[{"data":1,"prerenderedAt":1104},["ShallowReactive",2],{"layer:shape-and-space:discover":3},{"layer":4,"contentHash":1083,"dependencyHashes":1084,"approval":1097,"releaseId":1103},{"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":1078,"reviewStatus":1079,"authoring":1080},1,"shape-and-space","en","discover","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.",[13,14,15,16,17],"Tell 2D (flat) shapes from 3D (solid) shapes and give everyday examples of each.","Name polygons from triangle to decagon and count their sides and vertices.","Recognise the main triangles, quadrilaterals and parts of a circle.","Count the faces, edges and vertices of cubes, cuboids, prisms and pyramids.","Find lines of symmetry and describe a solid from its top, front and side views.",30,{"title":20,"rows":21},"Lesson plate",[22,25,28,31,34,37],{"label":23,"value":24},"Depth","Discover",{"label":26,"value":27},"Reading time","≈ 30 minutes",{"label":29,"value":30},"Prior knowledge","None: just curiosity",{"label":32,"value":33},"Chapters","11",{"label":35,"value":36},"Labs","2D\u002F3D sort, shape explorers, symmetry match",{"label":38,"value":39},"You will need","Paper, scissors, a box, a dice",[41,45,51,56,62,65,86,91,161,166,171,174,207,210,215,220,223,263,268,271,295,321,326,331,334,338,356,375,379,385,390,393,423,435,440,445,448,468,472,475,479,484,487,522,542,546,551,554,567,584,588,603,616,620,625,628,653,656,678,691,696,699,729,733,758,762,782,787,790,794,856,860,925,1042,1058,1062,1066],{"id":42,"type":43,"markdown":44},"intro-look-around","prose","Look around the room you are sitting in. The door is a tall **rectangle**. The clock on the wall is a **circle**. The carrom board is a **square**. Your pencil box is a **cuboid**, the steel tumbler is nearly a **cylinder**, and the laddoo on the plate is almost a **sphere**.\n\nShapes are everywhere, and people have been naming them for thousands of years so that they can talk about them clearly: a carpenter asking for a plank, an architect drawing a temple, a baker cutting a cake, a bee building a honeycomb (though bees never learned the names!).\n\nIn this layer you will meet the big families of shapes: **flat shapes** you can draw on paper, and **solid shapes** you can hold in your hand. You will learn how to count their sides, corners, faces and edges, see how a flat pattern folds into a box, look at objects from above and from the side, and find the magic of **symmetry** in butterflies, rangoli and the Taj Mahal.",{"id":46,"type":47,"variant":48,"title":49,"markdown":50},"intro-question","callout","question","The big question","What makes a square a square? Is a door a square or a rectangle? How many edges does a cube really have: 6, 8 or 12? Make a guess now. By the end of this layer you will be able to answer all three, and explain *why*.",{"id":52,"type":47,"variant":53,"title":54,"markdown":55},"intro-how","observation","How to use this lesson","Keep a pencil, some paper and a few household things nearby: a matchbox, a ball, a dice, a coin, a tumbler. Whenever you see **Try it**, do it for real. Shapes make much more sense in your hands than on a screen.",{"id":57,"type":58,"title":59,"eyebrow":60,"navLabel":61},"ch01","chapter","Flat or solid? 2D and 3D","Chapter 01","1 Flat or solid",{"id":63,"type":43,"markdown":64},"flat-solid","Draw a square on paper. You can measure how **long** it is and how **wide** it is, but you cannot pick it up off the page. It has no thickness. Shapes like this are called **two-dimensional**, or **2D** for short, because they have two measurements: length and breadth.\n\nNow pick up a matchbox. It has a length and a breadth, but it also has a **height** (or thickness). It takes up space. Shapes like this are called **three-dimensional**, or **3D**: they have three measurements.\n\nA **rangoli** on the floor is 2D: it is a pattern of colour lying flat. A **laddoo** is 3D: you can hold it, turn it round and take a bite. A photo of a laddoo is 2D again, because the photo is flat even though the laddoo in it is not.",{"id":66,"type":67,"tone":68,"items":69},"spec-2d-3d","spec","blue",[70,74,78,82],{"label":71,"big":72,"value":73},"2D shape","2 measurements","Length and breadth. Drawn on flat paper. Examples: square, triangle, circle, the outline of a leaf.",{"label":75,"big":76,"value":77},"3D shape","3 measurements","Length, breadth and height. Takes up space. Examples: cube, ball, brick, ice-cream cone.",{"label":79,"big":80,"value":81},"A 2D shape has","sides and corners","Straight or curved lines around its edge, and corners where they meet.",{"label":83,"big":84,"value":85},"A 3D shape has","faces, edges, corners","Flat or curved surfaces (faces), lines where faces meet (edges), and corners (vertices).",{"id":87,"type":47,"variant":88,"title":89,"markdown":90},"aha-flat-faces","aha","Every box is made of flat shapes","Look closely at a matchbox. Each of its six sides is a flat rectangle. A 3D shape is often built from 2D shapes stuck together along their edges. That is exactly how cardboard boxes are made: a flat sheet is cut, folded and glued. You will unfold boxes later in this layer.",{"id":92,"type":93,"component":94,"componentVersion":5,"config":95,"objective":154,"textAlternative":155,"help":156},"lab-sort-2d-3d","interactive","sort-game",{"prompt":96,"bins":97,"items":104,"seconds":153},"Is it flat (2D) or solid (3D)? Sort each thing into the right bin.",[98,101],{"id":99,"label":100},"flat","Flat: 2D",{"id":102,"label":103},"solid","Solid: 3D",[105,109,113,117,121,125,129,133,137,141,145,149],{"id":106,"label":107,"bin":99,"why":108},"rangoli","A rangoli pattern drawn on the floor","It lies flat on the floor; it has length and breadth but no real thickness.",{"id":110,"label":111,"bin":102,"why":112},"laddoo","A laddoo","You can hold it and turn it round. It is (almost) a sphere, a 3D shape.",{"id":114,"label":115,"bin":102,"why":116},"brick","A brick","A brick has length, breadth and height: it is a cuboid.",{"id":118,"label":119,"bin":99,"why":120},"flag-drawing","A drawing of the national flag in your notebook","A drawing on paper is flat: a rectangle with a circle in the middle.",{"id":122,"label":123,"bin":102,"why":124},"tumbler","A steel tumbler","It is roughly a cylinder: it takes up space and holds water.",{"id":126,"label":127,"bin":99,"why":128},"shadow","The shadow of a ball on the ground","A shadow is a flat patch of darkness. The ball is 3D, but its shadow is a 2D circle.",{"id":130,"label":131,"bin":102,"why":132},"dice","A dice from Ludo","A dice is a cube: six square faces enclosing a space.",{"id":134,"label":135,"bin":99,"why":136},"ticket","The outline of a train ticket","The outline is a rectangle drawn on a flat surface. (The paper itself is very thin, so we treat it as flat.)",{"id":138,"label":139,"bin":102,"why":140},"cone","An ice-cream cone","A cone has a round base and a point at the top. It takes up space.",{"id":142,"label":143,"bin":99,"why":144},"photo","A photograph of the Taj Mahal","The Taj Mahal is 3D, but a photograph of it is flat.",{"id":146,"label":147,"bin":102,"why":148},"football","A football","A football is (nearly) a sphere.",{"id":150,"label":151,"bin":99,"why":152},"kolam","A kolam pattern of dots and loops","Kolam is drawn on the ground with rice flour. It is a flat pattern.",0,"Decide whether everyday things are flat 2D shapes or solid 3D shapes.","This game has two bins, **Flat: 2D** and **Solid: 3D**, and twelve cards to sort.