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.

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Mixing Lemonade

Stage: 3 Challenge Level: Challenge Level:1

Can you work out which drink has the stronger flavour?

Triathlon and Fitness

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

Olympic Measures

Stage: 3 Challenge Level: Challenge Level:1

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

Speed-time Problems at the Olympics

Stage: 4 Challenge Level: Challenge Level:1

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

Witch's Hat

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

Place Your Orders

Stage: 3 Challenge Level: Challenge Level:1

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

Temperature

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Isometric Drawing

Stage: 3 Challenge Level: Challenge Level:1

Explore the properties of isometric drawings.

Toad in the Hole

Stage: 3 Challenge Level: Challenge Level:1

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?

Does This Sound about Right?

Stage: 3 Challenge Level: Challenge Level:1

Examine these estimates. Do they sound about right?

Olympic Records

Stage: 3 Challenge Level: Challenge Level:1

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

Pinhole Camera

Stage: 3 Challenge Level: Challenge Level:1

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

Fill Me Up

Stage: 3 Challenge Level: Challenge Level:1

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

How Would You Score It?

Stage: 3 Challenge Level: Challenge Level:1

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

Chocolate Cake

Stage: 3 Challenge Level: Challenge Level:1

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

Make Your Own Pencil Case

Stage: 3 Challenge Level: Challenge Level:1

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

Investigating Epidemics

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

Far Horizon

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Maths Filler 2

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Mystery Procedure

Stage: 4 Challenge Level: Challenge Level:1

Can you work out what this procedure is doing?

Immersion

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Counting Dolphins

Stage: 4 Challenge Level: Challenge Level:1

How would you go about estimating populations of dolphins?

Fill Me up Too

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

Global Warming

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

How much energy has gone into warming the planet?

Track Design

Stage: 4 Challenge Level: Challenge Level:1

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

Big and Small Numbers in Physics

Stage: 4 Challenge Level: Challenge Level:1

Work out the numerical values for these physical quantities.

What's That Graph?

Stage: 4 Challenge Level: Challenge Level:1

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

Back Fitter

Stage: 4 Challenge Level: Challenge Level:1

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?

Big and Small Numbers in Biology

Stage: 4 Challenge Level: Challenge Level:1

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

Carbon Footprints

Stage: 4 Challenge Level: Challenge Level:1

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

Weekly Challenge 48: Quorum-sensing

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

This problem explores the biology behind Rudolph's glowing red nose.

More or Less?

Stage: 4 Challenge Level: Challenge Level:1

Are these estimates of physical quantities accurate?

Constantly Changing

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Bigger or Smaller?

Stage: 4 Challenge Level: Challenge Level:1

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

Perfect Eclipse

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use trigonometry to determine whether solar eclipses on earth can be perfect.

Choose Your Units

Stage: 4 Challenge Level: Challenge Level:1

Which units would you choose best to fit these situations?

Biology Measurement Challenge

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Guessing the Graph

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

Efficient Packing

Stage: 4 Challenge Level: Challenge Level:1

How efficiently can you pack together disks?

Genetics

Stage: 4 Challenge Level: Challenge Level:1

A problem about genetics and the transmission of disease.

Investigating the Dilution Series

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which dilutions can you make using only 10ml pipettes?

How Do You React?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Big and Small Numbers in Chemistry

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Get some practice using big and small numbers in chemistry.

Robot Camera

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?

Scientific Measurement

Stage: 4 Challenge Level: Challenge Level:1

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

Big and Small Numbers in the Living World

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

Electric Kettle

Stage: 4 Challenge Level: Challenge Level:1

Explore the relationship between resistance and temperature

A Question of Scale

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

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?

Big and Small Numbers in the Physical World

Stage: 4 Challenge Level: Challenge Level:1

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

Maths Filler

Stage: 4 Challenge Level: Challenge Level:1

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

3D Drawing

Stage: 3 and 4

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.

Perspective Drawing

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Explore the properties of perspective drawing.

Nutrition and Cycling

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

Who's the Best?

Stage: 3 and 4 Challenge Level: Challenge Level:1

Which countries have the most naturally athletic populations?

Designing Table Mats

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

Truth Tables and Electronic Circuits

Stage: 2, 3 and 4

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

Elastic Maths

Stage: 4 and 5

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.

Epidemic Modelling

Stage: 4 and 5 Challenge Level: Challenge Level:1

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.

David and Goliath

Stage: 4 and 5 Challenge Level: Challenge Level:1

Does weight confer an advantage to shot putters?

Approximately Certain

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

Alternative Record Book

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

Construct the Solar System

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

Stadium Sightline

Stage: 4 and 5 Challenge Level: Challenge Level:1

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

Logic, Truth Tables and Switching Circuits Challenge

Stage: 3, 4 and 5

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.

Air Nets

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:1

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

Speedy Sidney

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

Food Chains

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

When a habitat changes, what happens to the food chain?

Gym Bag

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can Jo make a gym bag for her trainers from the piece of fabric she has?

Vector Walk

Stage: 4 and 5 Challenge Level: Challenge Level:1

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