### Number Detective

Follow the clues to find the mystery number.

### Grouping Goodies

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

### Red Even

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

# Venn Diagrams

## 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.