algebra 2 – trig function unit circle unit 4. purpose standards learning progression lesson agenda...
TRANSCRIPT
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Algebra 2 – Trig FunctionUnit Circle
Unit 4
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Purpose
Standards Learning Progression
Lesson Agenda
Getting Ready for the
Lesson (Resources and Tips)
Vocabulary Activities
Lesson(Presentation
and Video)
Textbook Connections
Additional Resources
Provided is a lesson for teachers to use to help students understand unit circle and how it extends to trigonometric functions. Included are the following:
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Common Core Standards
F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. (Understand, 2) (Analyze, 2)
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Math Practices
MP4• Model with
mathematicsMP6• Attend to precision
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Trig FunctionsPrerequisite Skills: CC Geometry
http://commoncoretools.me/wp-content/uploads/2012/06/ccss_progression_sp_hs_2012_04_21_bis.pdf
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Middle School Focus
Source: California Framework
Grade 6
•Understand ratios and describe ratio relationships
Grade 7
•Graph and compare proportional relationships
Grade 8
•Use the Pythagorean Theorem to find missing measures in two dimensions and find the distance between two points in the coordinate plane
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High School Focus
Source: California Framework
Algebra 1•Use function notation to evaluate and interpret functions.•Use factoring to solve real-life problems•Translate, reflect, stretch, and shrink the graphs of linear functions•Explore inverses of functions
Geometry•Concept of Circles and Triangles•Understanding of right triangles•Understanding of similarity
Algebra 2•Find unknown side lengths and angle measures of right triangles
•Evaluate trigonometric functions of any angle
•Write and graph trigonometric functions; transform the graphs of sine and cosine functions
•Verify and use trigonometric identities
•Use sum and difference formulas to evaluate and simplify trigonometric expressions and to solve trigonometric equations
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Learning Progression: Trig Function
http://commoncoretools.me/wp-content/uploads/2012/06/ccss_progression_sp_hs_2012_04_21_bis.pdf
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Lesson Agenda
OVocabularyOVideoOLesson: Describe the features of
the graphs of sine and cosine by using the unit circle
OTextbook Connections
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Trig Function-Unit Circle
Planning for Instruction with understanding Trig Functions using
Unit Circles
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Getting ReadyO Pre-assessment- used to determine
understanding of prerequisite skillsO Prerequisite skills include
O F.BF.3O Identify the effect on the graph
O 8.G.B.7O Apply the Pythagorean Theorem to determine
unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions
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Misconceptions and Anticipated Issues
Common Issuesa. The value of radius
must always be positive
b. Mistake on evaluating trigonometric functions
c. Wrong interpretation of signs
d. Incorrect graph
Suggested Strategies/Resources
a. Use the additional practice worksheets from learnzilllion lesson
b. Use more than 1 vocabulary organizer to address key vocabulary
c. Allow students to use a calculator
d. Analyze the graph and understand the location of radius
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Required Resources
Materials RequiredSpecial Materials: Handouts:OLearnzillion presentation handoutsOLearnzillion additional worksheets
O https://learnzillion.com/lesson_plans/716
O
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Needed VocabularyO TrigonometryO RadiusO Unit Circle
O Reference AnglesO RadianO Pythagorean
Theorem Or you could use: World Map,
Frayer’s Model etc.
Layered Book
Example
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Learnzillion
For this lesson you need to create an account to access the handouts from Learnzillion.
This is a free account and you will have access to many more lessons.
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Trig Function using the Unit Circle
https://learnzillion.com/lesson_plans/716
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Planning and TimeActivities Time Notes
Preparation 2 hours Includes creating a pre-assessment, making copies, obtaining materials
Pre-lessons 2 hours Review of Algebra1 and Geometry Standards
Vocabulary 1 hour Defining Unit Circle
M&M Task-Lesson 2 hours Explanation and completion of work
Practice and Additional Tasks
2 hours Additional worksheets from LearnZillion, Textbook practice, Illustrative Mathematics Tasks
Total Time 10 hours
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Textbook ConnectionBig Ideas
O Textbook Algebra 2 Section 9.3O Classwork: Page 477-481 O Homework: Page 482-484
O Extra Practice: Algebra 2 Resources by Chapter Section 9.3 O Practice A and B page 301-302O Enrichment and Extension page 303O Puzzle Time Page 304
O Student Journal Algebra 2 Section 9.3O Trigonometric Functions of Any Angles Page 252-256
O Assessment Book Algebra 2 Section 9.3O Page 118-123
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Textbook ConnectionSpring Board
O Lesson 32-1 Placing the Unit Circle on the Coordinate PlaneO Classwork Page 487-492O Homework Page 493
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Textbook ConnectionCPM
O 7.1.6 Building a Unit CircleO Classwork Page 337-338O Homework Page 339-340
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Additional ResourcesO Illustrative Mathematics -
www.illustrativemathematics.comO Trig Functions and the Unit Circle
O Khan Academy - www.khanacademy.org
O Engage NY Common Core CurriculumO Algebra II Module 2
O https://www.engageny.org/resource/algebra-ii-module-2-topic-a-lesson-1
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Need Help?
Contact your Secondary Math
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