\n\nThe flat ones: a rangoli pattern, a drawing of the flag, the shadow of a ball, the outline of a train ticket, a photograph of the Taj Mahal and a kolam pattern. Each lies on a surface and has only length and breadth.\n\nThe solid ones: a laddoo (sphere), a brick (cuboid), a steel tumbler (cylinder), a Ludo dice (cube), an ice-cream cone (cone) and a football (sphere). Each takes up space and has length, breadth and height.\n\nThe trickiest cards are the shadow and the photograph: the object is 3D but the picture or shadow of it is 2D.",{"simplerExplanation":157,"hints":158},"Ask yourself: can I hold it and turn it round? If yes, it is 3D. If it only lies flat like a drawing, it is 2D.",[159,160],"A picture of something solid is still flat.","A shadow has no thickness at all.",{"id":162,"type":47,"variant":163,"title":164,"markdown":165},"misc-paper","nuance","Is a sheet of paper 2D?","Strictly, no: a sheet of paper has a tiny thickness, about a tenth of a millimetre, so it is a very thin 3D object. In maths we **pretend** it is perfectly flat, because the thickness is so small that it does not matter. A true 2D shape is an idea, like a perfect line: we can only draw pictures of it.",{"id":167,"type":58,"title":168,"eyebrow":169,"navLabel":170},"ch02","Open and closed: drawing without lifting your pencil","Chapter 02","2 Open and closed",{"id":172,"type":43,"markdown":173},"curves","Put your pencil on paper and draw without lifting it. Whatever you draw is called a **curve** in maths, even if it is made only of straight bits! (Yes, mathematicians call a straight line a kind of curve.)\n\nSome curves end where they began, and fence in a region, like the outline of a pond or a cricket ground. These are **closed** curves. Others have two free ends, like a piece of string lying on the table or the letter **S**. These are **open** curves.\n\nA closed curve that does **not cross itself** is called a **simple closed curve**. A figure of 8 is closed but not simple, because it crosses itself in the middle.",{"id":175,"type":176,"caption":177,"columns":178,"rows":183},"table-curves","table","Open or closed? Some familiar outlines",[179,180,181,182],"Figure","Open or closed?","Crosses itself?","Why",[184,189,193,197,200,203],[185,186,187,188],"The letter C","Open","No","Its two ends do not meet.",[190,191,187,192],"The letter O","Closed","It returns to where it started: a simple closed curve.",[194,191,195,196],"The digit 8","Yes","It returns to the start but crosses itself in the middle.",[198,186,187,199],"The letter S","Two free ends.",[201,191,187,202],"A cricket boundary rope","It goes all the way round the ground and joins up.",[204,191,205,206],"A kolam loop around dots","Often yes","Many kolams are one long loop that weaves over itself.",{"id":208,"type":43,"markdown":209},"inside-outside","A simple closed curve splits the page into three parts: the **interior** (inside), the **exterior** (outside) and the **boundary** (the curve itself). A cricket ground is a perfect example: the grass inside the rope is the interior, the stands are the exterior, and the rope is the boundary. If the ball touches the rope, it is on the boundary, and that is four runs!",{"id":211,"type":47,"variant":212,"title":213,"markdown":214},"tryit-maze","try_it","Inside or outside?","Draw a big wobbly simple closed curve. Put a dot somewhere. Now draw a straight line from the dot to the edge of the paper and count how many times it crosses your curve.\n\n- An **odd** number of crossings (1, 3, 5…) means the dot is **inside**.\n- An **even** number (0, 2, 4…) means it is **outside**.\n\nTry it with several dots. Can you explain why it works? (Each crossing takes you from inside to outside or back again.)",{"id":216,"type":58,"title":217,"eyebrow":218,"navLabel":219},"ch03","Polygons: shapes with straight sides","Chapter 03","3 Polygons",{"id":221,"type":43,"markdown":222},"polygon-meet","A **polygon** is a simple closed figure made only of **straight** line segments. The segments are its **sides**. The corners where two sides meet are its **vertices** (one corner is a **vertex**).\n\nA triangle is a polygon. A square is a polygon. The outline of a star drawn with five straight strokes (without crossing lines) is a polygon. But a circle is **not** a polygon, because it has no straight sides, and the letter C is not a polygon because it is open.\n\n*Poly* is an old Greek word meaning **many**, and *gon* comes from the word for **angle** or knee. So a polygon is a many-cornered shape.",{"id":224,"type":176,"caption":225,"columns":226,"rows":230},"table-poly-names","Naming polygons by the number of sides (a polygon has as many vertices as sides)",[227,228,229],"Sides","Name","Where you might see one",[231,235,239,243,247,251,255,259],[232,233,234],"3","Triangle","A samosa, a set square, a slice of pizza (nearly), a road warning sign",[236,237,238],"4","Quadrilateral","A door, a carrom board, a page of this book, a patang (kite)",[240,241,242],"5","Pentagon","The side view of a house with a sloping roof; the famous building in the USA",[244,245,246],"6","Hexagon","Honeycomb cells, the head of a nut and bolt, some floor tiles",[248,249,250],"7","Heptagon","Rare; some coins in other countries have seven curved sides",[252,253,254],"8","Octagon","A STOP sign; the shape of many old forts, towers and wells",[256,257,258],"9","Nonagon","Rare; the Lotus Temple in Delhi has nine sides around its middle",[260,261,262],"10","Decagon","Some coins and table tops",{"id":264,"type":47,"variant":265,"title":266,"markdown":267},"def-polygon","definition","Polygon","A **polygon** is a simple closed figure made up entirely of line segments. Its segments are **sides**; the points where two sides meet are **vertices**. A polygon with **n** sides also has **n** vertices and **n** angles.",{"id":269,"type":43,"markdown":270},"regular-irregular","Some polygons are extra neat: all their sides are the same length **and** all their angles are the same size. These are called **regular polygons**. A square is a regular quadrilateral. An equilateral triangle is a regular triangle. A honeycomb cell is (very nearly) a regular hexagon.\n\nPolygons that are not like this are **irregular**. The side view of a house with a roof is an irregular pentagon: its sides are not all equal. A rectangle that is not a square is irregular too: its angles are equal, but its sides are not.",{"id":272,"type":93,"component":273,"componentVersion":5,"config":274,"objective":288,"textAlternative":289,"help":290},"lab-sort-polygons","shape-explorer",{"solids":275,"polygons":276,"modes":286},[],[277,278,279,280,281,282,283,284,285],"triangle","square","rectangle","pentagon","hexagon","octagon","circle","trapezium","kite",[287],"sort","Answer quick yes-or-no questions about flat shapes, and name each shape from its picture.","This is an 8-round shape game with nine flat shapes: a triangle (drawn scalene), a square, a rectangle, a regular pentagon, a regular hexagon, a regular octagon, a circle, a trapezium and a kite.