Algebra 1 PARCC: racing cars

The following constructed-response question, explained here in hopes of helping algebra 1 students and their parents in Maryland and Illinois prepare for the PARCC test near the end of this school year, appears on the released version of PARCC’s Spring 2016 test for algebra 1 (#30):

Three cars are traveling to the same campground along the same route. The cars began at the same place but at different times. Car A began the trip at noon, and cars B and C began the trip at different times before noon. The miles traveled by cars A, B, and C are represented respectively, by the following graph, table, and equation.

Car A

Car B

Car C

D = 68t + 20

where D is the total distance, in miles, traveled by car C, and t is the number of hours after noon.

At what time, if ever, will car A pass each of the other cars? Describe any assumptions you made and justify your answer.

Enter your answer, your description, and your justification in the space provided.

Answer and references
Solution strategy (there are others)

Analysis of this question and online accessibility

The question is valid in that it tests students’ ability to construct a chain of reasoning about a mathematical scenario.

The question can be delivered online or on paper. However, because students cannot draw using the online tool and will be forced to use words, those who take the test online may be at a disadvantage with this question if they are accustomed to solving or explaining their solution to problems like this using diagrams or graphs. This solution strategy isn’t the only one available, though, but the PARCC test, with the “equation editor” tool, unnaturally forces students’ hand: they must explain their solution in paragraph form, not by laying out a table or drawing a model of the cars, if they are taking the test online.

This means validity and reliability measures for the item may suffer from the different test-taking environment, in terms of responding to the question, experienced by students who take the test on a keyboard and those who take it freehand.

No special accommodation challenges can be identified with this question, so the question is considered fair.

(Minor editorial concerns remain. The question is wordy. The question switches from the present tense to the past tense without any transition: the verb “began” is somewhat jarring, since the question starts out with the present tense verb “are traveling.” The comma before, but not after, the word “respectively” reflects inconsistent style and usage. The use of the word “respectively” is unnecessary since the representations are labeled and adds to the number of words students have to read. The passive voice in the final sentence before the graph is clumsy.)

Resources for further study

Ron Larson, Laurie Boswell, Timothy D Kanold, Lee Stiff. Algebra 2, Illinois edition. Evanston, Ill.: McDougal Littell, a division of Houghton Mifflin Company, 2008. The book is used in several algebra classes taught in Illinois high schools.

Foerster, Paul A. Algebra and Trigonometry: Functions and Applications, revised edition. Addison-Wesley, 1980, 1984. The book is used in several algebra classes taught in middle and high schools in both Illinois and Maryland.

Purpose of this series

To help algebra 1 students and their parents prepare for the PARCC test in math, as administered in at least six states, or to just master content on that test, we provide an analysis of every algebra 1 math problem PARCC released in 2016. The series can be found here.

About the Author

Paul Katula
Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.