Find 2/3

Task

Label the point where $\frac23$ belongs on the number line. Be as exact as possible.

IM Commentary

This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line.

First students must locate 1 by repeatedly marking off the length of the interval between 0 and $\frac14$, recognizing that $\frac44$ = 1. Students must then partition the interval between 0 and 1 into 3 equal parts and identify which of those points represent $\frac23$.

Many students will find it easier to do this on two separate number lines, but a few may be able to do it on a single number line. The solutions below reflect these two approaches.

The following lists related tasks in order of sophistication:

• Locating Fractions Less than One on the Number Line
• Locating Fractions Greater than One on the Number Line
• Closest to $\frac12$
• Find 1
• Find $\frac23$
• Which is Closer to 1?

Solutions

Solution: Two number lines

Students may choose to label none, some or all of the points they find on the the number line on the way to solving the problem. A correct solution only requires that the point $\frac23$ be labeled.

Solution: One number line

Students may choose to label none, some or all of the points they find on the the number line on the way to solving the problem. A correct solution only requires that the point $\frac23$ be labeled.