7.4A/7.4B STUDENT ACTIVITY #1

Transcription

1 7.4A/7.4B STUDENT ACTIVITY #1 Write a formula that could be used to find the radius of a circle, r, given the circumference of the circle, C. The formula in the Grade 7 Mathematics Chart that relates the radius of a circle to its circumference is C =. Rewrite the formula so that it gives r in terms of C. To do so, divide both sides of the equation by. C 2 r C r The new formula C can be used to find the of a circle when given the of a circle. TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 1

2 7.4A/7.4B STUDENT ACTIVITY #2 This graph shows the relationship between the between the length of a diameter of a circle and the circumference of a circle. y Circle Relationships Diameter x Build a table that represents the data in the above graph. Write the coordinates of the four points plotted on the graph. (, ), (, ), (, ), (, ) The x-coordinates of the points represent. The y-coordinates of the points represent. Fill in the table so that it shows the same relationship between the length of the diameter and the circumference of a circle. Circle Relationships Diameter TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 2

3 7.4A/7.4B STUDENT ACTIVITY #3 WHERE DID COME FROM? Materials: Scissors, 1" grid paper, peel-and-stick dots, colored markers, clear tape, curling ribbon, rulers (customary), circular lids of various sizes (4 per group of 4 students) Procedure: Work in groups of 4. Identify Student #1, Student #2, Student #3 and Student #4. Student #1 measures and records the diameter of Lid #1 in the Lid Measurements Data Record. Student #2 measures and records the diameter of Lid #2 in the Lid Measurements Data Record. Student #3 measures and records the diameter of Lid #3 in the Lid Measurements Data Record. Student #4 measures and records the diameter of Lid #4 in the Lid Measurements Data Record. Student #1 uses curling ribbon to measure and represent the circumference of Lid #1. Wrap the ribbon around the lid, cut it, measure its length (in inches), and record its length in the Lid Measurements Data Record. (As an alternative method, make a mark on the edge of the lid, place this mark at the end of the ribbon, roll the lid for one complete revolution, mark the ribbon, cut it, measure its length (in inches), and record its length in the Lid Measurements Data Record.) Student #2 follows the same procedure to measure and represent the circumference of Lid #2. Student #3 follows the same procedure to measure and represent the circumference of Lid #3. Student #4 follows the same procedure to measure and represent the circumference of Lid #4. Student #1 gives the data from Lid #1 to the other students in the group so they can record on the Lid Measurements Data Record. Student #2 gives the data from Lid #2 to the other students in the group so they can record on the Lid Measurements Data Record. Student #3 gives the data from Lid #3 to the other students in the group so they can record on the Lid Measurements Data Record. Student #4 gives the data from Lid #4 to the other students in the group so they can record on the Lid Measurements Data Record. Lid #1 #2 #3 #4 Diameter (in inches) (in inches) Any Lid d C C d C d = TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 3

4 Complete the table and answer the following questions: What do you observe about the ratio of C to d? What can you conclude from the table about the relationship between the circumference and diameter of a circle? Write an equation to represent the relationships between the circumference and diameter of a circle. Does this relationship hold true for all circles? Why or why not? Work together to graph the data from the table. Using the 1" grid paper, start the construction of a graph of the ordered pairs from the table (diameter, circumference) by placing Lid #1 with its diameter along the x-axis, one endpoint at the origin, and marking a point on the x-axis to correspond to the other end of the diameter. Take the ribbon corresponding to the circumference Lid #1 and tape one end of the ribbon at the endpoint of the diameter you just marked. Pull the ribbon up so that it forms a line segment parallel to the y-axis and secure the other end with a peel-and-stick dot. Repeat the process for Lid #2, Lid #3 and Lid #4 to make the graph on the 1" grid paper. Transfer the data from the table and the 1 grid paper to the grid below to make a graph. Title and label the graph. TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 4

