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

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

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

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

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

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?

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

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

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

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

Examine these estimates. Do they sound about right?

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

Get some practice using big and small numbers in chemistry.

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

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?

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

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

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

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

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.

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

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

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

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

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?

Explore the relationship between resistance and temperature

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

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

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

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

Which units would you choose best to fit these situations?

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?

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

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

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?

Work out the numerical values for these physical quantities.

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

Which dilutions can you make using only 10ml pipettes?

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. . . .