CCGPS Mathematics Unit-by-Unit Grade Level Webinar Analytic Geometry Unit 2: Right Triangle Trigonometry July 30, 2013 Session will be begin at 8:00 am While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.
Transcript
CCGPS MathematicsUnit-by-Unit Grade Level Webinar
Analytic GeometryUnit 2: Right Triangle Trigonometry
July 30, 2013
Session will be begin at 8:00 amWhile you are waiting, please do the following:
Configure your microphone and speakers by going to:Tools – Audio – Audio setup wizard
Document downloads:When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.
CCGPS MathematicsUnit-by-Unit Grade Level Webinar
Analytic GeometryUnit 2: Right Triangle Trigonometry
• Intent and focus of Unit 2 webinar.• Framework tasks.• GPB sessions on Georgiastandards.org.• Standards for Mathematical Practice. • Resources. • http://ccgpsmathematics9-10.wikispaces.com/• CCGPS is taught and assessed from 2013-2014 and beyond.
Parent Communication•Explanation to parents of the need for change in mathematics•What children will be learning in high school mathematics •Parents partnering with teachers•Grade level examples•Parents helping children learn outside of school•Additional resources
Parent Communication•An overview of what children will be learning in high school mathematics •Topics of discussion for parent-teacher communication regarding student academic progress•Tips for parents that will help their children plan for college and career
Parent Communication•An overview of what children will be learning in high school mathematics •Topics of discussion for parent-teacher communication regarding student academic progress•Tips for parents that will help their children plan for college and career
Question: Are we supposed to teach special right triangles? I only see this topic as a couple of small tasks, but it is not stated in the standards.
Wiki/Email Questions
Question: Are we not teaching the tangent ratio anymore? I only see reference to sine and cosine in the standards and tasks.
Question: Which trig ratios are we supposed to teach: Sine, Cosine, Tangent, Secant, Cosecant & Cotangent or just Sine, Cosine & Tangent?
MCC9-12.G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
MCC9-12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
Wiki/Email Questions
Question: Didn't students solve Pythagorean Theorem applied problems when they learned the Pythagorean Theorem?
8th Grade:MCC8.G.6 Explain a proof of the Pythagorean Theorem and its converse.MCC8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.MCC8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.Coordinate Algebra:MCC9-12.G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.Analytic GeometryMCC9-12.G.SRT.4 Prove theorems about triangles…; the Pythagorean Theorem proved using triangle similarity.MCC9-12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Wiki/Email Questions
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
6 cm
What’s the big idea?•Using similar triangles to develop understanding of trigonometric ratios.•Determine that trigonometric ratios can be used to solve application problems involving right triangles.• Standards for Mathematical Practice.
What’s the big idea?
Standards for Mathematical Practice
What’s the big idea?• SMP 1 – Make sense of
problems and persevere in solving them
• SMP 3 – Construct viable arguments and critique the reasoning of others
Identifying right triangles Ratios and proportional reasoning Pythagorean Theorem Similarity
• 10th-12th Trigonometric functions Trigonometry in general triangles
Examples & ExplanationsDetermine the following ratios:
Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone
Examples & ExplanationsDetermine the following ratios:
Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone
Examples & ExplanationsDetermine the following ratios:
Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone
37°
1
1.33
1.67
C”
B”
A”
Examples & ExplanationsWhat did you notice between the three similar triangles?
Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone
37°
3
4
5
C
B
A
37°
1.5
2
2.5
C’
B’
A’
37°
1
1.33
1.67
C”
B”
A”
Examples & ExplanationsUse a calculator and find the following:
Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone
Examples & ExplanationsUse a calculator and find the following:
How do these relate to the ratios found earlier?
Adapted from Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone
Examples & Explanations
A 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be?
Examples & ExplanationsA 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be?
Examples & ExplanationsA 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be?
15 ft
25 ft
10 ft
2 ft
50°
Examples & ExplanationsA 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be?
15 ft
25 ft
10 ft
2 ft
50°25 ft
Examples & ExplanationsA 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be?
15 ft
25 ft
10 ft
2 ft
50°25 ft
Examples & ExplanationsA 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be?
15 ft
25 ft
10 ft
2 ft
50°25 ft
Examples & ExplanationsA 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be?
15 ft
25 ft
10 ft
2 ft
50°25 ft
Examples & ExplanationsA 25-foot flag pole is erected on the top of a building 10 feet from the side. The guide wire must be anchored to the adjacent building 15 feet away and two feet from the top of the pole. The wire is at a 50° angle with the horizon. How long does the wire need to be?
