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

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

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?

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

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

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

Which dilutions can you make using only 10ml pipettes?

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

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

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

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

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. . . .

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?

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?

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

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?

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.

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

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

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

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

Use your skill and judgement to match the sets of random data.

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.

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

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

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

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

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?

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

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

Explore the relationship between resistance and temperature

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.

Invent a scoring system for a 'guess the weight' competition.

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

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

Which countries have the most naturally athletic populations?

How would you go about estimating populations of dolphins?

Work out the numerical values for these physical quantities.