New
New
Year 5

Use properties of numbers and the commutative and associative laws to simplify calculations

I can use properties of numbers and the commutative and associative laws to simplify calculations.

New
New
Year 5

Use properties of numbers and the commutative and associative laws to simplify calculations

I can use properties of numbers and the commutative and associative laws to simplify calculations.

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Lesson details

Key learning points

1. By rearranging a calculation it can be made easier to solve mentally

Common misconception

Pupils may struggle to find factors of a number if they do not have automatic recall of their times tables.

Provide children with a multiplication grid to help pupils understand the process of the calculations, however ensure additional support is in place for children to build towards automatic recall of times tables.

Keywords

• Factor - Factors are whole numbers which exactly divide another whole number.

• 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.

• 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.

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).

Starter quiz

6 Questions

Q1.
Tick the factors of 20
3
15
Q2.
The commutative law states that:
You must start multiplying with the first factor in an equation.
Correct answer: You can reorder the factors in an equation and the product will remain the same.
You can reorder the factors in an equation but the product will change.
Q3.
If a pair of brackets are placed around two factors such as in 2 × (4 × 7) = , this means:
Correct answer: You should multiply these factors first.
You should multiply these factors last.
You do not need to multiply these factors.
Q4.
Match the equation to the factor pairs that would be best used to help solve the calculations.
Correct Answer:25 × 36 = ___,4 and 9

4 and 9

Correct Answer:28 × 50 = ___,2 and 14

2 and 14

Correct Answer:20 × 65 = ___,5 and 13

5 and 13

Q5.
Find the product of this equation.
Correct Answer: 300, three hundred, 3 hundred
Q6.
Find the product of this equation. 50 × 54 =

Exit quiz

6 Questions

Q1.
Which factors would be best to associate together to calculate efficiently? 4 × 5 × 7 = ___
5 and 7
7 and 4
Q2.
Tick the three factor equations that would be equal to this two factor equation. 15 × 20 = ___ × ___ × ___
Correct answer: 15 × 4 × 5
15 × 3 × 5
Correct answer: 3 × 5 × 20
Correct answer: 15 × 2 × 10
Q3.
Tick the numbers that could be multiplied by a one digit number and would be equal to a multiple of 10.
9
Q4.
Find the product of this equation.
Correct Answer: 900, 9 hundred, nine hundred
Q5.
Match the 4 factor equations that are equal to the two factor equations.
Correct Answer:4 × 4 × 3 × 5,16 × 15

16 × 15

Correct Answer:3 × 6 × 4 × 6,18 × 24

18 × 24

Correct Answer:2 × 6 × 3 × 7,21 × 12

21 × 12

Correct Answer:4 × 11 × 3 × 5,33 × 20

33 × 20

Q6.
Find the product of this equation. 32 × 15 =