Apply commutative and associative laws to simplify multiplications | Maths

Starter quiz

What is the product of 7 and 9?

'63' ✓
What does the number 6 represent in the image below? 3 × 2 × 6

The number of rows.

The number of columns.

The number of trays. ✓
What is the missing number in the expression? 4 × ______ × 2 Use the image to help.

'3' ✓
Look at the equation. Which two numbers would you multiply together first? 2 × (7 × 4)

4 and 2

7 and 4 ✓

7 and 2
Which equations could you use to work out the total number of cubes?

4 × (5 × 3) ✓

(4 × 5) × 3 ✓

(3 × 5) × 3

(5 × 4) × 3 ✓
Match the expressions that are equal.

(20 × 4) × 8

⇔

80 × 8 ✓

3 × (4 × 1)

⇔

3 × 4 ✓

(2 × 5) × 8

⇔

10 × 8 ✓

(4 × 3) × 3

⇔

12 × 3 ✓

Exit quiz

Which is the most efficient method?

14 × 5 × 2 =

14 × (5 × 2) = ✓

5 × 14 × 2 =
Which equation is easiest to calculate?

51 × 25 × 4 =

4 × (51 × 25) =

51 × (4 × 25) = ✓
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.

True ✓
False
Which of these make 27 × 5 × 20 = easier to solve?

(27 × 5) × 20 =

20 × 27 × 5 =

27 × (5 × 20) = ✓
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?

16 × (2 × 5) = ✓

16 × 2 × 5 =

5 × 16 × 2 =
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

'300' ✓

Worksheet

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Lesson Details

Key learning points

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.