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

Starter quiz

Tick the equations that could represent this expression: 7 + 7 + 7
- 7 × 3 ✓
- 5 + 7
- 3 × 7 ✓
- 3 + 7
Tick the expressions that represent this image.
- $\frac{2}{5}$ × 30 ✓
- 30 × $\frac{2}{5}$ ✓
- 30 × 6
- 30 ÷ 5 ✓
Tick the equation that represent this image.
- $\frac{1}{3}$ × 8 = 24
- 24 × $\frac{1}{3}$ = 8 ✓
- $\frac{1}{8}$ × 3 = 24
- $\frac{1}{8}$ × 24 = 3
Tick the statements that are true.
- 24 is one-quarter times the size of 6
- 6 is 4 times the size of 24
- 24 is 4 times the size of 6 ✓
- 6 is one-quarter times the size of 24 ✓
$Write in the missing number for this equation. <Math> \frac{3}{5} </Math> × 20 = <span class="blank">______</span>$

Write in the missing number for this equation. $\frac{3}{5}$ × 20 = ______
- '12' ✓
Calculate $\frac{4}{5}$ × 20 = ______
- '16' ✓

Exit quiz

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

Worksheet

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Presentation

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Lesson Details

Key learning points

A calculation can represent scaling down or finding a fraction of the whole number.
A calculation can represent repeated addition or finding lots of the fraction.
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.