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?

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

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

Explore the relationship between resistance and temperature

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

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?

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

How would you go about estimating populations of dolphins?

Work out the numerical values for these physical quantities.

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

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

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

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

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

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

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?

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

Get some practice using big and small numbers in chemistry.

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?

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

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. . . .

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.

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

Which units would you choose best to fit these situations?

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

Which dilutions can you make using only 10ml pipettes?

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

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?

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.

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

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?

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

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

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

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?

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

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

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

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