Unit 1 Geometry PAP

9/15 – 9/26 Geometry Prep Lesson Plan Stage 1 – Desired Results TEKS/AP Standards: GEOM.3A Determine the validity of a conditional statement, its converse, inverse, and contrapositive using everyday situations and geometric properties that have been developed. GEOM.4A Select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic) that may be translated from a verbal description in order to solve problems GEOM.5A Analyze numeric and geometric patterns to develop algebraic expressions representing geometric properties. GEOM.9A Formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models, recognizing when two lines are parallel, perpendicular, skew, or intersecting. GEOM.5A Investigate patterns to make conjectures about geometric relationships, including angles formed by parallel lines cut by a transversal, criteria required for triangle congruence, special segments of triangles, diagonals of quadrilaterals, interior and exterior angles of polygons, and special segments and angles of circles choosing from a variety of tools. [aligns to current GEOM.3D and GEOM.5B] Enduring Essential Question(s): Student objectives Understandings (outcomes): (s)/goals: EU1: The student uses EQ1: How do you break down SO1.1: Identifying algebraic properties mathematical processes to problems to answer questions? SO1.2: Applying algebraic properties acquire and demonstrate SO1.3: Utilizing algebraic properties to mathematical understanding. solve and justify algebraic problems

EU2: The student uses the EQ2: What is the relationship SO2.1: Finding midpoint of 2 points process skills to understand the between the Pythagorean SO2.2: Finding distance between 2 connections between algebra Theorem and the distance points and geometry and uses the one- formula? SO2.3: Finding endpoint from point and and two-dimensional coordinate midpoint systems to verify geometric SO2.4: Writing algebraic equations for conjectures. geometric representations

EU3: Develop an awareness of EQ3: How do we formulate SO3.1: Writing conditionals, converses, the structure of a mathematical conditional statements and inverses and contrapositives system, connecting definitions, determine whether or not they are SO3.2: Determining validity of said postulates, logical reasoning, true or false? statements and theorems to verify SO3.3: Identifying type of conditional statements from original statement

EU4: The student uses the EQ4: What is necessary to find SO4.1: Applying induction to find next process skills with deductive the next steps in a process (with terms of process reasoning to understand pictures or numbers)? SO4.2: Finding rule from process table geometric relationships.

EU5: The student uses the EQ5: How do you justify your SO5.1: Identifying various algebraic process skills with deductive steps when solving an algebraic equality properties reasoning to prove and apply problem? SO5.2: Applying equality properties to theorems by utilizing a variety of justify algebraic steps methods such as coordinate, SO5.3: Writing algebraic solution to transformational, axiomatic and problem using equality properties formats such as two-column, aragraph, flow chart. Stage 2 – Assessment Evidence Performance Task(s) and Other Evidence: Formative Summative (Attach copy) SO1.1 SO1.2 SO1.3 SO1.4 SO2.1 SO2.2 SO2.3 SO3.1 SO3.2 SO3.3 SO4.1 SO4.2 SO4.3 SO5.1 SO5.2

Stage 3 – Learning Plan DIFFERENTIATION (I-3) There are several ways to individualize instruction for your students Date Activities (Do First, Introduction, Guided Practice, Independent Practice, Closure) 9/15 Topic: 2.2 Conditional Statements Do First: Spiral questions (Vertical angles, Distance) Introduction: While checking homework, go over truth of conditionals. GP: Students given midpoint problem and answer, put in conditional statement format. Switch with other students to find validity of statements. IP: Given set of spiraled problems, students find answers, write as conditionals and then tell truth values. Truth values posted for students to constantly check. Closure: Discussion: How can we use truth statements to check our work with other problems? 9/16 Topic: 2.2 Conditional Statements with 2.5 Reasoning with Algebra Do First: Supplementary problem with algebraic solution; students justify each step. Introduction: Describe each algebraic property along with reasoning for prior problems. GP: Give same set of problems from 9/15, have students justify each step of work. IP: Give new set of problems involving midpoint and distance for practice. Closure: What topics have we learned that will be on the test? (Students look through notes and discuss as class) 9/17-18 Topic: Test Review Do First: Without writing anything, students read through mirrored test review to preview what’s “in store.” Introduction: Before introducing rules of walkthrough, clarify any questions students have about what they read. Then give rules – students walk around completing the problems and checking their answers. GP: Students work in pairs to complete problems using their handouts. The problems will be posted around the classroom so they’re getting up and moving around. IP: Once all groups have completed review, they change partners and discuss problems they experienced. Closure: Answer any last minute questions and point students to the website for final review. 9/19 Topic: Test 2 HW: Watch videos and take notes (Identifying pairs of lines and angles) 9/22 Topic: 3.1 Identifying Pairs of Lines and Angles Do First: 3.1 Investigation – Draw and Interpret Lines Introduction: Make a list of all angle pairs learned so far – include list of angle pairs from transversals (Extend to creating vocabulary book) GP: Find examples of all types of line pairs in classroom & draw to place on walls IP: 3.1 worksheet Closure: Quick visual check on identifying types of angle pairs on transversals 9/23 Topic: 3.1/3.2 Identifying and Using Line Pairs (Parallels) and Angles Formed Do First: Matching worksheet Introduction: Recap previous lesson together (types of line pairs, types of angle pairs, naming line pairs) GP: 3.1 Challenge practice 1 – 4 Activity: Students work in groups, start on problem #1 individually, pass paper around, work next problem, etc. so that each page is collaborative but complete. IP: Switch papers with another group and grade assignments with projected answers and then correct Closure: What happens to the angle pairs when the lines are parallel? (HW: Write paragraph guessing what happens to corresponding angles when the lines are parallel and cut by transversal.) 9/24-25 Topic: 3.2 Use Parallel Lines and Transversals Do First: Read directions at station Introduction: Guide students through their stations GP: Students determine properties of angle pairs with parallel lines cut by transversals using station work. IP: Students create their own study guides from sections 3.1 to 3.2. Closure: Recap about student discoveries 9/26 Topic: Spiral Quiz GP: Students take a quiz over a variety of the topics they’ve struggled with, including: angle bisectors, supplementary/complementary angle problem set-ups, midpoint, distance, contrapositives, parallel line angle pairs (Use pair-share method for collaboration) IP: Students review their pages before they turn them in. Closure: List topics to study for the next test

Understanding (s)/goals [this is a goal, not an objective. List the big ideas or concepts that you want them to come away with, not facts that they must know] Essential Question(s): [What leading questions can you ask of students to get them to understand the Big Ideas?] [Address the heart of the discipline, are framed to provoke and sustain students interest; unit questions usually have no one obvious “right” answer Student objectives (outcomes): Students will be able to: [These are observable, measurable outcomes that students should be able to demonstrate and that you can assess. Your assessment evidence in Stage 2 must show how you will assess these.] [Your learning activities in Stage 3 must be designed and directly linked to having students be able to achieve the understandings, answer the essential questions, and demonstrate the desired outcomes Performance Tasks:  [Authentic, performance based tasks that have students apply what they have learned and demonstrate their understanding.]  [designed at least at the application level or higher on Bloom’s Taxonomy. ]  [Rubrics can be used to guide students in self-assessment of their performance]

Other Evidence:  [includes pre-assessment, formative assessment, and summative assessment evidence]  [Can be individual or group based]  [Can include informal methods (such as thumbs up, thumbs down, and formal assessments, such as quiz, answers to questions on a worksheet, written reflection, essay]