Year 6 - Maths
Solve problems where the known percentage part and size represents a change to the whole
Understanding percentages
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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 explain what percent means and how to represent a percentage in different ways. They will learn how to convert percentages to decimals and fractions and solve conversion problems.
Lesson Summary
You will learn to solve percentage problems where the whole is changed.
Key Notes
- Identify the part and how it relates to the whole.
- If the percentage part is a factor of 100, you can multiply the other part to calculate the whole.
- If the percentage part is not a factor of 100, you can use division and multiplication to calculate the whole.
Vocabulary To Learn
- Percentage: A percentage is a proportion of a whole.
Common Mistakes To Avoid
- Pupils may make mistakes in the second cycle, where they find the whole after a percentage change. They may think the part given (e.g. the new cost) is represented by the percentage change.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
Identify the part and how it relates to the whole. If the percentage part is a factor of 100, you can multiply the other part to calculate the whole.
2. Use this key word in a maths sentence and explain it clearly. 'Percentage'
A percentage is a proportion of 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: Pupils may make mistakes in the second cycle, where they find the whole after a percentage change. They may think the part given (e.g. the new cost) is represented by the percentage change. Correction: Use bar models to help make it clear that the price given is the part remaining after the percentage change. If pupils are struggling with this, simplify the problem by giving numbers easy to calculate with (e.g. 30% off; new price £7).
More Lessons In This Unit
- Explain how to convert a percentage to a fraction without a denominator of 100 Study Guide
- Explain how to convert percentages to decimals and fractions with a denominator of 100 Study Guide
- Explain how to solve problems where the percentage part and size is known but the whole is unknown Study Guide
- Explain what percent means and represent a percentage in different ways Study Guide
- Solve problems involving percentages in a range of contexts Study Guide
- Use knowledge of calculating 50%, 10% and 1% of a number to solve problems in a range of contexts Study Guide
- Use knowledge of calculating any percentage of a number to solve problems in a range of contexts Study Guide
- Use knowledge of calculating common percentages of a number to solve problems in a range of contexts Study Guide
- Use knowledge of fraction-decimal-percentage conversions to solve problems in a range of contexts Study Guide
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