Compare and order mixed numbers using fraction sense | Maths

Starter quiz

Look at the part-part-whole model. What is the value of the whole number part of this mixed number?

'9' ✓
Look at the number line and complete this sentence: Each interval between the integers on the line is divided into three equal parts. This allows us to count in __________.

halves

thirds ✓

quarters

fifths
On a number line, which integer would be before the mixed number $1 {{3} \over {8}}$ ?

'1' ✓
Complete the sentence: 999 is __________ than 1,001

wider

smaller ✓

longer

thinner

greater
Which of the following numbers is represented by the letter ‘A’?

${6} \over {7}$

$5{{1} \over {7}}$

$6{{1} \over {7}}$ ✓

$6{{6} \over {7}}$

$7{{1} \over {6}}$
Look at this number line. Match the letter to the number that it is representing.

A

⇔

${6} \over {8}$ ✓

B

⇔

$1{{1} \over {8}}$ ✓

C

⇔

$1{{5} \over {8}}$ ✓

D

⇔

$2{{1} \over {8}}$ ✓

Exit quiz

Identify the number represented by ‘A’

${2} \over {7}$

$1{{2} \over {8}}$

$1{{2} \over {7}}$ ✓

$1{{3} \over {7}}$
$Using the number line to compare the size of the numbers, complete the sentence using ‘greater’ or ‘less’: <Math> {3} \over {7}</Math> is __________ than <Math>1{{2} \over {7}}</Math>$

Using the number line to compare the size of the numbers, complete the sentence using ‘greater’ or ‘less’: ${3} \over {7}$ is __________ than $1{{2} \over {7}}$

greater

less ✓
Which of these statements are true?

${3} \over {7}$ < $1{{6} \over {7}}$ ✓

${3} \over {7}$ > $2{{3} \over {7}}$

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

$1{{6} \over {7}}$ < $1{{2} \over {7}}$
Which symbol makes this statement true? 9 ___ $9{{3} \over {7}}$

< ✓

>

=
Which symbol makes this statement true? $10{{3} \over {7}}$ ___ $9{{3} \over {7}}$

<

> ✓

=
Look at these numbers. Which is the smallest?

$6{{1} \over {7}}$

2

$1{{3} \over {7}}$ ✓

5

$2{{1} \over {7}}$

Worksheet

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Lesson Details

Key learning points

Mixed numbers can be positioned on a number line to help compare and order them.
When comparing or ordering mixed numbers, identify the integers that the mixed numbers sit between.
Mixed numbers where the whole number part is different can be compared or ordered based on their whole number part.

Common misconception

Children may count the marks rather than the equal parts between integers and may compare the fractional part of the mixed number first rather than the more significant whole number part.

Count the equal parts in between the given integers, not the marks to determine the unit that we are working with. When comparing and ordering, consider the whole number part first - this determines which integers the mixed number sits between.

Keywords

Mixed number - A mixed number is a whole number and a fraction combined.