Year 10 - Maths
Checking and securing understanding of equivalent ratios
Ratio
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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 will learn how to combine ratios, interpret algebraic ratios, and investigate quantity changes and their effect on ratios.
Lesson Summary
You will learn to appreciate that any two numbers can be connected via a multiplicative relationship.
Key Notes
- A multiplicative relationship is a proportional relationship.
- This multiplier can be thought of as a scaling factor.
- The multiplier can be deduced through unitising.
- Any value divided by itself is equal to one.
- One is the multiplicative identity.
Vocabulary To Learn
- Reciprocal: A 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
- Finding the additive relationship between two numbers instead of the multiplicative one.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A multiplicative relationship is a proportional relationship. This multiplier can be thought of as a scaling factor.
2. Use this key word in a maths sentence and explain it clearly. 'Reciprocal'
A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Finding the additive relationship between two numbers instead of the multiplicative one. Correction: When dealing with any proportional relationships, such as ratios, pupils should be reminded to look for the multiplicative relationship. Using 1 as a middle step can help. e.g. to connect 5 and 8, divide by 5 to make 1 and then multiply by 8.
More Lessons In This Unit
- Algebraic ratios Study Guide
- Changing ratios Study Guide
- Checking and securing understanding of converting between ratios, percentages and fractions Study Guide
- Checking and securing understanding of real world ratios Study Guide
- Checking and securing understanding of sharing in a ratio Study Guide
- Checking and securing understanding of simplifying and unitising ratios Study Guide
- Combining ratios Study Guide
- Problem solving with algebraic ratios Study Guide
- Problem solving with ratios Study Guide
- Writing equations from ratios Study Guide
Browse all guides in the Year 10 Maths guide library.