Year 6 - Maths
Explain why the product stays the same when one factor is doubled and the other is halved
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 explain why the product stays the same when one factor is doubled and the other is halved.
Key Notes
- When one factor is doubled and the other is halved, the product remains the same.
- Arrays can be rearranged to represent the product staying the same when one factor is doubled and the other halved.
- Doubling one factor and halving the other maintains equivalence.
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 of two or more numbers multiplied together.
Common Mistakes To Avoid
- Pupils may double or halve both factors, instead of doubling one and halving the other.
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 doubled and the other is halved, the product remains the same. Arrays can be rearranged to represent the product staying the same when one factor is doubled and the other halved.
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 double or halve both factors, instead of doubling one and halving the other. Correction: Spend time exploring arrays and the area models (from Cycle B of the lesson). Model these misconceptions, showing why they are incorrect (e.g. show how 4 x 8 cannot be equivalent to 8 x 16).
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
- Use knowledge of equivalence when scaling factors to solve problems Study Guide
Browse all guides in the Year 6 Maths guide library.