Symmetry

problem
Troublesome dice

Age

11 to 14

Challenge level

When dice land edge-up, we usually roll again. But what if we didn't...?
problem
Exploded squares

Age

5 to 7

Challenge level

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

Age

16 to 18

Challenge level

What groups of transformations map a regular pentagon to itself?
problem
Attractive rotations

Age

11 to 14

Challenge level

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
problem
Counters in the middle

Age

7 to 11

Challenge level

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
problem
Drawing Celtic knots

Age

11 to 14

Challenge level

Here is a chance to create some Celtic knots and explore the mathematics behind them.
problem
Trominoes

Age

11 to 16

Challenge level

Can all but one square of an 8 by 8 Chessboard be covered by Trominoes?
problem
Tiles in a public building

Age

7 to 11

Challenge level

What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?
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.