\n\nEach round shows one shape and either asks you to **name** it or asks a yes-or-no question about it: *Is it a quadrilateral? Does it have a pair of parallel sides? Are all its sides equal? Does it have a right angle?*\n\nUseful facts: the square, rectangle, trapezium and kite are the quadrilaterals (4 sides each). The square, rectangle and trapezium have parallel sides; the kite does not. All sides are equal in the square and the regular pentagon, hexagon and octagon, but not in the scalene triangle, the rectangle, the trapezium or the kite. The square and rectangle have right angles. The circle has no sides at all, so it is not a polygon.",{"simplerExplanation":291,"hints":292},"Count the straight sides first: that tells you the name. Then look for equal sides, parallel sides and square corners.",[293,294],"Four straight sides means quadrilateral, however stretched it looks.","A kite has two pairs of equal sides, but no parallel sides.",{"id":296,"type":297,"itemId":298,"prompt":299,"check":300,"hints":316,"feedback":318},"pr-which-polygon","practice","shape-and-space.discover-polygon","Which of these is a polygon?",{"kind":301,"options":302,"correct":315},"choice",[303,306,309,312],{"id":304,"label":305},"a","A circle",{"id":307,"label":308},"b","The letter C made of curves",{"id":310,"label":311},"c","A triangle",{"id":313,"label":314},"d","A figure of 8",[310],[317],"A polygon needs straight sides only, and must be closed without crossing itself.",{"correct":319,"incorrect":320},"Yes. A triangle is closed, simple and made of three straight sides.","A circle has no straight sides; the letter C is open; a figure of 8 crosses itself. Only the triangle fits every part of the definition.",{"id":322,"type":47,"variant":323,"title":324,"markdown":325},"example-honeycomb","example","Why bees build hexagons","A honeycomb is a sheet of six-sided wax cells. Hexagons fit together with **no gaps**, like tiles on a floor, and they use **less wax** for the space they enclose than squares or triangles would. Bees are not doing maths, of course; the wax cells start roughly round and are pulled into hexagons as the warm wax settles. But the result is one of nature's most efficient shapes. In 1999 the mathematician Thomas Hales finally **proved** that the hexagon grid is the best possible way to divide a flat surface into equal areas with the least total edge.",{"id":327,"type":58,"title":328,"eyebrow":329,"navLabel":330},"ch04","Triangles: the strongest shape","Chapter 04","4 Triangles",{"id":332,"type":43,"markdown":333},"tri-meet","A **triangle** has 3 sides, 3 vertices and 3 angles. It is the polygon with the **fewest** possible sides: you cannot close a shape with only two straight sides.\n\nTriangles are everywhere in building. Look at a railway bridge, an electricity tower or the frame of a roof: you will see triangles again and again. Why? Push on the corner of a square made of four sticks joined at the corners, and it squashes into a slanted shape. Push on a triangle made of three sticks and it **will not change shape** unless a stick bends or breaks. Three lengths fix a triangle completely. That makes triangles rigid, and engineers love them.",{"id":335,"type":47,"variant":212,"title":336,"markdown":337},"tryit-straws","The wobbly square and the stiff triangle","Take some straws or broom sticks and thread string or pipe cleaners through them to make a square and a triangle with loose joints.\n\n1. Push gently on one corner of the square. It leans over into a slanted shape (a rhombus).\n2. Push on the triangle. It holds firm.\n3. Now add one diagonal straw across the square. What happens? You have split it into two triangles, and now it is stiff too.\n\nThat single diagonal is exactly what you see on gates, bridges and scaffolding.",{"id":339,"type":176,"caption":340,"columns":341,"rows":343},"table-tri-sides","Three kinds of triangle by their sides",[228,227,342],"Everyday example",[344,348,352],[345,346,347],"Equilateral","All 3 sides equal","Each face of a triangular pyramid made from equal sticks; a billiards or carrom rack",[349,350,351],"Isosceles","Exactly 2 sides equal (or at least 2)","The gable end of a hut roof; a slice of round cake cut from the centre",[353,354,355],"Scalene","No two sides equal","Most triangles you draw quickly by hand",{"id":357,"type":176,"caption":358,"columns":359,"rows":362},"table-tri-angles","Three kinds of triangle by their biggest angle",[228,360,361],"Angles","Clue",[363,367,371],[364,365,366],"Acute-angled","All three angles smaller than a right angle","Looks pointy all round",[368,369,370],"Right-angled","One angle is exactly a right angle (90°)","One corner fits the corner of a page exactly",[372,373,374],"Obtuse-angled","One angle is bigger than a right angle","One corner is wide open, like a lazy V",{"id":376,"type":47,"variant":88,"title":377,"markdown":378},"aha-180","Tear off the corners","Cut any paper triangle. Tear off its three corners and place them side by side with their points touching. They always fit together to make a **straight line**. Since a straight angle is 180°, the three angles of **every** triangle add up to **180°**. You will prove this properly in a later layer.",{"id":380,"type":381,"conceptId":382,"relation":383,"explanation":384},"conn-angles-disc","connection","angles","related_to","Triangles are classified by their angles (acute, right, obtuse), and the three angles of any triangle add up to 180°. The Angles topic explains what these angle words mean.",{"id":386,"type":58,"title":387,"eyebrow":388,"navLabel":389},"ch05","Four-sided friends: quadrilaterals","Chapter 05","5 Quadrilaterals",{"id":391,"type":43,"markdown":392},"quad-meet","Any polygon with four sides is a **quadrilateral** (*quadri* means four, *lateral* means side). That covers a huge family: doors, windows, tiles, a cricket pitch, a carrom board, a diamond-shaped patang flying at Makar Sankranti, the slanted shape of a bench seen from the side.\n\nSome family members are so common that they have their own names.",{"id":394,"type":176,"caption":395,"columns":396,"rows":398},"table-quad-family","The quadrilateral family at a glance",[228,397,342],"What makes it special",[399,403,407,411,415,419],[400,401,402],"Square","4 equal sides and 4 right angles","A carrom board, a chessboard square",[404,405,406],"Rectangle","4 right angles; opposite sides equal","A door, a mobile phone screen, an exercise book",[408,409,410],"Rhombus","4 equal sides, but the corners need not be right angles","A diamond shape on a playing card; a tilted square tile",[412,413,414],"Parallelogram","Opposite sides parallel and equal","The shape a rectangle makes when you push it sideways; many tile patterns",[416,417,418],"Trapezium","At least one pair of opposite sides parallel","The side view of a bucket or a lampshade; some table tops",[420,421,422],"Kite","Two pairs of equal sides next to each other","A paper kite (patang), a diamond on a jewellery design",{"id":424,"type":425,"prompt":426,"options":427,"explanation":434},"pred-square-rectangle","prediction","Here is a tricky one. A rectangle is a four-sided shape with four right angles. Is a **square** a rectangle?",[428,430,432],{"id":304,"label":429},"Yes, a square has four right angles, so it is a special rectangle",{"id":307,"label":431},"No, a rectangle must have two long sides and two short sides",{"id":310,"label":433},"Only if it is turned on its side","**Yes.