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

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?

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?

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

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

How would you go about estimating populations of dolphins?

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

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

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

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

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

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

Explore the relationship between resistance and temperature

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

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

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

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?

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

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

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?

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.

Get some practice using big and small numbers in chemistry.

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?

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?

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

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

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. . . .

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.

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

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

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

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.

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

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

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?