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Year 5

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

I can explain the relationship between repeated addition of fractions and multiplication of fractions.

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New

Year 5

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

I can explain the relationship between repeated addition of fractions and multiplication of fractions.

Download all resources

Share activities with pupils

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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 __'

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.

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 ___ _________.

It is vital that pupils can make the shift from seeing multiples of a unit fraction to a unit comprised of a non-unit fraction. For example: moving from three, one-ninths to one lot of three-ninths. This will help pupils work more flexibly with calculations and link to their work on multiplication.

Teacher tip

Licence

This content is © Oak National Academy Limited (2025), 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 unit fraction this image represents.

$$ \frac{1}{6} $$

$$ \frac{1}{7} $$

Correct answer: $$ \frac{1}{8} $$

$$ \frac{1}{9} $$

$$ \frac{1}{10} $$

Q2.

The whole has been divided into 5 equal parts. Each part represents one .

Correct Answer: fifth

Q3.

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

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

Correct answer: $$ \frac{1}{4} $$ × 3

Correct answer: 3 × $$ \frac{1}{4} $$

$$ \frac{1}{4} $$ × $$ \frac{1}{4} $$

Q4.

2 × $$ \frac{1}{5} $$ is equal to:

Correct answer: $$ \frac{1}{5} $$ + $$ \frac{1}{5} $$

Correct answer: $$ \frac{1}{5} $$ × 2

5 × 2

$$ \frac{1}{5} $$ × $$ \frac{1}{5} $$

Q5.

Which expressions would match this image?

Correct answer: $$ \frac{1}{4} $$ + $$ \frac{1}{4} $$

Correct answer: $$ \frac{1}{4} $$ × 2

Correct answer: 2 × $$ \frac{1}{4} $$

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

$$ \frac{1}{5} $$ × 2

Q6.

Match the multiplicative expression to the additive expression.

Correct Answer:3 × $$ \frac{1}{7} $$,$$ \frac{1}{7} $$ + $$ \frac{1}{7} $$ + $$ \frac{1}{7} $$

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

Correct Answer:$$ \frac{1}{3} $$ × 2,$$ \frac{1}{3} $$ + $$ \frac{1}{3} $$

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

Correct Answer:2 × $$ \frac{1}{8} $$,$$ \frac{1}{8} $$ + $$ \frac{1}{8} $$

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

Correct Answer:3 × $$ \frac{1}{8} $$,$$ \frac{1}{8} $$ + $$ \frac{1}{8} $$ + $$ \frac{1}{8} $$

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

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6 Questions

Q1.

This counter represents one-

Correct Answer: seventh

Q2.

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

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

$$ \frac{1}{4} $$ × 7

Correct answer: 4 × $$ \frac{1}{7} $$

Correct answer: $$ \frac{1}{7} $$ × 4

Q3.

$$ \frac{3}{7} $$ + $$ \frac{3}{7} $$ is equal to:

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

Correct answer: $$ \frac{3}{7} $$ × 2

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

Correct answer: 2 × $$ \frac{3}{7} $$

Q4.

If each slice represents one seventh of the cake, tick the expressions that the image represents.

$$ \frac{1}{5} $$ × 2

$$ \frac{5}{7} $$ × 5

Correct answer: $$ \frac{5}{7} $$ × 2

Correct answer: 2 × $$ \frac{5}{7} $$

Q5.

Which expression represents this image?

$$ \frac{1}{6} $$ × 2

Correct answer: $$ \frac{3}{6} $$ × 2

$$ \frac{2}{6} $$ × 3

Correct answer: 2 × $$ \frac{3}{6} $$

Q6.

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

Correct Answer: An image in a quiz