Explain the use of the commutative and associative laws when multiplying three or more numbers | Maths

Starter quiz

What multiplication fact does this array represent?
- 5 x 7 = 35 ✓
- 6 x 7 = 42
- 5 x 6 = 30
- 7 x 5 = 35 ✓
What are the factors shown by this array?
- 7 and 6
- 6 and 5 ✓
- 6 and 30
- 30 and 5
Which of these are correct arrays for 36?
- A ✓
- B
- C
- D ✓
Complete the missing factor: 7 × ______ = 56
- '8' ✓
Which of these are not factors of 40?
- 5
- 10
- 4
- 9 ✓
- 3 ✓
Which factor is missing from the factor bug?
- '3' ✓

Exit quiz

Look at the image. What does the number 3 represent in this expression? 2 × 3 × 4
- The number of columns in each tray. ✓
- The number of rows in each tray.
- The number of trays.
One layer has three rows and four columns. There are two layers. What does the 3 represent?
- The number of columns in a layer.
- The number of layers.
- The number of rows in a layer ✓
Select the equation that most accurately matches this representation.
- 3 x 4 x 5
- 4 x 3 x 5 ✓
- 5 x 3 x 4
Select the missing equation?
- 4 x 5 x 3
- 5 x 3 x 4 ✓
- 3 x 3 x 5
- 3 x 5 x 4
Look at the equation. Which two numbers would you multiply together first? 3 × (4 × 6)
- 3 and 4
- 3 and 6
- 4 and 6 ✓
Match the statements.
- This is known as the associative law.
  
  ⇔
  
  Multiply different pairs of factors & the product will stay the same. ✓
- This is known as the commutative law.
  
  ⇔
  
  Changing the order of the factors, the product remains the same. ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

You can change the order of the factors or group them in different ways and the product remains the same.

Common misconception

Pupils only ever calculate an equation from left to right.

Ensure pupils are given time to explore where the commutative law might be best used and where the associative law might be better used. Pupils should be expected to reason why they have chosen to adopt a strategy.

Keywords

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.