New
New
Year 7

Checking and securing understanding of the distributive law

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

New
New
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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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.

Keywords

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

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

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

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).

Lesson video

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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

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