Lesson 4 Furniture design

Episode 1

Reasoning Resources: Furniture/wardrobe catalogue or pictures (optional)
Whole class preparation
Widest engagement possible by using a familiar context.

In real-life decisions we progress from intuitive choices to clearly defining the features of importance.

We then try to measure or quantify these features in some standard way — this is mathematical modelling at its most simple.

Start with a story or otherwise asking the pupils to imagine they are to buy or design a wardrobe to suit them. Have a short discussion about their ideas on what makes a good wardrobe. (Use of pictures, internet links, furniture catalogues would help here, including some extreme sizes.)

Possible pupil ideas may include ‘colour; ‘material; ‘shelves, ‘hanging space; ‘size, ‘big, ‘has to fit.
Paired work on main features
Give the class 2-3 minutes for each pair to decide upon their three most important features of a wardrobe.
Whole class sharing: gradual focusing on dimensions
Precision of language and in measuring.

This lesson aims to increases precision in the use of dimensional terms. ‘Too long/small’ allows the abstraction of one, say length, but the other two will need to be carefully differentiated from the plethora of their daily inaccurate language of big, tall, short, low etc
Note down all the ideas/features on the board, some of which will be repeats by different pairs. Ask them to identify the mathematical features, and then focus on those relevant to size. Some pupils will use simplistic language to describe how big the wardrobe is, while others refer to dimensions.The move to address the three components would involve using natural language before arriving at: length, width and height.

Circle words referring to size and label as lengthrwidth' or 'height:

Explore the difference between 2-D and 3-D and which games are actually in 3-D (virtual reality and some arcade games).

There may be some discussion on the difference between width and breadth, length and height, etc. Explore the idea that some words refer to the properties of objects themselves, i.e. the three dimensions of length, width and height, while other words (like breadth and depth) are used in everyday speech, and that such confusion is natural and is resolved by agreement.
Paired work on sketches
The use of terms such as 3-D and 2-D (linked to computer games and other familiar contexts) will help them to both grasp and retain the concepts. Give pupils paper and felt tip pens, and allow 3-4 minutes for each pupil to sketch their wardrobe in 3-D to best show the dimensions length, width and height, and discuss it in their pairs. Going around the class note the variety of representations before collecting a summary to show to the class.
Whole class sharing/discussion
No requirements for accuracy in sketching, rather usefulness in showing the three dimensions.

Pupils then relate the dimensions of the wardrobe to their own bodies.
Allow the class a few minuted to look at a few typical wardrobe sketches to decide which they think best shows length, width and height, not which is the best drawing. Allow each pupil the time to justify their ideas. Some of the drawings will show perspective whereas others will not; some are pretty and others are useful to show dimensions clearly ('You can see the sides') while not showing perspective. Some sketches are 'flat' and are understood by the person drawing them, but not by others.

Once they have decided upon a type of sketch that shows three dimensions, show them a 3-D sketch, with length, width and height marked. Now the issue is to personalise each wardrobe.

Explore the personal dimensions for yourself and one average pupil. How far do they reach easily in height, sideways with arms spread, and forward with arm forward.

They are now ready for taking their measurements.


Thinking Mathematics Lessons Copyright © by Michael Shayer and Mundher Adhami. All Rights Reserved.

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