New
New
Year 6

Explain when it is efficient to use factorising or long multiplication to multiply by 2-digits

I can explain when it is efficient to use factorising or long multiplication to multiply by 2-digit numbers.

New
New
Year 6

Explain when it is efficient to use factorising or long multiplication to multiply by 2-digits

I can explain when it is efficient to use factorising or long multiplication to multiply by 2-digit numbers.

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Lesson details

Key learning points

  1. Multiplication can be simplified by factorising one of the factors.
  2. If the multiplication will involve regrouping then a written method may be more efficient.
  3. If the multiplication will not involve regrouping then a mental or informal method may be more efficient.

Keywords

  • Associative law - 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.

  • Efficient / efficiently - Working efficiently means finding a way to solve a problem quickly whilst also maintaining accuracy.

Common misconception

Pupils can 'default' to using a written algorithm when learned regardless of the values of the calculation.

Consider using confident mathematicians in a race to show efficiency of different methods. Encourage pupils to 'interrogate' the values of the calculation in order to identify more efficient approaches.

Part of this lesson involves identification of prime numbers. Consider how confident your pupils are when reasoning about whether 2-digit numbers are prime or not and how you may support them to do this.
Teacher tip

Equipment

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).

Lesson video

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6 Questions

Q1.
Select the prime numbers.
27
Correct answer: 47
Correct answer: 53
Correct answer: 59
65
Q2.
Select the factor pairs of 30
1 and 29
Correct answer: 2 and 15
Correct answer: 3 and 10
10 and 4
Correct answer: 5 and 6
Q3.
Look at the numbers below and select the composite numbers.
23
Correct answer: 25
Correct answer: 69
89
97
Q4.
Select the equivalent expressions which would make this equation correct. 36 × 24 =
36 × 1 × 23
Correct answer: 36 × 12 × 2
36 × 12 × 12
Correct answer: 36 × 6 × 4
Q5.
Find the expressions that are equivalent to 35 × 4 × 8
Correct answer: 7 × 32 × 5
32 × 8 × 5
Correct answer: 7 × 5 × 32
Correct answer: 35 × 32
Q6.
Look at the equation. Find the missing number. 42 × 49 = 42 × 7 ×
Correct Answer: 7

6 Questions

Q1.
Select equivalent expressions to 21 × 30
Correct answer: 21 × 5 × 6
Correct answer: 21 × 6 × 5
30 × 7 × 4
Correct answer: 30 × 7 × 3
30 × 3 × 8
Q2.
Which method is more efficient to solve 47 × 16 = ?
Long multiplication algorithm
Correct answer: Multiplying by factors
Q3.
Which method is more efficient to solve 132 × 15 = ?
Long multiplication algorithm
Multiplying by factors
Correct answer: Partitioning 15 into 10 and 5
Q4.
Which factorised example would be most efficient to solve 36 × 12?
36 × 1 × 12
Correct answer: 36 × 6 × 2
Q5.
Use an efficient method to solve: The Olympic event is selling tickets. Each ticket costs £32 and 29 tickets are sold in the first five minutes. What is the total amount spent? £
Correct Answer: 928, 928.00
Q6.
Use an efficient method to solve: 407 × 15 =
Correct Answer: 6,105

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