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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.

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Focus

The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. For geometry, the major clusters, account for 65% of time spent on instruction.Supporting Content - information that supports the understanding and implementation of the major work of the grade.Additional Content - content that does not explicitly connect to the major work of the grade yet it is required for proficiency.

Coherence

Thinking across grades:The Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Linking to major topics:Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor

Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. While high school standards for math do not list high school fluencies, there are fluency standards for algebra 1, geometry, and algebra 2..Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.

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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 high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:

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The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers can access the Tennessee State standards, which are featured throughout this curriculum map and represent college and career ready learning at reach respective grade level.

Standards for Mathematical PracticeMathematical Practice Standardshttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers can access the Mathematical Practice Standards, which are featured throughout this curriculum map. This link 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 StandardsThe 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.

ContentWeekly 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.

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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

OverviewDuring 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 Fluency , Conceptual

Understanding & Application8.G.A.1, 2,3, 4,5 Defining Parallel Lines; Defining

Perpendicular Lines ; Fixed Points of Rigid Motion; C-CO.A.4 Tasks; G-CO.A.5 Tasks

G-CO.B.6, 7, 8 Conceptual Understanding & Application 8.G.A.1, 2,3, 4,5 Hexagon Art; Parallelogram

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G-CO.C.9, 10 Conceptual Understanding & Application 8.G.A.1, 2,3, 4,5 G-CO.C.9 Tasks; G-CO.C.10 TasksG-CO.D.12 Conceptual Understanding & Application 8.G.A.5; 8.EE.B.6 G-CO.C.12 TasksG-GPE.B.4, 5 Procedural Skill and Fluency 8.EE.B.6 Lucio’s Ride

** TN Tasks are available at http://www.edutoolbox.org/ and can be accessed by Tennessee educators with a login and password.

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/

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESProperties of Triangles and Triangle Congruence with

Applications (Allow 3 weeks for instruction, review, and assessment)

Domain: G-CO Congruence Cluster: Prove geometric theorems G-CO.C.10 Prove theorems about

triangles.

Domain: G-CO Congruence Cluster: Make geometric constructions G-CO.D.12 Make formal geometric

constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Enduring Understanding(s)The properties of triangles create a basis for understanding and reasoning that extends to other geometric figures.

Essential Question(s)How do the properties of triangles contribute to the geometric understanding of the world around us?

Objective(s):• Students will identify and classify

triangles by angle measure• Students will identify and classify

triangles by side measure

Lesson 4.1 Classifying Triangles, pp.235-242 Vocabularyacute triangle, equiangular triangle, obtuse triangle, right triangle, equilateral triangle isosceles triangle, scalene triangle

Activity with DiscussionPair the categories of classifications of sides of triangles with the categories of classifications of angles to determine which combinations can exist and which ones cannot exist. Explain why certain combinations cannot exist. (Example, can a right equilateral triangle exist?)Error Analysispg. 241, #56 (H.O.T. Problem)

Domain: G-CO Congruence Cluster: Prove geometric theorems G-CO.C.10 Prove theorems about

triangles.

Domain: G-CO Congruence Cluster: Make geometric constructions G-CO.D.12 Make formal geometric

constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding,

Enduring Understanding(s)Many relationships exist between the measure of the angles of a triangle and the measure of the sides of the triangle.

Essential Question(s)What can you say about the interior and exterior angles of a triangle and other polygons?

Lesson 4.2 Angles of Triangles, pp. 243-252

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)Geometry Lab: Angles of Triangles p. 243

VocabularyAuxiliary line, exterior angle, remote interior angles, flow proof, corollary

Writing in MathExplain in words how to find the measure of a missing angle of a triangle if you know two of the angles. (Have students write this as if they were explaining it to someone

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESdynamic geometric software, etc.). Objective(s):

• Students will apply the Triangle Angle Sum Theorem

• Students will prove the measures of interior angles of a triangle have a sum of 180º.

who has never taken geometry before.)

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: 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.

Domain: G-CO Congruence Cluster: Understand congruence in terms of rigid motions G-CO.B.7 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.

Domain: G-CO Congruence Cluster: Understand congruence in terms of rigid motions G-CO.B.8 Explain how the criteria for

triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Domain: G-CO Congruence Cluster: Make geometric constructions G-CO.D.13 Construct an equilateral

triangle, a square, and a regular hexagon

Enduring Understanding(s)There exist methods for proving triangles congruent.

Essential Question(s)What does the SAS Triangle Congruence Theorem tell you about triangles?What does the SSS Triangle Congruence Theorem tell you about triangles?

Objective(s):• Students will use the SSS Postulate to

test for triangle congruence.• Students will use the SAS Postulate to

test for triangle congruence.• Students will write two-column proofs to

show that two triangles are congruent by SSS or SAS.

Lesson 4.4 Proving Triangles Congruent – SSS, SAS, pp. 262-271Lesson 4.4 Extension – Geometry Lab: Proving Constructions p. 271

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and Proofs

Investigating Congruence in Terms of Rigid Motion (TN Task Arc)

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 D, Lesson 22 – Triangle Congruence

Proving properties of Geometric Figures, students use what they have learned in Topics A through C to prove properties(Students learn why any two triangles that satisfy the

VocabularyIncluded angleWriting in MathCreate a chart for triangle congruence theorems (theorem, definition, and picture) highlighting the sides and angles that are congruent in each pair of triangles. Compare and contrast the theorems in your own words. Be sure to include both similarities and differences between the theorems.

p. 269 #30, (H.O.T. Problems)

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inscribed in a circle SAS congruence criter.

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: 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.

Domain: G-CO Congruence Cluster: Understand congruence in terms of rigid motions G-CO.B.7 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.

Domain: G-CO Congruence Cluster: Understand congruence in terms of rigid motions G-CO.B.8 Explain how the criteria for

triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

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

Enduring Understanding(s)There exist methods for proving triangles congruent.

Essential Question(s)What does the ASA Triangle Congruence Theorem tell you about triangles?What does the AAS Triangle Congruence Theorem tell you about triangles?What does the HL Triangle Congruence Theorem tell you about two triangles?

Objective(s):• Students will use the ASA Postulate to

test for triangle congruence.• Students will use the AAS Postulate to

test for triangle congruence.• Students will explore congruence in right

triangles.• Students will write formal proofs to show

that two triangles are congruent by AAS, ASA or HL.

Lesson 4.5 Proving Triangles Congruent – ASA, AAS. Pp.273-280Lesson 4.5 ext Congruence in Right Triangles p.281-282Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and Proofs

Analyzing Congruency Proofs Are the Triangles Congruent?

VocabularyIncluded side

Writing in MathExplain why identifying two pairs of congruent angles with their included sides congruent is enough to prove that two triangles are congruent.

Domain: G-CO Congruence Cluster: Prove geometric theorems

Enduring Understanding(s)Many relationships exist between the measure

Lesson 4.6 Isosceles and Equilateral Triangles, pp. 283-291

VocabularyPythagorean triple

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G-CO.C.10 Prove theorems about triangles.

Domain: G-CO Congruence Cluster: Make geometric constructions G-CO.D.12 Make formal geometric

constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: 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.

of the angles of a triangle and the measure of the sides of the triangle.

Essential Question(s)What are the special relationships among angles and sides in isosceles and equilateral triangles?

Objective(s):• Students will use properties of isosceles

triangles.• Students will use properties of equilateral

triangles.• Students will prove base angles of

isosceles triangles are congruent.

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

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 D, Lesson 23 – Isosceles Triangles

Writing in Mathp. 290 #45 Challenge – proof (H.O.T. problem)

Special Segments in Triangles(Allow 2.5 weeks for instruction, review, and assessment)

Domain: G-CO Congruence Cluster: Prove geometric theorems G-CO.C.10 Prove theorems about

triangles.

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in modeling situations G-MG.A.3 Apply geometric methods

to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on

Enduring Understanding(s)The properties of triangles create a basis for understanding and reasoning that extends to other geometric figures.

Essential Question(s)How can you use perpendicular bisectors to find the point that is equidistant from all the vertices of a triangle?How can you use angle bisectors to find the point that is equidistant from all the sides of a triangle?

