## In the Money

There are a number of coins on a table.

One quarter of the coins show heads.

If I turn over two coins, then one third show heads. How many coins are there altogether?

### Why do this problem?

This problem challenges children to calculate with fractions, using higher-order thinking skills. It is a good context in which to discuss the merits of a trial and improvement approach.

### Possible approach

You could start by asking children to find a quarter of different numbers, or by listing some numbers and asking them to say which have whole-number quarters. This can lead into a discussion about multiples of $4$ and methods for finding quarters.

Present the problem itself and ask children to work in pairs on it. Mini-whiteboards might be useful at this stage. Listen out for sound reasoning and helpful strategies for solving the problem. After some time, give an opportunity for learners to share their solutions and methods. At this stage it might also be appropriate to draw attention to useful vocabulary which the children are using,
for example factor, multiple.

A follow-up question of a similar sort could be useful for a plenary or second activity. For example: $\frac{1}{6}$ of the coins are heads up. If I turn over four more, then $\frac{1}{5}$ are heads. How many coins are on the table?

### Key questions

What do you know about the total number of coins?

Have you tried out any possible numbers?

### Possible extension

Another problem could be given, such as: $\frac{1}{5}$ of the coins are heads up. If I turn over four more, then $\frac{1}{4}$ are heads. How many coins are on the table? Pupils will also be able to create their own.

### Possible support

Using coins to try out possibilities will help some pupils.