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Locating Fractions Greater than One on the Number Line
Task
Mark and label points on the number line for $\frac12$, $\frac22$, $\frac32$, $\frac42$, $\frac52$, and $\frac62$.
Mark and label a point on the number line for $\frac{11}{3}$. Be as exact as possible.
IM Commentary
This first part of this task requires students to represent a fraction $\frac{a}{b}$ on a number line diagram by marking off $a$ intervals of length $\frac1b$ (in this case $\frac12$) starting at 0.
Students may solve the second part of the task either by marking of 11 intervals of length $\frac13$ or by knowing that $\frac{11}{3}$ is $\frac23$ of the way between 3 and 4. Although a few students may be able to do it using the later of these approaches, most students will identify all of the points related to $\frac13$, $\frac23$, $\frac33$, etc., even if they do not label those points.
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?
Solution
Here is one way to draw and label the number line for this task:

Here is one way to draw and label the number line for this task:
Locating Fractions Greater than One on the Number Line
Mark and label points on the number line for $\frac12$, $\frac22$, $\frac32$, $\frac42$, $\frac52$, and $\frac62$.
Mark and label a point on the number line for $\frac{11}{3}$. Be as exact as possible.
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