New
New
Year 5

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

I can apply the commutative and associative laws to simplify problems in a range of contexts.

New
New
Year 5

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

I can apply the commutative and associative laws to simplify problems in a range of contexts.

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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 solve unknown factor calculations where the volume is known.

Ensure pupils record missing factor problems as a multiplication equation. You may choose to build up the number of missing factors from one to two. You may also choose to build up from a missing factor in a 2 factor equation to a 3 factor equation.

Keywords

  • 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 represent each problem using either cubes or drawings to show where the numbers from each problem come from and how this impacts upon the calculation.
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.
Tick the factors of 84.
Correct answer: 1
Correct answer: 2
Correct answer: 4
8
10
Q2.
How many factors does the number 14 have?
Correct Answer: 4
Q3.
Complete the sentence. If a box is 36 cm long, 4 cm wide and 3 cm deep then it has a volume of m$$^3$$.
Correct Answer: 432
Q4.
Which box has the greatest volume?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q5.
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?
70 cm and 2 cm
Correct answer: 6 cm and 12 cm
Correct answer: 8 cm and 9 cm
10 cm and 72 cm
Q6.
The volume of a drawer is 240 cm$$^3$$. The height is 6 cm. What could the length and width be?
Correct answer: 4 and 10
24 and 10
Correct answer: 2 and 20
Correct answer: 8 and 5

6 Questions

Q1.
Which image matches this expression? 2 × (3 × 4)
An image in a quiz
A
Correct answer: B
C
Q2.
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?
An image in a quiz
Correct Answer: 80, eighty
Q3.
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?
Correct answer: 30 × 5 × 5 =
3 × 5 × 5 =
25 × 5 × 5 =
Correct answer: 25 × 6 × 5 =
Q4.
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? £
An image in a quiz
Correct Answer: 216, 216.00
Q5.
What could the missing factors be? ___ × ___ × 30 = 360
3 and 5
Correct answer: 3 and 4
Correct answer: 6 and 2
4 and 4
Q6.
___ × ___ × 2 = 168 Tick all the other numbers that could be the other factors.
Correct answer: 3
5
Correct answer: 6
Correct answer: 12
Correct answer: 14