Copyright © University of Cambridge. All rights reserved.

'Venn Diagrams' printed from http://nrich.maths.org/

Show menu

Venn Diagrams


Can you place the numbers from $1$ to $40$ into this Venn diagram?
How do you know where to put each number?
You might like to print off this sheet if you do not want to use the interactivity.
Full screen version
This text is usually replaced by the Flash movie.



Here is another one for you to try. If you'd prefer to work on paper, print off this sheet.
Full screen version
This text is usually replaced by the Flash movie.

Why do this problem?

This problem provides an opportunity for children to become familiar with Venn diagrams, whilst reinforcing knowledge of number properties. Placing numbers in a Venn diagram requires children think of more than one property of a number at the same time and this problem will encourage them to explain their reasons for placing the numbers.


Possible approach

You could introduce the group to Venn diagrams using this simple interactivity on an interactive whiteboard. If the idea is completely new you could start by putting numbers into two single circles and show how the intersection takes numbers that have both properties.

If children work on these problems in pairs (either on paper or using the interactivity) it will encourage them to construct mathematical arguments to convince each other where on the diagram each number belongs. Explaining out loud in this way often helps to clarify thinking and will give a purpose for accurate use of mathematical vocabulary.

You could use the interactivities on an interactive whiteboard to help share their solutions in a plenary.


Key questions

What can you tell me about this number?
Where does this number go, in this circle, in that one, in both or in neither?

Possible extension

Children who find these problems easy could try the third interactivity in this problem .


Possible support

Some learners might find it easier to collect numbers with a certain property, for example, even numbers or numbers less than 10, in single circles. Then to look at those that should go in both circles.