Transcript File - Science Math Master

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
C
100o
a
b
Explore Arc Length
Materials
• String
• 1 can for each group (different sizes)
• Rulers
• Markers
• Scissors
• Worksheets
4/10/2015
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
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?
A.
B.
C.
D.
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.
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?
A.
B.
C.
D.
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.
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.
The moon is at ____________________o
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%20Uni
t%20Plan.pdf
 http://www.nsa.gov/academia/_files/collected_learnin
g/high_school/modeling/staggered_starts.pdf
Quiz #1
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
B) 80º
C) 120º
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
meters
C) 52.5 square
meters
D) 22.9 square
meters
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
Focus Questions
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.
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.)
A.
B.
C.
D.
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.
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.)
A.
B.
C.
D.
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.
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.
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?
A.
B.
C.
D.
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.
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?
A.
B.
C.
D.
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.
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?
A. 11 inches2
B. 42 inches2
C. 64 inches2
D. 254 inches2
MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length,
and areas of circles and sectors.
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?
A. 11 inches2
B. 42 inches2
C. 64 inches2
D. 254 inches2
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?
A.
cup
B. 1 cups
C. 2 cups
D. 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?
A.
cup
B. 1 cups
C. 2 cups
D. 4 cups
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.
MA.912.G.6.5: Solve real-world problems using measures of circumference, arc length,
and areas of circles and sectors.
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?
A.
B.
C.
D.
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.
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?
A.
B.
C.
D.
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.