# How Big Are Classes 5, 6 and 7?

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

Ben and Ali found out how many children there were in Classes 1, 2 and 3.

Katie and Charlene found about Classes 5, 6 and 7.

Of course they all knew the number of children in Class 4.

Ben and Ali drew a bar chart. It looked like this:

Katie and Charlene drew this pictogram:

Kate and Charlene have forgotten to add a key to their pictogram. What should the key say?

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

You can work out the number that each pin-man stands for from the two graphs for Class $4$.

Mikey from Archibishop of York C of E Junior School thought hard about this problem. He says:

Using the bar graph for class 4 gives 36 pupils but this allows several possible answers:

$5\times4 + 4\times4 = 36$ but so does

$6\times4 + 3\times4$,

$7\times4 + 2\times4$,

$8\times4 + 1\times4$.

All these are the same as 9$\times$4. We know big plus small must equal 9 but not the split from the info given. Maybe if Katie and Charlene had done classes 1 to 3 as well we would have been able to work it out.

Well done, Mikey for seeing that there are several possible solutions - not many of you realised this. What answers are possible then? Might some be more likely than others do you think?

Lizzi from Bampton C of E Primary School wrote:

By looking at the amount of pupils in class 4 on the bar graph, you can tell that the big people on the graph equal 6 and the little people equal 3 people, so therefore there are 42 people in class 7, 39 people in class 6 and 30 people in class 5 which equals 111 pupils.

This is certainly one of the possibilities. Freddie from Whitehall Primary School calculated another one:

Big people = 7

Small people = 2

Year 5 = 35 Year 6 = 38 Year 7 = 40

Total = 113

Joshua from BMGS suggests:

... for each big figure it was 8 and for each small one it was 1. Then it was a simple solution of adding up all of years 5, 6 and 7. The total answer was 115.

James, a teacher at Christchurch Purley C of E Primary School wrote to say:

The class really enjoyed getting stuck into the problems and discovering the different solutions.

I was really impressed with two of my children who I asked to find more solutions once they had found one. They thought of the large stickmen representing 10 and the small stickmen representing -1. I understand that this is not normally how pictograms would work but I thought it was fantastic 'out of the box' thinking and a great way to find more solutions to the problem. After this they thought of the stickmen representing 11 and -2.

Another pair of children claimed the solutions they had found had the pairs of stickmen always adding to 9. We were then able to back this up as a class with the solutions involving negative numbers that also equalled 9.

Thank you for sharing this, James, and well done to the class!

We are still left without the solution for a big stickman representing 5 children and a small stickman representing 4 children, but thank you for all your contributions.

**Why do this problem?**

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