Grade 8
IntroductionIn 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 ready90% of students will graduate on time100% of our students who graduate college or career ready will enroll in a post-secondary opportunityIn 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. 42291023279100-571500-1270The 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:The TN Mathematics StandardsThe Tennessee Mathematics Standards: 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 Practice Mathematical Practice Standards 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 MapsThis curriculum framework or map is meant to help teachers and their support providers (e.g., coaches, leaders) on their path to effective, college and career ready (CCR) aligned instruction and our pursuit of Destination 2025. It is a resource for organizing instruction around the TN State Standards, which define what to teach and what students need to learn at each grade level. The framework is designed to reinforce the grade/course-specific standards and content—the major work of the grade (scope)—and provides a suggested sequencing and pacing and time frames, aligned resources—including sample questions, tasks and other planning tools. Our hope is that by curating and organizing a variety of standards-aligned resources, teachers will be able to spend less time wondering what to teach and searching for quality materials (though they may both select from and/or supplement those included here) and have more time to plan, teach, assess, and reflect with colleagues to continuously improve practice and best meet the needs of their students.The map is meant to support effective planning and instruction to rigorous standards; it is not meant to replace teacher planning or prescribe pacing or instructional practice. In fact, our goal is not to merely “cover the curriculum,” but rather to “uncover” it by developing students’ deep understanding of the content and mastery of the standards. Teachers who are knowledgeable about and intentionally align the learning target (standards and objectives), topic, task, and needs (and assessment) of the learners are best-positioned to make decisions about how to support student learning toward such mastery. Teachers are therefore expected--with the support of their colleagues, coaches, leaders, and other support providers--to exercise their professional judgement aligned to our shared vision of effective instruction, the Teacher Effectiveness Measure (TEM) and related best practices. However, while the framework allows for flexibility and encourages each teacher/teacher team to make it their own, our expectations for student learning are non-negotiable. We must ensure all of our children have access to rigor—high-quality teaching and learning to grade-level specific standards, including purposeful support of literacy and language learning across the content areas. Additional Instructional SupportShelby County Schools adopted our current math textbooks for grades 6-8 in 2010-2011. ?The textbook adoption process at that time followed the requirements set forth by the Tennessee Department of Education and took into consideration all texts approved by the TDOE as appropriate. ?We now have new standards; therefore, the textbook(s) have been vetted using the Instructional Materials Evaluation Tool (IMET). This tool was developed in partnership with Achieve, the Council of Chief State Officers (CCSSO) and the Council of Great City Schools. The review revealed some gaps in the content, scope, sequencing, and rigor (including the balance of conceptual knowledge development and application of these concepts), of our current materials.?The additional materials purposefully address the identified gaps in alignment to meet the expectations of the CCR standards and related instructional shifts while still incorporating the current materials to which schools have access. ?Materials selected for inclusion in the Curriculum Maps, both those from the textbooks and external/supplemental resources (e.g., EngageNY), have been evaluated by district staff to ensure that they meet the IMET criteria.How to Use the Mathematics Curriculum MapsOverviewAn overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.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 that 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 teacher’s responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard. ContentTeachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.). Support for the development of these lesson objectives 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 objectives provide specific outcomes for that standard(s). Best practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks, i-Ready lessons and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation. Topics Addressed in QuarterTools of GeometryReasoning & ProofTransformations, Congruence & SimilarityLines & AnglesOverviewRotations, reflections, translations and congruency are developed experimentally in grade 8, and this experience is built upon in geometry, giving greater attention to precise definitions and formal reasoning. Properties of lines and angles, triangles and parallelograms were investigated in Grades 7 and 8. In geometry, these