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

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.

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?

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

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

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

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

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

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

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

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

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

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

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?

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

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

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.

Which units would you choose best to fit these situations?

Explore the relationship between resistance and temperature

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

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

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

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

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

How would you go about estimating populations of dolphins?

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.

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.

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?

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?

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. . . .

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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