Fractions

problem
Light blue - dark blue

Age

7 to 11

Challenge level

Investigate the successive areas of light blue in these diagrams.
problem
Farey sequences

Age

11 to 14

Challenge level

There are lots of ideas to explore in these sequences of ordered fractions.
problem
Modular fractions

Age

16 to 18

Challenge level

We only need 7 numbers for modulus (or clock) arithmetic mod 7 including working with fractions. Explore how to divide numbers and write fractions in modulus arithemtic.
problem
Hello again

Age

11 to 14

Challenge level

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?
problem
Smaller and smaller

Age

7 to 14

Challenge level

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?
problem
Repetitiously

Age

14 to 16

Challenge level

Can you express every recurring decimal as a fraction?
problem
Tiny nines

Age

14 to 16

Challenge level

What do you notice about these families of recurring decimals?
problem
Halving

Age

5 to 7

Challenge level

These pictures show squares split into halves. Can you find other ways?
problem
Matching fractions, decimals and percentages

Age

7 to 14

Challenge level

Can you match pairs of fractions, decimals and percentages, and beat your previous scores?
problem
Egyptian fractions

Age

11 to 14

Challenge level

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.