New York State Testing Program, 2010, #16

SourceNew York State Testing Program, Grade 6, Book 1, 2010, #16


(Note:  In the actual question, the fractions are written vertically, with a horizontal bar between the numerator and denominator.)

16.  Mica and Denise are reading the same novel.  Mica has read 1/2 of the novel, and Denise has read 1/3 of the novel.  How much more of the novel has Mica read than Denise?

A.  1/6
B.  2/5

C.  3/5

D.  5/6

Answer:  A

What Are The Flaws in This Question?

  1. The correct answer, 1/6, sticks out because it is the only choice with "1" in the numerator and looks similar to the fractions in the question because they also have "1" in the numerator.  So students may choose the option that looks different and get the right answer, even though they don't know how to subtract fractions.  In a way, this is giving away the answer.
  2. The wrong choices, called "distractors," should be the result of common math mistakes, so that if a student chooses one of them, you have information on what they probably did wrong.  The options B, C, and D are not good distractors because they are not the result of common mistakes in subtracting fractions, which is what this question is testing. Option B is the result of adding the numerators and adding the denominators, which is a common mistake when *adding* fractions, but this question is about *subtracting* fractions, so option B is partly the result of reading and comprehension errors, not an error in subtracting fractions.  Option D is purely the result of reading and comprehension errors, since it is, in fact, the result of correctly adding the fractions.  It is unclear where option C comes from.  The denominator is the result of adding the denominators in the given fractions, but where does the "3" in the numerator come from?
  3. The word "novel" may be unfamiliar to some students, and can be used as an adjective as well as a noun.  This disadvantages special education students and English-language learners (ELL) because they may find it confusing.  Why not use the more-familiar, friendlier word "book"?

How to Fix This Question:

  1. One way to fix this question is to eliminate the context altogether to avoid the chance of reading and comprehension errors, and just make it a question testing raw computation.  In this case, an expression showing the subtraction of one fraction from another would be given.  However, sometimes a context makes the question more engaging.  If there is to be a context, it should be one that makes it clear that subtraction is required instead of addition.
  2. No option should stick out, and all the distractors should be the result of common math mistakes.
  3. Change "novel" to "book."