Year 7 - Maths
Using the associative, commutative and distributive laws together
Arithmetic procedures with integers and decimals
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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 develop their ability and efficacy with the four operations including more complicated and challenging calculations involving fractions, decimals and negative numbers. This leads into an exploration of the priority order of operations.
Lesson Summary
You will learn to use the associative, distributive and commutative laws to flexibly and efficiently solve problems.
Key Notes
- A calculation may be made easier by applying more than one of the associative, commutative or distributive laws.
- Steps taken should progress the calculation steps.
- If a more efficient way cannot be spotted, the calculation can still be calculated using other methods.
Vocabulary To Learn
- Commutative: An operation is commutative if the values it is operating on can be written in either order without changing the calculation.
- Associative: The associative law states that a repeated application of the operation produces the same result regardless how pairs of values are grouped.
- Distributive: The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.
Common Mistakes To Avoid
- The common multiplier is the number seen to be common eg. 1.2 x 20 + 1.2 x 30 + 1.2 x 10
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A calculation may be made easier by applying more than one of the associative, commutative or distributive laws. Steps taken should progress the calculation steps.
2. Use this key word in a maths sentence and explain it clearly. 'Commutative'
An operation is commutative if the values it is operating on can be written in either order without changing the calculation. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: The common multiplier is the number seen to be common eg. 1.2 x 20 + 1.2 x 30 + 1.2 x 10. Correction: Students can use the associative law to find more common multipliers eg. 1.2 x 10 x 2 + 1.2 x 10 x3 + 1.2 x 10 = 12 x 2 + 12 x 3 + 12 x 1.
More Lessons In This Unit
- Addition of positive and negative integers Study Guide
- Checking and securing understanding of multiplication and division Study Guide
- Checking and securing understanding of negative numbers in context Study Guide
- Checking and securing understanding of written addition and subtraction strategies Study Guide
- Checking understanding of arithmetic procedures with integers and decimals Study Guide
- Dividing with decimals Study Guide
- Multiplication and division where only one value is negative Study Guide
- Multiplication and division where two or more values are negative Study Guide
- Multiplying with decimals Study Guide
- Priority of operations with positive and negative integers and decimals Study Guide
- Priority of operations with positive integers Study Guide
- Problem solving with integers and decimals Study Guide
- Securing understanding of arithmetic procedures with integers and decimals Study Guide
- Simplifying multiplication and division using multiples of 10 Study Guide
- Subtraction of positive and negative integers Study Guide
- Using your calculator efficiently Study Guide
Browse all guides in the Year 7 Maths guide library.