Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Change the ring so that there are only 3 squares.
Can you place three different numbers in them so that their differences are odd?
Can you make the differences even?
What do you notice about the sum of each pair in each case?

Try with different numbers of squares around the ring.
What happens with 5 squares? 6 squares?
What do you notice?

This problem is based on an idea taken from "Apex Maths Pupils' Book 2" by Ann Montague-Smith and Paul Harrison, published in 2003 by Cambridge University Press. To order a copy of this book, or others published by CUP, see their online catalogue .

Why do this problem?

This problem builds on Ring a Ring of Numbers. It encourages children to start from different examples and then begin to draw some more general conclusions based on their understanding of odd and even numbers.

Key questions

What happens when you put one more number in the ring?

What happens when you put two more numbers in the ring?

What happens when there is an odd number of numbers in the ring?

What happens when there is an even number of numbers in the ring?

Some children will benefit from spending more time on the Ring a Ring of Numbers problem. Having digit cards to move around on a large piece of paper will also help if they are not using the interactivity. Pupils might also find it useful to have sheets of blank rings so that they can try different combinations of numbers: