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

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

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

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?

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?

Get some practice using big and small numbers in chemistry.

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.

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

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

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

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

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

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

How would you go about estimating populations of dolphins?

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

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

Which dilutions can you make using only 10ml pipettes?

Explore the relationship between resistance and temperature

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

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

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 physical contexts.

Which units would you choose best to fit these situations?

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. . . .

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

Examine these estimates. Do they sound about right?

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?

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

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

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

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

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

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

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?

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.

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

Which countries have the most naturally athletic populations?

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

Work out the numerical values for these physical quantities.

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?

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