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

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

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

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.

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.

Is it really greener to go on the bus, or to buy local?

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?

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

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?

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?

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

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

Examine these estimates. Do they sound about right?

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

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

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

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

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. . . .

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

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?

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

Which units would you choose best to fit these situations?

How would you go about estimating populations of dolphins?

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

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

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?

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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

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

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

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?

Use your skill and judgement to match the sets of random data.

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