[{"data":1,"prerenderedAt":977},["ShallowReactive",2],{"layer:patterns:discover":3},{"layer":4,"contentHash":959,"dependencyHashes":960,"approval":970,"releaseId":976},{"schemaVersion":5,"conceptId":6,"locale":7,"depth":8,"revision":5,"title":9,"subtitle":10,"summary":11,"objectives":12,"estimatedMinutes":18,"plate":19,"blocks":40,"sourceIds":954,"reviewStatus":955,"authoring":956},1,"patterns","en","discover","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.",[13,14,15,16,17],"Tell a repeating pattern from a growing or shrinking pattern, and find the repeating unit.","Find the difference between neighbouring terms and use it to continue a number pattern.","Recognise counting patterns, odd and even numbers, and patterns in the hundred square and calendar.","Count matchsticks and dots in growing shape patterns and predict the next picture.","Describe a rule in words and use “jumps” to find a far-away term.",35,{"title":20,"rows":21},"Lesson plate",[22,25,28,31,34,37],{"label":23,"value":24},"Depth","Discover",{"label":26,"value":27},"Reading time","≈ 35 minutes",{"label":29,"value":30},"Prior knowledge","Counting, adding and times tables to 10",{"label":32,"value":33},"Chapters","10",{"label":35,"value":36},"Labs","Pattern machine ×2, sort game, match pairs",{"label":38,"value":39},"Big idea","Find the rule, then predict",[41,45,51,57,60,65,86,89,156,161,164,178,195,198,203,208,230,235,238,241,261,274,278,283,286,327,332,377,382,385,412,431,435,440,443,474,487,491,504,509,511,521,525,530,533,536,564,575,579,584,587,592,654,684,695,699,712,717,788,912,916,922,927,931,945],{"id":42,"type":43,"markdown":44},"intro-question","prose","Look at this row of numbers: **2, 4, 6, 8, …** What comes next? Almost everyone says **10** straight away. Now try **1, 4, 9, 16, …** That one takes a moment longer, but many people spot it: **25**.\n\nHow did you know? Nobody told you the answer. You looked at the numbers you had, noticed something that stayed the same each time, and trusted it to carry on. That noticing is the heart of mathematics. A **pattern** is something that repeats or grows in a way you can describe, and the description is called the **rule**.\n\nIn this layer you will hunt for patterns in bangles and beads, in rangoli and kolam borders, in steps and stacks, in the hundred square and on the calendar, and in shapes made from matchsticks and dots. By the end you will be able to answer the question on the cover of this topic: **how can you predict the 100th term without drawing 100 pictures?**",{"id":46,"type":47,"variant":48,"title":49,"markdown":50},"how-to-use","callout","observation","How to use this layer","Read the chapters in order the first time. Whenever you see a **prediction**, choose an answer *before* you read on. Try every lab: they are games, and the pattern machine gives you a new puzzle each round. Keep a pencil and some paper (or a few matchsticks or buttons) nearby. Patterns are much easier to see when you build them.",{"id":52,"type":53,"title":54,"eyebrow":55,"navLabel":56},"ch01","chapter","Patterns are everywhere","Chapter 01","1 Patterns everywhere",{"id":58,"type":43,"markdown":59},"everywhere","Before you learned to read, you were already reading patterns. Day follows night follows day. Monday follows Sunday. In a song, the chorus comes back. On a train journey, the wheels go *clickety-clack, clickety-clack* over the rail joints.\n\nWalk around your home or school and you will find more:\n\n- **Floor tiles** that repeat square after square.\n- **Bangles** stacked green, gold, green, gold.\n- **A rangoli or kolam** at the door, where the same little shape is drawn again and again around a border.\n- **Steps** on a staircase, each one the same height above the one before.\n- **Cricket overs**: six balls, then a new over, then six more balls.\n- **The ticking of a clock**: after 12 comes 1 again.\n\nA pattern lets you **predict**. If you know the rule, you know what comes next without waiting to see it. That is why patterns matter so much: in music, weaving, building, computer programs, weather records and in all of mathematics.",{"id":61,"type":47,"variant":62,"title":63,"markdown":64},"def-pattern","definition","Pattern and rule","A **pattern** is an arrangement of things (colours, shapes, sounds or numbers) that repeats or changes in a regular way.\n\nThe **rule** is the instruction that tells you how the pattern carries on. For 2, 4, 6, 8, … the rule could be said as *\"start at 2 and add 2 each time\"*.\n\nEach item in a number pattern is called a **term**. In 2, 4, 6, 8, … the first term is 2, the second term is 4, and so on.",{"id":66,"type":67,"tone":68,"items":69},"spec-two-kinds","spec","amber",[70,74,78,82],{"label":71,"big":72,"value":73},"Repeating","AB AB AB","The same group of things comes round again and again, like green, gold, green, gold bangles.",{"label":75,"big":76,"value":77},"Growing","1, 3, 6, 10","Each step gets bigger (or smaller) by a rule, like a stack of cups with one more row each time.",{"label":79,"big":80,"value":81},"Number","5, 10, 15","A list of numbers that follows a rule: counting in fives.",{"label":83,"big":84,"value":85},"Shape","□ □□ □□□","Pictures that follow a rule, like squares made of matchsticks, one more square each time.",{"id":87,"type":43,"markdown":88},"two-kinds","Mathematicians sort patterns in many ways, but two big families are enough to start with.\n\nIn a **repeating pattern**, a small group of things, the **repeating unit** (sometimes called the *core*), comes round again and again. The pattern never really gets bigger; it just keeps going.\n\nIn a **growing pattern**, each step changes the one before by the same kind of rule: one more row, two more sticks, double the dots. The pattern keeps getting bigger (or, in a **shrinking pattern**, smaller).