Explain how to compare pairs of non-related fractions using fraction sense | Maths

Starter quiz

Tick the fractions greater than one half.

${3} \over {4}$ ✓

${2} \over {7}$

${2} \over {3}$ ✓

${8} \over {14}$ ✓

${4} \over {10}$
Two or more fractions can only be compared when:

they have the same denominator.

they have the same numerator.

they have the same size whole. ✓

they have different-sized wholes.
Which letter represents the best estimate for where one-fifth sits on the number line?

a ✓

b

c

d
Order the fractions from largest to smallest.

1

⇔

${6} \over {8}$

2

⇔

${3} \over {6}$

3

⇔

${4} \over {9}$
Use the correct symbol to compare: ${4} \over {8}$ ___ ${3} \over {10}$

<

> ✓

=
Use the correct symbol to compare: $1 {{1} \over {5}}$ ___ $1 {{1} \over {6}}$

<

> ✓

=

Exit quiz

The magnitude of a fraction can also be known as the ______ of a fraction.

'size' ✓
Compare these two fractions: ${2} \over {6}$ ___ ${4} \over {6}$

< ✓

>

=
Compare these two fractions: ${3} \over {7}$ ___ ${3} \over {9}$

<

> ✓

=
Compare these two fractions: ${2} \over {3}$ ___ ${3} \over {7}$

<

> ✓

=
Compare these two fractions: ${5} \over {6}$ ___ ${9} \over {10}$

< ✓

>

=
Compare these two fractions: ${5} \over {7}$ ___ ${7} \over {9}$

< ✓

>

=

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Lesson Details

Key learning points

In fractions equivalent to a whole, the numerator is the same as the denominator.
The size of the denominator tells you the size of one part of the whole.
The greater the denominator, the smaller the parts of the whole.
The smaller the denominator, the smaller the parts of the whole.

Common misconception

Pupils automatically want to compare fractions using common denominators, following a procedure to convert fractions to an equivalent with the same denominator.

Spend time looking at a variety of examples that can be reasoned about without the need to convert to common denominators. It can be helpful to represent these examples using bar model help discuss the relationships between the whole and its parts.

Keywords

Magnitude - The magnitude of something refers to the size of something.