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Year 9

Checking and further securing understanding of the commutative law

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

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New
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Year 9

Checking and further securing understanding of the commutative law

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

Download all resources
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Share activities with pupils
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Lesson details

Key learning points

  1. A number can be expressed as the product of prime factors.
  2. By using the commutative law, you can chose which factors to multiply together first.
  3. Using the commutative law can make calculations easier.

Keywords

  • Exponential form - When a number is multiplied by itself multiple times, it can be written more simply in exponential form.

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

  • Prime number - A prime number is an integer greater than one with exactly 2 factors. All integers greater than 1 are either composite or prime.

  • Prime factor - Prime factors are the factors of a number that are, themselves, prime.

  • Prime factorisation - Prime factorisation is a method to find the prime factors of a given integer.

Common misconception

Use of addition instead of multiplication when finding factors.

Reiterate that the product of prime factors is unique.

Encourage students to check their answers using the prime factorisation button on their calculator.
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).

Lesson video

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Starter quiz

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6 Questions

Q1.
Using the Gattegno chart or otherwise, work out which of the following calculations equate to 48.
An image in a quiz
Correct answer: $$6\times8$$
Correct answer: $$0.04\times1200$$
$$0.6\times800$$
Correct answer: $$60\times0.8$$
$$400\times1.2$$
Q2.
Using the Gattegno chart or otherwise, match each calculation to its correct answer.
An image in a quiz
Correct Answer:2 × 4 = 0.2 × 40 = 0.4 × 20,8

8

Correct Answer:6 × 2 = 0.6 × 20 = 0.2 × 60,12

12

Correct Answer:0.7 × 30 = 0.3 × 70 = 7 × 3,21

21

Correct Answer:0.3 × 30 = 3 × 3 = 0.003 × 3000,9

9

Q3.
Using the associative law to partition 5000 and 7000 into powers of 10, find the calculations that are equivalent to 7000 × 5000.
$$3.5\times 10^6$$
$$35\times 10^7$$
Correct answer: $$7\times1000\times5\times1000$$
Correct answer: $$35\times 10^6$$
Correct answer: $$3.5\times 10^7$$
Q4.
Which of the following calculations are equivalent to $$3000\times2000$$?
Correct answer: $$3\times2\times 1000\times 1000$$
Correct answer: $$6\times 10^6$$
$$3\times2\times 100\times 100$$
$$3\times2\times 10000\times 1000$$
$$3\times10000\times2\times1000$$
Q5.
Without using a calculator, work out 0.007 × 30.
Correct Answer: 0.21
Q6.
Which of the following calculations are equivalent to $$4.5\times0.05$$?
$$\frac{45\times5}{10^2}$$
Correct answer: $$\frac{45\times5}{1000}$$
$$\frac{45\times5}{10000}$$
Correct answer: $$\frac{45\times5}{10^3}$$
Correct answer: $$\frac{225}{10^5}$$

Exit quiz

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6 Questions

Q1.
A number is an integer greater than one with exactly two factors.
Correct Answer: prime
Q2.
Which of the following products only use prime numbers?
4 × 5 × 13
Correct answer: 2 × 3 × 19
9 × 11 × 13
Correct answer: 11 × 13 × 17
11 × 13 × 15 × 19
Q3.
Write 200 as a product of its prime factors.
2² × 5²
2³ × 5
Correct answer: 2³ × 5²
2 × 4 × 5²
Q4.
Use the fact that 60 = 2² × 3 × 5 to write 180 as a product of its prime factors.
2³ × 3 × 5
2² × 3 × 5²
Correct answer: 2² × 3² × 5
2² × 3³ × 5
Q5.
Use the fact that 60 = 2² × 3 × 5 to write 20 as a product of its prime factors.
2² × 3 × 5 ÷ 3
2 × 3 × 5
2² × 3
Correct answer: 2² × 5
Q6.
165 = 3 × 5 × 11 and 42 = 2 × 3 × 7. Which of the following is the most useful arrangement to calculate 165 × 42?
3 × 5 × 11 × 2 × 3 × 7
2 × 3 × 3 × 5 × 7 × 11
2 × 11 × 5 × 3 × 3 × 7
Correct answer: 2 × 5 × 3 × 3 × 7 × 11