\n\nNumber patterns and shape patterns can be either kind. Most of this topic is about growing patterns, because they are where the surprises are.",{"id":90,"type":91,"title":92,"prompt":93,"options":94},"explorer-hunt","explorer","A pattern hunt around India","Pick a place to see the pattern hiding there and its rule.",[95,106,115,125,135,146],{"id":96,"label":97,"chain":98,"badge":103,"note":105},"kolam","Kolam at the door",[99,100,101,102],"Grid of dots","Loop around a dot","Repeat the loop","Border all round",{"text":71,"tone":104},"yes","The same small loop is drawn around dot after dot. The unit repeats by sliding along the border, and in the middle it repeats by turning around a centre. Rule: “loop, line, loop, line, …”.",{"id":107,"label":108,"chain":109,"badge":113,"note":114},"bangles","Bangles on a wrist",[110,111,110,111,112],"Green","Gold","and so on",{"text":71,"tone":104},"A unit of two bangles. Every odd-numbered bangle is green and every even-numbered bangle is gold, so the 20th is gold and the 21st is green.",{"id":116,"label":117,"chain":118,"badge":123,"note":124},"steps","Ghat steps",[119,120,121,122],"Step 1: 15 cm","Step 2: 30 cm","Step 3: 45 cm","Add 15 cm each step",{"text":75,"tone":104},"The steps down to a river or a temple tank are the same height, so the height above the water grows by the same amount each step. With 15 cm steps, the 10th step is 150 cm up.",{"id":126,"label":127,"chain":128,"badge":133,"note":134},"sunflower","A sunflower head",[129,130,131,132],"Seeds in spirals","Count one way: 34","Count the other way: 55","Neighbours in 1, 1, 2, 3, 5, 8, …",{"text":75,"tone":104},"The seeds form two sets of spirals. In many sunflowers there are 34 one way and 55 the other: two neighbouring numbers of the pattern 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, where each number is the sum of the two before. Not every head follows it — about one sunflower count in five does not — so count for yourself. You will meet this pattern properly in the Understand layer.",{"id":136,"label":137,"chain":138,"badge":143,"note":145},"calendar","A wall calendar",[139,140,141,142],"7 columns","Down a column: +7","Across a row: +1","Weekdays repeat",{"text":144,"tone":104},"Both kinds","The dates grow (1, 2, 3, …) while the weekdays repeat (Mon, Tue, …, Sun). Because a week has 7 days, every column goes up in sevens.",{"id":147,"label":148,"chain":149,"badge":154,"note":155},"honeycomb","A honeycomb",[150,151,152,153],"Six-sided cells","Each cell touches 6","No gaps","Repeats in every direction",{"text":71,"tone":104},"Bees build hexagonal cells that fit together with no gaps. A pattern that covers a flat surface with no gaps or overlaps is called a tessellation; you will meet it again in the Extend layer.",{"id":157,"type":53,"title":158,"eyebrow":159,"navLabel":160},"ch02","Repeating patterns: bangles, beads and borders","Chapter 02","2 Repeating",{"id":162,"type":43,"markdown":163},"repeat-unit","Look at a string of beads: **red, red, blue, red, red, blue, red, red, blue, …**\n\nThe group **red, red, blue** repeats. That group is the **repeating unit**. It has 3 beads in it, so we can call it an *AAB* pattern: two of one thing, then one of another.\n\nOther repeating units you will meet:\n\n| Name | Example | Unit length |\n| --- | --- | --- |\n| AB | green, gold, green, gold, … | 2 |\n| ABC | ▲ ● ■ ▲ ● ■ … | 3 |\n| AAB | red, red, blue, … | 3 |\n| ABB | clap, stamp, stamp, … | 3 |\n| ABCD | Mon, Tue, Wed, Thu, … (only part of the week) | 4 |\n\nThe trick for any repeating pattern is to **find the unit first**, then count in units.",{"id":165,"type":166,"title":167,"problem":168,"steps":169,"help":175},"we-bead-20","worked_example","Which colour is the 20th bead?","A necklace is made with the repeating unit **red, red, blue**. What colour is the **20th** bead?",[170,171,172,173,174],"Find the repeating unit: red, red, blue. It has **3** beads.","Beads 3, 6, 9, 12, 15, 18 are the ends of complete units, and they are all **blue**.","After bead 18 a new unit starts: bead 19 is the 1st in its unit (red) and bead 20 is the 2nd (red).","Another way: 20 ÷ 3 = 6 remainder 2. Six whole units, then 2 more beads. The 2nd bead of a unit is **red**.","So the 20th bead is **red**. Check with the 30th: 30 ÷ 3 = 10 remainder 0, so it ends a unit: **blue**. ✓",{"simplerExplanation":176,"anotherExample":177},"Count along in groups of 3 (red, red, blue) until you pass 20. Six groups take you to 18. Then red (19), red (20).","Bangles green, gold, green, gold, … have a unit of 2. Every even-numbered bangle is gold, so the 20th is gold and the 25th is green.",{"id":179,"type":180,"prompt":181,"options":182,"explanation":194},"predict-bangle","prediction","A girl stacks her bangles in the order **red, green, yellow, red, green, yellow, …**. Without counting one by one, what colour is the **13th** bangle?",[183,186,188,191],{"id":184,"label":185},"a","Red",{"id":187,"label":110},"b",{"id":189,"label":190},"c","Yellow",{"id":192,"label":193},"d","It is impossible to tell without drawing them","**Red.** The unit is red, green, yellow: 3 bangles. 13 ÷ 3 = 4 remainder 1, so after four whole units (12 bangles) the 13th bangle is the 1st of a new unit, which is **red**. Bangles 1, 4, 7, 10, 13, 16, … are all red: they go up in threes.",{"id":196,"type":43,"markdown":197},"kolam-rangoli","Repeating patterns are one of the oldest kinds of art in India.\n\nA **kolam**, drawn every morning at the doorstep in many homes in Tamil Nadu and neighbouring states, starts with a grid of dots made from rice flour. Lines loop around the dots, and in a kolam border the same loop shape is drawn again and again all the way along. Muggulu in Andhra Pradesh and Telangana, rangoli in Maharashtra and Gujarat, alpana in Bengal and mandana in Rajasthan use the same idea.\n\nLook closely and you will see two kinds of repetition:\n\n- **Along a line** (a border): the unit is repeated by *sliding* it along. This is called a **frieze** or strip pattern.\n- **Around a centre** (a flower or star shape): the unit is repeated by *turning* it. This makes the design look the same when you turn it by a quarter or a sixth of a turn.\n\nBlock-printed saris from Bagru and Sanganer, Kanchipuram silk borders, beadwork from the Toda and Banjara communities, the jali screens of old buildings, and the tiles on a railway station floor all use repeating units in the same way.",{"id":199,"type":47,"variant":200,"title":201,"markdown":202},"try-kolam","try_it","Draw a kolam border","1. Make a row of 10 dots, about two finger-widths apart.\n2. Invent a small unit: for example, a loop around one dot, then a line under the next dot.\n3. Repeat your unit all the way along the row.\n4. Ask a friend to guess your unit from the border, and to say what would be drawn around the 25th dot.