Lesson 19 Accuracy and errors

Episode 2

Reasoning Resources: Worksheet 2, rulers and tape measures (cm and mm)
Whole class and short periods of paired work
Because of weakness in daily language to handle some concepts ahead of formal mathematics, the main benefit comes from pooling ideas and words from the whole class. This highlights Vygotsky's idea that a teacher's language may simply be too polished and formal in scope to be of any help to 12-year-olds. However, the insights they get from their peers who are only just ahead of them, and floundering as they make progress, will be far more fruitful. For this we celebrate emergent pupils‘ language and only gradually steer them towards scientific notions. Give out Worksheet 2 to pairs. For many groups the best approach is to treat each question as a mini-episode, the length of which you decide through judgement on how appropriate the challenge is, You are looking for most of the class struggling but managing to extend to ideas slightly above their thinking level for a time.

For question 1 ask:How do people decide whether an error is important or not? Likely answers would be:‘always important, even few pennies', 'the big shop has to be more honest’, 'for every four chocolate bars you could have another, but the bike is different', ‘some errors are understandable’, ‘it is all this ending shop prices with a 9'.

For question 2 the ideas may include:'If all the desks have the same error then it doesn't matter’, 'you always make a couple of mm error’, ‘if you want to fit the desk into an alcove then you have to measure accurately, if you just want a table cloth then not’.

Further questions could be: ‘How big is the error? has two answers or two meanings. Explain the two ways of looking at an error. When we talk about large numbers we round them. For example, if you buy a car for £4723 you may say ‘about £4000 Can you give sore examples of when the error in rounding is not important?

In all of the questions, allow various forms of saying ‘it depends...' extracting from the class that it is the use of a measurement, as much as the actual value, that decides what level of accuracy is needed.
Whole class reflection
Throughout the lesson pupils are addressing intuitive aspects of proportionality, often without these being named as such. If the lesson ends with this episode, let the class talk about wider related issues. For example:Why might a company such as telephone or gas, add 0.5p on to each consumers bill? Would each individual notice it? What would happen if they did it to 1 million consumers?

Pupils know that accuracy is relative: sometimes it is important to be precise; sometimes rough and rounded figures are sufficient. Give pupils the chance to clarify that intuition in accessible contexts. They should start and end with the purpose for the measurement and decide the appropriate accuracy.

You could also discuss the difference between estimating (when the error is unknown) and approximation or rounding when the error can be decided. This can focus the pupils upon acceptable degrees of accuracy and that these are often related to what ‘people’ can understand quickly.