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One Reflection Implies Another
problem

One Reflection Implies Another

14 to 16

When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that was impossible, could you explain why ?

A jar of teddies
problem

A Jar of Teddies

7 to 14
How many teddies are in the jar? How many teddies could you fit in your classroom?
Cuboid challenge
problem
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Cuboid Challenge

11 to 16

What's the largest volume of box you can make from a square of paper?

problem
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Noah

5 to 7

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

Zargon Glasses
problem

Zargon Glasses

7 to 11
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Rotations Are Not Single Round Here
problem

Rotations Are Not Single Round Here

14 to 16

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 ?

Pyramid numbers
problem

Pyramid Numbers

7 to 11
What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?
A Shapely Network
problem

A Shapely Network

7 to 11

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

How far does it move?
problem
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How Far Does It Move?

11 to 14

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

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