Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,  80% of our students will graduate from high school college or career ready  90% of students will graduate on time  100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts.

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some

Shelby County Schools 2016/2017 Revised 9/2/16 1 of 19 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:

The TN Mathematics Standards The Tennessee Mathematics Standards: Teachers can access the Tennessee State standards, which https://www.tn.gov/education/article/mathematics- are featured throughout this curriculum map and represent standards college and career ready learning at reach respective grade level. Standards for Mathematical Practice Mathematical Practice Standards Teachers can access the Mathematical Practice Standards, https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1 which are featured throughout this curriculum map. This link pGdEJTYkE/view contains more a more detailed explanation of each practice along with implications for instructions.

Purpose of the Mathematics Curriculum Maps

The Shelby County Schools curriculum maps are intended to guide planning, pacing, and sequencing, reinforcing the major work of the grade/subject. Curriculum maps are NOT meant to replace teacher preparation or judgment; however, it does serve as a resource for good first teaching and making instructional decisions based on best practices, and student learning needs and progress. Teachers should consistently use student data differentiate and scaffold instruction to meet the needs of students. The curriculum maps should be referenced each week as you plan your daily lessons, as well as daily when instructional support and resources are needed to adjust instruction based on the needs of your students.

How to Use the Mathematics Curriculum Maps

Tennessee State Standards 2 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY The TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards the supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teachers' responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

Content Weekly and daily objectives/learning targets should be included in your plan. These can be found under the column titled content. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the learning targets/objectives provide specific outcomes for that standard(s). Best practices tell us that making objectives measureable increases student mastery.

Instructional Support and Resources District and web-based resources have been provided in the Instructional Support and Resources column. The additional resources provided are supplementary and should be used as needed for content support and differentiation.

Topics Addressed in Quarter  Triangle Congruence with Applications  Properties of Triangles  Special Segments in Triangles  Properties of Quadrilaterals with Coordinate Proof

Overview Shelby County Schools 2016/2017 Revised 9/2/16 3 of 19 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY During the second quarter, students will continue to work with the concept of rigid motion and congruency. They will determine if two triangles are congruent by SSS, SAS, ASA, AAS, or HL and then provide appropriate reasoning for why they are congruent. They also will gain a deeper insight into constructing two-column, paragraph, and coordinate proofs. Students will classify triangles based on its’ angles and side measures and determine whether a triangle exists given three side measures and find the range of the third side when given two side measures. Students will compare the sides or angles of a given triangle and apply the Hinge theorem. Students will learn how to find missing angles in triangles both interior and exterior angles. They will investigate the special segments of a triangle; altitude, angle bisector, perpendicular bisector, and median. They will also practice with the points of concurrency; orthocenter, incenter, circumcenter, and centroid. Identifying quadrilaterals using given properties concludes the second quarter. Students should be able to solve equations to find various missing parts of the quadrilaterals as well as write two-column, paragraph and coordinate proofs using definitions and properties.

Content Standard Type of Rigor Foundational Standards Sample Assessment Items** G-CO.A.1,2,3,4,5 Procedural Skill and 8.G.A.1, 2,3, 4,5 Defining Parallel Lines; Defining Fluency , Conceptual Perpendicular Lines ; Fixed Points Understanding & of Rigid Motion; C-CO.A.4 Tasks; Application G-CO.A.5 Tasks G-CO.B.6, 7, 8 Conceptual 8.G.A.1, 2,3, 4,5 Hexagon Art; Parallelogram Understanding & Application G-CO.C.9, 10 Conceptual 8.G.A.1, 2,3, 4,5 G-CO.C.9 Tasks; G-CO.C.10 Tasks Understanding & Application G-CO.D.12 Conceptual 8.G.A.5; 8.EE.B.6 G-CO.C.12 Tasks Understanding & Application G-GPE.B.4, 5 Procedural Skill and 8.EE.B.6 Lucio’s Ride Fluency

** TN Tasks are available at ht t p://w ww. e du toolbox.org/ and can b e acc e s s e d b y Tennes s e e e ducators wi th a login and pas s w ord.

