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

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

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?

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

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

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

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

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

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

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

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?

In which Olympic event does a human travel fastest? Decide which events to include in your Alternative Record Book.

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

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.

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

Get some practice using big and small numbers in chemistry.

Examine these estimates. Do they sound about right?

Work out the numerical values for these physical quantities.

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

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.

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

Which countries have the most naturally athletic populations?

Can you deduce which Olympic athletics events 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 calculate various quantities in physical contexts.

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

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

Explore the relationship between resistance and temperature

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. . . .

Which units would you choose best to fit these situations?

Which dilutions can you make using only 10ml pipettes?

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

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?

How would you go about estimating populations of dolphins?

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.

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. . . .

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

Use trigonometry to determine whether solar eclipses on earth can be perfect.