Download Common Core Geometry Critical Area 3: Right Triangle Trigonometry

Common Core Geometry
Critical Area 3: Right Triangle Trigonometry
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Pacing: Weeks 14 - 18
Right Triangle Trigonometry
Similarity, Right Triangles , and Trigonometry
G-SRT
B. Prove theorems involving similarity
4. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean
Theorem proved using triangle similarity.
5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
C. Define trigonometric ratios and solve problems involving right triangles
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.
7. Explain and use the relationship between the sine and cosine of complementary angles.
8. Use trigonometric rations and the Pythagorean Theorem to solve right triangles in applied problems.
Key Student Understandings
 Students will utilize side and angle relationships in right triangles to

define trigonometric properties.
Students will apply trigonometric properties to solve right triangle
problems.
Assessment
Formative Assessment Strategies
Evidence for Standards-based Grading
**Common SBG Evidence Items
Rubric
Folding a Square into Thirds (G-SRT.B, SMP.8)
Mighty Redwood (G-SRT.C, SMP.1)
Disciplinary Literacy

Disciplinary Literacy Framework
Instructional Guide for Common Core Geometry
Property of MPS
Page | 1
Rev 7.18.16
Common Core Geometry
Critical Area 3: Right Triangle Trigonometry
Common Misconceptions/Challenges
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Students see the answers to the sine, cosine or tangent of an angle as a “magical” number that helps to solve triangles and not as a ratio of sides of all right
triangles with the given acute angle.
Using memory devices (like SOHCAHTOA) help students to remember which ratio of two sides each trigonometric function uses. However, care must be taken
that these do not mute the conceptual understanding of the ratios of similar triangles.
Some students believe that right triangles must be oriented a particular way.
Some students do not realize that opposite and adjacent sides need to be identified with reference to a particular acute angle in a right triangle.
Some students believe that the trigonometric ratios defined in this cluster apply to all triangles, but they are only defined for acute angles in right triangles.
Instructional Practices
Suggested
Timeline
Side and Angle
Relationships
in
Trigonometry
(Weeks 14-16)
Suggested Learning
Experiences
Investigate Right
Triangle
Trigonometry based
on similarity
Prove Pythagorean
Theorem using
multiple methods
Explore special right
triangles
Resources
**Common SBG Evidence Items
Students now have the necessary knowledge to prove the Pythagorean Theorem through similarity.
 Using http://mathworld.wolfram.com/PythagoreanTheorem.html you can find a proof that uses similarity starting
at line 28.
 Another site with a more scaffolded proof and ideas for making it into an investigation is
http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/pythagorean.html
Discovering Geometry: Lesson 12.1 Emphasize page 640 because of the explanation of trigonometric ratios through similar
triangles, and the One Step from the Blue Matter would turn that emphasis into an Investigation. Expand the Investigation
“Trigonometric Tables” to include multiple complementary angles in order to emphasize the relationship between sin(A) and
cos(B) in those complementary angle pairs; pg. 648 (10-16)
Virginia Department of Education: Special Right Triangles and Right Triangle Trigonometry
Illustrative Mathematics: Pythagorean Theorem (TE); Folding a Square into Thirds** (TE)
Mathematics Assessment Resource Service: Proving the Pythagorean Theorem
Engage NY: Geometry Module 2 Topic D
Instructional Guide for Common Core Geometry
Property of MPS
Page | 2
Rev 7.18.16
Common Core Geometry
Critical Area 3: Right Triangle Trigonometry
Problem
Apply Trigonometry
Solving
in appropriate
(Weeks 16–18) situations
Discovering Geometry: Lesson 9.1; Lesson 9.4; pg. 578; Lesson 11.1; Lesson 11.2; Lesson 11.3; Lesson 11.4; Lesson 11.7
Additional District Created Items: Mighty Redwood**
Mathematics Assessment Resource Service: Deducing Relationships: Floodlight Shadows
Engage NY: Fisherman’s Route, Geometry Module 2 Topic E
Differentiation
Literacy Connections
Geometry Teacher’s Edition - Differentiated Instruction CK-12 Foundation

Academic Vocabulary
Have students use a variety of hands-on tools (i.e. manipulatives,
software, patty paper, etc.) to experience a dilation of a figure. Some
students may be able to understand similarity with graph paper,
while other may need to use geometric tools.
Vocabulary Strategies
Literacy Strategies
Additional Resources
Discovering Mathematics Online Textbook
Desmos Online Graphing Calculator
cK-12
learnzillion
GeoGebra
Georgia Geometry Unit 3
Instructional Guide for Common Core Geometry
Property of MPS
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Rev 7.18.16