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

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

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

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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

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?

How do you write a computer program that creates the illusion of stretching elastic bands between pegs of a Geoboard? The answer contains some surprising mathematics.

Have you ever wondered what it would be like to race against Usain Bolt?

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

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. . . .

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

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?

Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.

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

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?

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

Which countries have the most naturally athletic populations?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Which units would you choose best to fit these situations?

Where should runners start the 200m race so that they have all run the same distance by the finish?

Can you work out which processes are represented by the graphs?

When you change the units, do the numbers get bigger or smaller?

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

This problem explores the biology behind Rudolph's glowing red nose.

Explore the relationship between resistance and temperature

Analyse these beautiful biological images and attempt to rank them in size order.

How would you design the tiering of seats in a stadium so that all spectators have a good view?

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

Get some practice using big and small numbers in chemistry.

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

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Can you draw the height-time chart as this complicated vessel fills with water?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?