Algebraic Reasoning Class Summary 12/9/13

with Kim Rodgers

Area and Perimeter

On Monday we talked about using algebra in the real world. Many students had thought about it during the week. One even had a list of professions which use algebra that was a page long! 

Professor Arbegla had been talking about this topic with her students in the college class she teaches, when she realized that algebra was used when she remodeled her bathroom. She was planning on tiling the bathroom floor. She knew the dimensions of the floor (6’ x 7’) and was ready to pick out tiles. Since they were so expensive, she wanted to have an idea of how many tiles she should purchase before going to the store. That’s where our class came in. Each tile was one foot square. The students spent some time figuring out how she could know how many to buy. Some drew pictures. Some knew intuitively that multiplying the number of rows by the number of columns would give us the number of tiles. We discussed why multiplying works and how finding the area of the room could help her with her project. We assigned the letter “l” for length and “w” for width and came up with a rule for area to put on our toolkit.

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l x w = area

We also talked about the terms we use when discussing area. In this specific case each tile is a foot square so we call that square feet. We contrasted that with perimeter. Perimeter is a linear measurement, so we just use “feet” as the measurement. The students came up with a few ways to express perimeter:

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l + l + w + w = perimeter
2l + 2w = perimeter
2(l + w) = perimeter

• The students were then challenged to write as many equations as they could where the dimensions of the room equaled an area of 36 square feet. Those who finished early were further challenged to come up with dimensions of the room that weren’t whole numbers! After coming up and sharing nine possible equations using whole numbers, they mapped each one out on graph paper. In the midst of this, it came up that each room had a “partner” room, or a room which had the same dimensions but switched as to the length and width, except for a room with the dimensions of 6’ x 6’. We talked about the area of the partner rooms and if they were the same or not. Shapes with the same size and shape are called congruent shapes, which led us into discussing the commutative property of multiplication: 

• a x b = b x a which we recorded on our toolkit as well. 

Next week we continue discussing area and planning spaces to be used for particular purposes. How does its purpose affect how we lay out the area of the enclosure? What’s the best set up for the enclosure? Some students were interested in pursuing the area of triangles and circles, so they decided to look into that for homework to share with the class next week. I look forward to letting them teach the class a thing or two!

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