# Pairs of Numbers

## Problem

*Pairs of Numbers printable sheet*

If you have ten counters numbered $1$ to $10$, how many can you put into pairs that add to $10$?

Can you use them all?

Say how you got your answer.

Now put the counters into pairs to make $12$.

- Can you use them all?
- Say how you got your answer.

Now put the counters into pairs to make $13$.

- Can you use them all?
- Say how you got your answer.

Now put the counters into pairs to make $11$.

- Can you use them all?
- Say how you got your answer.

## Getting Started

It might help to have counters numbered from $1$ - $10$ to do this problem.

## Teachers' Resources

**Why do this problem?**

This problem looks simple to start with, but it has a certain complexity. It is a great opportunity to encourage children to justify their thinking, which they may find quite difficult at first.

Possible approach

All children will need access to ten counters or number cards numbered from $1$ - $10$. Having counters to move around will help free up their thinking and means they can try out lots of ways without the fear of having something committed to paper which might be wrong. Some children may also need some unnumbered counters or Multilink cubes to help them with the calculations.

### Key questions

What goes with this number to make $10$/$11$ etc?

### Possible extension

Children could try to find other numbers of which can be made from pairs of the numbers $1$ - $10$. Are there any number which can't be used?

What can they do if they use the numbers from $1$ - $12$ instead of $1$ - $10$?

### Possible support

Some learners may need support with the calculations, so having number lines, blank counters or other equipment available will be useful. This task offers children the chance to practice adding numbers in a meaningful context.