Florida Comprehensive Assessment Test (FCAT), 2007, #9

SourceFlorida Comprehensive Assessment Test (FCAT), Grade 6, 2007, #9

Question:

9.  Ms. Berg bought a tent for her camping trip.  The tent cost $117.00, and a 7% sales tax was added at the register.  Ms. Berg gave the cashier seven $20 bills.  How much change should she have received?

F.   $    8.19
G.   $  14.81
H.   $  23.00
I.    $125.19

Answer:  G    [According to the Web site, only 42% of students chose this answer!]


What Are The Flaws in This Question?

  1. There are way too many computational steps, which greatly increases the chance that students will make a careless mistake, even though they understand how to solve the problem.  Here are the steps:  convert 7% to .07, multiply 117 by .07 to get 8.19, add 8.19 to 117.00 to get 125.19, multiply 20 by 7 to get 140, subtract 125.19 from 140 to get 14.81.  This is too much for a multiple-choice problem.  If a student gets the wrong answer, we don't know where the student went wrong.
  2. There are too many concepts being tested.  One concept is knowing how to handle percents.  Another concept is knowing how to perform arithmetic computations.  The Content Focus given on the Web site is "sales tax," but there's a lot more going on.
  3. Option I sticks out because it's a number much greater than the other options.  It also doesn't make sense in the context of the question.  So it is not surprising that, according to the Web site, only 5% of the students chose it.
  4. There may be words unfamiliar to students, namely, "register" and "cashier."  This language may also be confusing.


How to Fix This Question:

To keep this as a multiple-choice question, it would need to be greatly simplified and test only one thing, e.g., what the total cost would be for the tent after the sales tax was added.

Another 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.