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