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# Through the Window

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Age 7 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
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We had these submissions from Ben and Will at Colwich Primary School:

There are six windows shown and you could put them in pairs of windows which have the same perimeter but different areas, or the same areas but different perimeters.

We chose to work with the £150 and £140 windows which have the same perimeter, but different areas.

For the £150 window, A = 9 and P = 12. For the £140 window, A = 8 and P = 12.

This showed us that 1 square of A = £10.

For the £140 window, this means that A = £80 and P = £60, which means that 1P = £5.

So the answer is that a piece of glass costs £10 for every square of area, plus £5 for every square edge.

We checked our answers on all the other pieces of glass, and it worked every time.

Thank you very much for sending in these ideas.

We were also sent the following solutions from Emily, Ebony, Rose, Alex and Paul from Wold Newton Foundation School, which go into more detail about a similar method to the one Ben and Will used. These pictures can be clicked on to make them bigger:

(These children are using the notation 9² to mean 9m².)

These are really good ideas - I like the way everybody has decided to find pairs of windows that either have the same area or the same perimeter to help them. Having pairs of similar windows makes it really clear what the difference is between them, and you've used that to find the price of a single square metre of glass or a single metre of frame. Thank you for sharing these ideas with us!