The following dropdown-menu 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 (#4):
The polynomial (2x – 1)(x2 – 2) – x (x2 – x – 2) can be written in the form ax3 + bx2 + cx + d, where a, b, c, and d are constants.
What are the values of a, b, c, and d?
(Only five choices are available for each:
Analysis of this question and online accessibility
The question is valid in that it tests students’ ability to perform standard arithmetic operations on polynomials.
Guessing is not easy, but the presentation of only five drop-down choices for each of the four coefficients gives this question the feel of four multiple-choice questions, which would tend to promote guessing. It takes longer, though, to guess and check, so most students, I suspect, will just work the problem.
Multiple-choice varieties like this one can be delivered online or on paper, and reliability, validity, and fairness performance should be equivalent, regardless of the delivery mode.
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 arithmetic operations on polynomials, including pages that show you how to combine like terms, add polynomials, and use the FOIL strategy.
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.