Identify when unit fractions cannot be compared | Maths

Starter quiz

Which inequality symbol goes into the gap? 65 ___ 56

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> ✓
Which inequality symbol goes into the gap? 300 + 30 ___ 400 − 50

< ✓

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Which inequality symbol goes into the box to show which glass is more full?

'<' ✓
Which of the following is the definition of a numerator?

The number of equal parts that a whole has been divided into.

The number of selected equal parts. ✓

A line to show that a whole has been divided into equal parts.
$What fraction of the whole is the shaded part in the image?$

What fraction of the whole is the shaded part in the image?

$\frac{1}{5}$

$\frac{1}{3}$

$\frac{1}{4}$ ✓

$\frac{1}{2}$
$What fraction of the whole is the shaded part in the image?$

What fraction of the whole is the shaded part in the image?

$\frac{1}{6}$

$\frac{1}{7}$

$\frac{1}{10}$

$\frac{1}{8}$ ✓

Exit quiz

“Let’s have one-half of a cake each.” Does the image show a fair or unfair version of this statement?

Fair ✓

Unfair
“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?

Fair

Unfair ✓
Which proof shows one-quarter that is less than one-half?
What does this visual proof show?

One-quarter is equal to one-half.

When the wholes are the same, one-quarter is equal to one-half.

When the wholes are different, one-half and one-quarter can be equal size. ✓
What is special about the whole when comparing fractions using notation?

The whole can be different.

The whole is the same or equal. ✓

The wholes are different.
$Which inequality symbol goes in between these two fractions?$

Which inequality symbol goes in between these two fractions?

'<' ✓

Worksheet

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Lesson Details

Key learning points

If the whole is not the same, the fractions cannot be compared.
If the parts of the whole are not equal, the fractions cannot be compared.
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