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Year 11 - Maths

Checking and further securing understanding of direct proportion in context

Compound measures

Unit Summary

In this unit, pupils explore the multiplicative relationship between different compound meaures and units such as speed, rates of pay, density and pressure.

Lesson Summary

You will learn to recognise direct proportion in a range of contexts, including compound measures.

Key Notes

  • Direct proportion can be used in a number of contexts, for example in currency conversion.
  • Proportional relationships can be expressed as ratios, often in unitary form.
  • A ratio is in unitary form if one of the parts is equal to one.
  • It is useful to be able to recognise which contexts involve direct proportion.

Vocabulary To Learn

  • Rate: A rate is a relationship between two units. For example miles per hour (mph) is a rate called speed which relates distance and time.
  • Exchange rate: An exchange rate is the rate at which one currency is exchanged for another. The two currencies are in proportion because they have a constant multiplicative relationship.
  • Direct proportion: Two variables are in direct proportion if they have a constant multiplicative relationship.

Common Mistakes To Avoid

  • When considering meter readings, using the 'new reading' rather than the units used to calculate the cost.

3 Quick Questions (With Answers)

1. Solve this in steps: explain the method from this lesson and why each step matters.

Direct proportion can be used in a number of contexts, for example in currency conversion. Proportional relationships can be expressed as ratios, often in unitary form.

2. Use this key word in a maths sentence and explain it clearly. 'Rate'

A rate is a relationship between two units. For example miles per hour (mph) is a rate called speed which relates distance and time. Use this word when showing your method, then check your final answer is reasonable.

3. Spot and fix this common maths mistake.

Mistake: When considering meter readings, using the 'new reading' rather than the units used to calculate the cost. Correction: Emphasise that it is the change in readings that indicates the units used during a time period. The 'new reading' alone shows the total number of units used since the meter was installed.

More Lessons In This Unit

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