Year 7 - Maths
Equivalent multiplicative relationships
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 appreciate that there are an infinite number of pairs of numbers for any given multiplicative relationship.
Key Notes
- There is a multiplicative relationship between the ratio parts, and other equivalent ratios.
- Ratios can be expressed as fractions.
- There are infinitely many equivalent fractions.
- There are infinitely many equivalent ratios.
Vocabulary To Learn
- Proportionality: Proportionality means when variables are in proportion if they have a constant multiplicative relationship.
Common Mistakes To Avoid
- Using multiplication as repeated addition leads to incorrect additive strategies of ratios.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There is a multiplicative relationship between the ratio parts, and other equivalent ratios. Ratios can be expressed as fractions.
2. Use this key word in a maths sentence and explain it clearly. 'Proportionality'
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: Using multiplication as repeated addition leads to incorrect additive strategies of ratios. Correction: Focus on the multiplicative relationships between parts to whole or whole to parts. Ratio tables can help see this more easily.
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
- Expressing multiplicative relationships as ratios and fractions 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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