Year 7 - Maths
Problem solving with fractions and ratios
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 use your knowledge of fractions and ratios to solve problems.
Key Notes
- Any fraction can be turned into a ratio.
- Moving between fractions and ratios can make a problem easier.
- There can be lots of information, it is important to think about what is required to solve the problem.
Vocabulary To Learn
- Proportion: Proportionality means when variables are in proportion if they have a constant multiplicative relationship.
- Ratio: A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.
Common Mistakes To Avoid
- Always dividing the amount by the sum of the 'parts' of the ratio to get one 'part'.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Any fraction can be turned into a ratio. Moving between fractions and ratios can make a problem easier.
2. Use this key word in a maths sentence and explain it clearly. 'Proportion'
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: Always dividing the amount by the sum of the 'parts' of the ratio to get one 'part'. Correction: Offer opportunities to match problems to bar models ensure the same numbers are used to highlight the differences.
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 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
- 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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