** The definition of a rectangle only asks for four right angles. A square has four right angles, so it passes the test. It is a very special rectangle whose sides happen to be all equal. It is like saying a mango is a fruit: true, even though not every fruit is a mango. Every square is a rectangle, but not every rectangle is a square. You will explore the whole family tree in the next layer.",{"id":436,"type":47,"variant":437,"title":438,"markdown":439},"misc-diamond","misconception","“A square turned on its corner is a diamond, not a square”","Turning a shape does **not** change what it is. A square tile tilted so a corner points up still has four equal sides and four right angles, so it is still a square. The word *diamond* is not a maths name; people use it for squares on a corner and for rhombuses. Always check the sides and angles, not the direction the shape is facing.",{"id":441,"type":58,"title":442,"eyebrow":443,"navLabel":444},"ch06","Round and round: circles","Chapter 06","6 Circles",{"id":446,"type":43,"markdown":447},"circle-meet","Tie a string to a peg in the ground, pull it tight and walk around the peg with a stick in the other hand, scratching the soil. The mark you make is a **circle**: every point on it is exactly the same distance from the peg. Gardeners in India still mark out round flower beds this way.\n\nThe peg is the **centre** of the circle. The length of the string is the **radius**. A line straight across the circle through the centre is a **diameter**, and it is always **twice** the radius. The distance all the way round the circle is called the **circumference**.",{"id":449,"type":67,"tone":450,"items":451},"spec-circle","amber",[452,456,460,464],{"label":453,"big":454,"value":455},"Centre","the middle point","Every point of the circle is the same distance from it.",{"label":457,"big":458,"value":459},"Radius","centre → edge","The string length in the peg-and-string trick.",{"label":461,"big":462,"value":463},"Diameter","= 2 × radius","All the way across, through the centre. A bangle of radius 3 cm has diameter 6 cm.",{"label":465,"big":466,"value":467},"Circumference","the way round","A little more than 3 times the diameter. Wrap a thread round a bangle and measure it.",{"id":469,"type":47,"variant":323,"title":470,"markdown":471},"example-chakra","The Ashoka Chakra","The wheel in the middle of India's national flag is the **Ashoka Chakra**. It is a circle with **24 spokes**, each one a radius running from the centre to the rim. All 24 spokes are the same length, because every radius of a circle is the same length. The spokes are evenly spaced, so the angle between two neighbours is 360° ÷ 24 = **15°**.",{"id":473,"type":43,"markdown":474},"why-wheels","Why are wheels round? Because the axle at the centre is always the **same distance** (one radius) from the road. As a round wheel rolls, the axle glides along at a steady height and the cart does not bump. Try to imagine a square wheel: the axle would rise up as the wheel tipped onto a corner and crash down again as it landed on the next side. Every cart, cycle, bullock-cart and train in the world uses the circle's special property.",{"id":476,"type":381,"conceptId":477,"relation":383,"explanation":478},"conn-constructing-disc","constructing-angles","A compass draws a circle by keeping the pencil a fixed distance (the radius) from the centre. The same tool is used to construct angles accurately.",{"id":480,"type":58,"title":481,"eyebrow":482,"navLabel":483},"ch07","Solid shapes you can hold","Chapter 07","7 Solids",{"id":485,"type":43,"markdown":486},"solids-meet","Now let us leave the page and pick things up. Here are the solid shapes you will meet most often, with something from an Indian home or street for each one.",{"id":488,"type":176,"caption":489,"columns":490,"rows":493},"table-solids","Common 3D shapes and where to find them",[491,492,342],"Solid","What it looks like",[494,498,502,506,510,514,518],[495,496,497],"Cube","Six equal square faces","A Ludo dice, a sugar cube, a Rubik’s cube",[499,500,501],"Cuboid","Six rectangular faces, like a box","A brick, a matchbox, a tiffin box, a textbook",[503,504,505],"Cylinder","Two equal circles joined by a curved surface","A steel tumbler, a gas cylinder, a pencil (almost), a drum",[507,508,509],"Cone","A circle at the bottom, a curved surface rising to a point","An ice-cream cone, a birthday cap, a traffic cone, a mehndi cone",[511,512,513],"Sphere","Perfectly round in every direction","A laddoo, a cricket ball, a marble, a globe",[515,516,517],"Pyramid","A flat base and triangular sides meeting at a point","The Great Pyramid of Giza; many temple towers are pyramid-like",[519,520,521],"Prism","Two matching ends joined by rectangles","A camping tent (triangular prism), a Toblerone-style chocolate box, a pencil (hexagonal prism)",{"id":523,"type":93,"component":273,"componentVersion":5,"config":524,"objective":535,"textAlternative":536,"help":537},"lab-explore-solids",{"solids":525,"polygons":532,"modes":533},[526,527,528,138,529,530,531],"cube","cuboid","cylinder","sphere","square-pyramid","triangular-prism",[],[534],"explore","Turn common solids round to see every face, including the hidden ones, and read off their faces, edges and vertices.","Pick one of seven solids: a cube, a cuboid, a cylinder, a cone, a sphere, a square pyramid or a triangular prism. Drag the solid, or use the Turn and Tilt sliders, to rotate it; hidden edges show as dashed lines. You can highlight its faces, edges or vertices, and for a polyhedron the Net button unfolds it flat.\n\nThe **cube** has six identical square faces; the **cuboid** has six rectangles in three matching pairs. Both show 6 faces, 12 edges, 8 vertices. The **square pyramid** has a square base and four triangles meeting at the top (5, 8, 5). The **triangular prism** has two triangle ends and three rectangles (5, 9, 6). The **cylinder** shows 3 faces (2 flat circles and 1 curved surface), 2 edges and 0 vertices; the **cone** 2 faces (1 flat, 1 curved), 1 edge, 1 vertex; the **sphere** 1 curved face and no edges or vertices.