Year 10 - Maths
Problem solving with algebraic 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 use your knowledge of ratio to solve problems.
Key Notes
- It is important to preserve the relationship between the parts of a ratio.
- There is a functional relationship between the quantities in a ratio.
- This relationship can be represented algebraically.
Vocabulary To Learn
- Ratio: A ratio shows the relative sizes of two or more values and allows you to compare a part with another part in a whole.
- Coordinates: Coordinates are a set of values that show an exact position.
- Expression: An expression contains one or more terms, where each term is separated by an operator.
- Probability: The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.
Common Mistakes To Avoid
- Procedural understanding of sharing in a ratio where pupils add the parts, divide the amount by this and then multiply by each part without considering the information in the question.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
It is important to preserve the relationship between the parts of a ratio. There is a functional relationship between the quantities in a ratio.
2. Use this key word in a maths sentence and explain it clearly. 'Ratio'
A ratio shows the relative sizes of two or more values and allows you to compare a part with another part in a whole. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Procedural understanding of sharing in a ratio where pupils add the parts, divide the amount by this and then multiply by each part without considering the information in the question. Correction: In the lesson encourage pupils to look for keywords in the question which indicate if the amount given is the total, one part or the difference. The use of a bar model to display the information can also be used to help pupils.
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 equivalent ratios 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 ratios Study Guide
- Writing equations from ratios Study Guide
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