15 ft
25 ft
10 ft
2 ft
50°25 ft
ft
Examples & Explanations
Landing in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
100 ft
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
100 ft
30°
21°
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
100 ft
30°
21°
51° 30°
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
x
100 ft
30°
21°
51° 30°
y
x
100 ft
30°
21°
51° 30°
y
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
x
100 ft
30°
21°
51° 30°
y
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
x
100 ft
30°
21°
51° 30°
y
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
x
100 ft
30°
21°
51° 30°
y
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
x
100 ft
30°
21°
51° 30°
y
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
x
100 ft
30°
21°
51° 30°
y
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
x
100 ft
30°
21°
51° 30°
y
Examples & ExplanationsLanding in a hot air balloon, you notice the landing spot and your car. From 100 ft. in the air, you have to look down at a 30° angle to your car and an additional 21° to the landing spot. How far will you have to walk to your car after landing?
Walking distance 92 feet
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
6 cm
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
Q
O
R
P
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
Q
O
R
P3
3
tt
t
t
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
Q
O
R
P3
3
tt
t
t
45°
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
Q
O
R
P3
3
tt
t
t
45°
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
Q
O
R
P3
3
tt
t
t
45°
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
Q
O
R
P3
3
tt
t
t
45°
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
Q
O
R
P3
3
tt
t
t
45°
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
Q
O
R
P3
3
tt
t
t
45°
If four circles are placed around a central circle with diameter of 6 cm, as pictured below, what is the radius length of each of the outer circles?
Activate your Brain
Adapted from Illustrative Mathematics G.SRT Seven Circle III
Q
O
R
P3
3
tt
t
t
45°
AssessmentJuly 22, 2013 – State School Superintendent Dr. John Barge and Gov. Nathan Deal announced today that Georgia is withdrawing from the Partnership for Assessment of Readiness for College and Careers (PARCC) test development consortium. Instead, the Georgia Department of Education (GaDOE) will work with educators across the state to create standardized tests aligned to Georgia’s current academic standards in mathematics and English language arts for elementary, middle and high school students. Additionally, Georgia will seek opportunities to collaborate with other states. The press release in its entirety can be found at: http://www.gadoe.org/External-Affairs-and-Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123
Assessment As GaDOE begins to build new assessments, please note that our Georgia assessments:will be aligned to the math and English language arts state standards;will be high-quality and rigorous;will be developed for students in grades 3 through 8 and high school;will be reviewed by Georgia teachers;will require less time to administer than the PARCC assessments;will be offered in both computer- and paper-based formats; andwill include a variety of item types, such as performance-based and multiple-choice items.The press release in its entirety can be found at: http://www.gadoe.org/External-Affairs-and-Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123
AssessmentWe will continue to work with Georgia educators, as we have in the past, to reconfigure and/or redevelop our state assessments to reflect the instructional focus and expectations inherent in our rigorous state standards in language arts and math. This is not a suspension of the implementation of the CCGPS in language arts and math.
~ Dr. John Barge(excerpt from a letter to state Superintendents from Dr. Barge)
Resource List
The following list is provided as a sample of available resources and is for informational purposes only. It is your responsibility to investigate them to determine their value and appropriateness for your district. GaDOE does not endorse or recommend the purchase of or use of any particular resource.
• Common Core Resources SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtc Illustrative Mathematics - http://www.illustrativemathematics.org/ Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/ Common Core Standards - http://www.corestandards.org/ Tools for the Common Core Standards - http://commoncoretools.me/ Phil Daro talks about the Common Core Mathematics Standards - http://bit.ly/URwOFT LearnZillion - http://learnzillion.com/
• Blogs Dan Meyer – http://blog.mrmeyer.com/ Timon Piccini – http://mrpiccmath.weebly.com/3-acts.html Dan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/
• Unit Resource Right Triangle Trigonometry, and Trigonometric Functions: Doris Santarone - http://
The Morris family is on a road trip through California. One day they are driving from Death Valley to Sequoia National Park. Death Valley is home to the lowest point in the US at Badwater Basin with 282 feet below sea level. Sequoia National Park is home to Mt. Whitney, the highest point in the lower 48 states with 14,505 feet. Jerry is estimating from the map that the two places are only 85 miles apart as the crow flies. He is wondering:
If you hike to the top of Mt. Whitney, can you see Badwater Basin on a clear day?
Find an answer to Jerry's question and support it with an appropriate mathematical model.
(Note: In this task you may neglect the curvature of the earth and just assume that you can see long distances.)
