Teaching mathematics
Teaching mathematics

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Teaching mathematics

1.6 Extending measures to compound measures

Compound measures are comprised of at least two other measures. Perhaps the most commonly used example is speed which is the distance travelled in one unit of time (i.e. it uses a combination of length and time measures). It is measured in miles per hour, km per hour, metres per second, etc.

When introducing compound measures to my learners I used to pose this question:

‘Which is heavier: a ton of lead or a ton of feathers?’

My learners, being smart young people, would think about this question and then say ‘They weigh the same because you said they weighed a ton’. I would then ask:

‘What is the obvious difference between the ton of feathers and the ton of lead?’

The answer is that the ton of feathers takes up much more space than the ton of lead. This leads to a consideration of volume and weight. Lead is denser than feathers as it is more compact. We would use this to work out that density is the weight per unit volume of a substance.

One year I had a thoughtful group of learners who replied that if a ton of lead fell on you it would probably kill you whereas you would be likely to survive having a ton of feathers falling on you. Cue the class clown brilliantly miming someone climbing out of a ton of feathers!


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