New York State Testing Program, 2010, #15
Source: New York State Testing Program, Grade 6, Book 1, 2010, #15
Question:
15. Simplify the expression below.
7^{2}  9 + 1^{3}
A. 37 B. 39 C. 41 D. 43
Answer: C
What Are The Flaws in This Question?
 Because of the last term in the expression, students can get the right answer for the wrong reason. Not only does 1^{3} = 1, but also 1^{2} = 1, 1^{4} = 1, etc. Therefore, if a student ignores the exponent or uses a different exponent, the student will still get the correct answer of 1.
 None of the wrong choices (i.e., A, B, D) is testing the most common mistake students would make, which is thinking that 7^{2} 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?
7^{2}  9 + 2^{3}
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
