Order sets of non-related fractions using a range of strategies | Maths

Starter quiz

An improper fraction is:

a fraction with a numerator of one.

a fraction with a numerator that is larger than the denominator. ✓

a fraction that has the same numerator and denominator.

a fraction with a denominator that is larger than the numerator.
Use reasoning to compare these two fractions: ${2} \over {10}$ ___ ${6} \over {7}$

< ✓

>

=
Use reasoning to identify which of these fractions is greater than ${2} \over {5}$

${4} \over {5}$ ✓

${3} \over {5}$ ✓

${1} \over {10}$

${4} \over {10}$
Use reasoning to identify the fraction which would complete the inequality: ${5} \over {7}$ > _____

${5} \over {20}$ ✓

${7} \over {7}$

${7} \over {5}$
Use reasoning to compare these two fractions: ${9} \over {10}$ ___ ${6} \over {7}$

<

> ✓

=
Use reasoning to compare these two fractions: ${4} \over {7}$ ___ ${5} \over {8}$

< ✓

>

=

Exit quiz

Tick the sequences where the fractions are increasing in size each time.

${1} \over {4}$ ${1} \over {3}$ ${1} \over {2}$ ✓

${1} \over {8}$ ${1} \over {4}$ ${1} \over {6}$

${1} \over {8}$ ${2} \over {7}$ ${3} \over {6}$ ✓

${9} \over {9}$ ${9} \over {10}$ ${9} \over {11}$
Tick the sequence where the fractions are decreasing in size each time.

${1} \over {9}$ ${1} \over {8}$ ${1} \over {7}$

${2} \over {5}$ ${3} \over {4}$ ${4} \over {1}$

${1} \over {8}$ ${1} \over {9}$ ${1} \over {10}$ ✓

${3} \over {9}$ ${4} \over {10}$ ${5} \over {11}$
Order the fractions from largest to smallest.

1

⇔

${5} \over {7}$

2

⇔

${5} \over {10}$

3

⇔

${5} \over {15}$
Tick the largest fraction and the smallest fraction in this list.

${6} \over {10}$ ✓

${1} \over {2}$

${3} \over {9}$

${1} \over {12}$ ✓
Tick the fractions that could fit in the gap in this increasing sequence. ${2} \over {3}$ ${5} \over {6}$ __________ ${9} \over {10}$

${7} \over {8}$ ✓

${6} \over {7}$ ✓

${7} \over {10}$

${6} \over {9}$
Order the fractions in ascending order.

1

⇔

${3} \over {7}$

2

⇔

${3} \over {6}$

3

⇔

${4} \over {5}$

4

⇔

${25} \over {30}$

5

⇔

${9} \over {7}$

Worksheet

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Lesson Details

Key learning points

There are many ways to compare and order fractions.
If the numerator is the same, the greater the denominator, the smaller the fraction.
If the denominator is the same, the greater the numerator, the larger the fraction.
In fractions equivalent to a whole, the numerator is the same as the denominator.
In fractions equivalent to a half, the numerator is half the value of the denominator.

Common misconception

Pupils convert to common denominators to order fractions rather then use their sense of magnitude for each fraction they are comparing.

Encourage pupils to step back at first from procedure and ask themselves what they notice about the fractions. Can they spot fractions that are equivalent to a quarter or a half?

Keywords

Improper fraction - An improper fraction is a fraction where the numerator is greater than the denominator.
Proper fraction - A proper fraction is a fraction where the numerator is less than the denominator.