Lesson 1

Geometry

Properties of a Circle

Pre-Reading

I. Motivation: “Today, in math class we are going to learn about circles and their properties. First of all we are going to learn an easy and fun way to create our own circles. I want everyone to get out a pencil, and then I will come around and deliver a piece of string and two pieces of tape. Now watch me as I demonstrate how to create an easy symmetrical circle. First I am going to tape a piece of string to the pencil. Next I am going to tape the other end of the string to the center of the paper. Now watch as I make sure the string is tight and now I will move my pencil completely around to create a circle.”

II. Prior Knowledge: “We just discussed in the last class the characteristics of polygons, so in what ways is a circle like a polygon? (Both are closed plan figures.) How do they differ? (A circle has no vertices and no straight sides.) I want you to tell me why else is a circle not a polygon? (All points on a circle are the same distance from the center). Why is that not true for a polygon, could someone come up to the board and demonstrate why the polygon does not have all points equal distance from the center.” Is there a polygon that has all points the same distance from the center? (No, that is one reason why the circle is so unique.)

III. Purpose: "Today, we are going to learn about the special properties of the circle, which include some key terms such as circumference, radius, radii and diameter. To get all of us thinking about the properties of the circle, we will use a brainstorming technique. Then we will read an informational text that informs us the basic parts of the circle."

IV. Explicit Strategy Instruction: Brainstorming using Webbing
“To help us gather our ideas about the special properties of circles. We will be brainstorming our ideas into a web describing the special properties of circles. I would like all of you to take a moment and think about what you already know about circles and their special characteristics.

First we will:
1. State (restate) concept or topic: Properties of circles
2. Establish time limit: 10 minutes
3. Fulfill your role: Break students up into groups of four assigning each student their own role for the activity.
Recorder: This person is in charge of recording the information into the web. The recorder must make sure the web is neat and legible. Correct spelling is not a concern at this point.
Timekeeper: This student is in charge of looking at the clock to be sure the group is pacing themselves appropriately to complete all the terms in the established 10 minute time period.
ALL: “I want everyone to make sure everyone including those with assigned jobs must think freely and critically to come up with ways to tie the key terms together with one another in a webbing format. The main purpose of brainstorming is to record as many ideas as possible in the short time period”

I will model the first step. First I will write the word circle in the middle of the paper. Then I will branch the word circumfernce off the word circle. The word formula can be branched off the word circumference, because I know there is a formula you can use to find the circumference. Now I want you to brainstorm as many ideas as possible about the circle in a short amount of time.
I will walk around the room and guide the students to record as many ideas as possible using their prior knowledge about circles.

(After brainstorming) “Great job class! Now I would like each group to share their webs with the class. You will be able to see how your web compares with the rest of the class. You will also be able to identify special characteristics you may not have in your own web.”
“What are some other subjects you can use with brainstorming?” (reading, social studies, science, math; brainstorming can be incorporated into lots of subjects)
“What are some other topics in math we could use brainstorming to gather our ideas and concepts for to better understand the overall picture?” (other shapes, almost any basic math concept)

During Reading

"Now I will read the story Sir Cumference and the First Round Table, by Cindy Neuschwander and Wayne Geehan. The story Sir Cumference and the First Round Table uses ideas offered by the Knight’s wife and son to find the perfect shape for his table. Listen carefully as this text informs us about the basic parts of the circle which include the radius, diameter and circumference."

Geehan, W., & Neuschwander, C. (1997). Sir Cumference and the first round table. Massachusetts: Charlesbridge.

Readability: 4.6 grade level using the Flesh-Kincaid; this narrative is great read aloud story for the whole class because it uses instructional level vocabulary words. This story contains math vocabulary words that will be challenging to some fourth graders. The text has a lot of context clues to help the students identify and define the key math concepts. The narrative story uses an assortment of description context clues, which include both semantic and syntactic clues. The graphic clues are very beneficial because they visually illustrate the math concepts. The text font and size can be easily be read by both the teacher and students. The students should have a strong schematic background with King Arthur, if not they should be informed prior to reading the story. The students should also have some prior knowledge with the properties of circles from previous grades. The readability of 4.6 is compatible with the fourth grade instructional level students while keeping their interest.

