## How Big Are Classes 5, 6 and 7?

Class 4 were making graphs. Ben, Ali, Katie and Charlene decided to make graphs of the sizes of the seven classes in the school.

They went to the office to collect the numbers of children in all the other classes. Ben and Ali wrote down the numbers for Classes $1$, $2$ and $3$. Katie and Charlene wrote down the numbers for Classes $5, 6$ and $7$. Of course they all knew the number of children in Class $4$.

Ben and Ali drew a block graph. It looked like this:

Katie and Charlene decided to make theirs differently. They drew this graph:

Miss Brown came along to look at their work.

"It's an interesting graph," she said, "but it's difficult to tell how many children are in each class. Please can you make a scale on it so we can all read it?"

Katie and Charlene did what they were told.

How many children were there altogether in Classes $5, 6$ and $7$?

### Why do this problem?

This problem is useful when learners are being introduced to or revising different ways of representing data and the scales needed when making bar charts and pictograms. The question encourages them to contrast different ways of representing similar data and helps to make explicit their interpretation of what
the data represents in order to solve the problem.

Later on in secondary school children often leave out the labels on axes so rendering the representation meaningless. This question will help children to realise the significance of the labels.

### Possible approach

You could start by doing another, simpler problem, for example,

The Pet Graph. Alternatively, you could get the numbers of children in classes in your own school and make a rough bar chart of them on the board.

After this learners could work in pairs on the actual problem on a computer or from a printed sheet so that they are able to talk through their ideas with a partner. They should be encouraged to think about the question and talk about it in pairs before a class discussion.

At the end of the lesson you should discuss not only the answers to the problem itself, and how these were reached, but also to stress why it is important not to leave out the labels on axes of a graph.

### Key questions

What is a reasonable number to try?

What can you find out about Class $4$ from the bar graph?

Can you work out the number that each pin-man stands for from the two graphs for Class $4$?

### Possible extension

Learners could make different graphs and representations of the numbers in the classes in their own school or do another problem such as

You Never Get a Six.

### Possible support

Suggest trying

The Pet Graph first which is simpler and easier to understand.