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 Understandings (s)/goals: |Essential Question(s): |Student objectives (outcomes): |

|EU1: The student uses mathematical processes |EQ1: How do you break down problems to answer |SO1.1: Identifying algebraic properties |

|to acquire and demonstrate mathematical |questions? |SO1.2: Applying algebraic properties |

|understanding. | |SO1.3: Utilizing algebraic properties to solve and |

| | |justify algebraic problems |

|EU2: The student uses the process skills to |EQ2: What is the relationship between the |SO2.1: Finding midpoint of 2 points |

|understand the connections between algebra and|Pythagorean Theorem and the distance formula? |SO2.2: Finding distance between 2 points |

|geometry and uses the one- and two-dimensional| |SO2.3: Finding endpoint from point and midpoint |

|coordinate systems to verify geometric | |SO2.4: Writing algebraic equations for geometric |

|conjectures. | |representations |

|EU3: Develop an awareness of the structure of |EQ3: How do we formulate conditional statements|SO3.1: Writing conditionals, converses, inverses and |

|a mathematical system, connecting definitions,|and determine whether or not they are true or |contrapositives |

|postulates, logical reasoning, and theorems to|false? |SO3.2: Determining validity of said statements |

|verify statements | |SO3.3: Identifying type of conditional from original |

| | |statement |

|EU4: The student uses the process skills with |EQ4: What is necessary to find the next steps |SO4.1: Applying induction to find next terms of process|

|deductive reasoning to understand geometric |in a process (with pictures or numbers)? |SO4.2: Finding rule from process table |

|relationships. | | |

|EU5: The student uses the process skills with |EQ5: How do you justify your steps when solving|SO5.1: Identifying various algebraic equality |

|deductive reasoning to prove and apply |an algebraic problem? |properties |

|theorems by utilizing a variety of methods | |SO5.2: Applying equality properties to justify |

|such as coordinate, transformational, | |algebraic steps |

|axiomatic and formats such as two-column, | |SO5.3: Writing algebraic solution to problem using |

|aragraph, flow chart. | |equality properties |

|Stage 2 – Assessment Evidence |

|Performance Task(s) and Other Evidence: |

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|Formative |

|Summative (Attach copy) |

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|SO1.1 |

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|SO1.2 |

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|SO1.3 |

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|SO1.4 |

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|SO2.1 |

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|SO2.2 |

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|SO2.3 |

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|SO3.1 |

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|SO3.2 |

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|SO3.3 |

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|SO4.1 |

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|SO4.2 |

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|SO4.3 |

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|SO5.1 |

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|SO5.2 |

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|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][pic]

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