Running to School, Variation 3
Task
Rosa ran \frac13 of the way from her home to school. She ran \frac14 mile. How far is it between her home and school?
IM Commentary
This task builds on a fifth grade fraction multiplication task, “5.NF Running to School, Variation 1.” “6.NS Running to School, Variation 3” uses the identical context, but asks the corresponding “Group Size Unknown” division problem. See “6.NS Running to School, Variation 2” for the “Number of Groups Unknown” version.
The purpose of this task is to help students extend their understanding of division of whole numbers to division of fractions, and given the simple numbers used, it is most appropriate for students just learning about fraction division because it lends itself easily to a pictorial solution.
Solutions
Solution: Solution
We know that Rosa ran \frac13 of the way to school, which is \frac14 of a mile.

So far, all we know is that \frac13 of the trip to school is \frac14 of a mile. What we are really interested in knowing is the length of the whole trip to school. Thus, the question we're asked to answer is "\frac13 of what distance is \frac14 mile?" \frac13 \times ? = \frac14

Re-labeling the picture will make the answer much easier to see.

Solution: A computational approach
This question is equivalent to asking, "\frac13 of what distance is \frac14 mile?" We can write this symbolically as \frac13 \times ? = \frac14
The distance to Rosa's school is \frac34 miles.
Running to School, Variation 3
Rosa ran \frac13 of the way from her home to school. She ran \frac14 mile. How far is it between her home and school?