4 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY Fluency

The high school standards do not set explicit expectations for fluency, but fluency is important in high school mathematics. Fluency in algebra can help students get past the need to manage computational and algebraic manipulation details so that they can observe structure and patterns in problems. Such fluency can also allow for smooth progress toward readiness for further study/careers in science, technology, engineering, and mathematics (STEM) fields. These fluencies are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students gain fluency. Fluency is not meant to come at the expense of conceptual understanding. Rather, it should be an outcome resulting from a progression of learning and thoughtful practice. It is important to provide the conceptual building blocks that develop understanding along with skill toward developing fluency.

The fluency recommendations for geometry listed below should be incorporated throughout your instruction over the course of the school year.  G-SRT.B.5 Fluency with the triangle congruence and similarity criteria  G-GPE.B.4,5,7 Fluency with the use of coordinates  G-CO.D.12 Fluency with the use of construction tools

References:  http://www.tn.gov/education/article/mathematics-standards  http://www.corestandards.org/  http://www.nctm.org/  http://achievethecore.org/

Shelby County Schools 2016/2017 Revised 9/2/16 5 of 19 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Properties of Triangles and Triangle Congruence with Applications (Allow 3 weeks for instruction, review, and assessment) Domain: G-CO Congruence Enduring Understanding(s) Lesson 4.1 Classifying Triangles, pp.235- Vocabulary Cluster: Prove geometric theorems The properties of triangles create a 242 acute triangle, equiangular triangle,  G-CO.C.10 Prove theorems basis for understanding and reasoning obtuse triangle, right triangle, about triangles. that extends to other geometric equilateral triangle isosceles triangle, figures. scalene triangle Domain: G-CO Congruence Cluster: Make geometric constructions Essential Question(s) Activity with Discussion How do the properties of triangles Pair the categories of classifications of  G-CO.D.12 Make contribute to the geometric sides of triangles with the categories formal geometric understanding of the world around of classifications of angles to constructions with a variety us? of tools and methods determine which combinations can (compass and straightedge, exist and which ones cannot exist. Objective(s): string, reflective devices, Explain why certain combinations paper folding, dynamic • Students will identify and cannot exist. (Example, can a right geometric software, etc.). classify triangles by angle measure equilateral triangle exist?) • Students will identify and Error Analysis classify triangles by side measure pg. 241, #56 (H.O.T. Problem)

Domain: G-CO Congruence Enduring Understanding(s) Lesson 4.2 Angles of Triangles, pp. 243- Vocabulary Cluster: Prove geometric theorems Many relationships exist between the 252 Auxiliary line, exterior angle, remote  G-CO.C.10 Prove theorems measure of the angles of a triangle interior angles, flow proof, corollary about triangles. and the measure of the sides of the Choose from the following triangle. Domain: G-CO Congruence resources to ensure that the Writing in Math intended outcome and level of Cluster: Make geometric Explain in words how to find the constructions Essential Question(s) rigor (mainly conceptual understanding and application) measure of a missing angle of a 6 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES  G-CO.D.12 Make formal geometric What can you say about the interior of the standards are met. triangle if you know two of the constructions with a variety of and exterior angles of a triangle and Task(s) angles. (Have students write this tools and methods (compass and other polygons? as if they were explaining it to Geometry Lab: Angles of Triangles p. straightedge, string, reflective someone who has never taken 243 devices, paper folding, dynamic geometry before.) Objective(s): geometric software, etc.). • Students will apply the Triangle Angle Sum Theorem • Students will prove the measures of interior angles of a triangle have a sum of 180º.

