Shapes, angles, symmetry and space.
Geometry is the study of shape and space: naming 2D and 3D shapes by their sides, corners and faces, then working with angles, symmetry and positions on a coordinate grid. A shape keeps its name however it is turned.
One error to watch for: deciding a shape changes when it is turned. For example, calling a square stood on its corner a different shape.
Geometry is the mathematics of shape, size and position — naming and sorting shapes, measuring angles, finding area and perimeter, and describing where things are and how they move.
It is the strand where children who find arithmetic hard most often do well, because it rewards visual and spatial reasoning rather than recall. That makes it worth taking seriously rather than treating as the light relief between number topics: for some children it is where mathematical confidence starts.
Interactive practice with instant feedback — free, ad-free and playable in the browser.
5-7 · drag-drop
Children sort 3D shapes by whether they roll, exploring the properties of spheres, cubes, cylinders, cones and more.
8-10 · puzzle
Solve angle clues on an evidence grid at a detective agency, placing the right number of degrees to crack each case, for ages 8 to 10.
8-10 · quiz
Compare volumes and capacities at a water engineering center, choosing which container holds more, for ages 8 to 10.
8-10 · builder
Select every line of symmetry of crystal shapes in a mirror kingdom, then check your balanced design, for ages 8 to 10.
8-10 · quiz
Calculate the perimeter of rectangle blueprints in an architect design studio, for ages 8 to 10.
8-10 · builder
Construct target angles with a virtual protractor in an engineering innovation lab, for ages 8 to 10.
11-12 · builder
Read cube and cuboid models, toggle their nets, and calculate volume and surface area on a space colony build site, for ages 11 to 12.
11-12 · puzzle
Complete Pythagorean triples on a grid in an ancient geometry archive, finding each missing side, for ages 11 to 12.
11-12 · builder
Apply circle theorems to find missing angles in a celestial observatory, for ages 11 to 12.
13-14 · builder
Read a curve and its tangent, then find the gradient at a point in an autonomous vehicle engineering lab, for ages 13 to 14.
13-14 · puzzle
Apply advanced circle theorems to fill a logic grid in the astronomical navigation archives, for ages 13 to 14.
13-14 · quiz
Add vectors and find magnitudes in a space navigation academy, for ages 13 to 14.
Showing 12 of 16. Browse all games
Every worksheet prints as a clean A4 PDF with a separate answer key.
2-4 · tracing
Trace ovals and diamonds along dotted guides, then copy each shape. An early shape and pencil-control activity for ages 2–4.
5 levels · PDF + answer key
2-4 · true-false
Look at each shape and decide — is it a rectangle? A true-or-false shape-recognition activity for ages 2–4.
5 levels · PDF + answer key
5-7 · true-false
Decide whether statements about a shape's symmetry are true or false. A Grade 2 geometry reasoning worksheet with answer keys.
5 levels · PDF + answer key
8-10 · grid
Complete a 6×6 addition square by adding the row and column headers. A Grade 3 addition-fluency grid with answer keys.
5 levels · PDF + answer key
8-10 · match
Match each polygon name to its number of sides. A Grade 4–5 geometry matching worksheet with answer keys.
5 levels · PDF + answer key
8-10 · true-false
Decide whether statements about parallel and perpendicular lines are true or false. A Grade 4 geometry reasoning worksheet with answer keys.
5 levels · PDF + answer key
8-10 · grid
Complete a 6×6 multiplication square for the 1–6 times tables. A Grade 3 times-table grid with answer keys.
5 levels · PDF + answer key
8-10 · true-false
Decide whether statements about shapes and their lines of symmetry are true or false. A Grade 4 geometry worksheet with answer keys.
5 levels · PDF + answer key
8-10 · grid
Complete an 8×8 fact grid to practise division facts. A Grade 3–4 division-fluency grid with answer keys.
5 levels · PDF + answer key
8-10 · multiple-choice
Calculate the volume of boxes and the total mass of groups, choosing from four options. A Grade 5 measurement worksheet with answer keys.
5 levels · PDF + answer key
11-12 · multiple-choice
Find the hypotenuse of a right-angled triangle using Pythagoras, choosing from four options. A Grade 7–8 geometry worksheet with answer keys.
5 levels · PDF + answer key
11-12 · multiple-choice
Find the area and circumference of circles in terms of π, choosing from four options. A Grade 7 geometry worksheet with answer keys.
5 levels · PDF + answer key
Showing 12 of 21. Browse all worksheets
Geometry & Shapes appears across several grades on this site, with the skills becoming more advanced over time. Jump to a grade page for a broader set of activities at that level.
Handle real objects wherever possible. A shape held and turned teaches something a picture of it does not, particularly for 3-D work, where a drawing has already flattened the thing being described.
Area and perimeter are confused constantly, and the reliable fix is language rather than formulas: perimeter is the fence around the garden, area is the grass inside it. Ask which one a question wants before any calculation starts.
Browse Math by Grade for a full set of age-appropriate activities rather than a single strand.
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