|New York State Testing Program, 2010, #15
Source: New York State Testing Program, Grade 6, Book 1, 2010, #15
15. Simplify the expression below.
72 - 9 + 13
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 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.
- 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]