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?

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

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

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?

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

Explore the relationship between resistance and temperature

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

How would you go about estimating populations of dolphins?

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

Get some practice using big and small numbers in chemistry.

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

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

Which countries have the most naturally athletic populations?

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

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. . . .

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 calulate various quantities in biological contexts.

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

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

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

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

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

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.

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

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

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. . . .

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

Which dilutions can you make using only 10ml pipettes?

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

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

Examine these estimates. Do they sound about right?

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?

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

Which units would you choose best to fit these situations?

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

Work out the numerical values for these physical quantities.

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

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

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

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.