5 After completing the graph answer the following questions: What does the length of the ribbon represent? What is the relationship between the ordered pairs on the graph and the data in the table? What appears to be true about the points represented by the peel-and-stick dots? Find the ratio of the length of the ribbon to the distance from the origin to the ribbon for each circle. Lid #1 Lid #2 Lid #3 Lid #4 Length of ribbon Distance from origin to ribbon length of ribbon dis tance from origin to ribbon Any Lid C d What does this ratio represent? Interpret the meaning of any ordered pair (d, C) on the graph using the ratio and the shape of the graph. Record your interpretation below. Use the graph to predict the diameter of a circle with a circumference of 24 inches. How did you determine your prediction? Use the graph to find the value of C in the ordered pair (9, C). TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 5

6 7.4A/7.4B OPEN ENDED #1 Express the radius of a circle, r, in terms of the circumference C. r = Express the diameter of a circle, d, in terms of the circumference C. d = If a circle has a circumference of approximately 36 units, write an expression to represent the radius. If a circle has a circumference of approximately 48 units, write an expression to represent the diameter. 1. What mathematical concepts and vocabulary do I need to know to be able to work this problem? 2. Will the Grade 7 Mathematics Formula Chart be helpful on this problem? Why or why not? 3. Will a picture or diagram help me on this problem? Why or why not? 4. What problem-solving strategy or strategies will I use to help solve this problem? 5. Extension (7.3B): A circle has a circumference of feet. How many inches long is the circumference? TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 6

7 7.4A/7.4B OPEN ENDED #2 The relationship between the radius of a circle and the circumference of the circle is given in the table. The approximation for the circumference has been given using 3 for. Radius, x, y Extend the table to contain radii lengths of 3, 3.5, 4 and 4.5. Plot the new values on the grid. Write a number sentence that describes the relationship between C and r. 1. What mathematical concepts and vocabulary do I need to know to be able to work this problem? 2. Will the Grade 7 Mathematics Formula Chart be helpful on this problem? Why or why not? 3. Is this a proportional relationship? Why or why not? 4. What problem-solving strategy or strategies will I use to help solve this problem? 5. Extension (7.3B): If the radius of a circle is doubled, what happens to the circumference? TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 7

8 NAME DATE SCORE /5 7.4A/7.4B Homework #1 1. The diagram below was created by inscribing four circles in a square. The side of the square is 20 units. Write a formula that will correctly calculate the circumference of the four circles. 2. Two circles are drawn so that the diameter of the larger circle is 6 times the smaller circle s diameter. Write a formula that can be used to find the circumference, C, of the larger circle using the variable d. Diameter: d Diameter: 6d 3. The following graph shows the relationship between the radius and circumference of a circle. Estimate the circumference of a circle with radius 2.5 units. Explain how you estimated your answer Radius TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 8

9 4. Mrs. Jamison has a table with a circumference of approximately 40 feet. Write an expression that can be used to represent the diameter of the table. 5. A circular table has a circumference of 75 inches. Explain the process you can use to find the radius of the table. Show any formulas you use. TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 9

10 NAME DATE SCORE /5 7.4A/7.4B Homework #2 1. Mr. Smith wants to increase the size of his circle s radius by 2 feet. Write a formula that can be used to find the circumference of the larger circle. r r A circular sign has a radius of 6 feet. What is the circumference of the sign to the nearest whole foot? Show your work to support your answer. 3. The table shows the relationship between the radius of a circle and its circumference. Length of radius (inches) (inches) Using the data from the table, what is the best estimate of the circumference of a circle with a radius of 1.5 units? Explain your answer. TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 10

11 4. A carpenter has a piece of wire that is 48 feet long. He wants to shape the wire into 6 circles of equal size. Write an expression he could use to determine the diameter of each circle. Explain your expression. 5. A circle has a circumference of approximately feet. It is to be enlarged so that the circumference is twice the original circumference. What will be the radius of the larger circle? Show any formulas you use and your work. TEKSING TOWARD TAKS Weeks 3 - Lesson 7 Page 11