|Florida Comprehensive Assessment Test (FCAT), 2007, #2
Source: Florida Comprehensive Assessment Test (FCAT), Grade 6, 2007, #2
2. In the parking lot of Flora's apartment complex there are 6 rows of parking spaces. In each row there are 10 parking spaces on the left and 12 parking spaces on the right. The total number of parking spaces in 6 rows of the lot is represented by the expression below.
6 x (10 + 12)
Which of the following is equivalent to this expression?
F. 6 x 12 + 10
G. 6 x 10 x 12
H. (6 x 10) + 12
I. 6 x (12 + 10)
What Are The Flaws in This Question?
This question tests the commutative property of addition (as specified as the Content Focus on the Web site), namely, that you can add numbers in any order. This is a simple, straightforward concept. However, the context - parking spaces in a parking lot of an apartment complex - can get in the way of testing this concept and may cause students who understand this property to get the wrong answer. Sometimes it's appropriate to add a context to show how the numbers might occur in real life, but this context is particularly unengaging and may not even be familiar to many students. Also, there is no reason given as to why you want to know the total number of parking spaces. Thus, this context just adds complexity and an extra reading load for no reason. In fact, it may hurt students because they may be turned off by all the confusing language and skip the question altogether. The extra verbiage and unfamiliar context may be particularly disadvantageous to special education students and English-language learners (ELL).
This question can be solved without understanding anything about the commutative property of addition. The question is really testing order of operations, because students can just work out the value of the given expression and then work out the value of each option, and choose the option that matches.
How to Fix This Question:
Remove the context altogether. Just ask the question: "Which of the following is equivalent to the expression below?" and then give the expression.
Note: If you want to give a context, then a better question would be to describe a context (one that is engaging, familiar, and without too many words) and then ask students to choose the expression that describes the context. In other words, change the question to one about mathematical modeling of real-life situations instead of the commutative property of addition.