Lesson 4 Furniture design

# Episode 2

Reasoning Resources
Whole class demonstration of three personal measurements
Agreeing on rules for measurements: starting from zero, using the same units throughout the class.

Agreeing what to measure.

Collaborating in measurements and recording of data; correcting each others’ mistakes. The task fosters collaboration.

There are practical difficulties whenever pupils use tapes etc. to measure. They may be in the understanding of unit, scales, starting point and/or recording.
Work with one child and a measuring tape to record the height, length and width of the cupboard best suited to them. Agree rules for use of tape and what to measure for example:

• height should not be greater than floor to finger tips when you raise your arm,
• length should be what you reach when you spread your arms,
• width should be your forward arm, reach, measured on the inside arm.

Now ask them to find appropriate dimensions for a wardrobe suitable for use by anyone in a group.
• Small group work (10-15 minutes)
The aim here is not to practice measuring skills, so this should be simplified as far as possible. All tapes should be of the same units (metre and centimetre) and all measurements taken to the nearest centimetre.

Comparing the mean, the mode and the median is possible here for the purpose of homing in on a measurement for each dimension which is not too far from the smallest or the largest.
Give out a measuring tape and Worksheet 1 to each pair. Once pairs have completed their measurements they swap data with another pair. Help pupils with measurements and collecting data. Groups who have their measurements should take Worksheet 2 and fill in the table.

You may wish to stop the class to show them what is needed in Worksheet 2. In particular they need to know they have to order the values separately in each measurement, and find the middle value (median) in each group of 4, and the range in that group, You may wish to have a discussion on what the middle number is, accepting that the mean is a possible middle number before homing in on the median. In reply to ‘You cannot find the middle of four numbers!’ ask them to think of a creative solution.

(If time is a problem they can concentrate on one measurement only, say height.)
Whole class sharing and discussion
This measurement may not fit anyone in particular.

Other constraints, such as fitting a given space, are likely to be discussed towards the end of this episode.

As part of the discussion pupils will volunteer how they arrive at the median value in a range of situations that may involve rounding, the use of calculators.

Range and median are enough to compare two sets of data.

All man-made objects, including heights of ceilings, are designed with data from personal measurements.
The initial part of this discussion simply involves reporting upon both their results and their strategies for calculating the middle, and the language they use for this, They would include halving the difference between two middle measurements and adding or subtracting, folding two points on the tape, and adding and dividing by 2.

The problem over the meaning of middle (median or mean) may arise again, and whether it is OK to use half-way between the largest and the smallest rather than the two middle measurements. It is indeed practically OK, provided everyone agrees on this meaning of ‘middle’. Pupils will note that by finding the class median we are now ignoring their personal measurements to find a cupboard for a ‘middle’ person, who does not actually exist.

Worksheet 3 is best worked on as a whole class, e.g. on board or OHP. Ask why people making furniture prefer to use a ‘middle’ group measurement.

A discussion of the importance of the range may be useful for some groups. Pupils would appreciate that the range is not the same in the three dimensions. Some pupils may suggest that there are other considerations that are important for the size of a wardrobe, e.g. the length and height could be along a whole wall, or smaller because there isn’t enough wall in their room.

In preparation for Episode 3 (or as an end of lesson) ask what other objects we buy or have in the home and in life which also rely on personal measurements in some form.