\n\nThe key discovery: turning a solid never changes it, but from any one direction some faces are hidden at the back.",{"simplerExplanation":538,"hints":539},"Spin each shape slowly. Count the flat parts you can see, then turn it over to find the hidden ones.",[540,541],"A cylinder can roll and it can also stand flat. Which parts let it do each?","Press Net on the cube: what flat shape do you get?",{"id":543,"type":47,"variant":53,"title":544,"markdown":545},"obs-roll-slide","Roll, slide or both?","Solids with a curved surface can **roll**: a sphere rolls in every direction, a cylinder rolls in a straight line, and a cone rolls round in a circle about its point. Solids with only flat faces **slide** but do not roll. That is why balls and wheels are round and why boxes stay where you put them.",{"id":547,"type":58,"title":548,"eyebrow":549,"navLabel":550},"ch08","Faces, edges and corners","Chapter 08","8 Faces and edges",{"id":552,"type":43,"markdown":553},"fev-meet","To describe a solid shape exactly, we count three things:\n\n- **Faces**: the flat surfaces. A dice has 6 faces, each with a different number of dots.\n- **Edges**: the lines where two faces meet. Run your finger along the edge of a matchbox and you feel a sharp line.\n- **Vertices**: the corners, where edges meet. A corner of a brick is a vertex.\n\nCounting them carefully is harder than it sounds, because you cannot see them all at once. The trick is to count in an organised way.",{"id":555,"type":556,"title":557,"problem":558,"steps":559,"help":565},"we-cube-count","worked_example","Counting the edges of a dice","A Ludo dice is a cube. How many edges does it have?",[560,561,562,563,564],"Put the dice on the table. Look at the **top face**: it is a square with **4 edges** around it.","Look at the **bottom face**, touching the table: another **4 edges**.","Now count the **upright edges** running from the top down to the bottom, one at each corner: **4 edges**.","Total: 4 + 4 + 4 = **12 edges**.","Use the same trick for corners: 4 on top + 4 on the bottom = **8 vertices**. And faces: top, bottom, front, back, left, right = **6 faces**.",{"simplerExplanation":566},"Top ring of 4, bottom ring of 4, and 4 standing up in between. That is 12.",{"id":568,"type":176,"caption":569,"columns":570,"rows":574},"table-fev-disc","Faces, edges and vertices of common solids",[491,571,572,573],"Faces","Edges","Vertices (corners)",[575,577,578,580,582],[495,244,576,252],"12",[499,244,576,252],[579,240,256,244],"Triangular prism",[581,240,252,240],"Square pyramid",[583,236,244,236],"Triangular pyramid",{"id":585,"type":47,"variant":437,"title":586,"markdown":587},"misc-guess-6","“A cube has 6 edges”","Many people mix up faces and edges. A cube has **6 faces** (the flat squares) but **12 edges** (the lines where two squares meet). Each face has 4 edges around it, which gives 6 × 4 = 24, but every edge is shared by **two** faces, so there are only 24 ÷ 2 = 12 different edges.",{"id":589,"type":93,"component":273,"componentVersion":5,"config":590,"objective":596,"textAlternative":597,"help":598},"lab-count-solids",{"solids":591,"polygons":593,"modes":594},[526,527,530,531,592],"triangular-pyramid",[],[534,595],"count","Explore five solids, then play the counting game: type the number of faces, edges and vertices of each solid shown.","Explore first: Drag the solid, or use the Turn and Tilt sliders, to rotate it; hidden edges show as dashed lines. You can highlight its faces, edges or vertices, and for a polyhedron the Net button unfolds it flat. The readout shows the counts.\n\nThen play **count**: a solid appears and you type its faces, edges and vertices. The answers: **cube** 6 faces, 12 edges, 8 vertices; **cuboid** 6, 12, 8 (the same as a cube, because a cube is a special cuboid); **square pyramid** 5 faces (1 square and 4 triangles), 8 edges (4 round the base and 4 slanting up), 5 vertices; **triangular prism** 5 faces (2 triangles and 3 rectangles), 9 edges, 6 vertices; **triangular pyramid** 4 faces, 6 edges, 4 vertices.\n\nA good strategy is to count by layers: the bottom, the top, then everything in between.",{"simplerExplanation":599,"hints":600},"Faces are the flat parts, edges are the fold lines, vertices are the pointy corners. Count one kind at a time.",[601,602],"For a pyramid, count the base first, then everything that meets at the top.","For a prism, the two ends are the same shape. Count one end and double it.",{"id":604,"type":297,"itemId":605,"prompt":606,"check":607,"hints":610,"feedback":613},"pr-pyramid-edges","shape-and-space.discover-pyramid-edges","A square pyramid (like the Great Pyramid of Giza) has a square base and four triangular sides meeting at the top. How many **edges** does it have?",{"kind":608,"answer":609,"tolerance":153},"number",8,[611,612],"Count the edges round the square base first.","Then count the edges that climb up to the top point.",{"correct":614,"incorrect":615},"Yes: 4 edges round the base and 4 slanting up to the top, 4 + 4 = 8.","Count in two groups: 4 edges round the square base, and 4 more running up to the tip. That makes 8.",{"id":617,"type":47,"variant":163,"title":618,"markdown":619},"nuance-curved","What about round solids?","A cylinder has **2 flat faces** and **1 curved surface**, and **2 curved edges** where they meet (the rims), but **no vertices**. A cone has **1 flat face**, **1 curved surface**, **1 curved edge** and **1 vertex** (the tip). A sphere has **1 curved surface** and nothing else. Some books count curved surfaces as faces and some do not, so always say which you mean.",{"id":621,"type":58,"title":622,"eyebrow":623,"navLabel":624},"ch09","Unfold a box: nets and views","Chapter 09","9 Nets and views",{"id":626,"type":43,"markdown":627},"nets-meet","Take an empty toothpaste box or a sweet box and carefully open it out along its glued flap until it lies flat. The flat shape you get is called a **net** of the box. Fold it back up along the creases and the box appears again.\n\nA **net** is a flat pattern that folds up to make a solid. The net of a cube is made of **6 squares** joined edge to edge. One famous cube net looks like a cross: a line of four squares with one extra square sticking out above and one below.",{"id":629,"type":630,"title":631,"items":632},"steps-make-cube","steps","Make your own cube from a net",[633,637,641,645,649],{"title":634,"tag":635,"text":636},"Draw","on thick paper","Draw a row of 4 equal squares, 5 cm each. Add one square above the second square and one below it: a cross shape.",{"title":638,"tag":639,"text":640},"Add flaps","for glue","On some edges add small tabs to glue. Leave the others plain.",{"title":642,"tag":643,"text":644},"Cut","around the outside","Cut round the whole outline, not between the squares.",{"title":646,"tag":647,"text":648},"Fold","along every line","Crease every line between two squares so all the squares stand up.",{"title":650,"tag":651,"text":652},"Glue","close it up","Fold up the row into a ring, fold the top and bottom squares down, and glue. You have a cube!",{"id":654,"type":43,"markdown":655},"views-meet","Now put a tumbler on the table. Look at it from the **side**: you see a rectangle. Look straight down from the **top**: you see a circle. The same solid looks like different flat shapes from different directions. These are called **views**.