\n\nIf your unit uses 2 dots, the 25th dot is the 1st dot of a unit (25 ÷ 2 = 12 remainder 1). If it uses 3 dots, the 25th dot is also the 1st (25 ÷ 3 = 8 remainder 1). Check with your own drawing.",{"id":204,"type":47,"variant":205,"title":206,"markdown":207},"mis-repeat","misconception","“A repeating pattern is just the first two things”","It is tempting to look at **red, red, blue, red, red, blue** and say *\"red, blue, red, blue\"*. But the unit is the **whole** group that repeats, here **red, red, blue**. A safe test: write the unit out three times in a row and check it matches the whole pattern. If it doesn't, your unit is wrong or too short.",{"id":209,"type":210,"itemId":211,"prompt":212,"check":213,"hints":225,"feedback":227},"pr-unit","practice","patterns.discover-unit","What is the repeating unit of this pattern? **clap, clap, stamp, clap, clap, stamp, clap, clap, stamp**",{"kind":214,"options":215,"correct":224},"choice",[216,218,220,222],{"id":184,"label":217},"clap, stamp",{"id":187,"label":219},"clap, clap, stamp",{"id":189,"label":221},"clap, clap, stamp, clap",{"id":192,"label":223},"stamp, clap",[187],[226],"Say the pattern out loud and listen for where it starts again.",{"correct":228,"incorrect":229},"Yes. The unit is clap, clap, stamp: three actions, then it starts again.","Write your answer out three times in a row and compare it with the pattern. Only clap, clap, stamp matches exactly.",{"id":231,"type":53,"title":232,"eyebrow":233,"navLabel":234},"ch03","Growing patterns: stacks, steps and towers","Chapter 03","3 Growing",{"id":236,"type":43,"markdown":237},"growing-intro","At a birthday party someone builds a pyramid of paper cups. The top row has 1 cup. The row under it has 2. Then 3, then 4, then 5.\n\nHow many cups altogether for a pyramid with 1 row, 2 rows, 3 rows, …?\n\n| Rows | Cups in the new bottom row | Total cups |\n| --- | --- | --- |\n| 1 | 1 | 1 |\n| 2 | 2 | 1 + 2 = 3 |\n| 3 | 3 | 3 + 3 = 6 |\n| 4 | 4 | 6 + 4 = 10 |\n| 5 | 5 | 10 + 5 = 15 |\n\nThe totals **1, 3, 6, 10, 15** make a growing pattern. Each time, you add **one more than last time**: add 2, then 3, then 4, then 5. These numbers are so famous they have a name, the **triangular numbers**, because you can arrange that many dots in a triangle.",{"id":239,"type":43,"markdown":240},"growing-steps","Not every growing pattern grows by a changing amount. Some grow by **the same amount every time**:\n\n- A tower of blocks, adding 2 blocks each day: 2, 4, 6, 8, …\n- A staircase in a building where each step is 15 cm higher: 15, 30, 45, 60, … cm above the ground.\n- Your piggy bank, if you put in ₹10 every Sunday and started with ₹50: ₹50, ₹60, ₹70, ₹80, …\n\nA good first question for any growing pattern is: **\"By how much does it change each time?\"** Write the changes (the *differences*) underneath the pattern. If they are all the same, the pattern grows steadily. If they change, look for a pattern in the differences themselves.",{"id":242,"type":116,"title":243,"items":244},"steps-difference","Finding what changes: the difference trick",[245,248,252,255,258],{"title":246,"text":247},"Write the terms in a row","e.g. 3, 7, 11, 15, 19",{"title":249,"tag":250,"text":251},"Subtract neighbours","from the 2nd term on","7 − 3 = 4, 11 − 7 = 4, 15 − 11 = 4, 19 − 15 = 4.",{"title":253,"text":254},"Look at the differences","All 4. So the rule is “add 4 each time”.",{"title":256,"text":257},"Use the rule","The next term is 19 + 4 = 23, then 27, then 31.",{"title":259,"text":260},"If the differences change","For 1, 3, 6, 10 the differences are 2, 3, 4: they go up by 1. So the next difference is 5 and the next term is 15.",{"id":262,"type":180,"prompt":263,"options":264,"explanation":273},"predict-cups","A cup pyramid has rows of 1, 2, 3, 4, 5 cups: **15 cups**. How many cups would a pyramid with **6 rows** need?",[265,267,269,271],{"id":184,"label":266},"18",{"id":187,"label":268},"20",{"id":189,"label":270},"21",{"id":192,"label":272},"30","**21.** A sixth row needs 6 more cups, so 15 + 6 = **21**. A common slip is to say 30 (doubling 15) or 18 (adding 3, like last time). The amount added grows by one each time, so this time you add 6.",{"id":275,"type":47,"variant":48,"title":276,"markdown":277},"obs-shrinking","Shrinking patterns count too","Patterns can go down as well as up. A rocket countdown goes 10, 9, 8, …, 1. A 1-litre bottle of water shared out 200 ml at a time leaves 1,000, 800, 600, 400, 200, 0 ml. The rule is still a rule: *subtract 200 each time*.",{"id":279,"type":53,"title":280,"eyebrow":281,"navLabel":282},"ch04","Counting on and counting back","Chapter 04","4 Skip counting",{"id":284,"type":43,"markdown":285},"skip-counting","The very first number patterns you learned were **counting patterns**:\n\n- Counting on in ones: 1, 2, 3, 4, 5, …\n- Counting in twos: 2, 4, 6, 8, … (pairs of socks, pairs of shoes)\n- Counting in fives: 5, 10, 15, 20, … (fingers on hands, ₹5 coins)\n- Counting in tens: 10, 20, 30, 40, … (₹10 notes)\n- Counting in hundreds: 100, 200, 300, … (₹100 notes)\n\nCounting in threes gives the **3 times table**: 3, 6, 9, 12, 15, … Counting in any number gives that number's times table, and the numbers you land on are its **multiples**.\n\nYou can also **count back**: 50, 45, 40, 35, … (take away 5 each time) or 100, 90, 80, 70, … (take away 10).",{"id":287,"type":288,"caption":289,"columns":290,"rows":294},"table-skip","table","Counting patterns side by side (first eight terms, computed)",[291,292,293],"Count in","First eight terms","Where you see it",[295,299,303,307,311,315,319,323],[296,297,298],"2s","2, 4, 6, 8, 10, 12, 14, 16","Pairs of shoes, wheels on bicycles",[300,301,302],"3s","3, 6, 9, 12, 15, 18, 21, 24","Wheels on autorickshaws",[304,305,306],"4s","4, 8, 12, 16, 20, 24, 28, 32","Legs on cows, wheels on cars",[308,309,310],"5s","5, 10, 15, 20, 25, 30, 35, 40","₹5 coins, fingers on hands",[312,313,314],"6s","6, 12, 18, 24, 30, 36, 42, 48","Balls in cricket overs",[316,317,318],"7s","7, 14, 21, 28, 35, 42, 49, 56","Days in weeks",[320,321,322],"10s","10, 20, 30, 40, 50, 60, 70, 80","₹10 notes",[324,325,326],"Back in 5s from 50","50, 45, 40, 35, 30, 25, 20, 15","Minutes left in a 50-minute class",{"id":328,"type":47,"variant":329,"title":330,"markdown":331},"aha-fives","aha","The last-digit trick","Look only at the **last digit** of the counting-in-fives pattern: 5, 0, 5, 0, 5, 0, … A growing pattern hides a repeating one!