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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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

Which countries have the most naturally athletic populations?

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

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

How would you go about estimating populations of dolphins?

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

Get some practice using big and small numbers in chemistry.

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?

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 calulate various quantities in biological contexts.

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

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

Explore the relationship between resistance and temperature

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

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?

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

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

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?

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.

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

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

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. . . .

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

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.

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.

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

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

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

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

Work out the numerical values for these physical quantities.

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?