Checking and securing understanding of the commutative and associative laws | Maths

Starter quiz

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

Division

Multiplication ✓

Addition

Subtraction
Match each multiplication to its answer.

$9\times3$

⇔

$27$ ✓

$8\times6$

⇔

$48$ ✓

$7\times9$

⇔

$63$ ✓

$6\times7$

⇔

$42$ ✓
Work out the missing number: 7 × ______ = 7000

'1000' ✓
Select all the correct statements.

8 + 4 is equal to 4 + 8 ✓

8 − 4 is the same 4 − 8

8 × 4 is equal to 4 × 8 ✓

8 ÷ 4 is equal to 4 ÷ 8
Without using a calculator, work out: 168 + 235 − 149 = ______

'254' ✓
Without using a calculator, work out: 23 × 15 = ______

'345' ✓

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

using division and subtraction only

in either order without changing the calculation ✓

left to right only
Select all the examples of the associative law.

3 + 4 = 4 + 3

2 × 7 × 10 = (2 × 7) × 10 ✓

11 − 10 = 10 − 11

5 + (2 + 4) = (5 + 2) + 4 ✓

(7 + 5) + 5 = 7 + (5 + 5) ✓
Find the missing number in this equation. 3 × (4 × 5) = (3 × ______) × 5

'4' ✓
Match each calculation to an equivalent commutative calculation.

$2 + 3$

⇔

$3 + 2$ ✓

$2\times3$

⇔

$3\times2$ ✓

$A + 2 + 3$

⇔

$2 + 3 + A$ ✓
Laura says, "Division is commutative because $2\div1$ is the same as $1\div2$ ." Select the correct statement.

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

'210' ✓

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Division is commutative given some divisions can give the same answer. eg. 8000/4/2 = 8000/2/4

To check for all rearrangements of the number e.g. 2/4/8000 does not equal 8000/4/2

Commutative law - An operation is commutative if the values it is operating on can be written in either order without changing the calculation
Associative law - An operation is associative if a repeated application of an operation produces the same result regardless of how pairs of values are grouped