Ring a Ring of Numbers
Choose four of the numbers from this list: 1, 2, 3, 4, 5, 6, 7, 8, 9 to put in the four squares below so that the difference between joined squares is odd.
Only one number is allowed in each square. You must use four different numbers.
What can you say about the sum of each pair of joined squares?
What must you do to make the difference even?
What do you notice about the sum of the pairs now?
Here .doc .pdf
are some sheets for recording your solutions.
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 find out more about this book, and order a copy go to the CUP website.
Why do this problem?
provides a context in which children can recognise odd and even numbers, and begin to think about their properties. It also offers practice of addition and subtraction.
It would be good to have the image of the 'ring' on the interactive whiteboard, or projected onto a screen. Begin by writing any four numbers in the ring and asking questions about them, for example:
- Which pair of numbers has a total of ...?
- Which pair of numbers has a difference of ...?
- Which pair of numbers has the highest/lowest total?
- Which pair of numbers has the greatest/least difference?
These questions will help children become familiar with the vocabulary of the problem and so you can then lead into the main activity. Having asked the question, give pairs of children chance to find at least one way of making odd differences. They could use this sheet of blank circles .doc .pdf
to try out their ideas. As they find arrangements that work, you could invite them to record them on the board on some pre-drawn rings.
Once you have several ways on the board, invite learners to comment on what they notice. What do all the arrangements have in common? You can work through the rest of the problem in a similar way, drawing the whole class together as appropriate.
It is important to encourage the children to explain why the arrangements of odd/even numbers produce these results. You could make drawings .doc .pdf
using paired joined squares to help them understand.
What do you notice about the numbers in the ring when the difference between joined pairs is odd?
What do you notice about the numbers in the ring when the difference between joined pairs is even?
Can you explain why?
Some learners might benefit from having counters or other objects to help with their addition and subtraction.