MATH 329 Productive Failure Three

Reflection:

The conceptual problem I ran into with this problem stemmed from visualization. Originally, when I visualized a room, I was thinking that wherever the doors were, carpet would not be. However, after going back and looking at this problem again, I looked around my room and realized that there still is carpet where the door of my room is. Truly thinking of the problem realistically and comparing it to my actual room, I realized that if we are talking about wall to wall carpeting, then we are accounting for the entire area of the room, there is no lengths or widths that need to be subtracted.

From this problem I have learned that using real life models and applications can be extremely beneficial, especially when it comes to problems like these where you must visualize a room. Sometimes, like in my case, we overcomplicate the problem, when, if we take a glimpse of an actual room, it becomes clear to see that wall to wall carpeting would contain the entire area of the room, without subtracting the lengths and width of the doors in the room.