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?

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

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

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

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

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

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

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

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.

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. . . .

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.

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

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

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

If I don't have the size of cake tin specified in my recipe, will the size I do have be OK?

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?

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

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

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

Examine these estimates. Do they sound about right?

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.

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

Explore the relationship between resistance and temperature

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

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

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

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

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

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

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?

How would you go about estimating populations of dolphins?