Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple simulation game to investigate the properties of such systems.

What shape and size of drinks mat is best for flipping and catching?

Make your own pinhole camera for safe observation of the sun, and find out how it works.

Can you work out which drink has the stronger flavour?

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

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?

Is there a temperature at which Celsius and Fahrenheit readings are the same?

Examine these estimates. Do they sound about right?

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

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

What shape would fit your pens and pencils best? How can you make it?

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

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.

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

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

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

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

Which units would you choose best to fit these situations?

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

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

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

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

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

Get some practice using big and small numbers in chemistry.

Which dilutions can you make using only 10ml pipettes?

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

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

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?

How would you go about estimating populations of dolphins?

Explore the relationship between resistance and temperature

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

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

Work out the numerical values for these physical quantities.

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

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

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?

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

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

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

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