The commutative law states that you can write the values of a calculation in a different order without changing the solution; the result is the same. It applies to addition and multiplication.

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 to addition and multiplication.

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

Maths

Apply commutative and associative laws to simplify multiplications

Explain the reasons for changing two-factor multiplication calculations to three-factor calculations

Apply the commutative and associative laws to simplify volume calculations

Apply the commutative and associative laws to simplify problems in a range of contexts

In this unit pupils will explain the use of the commutative and associative laws when multiplying three or more numbers. In the future unit pupils will explain reasons for changing 2-factor multiplication calculations to 3-factor multiplications explaining what a factor is and how to use arrays and multiplication/division facts to find them. They will identify prime numbers and composite numbers.

 In the prior unit pupils explained volume using a range of contexts and described the units used to measure volume. They explained how to calculate the volume of a cuboid and explained what a cube number is. In this unit pupils will explain the use of the commutative and associative laws when multiplying three or more numbers.

In this unit pupils will explain the use of the commutative and associative laws to rearrange and simplify calculations when multiplying three or more numbers.

Multiply 3 or more numbers (commutative and associative laws)

Look at the image. What does the number 3 represent in this expression? 2 × 3 × 4

One layer has three rows and four columns. There are two layers.  What does the 3 represent?

Select the equation that most accurately matches this representation.

Look at the equation. Which two numbers would you multiply together first?    3 × (4 × 6)

Multiply different pairs of factors & the product will stay the same.

Changing the order of the factors, the product remains the same. 

What multiplication fact does this array represent?

What are the factors shown by this array?

Which of these are correct arrays for 36?

Complete the missing factor:    7 × {{ }} = 56 

Which factor is missing from the factor bug?

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

Lesson outcome