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Year 5

Explain the use of the commutative and associative laws when multiplying three or more numbers

I can explain the use of the commutative and associative laws when multiplying three or more numbers.

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New
New
Year 5

Explain the use of the commutative and associative laws when multiplying three or more numbers

I can explain the use of the commutative and associative laws when multiplying three or more numbers.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. You can change the order of the factors or group them in different ways and the product remains the same.

Common misconception

Pupils only ever calculate an equation from left to right.

Ensure pupils are given time to explore where the commutative law might be best used and where the associative law might be better used. Pupils should be expected to reason why they have chosen to adopt a strategy.

Keywords

  • Commutative - The commutative law states that you can write the values of a calculation in a different order without changing the calculation; the result is the same. It applies for addition and multiplication.

  • Associative - The associative law states that it doesn't matter how you group or pair values (i.e. which we calculate first), the result is still the same. It applies for addition and multiplication.

Encourage pupils to construct representations of problems using cubes to help reveal the rows, columns and layers. Using the language 'x rows times x columns. x times' will help pupils to verbalise the structure of rows, columns and layers.
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.
What multiplication fact does this array represent?
An image in a quiz
Correct answer: 5 x 7 = 35
6 x 7 =42
5 x 6 = 30
Correct answer: 7 x 5 = 35
Q2.
What are the factors shown by this array?
An image in a quiz
7 and 6
Correct answer: 6 and 5
6 and 30
30 and 5
Q3.
Which of these are correct arrays for 36?
An image in a quiz
Correct answer: A
B
C
Correct answer: D
Q4.
Complete the missing factor: 7 × = 56
Correct Answer: 8, eight
Q5.
Which of these are not factors 40?
5
10
4
Correct answer: 9
Correct answer: 3
Q6.
Which factor is missing from the factor bug?
An image in a quiz
Correct Answer: 3, three

Exit quiz

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6 Questions

Q1.
Look at the image. What does the number 3 represent in this expression? 2 × 3 × 4
An image in a quiz
Correct answer: The number of columns in each tray.
The number of rows in each tray.
The number of trays.
Q2.
One layer has three rows and four columns. There are two layers. What does the 3 represent?
An image in a quiz
The number of columns in a layer.
The number of layers.
Correct answer: The number of rows in a layer
Q3.
Select the equation that most accurately matches this representation.
An image in a quiz
3 x 4 x 5
Correct answer: 4 x 3 x 5
5 x 3 x 4
Q4.
Select the missing equation?
An image in a quiz
4 x 5 x 3
Correct answer: 5 x 3 x 4
3 x 3 x 5
3 x 5 x 4
Q5.
Look at the equation. Which two numbers would you multiply together first? 3 × (4 × 6)
3 and 4
3 and 6
Correct answer: 4 and 6
Q6.
Match the statements.
Correct Answer:This is known as the associative law.,Multiply different pairs of factors & the product will stay the same.

Multiply different pairs of factors & the product will stay the same.

Correct Answer:This is known as the commutative law.,Changing the order of the factors, the product remains the same.

Changing the order of the factors, the product remains the same.