Allyson, Amanda, Christy, Lisa, and Jordan Circles Allyson, Amanda, Christy, Lisa, and Jordan

Answer Key 2/3 x = 56.25 C=69.71 ft 1200 A = 615.75 km2

Ferris Wheel The amusement park has discovered that the brace that provides stability to the Ferris wheel has been damaged and needs work. The arc length of steel reinforcement that must be replaced is between the two seats shown below. If the central angle is approximately 25.7 and the radius is 12 feet, what is the length of steel that must be replaced? Describe the steps you used to find your answer. Brace that provides stability to ride

Arc Measure vs. Arc Length 100o C The measure of arc a is equal to the measure of arc b, but the arc lengths are obviously different. The point of this slide is to emphasize the difference between arc measure and arc length and to supply a real world application for arc length rather than arc measure. b

Explore Arc Length Materials String 1 can for each group (different sizes) Rulers Markers Scissors Worksheets 4/20/2017

Explore Arc Length

Ferris Wheel The amusement park has discovered that the brace that provides stability to the Ferris wheel has been damaged and needs work. The arc length of steel reinforcement that must be replaced is between the two seats shown below. If the central angle is approximately 25.7 and the radius is 12 feet, what is the length of steel that must be replaced? Describe the steps you used to find your answer. Brace that provides stability to ride

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Martinique's garden looks like two intersecting circles Martinique's garden looks like two intersecting circles. One circle has a radius of 6 feet and the other has a radius of 4 feet. The diagram below shows the garden with a path around the edge. Martinique walks along the path to admire her garden daily. If she does one rotation along the path, approximately how many feet has she walked? 15 feet 47 feet 63 feet 124 feet MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. 13

Martinique's garden looks like two intersecting circles Martinique's garden looks like two intersecting circles. One circle has a radius of 6 feet and the other has a radius of 4 feet. The diagram below shows the garden with a path around the edge. Martinique walks along the path to admire her garden daily. If she does one rotation along the path, approximately how many feet has she walked? 15 feet 47 feet 63 feet 124 feet MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. 14

Race track Use the diagram to complete the following problems. Turns 1,2,4,5,6,8, and 9 all have a radius of 3 meters. Turns 3 and 7 each have a radius of 2.25 meters. Calculate the length of the track. How many laps do you need to make to travel 1609 meters (about 1 mile)?

Enrichment: The Journey of the Moon In this activity, the students will use the concept of arc length to determine the distance the moon moves in an hour. Learning Objectives: Students will: Predict how far the moon travels in an hour. Collect data using a clinometer. Use the data to determine the distance the moon travels in an hour.

Enrichment: The Journey of the Moon Materials: Protractor Pen Straw Pencil Index card Paper String Calculator Paper clip Tape

Enrichment: The Journey of the Moon Instructional Plan: 1. Ask the students how many miles they think the moon travels in an hour? This should bring up a discussion on what information is needed in order to make a guess. 2. Provide the following information: The moon travels a distance of 1,423,000 miles around the earth. 3. Show the following link and work with students to have each make a clinometers. www.youtube.com/watch?v=GMLcU1Qknts 4. Work on the Moon Activity Sheet. 5. Have a class discussion on the results and reflections of the activity.

Enrichment: The Journey of the Moon In this activity, you will determine how far the moon travels in an hour. 1. What is your prediction? I believe that the moon travels ___________________ miles in one hour. 2. Tonight, at the top of the hour (any time after 7:00 pm), measure the position of the moon using your clinometers. The moon is at ____________________o 3. An hour later, repeat step 2. 4. How far did the moon travel within that hour? 5. Was your prediction accurate? If not, what could have been the reason(s) for the inaccuracy?

Authentic Tasks (CCSS) http://uhaweb.hartford.edu/MITESSER/Circle%20Unit%20Plan.pdf http://www.nsa.gov/academia/_files/collected_learning/high_school/modeling/staggered_starts.pdf

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Quiz #2

Quiz #3 3. Vicky looked at the outside of a circular stadium with binoculars. She estimated the angle of her vision was reduced to 60º. She is positioned so that the line of site on either side is tangent to the stadium. What was the measure of the arc of the stadium intercepted by the lines of site? A) 60º C) 120º B) 80º D) 160º

Quiz #4 4. The figure represents the overhead view of a deck surrounding a hot tub. What is the approximate area of the deck? A) 278.7 square meters B) 75.4 square C) 52.5 square D) 22.9 square

Quiz #5 5. An athlete is running along a circular path that has a diameter of 250 yards. The arc traveled by the athlete is 120°. Using 3.14 for π, how many yards did the athlete run? Round the answer to the nearest yard. A) 131 yards B) 262 yards C) 376 yards D) 545 yards

Quiz Answer Key

Quiz Answer Key

MA.912.G.6.5 Focus Questions

A. 133 inches2 B. 452 inches2 C. 531 inches2 D. 907 inches2 Gabriel inscribed quadrilateral ABCD in a circle, as shown below. Arcs AB and BC both measure 85° and arcs CD and DA both measure 95°. If line segment AB is 5 inches long and line segment length CD is 12 inches long, what is the area of the circle to the nearest whole square inch? A. 133 inches2 B. 452 inches2 C. 531 inches2 D. 907 inches2 MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. 30

