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?

Invent a scoring system for a 'guess the weight' competition.

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

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

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

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.

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

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

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?

Which countries have the most naturally athletic populations?

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

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. . . .

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

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?

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

Get some practice using big and small numbers in chemistry.

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

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

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. . . .

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 work out which processes are represented by the graphs?

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

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

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

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.

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?

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

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?

Which dilutions can you make using only 10ml pipettes?

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

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

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

Which units would you choose best to fit these situations?

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

How would you go about estimating populations of dolphins?

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

Explore the relationship between resistance and temperature

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