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?

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?

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?

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

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

Which dilutions can you make using only 10ml pipettes?

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

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?

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

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

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. . . .

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

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

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

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

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?

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?

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

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

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

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

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.

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

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.

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

Which units would you choose best to fit these situations?

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

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

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

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

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

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

Which countries have the most naturally athletic populations?

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?

Work out the numerical values for these physical quantities.