Lesson 5.1 Bisectors of Triangles pp. 321-331

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)Centers of TrianglesCenters of Triangles SolutionsHospital LocatorDividing a Town into Pizza Delivery RegionsGeometry Lab - Constructing Bisectors p. 321

VocabularyPerpendicular bisector, concurrent lines, point of concurrency, circumcenter, incenter

Writing in MathCompare and contrast the perpendicular bisectors and angle bisectors of a triangle. Be sure to include their points of concurrency.

Why are the points of concurrency called incenter for angle bisectors of triangles and circumcenter for the perpendicular bisectors?

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESratios). ★ Objective(s):

• Students will identify and use 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 Geometry Cluster: Apply geometric concepts in modeling situations G-MG.A.3 Apply geometric methods

to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★

Enduring Understanding(s)The properties of triangles create a basis for understanding and reasoning that extends to other geometric figures.

Essential Question(s)How can you find the balance point or center of gravity of a triangle?

Objective(s):• Students will identify and use medians in

triangles• Students will identify and use altitudes in

triangles.• Students will construct the special

segments (medians and altitudes) in acute, right and obtuse triangles.

• Students will prove the medians and the altitudes of a triangle meet at a point.

Lesson 5.2 Medians and Altitudes of Triangles pp. 332-341Use 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 30 – Medians of Triangles

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsGeometry Lab - Constructing Medians and Altitudes p. 332The Centroid of a Triangle

VocabularyMedian, centroid, altitude, orthocenter

Writing in MathSummarize the special segments of a triangle including their names, properties and diagrams into a chart or booklet.

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Balancing ActExploring the Centroid of a Triangle

Domain: G-CO Congruence Cluster: Prove geometric theorems G-CO.C.10 Prove theorems about

triangles.

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in modeling situations G-MG.A.3 Apply geometric methods

to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★

Enduring Understanding(s)Many relationships exist between the measure of the angles of a triangle and the measure of the sides of the triangle.

Essential Question(s)How can you use inequalities to describe the relationships among side lengths and angle measures in a triangle?

Objective(s):• Students will recognize and apply

properties of inequalities to the measures of the angles of a triangle.

• Students will recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle.

Lesson 5.3 Inequalities in one triangle pp. 342-349Lesson 5.5 The Triangle Inequality Theorem pp.359-366

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)Graphing Technology Lab - The Triangle Inequality p. 359Triangle Inequality TaskTriangle Inequalities

Writing in Mathp. 348 #43 & 48 (H.O.T. Problems)p. 365 #45 & 48 (H.O.T. Problems)

Domain: G-CO Congruence Cluster: Prove geometric theorems G-CO.C.10 Prove theorems about

triangles.

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in modeling situations G-MG.A.3 Apply geometric methods

to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on

Enduring Understanding(s)Many relationships exist between the measure of the angles of a triangle and the measure of the sides of the triangle.

Essential Question(s)In what ways can congruence be useful?

Objective(s):• Students will apply the Hinge Theorem or

its converse to make comparisons in two triangles

• Prove triangle relationships using the

Lesson 5.6 Inequalities in Two Triangles pp. 367-376Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)Inequalities in Two Triangles Activity

Writing in MathCompare and contrast the Hinge Theorem to the SAS Postulate for Triangle Congruence.

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TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESratios). ★ hinge theorem or its converse

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Prove theorems involving similarity G-SRT.B.4 Prove theorems about

triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: 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.

Enduring Understanding(s)Many relationships exist between the measure of the angles of a triangle and the measure of the sides of the same triangle.

Essential Question(s)How are the segments that join the midpoints of a triangle’s sides related to the triangle’s sides?

Objective(s):• Students will use proportional parts within

triangles.• Students will use proportional parts with

parallel lines.• Students will prove the segment joining

midpoints of two sides of a triangle is parallel to the third side and half the length.

Lesson 7.4 Parallel Lines and Proportional Parts (mid-segments of triangles) pp. 484-493

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)TN Geometry Task: Midpoint Madness See Mathematics, Instructional Resources, GeometryTN Task Arc: How Should We Divide This See Mathematics, Instructional Resources, Geometry, Task Arc: Investigating Coordinate GeometryUse 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 29 – Mid-segments of Triangles

Vocabularymid-segment of a triangle

Writing in MathDraw all of the mid-segments of one triangle. Explain what you see. Give as much detail as possible.

