Reasoning, convincing and proving

Pizza, Indian or Chinese takeaway? If everyone liked at least one, how many only liked Indian?

Sarah's average speed for a journey was 2 mph, and her return average speed was 4 mph. What is her average speed for the whole journey?

The squares of this grid contain one of the letters P, Q, R and S. Can you complete this square so that touching squares do not contain the same letter? How many possibilities are there?

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Drawing a triangle is not always as easy as you might think!

Can you work out which drink has the stronger flavour?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?