Formulate and investigate a simple mathematical model for the design of a table mat.

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

Can Jo make a gym bag for her trainers from the piece of fabric she has?

Examine these estimates. Do they sound about right?

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Work with numbers big and small to estimate and calculate various quantities in biological contexts.

Make your own pinhole camera for safe observation of the sun, and find out how it works.

If I don't have the size of cake tin specified in my recipe, will the size I do have be OK?

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?

Invent a scoring system for a 'guess the weight' competition.

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

Which countries have the most naturally athletic populations?

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the. . . .

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

These Olympic quantities have been jumbled up! Can you put them back together again?

Investigate circuits and record your findings in this simple introduction to truth tables and logic.

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

What shape would fit your pens and pencils best? How can you make it?

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

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

Is it cheaper to cook a meal from scratch or to buy a ready meal? What difference does the number of people you're cooking for make?