Research and report on Sierpinski's triangle

Properties of Quadrilaterals and Coordinate Proof (Allow 2.5 weeks for instruction, review, and assessment)

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in modeling situations G-MG.A.1 Use geometric shapes,

their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). ★

Enduring Understanding(s)There exist certain patterns in the angle measures of polygons.

Essential Question(s)Is there a limit to the sum of the interior/exterior angles of a polygon why or why not?

Lesson 6.1 Angles of Polygons pp. 389-398Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)Angle Sums

Vocabularydiagonal

Writing in Mathp. 396 #52 Open ended - Sketch a polygon and find the sum of its interior angles. How many sides does a polygon with twice this

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Objective(s):• 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

Spreadsheet Lab p. 398 interior angles sum have? Justify your answer

Domain: G-CO Congruence Cluster: Prove geometric theorems G-CO.C.11 Prove theorems about

parallelograms.

Domain: G-GPE Expressing Geometric Properties with EquationsCluster: Use coordinates to prove simple geometric theorems algebraically G-GPE.B.4 Use coordinates to prove

simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2).

Enduring Understanding(s)The properties of quadrilaterals help you to categorize quadrilaterals.Essential Question(s)What can you conclude about the sides, angles, and diagonals of a parallelogram?

Objective(s):• Students will recognize and apply

properties of the sides and angles of parallelograms

• Students will recognize and apply properties of parallelograms

Lesson 6.2 Parallelograms, pp. 399-408Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsTN Task: Expanding Triangles See Mathematics, Instructional Resources, GeometryTN Task: Parallelograms 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

Vocabularyparallelogram

Writing in Mathp. 406 # 43 Open ended - Provide a counterexample to show that parallelograms are not always congruent if their corresponding sides are congruent. (H.O.T. Problem)

Domain: G-CO Congruence Cluster: Prove geometric theorems

Enduring Understanding(s)The properties of quadrilaterals help you to categorize quadrilaterals

Lesson 6.3 Tests for Parallelograms pp.409-417 Writing in MathJournal Question: Are two parallelograms congruent if they both have four congruent

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G-CO.C.11 Prove theorems about parallelograms.

Domain: G-GPE Expressing Geometric Properties with EquationsCluster: Use coordinates to prove simple geometric theorems algebraically G-GPE.B.4 Use coordinates to prove

simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2).

Essential Question(s)What criteria can you use to prove that a quadrilateral is a parallelogram?

Objective(s):• Students will recognize the conditions

that ensure a quadrilateral is a parallelogram.

• Students will prove that a set of points forms a parallelogram in the coordinate plane.

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsGraphing Technology Lab - Parallelograms p. 408Whitebeard's Treasure Task TN Task: Park CitySimilarity, Congruence & Proofs

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

angles? Justify your answer

Domain: G-CO Congruence Cluster: Prove geometric theorems G-CO.C.11 Prove theorems about

parallelograms.

Domain: G-GPE Expressing Geometric Properties with EquationsCluster: Use coordinates to prove simple geometric theorems algebraically G-GPE.B.4 Use coordinates to prove

simple geometric theorems algebraically.

Enduring Understanding(s)The properties of quadrilaterals help you to categorize quadrilaterals

Essential Question(s)How are the properties of rectangles, rhombi, and squares used to classify quadrilaterals?How can you use given conditions to prove that a quadrilateral is a rectangle, rhombus or square?

Lesson 6.4 RectanglesLesson 6.5 Rhombi and Squares

Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)TN Task: Getting in ShapeTN Task: Lucio’s Ride

Vocabularyrectangle, rhombi, and square.

Writing in MathSee Engageny lessons

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Major Content Supporting Content Additional Content

Curriculum and Instruction – Office of Mathematics

Quarter 2 GEOMETRY

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESFor example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2).

Objective(s):• Students will recognize and use the

properties of rectangles• Students will determine whether

parallelograms are rectangles• Students will recognize and apply the

properties of rhombi and squares.• Students will determine whether

quadrilaterals are rectangles, rhombi, or squares.

