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Year 7

Checking and securing understanding of the commutative and associative laws

I can state the commutative and associative laws and use them to calculate efficiently.

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New
New
Year 7

Checking and securing understanding of the commutative and associative laws

I can state the commutative and associative laws and use them to calculate efficiently.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Addition is commutative and associative.
  2. Subtraction is neither commutative nor associative.
  3. Multiplication is commutative and associative.
  4. Division is neither commutative nor associative.

Common misconception

Division is commutative given some divisions can give the same answer. eg. 8000/4/2 = 8000/2/4

To check for all rearrangements of the number e.g. 2/4/8000 does not equal 8000/4/2

Keywords

  • Commutative law - An operation is commutative if the values it is operating on can be written in either order without changing the calculation

  • Associative law - An operation is associative if a repeated application of an operation produces the same result regardless of how pairs of values are grouped

To check for understanding, go around the class and ask them to say 100 in a different way using the commutative and/or associative law. eg. 100 = 99 + 1 = 1+99 = 50 x 2 = 2 x 50 = 25 x 2 + 2 x 25
Teacher tip

Equipment

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
Which operation is the mathematical operation of scaling one number by another?
Division
Correct answer: Multiplication
Addition
Subtraction
Q2.
Match each multiplication to its answer.
Correct Answer:$$9\times3$$ ,$$27$$

$$27$$

Correct Answer:$$8\times6$$ ,$$48$$

$$48$$

Correct Answer:$$7\times9$$ ,$$63$$

$$63$$

Correct Answer:$$6\times7$$ ,$$42$$

$$42$$

Q3.
Work out the missing number: 7 × = 7000
Correct Answer: 1000
Q4.
Select all the correct statements.
Correct answer: 8 + 4 is equal to 4 + 8
8 − 4 is the same 4 − 8
Correct answer: 8 × 4 is equal to 4 × 8
8 ÷ 4 is equal to 4 ÷ 8
Q5.
Without using a calculator, work out: 168 + 235 − 149 =
Correct Answer: 254
Q6.
Without using a calculator, work out: 23 × 15 =
Correct Answer: 345

Exit quiz

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6 Questions

Q1.
Select the correct statement. The commutative law states that the values it is operating on can be written __________.
using division and subtraction only
Correct answer: in either order without changing the calculation
left to right only
Q2.
Select all the examples of the associative law.
3 + 4 = 4 + 3
Correct answer: 2 × 7 × 10 = (2 × 7) × 10
11 − 10 = 10 − 11
Correct answer: 5 + (2 + 4) = (5 + 2) + 4
Correct answer: (7 + 5) + 5 = 7 + (5 + 5)
Q3.
Find the missing number in this equation. 3 × (4 × 5) = (3 × ) × 5
Correct Answer: 4
Q4.
Match each calculation to an equivalent commutative calculation.
Correct Answer:$$2 + 3 $$,$$3 + 2$$

$$3 + 2$$

Correct Answer:$$2\times3$$,$$3\times2$$

$$3\times2$$

Correct Answer:$$A + 2 + 3$$,$$2 + 3 + A$$

$$2 + 3 + A$$

Q5.
Laura says, "Division is commutative because $$ 2\div1 $$ is the same as $$ 1\div2 $$." Select the correct statement.
She is correct. They both equal the same answer, 2
Correct answer: She is incorrect because $$ 2\div1 =2$$ and $$ 1\div2 $$ = $${1} \over {2}$$
She is correct because both calculations use division.
Q6.
Without using a calculator, use the associative and commutative law to work out the sum the first 20 integers. The sum is
Correct Answer: 210