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

      I can use repeated addition of a unit fraction to form a non-unit fraction.

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      Lesson 1 of 10
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      • Year 3

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

      I can use repeated addition of a unit fraction to form a non-unit fraction.

      Lesson details

      Key learning points

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

      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.

      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.

      Counting together is a great way of learning here. Call and response or turn taking can really help to deepen children's understanding.
      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).

      Lesson video

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      Prior knowledge starter quiz

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      6 Questions

      Q1.
      Which of these definitions describes a unit fraction?

      Correct answer: The numerator is 1
      The numerator is greater than 1
      The numerator and the denominator are equal.

      Q2.
      Which of these definitions describes a non-unit fraction?

      The numerator is 1
      Correct answer: The numerator is greater than 1
      The numerator and the denominator are equal.

      Q3.
      Which of these are unit fractions?

      Correct answer: $$ \frac{1}{3} $$
      Correct answer: $$ \frac{1}{4} $$
      $$ \frac{3}{4} $$
      $$ \frac{2}{5} $$

      Q4.
      Which of these are non-unit fractions?

      Correct answer: $$ \frac{3}{4} $$
      $$ \frac{1}{7} $$
      $$ \frac{1}{4} $$
      Correct answer: $$ \frac{6}{12} $$

      Q5.
      What unit fraction is represented here?

      An image in a quiz
      $$ \frac{5}{6} $$
      $$ \frac{1}{7} $$
      Correct answer: $$ \frac{1}{6} $$
      $$ \frac{1}{5} $$

      Q6.
      What non-unit fraction is represented here?

      An image in a quiz
      Correct answer: $$ \frac{2}{6} $$
      $$ \frac{2}{7} $$
      $$ \frac{2}{5} $$
      $$ \frac{1}{4} $$

      Assessment exit quiz

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      6 Questions

      Q1.
      Look at the picture. What non-unit fraction is being represented by the green triangles here?

      An image in a quiz
      Correct answer: $$ \frac{3}{6} $$
      $$ \frac{3}{7} $$
      $$ \frac{3}{5} $$
      $$ \frac{3}{4} $$

      Q2.
      Match the counting labels.

      Correct Answer:one one-sixth ,one-sixth
      Correct Answer:two one-sixths ,two-sixths
      Correct Answer:three one-sixths,three-sixths

      Q3.
      What is missing from the counting label?

      An image in a quiz
      Correct answer: one-sixth
      sixth
      one-fifth
      fifth

      Q4.
      What is the missing counting label here?

      An image in a quiz
      One more one-quarter
      Another one-quarter
      Correct answer: Two one-quarters

      Q5.
      Which repeated addition equations represent the non-unit fraction shown here?

      An image in a quiz
      Correct answer: $$ \frac{1}{5} $$ + $$ \frac{1}{5} $$ = $$ \frac{2}{5} $$
      $$ \frac{1}{6} $$ + $$ \frac{1}{6} $$ = $$ \frac{2}{6} $$
      $$ \frac{1}{5} $$ + $$ \frac{1}{4} $$ = $$ \frac{2}{3} $$
      $$ \frac{2}{5} $$ = $$ \frac{1}{5} $$ + $$ \frac{1}{5} $$

      Q6.
      Which repeated addition equation represents the fraction of pandas wearing hats here?

      An image in a quiz
      $$ \frac{2}{3} $$ + $$ \frac{2}{3} $$ = $$ \frac{1}{3} $$
      $$ \frac{1}{3} $$ + $$ \frac{2}{3} $$ = $$ \frac{2}{3} $$
      $$ \frac{3}{1} $$ + $$ \frac{3}{1} $$ = $$ \frac{2}{3} $$
      Correct answer: $$ \frac{1}{3} $$ + $$ \frac{1}{3} $$ = $$ \frac{2}{3} $$

      Lesson appears in

      UnitMaths / Composition of non-unit fractions: addition and subtraction

      Maths

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