Algebra I (CC) June 2016 question 24: Could (Should?) it be better? (update July 20, 2016)

The question above seems sort of innocuous. It appeared on the June 2016 New York State Regents Exam in Algebra I (Common Core).

It seems to overlook the option of a student not to set it up this way:

A student who begins with this approach would then be slightly befuddled as to what the question is asking. This student could easily fall into the "guess trap", with a 75% chance of picking the expected answer.

The question could be improved by changing "should" to "could". That would urge this student to tweak their thoughts by allowing for the possibility of different approaches.

Exam writers should go out of their way to create questions that do not penalize students for applying good mathematics just because it does not meet a certain "prescription".

Update: Take note that in order for two integers to multiply to 156, all a student needs to recognize is

156 = 2 * 78 and 
156 = 3 * 52 and 
156 = 4 * 39 and 
156 = 6 * 26 and
156 = 12* 13 and 

Then recognize that 12 and 13 are consecutive integers. The student needs to remember to include negatives as well. 

At no point is an equation necessary. Equations should not be viewed as a first resort, but as a last resort. Number sense should rule. 

Suppose the question had used the number 6 instead of 156. Absolutely no change in question style. Would you still tell students that they should be using an equation?