Thurs, Feb 13

This tree map was included in a geometry unit designed to help students differentiate the notation and vocabulary of basic geometric structures. It was a topic the teacher felt the students had struggled with in the past that prevented them from doing more complex geometry. Before creating the tree map the students had created circle maps for each of the basic words (see the posting on Thur, Jan 24), and they defined them using NUA's defining format. Immediately before creating this tree map, the students did a List Group Label activity. Groups of 4 were given index cards with each of the phrases you see on the tree map mixed together in no particular order. They sorted the cards based on their own categories and then made the tree map based on their categories.

Thur, Jan 24

Teacher S and I are working on using NUA strategies to help students compare and contrast the definitions and notations for lines, rays, line segments, angles, and triangles. The problem seems to be one of literacy, so we are approaching the lessons with an emphasis on vocabulary development using circle maps, defining format, a list-group-label activity, tree maps, and some activities involving movement. Perhaps we will use a double-bubble as well.

The first activity was to ask students to create 4 different circle maps - one for each of the words line, line segment, ray, and angle. The were asked to write down words or pictures or symbols related to the given word. After about 8 minutes, students were asked to stand up and walk to the poster paper hanging at the front of the room and write down one of their words on the corresponding circle map. The circle maps for ray and line segment are shown in the pictures. We forgot to write the given word in the circle in the center, and we did not discuss the frame. We should have. These were mistakes simply because we are beginners at this! A good question for the frame could have been “What words or symbols come to mind when you see the word ray?”

As in the volume circle maps, there are many associations with the word ray that are not a part of the formal geometric definition of ray. However, having a time and place to write those associations and see them seems to be helpful because it acknowledges that the students have previous experience with the word ray. It is not until day 2 that we will formally define ray using the defining format.

After discussing various words and symbols and the circle maps we moved to a 10 minute post-it note activity. Five diagrams were already drawn on the whiteboard that consisted of a large variety of lines, line segments, rays, angles, and triangles. Each student was given 5 post-it notes. Their work was to find an example of a line segment somewhere in one of the diagrams and to write the formal notation for it on the first post it note. They did the same for line, ray, etc. Next, the students walked to the whiteboard and stuck their post-it notes directly on the segments, rays, etc, they described. This was a great assessment tool for the teacher! Teacher S could quickly see whether or not the class could correctly identify and label the 5 geometric literacy terms of the lesson. He could also see common errors and share them with the class. Everybody participated and yet nobody was singled out by not having complete comprehension. See the corresponding picture.

Wed, Dec 19 #6

Here is a teacher generated Tree Map about graphing rational functions. I used it to summarize three days of activities, discussions and examples about the complexities of rational functions. The students were asking lots of questions about particular procedures and parts of the examples, but I didn't think they had a strong grasp of the whole picture. Using the Tree Map was very helpful because it made obvious the differences between local and global behavior. It also helped to categorize all of the procedures and definitions and examples we had discussed.

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.