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Lesson 17 of 17
  • Year 7

Using the associative, commutative and distributive laws together

I can use the associative, distributive and commutative laws to flexibly and efficiently solve problems

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Lesson 17 of 17
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  • Year 7

Using the associative, commutative and distributive laws together

I can use the associative, distributive and commutative laws to flexibly and efficiently solve problems

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These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. A calculation may be made easier by applying more than one of the associative, commutative or distributive laws.
  2. Steps taken should progress the calculation steps.
  3. If a more efficient way cannot be spotted, the calculation can still be calculated using other methods.

Keywords

  • 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 misconception

The common multiplier is the number seen to be common eg. 1.2 x 20 + 1.2 x 30 + 1.2 x 10

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


To help you plan your year 7 maths lesson on: Using the associative, commutative and distributive laws together, download all teaching resources for free and adapt to suit your pupils' needs...

Encourage student to see more factors of multipliers using the associative law. Give the class 2.4 x 30 - 2.4 x 20 and ask to rewrite it e.g 2.4 x 10 x 3 - 2.4 x 10 x 2 etc and decide which calculation is easiest to work out the answer.
Teacher tip

Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Prior knowledge starter quiz

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6 Questions

Q1.
Match each law with an example of the law

Correct Answer:Commutative law,$$3 + 10 + 8 = 8 + 10 + 3$$

$$3 + 10 + 8 = 8 + 10 + 3$$

Correct Answer:Associative law,$$6\times5\times4= (6\times5)\times4$$

$$6\times5\times4= (6\times5)\times4$$

Correct Answer:Distributive law,$$45\times(0.7+0.3)=45\times0.7 + 45\times0.3$$

$$45\times(0.7+0.3)=45\times0.7 + 45\times0.3$$

Q2.
Which of the following is an example of the distributive law for this calculation $$39\times99$$?

$$99\times39$$
Correct answer: $$39\times(100 - 1)$$
$$39\times(9 \times 9)$$

Q3.
Which of the following is an example of the distributive law for this calculation: $$22\times42$$

Correct answer: $$22\times(40+2)$$
$$22\times(21\times 2)$$
$$22\times(4+2)$$
Correct answer: $$22\times(10+10+10+10+2)$$

Q4.
Without using a calculator, use the distributive law to work out: $$4.8 \times 6.1 + 4.8 \times 3.9 = $$

Correct Answer: 48

Q5.
Work out the missing number: $$5.67 \times 0.3 + 5.67 \times$$ $$= 5.67$$

Correct Answer: 0.7, 7/10

Q6.
Work out the missing number: $$23 \times 0.8 + 23 \times 1.4 − 23 \times$$ $$= 46$$

Correct Answer: 0.2, 2/10, 1/5

Assessment exit quiz

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6 Questions

Q1.
Select the calculation that is equivalent to $$8\times(10+12)$$.

$$80 + 92$$
Correct answer: $$8\times 10 + 8\times12$$
$$8 \times2$$

Q2.
Select the calculation that is equivalent to $$4\times9 + 4\times11$$.

Correct answer: $$4\times20$$
$$4\times9\times 11$$
$$4\times13$$

Q3.
Select the calculations that are equivalent to $$ 24\times44$$.

Correct answer: $$24\times(40+4)$$
Correct answer: $$6\times4\times11\times4$$
$$2\times(12\times22)$$
Correct answer: $$16\times66$$
$$20\times4 + 40\times4$$

Q4.
Work out the missing number: $$14.3 \times 0.6 + 14.3 \times$$ $$= 14.3$$

Correct Answer: 0.4, 4/10, 2/5

Q5.
Select the calculations that are equivalent to $$70\times4 + 12\times4+9\times8$$.

$$4\times(70+12+9)$$
Correct answer: $$4\times(70+12+18)$$
Correct answer: $$8\times(35+6+9)$$
$$8\times(70+12+9)$$

Q6.
The same number is written in each square: $$(3\times\square+5\times\square)+\square = \triangle \times \square$$. Find the number that should go in the triangle so that the equation is always true.

Correct Answer: 9, nine