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

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 physical contexts.

Get some practice using big and small numbers in chemistry.

Work out the numerical values for these physical quantities.

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.

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

How would you go about estimating populations of dolphins?

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

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?

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

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

Examine these estimates. Do they sound about right?

Explore the relationship between resistance and temperature

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

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

Which units would you choose best to fit these situations?

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

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

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. . . .

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?

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

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

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.