Reasoning, convincing and proving

problem
Hiking the hill

Age

14 to 16

Challenge level

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?
problem
Kept apart

Age

11 to 14

Challenge level

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?
problem
L-triominoes

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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?
problem
How do you do it?

Age

7 to 11

Challenge level

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
problem
Close to triangular

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

Can you work out which drink has the stronger flavour?
problem
Times tables shifts

Age

7 to 11

Challenge level

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