A. 133 inches2 B. 452 inches2 C. 531 inches2 D. 907 inches2 Gabriel inscribed quadrilateral ABCD in a circle, as shown below. Arcs AB and BC both measure 85° and arcs CD and DA both measure 95°. If line segment AB is 5 inches long and line segment length CD is 12 inches long, what is the area of the circle to the nearest whole square inch? A. 133 inches2 B. 452 inches2 C. 531 inches2 D. 907 inches2 MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

Jeremy walked along the edge of a circular pond with an 8 foot diameter, as shown in the image below. What distance along the edge of the pond did Jeremy walk? (Round to the nearest foot.) 2 feet 4 feet 5 feet 10 feet MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. 32

Jeremy walked along the edge of a circular pond with an 8 foot diameter, as shown in the image below. What distance along the edge of the pond did Jeremy walk? (Round to the nearest foot.) 2 feet 4 feet 5 feet 10 feet MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

Sam has a circular dining room table, with a 5 foot diameter, that normally seats 5 people. The table expands to seat 10 people by separating the table in the middle of the circle and inserting a 5 foot by 3 foot leaf in the middle. The diagram below shows the expanded table. Sam needs a table cloth in the shape of the elongated table. The smallest table cloth he can buy to cover the elongated table is one that covers which of the following? A. 25 square feet. B. 35 square feet. C. 65 square feet. D. 75 square feet. MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. 34

Sam has a circular dining room table, with a 5 foot diameter, that normally seats 5 people. The table expands to seat 10 people by separating the table in the middle of the circle and inserting a 5 foot by 3 foot leaf in the middle. The diagram below shows the expanded table. Sam needs a table cloth in the shape of the elongated table. The smallest table cloth he can buy to cover the elongated table is one that covers which of the following? A. 25 square feet. B. 35 square feet. C. 65 square feet. D. 75 square feet. MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

32 inches2 127 inches2 254 inches2 1017 inches2 Shawn bought a large pizza. The pizza was delivered in a square box with length 18 inches. The pizza fit perfectly in the box, as shown in the image below. If the pizza is cut into 8 slices, what is the area of each slice of pizza to the nearest whole square inch? 32 inches2 127 inches2 254 inches2 1017 inches2 MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

32 inches2 127 inches2 254 inches2 1017 inches2 Shawn bought a large pizza. The pizza was delivered in a square box with length 18 inches. The pizza fit perfectly in the box, as shown in the image below. If the pizza is cut into 8 slices, what is the area of each slice of pizza to the nearest whole square inch? 32 inches2 127 inches2 254 inches2 1017 inches2 MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. 37

11 inches2 42 inches2 64 inches2 254 inches2 Mario bought a pecan pie to bring to a small party. The pie was perfectly placed in a 9 inch square box, as shown in the image below. If the pie is cut into 6 slices, what is the area of each slice to the nearest whole square inch? 11 inches2 42 inches2 64 inches2 254 inches2 MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

11 inches2 42 inches2 64 inches2 254 inches2 Mario bought a pecan pie to bring to a small party. The pie was perfectly placed in a 9 inch square box, as shown in the image below. If the pie is cut into 6 slices, what is the area of each slice to the nearest whole square inch? 11 inches2 42 inches2 64 inches2 254 inches2 MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. 39

Aimee wants to make a heart shaped cake, but she does not have a heart shaped baking pan. She decided to bake half of the batter in an 8 inch square pan and the other half in an 8 inch circular pan. Then she will cut the circular cake in half and place it on two consecutive sides of the square cake to make a heart, as shown in the diagram below. A quarter cup of icing covers approximately 23 inches2 of cake. What is the least amount of icing Aimee needs to make to cover just the top of the heart shaped cake? cup 1 cups 2 cups 4 cups MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

Aimee wants to make a heart shaped cake, but she does not have a heart shaped baking pan. She decided to bake half of the batter in an 8 inch square pan and the other half in an 8 inch circular pan. Then she will cut the circular cake in half and place it on two consecutive sides of the square cake to make a heart, as shown in the diagram below. A quarter cup of icing covers approximately 23 inches2 of cake. What is the least amount of icing Aimee needs to make to cover just the top of the heart shaped cake? cup 1 cups 2 cups 4 cups MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. 41

MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. 43

79 inches2 113 inches2 201 inches2 314 inches2 Elizabeth inscribed quadrilateral ABCD in a circle, as shown below. Arcs AB and DC both measure 118° and arcs AD and BC both measure 62°.If line segment AB is 8 inches and line segment length AD is 6 inches, what is the area of the circle to the nearest whole square inch? 79 inches2 113 inches2 201 inches2 314 inches2 MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors.

79 inches2 113 inches2 201 inches2 314 inches2 Elizabeth inscribed quadrilateral ABCD in a circle, as shown below. Arcs AB and DC both measure 118° and arcs AD and BC both measure 62°.If line segment AB is 8 inches and line segment length AD is 6 inches, what is the area of the circle to the nearest whole square inch? 79 inches2 113 inches2 201 inches2 314 inches2 MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length, and areas of circles and sectors. 45