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.

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.

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

Maths

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.

Multiply 3 or more numbers (commutative and associative laws)

Which image matches this expression?    2 × (3 × 4)

A gardener is planting seeds to grow some leeks. She uses 5 of the pictured trays to plant the seeds. In each tray cell, she plants 4 seeds. How many leeks could she grow altogether? 

Jacob spends 25 minutes a day reading. He does this for all 30 days in April. How many minutes did Jacob read for in April? Which calculation gives the correct answer?

Cupcakes are baked on 6 of these trays. Each cupcake is sold for £3.00  If all the cupcakes sell. How much money will be made? £{{ }}

What could the missing factors be? ___ × ___ × 30 = 360

___ × ___ × 2 = 168  Tick all the other numbers that could be the other factors.

How many factors does the number 14 have?

Complete the sentence. If a box is 36 cm long, 4 cm wide and 3 cm deep then it has a volume of {{ }} m$$^3$$. 

A box of rice has a length of 10 cm. The volume of the pack is 720 cm$$^3$$. What could the width and height of the box be?

The volume of a drawer is  240 cm$$^3$$. The height is 6 cm. What could the length and width be?

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