Domain: G-SRT Similarity, Right Enduring Understanding(s) Lesson 4.4 Proving Triangles Congruent Vocabulary Triangles and Trigonometry There exist methods for proving – SSS, SAS, pp. 262-271 Included angle Cluster: Prove theorems involving triangles congruent. Lesson 4.4 Extension – Geometry Lab: Writing in Math similarity Proving Constructions p. 271 Create a chart for triangle  G-SRT.B.5 Use congruence Essential Question(s) congruence theorems (theorem, and similarity criteria for triangles to What does the SAS Triangle Choose from the following definition, and picture) highlighting solve problems and to prove resources to ensure that the the sides and angles that are relationships in geometric figures. Congruence Theorem tell you about triangles? intended outcome and level of congruent in each pair of triangles. Domain: G-CO Congruence rigor (mainly conceptual Compare and contrast the theorems What does the SSS Triangle Cluster: Understand congruence in understanding and application) in your own words. Be sure to Congruence Theorem tell you about terms of rigid motions of the standards are met. include both similarities and triangles? differences between the theorems.  G-CO.B.7 Use the definition of Task(s) Select appropriate tasks from congruence in terms of rigid Objective(s): motions to show that two GSE Analytic Geometry Unit p. 269 #30, (H.O.T. Problems) triangles are congruent if and • Students will use the SSS 1: Similarity, Congruence and only if corresponding pairs of Postulate to test for triangle Proofs sides and corresponding pairs of congruence. angles are congruent. • Students will use the SAS Investigating Congruence in Terms of Domain: G-CO Congruence Postulate to test for triangle Rigid Motion (TN Task Arc) Cluster: Understand congruence in congruence.

Shelby County Schools 2016/2017 Revised 9/2/16 7 of 19 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES terms of rigid motions • Students will write two- Use the following Engageny Lessons to introduce the concepts/build G-CO.B.8 Explain how the column proofs to show that two  conceptual understanding. If used, criteria for triangle congruence triangles are congruent by SSS or SAS. these lessons should be used before (ASA, SAS, and SSS) follow from the the lessons from the textbooks. definition of congruence in terms of Additional Lesson(s): rigid motions. Engage ny Geometry Module 1, Topic Domain: G-CO Congruence D, Lesson 22 – Triangle Congruence Cluster: Make geometric Proving properties of Geometric Figures, constructions students use what they have learned in Topics  G-CO.D.13 A through C to prove properties(Students learn Construct an equilateral why any two triangles that satisfy the SAS triangle, a square, and a congruence criter. regular hexagon inscribed in a circle

Domain: G-SRT Similarity, Right Enduring Understanding(s) Lesson 4.5 Proving Triangles Congruent Vocabulary Triangles and Trigonometry There exist methods for proving – ASA, AAS. Pp.273-280 Included side Cluster: Prove theorems involving triangles congruent. Lesson 4.5 ext Congruence in Right similarity Triangles p.281-282 Writing in Math  G-SRT.B.5 Use congruence Choose from the following Essential Question(s) Explain why identifying two pairs of and similarity criteria for triangles to resources to ensure that the What does the ASA Triangle congruent angles with their included solve problems and to prove intended outcome and level of Congruence Theorem tell you about sides congruent is enough to prove relationships in geometric figures. rigor (mainly conceptual triangles? that two triangles are congruent. Domain: G-CO Congruence understanding and application) What does the AAS Triangle Cluster: Understand congruence in of the standards are met. Congruence Theorem tell you about terms of rigid motions Task(s) triangles? Select appropriate tasks from  G-CO.B.7 Use the definition of What does the HL Triangle Congruence GSE Analytic Geometry Unit congruence in terms of rigid Theorem tell you about two triangles? motions to show that two 1: Similarity, Congruence and triangles are congruent if and Proofs only if corresponding pairs of Objective(s): sides and corresponding pairs of • Students will use the ASA 8 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES angles are congruent. Postulate to test for triangle Analyzing Congruency Proofs Domain: G-CO Congruence congruence. Are the Triangles Congruent? Cluster: Understand congruence in • Students will use the AAS terms of rigid motions Postulate to test for triangle congruence.  G-CO.B.8 Explain how the • Students will explore criteria for triangle congruence congruence in right triangles. (ASA, SAS, and SSS) follow from the definition of congruence in terms of • Students will write formal rigid motions. proofs to show that two triangles are congruent by AAS, ASA or HL. Domain: G-CO Congruence Cluster: Make geometric constructions  G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle

