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

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

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

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

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

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

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.

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

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

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.

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

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?

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

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. . . .

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

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

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?

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

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

How would you go about estimating populations of dolphins?

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

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

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

Work out the numerical values for these physical quantities.

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

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

Explore the relationship between resistance and temperature

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

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

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

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 dilutions can you make using only 10ml pipettes?

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?

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