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Year 11 - Maths

Finding the constant of proportionality for directly proportional relationships

Direct and inverse proportion

Unit Summary

In this unit, pupils learn how to represent direct and inverse proportion algebraically as an extension of work done in the linear graphs unit.

Lesson Summary

You will learn to use the general form for the directly proportional relationship y = kx^n to find k.

Key Notes

  • y can be directly proportional to x^n
  • This is because x^n could be written as a different variable.

Vocabulary To Learn

  • Direct proportion: Two variables are in direct proportion if they have a constant multiplicative relationship

Common Mistakes To Avoid

  • Setting up the initial proportion statement and hence the general form of the equation the wrong way around.

3 Quick Questions (With Answers)

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

y can be directly proportional to x^n. This is because x^n could be written as a different variable.

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

Two variables are in direct proportion if they have a constant multiplicative relationship. Use this word when showing your method, then check your final answer is reasonable.

3. Spot and fix this common maths mistake.

Mistake: Setting up the initial proportion statement and hence the general form of the equation the wrong way around. Correction: Pay particularly attention to the language used. Give pupils the opportunity to verbalise what different proportion statements mean. E.g. y ∝ x^2, 'read this aloud using the correct mathematical vocabulary'.

More Lessons In This Unit

Browse all guides in the Year 11 Maths guide library.