Being resourceful

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

These Olympic quantities have been jumbled up! Can you put them back together again?

Can you find the squares hidden on these coordinate grids?

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Imagine a very strange bank account where you are only allowed to do two things...