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Solve problems involving comparing unit fractions

Lesson details

Learning outcome

I can solve problems involving comparing unit fractions.

Key learning points

  1. When comparing unit fractions, the greater the denominator, the smaller the fraction.
  2. When comparing unit fractions, the smaller the denominator, the larger the fraction.
  3. Equal parts may not look the same.

Keywords

  • Whole - The whole is all of a group or number.

  • Part - A part is a section of the whole.

  • Denominator - A denominator is the bottom number in a fraction. It shows how many parts a whole has been divided into.

  • Unit fraction - A unit fraction is a fraction where the numerator is 1

Common misconception

Children may still fall into the habit of considering the greater denominator to be a greater fraction.

Continue to revisit a fraction wall where possible and use real life contexts and images. Ensure that the statement, 'When the whole is equal, the greater the denominator, the smaller the fraction.' is visible and constantly refer to it.

Teacher tip

Some children compare by process without conceptualising the size of fractions. Challenge them to draw representations of fractions instead of notation for their futoshiki answers. Children could create their own futoshiki by arranging a grid of fractions first and then placing 3 inequalities in.

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

6 Questions

Q1.
Look at the picture. How many equal parts has the whole been divided into?

An image in a quiz
Correct Answer: 3, three, 3 parts, three parts, 3 equal parts

Q2.
What fraction of the whole is indicated by each circled group in the picture?

An image in a quiz
$$ \frac{1}{9} $$
Correct answer: $$ \frac{1}{3} $$
$$ \frac{1}{4} $$
$$ \frac{1}{6} $$

Q3.
Tick the fractions which are smaller than one-third.

An image in a quiz
$$ \frac{1}{2} $$
$$ \frac{1}{3} $$
Correct answer: $$ \frac{1}{5} $$
Correct answer: $$ \frac{1}{20} $$

Q4.
Which inequality symbol completes this statement? $$ \frac{1}{2} $$ $$ \frac{1}{5} $$

An image in a quiz
Correct Answer: >

Q5.
Which inequality symbol completes this statement? $$ \frac{1}{6} $$ $$ \frac{1}{4} $$

An image in a quiz
Correct Answer: <

Q6.
What is fraction of the whole is the shaded part below?

An image in a quiz
$$ \frac{1}{2} $$
Correct answer: $$ \frac{1}{4} $$
$$ \frac{1}{5} $$
$$ \frac{1}{8} $$

6 Questions

Q1.
Select the correct symbol to make the statement correct.

An image in a quiz
Correct answer: <
>
=

Q2.
Select the correct symbol to make the statement correct.

An image in a quiz
<
Correct answer: >
=

Q3.
Select the correct symbol to make the statement correct.

An image in a quiz
<
Correct answer: >
=

Q4.
Which numbers could you use as a denominator to make this correct?

An image in a quiz
Correct answer: 2
Correct answer: 5
12
20
100

Q5.
Which numbers could you use as a denominator to make this correct?

An image in a quiz
Correct answer: 2
Correct answer: 4
10
12
100

Q6.
Which of these unit fractions could go in the empty box?

An image in a quiz
$$ \frac{1}{2} $$
Correct answer: $$ \frac{1}{4} $$
Correct answer: $$ \frac{1}{5} $$
$$ \frac{1}{8} $$

To help you plan your 3 maths lesson on: Solve problems involving comparing unit fractions, download all teaching resources for free and adapt to suit your pupils' needs...