Compare Fractions on a Number Line in Common Core Math

By Christopher Danielson

In Common Core math, third graders use a number line to see how fractions relate to each other. A number line is useful for showing the relative location of fractions, as well as their distance from each other.

You may remember a number line running across the front wall of an elementary classroom when you were in school, with a point for zero, a point to the right of that marked 1, then 2 and so on, with an arrow on the end to suggest that the line and the numbers continue forever.

The two most important numbers on a number line are 0 and 1. After you mark them on the number line, every other number has a defined location. Correspondingly, when third graders use the number line to study fractions, they mark 0 and 1 and then partition the interval between these numbers into same‐sized pieces.

For example, the number line in the figure shows the interval between 0 and 1 partitioned into fifths. The mark closest to 0 is labeled one‐fifth, which is a unit fraction. The remaining marks are labeled as multiples of one‐fifth. Students think about three‐fifths as being the distance from zero which ends at the third mark to the right of 0 when the interval is cut into fifths.

Fifths on the number line.

Fifths on the number line.

Third graders basically show numbers on a number line in two ways:

  • They show a fraction as a location on the number line as the figure demonstrates.

  • More importantly, they also think of a fraction as a distance on the number line. One-fifth isn’t just the tick mark labeled


    it’s also the distance between adjacent pairs of tick marks on this number line.