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Year 5

Explain when a calculation represents scaling down and when it represents repeated addition

I can explain when a calculation represents scaling down and when it represents repeated addition

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New
New
Year 5

Explain when a calculation represents scaling down and when it represents repeated addition

I can explain when a calculation represents scaling down and when it represents repeated addition

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. A calculation can represent scaling down or finding a fraction of the whole number.
  2. A calculation can represent repeated addition or finding lots of the fraction.
  3. Multiplication is commutative so the product will be the same.

Common misconception

Pupils divide by the denominator and then multiply by the numerator without any conceptual understanding for why this works.

Ensure pupils spend time exploring how dividing and multiplying by either the numerator or denominator works in relation to a scaling or repeated addition strategy. Encourage pupils to reason when they would use one strategy over the other.

Keywords

  • Scaling - Scaling is when something is transformed, through either shrinking or enlarging by a scale factor.

  • Repeated addition - Repeated addition is when the same object or value is added to itself more than once.

  • Numerator - The numerator is the number on the top of a fraction. It tells us how many parts we have/need.

  • Denominator - The denominator is the number on the bottom of a fraction. It tells us how many parts the whole has been divided into.

Provide time for pupils to explore both strategies in depth and apply these to finding a non-unit fraction of a larger amount once pupils are secure with the structures.
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).

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Starter quiz

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6 Questions

Q1.
Tick the equations that could represent this expression: 7 + 7 + 7
Correct answer: 7 × 3
5 + 7
Correct answer: 3 × 7
3 + 7
Q2.
Tick the expressions that represent this image.
An image in a quiz
Correct answer: $$ \frac{2}{5} $$ × 30
Correct answer: 30 × $$ \frac{2}{5} $$
30 × 6
Correct answer: 30 ÷ 5
Q3.
Tick the equation that represent this image.
An image in a quiz
$$ \frac{1}{3} $$ × 8 = 24
Correct answer: 24 × $$ \frac{1}{3} $$ = 8
$$ \frac{1}{8} $$ × 3 = 24
$$ \frac{1}{8} $$ × 24 = 3
Q4.
Tick the statements that are true.
An image in a quiz
24 is one-quarter times the size of 6
6 is 4 times the size of 24
Correct answer: 24 is 4 times the size of 6
Correct answer: 6 is one-quarter times the size of 24
Q5.
Write in the missing number for this equation. $$ \frac{3}{5} $$ × 20 =
An image in a quiz
Correct Answer: 12, twelve
Q6.
Calculate $$ \frac{4}{5} $$ × 20 =
Correct Answer: 16

Exit quiz

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6 Questions

Q1.
Look at the equation. Complete the sentence with an appropriate word: The product will be than the whole number.
An image in a quiz
Correct Answer: smaller, less, lesser
Q2.
Tick the descriptions that could best match this bar model.
An image in a quiz
Correct answer: There are 4 lots of two-thirds
Correct answer: Two-thirds times 4
Correct answer: Two-thirds, four times
Two thirds divided by 4
Q3.
Tick the expressions best solved using a scaling strategy.
Correct answer: $$ \frac{4}{5} $$ × 20
$$ \frac{4}{5} $$ × 22
$$ \frac{4}{5} $$ × 24
Correct answer: $$ \frac{4}{5} $$ × 25
Q4.
Tick the expressions best solved using a repeated addition strategy.
Correct answer: $$ \frac{2}{3} $$ × 10
$$ \frac{2}{3} $$ × 9
Correct answer: $$ \frac{2}{3} $$ × 11
$$ \frac{2}{3} $$ × 12
Q5.
Calculate $$ \frac{3}{7} $$ × 21 =
Correct Answer: 9
Q6.
Calculate $$ \frac{2}{5} $$ × 15 =
Correct Answer: 6