### Graphing Number Patterns

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

### Dining Ducks

Use the information about the ducks on a particular farm to find out which of the statements about them must be true.

### You Never Get a Six

Charlie thinks that a six comes up less often than the other numbers on the dice. Have a look at the results of the test his class did to see if he was right.

# How Big Are Classes 5, 6 and 7?

##### Age 7 to 11Challenge Level

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.