Domain: G-CO Congruence Enduring Understanding(s) Lesson 4.6 Isosceles and Equilateral Vocabulary Cluster: Prove geometric theorems Many relationships exist between the Triangles, pp. 283-291 Pythagorean triple  G-CO.C.10 Prove theorems measure of the angles of a triangle and the measure of the sides of the about triangles. Choose from the following Writing in Math triangle. resources to ensure that the intended outcome and level of p. 290 #45 Challenge – proof Domain: G-CO Congruence (H.O.T. problem) Cluster: Make geometric Essential Question(s) rigor (mainly conceptual constructions understanding and application) What are the special relationships of the standards are met.  G-CO.D.12 Make formal among angles and sides in isosceles geometric constructions with and equilateral triangles? a variety of tools and Use the following Engageny Lessons methods (compass and Objective(s): to introduce the concepts/build straightedge, string, • Students will use properties of conceptual understanding. If used, Shelby County Schools 2016/2017 Revised 9/2/16 9 of 19 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES reflective devices, paper isosceles triangles. these lessons should be used before folding, dynamic geometric • Students will use properties of the lessons from the textbooks. software, etc.). equilateral triangles. Additional Lesson(s): ny • Students will prove Engage Geometry Module 1, Topic Domain: G-SRT Similarity, Right base angles of isosceles D, Lesson 23 – Isosceles Triangles Triangles and Trigonometry triangles are congruent. Cluster: Prove theorems involving similarity  G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Special Segments in Triangles (Allow 2.5 weeks for instruction, review, and assessment) Domain: G-CO Congruence Enduring Understanding(s) Lesson 5.1 Bisectors of Triangles pp. Vocabulary Cluster: Prove geometric theorems The properties of triangles create a 321-331 Perpendicular bisector, concurrent  G-CO.C.10 Prove theorems basis for understanding and reasoning lines, point of concurrency, about triangles. that extends to other geometric Choose from the following circumcenter, incenter figures. resources to ensure that the intended outcome and level of Domain: G-MG Modeling with Writing in Math rigor (mainly conceptual Geometry Essential Question(s) understanding and application) Compare and contrast the Cluster: Apply geometric concepts How can you use perpendicular of the standards are met. perpendicular bisectors and angle in modeling situations bisectors to find the point that is bisectors of a triangle. Be sure to equidistant from all the vertices of a Task(s) include their points of concurrency.  G-MG.A.3 Apply triangle? Centers of Triangles geometric methods to solve How can you use angle bisectors to Centers of Triangles Solutions design problems (e.g., Why are the points of concurrency find the point that is equidistant from designing an object or Hospital Locator called incenter for angle bisectors of all the sides of a triangle? structure to satisfy physical Dividing a Town into Pizza Delivery triangles and circumcenter for the constraints or minimize cost; Regions perpendicular bisectors? working with typographic grid Objective(s): Geometry Lab - Constructing Bisectors systems based on ratios). ★ • Students will identify and use p. 321 10 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES perpendicular bisectors in triangles • Students will identify and use angle bisectors in triangles. • Students will construct the special segments (perpendicular bisectors and angle bisectors) in acute, right and obtuse triangles. • Students will prove the perpendicular bisectors and the angle bisectors of a triangle meet at a point.

