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Year 3

Identify when unit fractions cannot be compared

I can identify when unit fractions cannot be compared.

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New
New
Year 3

Identify when unit fractions cannot be compared

I can identify when unit fractions cannot be compared.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. If the whole is not the same, the fractions cannot be compared.
  2. If the parts of the whole are not equal, the fractions cannot be compared.
  3. Equal parts may not look the same.

Common misconception

Children might want to use inequality symbols between representations showing different wholes.

Explain that inequalities can only be used when the whole is the same. Provide them with examples they may be familiar with such as offering half of a large and small apple and identifying that these are not the same because the wholes differ.

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

Whilst this is a relatively small teaching point, it's crucial that the children grasp this concept. This is a small but significant step in understanding the difference between comparing fractions of quantities (fraction as an operator) and comparing the actual values of different fractions.
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).

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Starter quiz

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6 Questions

Q1.
Which inequality symbol goes into the gap? 65 ___ 56
<
Correct answer: >
Q2.
Which inequality symbol goes into the gap? 300 + 30 ___ 400 − 50
Correct answer: <
>
Q3.
Which inequality symbol goes into the box to show which glass is more full?
An image in a quiz
Correct Answer: <
Q4.
Which of the following is the definition of a numerator?
The number of equal parts that a whole has been divided into.
Correct answer: The number of selected equal parts.
A line to show that a whole has been divided into equal parts.
Q5.
What fraction of the whole is the shaded part in the image?
An image in a quiz
$$ \frac{1}{5} $$
$$ \frac{1}{3} $$
Correct answer: $$ \frac{1}{4} $$
$$ \frac{1}{2} $$
Q6.
What fraction of the whole is the shaded part in the image?
An image in a quiz
$$ \frac{1}{6} $$
$$ \frac{1}{7} $$
$$ \frac{1}{10} $$
Correct answer: $$ \frac{1}{8} $$

Exit quiz

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6 Questions

Q1.
“Let’s have one-half of a cake each.” Does the image show a fair or unfair version of this statement?
An image in a quiz
Correct answer: Fair
Unfair
Q2.
“I’ve read one-half of a book and you’ve only read one-third so I have read more.” Does the image show a fair or unfair version of this statement?
An image in a quiz
Fair
Correct answer: Unfair
Q3.
Which proof shows one-quarter that is less than one-half?
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Q4.
What does this visual proof show?
An image in a quiz
One-quarter is equal to one-half.
When the wholes are the same, one-quarter is equal to one-half.
Correct answer: When the wholes are different, one-half and one-quarter can be equal size.
Q5.
What is special about the whole when comparing fractions using notation?
The whole can be different.
Correct answer: The whole is the same or equal.
The wholes are different.
Q6.
Which inequality symbol goes in between these two fractions?
An image in a quiz
Correct Answer: <