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?

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

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

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

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

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?

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

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?

Examine these estimates. Do they sound about right?

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

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

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

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

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

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?

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

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

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

Get some practice using big and small numbers in chemistry.

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?

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

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

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?

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

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

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.

How would you go about estimating populations of dolphins?

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

Work out the numerical values for these physical quantities.

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?

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

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?