. 7.9A STUDENT ACTIVITY #1
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1 . 7.9A STUDENT ACTIVITY #1 Problem #1: Morgan is designing a circular spirit sign to put in the front yard of the middle school athletes. The sign will have a circumference of 94 inches. What is the minimum width to the nearest inch of the piece of wood from which she can cut a sign? Identify the formula that applies to the problem you are solving. The minimum width of the piece of wood she can use is equal to the of the circle. Use the formula for the circumference of a circle to find the diameter. The formula for the circumference of a circle is or. Identify what the variables in the formula stand for. Substitute for C and for. The formula for the circumference of a circle contains, so the answer will be. Substitute the variables in the formula with their values from the problem. C = d d Perform the calculations. Remember to use the correct order of operations. Solve for d. d d d State the solution to the problem using the appropriate units of measurement. The diameter of the circle is about inches. Therefore, the minimum width to the nearest inch of the piece of wood from which Morgan can cut the sign is inches. TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 1
2 Problem #2: Trisha is putting gold glitter on the shaded part of the larger circle below. Approximately how many square inches will she glitter? 8 in. 20 in. Identify the that applies to the problem. Find the area of the shaded part of the larger circle by the of the circle with a radius of inches from the area of the circle with a radius of inches. The problem involves the formula for the of a circle. The formula is. Identify what the in the formula stand for. A stands for, has an estimated value of, and r stands for. Replace the in the formula with their values from the problem. Find the area of the circle with a radius (r) of 20 inches. Use 3.14 as an estimate of the value of. A ( )( 2 ) Solve for. A ( )( ) in. 2 Find the area of the circle with a radius (r) of 8 inches. Use 3.14 as an estimate of the value of. A ( )( 2 ) Solve for. A ( )( ) in. 2 State the solution to the problem using the appropriate units of measurement. To find the of the shaded part, subtract the of the -inch circle from the of the -inch circle. - in. 2 Trisha will glitter about square. TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 2
3 Problem #3: Kamil painted only the circumference of a circle with a radius of 10 inches on a park playground, then he painted an entire circle with a diameter of 10 inches inside the first circle. What is the approximate unpainted area of the first circle Kamil painted? 10 in. 10 in. Identify the that applies to the problem. Find the unpainted area of the larger circle by the of the circle with a diameter of inches from the area of the circle with a radius of inches. The problem involves the formula for the of a circle. The formula is. Identify what the in the formula stand for. A stands for, has an estimated value of, and r stands for. Replace the in the formula with their values from the problem. Find the area of the circle with a radius of 10 inches. Use 3.14 as an estimate of the value of. Solve for. A ( )( 2 ) A ( )( ) in 2 Find the area of the circle with a diameter of 10 inches. The radius of that circle is inches. Use 3.14 as an estimate of the value of. Solve for. A ( )( 2 ) A ( )( ) in 2 State the solution to the problem using the appropriate units of measurement. To find the of the unshaded part of the larger circle, subtract the of the - inch circle from the of the -inch circle. - in 2 The approximate unpainted area of the first circle Kamil painted is about square. TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 3
4 Problem #4: Jillian made a silver circular disk as a base for a large pendant for a necklace. Use the ruler on the Mathematics Chart to measure the radius of the center in centimeters. What is the approximate area of the silver disk? Silver Disk Identify the formula that applies to the problem you are solving. The formula for the area of a circle is. Identify what the variables in the formula stand for. Measure the of the circle using your Grade 7 Mathematics Chart. Substitute for and for r. The formula for the area of a circle contains, so the answer will be. Substitute the variables in the formula with their values from the problem. A ( )( 2 ) Perform the calculations. Remember to use the correct order of operations. Solve for. A ( )( ) cm 2 State the solution to the problem using the appropriate units of measurement. The area of the silver disk is about centimeters. Problem #5: Ms. Beverly wants to redesign the front entrance to her office. One rectangular window in the front measures 4.5 feet by 3 feet. If she replaces the rectangular window with a circular window that has a diameter of 5 feet, about how much more will the area of the circular window be than the area of the rectangular window? Identify the formula that applies to the problem you are solving. Identify what the variables in the formula stand for. Substitute the variables in the formula with their values from the problem. Perform the calculations. Remember to use the correct order of operations. Show your work on the back of this page. State the solution to the problem using the appropriate units of measurement. TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 4
