Fractions

problem
Six notes all nice ratios

Age

14 to 16

Challenge level

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.
problem
Fractions jigsaw

Age

11 to 14

Challenge level

A jigsaw where pieces only go together if the fractions are equivalent.
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
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
Fraction fascination

Age

7 to 11

Challenge level

This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.
problem
Family fortune

Age

11 to 14

Challenge level

If three brothers will get £20 more if they do not share their money with their sister, how much money is there?
problem
Couples

Age

11 to 14

Challenge level

In a certain community two thirds of the adult men are married to three quarters of the adult women. How many adults would there be in the smallest community of this type?
problem
Once upon a time

Age

7 to 11

Challenge level

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?
problem
Harmonic triangle

Age

14 to 16

Challenge level

Can you see how to build a harmonic triangle? Can you work out the next two rows?
problem
Fractions made faster

Age

7 to 11

Challenge level

Use the fraction wall to compare the size of these fractions - you'll be amazed how it helps!