\n\nArchitects draw a **top view** (called a *plan*), a **front view** and a **side view** of every building, so that builders know exactly what to make. A map is a giant top view of a town.",{"id":657,"type":176,"caption":658,"columns":659,"rows":663},"table-views","The same solid seen from different directions",[491,660,661,662],"Top view","Front view","Side view",[664,667,670,672,676],[665,666,404,404],"Tumbler (cylinder, standing up)","Circle",[668,669,233,233],"Ice-cream cone (point up)","Circle (with a dot in the middle)",[671,400,400,400],"Dice (cube)",[673,404,674,675],"Brick lying flat","Rectangle (a thinner one)","Rectangle (a small one)",[677,666,666,666],"Ball (sphere)",{"id":679,"type":425,"prompt":680,"options":681,"explanation":690},"pred-view","A solid looks like a **circle** from the top and like a **triangle** from the front. What could it be?",[682,684,686,688],{"id":304,"label":683},"A cylinder",{"id":307,"label":685},"A cone standing on its base",{"id":310,"label":687},"A cube",{"id":313,"label":689},"A sphere","**A cone.** From above you see its round base (with the tip right in the middle). From the front, its sloping sides make a triangle. A cylinder would look like a rectangle from the front, and a sphere would look like a circle from every side.",{"id":692,"type":58,"title":693,"eyebrow":694,"navLabel":695},"ch10","Mirror magic: symmetry","Chapter 10","10 Symmetry",{"id":697,"type":43,"markdown":698},"sym-meet","Fold a paper butterfly down the middle and the two halves fit exactly on top of each other. The fold line is called a **line of symmetry**, or a **mirror line**, because if you stand a mirror on it, the reflection of one half looks just like the other half.\n\nA shape with at least one line of symmetry is called **symmetrical**. You can find symmetry in a leaf, a human face (nearly), the letter A, a rangoli, a temple doorway and the most famous building in India: the **Taj Mahal**, whose front is almost perfectly symmetrical about a line down the middle of its great arch and dome.",{"id":700,"type":176,"caption":701,"columns":702,"rows":706},"table-sym-count","How many lines of symmetry?",[703,704,705],"Shape","Lines of symmetry","Where they go",[707,711,714,717,719,722,725],[708,709,710],"Isosceles triangle","1","Down the middle, from the top corner to the middle of the base",[712,232,713],"Equilateral triangle","From each corner to the middle of the opposite side",[404,715,716],"2","One across the middle and one down the middle (not along the diagonals!)",[400,236,718],"Across, down, and along both diagonals",[720,244,721],"Regular hexagon","Three through opposite corners and three through the middles of opposite sides",[666,723,724],"Countless","Any line through the centre",[726,727,728],"Scalene triangle","0","No fold makes the halves match",{"id":730,"type":47,"variant":437,"title":731,"markdown":732},"misc-rect-diag","“A rectangle folds along its diagonal”","Try it with a rectangular sheet of paper that is not a square. Fold it corner to corner. The two halves are the same **size**, but when you fold them they do **not** land on top of each other: the corners stick out. A diagonal cuts a rectangle into two equal triangles, but it is not a mirror line. A rectangle has only **2** lines of symmetry; only the square gets the extra 2 along its diagonals.",{"id":734,"type":93,"component":735,"componentVersion":5,"config":736,"objective":753,"textAlternative":754,"help":755},"lab-match-shapes","match-pairs",{"prompt":737,"mode":738,"pairs":739},"Match each shape to its number of lines of symmetry.","memory",[740,742,745,747,749,751],{"a":400,"b":741},"4 lines of symmetry",{"a":743,"b":744},"Rectangle (not a square)","2 lines of symmetry",{"a":712,"b":746},"3 lines of symmetry",{"a":708,"b":748},"1 line of symmetry",{"a":726,"b":750},"No lines of symmetry",{"a":720,"b":752},"6 lines of symmetry","Remember and match each shape with how many mirror lines it has.","This is a memory game with twelve face-down cards: six shapes and six numbers of lines of symmetry. Turn two over at a time and try to find matching pairs.\n\nThe pairs are: square and 4 lines; rectangle (not a square) and 2 lines; equilateral triangle and 3 lines; isosceles triangle and 1 line; scalene triangle and no lines; regular hexagon and 6 lines.\n\nNotice the pattern in the regular shapes: an equilateral triangle (3 sides) has 3 lines, a square (4 sides) has 4, a regular hexagon (6 sides) has 6. A regular polygon has as many lines of symmetry as it has sides.",{"hints":756},[757],"For regular shapes, the number of lines equals the number of sides.",{"id":759,"type":47,"variant":212,"title":760,"markdown":761},"tryit-ink","Ink-blot and rangoli symmetry","Fold a sheet of paper in half, open it, and drop a few blobs of paint on one side near the fold. Fold it again, press, and open: a perfectly symmetrical pattern!\n\nNext Diwali or Pongal, look carefully at rangoli and kolam designs. Many have 4 or 8 lines of symmetry, and many also look the same when you turn them round by a quarter turn. That second kind of symmetry is called **rotational symmetry**, and you will meet it later.",{"id":763,"type":297,"itemId":764,"prompt":765,"check":766,"hints":777,"feedback":779},"pr-letters","shape-and-space.discover-letters","Which of these capital letters, written as plain block capitals, has a **vertical** line of symmetry (a mirror line straight down the middle)?",{"kind":301,"options":767,"correct":776},[768,770,772,774],{"id":304,"label":769},"F",{"id":307,"label":771},"A",{"id":310,"label":773},"R",{"id":313,"label":775},"J",[307],[778],"Imagine a mirror standing straight up through the middle of the letter.",{"correct":780,"incorrect":781},"Right. A is the same on both sides of a vertical line through its point.","F, R and J all point one way, so their left and right halves do not match. A does: its two sloping strokes mirror each other.",{"id":783,"type":58,"title":784,"eyebrow":785,"navLabel":786},"ch11","Puzzles and shapes in India","Chapter 11","11 Puzzles and India",{"id":788,"type":43,"markdown":789},"tangram","A **tangram** is an old puzzle from China made by cutting one square into **7 pieces**: 2 large triangles, 1 medium triangle, 2 small triangles, 1 square and 1 parallelogram. The challenge is to use **all seven** pieces, without overlapping, to make pictures: a cat, a boat, a running man, a house, even the letters of your name. Every picture has exactly the same area as the original square, because it uses the same pieces.\n\nPuzzles like this train the eye to see how shapes fit together, turn and flip, which is exactly the skill architects, tailors and tile-layers use every day.",{"id":791,"type":47,"variant":212,"title":792,"markdown":793},"tryit-tangram","Make a tangram","Take a square sheet of paper, 16 cm each side.\n\n1. Fold and cut along one diagonal: two big triangles.\n2. Fold one of them in half and cut: these are the **2 large triangles**.\n3. From the other half, cut off the top corner (fold the corner to the middle of the long side): the **medium triangle**.\n4. Cut the remaining strip into a **square**, a **parallelogram** and **2 small triangles**.