Working efficiently means finding a way to solve a problem quickly whilst also maintaining accuracy.

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.

Apply commutative and associative laws to simplify multiplications

Maths

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

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)

Aisha has used associative law to make 36 × 50 × 2  =  into  36 × (50 × 2) =  True or false: Aisha has made the calculation easier to solve.

(27 × 5) × 20 =                            

Which of these make 27 × 5 × 20  =  easier to solve? 

Which equation is most efficient? There were 16 bikes in a shed. Each bike has 2 wheels and each wheel has 5 spokes. How many spokes are there altogether?

Jun and his 3 friends went to the ice cream van. He buys them each an ice cream with 3 scoops. One scoop costs 25 p. How much money did Jun spend altogether?  {{ }} p

What does the  number 6 represent in the image below?  3 × 2 × 6

What is the missing number in the expression? 4 × {{ }} × 2 Use the image to help.

Look at the equation. Which two numbers would you multiply together first?  2 × (7 × 4)

Which equations could you use to work out the total number of cubes?

Apply commutative and associative laws to simplify multiplications

Lesson outcome