Symmetry

problem

Symmetric Trace

Age

14 to 16

Challenge level

Points off a rolling wheel make traces. What makes those traces have symmetry?
problem

Rotations Are Not Single Round Here

Age

14 to 16

Challenge level

I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only one centre of rotation ? Or if you thought that was impossible, could you say why ?
problem
Favourite

Exploded Squares

Age

5 to 7

Challenge level

Can you create symmetrical designs by cutting a square into strips?
problem
Favourite

Poly Plug Pattern

Age

5 to 7

Challenge level

Create a pattern on the small grid. How could you extend your pattern on the larger grid?
problem
Favourite

Colouring Triangles

Age

5 to 7

Challenge level

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?
problem

Animated Triangles

Age

5 to 7

Challenge level

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
problem

Triangle Shapes

Age

5 to 11

Challenge level

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
problem
Favourite

Always, Sometimes or Never? Shape

Age

7 to 11

Challenge level

Are these statements always true, sometimes true or never true?
problem
Favourite

A Cartesian Puzzle

Age

7 to 11

Challenge level

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.
problem

Symmetrical Semaphore

Age

7 to 11

Challenge level

Someone at the top of a hill sends a message in semaphore to a friend in the valley. A person in the valley behind also sees the same message. What is it?