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

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

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

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?

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

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

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

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 rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

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

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?

Examine these estimates. Do they sound about right?

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

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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. . . .

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

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

Work out the numerical values for these physical quantities.

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

Explore the relationship between resistance and temperature

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

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?

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

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

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

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

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

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

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

Is there a temperature at which Celsius and Fahrenheit readings are the same?

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?

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

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.

Use your skill and judgement to match the sets of random data.

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