# Keeping a sense of scale

A Tell your student that artists don't just paint pictures. There is a variety of careers in art that rely heavily on maths - eg graphic design, painting, photography, three-dimensional graphics. Even fine artists use business maths: for forward planning; costing of materials, studio space and galleries; calculating sale price and so on. Does your student realise that some devote a whole career to colour theory, which involves algebra.

Graphic designers use mathematical images frequently and an understanding of the underlying maths is essential - otherwise there is a danger of confusing customers or damaging a client's reputation.

A great lesson could be created around how maths is used in promotional literature. For example, lead into a lesson on scale with the image (left), used by the marketing team for Sainsbury's Nectar points. It will have been created by a graphic design team.

The image is mathematically misleading and also confusing if numbers aren't your strong point. Sainsbury's admits some customers have been confused by it. A thermometer was chosen to show customers how their Nectar points are accumulating. This one was sent to me. Ask if any pupils know about Nectar points and how they are collected. Explain that the image shows how many points a real customer has collected.

Open a class discussion on the thermometer values. Perhaps cover all the labels except the 500-point marker and ask what values should be written on the dividing marks. Having used this as a means to explain how to calculate the subdivisions, ask pupils if they can create a more representative thermometer. I started to play with some assumptions.

Scenario 1

Let's assume that the liquid below the first mark, including the bulb, has the same volume as in each of the subdivisions above, and so represents the same number of Nectar points.

Then assume that the 500-point mark is in the correct position. There are two subdivisions below this, so each is worth 500 V 2 = 250 points. I have re-labelled the thermometer (left) using this value, clearly showing that the 1,000-point mark in the original image is in the wrong position.

Scenario 2

Now let's assume that the 1,000 and 500 marks in the original image are in the correct places: "1,000" is printed on the thermometer about halfway between the top two subdivision marks. If we make a halfway mark along each subdivision (left), the space between the 500 mark and the 1,000 level is then divided into seven equal parts. This gives 500 V 7 = 71.4 (to one decimal place) points for each division. But taking this to the bottom of the thermometer would mean starting the scale from a base of 285.8 rather than 0.

Scenario 3

What if all the information on the original image is spurious, except:

"Your Nectar balance is 155." How many points would I need to fill a whole thermometer then? I measured the thermometer in millimetres, but this gave horrible numbers for the scale. So I changed to 16ths of an inch - an excuse to use fractions.

In the original Nectar leaflet which was sent to me, the thermometer measured 3 inches (4816 inches) in total and the section representing 155 points (to the top of the coloured liquid) was 3116 inches. There are 155 V 31 = 5 points for each 116 of an inch. And, each subdivision measuring 816 inch represents 5 x 8 = 40 points. Using this scale, filling the thermometer to the top takes 250 points.

* Wendy Fortescue-Hubbard will host a question-and-answer session at the Education Show at the Birmingham NECon March 13. Free copies of a CD-Rom of her Perfect Times game will be given to the first five visitors to the session quoting "TESTeacher offer".

Email your questions to Mathagony Aunt at teacher@tes.co.uk Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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