New
New
Year 5

# Apply commutative and associative laws to simplify multiplications

I can apply the commutative and associative laws to simplify multiplications of three or more numbers.

New
New
Year 5

# Apply commutative and associative laws to simplify multiplications

I can apply the commutative and associative laws to simplify multiplications of three or more numbers.

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## Lesson details

### Key learning points

1. Rearranging or grouping the factors in a multiplication can make it easier to solve.

### Common misconception

Pupils continue to work only from left to right in calculations, therefore making calculations more time-consuming.

Support pupils to find pairs of factors that are easy to multiply with. For example, finding factors that make a power of ten often make calculations easier as they can multiply by 10, 100 or 1000 for example at the end.

### Keywords

• Efficient - Working efficiently means finding a way to solve a problem quickly whilst also maintaining accuracy.

• 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.

You might like to recap multiplying a number by 10, 100 or 1000 prior to the lesson as a necessary pre-requisite for this lesson. You may also consider how the product changes when a factor is made 10 or 100 times the size.
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).

## Starter quiz

### 6 Questions

Q1.
What is the product of 7 and 9?
Correct Answer: 63, sixty three
Q2.
What does the number 6 represent in the image below? 3 × 2 × 6
The number of rows.
The number of columns.
Correct answer: The number of trays.
Q3.
What is the missing number in the expression? 4 × × 2 Use the image to help.
Correct Answer: 3, three
Q4.
Look at the equation. Which two numbers would you multiply together first? 2 × (7 × 4)
4 and 2
Correct answer: 7 and 4
7 and 2
Q5.
Which equations could you use to work out the total number of cubes?
Correct answer: 4 × (5 × 3)
Correct answer: (4 × 5) × 3
(3 × 5) × 3
Correct answer: (5 × 4) × 3
Q6.
Match the expressions that are equal.
Correct Answer:(20 × 4) × 8,80 × 8

80 × 8

Correct Answer:3 × (4 × 1),3 × 4

3 × 4

Correct Answer:(2 × 5) × 8,10 × 8

10 × 8

Correct Answer:(4 × 3) × 3,12 × 3

12 × 3

## Exit quiz

### 6 Questions

Q1.
Which is the most efficient method?
14 × 5 × 2 =
Correct answer: 14 × (5 × 2) =
5 × 14 × 2 =
Q2.
Which equation is easiest to calculate?
51 × 25 × 4 =
4 × (51 × 25) =
Correct answer: 51 × (4 × 25) =
Q3.
Aisha has used associative law to make 36 × 50 × 2 = into 36 × (50 × 2) = True or false: Aisha has made the calculation easier to solve.
False
Q4.
Which of these make 27 × 5 × 20 = easier to solve?
(27 × 5) × 20 =
20 × 27 × 5 =
Correct answer: 27 × (5 × 20) =
Q5.
Which equation is most efficient? There were 16 bikes in a shed. Each bike has 2 wheels and each wheel has 5 spokes. How many spokes are there altogether?
Correct answer: 16 × (2 × 5) =
16 × 2 × 5 =
5 × 16 × 2 =
Q6.
Jun and his 3 friends went to the ice cream van. He buys them each an ice cream with 3 scoops. One scoop costs 25 p. How much money did Jun spend altogether? p
Correct Answer: 300, 300 p, 300 pence