Fractions on Number Lines
A number line is a straight line with numbers marked in order, and it can show fractions as points sitting between the whole numbers. In Year 3 (ACARA v9), students learn to place unit fractions like 1/2, 1/3 and 1/4 on a number line by splitting the space between 0 and 1 into equal parts. The key idea: the bottom number (denominator) tells you how many equal parts to split the line into, and the top number (numerator) tells you how many parts to count along. Seeing fractions on a line — not only as slices of pizza — helps children understand that a fraction is a number with a size and a place, which sets up comparing and adding fractions later.
Worked examples
Show 1/2 on a number line from 0 to 1.
The denominator is 2, so split the line between 0 and 1 into 2 equal parts. Count 1 part along from 0.
Answer: 1/2 sits exactly halfway between 0 and 1
Place 3/4 on a number line from 0 to 1.
The denominator is 4, so split 0 to 1 into 4 equal parts. Count 3 parts along from 0.
Answer: 3/4 is at the third mark, one step before 1
A ribbon is marked in thirds. Where does 2/3 sit between 0 and 1?
Split the line into 3 equal parts (thirds). Count 2 parts along from 0.
Answer: 2/3 is at the second mark, two-thirds of the way along
On a line from 0 to 1 split into quarters, which is bigger: 1/4 or 3/4?
Both sit on the same line. 1/4 is one part from 0; 3/4 is three parts from 0. The point further from 0 is bigger.
Answer: 3/4 is bigger
Tips
- •Split first, then count. The denominator tells you how many equal parts to cut the line into before you count along — get the equal parts right and the rest follows.
- •Equal parts matter. The gaps between the marks must be the same size; if a child spaces them unevenly, the fraction lands in the wrong place.
- •Common mistake to watch for: children sometimes count the marks instead of the spaces, or start counting at 1 instead of 0. Always start at 0 and count the jumps, not the lines.
- •Fold paper to see it. Fold a paper strip into equal parts, lay it along a line from 0 to 1, and the creases show exactly where each fraction sits.