1. Estimation and calculation
Human body surface area
Estimation and calculation

2. About this task
You will develop a simple mathematical model and practise estimation using standard units.
You will carry out calculations and compare the results to your estimates.
You will need to provide a range of measuring instruments: as a minimum you will need rulers and a set of scales, but other equipment (including tape measures, metre rules, a trundle wheel and callipers) might also be useful. Students will need access to calculators.

3. Starter: Estimation Estimate: The height of the door (cm)
The volume of the cupboard (cm3)
The mass (‘weight’) of the box of books (g)
The surface area of the table (m2)
Once you have agreed and recorded your estimates, measure and calculate the values.
Adapt this slide to include a number of objects that are readily available in your classroom.
The important thing is to ensure that you specify units and include a range of measurements – area, volume, mass, etc.
Students should work in groups on this task. They need to discuss and agree their answers, and they are allowed to do pretty much anything except measure! So, they could stand a person with a known height beside a door to get a good estimate, or measure a table using hand spans and then multiply by the estimated size of a hand span in centimetres.
Once everyone has their estimates, ask the students to measure all of the objects using the instruments provided.
You should now collect and record answers from the group. A spreadsheet provides a convenient method for doing this. You may wish to calculate the ‘official’ answers in advance!
Discuss the results. Likely points arising include:
The estimates vary a lot, but the calculated values (barring errors!) are very similar.
Estimates of lengths are generally better than those of area; estimates of volumes are worst of all. (Discuss reasons for this.)
Some standard units (like the centimetre) are quite familiar; others (like the gram) may be less so.
If time permits, you could now ask students to calculate the percentage error for their estimates.

4. Main activity: Skin area
You are going to estimate the surface area of a volunteer from your group.
The volunteer must be willing to be measured and weighed.
Explain that the ‘weighing’ part of the activity will only be needed later, when we use some suggested formulae to estimate the surface area of our volunteers.
For now, ask each group to identify their volunteer, and then to start work on producing their estimate.
It is important to make sure that groups take their time, and work carefully to produce a sensible estimate that they are able to justify.
If groups are confident to make a start with this exercise, let them do so without any further guidance. Alternatively, you could use the next slide to demonstrate one possible approach.

5. Modelling the human body
The human body can be represented as a collection of regular 3D shapes.
Explain that the diagram shows one very simple way of modelling the human body as a set of geometrical shapes.
Students should be able to calculate the relevant surface areas – cylinders, cuboids and sphere.
The task is now to find a ‘best fit’ size for each of these shapes to match the surface area of the volunteer.

6. Suggested standard formulae
Results
Group
Height
H (cm)
Mass
W (kg)
Est. Area (m2)
Suggested standard formulae 1 2 3 4
Suggested formulae
1. (DuBois & DuBois)
2. (Gehan)
3. (Haycock)
4. (Mosteller)
Get the students to record their results in a table like this one. Group names go in the first column, the measured height and weight of the group volunteer go into H and W, and the next column contains their estimate for the total surface area.
The four columns at the right can then be filled in with the results obtained by evaluating the four formulae shown on the slide, each of which has been suggested as a simple means of estimating human body (or skin) area.
Discuss the results. For example:
How close were the results of the formulae to the groups’ estimates?
What are the advantages of using a formula, rather than modelling the body as a series of standard components?
Which formula is easiest to use?
If time permits, some students may wish to explore the behaviour of the four formulae more closely, investigating their values over a range of values of H and W.
Formulae are from