Domain: G-MG Modeling with Enduring Understanding(s) Lesson 5.2 Medians and Altitudes of Vocabulary Geometry The properties of triangles create a Triangles pp. 332-341 Median, centroid, altitude, Cluster: Apply geometric concepts basis for understanding and reasoning Use the following Engageny Lessons orthocenter in modeling situations that extends to other geometric to introduce the concepts/build figures. conceptual understanding. If used,  G-MG.A.3 Apply these lessons should be used before Writing in Math geometric methods to solve the lessons from the textbooks. Summarize the special segments of a design problems (e.g., Essential Question(s) Additional Lesson(s): triangle including their names, designing an object or How can you find the balance point or Engage ny Geometry Module 1, Topic E, properties and diagrams into a chart structure to satisfy physical center of gravity of a triangle? Lesson 30 – Medians of Triangles or booklet. constraints or minimize cost; working with typographic grid Objective(s): systems based on ratios). ★ Choose from the following • Students will identify and use resources to ensure that the medians in triangles intended outcome and level of • Students will identify and use rigor (mainly conceptual altitudes in triangles. understanding and application) of the standards are met. • Students will construct the special segments (medians and Task(s) altitudes) in acute, right and obtuse Select appropriate tasks from triangles. GSE Analytic Geometry Unit • Students will prove the 1: Similarity, Congruence and Shelby County Schools 2016/2017 Revised 9/2/16 11 of 19 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES medians and the altitudes of a Proofs triangle meet at a point. Geometry Lab - Constructing Medians and Altitudes p. 332 The Centroid of a Triangle Balancing Act Exploring the Centroid of a Triangle Domain: G-CO Congruence Enduring Understanding(s) Lesson 5.3 Inequalities in one triangle Writing in Math Cluster: Prove geometric theorems Many relationships exist between the pp. 342-349 p. 348 #43 & 48 (H.O.T. Problems)  G-CO.C.10 Prove theorems measure of the angles of a triangle Lesson 5.5 The Triangle Inequality p. 365 #45 & 48 (H.O.T. Problems) about triangles. and the measure of the sides of the Theorem pp.359-366 triangle. Domain: G-MG Modeling with Choose from the following Geometry Essential Question(s) resources to ensure that the intended outcome and level of Cluster: Apply geometric concepts How can you use inequalities to rigor (mainly conceptual in modeling situations describe the relationships among side lengths and angle measures in a understanding and application)  G-MG.A.3 Apply geometric triangle? of the standards are met. methods to solve design Task(s) problems (e.g., designing an Objective(s): Graphing Technology Lab - The object or structure to satisfy Triangle Inequality p. 359 physical constraints or • Students will recognize and minimize cost; working with apply properties of inequalities to Triangle Inequality Task typographic grid systems the measures of the angles of a Triangle Inequalities based on ratios). ★ triangle. • Students will recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle. Domain: G-CO Congruence Enduring Understanding(s) Lesson 5.6 Inequalities in Two Triangles Writing in Math Cluster: Prove geometric theorems Many relationships exist between the pp. 367-376 Compare and contrast the Hinge  G-CO.C.10 Prove theorems measure of the angles of a triangle Choose from the following Theorem to the SAS Postulate for about triangles. and the measure of the sides of the resources to ensure that the Triangle Congruence. triangle. intended outcome and level of 12 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Domain: G-MG Modeling with rigor (mainly conceptual Geometry Essential Question(s) understanding and application) of the standards are met. Cluster: Apply geometric concepts In what ways can congruence be in modeling situations useful? Task(s)  G-MG.A.3 Apply Inequalities in Two Triangles Activity geometric methods to solve Objective(s): design problems (e.g., designing an object or • Students will apply the Hinge structure to satisfy physical Theorem or its converse to make constraints or minimize cost; comparisons in two triangles working with typographic grid • Prove triangle relationships systems based on ratios). ★ using the hinge theorem or its converse

