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?

How would you go about estimating populations of dolphins?

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

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

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

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

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

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?

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

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

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

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

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?

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. . . .

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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.

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

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

Explore the relationship between resistance and temperature

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

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

Which dilutions can you make using only 10ml pipettes?

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

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?

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

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.

Work out the numerical values for these physical quantities.

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

Which units would you choose best to fit these situations?

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

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

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