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

### 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.