New
New
Year 5

Apply the commutative and associative laws to simplify volume calculations

I can apply the commutative and associative laws to simplify volume calculations.

New
New
Year 5

Apply the commutative and associative laws to simplify volume calculations

I can apply the commutative and associative laws to simplify volume calculations.

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Lesson details

Key learning points

  1. To simplify a multiplication calculation, you can change the order of the factors.
  2. To simplify a multiplication calculation you can group the factors in different ways.

Common misconception

Pupils struggle to understand that a 3 factor calculation problem with two unknown factors can be represented as a 2 factor calculation with one unknown factor.

Spend time manipulating 2 factor calculations into 3 factors and vice versa. Once pupils are confident with this, apply this to a context where the numbers are kept simple to support pupils to see the structure of the problems.

Keywords

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

  • 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.

  • 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.

Encourage pupils to roughly represent missing volume problems by teaching them to draw cuboids in two dimensions. This may support pupils to consider how the problem can be expressed as an equation once they have jotted on the known dimensions.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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6 Questions

Q1.
What number is represented by the factor bug?
An image in a quiz
Correct Answer: 36
Q2.
50 x 8 =
Correct Answer: 400
Q3.
Tick all the factors of 28
3
Correct answer: 4
6
Correct answer: 7
Correct answer: 14
Q4.
What is the missing factor of 72 from this list? 1, 2, 3, 4, 6, 8, 9, 18, 24, 36, and 72
Correct Answer: 12
Q5.
Put these calculations in order from lowest to highest.
1 - 12 × 10 × 1
2 - 2 × 14 × 5
3 - 16 × (5 × 2)
4 - 9 × (4 × 5)
Q6.
What is the most efficient calculation for 86 × 5?
80 × 6 × 5
(43 × 2) × 5
Correct answer: 43 × (2 × 5)
2 × (43 × 5)

6 Questions

Q1.
The box is 40 cm long, 10 cm wide and 2 cm deep. What is the volume of the box? cm$$^3$$
An image in a quiz
Correct Answer: 800, 800cm, 800cm3
Q2.
Whose box has the greatest volume?
An image in a quiz
Lucas whose box is 30 cm long.
Correct answer: Sam whose box is 36 cm long.
Q3.
Which box has a volume of 60 m$$^3$$?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q4.
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
Correct Answer: 7, 7 cm
Q5.
The volume of a warehouse is 216 m$$^3$$. The height is 6 m. What could the length and width be?
7 m and 6 m
Correct answer: 9 m and 4 m
9 m and 3 m
Correct answer: 18 m and 2 m
Q6.
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?
Correct answer: 12 cm and 3 cm
8 cm and 6 cm
Correct answer: 9 cm and 4 cm