Ring of numbers
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Problem
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.
Getting Started
Try putting one of the numbers in any square to start with. What numbers could go on each side of it?
When you add the numbers in two joined squares, what kind of number do you get?
You might like to print off this sheet of blank rings to help you try out some different numbers.
Student Solutions
Oli from Oakmeeds School began the first part of this question where we had to make odd differences between pairs of numbers.
You need odd, even, odd, even as odd + even make odd. Each pair has an odd and an even.
Rukmini from Hopscotch Nursery also said:
When the differences are all odd, the sums are all odd.
Rukmini then went on to say:
To make the differences even, you need the numbers 2, 4, 6, 8. Then the sums are also even.
Absolutely right - well done to both Oli and Rukmini. What about the order of the numbers 2, 4, 6 and 8 in the ring? Does it matter? I'll leave you all to ponder on that.
Teachers' Resources
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?
Possible approach
- 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?
Key questions
Possible extension
Possible support