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Main Curriculum Tie:
Background For Teachers:
Enduring Understanding (Big Ideas):
Ways to Gain/Maintain Attention (Primacy):
Lesson Segment 1: What information is needed to find circumference of a circle?
Literature: Read “Sir Cumference and the First Round Table” (Cindy Neuschwander, 1997). As you come to shapes for each table, have the students sketch and label an example on the Math Journal page, Sir Cumference and the First Round Table Vocabulary. Especially focus on the words pertaining to the circle: circumference, diameter, radius.
Estimating: Circumference Guess
Helping Students Visualize Circumference
Tell them estimating distance around is very difficult to do. The way you guess is to estimate the distance across the center (the diameter) and try to visualize a little more than three of those distances. That will be the distance around or the circumference. Ss you visually estimate the height of the object as compared to the circumference, you try to estimate about three diameters and compare that to the height. Tell them this relationship between the diameter and the circumference of a circle is called Pi. In any true circle the circumference will always be a little more than three diameters. Have them look at the formula on their Class Reference Sheet connecting this idea with the formula, C = πd, or C=2πr. Using the tennis ball canister is especially effective since it contains three round balls. The height should be very close to the circumference for this object.
In order to find circumference, then, we need the measure of the diameter, or of the radius. Q. Think-Team-Share: If we only know the measure of the radius, how could we know the measure of the diameter?
Movement: Use team formations where student groups stand and demonstrate circumference, diameter and radius.
Journal: Work with students to complete the Diameter, Radius, and Circumference sections of the Frayer Model for vocabulary.
Lesson Segment 2: How can I find the circumference?
Lesson Segment 3: What information is needed for finding area of a circle?
Have students predict the total number of square centimeters in the whole box of the Counting The Area of a Circle worksheet (100 x 4 = 400) and write their prediction.
Just like we need to know the length of a side of a square to find the area by squaring that number, we also need to know the length of the radius to find the area by squaring that number. Pi is also needed for the formula.
Have student write the answer for the questions below the box on the Counting Area of a Circle worksheet as you discuss these ideas.
Work with students to complete the Area part of the Frayer Model
Lesson Segment 4: How can I find area for a circle?
Do Mix-Freeze-Pair where students move around the room until you say freeze. The person closest to them becomes their partner. Sketch a circle on the overhead giving the radius length. Ask students to think about what the diameter would be. Then, ask the “partner with the fewest pets” to be the speaker to tell the other partner the answer and how they know. Have students mix-freeze again and sketch a second circle giving the measurement for the diameter. Ask them to think about how they would know the radius length. Ask “partner with lightest colored shoes” to be the responder.
Practice: Play Red Rover for some problems for circumference and area of a circle from an appropriate text assignment. In Red Rover, teacher gives a problem to the class. Students work the problem discussing with team. Then all teams simultaneously call a person to come to their team from the next higher numbered team. That Rover comes over to the team, sits down and explains how their team found the answer. The listening team then agrees or disagrees and discusses why. If the Rover explained correctly, the Rover’s team gets a point.
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