Fractions

problem
Stretching fractions

Age

14 to 16

Challenge level

Imagine a strip with a mark somewhere along it. Fold it in the middle so that the bottom reaches back to the top. Stetch it out to match the original length. Now where's the mark?
problem
The Cantor set

Age

11 to 14

Challenge level

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you picture it?
problem
How long is the Cantor set?

Age

11 to 14

Challenge level

Take a line segment of length 1. Remove the middle third. Remove the middle thirds of what you have left. Repeat infinitely many times, and you have the Cantor Set. Can you find its length?
problem
Equal temperament

Age

14 to 16

Challenge level

The scale on a piano does something clever : the ratio (interval) between any adjacent points on the scale is equal. If you play any note, twelve points higher will be exactly an octave on.
problem
Investigating the dilution series

Age

14 to 16

Challenge level

Which dilutions can you make using only 10ml pipettes?
problem
Fraction card game

Age

5 to 7

Challenge level

Can you match the halves in this interactive game?
problem
A bowl of fruit

Age

5 to 7

Challenge level

Can you work out how many apples there are in this fruit bowl if you know what fraction there are?
problem
Halving

Age

5 to 7

Challenge level

These pictures show squares split into halves. Can you find other ways?
problem
Making longer, making shorter

Age

5 to 7

Challenge level

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
problem
Happy halving

Age

5 to 7

Challenge level

Can you split each of the shapes below in half so that the two parts are exactly the same?