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Year 7

Checking and securing understanding of the distributive law

I can state the distributive law and use it to calculate efficiently

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New
New
Year 7

Checking and securing understanding of the distributive law

I can state the distributive law and use it to calculate efficiently

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. The distributive law can be used when two (or more) values have a common factor.
  2. By using the distributive law, calculations can be made easier.
  3. Any common factor can be used but the highest is often the most efficient.

Common misconception

The distributive law only uses addition eg 24 x 99 = 24 x (90 + 9) = 24 x 90 + 24 x 9

Subtraction is important as it can simplify the calculation 24 x 99 = 24 x (100 - 1) = 24 x 100 - 24 x 1

Keywords

  • Distributive law - The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.

Ask students in the class to come up with a distributive calculation for 24 x 12 and list on the board. 24 x (10+2), 24 x (15 - 3), 24 x (9+3) etc. Decimals can be used for more of a challenge.
Teacher tip

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.
An operation is __________ if a repeated application of the operation produces the same result regardless of how pairs of values are grouped.
commutative
Correct answer: associative
irregular
unneeccary
Q2.
Select all the examples of the associative law.
31 + 4 = 4 + 31
Correct answer: (17 + 3) + 3 = 17 + (3 + 3)
Correct answer: 2 × 8 × 5 = 2 × (8 × 5)
15 – 10 = 10 – 15
Q3.
Use the commutative law you can rewrite 10 + 4 as .
Correct Answer: 4 + 10
Q4.
Match each calculation to an equivalent commutative calculation.
Correct Answer:3 + 12 + 4,12 + 3 + 4

12 + 3 + 4

Correct Answer:3 × 12 × 4,4 × 3 × 12

4 × 3 × 12

Correct Answer:A + 3 + B,B + A + 3

B + A + 3

Q5.
Andeep says, "Division is commutative because 12 ÷ 4 ÷ 3 = 1 and is the same as 12 ÷ 3 ÷ 4 = 1." Select the correct statement.
He is correct as both answers do equal 1.
Correct answer: He is incorrect as the commutative law would also give 4 ÷ 3 ÷ 12 which isn't 1
He is correct as he has repositioned all the numbers.
Q6.
The sum of the first 10 integers is . (Do not use a calculator.)
Correct Answer: 55

Exit quiz

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6 Questions

Q1.
The __________ says that multiplying a sum is the same as multiplying each addend and summing the result.
commutative law
associative law
Correct answer: distributive law
Q2.
Match each law with an example of the law.
Correct Answer:Commutative,$$9 + 10 + 11 = 9 + 11 + 10$$

$$9 + 10 + 11 = 9 + 11 + 10$$

Correct Answer:Associative,$$(5 × 4) × 2 = 5 × (4 × 2)$$

$$(5 × 4) × 2 = 5 × (4 × 2)$$

Correct Answer:Distributive,$$12 × (4 + 3) = 48 + 36$$

$$12 × (4 + 3) = 48 + 36$$

Q3.
Without using a calculator, use the distributive law to work out: $$1.3\times7.2 + 1.3\times2.8$$ =
Correct Answer: 13
Q4.
Without using a calculator, use the distributive law to work out: $$50\times99$$ =
Correct Answer: 4950
Q5.
Work out the missing number: $$22 \times 0.3 + 22 \times $$ $$= 22$$
Correct Answer: 0.7, 7/10
Q6.
Work out the missing number: $$4.8 \times 0.6 + 4.8 \times 1.2 − 4.8 \times$$ $$= 4.8$$
Correct Answer: 0.8, 8/10