Domain: G-SRT Similarity, Right Enduring Understanding(s) Lesson 7.4 Parallel Lines and Vocabulary Triangles and Trigonometry Many relationships exist between the Proportional Parts (mid-segments of mid-segment of a triangle Cluster: Prove theorems involving measure of the angles of a triangle triangles) pp. 484-493 similarity and the measure of the sides of the Writing in Math  G-SRT.B.4 Prove theorems same triangle. Choose from the following about triangles. Theorems include: a resources to ensure that the Draw all of the mid-segments of one triangle. Explain what you see. Give line parallel to one side of a triangle Essential Question(s) intended outcome and level of divides the other two proportionally, rigor (mainly conceptual as much detail as possible. and conversely; the Pythagorean How are the segments that join the understanding and application) midpoints of a triangle’s sides related Theorem proved using triangle of the standards are met. Research and report on to the triangle’s sides? similarity. Task(s) Sierpinski's triangle TN Geometry Task: Midpoint Madness Domain: G-SRT Similarity, Right Objective(s): See Mathematics, Instructional Triangles and Trigonometry • Students will use proportional Resources, Geometry Cluster: Prove theorems involving parts within triangles. TN Task Arc: How Should We Divide similarity • Students will use proportional This See Mathematics, Instructional  G-SRT.B.5 Use congruence parts with parallel lines. Resources, Geometry, Task Arc: and similarity criteria for triangles to • Students will prove the Investigating Coordinate Geometry solve problems and to prove segment joining midpoints of two Use the following Engageny Lessons Shelby County Schools 2016/2017 Revised 9/2/16 13 of 19 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES relationships in geometric figures. sides of a triangle is parallel to the to introduce the concepts/build third side and half the length. conceptual understanding. If used, these lessons should be used before the lessons from the textbooks. Additional Lesson(s): Engage ny Geometry Module 1, Topic E, Lesson 29 – Mid-segments of Triangles

Properties of Quadrilaterals and Coordinate Proof (Allow 2.5 weeks for instruction, review, and assessment) Domain: G-MG Modeling with Enduring Understanding(s) Lesson 6.1 Angles of Polygons pp. 389- Vocabulary Geometry There exist certain patterns in the 398 diagonal Cluster: Apply geometric concepts angle measures of polygons. Choose from the following in modeling situations resources to ensure that the Writing in Math intended outcome and level of G-MG.A.1 Use Essential Question(s)  rigor (mainly conceptual p. 396 #52 Open ended - Sketch a geometric shapes, their Is there a limit to the sum of the understanding and application) polygon and find the sum of its measures, and their properties interior/exterior angles of a polygon of the standards are met. interior angles. How many sides to describe objects (e.g., why or why not? does a polygon with twice this Task(s) modeling a tree trunk or a interior angles sum have? Justify human torso as a cylinder). ★ Angle Sums your answer Objective(s): Spreadsheet Lab p. 398 • Students will find and use the sum of the measures of the interior angles of a polygon • Find and use the sum of the measures of the exterior angles of a polygon

Domain: G-CO Congruence Enduring Understanding(s) Lesson 6.2 Parallelograms, pp. 399-408 Vocabulary Cluster: Prove geometric theorems The properties of quadrilaterals help Choose from the following parallelogram  G-CO.C.11 Prove theorems you to categorize quadrilaterals. resources to ensure that the intended outcome and level of about parallelograms. Essential Question(s) Writing in Math 14 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Domain: G-GPE Expressing What can you conclude about the rigor (mainly conceptual p. 406 # 43 Open ended - Provide Geometric Properties with sides, angles, and diagonals of a understanding and application) a counterexample to show that Equations parallelogram? of the standards are met. parallelograms are not always Cluster: Use coordinates to prove congruent if their corresponding sides are congruent. (H.O.T. simple geometric theorems Objective(s): Task(s) algebraically Problem) • Students will recognize and Select appropriate tasks from  G-GPE.B.4 Use coordinates apply properties of the sides and GSE Analytic Geometry Unit to prove simple geometric theorems angles of parallelograms 1: Similarity, Congruence and algebraically. For example, prove or • Students will recognize and Proofs disprove that a figure defined by apply properties of parallelograms TN Task: Expanding Triangles See four given points in the coordinate Mathematics, Instructional Resources, plane is a rectangle; prove or Geometry disprove that the point (1, 3) lies on the circle centered at the origin and TN Task: Parallelograms containing the point (0, 2). Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lesson(s): Engage ny Geometry Module 1, Topic E, Lesson 28 – Properties of Parallelograms

