New York State Testing Program, 2010, #15

SourceNew York State Testing Program, Grade 6, Book 1, 2010, #15

Question:

15.  Simplify the expression below.

            72 - 9 + 13

A.  37
B.  39
C.  41
D.  43

Answer:  C


What Are The Flaws in This Question?

  1. Because of the last term in the expression, students can get the right answer for the wrong reason.  Not only does 13 = 1, but also 12 = 1, 14 = 1, etc.  Therefore, if a student ignores the exponent or uses a different exponent, the student will still get the correct answer of 1.
  2. None of the wrong choices (i.e., A, B, D) is testing the most common mistake students would make, which is thinking that 72 is 7 x 2.  It is important to have wrong choices that are the result of common mistakes to give information on how a student went wrong.


How to Fix This Question:

The following is a revised version of the question that avoids the flaws mentioned above.  The expressions in brackets show how the choices are determined.

Question - revised:

Revised 15.  What is the value of the expression below?

            72 - 9 + 23

A.  11                 [14 - 9 + 6:  wrong exponent values]
B.  21                 [(14 - 9 + 2) x 3:  wrong exponent values and wrong order]
C.  32                 [49 - (9 + 8):  adding before subtracting]
D.  48                 [49 - 9 + 8:  correct answer]

Answer:  D