Bee's POW - You Must Be Wrong

Bee's POW - You Must Be Wrong The POW (Problem of the Week) for the Bee's Unit Instructions and Grade

Grade:28/30

2 points off for process; see corrections below Instructions and Grade

A Microsoft Word version of this work is available here: Image:Bee's POW - You Must Be Wrong.doc

A PDF version of this work is available here: Image:Bee's POW - You Must Be Wrong.pdf

1. Problem Statement: In this simple POW you must find the area of two triangles. First, find the area of Dr. Rotoli’s original triangle that has side lengths of 6, 8, and 12 feet. Then you must find the area of Mr. Brown’s triangle with sides of 6, 8, and 10 feet. You must correctly determine which triangle has the largest area. This problem requires use of the “Crazy Triangle” process done twice.

2. Process: I started to solve this easy POW by finding the area of Dr. Rotoli’s original triangle. It had side lengths of 6, 8, and 12 feet. I used the “crazy triangle” process that we have learned in class.

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3. Solution: I can see it now. The shorter base results in a much greater angle for the two sides in relation to the base. This also greatly increases the height of the triangle. This results in a bigger area. However, Mr. Brown’s triangle is only about 2.6693 feet2 bigger then Dr. Rotoli’s triangle. So in conclusion, Mr. Brown’s triangle has a bigger area even though he has a shorter perimeter. This happens because the shorter base forces a higher height, which increases the area of the triangle enough to overcome the negative effect of shorting the base.

4. Extension: Not necessary to do.

5. Evaluation: This was an easy problem in knowing exactly what to do in order to solve the problem. Part of the fun of POWs in previous years was that one did not know what steps to take in order to solve the problem. In this POW I knew exactly how to solve the problem. However, there was a lot of math and steps that had to be shown. This takes time to recreate on the computer. I also made a mistake over the weekend where I thought that y goes on the larger side, not the smaller side. However, once I took a look at my notes I could quickly fix my mistakes on the computer. The write up also takes time.

The answer was surprising to me, as I was expecting that Mr. Brown be wrong. I guess we are so involved in rectangles, where a decrease in the perimeter, will decrease the area also. I learned that this is not always the case with triangle. In general, triangles are funny. The Pythagoras theorem, trig and the property that the sum of any 2 sides is larger then the third rules all play a part in contributing to the weirdness of triangles. I think this POW is a good problem because of this surprise answer. However, I do miss having to figure out the method to solve the problem as featured in last year’s POWs. I would not change the problem at all, but possibly throw it out and start over. However, that is not likely.