Last week we looked at some creative ways to find the area of various geometric figures from your textbook. For the first method, we used guess and check method and the other was a more exact measurement using a grid. I was pleased with the attention and eagerness that most of you demonstrated during this lesson. As I mentioned, the mathematics you are doing requires commitment. I was amazed to see all of you grow as you successfully completed the class assignment.
I instructed you to connect the grid squares at a minimum and try to estimate the area of the figure. All of you were quite successful at this task. Then we turned to the second method. As you discovered this method was more accurate. Here we connected more dots in the grid. Each part of the geometric figure became a part of a unit square , after which you determined the portion of the geometric figure by subtracting the portion from the unit square.
A more detailed analysis of the exact measurement would be the following:
1. Connect the grid dots creating unit squares all around and inside the
geometric figure.
2. Determine the size of the piece you are concerned with by subtracting
it from the total area of the unit square. In this case all pieces
will be fractions of 4ths. For instance if the piece occupies 1/4th or
a quarter of the unit square, there will be 3/4 that we are not
concerned with because the figure does not occupy that space. So we
have 3/4 + 1/4= 4/4=1, as you can see we have subtracted the piece of
our concern from the total area of the unit square.
3. Once you have determined the measurement of each piece within the
unit square, you add all the pieces up. Example: 1/4 + 1/4 +1 +1= 2.5
This concludes the assignment, it is my hope that this further reinforced the concept of finding the area...
Nice job, Melvin. Did you use this with your class? Later on this semester, you will will create tutorials which you can use to show students how to find area.
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