Year 7 - Maths
Expressing multiplicative relationships as ratios and fractions
Understanding multiplicative relationships: fractions and 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
This unit introduces the concept of multiplicative relationsihps, and connects fractions to the idea of ratios. Ratios are then explored in depth and used to solve contextual problems such as those involving exchange rates and general conversions.
Lesson Summary
You will learn to express a multiplicative relationship as a ratio or as a fraction.
Key Notes
- By expressing the multiplicative relationship as a ratio, it can be easier to scale further.
- The relationship can be represented using a bar model.
- A bar model shows both parts of the ratio as well as the whole.
- A multiplicative relationship can be expressed as a fraction.
- There are many different ways to express the relationship.
Vocabulary To Learn
- Proportionality: means when variables are in proportion if they have a constant multiplicative relationship.
- Ratio: shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.
- Fraction: shows us how many equal parts in a whole.
Common Mistakes To Avoid
- Pupils see the bar model and/or fraction as the whole as opposed to the proportion of the whole.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
By expressing the multiplicative relationship as a ratio, it can be easier to scale further. The relationship can be represented using a bar model.
2. Use this key word in a maths sentence and explain it clearly. 'Proportionality'
means when variables are in 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: Pupils see the bar model and/or fraction as the whole as opposed to the proportion of the whole. Correction: Emphasise equivalent fractions and equivalent bar models which show different parts to whole, but are the same proportion. e.g 3/5 = 60/100.
More Lessons In This Unit
- Checking and securing finding a fraction of a given amount Study Guide
- Checking understanding of multiplicative relationships Study Guide
- Deepening understanding with fractions of a given amount Study Guide
- Describing exchange rates with ratio Study Guide
- Describing more conversions with ratio Study Guide
- Determining the part Study Guide
- Determining the whole Study Guide
- Dividing a quantity into a given ratio Study Guide
- Equivalent multiplicative relationships Study Guide
- Expressing one number as a fraction of another Study Guide
- Multiplicative relationships Study Guide
- Multiplicative relationships in context Study Guide
- Problem solving with fractions and ratios Study Guide
- Ratio language and notation Study Guide
- Representing a multiplicative relationship Study Guide
- Securing understanding of ratio as a multiplicative relationship Study Guide
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