The following constructed-response question, explained here in hopes of helping algebra 2 students and their parents in Maryland prepare for the PARCC test near the end of this school year, appears on the released version of the PARCC Algebra 2 sample items released following the 2015 test.
The arrangement of a distribution center and four stores to which it delivers is shown on the grid. Each unit on the grid represents 5 miles. The grid lines represent the roads.
The distribution center operators will use a single vehicle and must decide between a large truck and a small van. They will base their decision on this information.
- fuel efficiency: 9 miles per gallon
- delivers to all stores in one round-trip
- uses the shortest route to go to Stores A through D and then back to the distribution center
- must pay a $3.00 fee at each store for using the loading dock
- fuel efficiency: 18 miles per gallon
- must return to the distribution center after delivery to each store
- uses the shortest route between the distribution center and each store
- no fee for using the loading dock
Create a model that shows the total cost to deliver to all the stores for each type of vehicle based only on the information provided. Justify your models, including any assumptions you made.
Enter your models and your justifications in the space provided.
Determine when it is more cost efficient to use the van for deliveries than it is to use the truck. Justify your answer.
Enter your answer and your justification in the space provided.
Note that the price for gas I found in part B differs from that shown on the PARCC scoring guidelines for this problem. Instead of keeping exact numbers, PARCC rounded to the nearest tenth in the models used for part A. That gave them an answer of $5.45 in part B, which is just as correct as mine, given that PARCC rounded.
They did all the right computations in their work and justification and executed them without error. Rounding is not an error, but it resulted in a difference in the exact number of 5 cents.
A lot was being made a few years ago about how “Common Core math” seemed to say several different answers would be considered correct, as long as they were justified properly, given the correct mathematics. That didn’t sit very well with some parents, who also thought everything we teach third graders through high school students has to meet the exacting standards of a graduate engineering student. This problem is a prime example of where an answer of $5.45 can be just as acceptable, and earn the student just as many points, as $5.40.
On a multiple-choice test, the two different answers would never be available to students, and on a constructed response question like this one on the PARCC test, the student gets most of the points on this problem for the modeling and the justification, not for the correct numerical value for the price of gas.