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.
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Can you work out which drink has the stronger flavour?
The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?
These Olympic quantities have been jumbled up! Can you put them back together again?
Have you ever wondered what it would be like to race against Usain Bolt?
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?
Explore the properties of isometric drawings.
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?
Examine these estimates. Do they sound about right?
Can you deduce which Olympic athletics events are represented by the graphs?
Make your own pinhole camera for safe observation of the sun, and find out how it works.
Can you sketch graphs to show how the height of water changes in different containers as they are filled?
Invent a scoring system for a 'guess the weight' competition.
If I don't have the size of cake tin specified in my recipe, will the size I do have be OK?
What shape would fit your pens and pencils best? How can you make it?
Simple models which help us to investigate how epidemics grow and die out.
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Can you draw the height-time chart as this complicated vessel fills
Can you work out what this procedure is doing?
Various solids are lowered into a beaker of water. How does the
water level rise in each case?
How would you go about estimating populations of dolphins?
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?
How much energy has gone into warming the planet?
Where should runners start the 200m race so that they have all run the same distance by the finish?
Work out the numerical values for these physical quantities.
Can you work out which processes are represented by the graphs?
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?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Is it really greener to go on the bus, or to buy local?
This problem explores the biology behind Rudolph's glowing red nose.
Are these estimates of physical quantities accurate?
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
When you change the units, do the numbers get bigger or smaller?
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Which units would you choose best to fit these situations?
Analyse these beautiful biological images and attempt to rank them in size order.
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
How efficiently can you pack together disks?
A problem about genetics and the transmission of disease.
Which dilutions can you make using only 10ml pipettes?
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Get some practice using big and small numbers in chemistry.
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Explore the relationship between resistance and temperature
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 with numbers big and small to estimate and calculate various quantities in physical contexts.
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
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.
Explore the properties of perspective drawing.
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
Which countries have the most naturally athletic populations?
Formulate and investigate a simple mathematical model for the design of a table mat.
Investigate circuits and record your findings in this simple introduction to truth tables and logic.
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 the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.
Does weight confer an advantage to shot putters?
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
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.
How would you design the tiering of seats in a stadium so that all spectators have a good view?
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 your findings.
Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
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
When a habitat changes, what happens to the food chain?
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Starting with two basic vector steps, which destinations can you reach on a vector walk?