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.

Find 2/3
Label the point where \frac23 belongs on the number line. Be as exact as possible.
