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?

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

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

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

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?

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

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

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.

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

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

Which dilutions can you make using only 10ml pipettes?

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. . . .

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?

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

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

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

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 work out which processes are represented by the graphs?

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

Get some practice using big and small numbers in chemistry.

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.

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

Examine these estimates. Do they sound about right?

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

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

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

How would you go about estimating populations of dolphins?

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

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

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

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

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

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

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

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

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.

Explore the relationship between resistance and temperature

Which units would you choose best to fit these situations?

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

Use your skill and judgement to match the sets of random data.