\n\nCounting in twos: last digits 2, 4, 6, 8, 0, 2, 4, 6, 8, 0, … (a unit of 5). Counting in fours: 4, 8, 2, 6, 0, 4, 8, 2, 6, 0, … Try counting in threes and write down only the last digits. How long before they repeat? (Answer: after 10 steps: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0.)",{"id":333,"type":334,"component":335,"componentVersion":5,"config":336,"objective":370,"textAlternative":371,"help":372},"lab-counting","interactive","pattern-machine",{"puzzles":337},[338,345,349,353,358,361,366],{"kind":339,"rule":340,"show":343,"ask":5,"hint":344},"number",{"type":341,"start":342,"step":342},"add",2,5,"Count in twos.",{"kind":339,"rule":346,"show":347,"ask":342,"hint":348},{"type":341,"start":343,"step":343},4,"Think of ₹5 coins.",{"kind":339,"rule":350,"show":347,"ask":342,"hint":352},{"type":341,"start":351,"step":351},3,"This is the 3 times table.",{"kind":339,"rule":354,"show":343,"ask":342,"hint":357},{"type":341,"start":355,"step":356},50,-5,"The numbers are getting smaller. By how much?",{"kind":339,"rule":359,"show":343,"ask":342,"hint":360},{"type":341,"start":5,"step":347},"Find the difference between neighbours.",{"kind":339,"rule":362,"show":347,"ask":342,"hint":365},{"type":341,"start":363,"step":364},100,-10,"Count back in tens.",{"kind":339,"rule":367,"show":347,"ask":351,"hint":369},{"type":341,"start":368,"step":368},7,"Days in 1 week, 2 weeks, 3 weeks…","Spot the step in counting patterns (forwards and backwards) and predict the next terms.","The pattern machine shows the first few terms of a counting pattern and asks you to type the next ones. You score a point for each correct term and build a streak for correct answers in a row.\n\nThe seven puzzles, with their answers:\n\n1. 2, 4, 6, 8, 10, … next: **12** (count in twos).\n2. 5, 10, 15, 20, … next: **25, 30** (count in fives).\n3. 3, 6, 9, 12, … next: **15, 18** (the 3 times table).\n4. 50, 45, 40, 35, 30, … next: **25, 20** (count back in fives).\n5. 1, 5, 9, 13, 17, … next: **21, 25** (add 4).\n6. 100, 90, 80, 70, … next: **60, 50** (count back in tens).\n7. 7, 14, 21, 28, … next: **35, 42, 49** (the 7 times table: days in weeks).\n\nFor every puzzle, the method is the same: subtract neighbouring terms to find the step, then keep adding it.",{"simplerExplanation":373,"hints":374},"Look at two numbers next to each other. How far apart are they? Keep jumping that far.",[375,376],"If the numbers get smaller, the step is a take-away.","Check your step works for every pair, not just the first two.",{"id":378,"type":53,"title":379,"eyebrow":380,"navLabel":381},"ch05","Odd and even numbers","Chapter 05","5 Odd and even",{"id":383,"type":43,"markdown":384},"odd-even","Try to share some sweets between two friends so that both get the same number, with none left over.\n\n- 6 sweets: 3 each. ✓\n- 7 sweets: 3 each and **1 left over**. ✗\n\nNumbers that can be split into **pairs** with nothing left over are **even**: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, … Numbers that always leave **one left over** are **odd**: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, …\n\nIf you line up counters in two rows, an even number makes two neat rows. An odd number always has one counter sticking out, like a little tail.\n\nThe **last digit** tells you straight away:\n\n- Even numbers end in **0, 2, 4, 6 or 8**.\n- Odd numbers end in **1, 3, 5, 7 or 9**.\n\nSo 3,578 is even and 1,00,001 is odd, however big they are. On a number line, odd and even take turns: odd, even, odd, even, … It is a repeating pattern with a unit of 2.",{"id":386,"type":288,"caption":387,"columns":388,"rows":393},"table-odd-even","What happens when you add odd and even numbers? (checked with pairs of counters)",[389,390,391,392],"Add","Example","Result","Why",[394,399,403,408],[395,396,397,398],"even + even","4 + 6 = 10","even","Pairs plus pairs are still all pairs.",[400,401,397,402],"odd + odd","3 + 5 = 8","The two leftover counters pair up with each other.",[404,405,406,407],"odd + even","3 + 4 = 7","odd","One leftover counter has no partner.",[409,410,406,411],"even + odd","6 + 1 = 7","Same as above, in the other order.",{"id":413,"type":210,"itemId":414,"prompt":415,"check":416,"hints":425,"feedback":428},"pr-odd-even","patterns.discover-odd-sum","Priya adds **three odd numbers** together. Is her answer odd or even?",{"kind":214,"options":417,"correct":424},[418,420,422],{"id":184,"label":419},"Always odd",{"id":187,"label":421},"Always even",{"id":189,"label":423},"Sometimes odd, sometimes even",[184],[426,427],"Add the first two odd numbers. What kind of number do you get?","Then add the third odd number to that.",{"correct":429,"incorrect":430},"Right. odd + odd = even, then even + odd = odd. Try 1 + 3 + 5 = 9 or 7 + 7 + 7 = 21: always odd.","Think in steps: odd + odd makes even (the two leftovers pair up). Then even + odd is odd. For example, 1 + 3 + 5 = 9.",{"id":432,"type":47,"variant":200,"title":433,"markdown":434},"try-house-numbers","Odd and even on your street","In many cities, houses on one side of a street have odd numbers and those on the other side have even numbers, so a postman walking down one side counts 1, 3, 5, 7, … Train seats, cinema rows and hotel rooms often use the same trick. Next time you are out, check whether the numbers on the left and right sides of a road follow this pattern.",{"id":436,"type":53,"title":437,"eyebrow":438,"navLabel":439},"ch06","Patterns in the hundred square","Chapter 06","6 Hundred square",{"id":441,"type":43,"markdown":442},"hundred-square","A **hundred square** is a grid of the numbers 1 to 100 in ten rows of ten. It is packed with patterns.\n\n- **Going across** a row, each number is **1 more** than the one before.\n- **Going down** a column, each number is **10 more** than the one above: 3, 13, 23, 33, … The last digit stays the same, and the tens digit goes up by one.\n- **The last column** is 10, 20, 30, …, 100: counting in tens.\n- **The diagonal going down to the right** goes up by 11: 1, 12, 23, 34, 45, …\n- **The diagonal going down to the left** goes up by 9: 10, 19, 28, 37, 46, … These are the multiples of 9 (plus the column shift): 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 sit on a slanting line.