Conjecturing and generalising

problem
Growing rectangles

Age

11 to 14

Challenge level

What happens to the area and volume of 2D and 3D shapes when you enlarge them?
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?
problem
Three dice

Age

7 to 11

Challenge level

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
problem
Handshakes

Age

11 to 14

Challenge level

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
problem
Mystic rose

Age

14 to 16

Challenge level

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem
Diminishing returns

Age

11 to 14

Challenge level

How much of the square is coloured blue? How will the pattern continue?
problem
Tower of Hanoi

Age

11 to 14

Challenge level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
problem
Christmas chocolates

Age

11 to 14

Challenge level

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
problem
How much can we spend?

Age

11 to 14

Challenge level

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
problem
Cyclic quadrilaterals

Age

11 to 16

Challenge level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?