Fractions on number lines | Year 4

01 / LEARN

The idea, step by step

Count spaces, not tick marks

First identify the whole interval, such as zero to one. Count the equal spaces inside that interval. Four equal spaces mean the scale counts quarters, even though there are five tick marks.

Count jumps from zero to the point. Three quarter-sized jumps land at three quarters.

Keep the scale past one

Continue with the same interval size beyond one. On a line split into quarters, the ticks after one are five quarters, six quarters and seven quarters.

Fractions farther to the right are larger. Use equivalent fractions when the denominators differ, or mark both on one accurately divided line.

A common trap

Using the number of tick marks as the denominator.

Instead: The denominator is the number of equal spaces between consecutive whole numbers, not the number of marks.

02 / WORKED EXAMPLES

See the thinking

Example 1

Read a point

The whole interval is split into four equal spaces. What is A?

A is six quarter-sized jumps from zero.
Four quarters make one whole, leaving two quarters.
Two quarters are one half.

A = \frac{6}{4} = 1 \frac{1}{2}

Example 2

Compare two positions

Which is farther right: $\frac{1}{2}$ or $\frac{3}{4}$ ?

Rename one half as two quarters.
Three quarters lies one quarter-jump to the right of two quarters.

\frac{3}{4}

Check your understanding

A line has three equal spaces from 0 to 1. What fraction is the second tick after 0?

Show answer

$\frac{2}{3}$

Each space is one third; two spaces reach two thirds.

03 / WORKSHEET

Your turn

6 questions · 9 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Read point A.
1 mark
Read B as a fraction and a mixed number.
2 marks
Mark $\frac{2}{3}$ on the supplied line.
1 mark
Order $\frac{1}{2}, \frac{3}{2}, \frac{5}{4}$ from smallest to largest.
2 marks
The line is labelled $0, \frac{1}{2}, 1, 1 \frac{1}{2}, 2$ . Between which two neighbouring marks does $\frac{7}{4}$ lie?
1 mark
Mark $\frac{3}{5}$ and explain how you chose its position.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Read point A.
1 mark
Four equal spaces fill one whole; A is one space from zero.
$\frac{1}{4}$
Read B as a fraction and a mixed number.
2 marks
B is seven quarter-sized jumps from zero. Four quarters make one whole, leaving three quarters.
$\frac{7}{4} = 1 \frac{3}{4}$
Mark $\frac{2}{3}$ on the supplied line.
1 mark
Each space is one third, so count two spaces from zero.
The second tick after 0.
Order $\frac{1}{2}, \frac{3}{2}, \frac{5}{4}$ from smallest to largest.
2 marks
They equal two, five and six quarters.
$\frac{1}{2}, \frac{5}{4}, \frac{3}{2}$
The line is labelled $0, \frac{1}{2}, 1, 1 \frac{1}{2}, 2$ . Between which two neighbouring marks does $\frac{7}{4}$ lie?
1 mark
The landmarks are six quarters and eight quarters.
$1 \frac{1}{2}$ and $2$
Mark $\frac{3}{5}$ and explain how you chose its position.
2 marks
Divide the zero-to-one interval into five equal spaces and count three spaces.
The third tick after 0.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Equivalence; counting beyond one; mixed numbers; number lines.

Official curriculum source ↗

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