MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing …

1 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing guide Division of Academics - Department of Mathematics Page 1 of 17 Topic II First Nine Weeks GEOMETRY Course Code: 120631001 Topic II: Lines, Angles, and Triangles Pacing Date(s) Traditional 28 09/15/17 10/26/17 Block 14 09/15/17 10/26/17 Topic II Assessment Window Administered after Topic III MATHEMATICS FLORIDA STATE STANDARDS (MAFS) & MATHEMATICAL PRACTICES (MP) ESSENTIAL CONTENT OBJECTIVES (from Item Specifications) : Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints.

2 ( , , and ) Achievement Level Description : Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. ( , and ) Achievement Level Description Also assesses: : Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. ( , and ) Achievement Level Description : Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

3 ( , , , ) Achievement Level Description A. Lines and Angles 1. Angles Formed by Intersecting Lines 2. Transversals and Parallel Lines 3. Proving Lines Are Parallel a) Constructing Parallel Lines 4. Perpendicular Lines a) Constructing Perpendicular Lines b) Constructing Perpendicular Bisectors 5. Equations of Parallel and Perpendicular Lines I can: Prove theorems about lines* Prove theorems about angles* Use theorems about lines to solve problems Use theorems about angles to solve problems Identify the result of a formal geometric construction Determine the steps of a formal geometric construction Prove the slope criteria for parallel lines* Prove the slope criteria for perpendicular lines* Find equations of lines using the slope criteria for parallel and perpendicular lines *Proofs include: narrative proofs, flow-chart proofs, two-column proofs, or informal proofs.

4 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing guide Division of Academics - Department of Mathematics Page 2 of 17 Topic II First Nine Weeks GEOMETRY Course Code: 120631001 MATHEMATICS FLORIDA STATE STANDARDS (MAFS) & MATHEMATICAL PRACTICES (MP) ESSENTIAL CONTENT OBJECTIVES (from Item Specifications) : Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. (Assessed with ) ( ) Achievement Level Description : Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

5 (Assessed with ) ( , and ) Achievement Level Description : Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. ( , , and ) Achievement Level Description : Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. ( , , , ) Achievement Level Description B. Triangle Congruence Criteria 1. Exploring What Makes Triangles Congruent 2. ASA Triangle Congruence 3. SAS Triangle Congruence 4.

6 SSS Triangle Congruence C. Applications of Triangle Congruence 1. Justifying Constructions 2. AAS Triangle Congruence 3. HL Triangle Congruence D. Properties of Triangles 1. Interior and Exterior Angles 2. Isosceles and Equilateral Triangles 3. Triangle Inequalities I can: Explain triangle congruence using the definition of congruence in terms of rigid motions Apply congruence to solve problems Use congruence to justify steps within the context of a proof Prove theorems about triangles* Use theorems about triangles to solve problems Use congruence criteria for triangles to solve problems Use congruence criteria for triangles to prove relationships in geometric figures Use similarity criteria for triangles to solve problems Use similarity criteria for triangles to prove relationships in geometric figures *Proofs include: narrative proofs, flow-chart proofs, two-column proofs, or informal proofs.

7 MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing guide Division of Academics - Department of Mathematics Page 3 of 17 Topic II First Nine Weeks GEOMETRY Course Code: 120631001 INSTRUCTIONAL TOOLS RECOMMENDED INSTRUCTIONAL DESIGN AND PLANNING CONTINUUM Before During After Prior to the lesson: Outline content standard(s). Determine learning targets. Anticipate student understanding and misconceptions. Determine prerequisite skills. Plan for learning experiences that target Rigor o Conceptual Understanding o Procedural Fluency o Application Determine the task students will demonstrate to reach the desired learning targets. Plan instructional delivery methods that will maximize initial engagement and sustain it throughout the lesson.

8 Decide how students will reflect upon, self-assess, and set goals for their future learning. During the lesson: Activate (or supply) prior knowledge and/or spiral back o Warm ups, Bell Ringers, Openers, etc. Tailor lesson experiences to the different needs and ability of the learners. Clarify vocabulary and mathematical notation. Incorporate a variety of higher order questions to encourage and increase critical thinking skills. Continuously check for student understanding and provide feedback. Provide opportunities for students to develop self-assessment and to reflect about their understanding and work. Bring closure to the lesson so that the students can articulate what they have learned. After the lesson: Analyze evidence of student learning to develop intervention, enrichment, and future instruction.

9 Discuss results of assessments with students. Engage students in reflective processes and goal setting. Engage in self-reflection to adapt/modify teaching strategies to improve instruction. Geometry Core Resources Geometry Intensive Math Resources Unit Resources Unit Resources Unit Tests A, B, and C Unit Test Modified Performance Assessment Module Resources Module Resources Module Test B Module Test Modified Common Core Assessment Readiness RTI T2 Strategic Intervention Advanced Learners Challenge Worksheets Skills Pre-Test, Skills Post Test, Skills Worksheets RTI T3 Intensive Intervention Worksheets Lesson Resources Lesson Resources Lessons Work text/Interactive Student Edition Practice and Problem Solving: D (modified) Practice and Problem Solving: A/B RTI T1 Lesson Intervention Worksheets Advanced Learners - Practice and Problem Solving.

10 C Reteaching Reading Strategies Success for English Learners PMT Preferences: Auto-assign for intervention and enrichment: NO Auto-assign for intervention and enrichment: NO PMT Preferences: Auto-assign for intervention and enrichment: YES Auto-assign for intervention and enrichment: NO Auto-assign for intervention and enrichment: YES Test and Quizzes Daily Intervention Homework Standard-Based Intervention Course Intervention Pacing Date(s) Traditional 28 09/15/17 10/26/17 Block 14 09/15/17 10/26/17 Topic II Assessment Window Administered after Topic III Core Text Book: Houghton Mifflin Harcourt - Geometry Geometry Course Description Geometry EOC Item Specifications INSTRUCTIONAL TOOLS MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing guide Division of Academics - Department of Mathematics Page 4 of 17 Topic II First Nine Weeks GEOMETRY Course Code: 120631001 STANDARDS MODULES TEACHER NOTES Module 4 Module 5 Module 6 Module 7 Geometry Core Block Schedule Suggested Pace Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Day 9 Day 10 Day 11 Day 12 Day 13 Day 14 Geometry Intensive Math - RTI T3 Intensive Intervention Worksheets Module 4 - Building Block Skills.