\n\nNow try to make a square again from all seven pieces. It is harder than it sounds!",{"id":795,"type":796,"title":797,"prompt":798,"options":799},"explorer-india","explorer","Shapes in Indian buildings and nature","Pick one to see which shapes are hiding inside it.",[800,812,823,834,845],{"id":801,"label":802,"chain":803,"badge":808,"note":811},"stepwell","Stepwell",[804,805,806,807],"Square pit dug deep","Flights of steps down three sides","Steps make triangles in side view","Water at the bottom",{"text":809,"tone":810},"Squares, triangles, symmetry","yes","Stepwells (*baori* or *vav*) were built in dry western India so people could reach water as its level rose and fell with the seasons. **Chand Baori** in Abhaneri, Rajasthan, has about 3,500 narrow steps arranged in a criss-cross pattern down three sides of a square pit, 13 storeys deep. Seen from above it is a square; seen from the side the steps make zigzags of triangles. It is beautifully symmetrical.",{"id":813,"label":814,"chain":815,"badge":820,"note":822},"shikhara","Temple shikhara",[816,817,818,819],"Square base (the sanctum)","Tower rises and narrows","Layers of smaller copies","Point or finial at the top",{"text":821,"tone":810},"Pyramid-like","The tower above the sanctum of many Hindu temples, the **shikhara** or **vimana**, starts on a square base and narrows as it rises, like a pyramid. The Brihadeeswarar Temple in Thanjavur has a tall, pyramid-shaped vimana built up in many storeys, each a smaller square than the one below. North Indian shikharas are more curved, like a bullet or a corn cob, built from many smaller copies of the same shape.",{"id":824,"label":825,"chain":826,"badge":831,"note":833},"honeycomb","Honeycomb",[827,828,829,830],"Wax cells","Six sides each","No gaps between cells","Least wax for the space",{"text":832,"tone":810},"Hexagons","A honeycomb is made of hexagonal cells that tile the comb with no gaps. The hexagon uses the least edge (wax) for the area it encloses, of all the shapes that fit together this way. You can see the same pattern in some floor tiles, on a football (with pentagons mixed in) and in the cells of a dragonfly's wing.",{"id":835,"label":836,"chain":837,"badge":842,"note":844},"taj","Taj Mahal",[838,839,840,841],"Square platform","Four minarets (cylinders)","Great dome (half of a sphere, plus more)","Arches and octagons",{"text":843,"tone":810},"Line symmetry","The Taj Mahal in Agra stands on a square platform with a tall cylindrical minaret at each corner. The main building's corners are cut off, so its outline from above is an octagon with unequal sides. The great dome is shaped like an onion: more than half of a sphere, pinched in at the base. The whole garden and building are laid out to be symmetrical about a central line.",{"id":846,"label":847,"chain":848,"badge":853,"note":855},"konark","Konark wheels",[849,850,851,852],"Stone temple as a chariot","24 carved wheels","Spokes are radii","Shadows tell the time",{"text":854,"tone":810},"Circles","The Sun Temple at Konark in Odisha is built as the chariot of the Sun god, with **24** huge carved stone wheels, 12 on each side. Each wheel has 8 broad, richly carved spokes; guides and popular accounts add a thinner spoke between each pair, 16 in all. People say the shadows of the spokes can be read like a sundial.",{"id":857,"type":858,"prompt":859},"reflect-home","reflection","Go on a shape hunt at home or in your street. Find at least one example each of a cube, a cuboid, a cylinder, a cone, a sphere, a triangle, a hexagon and something with a line of symmetry. Which shape was hardest to find, and why do you think it is rare?",{"id":861,"type":862,"title":863,"terms":864},"glossary-discover","glossary","Shape words to know",[865,868,872,875,879,883,886,889,892,896,898,901,903,905,907,911,915,919,922],{"term":71,"meaning":866,"example":867},"A flat shape with length and breadth but no thickness, such as a square or a circle.","The outline of a train ticket is a 2D rectangle.",{"term":869,"meaning":870,"example":871},"3D shape (solid)","A shape that takes up space, with length, breadth and height.","A brick, a ball and a cone are 3D shapes.",{"term":873,"meaning":874},"Curve","Any figure you can draw without lifting your pencil. In maths a straight line counts as a curve too.",{"term":876,"meaning":877,"example":878},"Closed curve","A curve that ends where it began, fencing in a region.","The letter O.",{"term":880,"meaning":881,"example":882},"Open curve","A curve with two loose ends that do not meet.","The letter C or S.",{"term":266,"meaning":884,"example":885},"A simple closed figure made only of straight line segments.","Triangle, square, hexagon.",{"term":887,"meaning":888},"Side","One of the straight line segments that make up a polygon.",{"term":890,"meaning":891},"Vertex (plural: vertices)","A corner: where two sides of a polygon, or several edges of a solid, meet.",{"term":893,"meaning":894,"example":895},"Regular polygon","A polygon with all sides equal and all angles equal.","A square; an equilateral triangle.",{"term":233,"meaning":897},"A polygon with 3 sides.",{"term":237,"meaning":899,"example":900},"A polygon with 4 sides.","Square, rectangle, kite.",{"term":666,"meaning":902},"A round closed curve whose every point is the same distance from the centre.",{"term":457,"meaning":904},"The distance from the centre of a circle to any point on it.",{"term":461,"meaning":906},"A straight line across a circle through its centre; twice the radius.",{"term":908,"meaning":909,"example":910},"Face","A flat surface of a solid.","A dice has 6 faces.",{"term":912,"meaning":913,"example":914},"Edge","A line where two faces of a solid meet.","A cube has 12 edges.",{"term":916,"meaning":917,"example":918},"Net","A flat pattern that can be folded to make a solid.","A cross of 6 squares folds into a cube.",{"term":920,"meaning":921},"Line of symmetry","A line that splits a shape into two halves that are mirror images of each other.",{"term":923,"meaning":924},"Tangram","A puzzle of 7 pieces cut from a square, used to make pictures.",{"id":926,"type":927,"title":928,"questions":929},"quiz-discover","quiz","Check your shape sense",[930,942,955,964,974,987,1000,1013,1024,1033],{"itemId":931,"prompt":932,"options":933,"correct":313,"why":941},"shape-and-space.discover-q-2d","Which of these is a 2D shape?",[934,936,937,939],{"id":304,"label":935},"A cricket ball",{"id":307,"label":115},{"id":310,"label":938},"A tumbler",{"id":313,"label":940},"The outline of a leaf drawn on paper","A drawing on paper is flat: it has length and breadth only. The others take up space.",{"itemId":943,"prompt":944,"options":945,"correct":304,"why":954},"shape-and-space.discover-q-polygon","Why is a circle **not** a polygon?",[946,948,950,952],{"id":304,"label":947},"It has no straight sides",{"id":307,"label":949},"It is too small",{"id":310,"label":951},"It is open",{"id":313,"label":953},"It has too many corners","A polygon must be made of straight line segments. A circle is one smooth curve with no straight sides and no corners.",{"itemId":956,"prompt":957,"options":958,"correct":307,"why":963},"shape-and-space.discover-q-hexagon","How many sides does a hexagon