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

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

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.

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

Which countries have the most naturally athletic populations?

Examine these estimates. Do they sound about right?

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?

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

Work out the numerical values for these physical quantities.

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

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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

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

Get some practice using big and small numbers in chemistry.

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

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.

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

Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?

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

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

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. . . .

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?

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

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

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 deduce which Olympic athletics events are represented by the graphs?

Which dilutions can you make using only 10ml pipettes?

Explore the relationship between resistance and temperature

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. . . .

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

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

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

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

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?

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

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

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

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

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