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

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

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?

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?

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

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

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

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

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

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

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

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?

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.

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

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

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.

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

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?

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

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.

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?

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

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.

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

How would you go about estimating populations of dolphins?

Which units would you choose best to fit these situations?

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?

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.

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

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