In our view, you can't do maths without reasoning! But what is mathematical reasoning and when do we need it? Have a go at these activities which give you chances to reason in different ways and for different purposes. Can you explain your solution, convince someone else it is correct and justify your conclusions?

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

There are six numbers written in five different scripts. Can you sort out which is which?

Can you go through this maze so that the numbers you pass add to exactly 100?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.