Download West Haven Public Schools Unit Four Planning Organizer

 West Haven Public Schools Unit Four Planning Organizer Subject: Geometry
​Grade: 10 Unit 4: Similarity, Proof and Trigonometry Pacing: 5 Weeks + 1 Week (re­teach/enrichment) Essential Question(s): 1. How are trigonometric functions used in real world applications? 2. How do you apply congruence and similarity criteria to solve problems? Big Idea(s): 1. Trigonometric functions are used to find lengths of sides of right triangles using the relationships between the sides when presented in real world situation. 2. Congruence and similarity criteria are used to determine side lengths and angles in congruent and similar figures. Common Core State Standards (includes West Haven’s “Priority” Common Core Standards in BOLD and “Supporting” Standards) CC.9­12.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. CC.9­12.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor: 1 Unit 4: Geometry ­ ​Similarity, Proof and Trigonometry ​ Revised 7/14 a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. CC.9­12.G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides CC.9­12.G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. CC.9­12.G.SRT.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. CC.9­12.G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. CC.9­12.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. CC.9­12.G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. CC.9­12.G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). 2 Unit 4: Geometry ­ ​Similarity, Proof and Trigonometry ​ Revised 7/14 “Unwrapped” Concepts and Skills, and Bloom Levels (BL) Concepts(Need to Know) ● D​efinitions o
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Skills(Able to Do) KNOW BL 1 Similarity Similarity ratio Dilation Enlargement Reduction ● Congruence / Similarity criteria for Triangles ● Trigonometry Ratios ● Pythagorean Theorem ● Right triangles in applied USE, SOLVE ​(problems) PROVE (relationships in geometric figures) 3 5 USE o SOLVE 3 3 3 problems o SOLVE Assessments Common Formative Pre­ Assessment (Followed by Data Team Analysis): See Test A on Similarity, Proof and Trigonometry Pre Requisite Skills Assessments A, B, C 3 Unit 4: Geometry ­ ​Similarity, Proof and Trigonometry ​ Revised 7/14 “Dipsticks” (Informal Progress Monitoring Checks): Classroom Teacher Made Data driven decisions Common Formative Post­ Assessment (Followed by Data Team Analysis): See Test B on Similarity, Proof and Trigonometry Instructional Planning Suggested Resources/Materials: ​Prentice Hall Geometry Text and Recommendations from Pacing Guide. Unit Four ­ Pacing Guide Standard: CC.9­12.G.SRT.5 CC.9­12.G.SRT.3 CC.9­12.G.SRT.4 Essential Question: How do I apply congruence and similarity criteria to solve problems? Time Frame: 6 Days Section 8­3: ​_
Postulate 8­1, Theorem 8­1 and 8­2; Example 1, 2, and 3; Section A #1­15; Section B p.437 #24­27; 4 Unit 4: Geometry ­ ​Similarity, Proof and Trigonometry ​ Revised 7/14 Section C #44 (Proof). Section 8­5: Theorem 8­4; Example 1 including Proof; Section A #1­3; Section B p.451 #47 Essential Question: Standard: CC.9­12.G.SRT.8 CC.9­12.G.SRT.6 How are trigonometric functions used in real world applications? Time Frame: 5 Days Section 9­1: Define: Tangent, Remind Students of Pythagorean Theorem Example 1, 2, and 3; Section A #1­20; Section B p.473­474 #27­29, 35­43. Standard: CC.9­12.G.SRT.8 CC.9­12.G.SRT.6 CC.9­12.G.SRT.6 Essential Question: How are trigonometric functions used in real world applications? Time Frame: 5 Days 5 Unit 4: Geometry ­ ​Similarity, Proof and Trigonometry ​ Revised 7/14 Section 9­2: Define: Sine, Cosine, Identity; Example 1, 2, and 3; Section A #1­16; Section B #21­24, 29, 36; Essential Question: Standard: How do I apply congruence and similarity criteria to solve problems? CC.9­12.G.CO.5 CC.9­12.G.SRT.1 CC.9­12.G.SRT.2 Time Frame: 5 Days Section 12­7
Define: Dilation, Enlargement, Reduction, and Scale Factor Examples: 1, and 2; Section A #1­14; Section B #37­40, 41(software required), 42, 43­45, 46 Performance Task for Unit 4 Suggested Websites http://www.insidemathematics.org/ http://www​.llustrativemathematics.org/ 6 Unit 4: Geometry ­ ​Similarity, Proof and Trigonometry ​ Revised 7/14 Buffer Zone ­ Enrich/Reteach if time permits
PH: Re­teaching 3­6 PH: Enrichment 3­5 PH: Enrichment 3­6 Other Re­teaching Days Suggested Research­based Effective Instructional Strategies: SEE APPENDIX A for a list of ALL Strategies Vocabulary/Word Wall Enrichment/Extension Tangent Enrichment 8­3 Pythagorean Theorem Enrichment 8­5 Sine Enrichment 9­2 Cosine Identity Dilation Enlargement Interdisciplinary Connections PH: Page 474 Engineering #31­34 PH: Page 478 Example 2 and page 481 #36 Astronomy PH: Page 677 #42 Copy Reduction 7 Unit 4: Geometry ­ ​Similarity, Proof and Trigonometry ​ Revised 7/14 Reduction Scale Factor 8 Unit 4: Geometry ­ ​Similarity, Proof and Trigonometry ​ Revised 7/14