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Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

What do you notice about these families of recurring decimals?

Can you match these calculations in Standard Index Form with their answers?

Can you work out which processes are represented by the graphs?

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Can you work out the probability of winning the Mathsland National Lottery?

This is an adding game for two players. Can you be the first to reach the target?