Domain: G-CO Congruence Enduring Understanding(s) Lesson 6.3 Tests for Parallelograms Writing in Math Cluster: Prove geometric theorems The properties of quadrilaterals help pp.409-417 Journal Question: Are two  G-CO.C.11 Prove theorems you to categorize quadrilaterals parallelograms congruent if they about parallelograms. Choose from the following both have four congruent angles? Justify your answer Essential Question(s) resources to ensure that the Domain: G-GPE Expressing intended outcome and level of What criteria can you use to prove that rigor (mainly conceptual Geometric Properties with a quadrilateral is a parallelogram? Equations understanding and application)

Shelby County Schools 2016/2017 Revised 9/2/16 15 of 19 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Cluster: Use coordinates to prove Objective(s): of the standards are met. simple geometric theorems • Students will recognize the Task(s) algebraically conditions that ensure a Select appropriate tasks from  G-GPE.B.4 Use coordinates to quadrilateral is a parallelogram. GSE Analytic Geometry Unit prove simple geometric theorems • Students will prove that a set 1: Similarity, Congruence and algebraically. For example, prove of points forms a parallelogram in Proofs or disprove that a figure defined the coordinate plane. Graphing Technology Lab - by four given points in the Parallelograms p. 408 coordinate plane is a rectangle; Whitebeard's Treasure Task prove or disprove that the point (1, 3) lies on the circle centered at the TN Task: Park City origin and containing the point (0, Similarity, Congruence & Proofs 2). Use the following Engageny Lessons to introduce the concepts/build conceptual understanding. If used, these lessons should be used before the lessons from the textbooks.

Additional Lesson(s): Engage ny Geometry Module 4, Topic D, Lesson 13 – Coordinate Proof

Domain: G-CO Congruence Enduring Understanding(s) Lesson 6.4 Rectangles Vocabulary Cluster: Prove geometric theorems The properties of quadrilaterals help Lesson 6.5 Rhombi and Squares rectangle, rhombi, and square.  G-CO.C.11 Prove theorems you to categorize quadrilaterals about parallelograms. Choose from the following resources to ensure that the Writing in Math Domain: G-GPE Expressing intended outcome and level of Essential Question(s) See Engageny lessons Geometric Properties with rigor (mainly conceptual How are the properties of rectangles, Equations understanding and application) rhombi, and squares used to classify of the standards are met. Cluster: Use coordinates to prove quadrilaterals? simple geometric theorems Task(s) How can you use given conditions to 16 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES algebraically prove that a quadrilateral is a TN Task: Getting in Shape rectangle, rhombus or square?  G-GPE.B.4 Use coordinates to TN Task: Lucio’s Ride prove simple geometric theorems algebraically. For example, prove Objective(s): Use the following Engageny Lessons or disprove that a figure defined • Students will recognize and to introduce the concepts/build by four given points in the use the properties of rectangles conceptual understanding. If used, coordinate plane is a rectangle; these lessons should be used before • Students will determine prove or disprove that the point (1, the lessons from the textbooks. whether parallelograms are 3) lies on the circle centered at the rectangles origin and containing the point (0, Additional Lesson(s): • Students will recognize and 2). ny apply the properties of rhombi and Engage Geometry Module 1, Topic D, squares. Lesson 33 – Review of the Assumptions 1 • Students will determine whether quadrilaterals are Engageny Geometry Module 1, Topic rectangles, rhombi, or squares. D, Lesson 34– Review of the Assumptions 2

