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?

Explore the relationship between resistance and temperature

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?

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.

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

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

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?

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

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

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.

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

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?

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

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

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

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

Learn about the link between logical arguments and electronic circuits. Investigate the logical connectives by making and testing your own circuits and fill in the blanks in truth tables to record. . . .

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.

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?

Which dilutions can you make using only 10ml pipettes?

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

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 the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.

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

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

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

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

Which units would you choose best to fit these situations?

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