Modified/ Supplementary Text
Since this is only a narrative text, it is appropriate to add a supplementary expository text with the struggling students. The students will be able to identify the key math concepts with graphic aids. The text is only a supplementary text that aids the reader with the narrative text.

Caron, L., & Jacques, P. (2001). Geometry. New Jersey: Enslow Publishers.

V. Text Structure
A. Narrative

VI. Vocabulary
"The following vocabulary words are very important. I want you to include those vocabualry words with their defintion in your journal."

The Circumference of a circle is another name for the perimeter of a circle.
(n)Circumference: The length of the boundary of a circle, which is another name for the perimeter of a circle.

The diameter of a circle is a line that passes through the center of the circle.
(n)Diameter: the longest line possible that passes through the center of the circle.

The radius of a circle is a line segment that has one endpoint on the circle and one endpoint at the center of the circle.
(n)Radius: is a line segment that has one endpoint on the circle and one endpoint at the center of the circle

VII. Content

Remember to keep the standard and Benchmark in tact to meet the curriculum needs of the students.

Mathematics
Geometry – Standard 4 – Benchmark 2
Standard 4: Students investigate and apply measurement systems to physical attributes and situational characteristics.

After Reading

VIII. QAR Questions
“Wow what a great story that included important key terms about circles.
(Text Explicit) Who was the King that had the problem with the first round table?
King Arthur. The answer is Right There because the author says, “King Arthur called upon his bravest and most trusted knights to plan what to do.

(Text Implicit) How does the author use vocabulary to explain mathematical concepts? Give two examples.
The author used the key circle concepts in replace of his knight’s team names. The author also uses diagrams to illustrate the important key vocabulary words. The answer is Think and Search because the answer can be found on several different pages in the book.

(Text Implicit) How does the author use diagrams to explain how geometric figures are related? Show your examples by drawing the diagrams. Check around the room to look over the student’s diagrams. The diagrams could include a rectangle (pg. 8), parallelogram (pg. 11), octagon (pg. 17), diameter example (pg. 29) and a radius example (pg. 30). The answer is Think and Search because the answer can be found in several pages of the book.

(Text Explicit and Text Implicit) Why do you think King Arthur chose the use the round table?
Everyone had an equal position around the table and no one had to shout or whisper. The answer is Author and Me because you would use knowledge you already know and use the text to find the answer.

(Script Implicit) What questions do you have about circles or other shapes?
The students will have various statements. The answer is On My Own because you don’t need the text to answer the question.

IX. Writing to Learn Activity

"I would like everyone to take out you journals. In your journal I want you to write about what you learned about circles and shapes from the story we had just read. This will be a reflection on what we learned today. I would also like to make sure you include these key vocabulary words in your entry, circumference, radius, and diameter. For example my model would include all the the key terms and in complete sentences. I want you to write as much as you need to in ten minutes. Remember to use complete sentences."

X. Closure

"I hope everyone enjoyed the reading the interesting yet formative narrative story. The purpose of this lesson today was to get informed about the special properties of circle. Let's review, what are the three properties of the circle we talked about today and their definition? (circumference, diameter and radius). So in what ways is a circle like a polygon? (Both are closed plan figures.) How do they differ? (A circle has no vertices and no straight sides.) I want you to tell me why else is a circle not a polygon? (All points on a circle are the same distance from the center) Can someone tell me why we used the brainstorming technique before we read the story? (the strategy was successful because we were able to draw upon previous knowledge and add to it with content knowledge from the story). Why was the QAR questioning helpful? (It made us comprehend the story in greater detail) Great job today and keep up the great work!"