Symmetry

problem

Square Pizza

Age

14 to 16

Challenge level

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
problem

Symmetric Trace

Age

14 to 16

Challenge level

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

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?
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

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

Polydron

Age

7 to 11

Challenge level

This activity investigates how you might make squares and pentominoes from Polydron.
problem

Prime Magic

Age

7 to 16

Challenge level

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
problem

Eight Dominoes

Age

7 to 16

Challenge level

Using the 8 dominoes, can you make a square where each of the columns and rows adds up to 8?