New England Common Assessment Program (NECAP), 2007

SourceNew England Common Assessment Program (NECAP), Grade 11, 2007

Question (no calculators allowed):

2.  Renata is a sales representative for a printer company.  She sells two models of printers - Model P and Model Q.

  • Last month she sold a total of 120 printers.
  • The ratio of Model P printers sold to Model Q printers sold was 3:5.

If Renata is paid a $25 commission for every Model P printer sold and a $20 commission for every Model Q printer sold, what was her total commission last month?

A.  $1480                               
B.  $2475
C.  $2625
D.  $2760

Answer:  C

What Are The Flaws in This Question?

  1. There are way too many steps required to solve this problem!  It takes approximately 14 steps to set up the algebraic equations, solve them, and calculate the total commission.  Having so many steps increases the likelihood that a student will make a careless calculation mistake, even though the student knows how to do all the steps.  Since this is a multiple-choice question, the student cannot get partial credit for correct work shown.  Thus, the question is not valid because it is not measuring whether a student understands the concepts being tested.
  2. Following from 1. above, there are also too many concepts being tested, so if a student gets the wrong answer, it is difficult to deduce which concepts the student doesn't understand.  Here are the various concepts being tested:  1) how to convert a ratio into a linear equation;  2) how to model a word problem as a system of linear equations;  3) how to solve a system of linear equations;  4) how to compute the total commission.
  3. The context of the question may be confusing to some students, especially special education students and English language learners, because of the word "commission."  Some students may not understand what that means, in which case they would not be able to perform the last step in solving the problem.
  4. The first choice, $1480, sticks out because it is not a number close to the other three choices (which are close to each other).  This is a bad idea because a student who doesn't know how to solve the problem may pick this choice because it looks different from the others.  Or the student may actually avoid the choice because it looks different.

How to Fix This Question:

One way to fix this question is to rewrite it as an open-response question instead of a multiple-choice question;  i.e., break it up into multiple parts, have students show their work, and give partial credit for correct work shown.  One part would ask students to write the word problem as a system of linear equations.  (This part alone could be a multiple-choice question.)  Another part would ask for the solutions.  And another part would ask for the total commission (but should use a word other than "commission" or explain what it means).