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Chapter 3 Unit Design Unit Title: Chapter 3: Parallel and Perpendicular Lines Course: Geometry Unit Length: 11 days Date Created: October 22, 2010 Updated: November 18, 2011 IL Goals/Standards: -Recognize angle pairs that occur with parallel lines 9B. 4 -Prove that two lines are parallel based on given angle relationships 9C 11.17. -Use the properties of parallel lines to determine congruent angles 9C. 11.17. -Use algebra to find angle measures 7A, B, C, 11. 03 -Find the slope of a line 9A. 11.9 -Use a slope to decide if two lines are, parallel, perpendicular or neither 9A. 11.9 -Write equations in point-slope and slope intercept form 9A 11. 09. -Recognize angle conditions that occur with parallel lines 9A 11. 05. -Prove that two lines are parallel based on given angle relationships 9C 11. 11 College Readiness Standards: Properties of Plane Figures: (16-19) Exhibit some knowledge of the angles associated with parallel lines;(20-23) Find the measure of an angle using properties of parallel lines; Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°); (24-27) Use several angle properties to find an unknown angle measure. Graphical Representations: (20-23) Exhibit knowledge of slope; (24-27) Determine the slope of a line from points or equations; Match linear graphs with their equations; (28-32) Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point. Unit Overview Unit Components 3.1 Parallel Lines Transversals Unit Vocabulary/ Concepts/Topics Parallel lines Parallel planes Skew lines Transversal Alternate exterior angles Alternate interior angles Consecutive interior angles Consecutive exterior angles Corresponding angles 3.2 Angles and Parallel Lines 3.3 Slopes of Lines Unit Vocabulary/ Concepts/Topics Corresponding Angles Postulate Alternate Interior Angles Theorem Consecutive Interior Angles Theorem Alternate Exterior Angles Theorem Perpendicular Transversal Theorem Learner/Performance Objectives: The student will . . . -identify the relationships between two lines or two planes -name angles formed by a pair of lines and a transversal -use the properties of parallel lines to determine congruent angles -use algebra to find angle measures including equations with decimals and fractions -find the slope of a line -use a slope to decide if two lines are parallel, perpendicular or neither -write equations in standard, point-slope and slope intercept form -recognize angle conditions that occur with parallel lines -prove that two lines are parallel based on given angle relationships Unit Vocabulary/ Concepts/Topics Slope (Algebra Skills Review with domain and range) Slopes of Parallel Lines Slopes of Perpendicular Lines 3.4 Equations of Lines Unit Vocabulary/ Concepts/Topics Slope-Intercept Form Point-Slope Form Standard Form Assessments/Evidence • Quizzes & Tests based on learner objectives (vocab, postulates, formulas) •Constructed response – POW, Bell-Ringer/Exit Slip •Related mini-projects (Frayer Model, crosswords, games) •Student presentations in small groups. •Daily openers (bell ringers) and summary. •Student Self-Assessment – via summaries and exit slips •Graded classwork activities 3.5 Proving Lines Parallel Unit Vocabulary/ Concepts/Topics Parallel Postulate Ways to prove lines parallel 3 Unit: Chapter 3: Parallel and Perpendicular Lines Resources/Materials: • Geometry Text • Kenwood Website – Homework Purposes; Additional Notes • Calculators Select/Create WIC-R Strategies Writing Inquiry Collaboration 1. Summary 1. Problem Solving 1. 2. 3. 4. 5. 6. 7. Reading Paraphrase and listen attentively to one another. Elaborate and build upon ideas and each others' contributions. Make use of specific and accurate knowledge. Provide evidence for claims and arguments. Create/invent something together. Teach each other. Think—Pair—Share (Bell-Ringer, In-class Activities) Adaptations/Accommodations/Differentiation Select/Create Possible Modifications Content Vary what students will learn and the materials that represent the content (Visual, auditory, tactile, written). Process Vary the activities through which students make sense of key ideas using essential skills (graphic organizers, Cornell notes, demonstrations, prompts, highlighting key information). Product Vary how students demonstrate and extend what they understand and can do as a result of a span of learning (Homework based on completion, boardwork, modified homework and assessments, projects, portfolios). Learning Environment Vary the classroom conditions that set the climate, expectations for learning, and physical conditions (Preferential seating, proximity control, posters, student work). 1. 2. 3. Understanding and Using Words (Vocabulary) Generalizations and Drawing Conclusions (Summary) B/D/A Strategy – Sequence Summary Corrective and Enrichment Activities/Practices/Strategies Select/Create Correctives •re-teaching •test corrections/ retakes •worksheets •study guides •academic games (crossword puzzles, simulations) •individual tutoring (TLC, office hours with teacher) •technology-assisted instruction (e.g., computers, LCD projectors) •Success Plans Select/Create Enrichments/Extensions •additional challenging homework and class problems •developing practice exercises •developing games, problems, and contests •locating background materials for future or current topics •developing modified formative assessments •creating bulletin boards and displays •applying knowledge to a real-world situation