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?

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

Work out the numerical values for these physical quantities.

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

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

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

Get some practice using big and small numbers in chemistry.

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

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

Examine these estimates. Do they sound about right?

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

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

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?

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

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

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?

Which dilutions can you make using only 10ml pipettes?

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

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

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

Which units would you choose best to fit these situations?

How would you go about estimating populations of dolphins?

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.

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

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

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?

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

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

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

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

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

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

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

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

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?

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

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

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

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