\n\nIf you shade every multiple of 2, you get stripes going down (columns 2, 4, 6, 8, 10). Shade the multiples of 5 and you get two stripes (columns 5 and 10). Shade the multiples of 3 and you get slanting lines. Shade the multiples of 9 and you get one slanting line.",{"id":444,"type":288,"caption":445,"columns":446,"rows":449},"table-hundred","Moves in the hundred square (ten numbers in each row)",[447,448,390],"Move","Change",[450,454,458,462,466,470],[451,452,453],"One step right →","+1","34 → 35",[455,456,457],"One step left ←","−1","34 → 33",[459,460,461],"One step down ↓","+10","34 → 44",[463,464,465],"One step up ↑","−10","34 → 24",[467,468,469],"Diagonal down-right ↘","+11","34 → 45",[471,472,473],"Diagonal down-left ↙","+9","34 → 43",{"id":475,"type":210,"itemId":476,"prompt":477,"check":478,"hints":481,"feedback":484},"pr-hundred","patterns.discover-hundred","In a hundred square, start at **23**. Move **two steps down** and then **one step right**. Which number do you land on?",{"kind":339,"answer":479,"tolerance":480},44,0,[482,483],"Each step down adds 10.","A step right adds 1.",{"correct":485,"incorrect":486},"Yes: 23 → 33 → 43 → 44.","Two steps down add 10 + 10 = 20, giving 43. One step right adds 1, giving 44.",{"id":488,"type":47,"variant":329,"title":489,"markdown":490},"aha-nines","The 9 times table has a secret","Write the 9 times table: **9, 18, 27, 36, 45, 54, 63, 72, 81, 90**.\n\n- The **tens digit** goes up by 1 each time: 0, 1, 2, 3, …\n- The **units digit** goes down by 1 each time: 9, 8, 7, 6, …\n- The two digits **always add up to 9**: 1 + 8, 2 + 7, 3 + 6, …\n\nThat is why the multiples of 9 make a neat slanting line in the hundred square.",{"id":492,"type":180,"prompt":493,"options":494,"explanation":503},"predict-column","In a hundred square, you start at **7** and keep moving **straight down**. Which of these numbers will you land on?",[495,497,499,501],{"id":184,"label":496},"70",{"id":187,"label":498},"76",{"id":189,"label":500},"87",{"id":192,"label":502},"98","**87.** Moving down adds 10 each time: 7, 17, 27, 37, 47, 57, 67, 77, 87, 97. The tens digit changes but the units digit stays **7**. 70 is in the last column (units digit 0), 76 is one column to the left and 98 one column to the right.",{"id":505,"type":53,"title":506,"eyebrow":507,"navLabel":508},"ch07","Calendar patterns","Chapter 07","7 Calendar",{"id":136,"type":43,"markdown":510},"A calendar page is a number grid with **7 columns**, one for each day of the week. That single fact creates lots of patterns.\n\nIn September 2026, the 1st is a Tuesday. The Mondays are the **7, 14, 21, 28**th: they go up by **7**, because a week has 7 days.\n\n- **Down a column** (same weekday, next week): add 7.\n- **Across a row**: add 1.\n- **Diagonal down-right**: add 8 (one week plus one day).\n- **Diagonal down-left**: add 6 (one week minus one day).\n\nSo if your birthday is on a Friday the 2nd, then the 9th, 16th, 23rd and 30th of that month are also Fridays. (In October 2026 the 2nd *is* a Friday; check a calendar.)",{"id":512,"type":166,"title":513,"problem":514,"steps":515,"help":519},"we-calendar","What day is it in 3 weeks?","Today is Wednesday the 5th. What date will it be on the Wednesday that is **3 weeks** later, and what day of the week will the 20th be?",[516,517,518],"Three weeks is 3 × 7 = 21 days. 5 + 21 = **26**, so it is Wednesday the 26th.","The Wednesdays are 5, 12, 19, 26 (add 7 each time).","The 20th is one day after Wednesday the 19th, so the 20th is a **Thursday**.",{"simplerExplanation":520},"Keep adding 7 to jump a whole week and land on the same weekday: 5, 12, 19, 26.",{"id":522,"type":47,"variant":200,"title":523,"markdown":524},"try-calendar","A calendar magic trick","Ask a friend to draw a square around **any 3 × 3 block** of nine dates on a calendar, and tell you only the date in the middle. Say, instantly, the total of all nine dates.\n\nThe secret: **multiply the middle date by 9.** If the middle is 15, the total is 135. (Check: 7 + 8 + 9 + 14 + 15 + 16 + 21 + 22 + 23 = 135.) You will find out why this always works in the Investigate layer.",{"id":526,"type":53,"title":527,"eyebrow":528,"navLabel":529},"ch08","Shape patterns with matchsticks and dots","Chapter 08","8 Sticks and dots",{"id":531,"type":43,"markdown":532},"matchsticks","Take some matchsticks (or toothpicks, or ice-cream sticks) and make a square: that needs **4** sticks. Now add a second square joined to the first. You do not need 4 more sticks, because the two squares **share a side**. You only need **3** more: 7 sticks for 2 squares.\n\n| Squares in a row | 1 | 2 | 3 | 4 | 5 | 6 |\n| --- | --- | --- | --- | --- | --- | --- |\n| Matchsticks | 4 | 7 | 10 | 13 | 16 | 19 |\n\nThe matchstick pattern goes **4, 7, 10, 13, 16, 19**: add 3 each time. Every new square needs one top, one bottom and one side, because the other side is already there.",{"id":534,"type":43,"markdown":535},"dots","Now try **dots**. Arrange dots in squares: a 1 by 1 square, a 2 by 2 square, a 3 by 3 square, and so on.\n\n| Size | 1 × 1 | 2 × 2 | 3 × 3 | 4 × 4 | 5 × 5 | 6 × 6 |\n| --- | --- | --- | --- | --- | --- | --- |\n| Dots | 1 | 4 | 9 | 16 | 25 | 36 |\n\nThese are the **square numbers**: 1, 4, 9, 16, 25, 36, … Each one is a number multiplied by itself.\n\nArrange dots in triangles instead (1 dot on top, 2 in the next row, 3 in the next, …) and you get **1, 3, 6, 10, 15, 21**: the same triangular numbers as the cup pyramid. A **staircase** of blocks, one block in the first column, two in the next, three in the next, is the same pattern again.",{"id":537,"type":334,"component":335,"componentVersion":5,"config":538,"objective":557,"textAlternative":558,"help":559},"lab-shapes",{"puzzles":539},[540,544,547,551,554],{"kind":541,"shape":542,"show":351,"askTerm":343,"hint":543},"shape","matchstick-squares","Each new square shares one side with the last.",{"kind":541,"shape":545,"show":351,"askTerm":343,"hint":546},"staircase","The new column is one block taller than the last one.",{"kind":541,"shape":548,"show":347,"askTerm":549,"hint":550},"dot-squares",6,"A 6 by 6 square of dots.",{"kind":541,"shape":552,"show":351,"askTerm":343,"hint":553},"matchstick-triangles","Triangles in a row share sides too.",{"kind":541,"shape":555,"show":351,"askTerm":549,"hint":556},"l-shapes","Each L grows by one tile on each arm.","Build growing shape patterns and predict how many sticks, dots or tiles a later picture needs.","The pattern machine draws the first few pictures of a growing shape pattern, counts them, and asks for the count in a later picture.\n\n1. **Matchstick squares in a row**: 4, 7, 10, … sticks. Picture 5 needs **16** sticks (add 3 each time: 13, then 16).\n2. **Block staircase**: 1, 3, 6 blocks. Picture 5 needs 1 + 2 + 3 + 4 + 5 = **15** blocks.\n3. **Square dot patterns**: 1, 4, 9, 16 dots. Picture 6 is 6 × 6 = **36** dots.\n4. **Matchstick triangles in a row**: 3, 5, 7 sticks. Picture 5 needs **11** sticks (add 2 each time).