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

An operation is associative if a repeated application of an operation produces the same result regardless of how pairs of values are grouped

Checking and securing understanding of the commutative and associative laws

Maths

Pupils use their understanding of place value and fluency with decimals from this unit in order to extend this understanding to fractions.  In the future unit, pupils will be asked to compare and order both fractions and decimals and will assess when conversion is required.

The prior unit on factors, multiples, squares and cubes helped pupils build on their understanding that any positive integer can be expressed as a product of its factors. This skill is used here to explore multiplying and dividing with decimals.

Arithmetic procedures with integers and decimals

in either order without changing the calculation

Select the correct statement. The commutative law states that the values it is operating on can be written __________.

Select all the examples of the associative law.

Find the missing number in this equation. 3 × (4 × 5) = (3 × {{ }}) × 5

Match each calculation to an equivalent commutative calculation.

She is correct. They both equal the same answer, 2

She is incorrect because $$ 2\div1 =2$$  and $$ 1\div2 $$ = $${1} \over {2}$$

She is correct because both calculations use division.

Laura says, "Division is commutative because $$ 2\div1 $$  is the same as $$ 1\div2 $$." Select the correct statement.

Without using a calculator, use the associative and commutative law to work out the sum the first 20 integers. The sum is {{ }}

Which operation is the mathematical operation of scaling one number by another?

Work out the missing number:  7 × {{ }} = 7000

Without using a calculator, work out: 168 + 235 − 149 = {{ }}

Without using a calculator, work out: 23 × 15 = {{ }}

This lesson will be removed by end of Summer Term 2025.

Checking and securing understanding of the commutative and associative laws

Lesson outcome

This lesson will be removed by end of Summer Term 2025.