Teacher S and I have been working together in Geometry. We used Flow Maps last week for an algorithm for working with the formula for the area of a trapezoid. See image above.
We are going to develop the equations for the circumference and area of a circle using some hands on activities. For the circumference, I will bring in about 20 different cans and bottles. Each student will have a string and a ruler and they will measure the diameter and radius of their can or bottle. They will enter their can's diameter in List1 on Teacher S's overhead TI-83, and their can's circumference in List2. I will plot a scatterplot and line of best fit and we will discuss how to use the line to find the circumference for a can with a given diameter. I will tell them the slope of the line is 2(pi), hence C = 2(pi)r. For the area of a circle, each student will be given a circle with various sizes of pieces of pie marked. Their job will be to cut out the pieces of pie and change their circle into a rectangle. The height of their rectangle will be r, and their length will be (1/2) of the circumference. Hence Area = r*(1/2)(2)(pi)(r) = (pi)(r)^2. See the image above.
We are going to develop the equations for the circumference and area of a circle using some hands on activities. For the circumference, I will bring in about 20 different cans and bottles. Each student will have a string and a ruler and they will measure the diameter and radius of their can or bottle. They will enter their can's diameter in List1 on Teacher S's overhead TI-83, and their can's circumference in List2. I will plot a scatterplot and line of best fit and we will discuss how to use the line to find the circumference for a can with a given diameter. I will tell them the slope of the line is 2(pi), hence C = 2(pi)r. For the area of a circle, each student will be given a circle with various sizes of pieces of pie marked. Their job will be to cut out the pieces of pie and change their circle into a rectangle. The height of their rectangle will be r, and their length will be (1/2) of the circumference. Hence Area = r*(1/2)(2)(pi)(r) = (pi)(r)^2. See the image above.
At the end of the chapter, the students will create a tree map of the areas of the shapes studied in the chapter. Instead of asking the students to create the tree map from scratch like we did in Lizzy's class, I have created a blank tree map with a list of labels. The students need to put the labels on the map in the correct places. See the two images above - one of the blank tree map and one of the scrambled labels.
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