Uses
HCF and LCMThe largest square tile that fits a rectangular floor exactly has a side equal to the HCF of its length and width.
Shape and space
What makes a square a square, and how many edges does a cube really have?
2D shapes and their properties, 3D solids and their faces, edges and vertices, nets, views from different sides, and symmetry.
5 depths≈ 220 min of reading80 practice questions
The ladder
Choose how deep to go
Every depth is open. Start where it feels interesting — you can always move back.
- Discoverabout 30 minShapes all around usMeet 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.Owner-accepted · not line-by-line reviewed
- Understandabout 40 minNaming shapes preciselyGive every shape an exact definition: polygons and diagonals, triangles by sides and angles, the quadrilateral family tree, the parts of a circle, perimeter, prisms and pyramids, nets, views and line symmetry, with worked examples and common mix-ups.Owner-accepted · not line-by-line reviewed
- Investigateabout 45 minTest it, fold it, count itPredict, then test: how fast diagonals multiply, which three sticks make a triangle, what polygon angles add up to, which statements are always true, the F + V − E pattern, which six-square shapes fold into a cube, symmetry in letters, measuring π and which shapes tile a floor.Owner-accepted · not line-by-line reviewed
- Go deeperabout 50 minWhy shapes behave as they doTurn patterns into proofs: the diagonal formula, why angles add to 180° and (n − 2) × 180°, the triangle inequality, quadrilateral inheritance, why wheels are round, a sketch proof of Euler’s formula and where it fails, cube-net rules, symmetry orders, and the history of π.Owner-accepted · not line-by-line reviewed
- Extendabout 55 minProjects, puzzles and the wider world of shapeBuild the five Platonic solids and hunt all 11 cube nets, design rangoli with rotational symmetry, explore tangram paradoxes and semi-regular tilings, count a football, see geometry in Indian monuments and nature, solve olympiad-style problems, and meet questions still unsolved.Owner-accepted · not line-by-line reviewed
Practise and apply
Question bank · 80 questions
9 sections from Foundation to Challenge, each with hints and a worked solution — or play a 10-question round for points and stars.
Foundation 19Core 31Stretch 19Challenge 11
The web
Connected ideas
Follow a connection when you’re curious — some lead into completely different areas.
Shape and space
Related to
Number and shape patternsGrowing shape patterns — matchstick squares, dot triangles — are geometry and number at the same time.
Related to
Lines, rays and line segmentsEvery polygon is built from line segments, and its sides can be parallel or perpendicular.
Related to
AnglesThe corners of shapes are angles: a square has four right angles and a triangle's angles add to 180°.
Uses
Measuring and constructing anglesDrawing accurate triangles, squares and regular polygons needs measured or constructed angles.
Usesanother area
Exploration: reasons and consequencesMaps, globes and navigation are geometry: a round Earth flattened onto paper without lying too much.
Words to know
80 words are explained in these lessons
2D shape3D shape (solid)CurveClosed curveOpen curvePolygonSideVertex (plural: vertices)Regular polygonTriangleQuadrilateralCircle+68 more