### Why do this problem?

The first two parts of

this problem provide an opportunity for learners to become familiar with Venn diagrams, whilst reinforcing knowledge of number properties. The final part introduces slightly higher-level thinking as learners then work "backwards".

### Possible approach

If the group are not familiar with Venn diagrams, you could introduce them using this simple

interactivity on an interactive whiteboard.

After the introduction learners could work on the problems either on paper or using the interactivity. If learners work on this in pairs 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 interactivity on an interactive whiteboard to help share their solutions in a plenary.

### Key questions

What can you tell me about this number?

Where would you put a number which is square but not odd?

Where would a square odd number go?

Where would a number which is odd but not square go?

Where would you put a number which is not square and not odd?

### Possible extension

Learners could try their hands at placing numbers in a Venn diagram with three circles. They could use three categories such as 'multiples of $7$', 'square numbers' and 'odd numbers'.

This sheet might be useful for this purpose.

### Possible support

You could try using this simpler

version instead which uses number properties that children usually encounter before those contained in this problem.