Age group: 6t h Grade Virginia - Mathematics Standards of Learning (2009): 6.10b Virginia - Mathematics Standards of Learning (2016): 6.7.a, 6.7.
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1 1 Lesson Plan Circumference and Area of Circles (Yard s) Age group: 6t h Grade Virginia - Mathematics Standards of Learning (2009): 6.10b Virginia - Mathematics Standards of Learning (2016): 6.7.a, 6.7.b, 6.7.c Fairfax County Public Schools Program of Studies: 6.10.b.1, 6.10.b.2, 6.10.b.3 Online resources: F e nc e d I n Opening Teacher present s Students pract ice Class discussion Closing M at h Obj ect ives E xpe ri e nc e a real-world example of circumference and area P rac t i c e squaring numbers Learn to calculate circumference and area of circles De vel o p geometry skills Ope ni ng 6
2 2 Ask the students to answer the following in their notebooks: What vocabulary do we need when we talk about circles? Define each of the words. When the students are done writing, share. Ask: What vocabulary describes circles? What does each word mean? Responses will vary, but should include the following: The di ame t e r is the line segment from one edge of the circle through the center to the other edge. The radi us is the line segment from the center of the circle to the edge. The c i rc umf e renc e is the distance around the circle. The area is the number of square units within the circle. Say: Today, we are going to investigate the circumference and area of a circle. Before we begin, let s look at the formulas. Write on the board: Ask: What is the value of π? Pi is an i rrat i o nal number, but we can approximate it using the value Say: Let s say we know the diameter. How do we find the radius? The radius is half the diameter. Say: Suppose the radius is 2 yards. What is the diameter? The diameter is 4 yards.
3 3 Say: Suppose the diameter is 10 yards. What steps do we take to find the area? We divide 10 by 2 to find that the radius is 5 yards. Then we square 5 to get 25. Finally, we multiply 25 by π, 3.14, to get 78.5 square yards. T e ac he r prese nt s M at h game : F e nc e d I n - Ci rc l e (yards) 12 Using Preset Mode, present Matific s episode F e nc e d I n - Ci rc l e (yards) to the class, using the projector. The goal of the episode is to measure a circular piece of land and calculate its circumference and area.
4 4 Say: Please read the question. The question asks, How many yards of fence will you need to surround the purple flower bed? Ask: What are we being asked to find? We need to find the circumference of the flower bed. Ask: Which formula should we use? What information do we need? We will use the formula circle.. We need to know the diameter of the Ask: What is the diameter of the flower bed?
5 5 The diameter of the flower bed is 1 yard. Ask: What is the circumference of the flower bed? How many yards of fence do we need? Click on the to enter the students answer. If the answer is correct, the episode will proceed to the next question. If the answer is incorrect, the question will wiggle. The episode will present a total of four questions. The second question is a circumference question; the final two questions ask about area. St ude nt s prac t i c e M at h game : F e nc e d I n - Ci rc l e (yards) 12 Have the students play F e nc e d I n - Ci rc l e (yards) on their personal devices. Circulate, answering questions as necessary. Cl ass di sc ussi o n 12 Display the following table: Say: Copy the table into your notebooks. Then take a few utes to calculate the circumference and area of each of the circles.
6 6 When the students are done working, share. Ask students to come to the board to complete the table. Ask: What is happening in the left hand column of the table? How is the radius changing? The radius is doubling. Double 1 is 2. Double 2 is 4. Say: Is this true of the circumference and area also? Are they doubling as we move down through the columns? The circumference is doubling. If we multiply 6.28 by 2, we get If we double 12.56, we get The area is not doubling. If we double 3.14, we do not get Ask: How is the area changing? The area is quadrupling. If we multiply the first entry, 3.14, by 4, we get the second entry, If we multiply by 4, we get the third entry, Say: If we continue this pattern, what do we expect the circumference and area to be for a circle with radius 8 yards? We expect the circumference to be and the area to be Say: Let s check. Are these two values correct? Does an 8-yard circle have circumference and area ? Yes, if we use the formulas, we do indeed get for circumference and for area.
7 7 Say: Let s look again at the formulas. Display the formulas again: Ask: Why does it make sense that as the radius doubles, the circumference doubles but the area quadruples? The circumference is found by multiplying π by the diameter. As the radius doubles, so does the diameter. Then the product of the diameter and π will also double. The area is found by multiplying π by the radius squared. As the radius doubles, the square of the radius quadruples. (When the radius is 1, is 1. When the radius is 2, is 4. When the radius is 4, is 16. When the radius is 8, is 64.) Then the product of π and will also quadruple. Run the episode and discuss the given situation. For example: Say: Let s measure the flower beds and find the area of each. Ask a student to come to the front to measure the diameter of each flower bed.
8 8 Write the diameters of each flower bed on the board. (Answers that follow are for when the purple and red flower beds each have diameter 1 yard and the white flower bed has diameter 2 yards.) Ask: What is the area of the purple flower bed? The area of the purple flower bed is square yards. Ask: What is the area of the red flower bed? The area of the red flower bed is square yards. Ask: What is the area of the white flower bed? The area of the white flower bed is 3.14 square yards. Say: Suppose we want to find the area of the rest of the park. How could we find the area of the park that is not covered by flower beds? First, we would measure the length and width of the park. Then we would multiply to find the area of the entire rectangle. From that number, we would subtract the areas of each of the flower beds in order to find the remaining area. Ask a student to come to the front to measure the length and width of the park. (The answer that follows is for when the park is 9 yards by 6 yards.) Ask: What is the area of the land in the park not covered by flower beds? The area is square yards.
9 9 Cl o si ng 5 Say: Suppose your friend was absent and missed class today. Let s think about how we would summarize today s class for that friend. How would you define circumference and area for him or her? Circumference is the distance around a circle. Area is the number of square units within a circle. Ask: How do we calculate area and circumference of a circle? To calculate area of a circle, we multiply π by the square of the radius. To calculate circumference of a circle, we multiply π by the diameter. Say: Give an example of a circumference problem. Responses will vary. A possible response: A circle has a radius of 3 yards. What is its circumference? Ask: What is the answer to the problem that we just stated? How do you find the answer? The circle has circumference yards. To find the circumference, we multiply π by the diameter. Since the radius is 3, then the diameter is twice 3, or 6 yards. When we multiply π, 3.14, by 6, we get
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