Find 2/3
Task
Label the point where $\frac23$ belongs on the number line. Be as exact as possible.
![3.nf.2_find_2_thirds_9f7dee15e4203577a953a80826e5037e](http://s3.amazonaws.com/illustrativemathematics/images/000/002/837/large/3.NF.2_find_2_thirds_9f7dee15e4203577a953a80826e5037e.jpg?1385478950)
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.
![3.nf.2_find_12_third_8572e61f94ceaed09fd4ad2457ca81f7](http://s3.amazonaws.com/illustrativemathematics/images/000/002/838/medium/3.NF.2_find_12_third_8572e61f94ceaed09fd4ad2457ca81f7.jpg?1385479022)
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.
![3.nf.2_find_12_third_1c1220aba0e7cd131f3d5aaa2ff6928a](http://s3.amazonaws.com/illustrativemathematics/images/000/002/839/medium/3.NF.2_find_12_third_1c1220aba0e7cd131f3d5aaa2ff6928a.jpg?1385479039)
Find 2/3
Label the point where $\frac23$ belongs on the number line. Be as exact as possible.
![3.nf.2_find_2_thirds_9f7dee15e4203577a953a80826e5037e](http://s3.amazonaws.com/illustrativemathematics/images/000/002/837/large/3.NF.2_find_2_thirds_9f7dee15e4203577a953a80826e5037e.jpg?1385478950)