In today's lesson, the students learn to identify polygons by their attributes. This aligns with 4.GA.2 because the students will classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size.
To get started, I tell the students that we will learn about polygons. I let them know that I am not going to tell them the definition of a polygon, they will have to tell me based upon the power point. But, before we start, we review the definitions for line segment and angles. I ask the students, "Who can tell me about a line segment?" I give the students a few minutes to think about the question. One student responds, "It has 2 end points." I tell the student that his response is correct. But, I want more information. "What does that mean?" I take a response from another student. "That means that it stops going in both directions." From there, we review the definition of an angle. "Name the angles that we have been studying and tell me about them." The students proceed to share. Student responses: acute angles are less than 90 degrees, a right angle is 90 degrees, an obtuse angle is greater than 90 degrees but less than 180 degrees, and a straight angle is 180 degrees.
I call the students to the carpet as we prepare for a whole class discussion. The What is a Polygon power point is already up on the Smart board. I like for my students to be near so that I can have their full attention while I'm at the Smart board.
Based upon what you see on the board, I want you to figure out the attributes of a polygon. On this side, I have two examples of a polygon. On this side, these three are not polygons. I want you to take a minute and look at the examples, then write down something that describes a polygon.
I give the students a few minutes to study the examples. Raise your hand and tell me, what is a polygon? I call one student who has shown vast improvement this school year. Her response, "They have straight lines with no curves." I ask the class if they agree, and they all agreed. That is correct, a polygon has straight lines without any curves. Can someone else tell me something else about a polygon? The student that I called on said that it is a closed figure. What makes you say that it is a closed figure? She pointed out the in the non example of a polygon, the shape was open. That is correct. I call on my new student to add on. She said that a polygon has faces. I let the class know that we are talking about two-dimensional shapes. We will discuss faces when we work on three-dimensional shapes. I have a student to say that polygons are made out of line segments. Are line segments straight or curved? They all tell me that line segments are straight. Finally, a student says that they have corners. Let's come up with a better word for corners. They have vertex or vertices. Vertices is plural for vertex. I point out a triangle on the Smart board. How many lines do we have in this shape? The students know that there are 3 line segments in a triangle. How many vertices do you see? I circle the vertices as we count together. There are 3 vertices. When you do your activity in your group, I want you to pay attention to the number of line segments and vertices in each shape.
We said that a polygon is made up of line segments. Can a polygon be made up of lines? Think about that before you speak. The students think about the question for a minute. Now, share with someone at your group. I call on students to respond. Does anyone think no that a polygon cannot be made up of lines? All of the students thought that a polygon could be made up of lines. Let's go back to lines and line segments. Someone tell me what a line is? A student responds, "It goes straight." I tell them I need something else about a line. Another students responds, it keeps going and never stops. So let me go back to my question again. Can a polygon be made up of lines? Most of the students said yes, while only a few said no. Why did you say no? I was proud of this student because she was one of the few who said no, she was not afraid to voice her reasoning. "Because if a line goes on and on, then it does not stop. If it does not stop, you can't make the shape."
I remind the students that these polygons will be made up of the types of angles that we discussed earlier. I review some names of polygons and introduce new ones by going over the definitions using the Polygon Vocabulary* on the Smart board before I put them into groups. I call students to the Smart board to match the definition with the correct polygon. We do this several times before the students work in groups. (*You can only use this document if you have the Smartboard notebook on your computer. Download it to your computer, then open using the notebook software.)
I give the students practice on this skill by letting them work together. I find that collaborative learning is vital to the success of students. Students learn from each other by justifying their answers and critiquing the reasoning of others.
For this activity, I put the students in pairs. I give each group a Polygon Group Activity Sheet and a ruler (MP5). The students must work together to draw polygons (MP4), then identify the number of sides and vertices. They must communicate precisely to others within their groups. They must use clear definitions and terminology as they precisely discuss this problem.
The students are guided to the conceptual understanding through questioning by their classmates, as well as by me. The students communicate with each other and must agree upon the answer to the problem. Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students. As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill. As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.
As they work, I monitor and assess their progression of understanding through questioning.
1. What is the name of this polygon? How do you know?
2. How many sides and vertices does this polygon have?
3. Can the number of sides and vertices be different?
As I walked around the classroom, I heard the students communicate with each other about the assignment. From the Video on Polygons, you can hear the classroom chatter and constant discussion among the students. Before Common Core, I thought that a quiet class working out of the book was the ideal class. Now, I am amazed at some of the conversation going on in the classroom between the students.
Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing.
To close the lesson, I have one or two students share their answers. This gives those students who still do not understand another opportunity to learn it. I like to use my document camera to show the students' work during this time. Some students do not understand what is being said, but understand clearly when the work is put up for them to see.
I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson. Students need to see good work samples, as well as work that may have incorrect information. More than one student may have had the same misconception. During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.
I ask, What have you noticed about the number of sides and vertices? A student shares, "They are the same." They are always they same, aren't they? If it is a 5-sided shape, it has 5 vertices. If it is a 3-sided shape, it has 3 vertices. Again, what are vertices? Some students yell out angles, the rest yell out points. A lot of you keep saying points. The two rays meet up together to form an angle. Vertices are your angles.
From the student responses, I know that we will continue to study vocabulary to help the students understand the difference between vertices and points.