Algebra 1 PARCC: system of inequalities

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 (#29):

A set of points in the xy-coordinate plane meets two conditions, as described.

  • Condition 1: The y-coordinate is positive.
  • Condition 2: The sum of the coordinates is greater than –2.

Part A

Create a system of inequalities described by the two conditions.

Enter your answer in the space provided.

Part B

A graph of the solution of the system includes points in different quadrants of the xy-coordinate plane. Explain why all points in the first quadrant are part of the solution.

Enter your answer 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 explain their reasons for what they know about the solution to inequalities on a coordinate plane.

The question can be delivered online or on paper. However, because students can’t 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 using a graph in their explanation, which is also a valid way of explaining a mathematical scenario, 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.

Resources for further study

Purple Math, developed by Elizabeth Stapel, a math teacher from the St Louis area, has developed several pages dealing with finding the solution to a system of two inequalities in two unknowns using the coordinate plane. Her lesson begins here.

In addition, Sal Khan, an engineer who developed the Khan Academy, a set of thousands of tutorial videos about math and a few other subjects, has created several videos about working with inequalities on the coordinate plane, beginning here.

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.

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