Use representations to describe and compare two fractions in a continuous context | Maths

Starter quiz

Match the word with the best definition.

The numerator

⇔

tells you how many parts are chosen or shaded. ✓

The denominator

⇔

tells you how many equal parts the whole as been divided into. ✓
Which glass is about half full?
$Which letter represents when <Math>{1}\over{2}</Math> would sit on this number line?$

Which letter represents when ${1}\over{2}$ would sit on this number line?

a

b ✓

c

d
Match the fractions to the statements.

${2}\over{4}$

⇔

is equal to ${1}\over{2}$ ✓

${5}\over{6}$

⇔

is greater than ${1}\over{2}$ ✓

${2}\over{5}$

⇔

is less than ${1}\over{2}$ ✓
Which four numbers could you use to create two fractions equivalent to ${1}\over{2}$ ?

3 ✓

5 ✓

6 ✓

9

10 ✓
$Which other fractions could sit at the same place as this fraction on the number line?$

Which other fractions could sit at the same place as this fraction on the number line?

${2}\over{4}$ ✓

${5}\over{6}$

${2}\over{5}$

${9}\over{18}$ ✓

Exit quiz

Which of these glasses of juice been labelled with the correct fraction to show how full they are?
Which of these glasses of juice would you say is around ${4}\over{5}$ full?
Which of these fractions would be closest to 0 on a 0 to 1 number line?

${1}\over{9}$ ✓

${1}\over{8}$

${1}\over{7}$
Which of these fractions would be closest to 1 on a 0 to 1 number line?

${8}\over{9}$ ✓

${7}\over{8}$

${6}\over{7}$
Which of these fractions would sit between ${1}\over{2}$ and 1 on a 0 to 1 number line?

${3}\over{4}$ ✓

${3}\over{9}$

${3}\over{5}$ ✓

${3}\over{10}$
$Match the fractions with the points they would sit at on the number line.$

Match the fractions with the points they would sit at on the number line.

a

⇔

${1}\over{4}$ ✓

a

⇔

${3}\over{12}$ ✓

b

⇔

${3}\over{4}$ ✓

b

⇔

${9}\over{12}$ ✓

c

⇔

${1}\over{3}$ ✓

c

⇔

${3}\over{9}$ ✓

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

Number lines and scales represent fractions in a continuous context.
The whole has been divided into __ equal parts and the line shows __ of them.

Common misconception

Children need to understand that fractions can also be fractions of 1 and have an exact position on a number line. There may be confusion over labelling an exact point rather than a part of the line.

Use the language of labelling a point on the line and avoid talking about 'half of the line' which is the language of parts of a whole. This helps children to see that fractions are numbers in their own right with a unique position on a number line.

Keywords

Continuous - Continuous means that every position on the line or scale has a value.
Equal - Equal means that something has exactly the same amount or value.