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

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.

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

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

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

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

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

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

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

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.

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?

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

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

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

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

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?

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

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

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

Which units would you choose best to fit these situations?

Get some practice using big and small numbers in chemistry.

Can you deduce which Olympic athletics events are represented by the graphs?

Which dilutions can you make using only 10ml pipettes?

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

Explore the relationship between resistance and temperature

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

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?

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?

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

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

How would you go about estimating populations of dolphins?

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

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?

Which countries have the most naturally athletic populations?

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. . . .

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

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