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

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?

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?

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

Examine these estimates. Do they sound about right?

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

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

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?

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

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

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

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

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

Work out the numerical values for these physical quantities.

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

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

Make an accurate diagram of the solar system and explore the concept of a grand conjunction.

Get some practice using big and small numbers in chemistry.

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

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

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

Explore the relationship between resistance and temperature

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

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 calulate various quantities in biological contexts.

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

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

Which units would you choose best to fit these situations?

How would you go about estimating populations of dolphins?

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

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

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.

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

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

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. . . .

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

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

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

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?

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

Is there a temperature at which Celsius and Fahrenheit readings are the same?