Maths supporting SET

Welcome to the Mathematics Supporting SET area of stemNRICH

Mathematics underpins the majority of science, design and technology. The following problems are tasks for the mathematics classroom which reinforce some of the key concepts in Science, Engineering, Design and Technology without requiring detailed knowledge outside of mathematics. If you are a mathematics teacher you can use these problems for directly teaching content from the mathematics curriculum. If you are a student you can use these problems to improve the mathematical skills needed to get the most from science and technology.

Stage 3 is roughly 11-14 years and Stage 4 roughly 14-16 years. The stars indicate how easily most learners can get into the problem, although most problems contain enough depth to challenge and stimulate all.

Back to main STEM pages.

problem

Air nets

Age

7 to 18

Challenge level

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

problem

Chocolate cake

Age

11 to 14

Challenge level

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

problem

How would you score it?

Age

11 to 14

Challenge level

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

problem

Olympic records

Age

11 to 14

Challenge level

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

problem

Place your orders

Age

11 to 14

Challenge level

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

problem

Triathlon and fitness

Age

11 to 14

Challenge level

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

problem

Pinhole camera

Age

11 to 14

Challenge level

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

problem

Designing table mats

Age

11 to 16

Challenge level

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

project

Make your own pencil case

11 to 14

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

problem

Olympic measures

Age

11 to 14

Challenge level

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

problem

Speedy Sidney

Age

11 to 14

Challenge level

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 two trains. How far does Sidney fly before he is squashed between the two trains?

problem

Witch's hat

Age

11 to 16

Challenge level

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

problem

Who's the best?

Age

11 to 14

Challenge level

Which countries have the most naturally athletic populations?

problem

Perspective drawing

Age

11 to 16

Challenge level

Explore the properties of perspective drawing.

problem

Temperature

Age

11 to 14

Challenge level

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

problem

Isometric drawing

Age

11 to 14

Challenge level

Explore the properties of isometric drawings.

problem

Fill me up

Age

11 to 14

Challenge level

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

problem

Toad in the hole

Age

11 to 14

Challenge level

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?

problem

Mixing lemonade

Age

11 to 14

Challenge level

Can you work out which drink has the stronger flavour?

problem

Bigger or smaller?

Age

14 to 16

Challenge level

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

problem

Square pair

Age

14 to 18

Challenge level

Explore the shape of a square after it is transformed by the action of a matrix.

problem

Choose your units

Age

14 to 16

Challenge level

Which units would you choose best to fit these situations?

problem

Efficient packing

Age

14 to 16

Challenge level

How efficiently can you pack together disks?

problem

Guessing the graph

Age

14 to 16

Challenge level

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

problem

Fill me up too

Age

14 to 16

Challenge level

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?

problem

Investigating the dilution series

Age

14 to 16

Challenge level

Which dilutions can you make using only 10ml pipettes?

problem

How do you react?

Age

14 to 16

Challenge level

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

problem

Construct the solar system

Age

14 to 18

Challenge level

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

problem

What's that graph?

Age

14 to 18

Challenge level

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

problem

Maths filler 2

Age

14 to 16

Challenge level

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

problem

Big and small numbers in the physical world

Age

14 to 16

Challenge level

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

problem

Nutrition and cycling

Age

14 to 16

Challenge level

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

problem

Immersion

Age

14 to 16

Challenge level

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

problem

Mystery procedure

Age

14 to 16

Challenge level

Can you work out what this procedure is doing?

problem

Global warming

Age

14 to 16

Challenge level

How much energy has gone into warming the planet?

problem

Counting dolphins

Age

14 to 16

Challenge level

How would you go about estimating populations of dolphins?

problem

Big and small numbers in physics

Age

14 to 16

Challenge level

Work out the numerical values for these physical quantities.

problem

Track design

Age

14 to 16

Challenge level

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

problem

Approximately certain

Age

14 to 18

Challenge level

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

problem

David and Goliath

Age

14 to 18

Challenge level

Does weight confer an advantage to shot putters?

problem

Back fitter

Age

14 to 18

Challenge level

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?