Visualising and representing

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?

What is the first term of a Fibonacci sequence whose second term is 4 and fifth term is 22?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

What are the possible areas of triangles drawn in a square?