Welcome to the Design Technology collection of stemNRICH resources.
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In these resources, maths is used as a tool to explore some aspect of design technology. Some might be best used in the maths lesson, with reference made to the science. Others could be taught as cross-curricular topics.
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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Problems with teacher support
The following problems contain detailed teacher support concerning how we might use the task in schools. However, since these problems are intended to be rich mathematical activities they can be used effectively in many ways and at many levels of sophistication, both in the classroom and by individuals.
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engNRICH
engNRICH is the area of the stemNRICH Advanced site devoted to the mathematics underlying the study of engineering
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Drawing Doodles and Naming Knots
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
problem
Tom learns to cook
Age
7 to 11
Challenge level
If Tom wants to learn to cook his favourite supper, he needs to make a schedule so that everything is ready at the same time.
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Troublesome Triangles
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple simulation game to investigate the properties of such systems.
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Playground Snapshot
Age
7 to 14
Challenge level
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
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Tiles in a public building
Age
7 to 11
Challenge level
What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?
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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.
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Mathematical Patchwork
Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
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Plaiting and Braiding
This article for students gives some instructions about how to make some different braids.
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Celtic Knotwork Patterns
This article for pupils gives an introduction to Celtic knotwork
patterns and a feel for how you can draw them.
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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?
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Flower Power
Age
11 to 16
Challenge level
Create a symmetrical fabric design based on a flower motif - and realise it in Logo.
problem
Hmm ... when should Tom have put the rice on ...
Age
11 to 16
Challenge level
Creating a schedule to cook a meal consisting of two different recipes, plus rice.
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Programming: Moiré patterns
We need computer programmers! Logo is a great entry-level programming language - and you can create stunning graphics while you learn.
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3D drawing
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.
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Tray Bake
Age
11 to 14
Challenge level
My recipe is for 12 cakes - how do I change it if I want to make a different number of cakes?
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stemNRICH - Technology
Age
11 to 16
Challenge level
This is the technology section of stemNRICH - Core.
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Designing table mats
Age
11 to 16
Challenge level
Formulate and investigate a simple mathematical model for the design of a table mat.
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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?
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Favourite
Sending a Parcel
Age
11 to 14
Challenge level
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
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Making Moiré Patterns
Age
11 to 18
Challenge level
Moiré patterns are intriguing interference patterns. Create your own beautiful examples using LOGO!
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Perspective Drawing
Age
11 to 16
Challenge level
Explore the properties of perspective drawing.
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Make your own pencil case
What shape would fit your pens and pencils best? How can you make it?
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Oblique Projection
Age
11 to 14
Challenge level
Explore the properties of oblique projection.
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The Codabar Check
This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.
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Isometric Drawing
Age
11 to 14
Challenge level
Explore the properties of isometric drawings.
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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?
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Gym Bag
Age
11 to 16
Challenge level
Can Jo make a gym bag for her trainers from the piece of fabric she has?
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Straw Scaffold
Age
11 to 14
Challenge level
Build a scaffold out of drinking-straws to support a cup of water
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Cool As Ice
Age
11 to 16
Challenge level
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
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Stadium Sightline
Age
14 to 18
Challenge level
How would you design the tiering of seats in a stadium so that all spectators have a good view?
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How the Velodrome found its form
The Velodrome was one of the most striking buildings in the London 2012 Olympic Park. This article explores how mathematics helped design the iconic building and its track.
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Carbon footprints
Age
14 to 16
Challenge level
Is it really greener to go on the bus, or to buy local?
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Mystery Procedure
Age
14 to 16
Challenge level
Can you work out what this procedure is doing?
problem
Favourite
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?
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Elastic maths
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.
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Chopped Dice
Age
14 to 16
Challenge level
Can you make a new type of fair die with 14 faces by shaving the
corners off a cube?
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Robot Camera
Age
14 to 16
Challenge level
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
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Public Key Cryptography
An introduction to coding and decoding messages and the maths behind how to secretly share information.
Problems without specific teacher support
The following problems are without specific teacher notes. These are often problems which would be difficult to fit into a typical curriculum area at school or are very open ended. They will be interesting for students interested in the general subject area to explore alone or for teachers to explore for ideas to bring to their own classrooms.
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