Explain the relationship between repeated addition of fractions and multiplication of fractions | Maths

Starter quiz

$Tick the unit fraction this image represents.$

Tick the unit fraction this image represents.

$\frac{1}{6}$

$\frac{1}{7}$

$\frac{1}{8}$ ✓

$\frac{1}{9}$

$\frac{1}{10}$
The whole has been divided into 5 equal parts. Each part represents one ______.

'fifth' ✓
$\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{1}{4}$ is equal to:

$\frac{1}{4}$ + 3

$\frac{1}{4}$ × 3 ✓

3 × $\frac{1}{4}$ ✓

$\frac{1}{4}$ × $\frac{1}{4}$
2 × $\frac{1}{5}$ is equal to:

$\frac{1}{5}$ + $\frac{1}{5}$ ✓

$\frac{1}{5}$ × 2 ✓

5 × 2

$\frac{1}{5}$ × $\frac{1}{5}$
Which expressions would match this image?

$\frac{1}{4}$ + $\frac{1}{4}$ ✓

$\frac{1}{4}$ × 2 ✓

2 × $\frac{1}{4}$ ✓

$\frac{1}{5}$ + $\frac{1}{5}$

$\frac{1}{5}$ × 2
Match the multiplicative expression to the additive expression.

3 × $\frac{1}{7}$

⇔

$\frac{1}{7}$ + $\frac{1}{7}$ + $\frac{1}{7}$ ✓

$\frac{1}{3}$ × 2

⇔

$\frac{1}{3}$ + $\frac{1}{3}$ ✓

2 × $\frac{1}{8}$

⇔

$\frac{1}{8}$ + $\frac{1}{8}$ ✓

3 × $\frac{1}{8}$

⇔

$\frac{1}{8}$ + $\frac{1}{8}$ + $\frac{1}{8}$ ✓

Exit quiz

This counter represents one- ______

'seventh' ✓
$\frac{1}{7}$ + $\frac{1}{7}$ + $\frac{1}{7}$ + $\frac{1}{7}$ is equal to:

$\frac{1}{7}$ + 4

$\frac{1}{4}$ × 7

4 × $\frac{1}{7}$ ✓

$\frac{1}{7}$ × 4 ✓
$\frac{3}{7}$ + $\frac{3}{7}$ is equal to:

$\frac{3}{7}$ + 3

$\frac{3}{7}$ × 2 ✓

$\frac{3}{7}$ + 7

2 × $\frac{3}{7}$ ✓
If each slice represents one seventh of the cake, tick the expressions that the image represents.

$\frac{1}{5}$ × 2

$\frac{5}{7}$ × 5

$\frac{5}{7}$ × 2 ✓

2 × $\frac{5}{7}$ ✓
Which expression represents this image?

$\frac{1}{6}$ × 2

$\frac{3}{6}$ × 2 ✓

$\frac{2}{6}$ × 3

2 × $\frac{3}{6}$ ✓
Which image matches the expression $\frac{4}{5}$ × 3

Worksheet

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Lesson Details

Key learning points

Multiplication can be represented as repeated addition
Use the language of unitising '__ groups of __ is equal to __'

Common misconception

Pupils struggle to group items to form unitised groups.

Ensure time is spent labelling items in relation to the whole then move to grouping these items. Use the sentence stem: There are ___ lots of ___ _________. This is equal to ___ _________.

Keywords

Unit fraction - A unit fraction is a fraction where the numerator is 1
Unitise - Unitising means treating groups that contain or represent the same number of things as units or ones.
Non-unit fraction - A non-unit fraction is a fraction where the numerator is greater than 1
Represent - To represent something is to show it in a different way.