Explaining, convincing and proving

Engage in a little mathematical detective work to see if you can spot the fakes.

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Can you deduce which Olympic athletics events are represented by the graphs?

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

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

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

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

Can you crack these cryptarithms?

Can you deduce the perimeters of the shapes from the information given?