Mon, October 22

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.

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.

Wed, Oct 10

The images above include the Telescop Lab with a student sample, a student sample of a Double Bubble used for comparing graphs, and Thinking Maps used for Direct and Inverse Variation.

Tues, Oct 2

Teacher J and I finished AA sections 2.1 and 2.2 using circle, tree and flow maps. If we were to do it again, I think we would stick with the tree map and flow map but not the circle map for problems involving direct and inverse variation. We were both very surprised at how many students found it very difficult to construct a tree map from the important information from a problem. I would definitely ask students to construct tree maps again because it puts them in the position of having to group and label before doing the algebra. If they cannot organize the information they will not be successful with the problem.

Time was an issue because fully asking students to create their own flow map, post them, and discuss them as a class would have taken 2 or 3 days longer than we wanted.

My conclusion is that there is a place for thinking maps in ch 2, but I would do less maps and spend a little time with the one I chose. They were a good way to organize a constructivist approach, but I don't think we wanted quite so much of a constructivist approach for lessons 2.1 and 2.2.

Teacher J had a great idea about using dubble bubbles for comparing and contrasting the graphs of y=kx, y=k/x, y=kx^2 and y=k/x^2. We will use these at the end of Ch 2.