Year 11 - Maths
Abstract direct proportion
Direct and inverse proportion
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
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 identify, write and solve direct proportion questions involving algebra.
Key Notes
- Direct proportion equations are of the form y = kx
- k is the constant of proportionality and it is also the gradient of the graph.
- To find the gradient, k, you can use a set of coordinates (pair of values).
Vocabulary To Learn
- Direct proportion: Two variables are in direct proportion if they have a constant multiplicative relationship.
- Reciprocal: The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1.
Common Mistakes To Avoid
- We use the term 'multiplicative relationship' when talking about direct proportion. Pupils may need reminding that division is equivalent to multiplying by the reciprocal.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Direct proportion equations are of the form y = kx. k is the constant of proportionality and it is also the gradient of the graph.
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: We use the term 'multiplicative relationship' when talking about direct proportion. Pupils may need reminding that division is equivalent to multiplying by the reciprocal. Correction: Allow opportunities to explore division of a number and multiplication of its reciprocal. Remind pupils that any non-zero number multiplied by its reciprocal is equal to 1.
More Lessons In This Unit
- Abstract inverse proportion Study Guide
- Checking and securing understanding of direct proportion graphs Study Guide
- Checking and securing understanding of inverse proportion graphs Study Guide
- Finding the constant of proportionality for direct proportion Study Guide
- Finding the constant of proportionality for directly proportional relationships Study Guide
- Finding the constant of proportionality for inverse proportion Study Guide
- Problem solving with direct and inverse proportion Study Guide
- Proportion modelled algebraically Study Guide
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