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

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?

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

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

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

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?

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

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

Is it really greener to go on the bus, or to buy local?

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

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

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

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

Examine these estimates. Do they sound about right?

Get some practice using big and small numbers in chemistry.

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

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

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

The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.

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.

Work out the numerical values for these physical quantities.

These Olympic quantities have been jumbled up! Can you put them back together again?

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

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. . . .

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 go about estimating populations of dolphins?

Which units would you choose best to fit these situations?

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

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

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

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

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.

Which dilutions can you make using only 10ml pipettes?

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

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

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

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

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

Explore the relationship between resistance and temperature

Is there a temperature at which Celsius and Fahrenheit readings are the same?