Mathematics News

NRICH is an innovative collaboration between the Faculties of Mathematics and Education at the University of Cambridge which focuses on problem solving and on creating opportunities for students to learn mathematics through exploration and discussion. 

NRICH provides thousands of free online mathematics resources for ages 3 to 18, covering all stages of early years, primary and secondary school education - completely free and available to all. 

Check out their website https://nrich.maths.org/ or have a go at some of the problems below.

Ring a Ring of Numbers

Age 5 to 7 Challenge Level **

Here is a picture of four numbers placed in squares on a circle so that each number is joined to two others:

What do you see?

What do you notice?

Choose four numbers from this list: 1, 2, 3, 4, 5, 6, 7, 8, 9 to put in the squares 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?

More Numbers in the Ring

Age 5 to 7 Challenge Level ***

Before doing this problem, it would be a good idea to look at the Ring a Ring of Numbers problem above. 

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?

Magic Vs

Age 7 to 11 Challenge Level *

Place each of the numbers 1 to 5 in the V shape below so that the two arms of the V have the same total.

How many different possibilities are there?

What do you notice about all the solutions you find?

Can you explain what you see?

Can you convince someone that you have all the solutions?

What happens if we use the numbers from 2 to 6? From 12 to 16? From 37 to 41? From 103 to 107?

What can you discover about a V that has arms of length four using the numbers 1 to 7?

Different Deductions

Age 7 to 11 Challenge Level **

Each symbol has a numerical value. The total for the symbols is written at the end of each row and column.

Can you find the missing total that should go where the question mark has been put?