Domain: G-MG Modeling with Enduring Understanding(s) Lesson 6.6 Trapezoids and Kites, pp.435- Vocabulary Geometry The properties of quadrilaterals help 446 trapezoid, bases, legs of a Cluster: Apply geometric concepts you to categorize quadrilaterals Choose from the following trapezoid, base angles, isosceles in modeling situations resources to ensure that the trapezoid, midsegment of a intended outcome and level of trapezoid G-MG.A.3 Apply geometric Essential Question(s)  rigor (mainly conceptual methods to solve design What are the properties of kites and understanding and application) Graphic Organizer problems (e.g., designing an trapezoids? of the standards are met. object or structure to satisfy Use a Venn Diagram to show the Objective(s): Task(s) physical constraints or minimize relationship of the quadrilaterals • Students will apply properties cost; working with typographic TN Task: Go Fly a Kite you studied in Chapter 6 of trapezoids grid systems based on ratios). ★. • Students will apply properties of kites

Shelby County Schools 2016/2017 Revised 9/2/16 17 of 19 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY

RESOURCE TOOLBOX Textbook Resources Standards Videos ConnectED Site - Textbook and Resources Common Core Standards - Mathematics Math TV Videos Glencoe Video Lessons Common Core Standards - Mathematics Appendix A TN Core The Teaching Channel Hotmath - solutions to odd problems CCSS Flip Book with Examples of each Standard Khan Academy Videos (Geometry) Geometry Model Curriculum Comprehensive Geometry Help: http://www.ccsstoolbox.org/ Online Math Learning (Geometry) http://insidemathematics.org/index.php/high-school- geometry NWEA MAP Resources:https://teach.mapnwea.org/as I LOVE MATH http://www.azed.gov/azcommoncore/mathstandards/hs math/ sist/help_map/ApplicationHelp.htm#Using NCTM Illuminations http://learnzillion.com/common_core/math/hs TestResults/MAPReportsFinder.htm - Sign New Jersey Center for Teaching & Learning (Geometry) http://www.livebinders.com/play/play/454480 in and Click the Learning Continuum Tab – https://www.livebinders.com/play/play?id=464831 this resources will help as you plan for Calculator http://www.livebinders.com/play/play?id=571735 intervention, and differentiating small Finding Your Way Around TI-83+ & TI-84+ North Carolina – Unpacking Common Core group instruction on the skill you are (mathbits.com) http://thegeometryteacher.wordpress.com/the- geometry-course/ currently teaching. (Four Ways to Impact Texas Instruments Calculator Activity Exchange http://math termind.blogspot.com/2012/07/common-core- Teaching with the Learning Continuum) Texas Instruments Math Nspired geometry.html https://support.nwea.org/khanrit - STEM Resources Utah Electronic School - Geometry These Khan Academy lessons are Casio Education for Teachers Ohio Common Core Resources aligned to RIT scores. *Graphing Calculator Note: TI tutorials are available Chicago Public Schools Framework and Tasks through Atomic Learning and also at the following Mathy McMatherson Blog - Geometry in Common Core link: Math Bits - graphing calculator steps Some activities require calculator programs and/or Interactive Manipulatives Literacy Resources applications. GeoGebra – Free software for dynamic math and science Literacy Skills and Strategies for Content Area Use the following link to access FREE software for learning Teachers (Math, p. 22) your MAC. This will enable your computer and TI Calculator to communicate: Free TI calculator NCTM Core Math Tools Glencoe Reading & Writing in the downloads http://www.keycurriculum.com/products/sketchpad (Not free) Any Mathematics Classroom activity using Geometer’s Sketchpad can also be done with any Graphic Organizers (9-12) software that allows construction of figures and measurement, such (teachervision.com) Tasks as Cabri, Cabri Jr. on the TI-83 or 84 Plus,TI-92 Plus, or TI-Nspire Edutoolbox (formerly TNCore) Tasks Inside Math Tasks Mars Tasks Dan Meyer's Three- Act Math Tasks Others NYC tasks Illustrative Math Tasks TN Ready Geometry Blueprint

18 Curriculum and Instruction – Office of Mathematics Quarter 2 GEOMETRY RESOURCE TOOLBOX UT Dana Center SCS Math Tasks State ACT Resources GSE Analytic Geometry Unit 1: Similarity, Congruence and Proofs

Shelby County Schools 2016/2017 Revised 9/2/16 19 of 19