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?

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

Examine these estimates. Do they sound about right?

Work out the numerical values for these physical quantities.

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

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

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

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

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

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

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?

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?

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

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

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

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?

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.

Get some practice using big and small numbers in chemistry.

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

Which units would you choose best to fit these situations?

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?

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

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. . . .

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

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

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. . . .

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.

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

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

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

How would you go about estimating populations of dolphins?

Invent a scoring system for a 'guess the weight' competition.