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

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

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

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?

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

Which countries have the most naturally athletic populations?

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?

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.

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?

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

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.

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Examine these estimates. Do they sound about right?

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

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

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

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?

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

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.

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

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.

Explore the relationship between resistance and temperature

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

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

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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

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?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

How would you go about estimating populations of dolphins?

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