\n5. **Growing L-shapes**: 1, 3, 5 tiles (one corner tile, with each arm getting one tile longer). Picture 6 needs **11** tiles (add 2 each time).\n\nThe machine can also show you the rule it used. Growing patterns that add the same amount each time are the easiest to predict far ahead.",{"simplerExplanation":560,"hints":561},"Count the first pictures, write the numbers down, and look at how much they go up by each time.",[562,563],"Draw the next picture if you are stuck, then count.","For the staircase, add one more than last time.",{"id":565,"type":210,"itemId":566,"prompt":567,"check":568,"hints":570,"feedback":572},"pr-sticks-5","patterns.discover-sticks-5","Matchstick squares in a row use 4, 7, 10, 13, … sticks. How many matchsticks do you need for **5 squares** in a row?",{"kind":339,"answer":569,"tolerance":480,"unit":531},16,[571],"Add 3 to the number for 4 squares.",{"correct":573,"incorrect":574},"Yes: 13 + 3 = 16 matchsticks.","The pattern adds 3 each time: 4, 7, 10, 13, then 13 + 3 = 16.",{"id":576,"type":47,"variant":205,"title":577,"markdown":578},"mis-shared-sides","“5 squares need 5 × 4 = 20 sticks”","That would be true only if every square stood on its own, apart from the others. In a row, neighbouring squares **share a side**, so you save a stick at every join. 5 squares in a row have 4 joins, so you need 20 − 4 = **16** sticks. Always check a rule against a real picture.",{"id":580,"type":53,"title":581,"eyebrow":582,"navLabel":583},"ch09","Rules in words: number machines","Chapter 09","9 Rules in words",{"id":585,"type":43,"markdown":586},"machines","Imagine a **number machine**. You feed a number in, the machine does something to it, and a new number comes out. Feed that number back in, and so on. The instruction inside the machine is the rule.\n\n- Machine **“add 3”**, start at 1: 1 → 4 → 7 → 10 → 13 → …\n- Machine **“double”** (multiply by 2), start at 1: 1 → 2 → 4 → 8 → 16 → …\n- Machine **“take away 4”**, start at 30: 30 → 26 → 22 → 18 → …\n- Machine **“halve”**, start at 64: 64 → 32 → 16 → 8 → 4 → …\n\nNotice how different “add 2” and “double” are, even when they start in the same place:\n\n| Start at 2 | 1st | 2nd | 3rd | 4th | 5th | 6th |\n| --- | --- | --- | --- | --- | --- | --- |\n| Add 2 | 2 | 4 | 6 | 8 | 10 | 12 |\n| Double | 2 | 4 | 8 | 16 | 32 | 64 |\n\nThey agree for the first two terms, then the doubling pattern races away. **Two terms are never enough to be sure of a rule.**",{"id":588,"type":47,"variant":589,"title":590,"markdown":591},"nuance-two-terms","nuance","How many terms do you need?","With just **2, 4, …** you cannot tell whether the rule is “add 2” or “double”. With **2, 4, 8, …** doubling looks likely, but other rules could still fit (you will meet a famous one in the Deepen layer that goes 1, 2, 4, 8, 16, 31). Mathematicians say what rule they are using, and then check it works for **every** term they can see.",{"id":593,"type":334,"component":594,"componentVersion":5,"config":595,"objective":650,"textAlternative":651,"help":652},"lab-sort-kinds","sort-game",{"prompt":596,"bins":597,"items":603,"seconds":480},"Is each pattern a repeating pattern or a growing (or shrinking) pattern?",[598,600],{"id":599,"label":71},"repeating",{"id":601,"label":602},"growing","Growing or shrinking",[604,607,611,615,619,622,626,630,634,638,642,646],{"id":107,"label":605,"bin":599,"why":606},"Bangles: green, gold, green, gold, …","The unit green, gold comes round again and again; nothing gets bigger.",{"id":608,"label":609,"bin":601,"why":610},"cups","Cup pyramid totals: 1, 3, 6, 10, …","Each pyramid adds a longer row, so the total keeps growing.",{"id":612,"label":613,"bin":599,"why":614},"days","Mon, Tue, Wed, Thu, Fri, Sat, Sun, Mon, …","The seven weekdays repeat every week.",{"id":616,"label":617,"bin":601,"why":618},"twos","2, 4, 6, 8, 10, …","Add 2 each time: the numbers keep getting bigger.",{"id":96,"label":620,"bin":599,"why":621},"A kolam border: loop, line, loop, line, …","The same loop-and-line unit is drawn again along the border.",{"id":623,"label":624,"bin":601,"why":625},"countdown","Countdown: 10, 9, 8, 7, …","A shrinking pattern: take away 1 each time. It changes by a rule rather than repeating.",{"id":627,"label":628,"bin":601,"why":629},"sticks","Matchstick squares: 4, 7, 10, 13, …","Each new square needs 3 more sticks.",{"id":631,"label":632,"bin":599,"why":633},"traffic","Traffic light: green, amber, red, green, amber, red, …","The three colours come round in the same order.",{"id":635,"label":636,"bin":599,"why":637},"clock","Clock hours: 10, 11, 12, 1, 2, …","After 12 the hours start again at 1: the unit 1 to 12 repeats.",{"id":639,"label":640,"bin":601,"why":641},"squares","Dot squares: 1, 4, 9, 16, …","Each square of dots is one row and one column bigger.",{"id":643,"label":644,"bin":599,"why":645},"lastdigit","Last digits of counting in 5s: 5, 0, 5, 0, …","Only two last digits appear, taking turns.",{"id":647,"label":648,"bin":601,"why":649},"savings","Savings: ₹50, ₹60, ₹70, ₹80, …","Add ₹10 each week.","Sort patterns into repeating and growing (or shrinking) families.","This sorting game shows 12 pattern cards to drop into two bins: **Repeating** and **Growing or shrinking**.\n\nRepeating (a unit comes round again): green, gold bangles; the days of the week; a kolam border of loop, line; traffic lights green, amber, red; clock hours 10, 11, 12, 1, 2 (after 12 the hours start again); and the last digits of counting in fives, 5, 0, 5, 0.\n\nGrowing or shrinking (each term changes by a rule): cup-pyramid totals 1, 3, 6, 10; counting in twos 2, 4, 6, 8; the countdown 10, 9, 8, 7 (shrinking by 1); matchstick squares 4, 7, 10, 13; dot squares 1, 4, 9, 16; and savings ₹50, ₹60, ₹70, ₹80.\n\nThe test: does the pattern come back to where it started (repeating), or does it keep moving further away (growing or shrinking)?",{"simplerExplanation":653},"If you will see the same thing again and again, it is repeating. If the numbers keep going up or down, it is growing or shrinking.",{"id":655,"type":334,"component":656,"componentVersion":5,"config":657,"objective":682,"textAlternative":683},"lab-match-rules","match-pairs",{"prompt":658,"mode":659,"pairs":660},"Match each pattern to its rule in words.","connect",[661,664,667,670,673,676,679],{"a":662,"b":663},"3, 6, 9, 12, …","Start at 3, add 3",{"a":665,"b":666},"1, 2, 4, 8, …","Start at 1, double",{"a":668,"b":669},"40, 35, 30, 25, …","Start at 40, take away 5",{"a":671,"b":672},"1, 4, 9, 16, …","Square numbers: 1 × 1, 2 × 2, 3 × 3, …",{"a":674,"b":675},"1, 3, 6, 10, …","Add 2, then 3, then 4, …",{"a":677,"b":678},"64, 32, 16, 8, …","Start at 64, halve",{"a":680,"b":681},"2, 5, 8, 11, …","Start at 2, add 3","Connect number patterns to the rules that make them.","Seven patterns and seven rules to connect:\n\n- 3, 6, 9, 12, … ↔ start at 3, add 3 (the 3 times table).