babylonian sexagesimal astronomy, closeness to the days in a year, many divisors of 360) and minutes and seconds of arc.","machine_checked",{"id":2480,"title":2504,"publisher":2505,"url":2506,"kind":2507,"accessed":2508,"usage":2509,"verification":2502},"Curiosity: Textbook of Science for Grade 6, Chapter 4 (Exploring Magnets)","NCERT","https:\u002F\u002Fncert.nic.in\u002Ftextbook\u002Fpdf\u002Ffecu104.pdf","educational","2026-09-21","Magnets and magnetic materials: which objects a magnet attracts (iron, nickel, cobalt) and which it does not; poles of a bar magnet; attraction and repulsion between poles; the magnetic compass and finding directions; keeping magnets safe. NCERT Class 6 Science (Curiosity), Reprint 2026-27."]