What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

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.

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

Find the decimal equivalents of the fractions one ninth, one ninety ninth, one nine hundred and ninety ninth etc. Explain the pattern you get and generalise.

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

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

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

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

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

Take a look at the video and try to find a sequence of moves that will take you back to zero.

It would be nice to have a strategy for disentangling any tangled ropes...

Can all unit fractions be written as the sum of two unit fractions?

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

A collection of short Stage 3 and 4 problems on fractions, decimals, percentages and ratio.