Use repeated addition of a unit fraction to form a non-unit fraction | Maths

Starter quiz

Which of these definitions describes a unit fraction?
- The numerator is 1 ✓
- The numerator is greater than 1
- The numerator and the denominator are equal.
Which of these definitions describes a non-unit fraction?
- The numerator is 1
- The numerator is greater than 1 ✓
- The numerator and the denominator are equal.
Which of these are unit fractions?
- $\frac{1}{3}$ ✓
- $\frac{1}{4}$ ✓
- $\frac{3}{4}$
- $\frac{2}{5}$
Which of these are non-unit fractions?
- $\frac{3}{4}$ ✓
- $\frac{1}{7}$
- $\frac{1}{4}$
- $\frac{6}{12}$ ✓
$What unit fraction is represented here?$

What unit fraction is represented here?
- $\frac{5}{6}$
- $\frac{1}{7}$
- $\frac{1}{6}$ ✓
- $\frac{1}{5}$
$What non-unit fraction is represented here?$

What non-unit fraction is represented here?
- $\frac{2}{6}$ ✓
- $\frac{2}{7}$
- $\frac{2}{5}$
- $\frac{1}{4}$

Exit quiz

$Look at the picture. What non-unit fraction is being represented by the green triangles here?$

Look at the picture. What non-unit fraction is being represented by the green triangles here?
- $\frac{3}{6}$ ✓
- $\frac{3}{7}$
- $\frac{3}{5}$
- $\frac{3}{4}$
Match the counting labels.
- one one-sixth
  
  ⇔
  
  one-sixth ✓
- two one-sixths
  
  ⇔
  
  two-sixths ✓
- three one-sixths
  
  ⇔
  
  three-sixths ✓
What is missing from the counting label?
- one-sixth ✓
- sixth
- one-fifth
- fifth
What is the missing counting label here?
- One more one-quarter
- Another one-quarter
- Two one-quarters ✓
$Which repeated addition equations represent the non-unit fraction shown here?$

Which repeated addition equations represent the non-unit fraction shown here?
- $\frac{1}{5}$ + $\frac{1}{5}$ = $\frac{2}{5}$ ✓
- $\frac{1}{6}$ + $\frac{1}{6}$ = $\frac{2}{6}$
- $\frac{1}{5}$ + $\frac{1}{4}$ = $\frac{2}{3}$
- $\frac{2}{5}$ = $\frac{1}{5}$ + $\frac{1}{5}$
$Which repeated addition equation represents the fraction of pandas wearing hats here?$

Which repeated addition equation represents the fraction of pandas wearing hats here?
- $\frac{2}{3}$ + $\frac{2}{3}$ = $\frac{1}{3}$
- $\frac{1}{3}$ + $\frac{2}{3}$ = $\frac{2}{3}$
- $\frac{3}{1}$ + $\frac{3}{1}$ = $\frac{2}{3}$
- $\frac{1}{3}$ + $\frac{1}{3}$ = $\frac{2}{3}$ ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

Non-unit fractions are composed from unit fractions.
Repeated addition of unit fractions forms non-unit fractions.
A number line represents the repeated addition of unit fractions.

Common misconception

Children may develop the misconception that unit fractions must be adjacent to be part of a repeated addition.

When using a number line, match it with another representation where possible in which the unit fractions aren't adjacent so children see that it is about the quantity of unit fractions rather than their position.

Keywords

Unit fraction - A unit fraction is a fraction where the numerator is 1
Non-unit fraction - A non-unit fraction is a fraction where the numerator is greater than 1
Denominator - A denominator is the bottom number in a fraction. It shows how many parts a whole has been divided into.
Numerator - A numerator is the top number in a fraction. It shows how many parts we have.