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?

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?

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. . . .

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

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

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

Explore the relationship between resistance and temperature

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

Get some practice using big and small numbers in chemistry.

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

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

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

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

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

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.

Examine these estimates. Do they sound about right?

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

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

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

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?

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

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?

This problem explores the biology behind Rudolph's glowing red nose.

Which countries have the most naturally athletic populations?

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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

How would you go about estimating populations of dolphins?

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

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

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

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

Work out the numerical values for these physical quantities.

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?

Which dilutions can you make using only 10ml pipettes?

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