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 D, Lesson 33 – Review of the Assumptions 1

Engageny Geometry Module 1, Topic D, Lesson 34– Review of the Assumptions 2

Domain: G-MG Modeling with Geometry Cluster: Apply geometric concepts in modeling situations G-MG.A.3 Apply geometric methods to

solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). ★.

Enduring Understanding(s)The properties of quadrilaterals help you to categorize quadrilaterals

Essential Question(s)What are the properties of kites and trapezoids?Objective(s):• Students will apply properties of

trapezoids• Students will apply properties of kites

Lesson 6.6 Trapezoids and Kites, pp.435-446Choose from the following resources to ensure that the intended outcome and level of rigor (mainly conceptual understanding and application) of the standards are met.

Task(s)TN Task: Go Fly a Kite

Vocabularytrapezoid, bases, legs of a trapezoid, base angles, isosceles trapezoid, midsegment of a trapezoid

Graphic OrganizerUse a Venn Diagram to show the relationship of the quadrilaterals you studied in Chapter 6

RESOURCE TOOLBOXTextbook ResourcesConnectED Site - Textbook and Resources Glencoe Video Lessons Hotmath - solutions to odd problems

StandardsCommon Core Standards - Mathematics Common Core Standards - Mathematics Appendix A TN CoreCCSS Flip Book with Examples of each Standard Geometry Model Curriculum

VideosMath TV VideosThe Teaching Channel Khan Academy Videos (Geometry)

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Major Content Supporting Content Additional Content

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Quarter 2 GEOMETRY

RESOURCE TOOLBOXComprehensive Geometry Help:Online Math Learning (Geometry) I LOVE MATHNCTM IlluminationsNew Jersey Center for Teaching & Learning (Geometry)

CalculatorFinding Your Way Around TI-83+ & TI-84+ (mathbits.com) Texas Instruments Calculator Activity ExchangeTexas Instruments Math NspiredSTEM ResourcesCasio Education for Teachers*Graphing Calculator Note: TI tutorials are available through Atomic Learning and also at the following link: Math Bits - graphing calculator steps Some activities require calculator programs and/or applications.

Use the following link to access FREE software for your MAC. This will enable your computer and TI Calculator to communicate: Free TI calculator downloads

TasksEdutoolbox (formerly TNCore) Tasks Inside Math Tasks Mars Tasks Dan Meyer's Three-Act Math TasksNYC tasks Illustrative Math TasksUT Dana Center SCS Math TasksGSE Analytic Geometry Unit 1: Similarity, Congruence and Proofs

http://www.ccsstoolbox.org/http://insidemathematics.org/index.php/high-school- geometry http://www.azed.gov/azcommoncore/mathstandards/hs math/ http://learnzillion.com/common_core/math/hs http://www.livebinders.com/play/play/454480https://www.livebinders.com/play/play?id=464831 http://www.livebinders.com/play/play?id=571735North Carolina – Unpacking Common Core http://thegeometryteacher.wordpress.com/the- geometry-course/ http://math termind.blogspot.com/2012/07/common-core- geometry.html Utah Electronic School - Geometry Ohio Common Core Resources Chicago Public Schools Framework and Tasks Mathy McMatherson Blog - Geometry in Common Core

NWEA MAP Resources:https://teach.mapnwea.org/assist/help_map/ApplicationHelp.htm#UsingTestResults/MAPReportsFinder.htm - Sign in and Click the Learning Continuum Tab – this resources will help as you plan for intervention, and differentiating small group instruction on the skill you are currently teaching. (Four Ways to Impact Teaching with the Learning Continuum)

https://support.nwea.org/khanrit - These Khan Academy lessons are aligned to RIT scores.

Interactive ManipulativesGeoGebra – Free software for dynamic math and science learningNCTM Core Math Tools http://www.keycurriculum.com/products/sketchpad (Not free) Any activity using Geometer’s Sketchpad can also be done with any software that allows construction of figures and measurement, such as Cabri, Cabri Jr. on the TI-83 or 84 Plus,TI-92 Plus, or TI-Nspire

Others TN Ready Geometry Blueprint

State ACT Resources

Literacy ResourcesLiteracy Skills and Strategies for Content Area Teachers (Math, p. 22)Glencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12) (teachervision.com)

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