Working systematically

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?

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?

Can you find six numbers to go in the daisy from which you can make all the numbers from 1 to a number bigger than 25?

What are the possible areas of triangles drawn in a square?

Can you crack these cryptarithms?