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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.

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New
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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.

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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 (2024), 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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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: $$ \frac{2}{6} $$
$$ \frac{2}{7} $$
$$ \frac{2}{5} $$
$$ \frac{1}{4} $$

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

one-sixth

Correct Answer:two one-sixths ,two-sixths

two-sixths

Correct Answer:three one-sixths,three-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: $$ \frac{1}{3} $$ + $$ \frac{1}{3} $$ = $$ \frac{2}{3} $$