Year 6 - Maths
Use knowledge of equivalence when scaling factors to solve problems
Using equivalence to calculate
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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 why the product stays the same when one factor is doubled and the other is halved using knowledge of equivalence. They will explain the effect on the quotient when scaling the dividend and divisor by the same amount.
Lesson Summary
You will learn to solve problems using equivalence by scaling factors.
Key Notes
- When one factor is scaled and the other is scaled down by the same amount, the product remains the same.
- Scaling one factor up and the other down by the same amount maintains equivalence.
- Factorising means describing a product using factors that multiply together.
Vocabulary To Learn
- Equivalent: Equivalent means having the same value.
- Factor: A factor is a number which exactly divides another whole number.
- Product: The product is the result when two or more numbers are multiplied together.
Common Mistakes To Avoid
- Pupils may struggle to know what to add if just one of the factors changes.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When one factor is scaled and the other is scaled down by the same amount, the product remains the same. Scaling one factor up and the other down by the same amount maintains equivalence.
2. Use this key word in a maths sentence and explain it clearly. 'Equivalent'
Equivalent means having the same value. 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 struggle to know what to add if just one of the factors changes. Correction: Refer to 'lots of' when discussing calculations. For example, if pupils know that 3 × 84 = 252, then 3 × 85 must be 3 more. 3 × 84 is '84 lots of 3' and 3 × 85 is '85 lots of 3'.
More Lessons In This Unit
- Explain the effect on the product when scaling the factors up and down by the same amount Study Guide
- Explain the effect on the quotient when scaling the dividend and the divisor by 10 Study Guide
- Explain the effect on the quotient when scaling the dividend and the divisor by the same amount Study Guide
- Explain why the product stays the same when one factor is doubled and the other is halved Study Guide
Browse all guides in the Year 6 Maths guide library.