Year 5 - Maths
Apply the commutative and associative laws to simplify volume calculations
Multiply 3 or more numbers (commutative and associative laws)
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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 the use of the commutative and associative laws to rearrange and simplify calculations when multiplying three or more numbers.
Lesson Summary
You will learn to apply the commutative and associative laws to simplify volume calculations.
Key Notes
- To simplify a multiplication calculation, you can change the order of the factors.
- To simplify a multiplication calculation you can group the factors in different ways.
Vocabulary To Learn
- represent: To represent something is to show it in a different way.
- associative: The associative law states that it doesn't matter how you group or pair values (i.e. which we calculate first), the result is still the same. It applies to addition and multiplication.
- commutative: The commutative law states that you can write the values of a calculation in a different order without changing the solution; the result is the same. It applies to addition and multiplication.
Common Mistakes To Avoid
- Pupils struggle to understand that a 3 factor calculation problem with two unknown factors can be represented as a 2 factor calculation with one unknown factor.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
To simplify a multiplication calculation, you can change the order of the factors. To simplify a multiplication calculation you can group the factors in different ways.
2. Use this key word in a maths sentence and explain it clearly. 'represent'
To represent something is to show it in a different way. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils struggle to understand that a 3 factor calculation problem with two unknown factors can be represented as a 2 factor calculation with one unknown factor. Correction: Spend time manipulating 2 factor calculations into 3 factors and vice versa. Once pupils are confident with this, apply this to a context where the numbers are kept simple to support pupils to see the structure of the problems.
More Lessons In This Unit
- Apply commutative and associative laws to simplify multiplications Study Guide
- Apply the commutative and associative laws to simplify problems in a range of contexts Study Guide
- Explain the reasons for changing two-factor multiplication calculations to three-factor calculations Study Guide
- Explain the use of the commutative and associative laws when multiplying three or more numbers Study Guide
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