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?

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

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?

How would you go about estimating populations of dolphins?

Explore the relationship between resistance and temperature

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

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

Work out the numerical values for these physical quantities.

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

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

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?

Get some practice using big and small numbers in chemistry.

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

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

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

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

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

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

Which dilutions can you make using only 10ml pipettes?

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?

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

Examine these estimates. Do they sound about right?

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

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

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

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

Which units would you choose best to fit these situations?

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

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

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

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

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.

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?

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

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. . . .

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. . . .

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

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