Visualising and representing

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

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?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

The large rectangle is divided into quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Can you deduce which Olympic athletics events are represented by the graphs?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?