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

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

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

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

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?

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

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

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

Work out the numerical values for these physical quantities.

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?

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

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?

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

Explore the relationship between resistance and temperature

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

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 calulate various quantities in biological contexts.

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

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

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

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

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?

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. . . .

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

How would you go about estimating populations of dolphins?

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

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

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.

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

Which dilutions can you make using only 10ml pipettes?

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. . . .

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

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