This article explores the process of making and testing hypotheses.

Which countries have the most naturally athletic populations?

Simple models which help us to investigate how epidemics grow and die out.

Is it the fastest swimmer, the fastest runner or the fastest cyclist who wins the Olympic Triathlon?

Build a mini eco-system, and collect and interpret data on how well the plants grow under different conditions.

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

A manager of a forestry company has to decide which trees to plant. What strategy for planting and felling would you recommend to the manager in order to maximise the profit?

Investigate how avalanches occur and how they can be controlled

Can you deduce which Olympic athletics events are represented by the graphs?

Three teams have each played two matches. The table gives the total number points and goals scored for and against each team. Fill in the table and find the scores in the three matches.

Engage in a little mathematical detective work to see if you can spot the fakes.

A farmer has a flat field and two sons who will each inherit half of the field. The farmer wishes to build a stone wall to divide the field in two so each son inherits the same area. Stone walls are. . . .

Square numbers can be represented on the seven-clock (representing these numbers modulo 7). This works like the days of the week.

Baker, Cooper, Jones and Smith are four people whose occupations are teacher, welder, mechanic and programmer, but not necessarily in that order. What is each person’s occupation?

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

After some matches were played, most of the information in the table containing the results of the games was accidentally deleted. What was the score in each match played?

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?