have?",[959,960,961,962],{"id":304,"label":240},{"id":307,"label":244},{"id":310,"label":248},{"id":313,"label":252},"Hexa means six. Honeycomb cells and the heads of nuts are hexagons.",{"itemId":965,"prompt":966,"options":967,"correct":310,"why":973},"shape-and-space.discover-q-cube-edges","How many edges does a cube have?",[968,969,970,971],{"id":304,"label":244},{"id":307,"label":252},{"id":310,"label":576},{"id":313,"label":972},"24","4 round the top, 4 round the bottom and 4 upright ones: 12. (6 is the number of faces, and 8 is the number of vertices.)",{"itemId":975,"prompt":976,"options":977,"correct":310,"why":986},"shape-and-space.discover-q-rigid","Why are bridges and electricity towers full of triangles?",[978,980,982,984],{"id":304,"label":979},"Triangles look nicer",{"id":307,"label":981},"Triangles use the most metal",{"id":310,"label":983},"A triangle keeps its shape when pushed",{"id":313,"label":985},"Triangles can roll","Three fixed side lengths fix a triangle completely, so a triangle frame is rigid. A four-sided frame can squash sideways.",{"itemId":988,"prompt":989,"options":990,"correct":307,"why":999},"shape-and-space.discover-q-square-rect","Which statement is true?",[991,993,995,997],{"id":304,"label":992},"Every rectangle is a square",{"id":307,"label":994},"Every square is a rectangle",{"id":310,"label":996},"A square and a rectangle have nothing in common",{"id":313,"label":998},"A tilted square is no longer a square","A rectangle needs four right angles. A square has four right angles (and equal sides as well), so it is a special rectangle.",{"itemId":1001,"prompt":1002,"options":1003,"correct":310,"why":1012},"shape-and-space.discover-q-diameter","A bangle has a radius of 4 cm. What is its diameter?",[1004,1006,1008,1010],{"id":304,"label":1005},"2 cm",{"id":307,"label":1007},"4 cm",{"id":310,"label":1009},"8 cm",{"id":313,"label":1011},"16 cm","The diameter goes all the way across through the centre, so it is two radii: 2 × 4 = 8 cm.",{"itemId":1014,"prompt":1015,"options":1016,"correct":313,"why":1023},"shape-and-space.discover-q-view","A tumbler standing on a table is seen from directly above. What shape do you see?",[1017,1019,1020,1022],{"id":304,"label":1018},"A rectangle",{"id":307,"label":311},{"id":310,"label":1021},"A square",{"id":313,"label":305},"From the top you look down at the round rim: a circle. From the side it looks like a rectangle.",{"itemId":1025,"prompt":1026,"options":1027,"correct":310,"why":1032},"shape-and-space.discover-q-symmetry","How many lines of symmetry does a square have?",[1028,1029,1030,1031],{"id":304,"label":709},{"id":307,"label":715},{"id":310,"label":236},{"id":313,"label":252},"Two lines through the middles of opposite sides and two along the diagonals: 4 in all.",{"itemId":1034,"prompt":1035,"options":1036,"correct":304,"why":1041},"shape-and-space.discover-q-roll","Which solid can roll in every direction?",[1037,1038,1039,1040],{"id":304,"label":511},{"id":307,"label":503},{"id":310,"label":507},{"id":313,"label":495},"A sphere is curved all over, so it rolls whichever way you push it. A cylinder rolls only in a straight line; a cone rolls in a circle.",{"id":1043,"type":1044,"title":1045,"points":1046},"cheat-discover","summary","Cheat sheet",[1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057],"**2D shapes** are flat (length and breadth). **3D shapes** take up space (length, breadth and height).","A **closed** curve ends where it starts; an **open** curve has loose ends. A **simple** closed curve does not cross itself.","A **polygon** is a simple closed figure made of straight sides. It has as many **vertices** as sides.","Names by sides: triangle 3, quadrilateral 4, pentagon 5, hexagon 6, heptagon 7, octagon 8, nonagon 9, decagon 10.","**Regular** polygons have all sides equal and all angles equal.","Triangles are **rigid**: that is why bridges and towers are built from them. The three angles of a triangle add up to 180°.","Every **square is a rectangle** (four right angles), but not every rectangle is a square.","Circle: **centre**, **radius**, **diameter = 2 × radius**, **circumference** (the distance round).","Cube and cuboid: **6 faces, 12 edges, 8 vertices**. Square pyramid: 5, 8, 5. Triangular prism: 5, 9, 6.","A **net** is a flat pattern that folds into a solid. **Views** (top, front, side) show a solid from different directions.","A **line of symmetry** splits a shape into mirror halves. Square 4, rectangle 2, equilateral triangle 3, circle countless.",{"id":1059,"type":381,"conceptId":1060,"relation":383,"explanation":1061},"conn-patterns-disc","patterns","Growing shape patterns, like matchstick squares and triangles, mix shape and number. Counting sides and corners in a pattern is the first step to finding its rule.",{"id":1063,"type":381,"conceptId":1064,"relation":383,"explanation":1065},"conn-lines-disc","lines","Sides of polygons are line segments, and edges of solids are line segments too. The Lines topic explains segments, rays and parallel lines.",{"id":1067,"type":1068,"sourceIds":1069},"sources-discover","sources",[1070,1071,1072,1073,1074,1075,1076,1077],"shape-and-space-ncert-class6","shape-and-space-khan-geometry","shape-and-space-mathsisfun-circle","shape-and-space-mathsisfun-quadrilaterals","shape-and-space-wiki-stepwell","shape-and-space-wiki-honeycomb","shape-and-space-sahapedia-konark","shape-and-space-wiki-lotus-temple",[1070,1071,1072,1073,1074,1075,1076,1077],"needs_review",{"generatedBy":1081,"notes":1082},"claude-code","Draft generated locally; pending owner review.","7a847eebea84c84c00cb6335fd0255548f042054e52c0ed3c38c2d1c4a319f71",{"component:sort-game@1":1085,"component:shape-explorer@1":1086,"logic:practice":1087,"component:match-pairs@1":1088,"source:shape-and-space-khan-geometry":1089,"source:shape-and-space-mathsisfun-circle":1090,"source:shape-and-space-mathsisfun-quadrilaterals":1091,"source:shape-and-space-ncert-class6":1092,"source:shape-and-space-sahapedia-konark":1093,"source:shape-and-space-wiki-honeycomb":1094,"source:shape-and-space-wiki-lotus-temple":1095,"source:shape-and-space-wiki-stepwell":1096},"b164f45a2c8ca08f26c450768ff0231e113e9fe45381eddb34dc6d0548596c38","a8965f19a8548e866e5fcd7f4fec4a9adac35ad54d43c9d5c416cdf3348e6198","3d6b0fe1b15255975a32b0fcd94e8019bc959ad45cbf12e136e86149549c6878","2a8ee4ac87460b4e1175a4bb13c96b03d577db06dde95670eb7fcfe4ad787899","10f385d6be5a688f5df4a8b9ea08a6c101d7bf683d87c29e7d9d2827a5e11963","ff337c822df6bd0ba5ef54450ce49945d4ef414438058441e656ee73ca685947","292166035f591d3d313675b23dcd587f26add442ae362358b916e3e15caa24b4","e1821bd507663f06793be51247da07646b65ba5a734a31c173a63c03f426f078","6ee0a23cfc409e91422c539b66809bbf228580cd24778343d949f96be8766016","4336a097e06982ba6b142ea63fb6f280c2335bc502b4e3e9f754af2d63e6771f","8d78c794c41f36e1fdbbdb5f4168dbb42eb9241d649f32fce9527faaf0da9f91","ebb0b8983fb1314b9a42f849c51f9d6b099115dd52fa9267eaa967e76262d35c",{"state":1098,"reviewer":1099,"selfReview":1100,"reviewedAt":1101,"method":1102},"approved","The library owner",true,"2026-09-20T10:18:37.581Z","owner_bulk","preview-7e1cbbcc4f",1789899598433]