\n- 1, 2, 4, 8, … ↔ start at 1, double.\n- 40, 35, 30, 25, … ↔ start at 40, take away 5.\n- 1, 4, 9, 16, … ↔ square numbers, 1 × 1, 2 × 2, 3 × 3, …\n- 1, 3, 6, 10, … ↔ add 2, then 3, then 4 (triangular numbers).\n- 64, 32, 16, 8, … ↔ start at 64, halve.\n- 2, 5, 8, 11, … ↔ start at 2, add 3.\n\nTwo patterns use the same step (add 3) but start in different places, so they are different patterns. A rule needs **both** a start and a step.",{"id":685,"type":166,"title":686,"problem":687,"steps":688,"help":693},"we-rule-words","Describe the rule in words","Describe the rule for **5, 9, 13, 17, 21, …** and use it to find the **8th** term.",[689,690,691,692],"Find the differences: 9 − 5 = 4, 13 − 9 = 4, 17 − 13 = 4, 21 − 17 = 4.","Rule in words: **start at 5 and add 4 each time.**","Keep going: 6th term 25, 7th term 29, 8th term **33**.","Check a quicker way: from the 1st term to the 8th term there are 7 jumps of 4. 5 + 7 × 4 = 5 + 28 = **33**. ✓",{"simplerExplanation":694},"Keep adding 4: 21, 25, 29, 33. The 8th term is 33.",{"id":696,"type":47,"variant":329,"title":697,"markdown":698},"aha-jumps","You can jump straight to a far-away term","To reach the 8th term you made **7 jumps**, not 8, because you started standing on the 1st term. So for “start at 5, add 4”, the **100th** term is 5 + 99 × 4 = 5 + 396 = **401**. No need to write 100 numbers! This “count the jumps” idea is how you will predict the 100th picture in the next layers.",{"id":700,"type":180,"prompt":701,"options":702,"explanation":711},"predict-100th","Matchstick squares in a row use 4, 7, 10, 13, … sticks. Using the jumps idea, how many sticks for **100 squares**?",[703,705,707,709],{"id":184,"label":704},"301",{"id":187,"label":706},"400",{"id":189,"label":708},"304",{"id":192,"label":710},"103","**301.** Start at 4 for 1 square, and make 99 jumps of 3 to reach 100 squares: 4 + 99 × 3 = 4 + 297 = **301**. Another way to see it: 1 starting stick plus 3 sticks for each of the 100 squares, 1 + 300 = 301. Choosing 400 forgets the shared sides.",{"id":713,"type":53,"title":714,"eyebrow":715,"navLabel":716},"ch10","Check what you have discovered","Chapter 10","10 Check yourself",{"id":718,"type":719,"title":720,"terms":721},"glossary-discover","glossary","Pattern words",[722,726,730,734,737,741,745,749,753,757,761,765,769,773,777,781,785],{"term":723,"meaning":724,"example":725},"pattern","An arrangement of shapes, colours, sounds or numbers that repeats or changes in a regular way.","green, gold, green, gold, …",{"term":727,"meaning":728,"example":729},"rule","The instruction that tells you how a pattern continues.","“Start at 3 and add 3 each time.”",{"term":731,"meaning":732,"example":733},"term","One item (usually one number) in a pattern or sequence.","In 2, 4, 6, 8 the third term is 6.",{"term":735,"meaning":736,"example":671},"sequence","A list of numbers or things in a definite order, usually following a rule.",{"term":738,"meaning":739,"example":740},"repeating pattern","A pattern in which the same group of items comes round again and again.","clap, clap, stamp, clap, clap, stamp",{"term":742,"meaning":743,"example":744},"repeating unit","The smallest group of items that repeats in a repeating pattern (sometimes called the core).","In red, red, blue, red, red, blue, the unit is red, red, blue.",{"term":746,"meaning":747,"example":748},"growing pattern","A pattern in which each step gets bigger by a rule.","Matchstick squares: 4, 7, 10, 13 sticks.",{"term":750,"meaning":751,"example":752},"shrinking pattern","A pattern in which each step gets smaller by a rule.","50, 45, 40, 35, …",{"term":754,"meaning":755,"example":756},"difference","How much one term changes to become the next; found by subtracting neighbouring terms.","In 3, 7, 11 the difference is 4.",{"term":758,"meaning":759,"example":760},"multiple","A number you land on when you count in steps of a given number; the answers in its times table.","Multiples of 6: 6, 12, 18, 24, …",{"term":762,"meaning":763,"example":764},"even number","A whole number that can be split into pairs with none left over; it ends in 0, 2, 4, 6 or 8.","14, 30, 256",{"term":766,"meaning":767,"example":768},"odd number","A whole number that leaves one over when split into pairs; it ends in 1, 3, 5, 7 or 9.","7, 21, 1,001",{"term":770,"meaning":771,"example":772},"square number","The number of dots in a square array; a number multiplied by itself.","5 × 5 = 25",{"term":774,"meaning":775,"example":776},"triangular number","The number of dots in a triangle with rows of 1, 2, 3, … dots.","1, 3, 6, 10, 15",{"term":778,"meaning":779,"example":780},"skip counting","Counting forwards or backwards in equal steps other than 1.","Counting in 5s: 5, 10, 15, 20",{"term":782,"meaning":783,"example":784},"hundred square","A 10 by 10 grid of the numbers 1 to 100, used to spot number patterns.","Down a column adds 10.",{"term":96,"meaning":786,"example":787},"A traditional South Indian floor design drawn with rice flour around a grid of dots, often built from repeating units.","A doorstep border of repeated loops.",{"id":789,"type":790,"title":791,"questions":792},"quiz-discover","quiz","Pattern spotter",[793,806,815,828,841,850,863,876,888,899],{"itemId":794,"prompt":795,"options":796,"correct":187,"why":805},"patterns.discover-q-unit","What is the repeating unit in ▲ ▲ ● ▲ ▲ ● ▲ ▲ ●?",[797,799,801,803],{"id":184,"label":798},"▲ ●",{"id":187,"label":800},"▲ ▲ ●",{"id":189,"label":802},"▲ ▲",{"id":192,"label":804},"●","The group ▲ ▲ ● comes round again and again, so it is the unit. It has 3 items.",{"itemId":807,"prompt":808,"options":809,"correct":184,"why":814},"patterns.discover-q-15th","Beads go blue, white, blue, white, … What colour is the 15th bead?",[810,812],{"id":184,"label":811},"Blue",{"id":187,"label":813},"White","Odd-numbered beads are blue and even-numbered beads are white. 