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.

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

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

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

Get some practice using big and small numbers in chemistry.

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?

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

Examine these estimates. Do they sound about right?

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

How would you go about estimating populations of dolphins?

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

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

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.

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

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

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. . . .

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

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

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

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

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

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

Work out the numerical values for these physical quantities.

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

Which units would you choose best to fit these situations?

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?

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

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

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

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