## Number Balance

This is a number balance.

It is also called a 'balance bar' or an 'equaliser'. It has weights:

These are hung below the numbers. It balances equal numbers, for example like this:

Where would you need to hang the weight to make the one below balance?

What about this one?

If you had to use two weights and make the one below balance, where could you put them?

How many different ways can you make it balance with two weights?

**Why do this problem?**

This problem requires children to utilise their knowledge of number bonds in an unusual context and requires them to explain and reason through their solutions.

### Possible approach

Before tackling Number Balance, pupils will need practical experience of working with balances, if possible.

To introduce the problem, show the class a balance and, without saying anything, hang weights to make it balance (two on each side if possible). Take the weights off and put on a different combination of two weights on each side to balance the equaliser. Repeat this a few times and invite learners to talk to each other in pairs about what they think is happening. You could then try the first
two examples in the problem as a whole group, asking the children to talk to each other about what to do before sharing ideas amongst the whole group.

In the main challenge, you may want the children to work on mini-whiteboards so they are confident to note down their ideas. After leaving time for them to work on this, bring them together and discuss their solutions. You could ask pairs to write up some solutions on individual strips of paper which can be stuck on the board. You could follow on by looking for patterns in the solutions, which
may lead to the children suggesting other possibilities. Alternatively (or in addition) you could focus on the number sentences that can be written from the pupils' solutions.

By inviting learners to talk through what is happening at each stage of this problem, you will be able to assess how well they have grasped addition and subtraction, and whether they can apply their understanding.

### Key questions

Can you tell me how a balance works?

How can you tell from the pictures which side we need to add a weight to?

What is the total of the weights on this side?

What is the total of the weights on the other side?

### Possible extension

You could encourage children to work systematically to find all the possible solutions to the final part of the problem.

### Possible support

Having lots of practical experience of real balances will help children access this task.