15 is odd, so it is blue.",{"itemId":816,"prompt":817,"options":818,"correct":187,"why":827},"patterns.discover-q-next","What comes next? 4, 9, 14, 19, …",[819,821,823,825],{"id":184,"label":820},"23",{"id":187,"label":822},"24",{"id":189,"label":824},"25",{"id":192,"label":826},"29","The difference is 5 each time, so 19 + 5 = 24.",{"itemId":829,"prompt":830,"options":831,"correct":187,"why":840},"patterns.discover-q-back","What comes next? 80, 72, 64, 56, …",[832,834,836,838],{"id":184,"label":833},"46",{"id":187,"label":835},"48",{"id":189,"label":837},"50",{"id":192,"label":839},"52","Each term is 8 less than the one before, so 56 − 8 = 48.",{"itemId":842,"prompt":843,"options":844,"correct":189,"why":849},"patterns.discover-q-tri","What comes next in 1, 3, 6, 10, 15, …?",[845,846,847,848],{"id":184,"label":266},{"id":187,"label":268},{"id":189,"label":270},{"id":192,"label":824},"The differences are 2, 3, 4, 5, so next you add 6: 15 + 6 = 21.",{"itemId":851,"prompt":852,"options":853,"correct":192,"why":862},"patterns.discover-q-odd","Which number is odd?",[854,856,858,860],{"id":184,"label":855},"1,234",{"id":187,"label":857},"5,670",{"id":189,"label":859},"9,008",{"id":192,"label":861},"4,321","Only the last digit matters. 4,321 ends in 1, which is odd.",{"itemId":864,"prompt":865,"options":866,"correct":187,"why":875},"patterns.discover-q-calendar","If the 3rd of a month is a Sunday, which of these dates is also a Sunday?",[867,869,871,873],{"id":184,"label":868},"13th",{"id":187,"label":870},"17th",{"id":189,"label":872},"21st",{"id":192,"label":874},"28th","Sundays go up by 7: 3, 10, 17, 24, 31. So the 17th is a Sunday.",{"itemId":877,"prompt":878,"options":879,"correct":189,"why":887},"patterns.discover-q-hundred","In a hundred square, what do you add to move one step straight down?",[880,882,884,885],{"id":184,"label":881},"1",{"id":187,"label":883},"9",{"id":189,"label":33},{"id":192,"label":886},"11","Each row has ten numbers, so the number below is 10 more.",{"itemId":889,"prompt":890,"options":891,"correct":189,"why":898},"patterns.discover-q-sticks","Matchstick triangles in a row use 3, 5, 7, 9, … sticks. How many for 6 triangles?",[892,893,895,897],{"id":184,"label":886},{"id":187,"label":894},"12",{"id":189,"label":896},"13",{"id":192,"label":266},"Add 2 each time: 3, 5, 7, 9, 11, 13. Six triangles need 13 sticks, not 6 × 3 = 18, because neighbours share sides.",{"itemId":900,"prompt":901,"options":902,"correct":187,"why":911},"patterns.discover-q-double","Which rule makes 3, 6, 12, 24, …?",[903,905,907,909],{"id":184,"label":904},"Add 3",{"id":187,"label":906},"Double",{"id":189,"label":908},"Add 6",{"id":192,"label":910},"Triple","Each term is twice the one before: 3 × 2 = 6, 6 × 2 = 12, 12 × 2 = 24. Adding 3 would give 3, 6, 9, 12.",{"id":913,"type":914,"prompt":915},"reflect-discover","reflection","Find **one repeating pattern** and **one growing pattern** in your home, school or street (a floor, a fence, a sari border, a staircase, a stack of plates…). For each one, write its rule in words and say what the 20th item or term would be.",{"id":917,"type":918,"conceptId":919,"relation":920,"explanation":921},"conn-number-system","connection","number-system","related_to","The hundred square and place value are full of patterns: moving down a column adds 10 because each place is ten times the one to its right.",{"id":923,"type":918,"conceptId":924,"relation":925,"explanation":926},"conn-four-ops","four-operations","helps_understand","Skip counting is repeated addition, and counting in 3s gives the 3 times table: patterns make multiplication facts easier to learn.",{"id":928,"type":918,"conceptId":929,"relation":920,"explanation":930},"conn-shape","shape-and-space","Kolam borders, tiles and matchstick squares are shape patterns: they repeat or grow using shapes such as squares, triangles and hexagons.",{"id":932,"type":933,"title":934,"points":935},"cheat-discover","summary","Cheat sheet",[936,937,938,939,940,941,942,943,944],"**Pattern:** something that repeats or changes in a regular way. **Rule:** the instruction that tells you how it continues. **Term:** one item in a number pattern.","**Repeating patterns** have a **unit** that comes round again (green, gold; red, red, blue). To find the 20th item, count in whole units: 20 ÷ 3 = 6 remainder 2, so it is the 2nd item of the unit.","**Growing patterns** get bigger (or smaller) by a rule. Find the **difference** between neighbouring terms first.","**Skip counting** gives multiples: 3, 6, 9, 12, … Counting back works too: 50, 45, 40, …","**Even** numbers end in 0, 2, 4, 6, 8; **odd** numbers end in 1, 3, 5, 7, 9. odd + odd = even, odd + even = odd.","**Hundred square:** right +1, down +10, diagonal ↘ +11, diagonal ↙ +9. **Calendar:** down +7, diagonal ↘ +8, diagonal ↙ +6.","**Matchstick squares in a row:** 4, 7, 10, 13, … (add 3). **Square numbers:** 1, 4, 9, 16, 25. **Triangular numbers:** 1, 3, 6, 10, 15.","**Jumps:** to reach the 100th term from the 1st, make 99 jumps. Start at 5, add 4: 5 + 99 × 4 = 401.","**Two terms are never enough:** 2, 4, … could be “add 2” or “double”. Say your rule and check it on every term.",{"id":946,"type":947,"sourceIds":948},"sources-discover","sources",[949,950,951,952,953],"patterns-ncert-ganita-prakash-6","patterns-ncert-class6-algebra","patterns-mathsisfun-sequences","patterns-wiki-kolam","patterns-mathsisfun-fibonacci",[949,950,951,952,953],"needs_review",{"generatedBy":957,"notes":958},"claude-code","Draft generated locally from a Python script with every number computed and asserted; pending owner review.","ed077498a6c162e51bd82a03899801a1c8388f6b767d716da4ba3c1e3722653b",{"logic:practice":961,"component:pattern-machine@1":962,"component:sort-game@1":963,"component:match-pairs@1":964,"source:patterns-mathsisfun-fibonacci":965,"source:patterns-mathsisfun-sequences":966,"source:patterns-ncert-class6-algebra":967,"source:patterns-ncert-ganita-prakash-6":968,"source:patterns-wiki-kolam":969},"3d6b0fe1b15255975a32b0fcd94e8019bc959ad45cbf12e136e86149549c6878","b3d384b49b4d138a00726767a816928da91f44fad70d7d5ccfca6db297c45839","b164f45a2c8ca08f26c450768ff0231e113e9fe45381eddb34dc6d0548596c38","2a8ee4ac87460b4e1175a4bb13c96b03d577db06dde95670eb7fcfe4ad787899","b77a2fee9032c27c6a0b903d14287fc8a01076a000aba32f0ffc0e3ff54db124","1c634ad2570a389d1bc96431d0a220aa359ad82b4d33f5b55eb0b12dab8bab4c","b31773e8224c076a8a34aa4e6df704febaac5ecd4d6e1d3ba5041a31aad871e1","36726d3ff16d73627216db999b62b46580dfaf514f313774e79669de57d7c595","f04bc658d82c029f670482f92ee9b676d695909de4758c42114516748a798bdb",{"state":971,"reviewer":972,"selfReview":973,"reviewedAt":974,"method":975},"approved","The library owner",true,"2026-09-20T10:18:37.581Z","owner_bulk","preview-7e1cbbcc4f",1789899598914]