5 7.9A STUDENT ACTIVITY #3 Circle Pi Materials: Centimeter grid paper, four circles that are the same and labeled A, B, C, D, E, F, G or H (whichever ones were given to your group), a safety compass, a centimeter ruler, and scissors Procedure: Work in groups of 4. Identify Student #1, Student #2, Student #3 and Student #4. Each member of your group needs centimeter grid paper, one of the circles from the baggie given to your group, a safety compass, centimeter ruler, and scissors Working independently to find the length of the diameter and radius to the nearest tenth of a centimeter for your circle and record your measurements on the Circle Measurements Record. Be sure to record which circle you measure in the title of the table. Use a safety compass to inscribe a circle with the same measurements as your circle in a square on centimeter grid paper. Use the centimeter grid paper to find an estimate for the area of the circle and record your estimate on the Circle Measurements Record. (Do not use any formulas to find the area.) After you have recorded your estimate, work with the other 3 people in your group to share the measurements everyone made independently and record on the Circle Measurements Record. Circle Measurements Record for Circle Student #1 #2 #3 #4 Group Data Diameter (in cm) Radius ( in cm) Area (in cm 2 ) Discuss the questions below as a group and record the answers. Then decide upon the group data. Record your decisions on the group data in the last row of the table. How did you find the diameter of your circle? How did you find the radius of your circle? Explain the method you used to determine the area of your circle. How could you get a better estimate of this area? How will you determine which data to report as the group data? Your teacher will put a Circle Pi transparency on the overhead projector. Student #4 transfers the data from his/her table to the appropriate table on the transparency. TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 5
6 Record the group data from the transparency in the table below, then answer the questions following the table. Group Data Circle Measurements Record Circle A B C D E F G H Diameter (in cm) Radius ( in cm) Area (in cm 2 ) What is the ratio of the diameter of circle A to the diameter of circle E? How does the ratio of the diameters compare to the ratio of the areas of circle A and E? What is the ratio of the area of circle G to the area of circle B? How does this compare to the ratio of the radius of circle G to the radius of circle B? Do you find a similar pattern between the radii (or diameters) of other circles and their areas? Explain. TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 6
7 Transfer the data from the Group Data Circle Measurements Record to graph the ordered pairs (radius, area) on the grid below. Title and label the graph. Answer the following questions: What do you observe about the shape of this graph? Use a pencil to extend the graph so that predictions can be made. Is it reasonable for this graph to contain the origin? Why or why not? Use the graph to: predict the area of a circle with a radius of 8 cm. find the radius of a circle with an area of 20 cm 2. Use your safety compass to draw a circle with a radius of 8 cm on centimeter grid paper. Estimate the area of the circle by counting squares. paper. For a better estimate, use the 1 2 cm grid Compare your prediction of the area of a circle with a radius of 8 cm using the graph with your estimate using the grid paper. TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 7
8 7.9A OPEN ENDED #1 Martha drew a circle with a circumference of approximately centimeters. Circumference: cm What dimension of the circle does Martha need to be able to determine the area of the circle? Describe a procedure she can use to determine the area of the circle. Find the area of the circle. Show your work. Martha has decided to cut a circle congruent to the one she drew above from a square piece of cardboard. What is the minimum side length of the piece of cardboard she will use? Show your work. 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. Explain the relationships of the diameter of her circle to the radius of her circle. 4. What problem-solving strategy or strategies will I use to help solve this problem? 5. Extension (7.4A): What is the ratio of the circumference to the diameter of any circle? TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 8
9 7.9A OPEN ENDED #2 MAT H E MAT I CS Mr. Garcia has a piece of wire that is 16 feet long. He cuts the wire into two equal pieces. He wants to form a square with one piece and a circle with the other piece. Determine the side length of the square he will form and the diameter of the circle he will form. Show your work. 16 feet 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. What role does the length of the wire have in each shape? 4. What problem-solving strategy or strategies will I use to help solve this problem? 5. Extension (TEKS 7.9A): Find the area of each of the shapes in the problem above. Show your work. TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 9
10 NAME DATE SCORE /5 7.9A Homework #1 1. The foul shot area of a basketball court is half a circle and rectangle composite figure. The dimensions of the rectangular section of the court are 19 ft by 12 ft. 19 feet 12 feet Describe the steps that can be used to find the area of the foul shot area. List the formulas that can be used. Steps: Formulas: 2. Describe the steps you would use to find the perimeter of the foul shot area described in #1 above. List any formulas you would use. Steps: Formulas: 3. You can pick up your favorite radio station s signal within a 100-mile radius of the station. What is the area of the region that picks up the radio station s signal? Record the formulas you use and show your work. 4. Which has the most area: a circle with a radius of 10 inches or a circle with a circumference of approximately 75 inches? Show your work and justify your answer. 5. A target board for a dart game is shown below. Find the area of the shaded part of the target. The largest circle has a diameter of 18 inches. Each of the other circles has a diameter half the length of the one before it. Record the formulas you use and show your work. TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 10
11 NAME DATE SCORE /5 7.9A Homework #2 1. Find the area of the shaded region in the figure below. Show your work including any formulas you use. 20 inches 6 inches 2. Which has the most area: a circle with a radius of 10 inches or a square with a side length of 20 inches? Show your work and justify your answer. 3. A circle with a diameter of 20 feet is divided into four parts. Two of the parts are colored blue as shown below. Find the area of the circle that is colored blue. Record the formulas you use and show your work. Blue Blue 4. Find the area of a circle with a circumference of 31.4 inches. Record the formulas you use and show your work. 5. Find the circumference and area of a circle with a diameter of 8 inches. Record the formulas you use and show your work. TEKSING TOWARD TAKS Weeks 3 - Lesson 8 Page 11
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