Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?

Explore the properties of these two fascinating functions using trigonometry as a guide.

What on earth are polar coordinates, and why would you want to use them?

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 what simple structures have been dressed up in these advanced mathematical representations?

Use functions to create minimalist versions of works of art.

Make a functional window display which will both satisfy the manager and make sense to the shoppers

Starting with two basic vector steps, which destinations can you reach on a vector walk?

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