Working systematically

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

Can all unit fractions be written as the sum of two unit fractions?

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

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

Can you find a way to identify times tables after they have been shifted up or down?

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Imagine flipping a coin a number of times. Can you work out the probability you will get a head on at least one of the flips?