Math with Mrs. D: Plane and Polygon Figures

Today we moved into defining some geometrical terms. I began with a formative assessment called "A&D Assessments." I found this in a book called Mathematics Formative Assessment by Page Keeley and Cheryl Rose Tobey. This is basically a "fact/fiction" statement. The students choose between (1) I agree, (2) I disagree, (3) It depends, and (4) I'm not sure. They are to justify their choice with their thoughts.

Our first A&D Assessment was: All of these shapes are plane figures. I asked the students to make their choice, justify it, and then stand by their chair. After everyone had completed their thought, I asked the students to go to a corner of the room based on their choice (4 Corners). Once in the corner, I asked the students to discuss their thoughts on their choice and look for any commonalities in their thinking. After a moment's discussion, I asked each group to share their thinking with the whole class. At first, they were a little hesitant, however, once they realized that this wasn't a grade and I just wanted to hear their thinking, they relaxed.

It was very interesting to hear their misconceptions about plane figures. For example, most of the students did not believe that the irregular hexagon was a plane figure because it was not a "normal" shape. .

After our discussions, I asked them to return to their seats and we took a few notes in our journal about plane figures. We determined that a plane figure is ANY closed, 2-d figure. Therefore the statement was true! All of the figures on the page were plane figures..... including the irregular hexagon!

Next, we moved on to defining the word polygon. I posed another A&D Assessment statement. Using the same figures, this time the students were asked if all of the shapes were polygons. The procedure went much more smoothly and students moved to the four corners much more readily. However, there were additional, and some surprising, misconceptions. The misconception that arose the most was that a figure was a polygon based on the number of sides. For example, a triangle is not a polygon.... it has too few sides, or a hexagon is not a polygon... it has too many sides. Students did not seem to understand that the term polygon is a more global term, not one associated with a single shape.

Once again, after our discussion we returned to the desks and

added this page to our journal. The students have been working with prefixes and suffixes in reading and were able to tell me that the prefix "poly" means "many." Using this knowledge, we defined polygon as a plane figure (2-d, closed) that is made up of at LEAST three line segments. Students now understood that the only figure on the paper that was not a polygon was the circle.

Our next activity required that the students use their prior knowledge of critical attributes of geometric figures to compare and contrast sets of polygons. I found this activity, called "Polygon Sets," in a book entitled Good Questions for Math Teaching, Grades 5-8 by Lainie Schuster and Nancy Canavan Anderson. The students were given a sheet of polygon sets. I posed the first question:

How are the polygons the same in each set?

We began by thinking of all of the ways that we classify geometric shapes. Students brainstormed a list of critical attributes to used to compare the figures:

# of sides
# of vertices
parallel lines
perpendicular lines
# and types of angles
symmetry

Using these attributes, they began working in table groups to find the reason that the shapes went together. Here is an example of the thinking from one class as we combined our answers and process of solving the problem: