To represent something is to show it in a different way.

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 volume calculations

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)

The box is 40 cm long, 10 cm wide and 2 cm deep. What is the volume of the box? {{ }} cm$$^3$$

The volume of a cuboid is 105 cm$$^3$$. The height is 5 cm and width is 3 cm.  What must the missing length be? {{ }} cm

The volume of a warehouse is 216 m$$^3$$. The height is 6 m.  What could the length and width be?

A box of tissues has a length of 25 cm. The volume of the pack is 900 cm$$^3$$. What could the width and height of the box be?

What number is represented by the factor bug?

What is the missing factor of 72 from this list?   1, 2, 3, 4, 6, 8, 9, 18, 24, 36, and 72

Put these calculations in order from lowest to highest.

What is the most efficient calculation for 86 × 5?

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