properties are revisited in a more formal setting, giving greater attention to precise statements of theorems and establishing these theorems by means of formal reasoning. During this quarter students will develop the relationship between transformations and congruency. Students will study Congruence (G-CO), namely experimenting with transformations in the plane, understanding congruence in terms of rigid motions, proving geometric theorems, prove geometric theorems, and make geometric constructions with a variety of tools. Students will also use congruence and similarity criteria for triangles to solve problems and to prove relationships (G-SRT). Additionally in this quarter, students will use coordinates to prove simple geometric theorems algebraically (G-GPE). Content StandardType of RigorFoundational StandardsSample Assessment Items**G-CO.A.1,2,3,4,5Procedural Skill and Fluency , Conceptual Understanding & Application8.G.A.1, 2,3, 4,5Defining Parallel Lines; Defining Perpendicular Lines; Fixed Points of Rigid Motion; C-CO.A.4 Tasks; G-CO.A.5 TasksG-CO.B.6, 7, 8Conceptual Understanding & Application8.G.A.1, 2,3, 4,5Hexagon Art; ParallelogramG-CO.C.9, 10Conceptual Understanding & Application8.G.A.1, 2,3, 4,5G-CO.C.9 Tasks; G-CO.C.10 TasksG-CO.D.12Conceptual Understanding & Application8.G.A.5; 8.EE.B.6G-CO.C.12 TasksG-GPE.B.4, 5Procedural Skill and Fluency8.EE.B.6Lucio’s Ride** TN Tasks are available at 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.12Fluency with the use of construction toolsReferences: STATE STANDARDS CONTENTINSTRUCTIONAL SUPPORT & RESOURCESTools of Geometry (Allow approximately 2 weeks for instruction, review, and assessment) Domain: G-CO Congruence Cluster: Experiment with transformations in the planeCluster: G-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.Domain: G-CO CongruenceCluster: Make geometric constructionsG-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)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)In what ways can congruence be useful?Objective(s):Students will explore and know precise definitions of basic geometric terms.Students will identify the undefined notions used in geometry (point, line, plane, distance).Students will use tools and methods to precisely copy a segment, copy an angle, bisect a segment, and bisect an angle.Students will informally perform the constructions listed above using string, reflective devices, paper folding, and/or dynamic geometric software.Lesson 1-1 Points, Lines and Planes, pp. 5 – 13Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s)Select appropriate task(s) from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsAdditional Resource(s)CCSS Flip Book with Examples of each StandardPoints, Lines, and Planes (Interactive Notebook/Foldables)VocabularyUndefined term, point, line, plane, collinear, coplanar, intersection, definition, defined term, spaceInclude Vocabulary from 3.1 - parallel lines, skew lines, parallel planes Writing in MathConnect the words collinear and coplanar to the prefix co-.Is it possible for two points on the surface of a prism to be neither collinear nor coplanar? Justify your answer.Domain: G-CO CongruenceCluster: Experiment with transformations in the planeG-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.Domain: G-CO CongruenceCluster: Make geometric constructionsG-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)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)Why are geometry and measurement important in the real world?Objective(s):Students will use a compass and straightedge to draw a segment and use a ruler to measure it.Students will identify the tools used in formal constructions.Students will use tools and methods to precisely copy a segment, copy an angle, bisect a segment, and bisect an angle.Lesson 1.2 – Linear Measure and Precision, pp. 14 – 24Constructing a Copy of a Line Segment p.17Use 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):HYPERLINK ""Engageny Geometry Module 1, Topic A, Lesson 1 – Construct an Equilateral TriangleVocabularyLine segment, betweeness of points, between, congruent segments, constructionDiscussionDiscuss the Ruler Postulate.Writing in MathWhy is it important to have a standard of measure? Refer to p. 14, and include an advantage and disadvantage to the builders of the pyramids.Domain: G-CO CongruenceCluster: Experiment with transformations in the planeG-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.Domain: G-CO CongruenceCluster: Make geometric constructionsG-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-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)Proving and applying congruence provides a basis for modeling situations geometrically.Algebra can be used to efficiently and effectively describe and apply geometric properties.Essential Question(s)Why are the Distance and Midpoint Formulas important in the real world? Objective(s):Students will connect two points on a coordinate plane to form a segment and use the Distance Formula to find its length.Students will find the midpoint of a segment and in the coordinate plane.Lesson 1.3 – Distance and Midpoint, pp. 25 – 35Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s)As the Crow Flies HYPERLINK "" TN Task Arc, Geometry - Investigating Coordinate Geometry and Its Use in Solving Mathematical ProblemsTask 1- My Point is That There Are Many Points!Task 2 - The Distance Between UsTask 3 - Will That Work for ANY Two Points?Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsVocabularyDistance, irrational number, midpoint, segment bisectorWriting in MathCompare the Distance and Midpoint Formulas. Draw an example of each on a grid.Domain: G-CO CongruenceCluster: Experiment with transformations in the planeG-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.Domain: G-CO CongruenceCluster: Make geometric constructionsG-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)Proving and applying congruence provides a basis for modeling situations geometrically Essential Question (s)How are number operations used to find and compare the measures of angles.Objective(s):Students will describe the characteristics, and identify angles, circles, perpendicular lines, parallel lines, rays, and line segments.Students will use tools and methods to precisely copy a segment, copy an angle, bisect a segment, and bisect an angle.Lesson 1.4 – Angle Measure, pp. 36 – 45Constructing a Copy of an Angle p. 39 Constructing an Angle Bisector p. 40Use 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):HYPERLINK ""Engageny Geometry Module 1, Topic A, Lesson 3 – Copy and Bisect and Angle Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsBisecting an Angle TaskVocabularyRay, angle, vertex, degree, right angle, acute angle, obtuse angleWriting in MathExplain the prefix bi- when discussing segment bisector.Connect the word degree to the idea of measurement.Discuss the similarity between the Protractor Postulate and the Ruler Postulate.Domain: G-CO CongruenceCluster: Experiment with transformations in the planeG-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.Domain: G-CO CongruenceCluster: Make geometric constructionsG-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)Proving and applying congruence provides a basis for modeling situations geometrically Essential Question(s)What are some real-life applications of congruence? Objective(s):Students will identify and use special pairs of angles.Students will identify perpendicular lines.Lesson 1.5 – Angle Relationships, pp. 46 – 55Use 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):HYPERLINK ""Engageny Geometry Module 1, Topic B, Lesson 6 – Solve for Unknown Angles – Angles and Lines at a Point Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsVocabularyAdjacent angles, linear pair, vertical angles, complementary angles, supplementary angles, perpendicularWriting in MathDiscuss the similarity between the postulates for angles and the postulates for segments.Describe three different ways you can determine that an angle is a right angle.See the Teacher version of the Engageny lesson which has a thorough graphic organizer of previously learned angle facts.Reasoning and Proof(Allow approximately 2 weeks for instruction, review, and assessment) Domain: G-CO Congruence Cluster: Prove geometric theorems G.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically Essential Question(s)How do you use inductive reasoning to make a conjecture?Objective(s):Students will make conjectures based on inductive reasoning.Students will find counterexamples.Lesson 2.1 – Inductive Reasoning and Conjecture, pp. 89 – 96Additional Resource(s)CCSS Flip Book with Examples of each StandardVocabularyInductive reasoning, conjecture, counterexampleWriting in MathConsider the conjecture: If two points are equidistant from a third point, then the three points are collinear. Is this conjecture true or false? If false, give a counterexample. Domain: G-CO Congruence Cluster: Prove geometric theorems G.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically Essential Question(s)How can theorems help prove figures congruent? Objective(s):Students will analyze statements in if-then form.Students will write converses, inverses, and contrapositives.Students will write biconditional statements.Lesson 2.3 – Conditional Statements, pp. 105 – 113Lesson 2.3 Extension – Geometry Lab: Biconditional Statements p. 114VocabularyConditional statement, if-then statement, hypothesis, conclusion, related conditionals, converse, inverse, contrapositive, logically equivalentWriting in MathDescribe a relationship between a conditional, its converse, its inverse, and its contrapositive. Domain: G-CO Congruence Cluster: Prove geometric theorems G.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically Essential Question(s)How are the properties used in geometry helpful in solving problems?Objective(s):Students will identify and use the properties of congruence and equality in proofs.Students will interpret geometric diagrams by identifying what can and cannot be assumed.Lesson 2.5 – Postulates and Paragraph Proofs, pp. 125-132VocabularyPostulate, axiom, proof, theorem, deductive reasoning, paragraph proof, informal proofWriting in MathExplain how undefined terms, definitions, postulates, and theorems are alike and how are they different. Domain: G-CO Congruence Cluster: Prove geometric theorems G.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically Essential Question(s)How can information, definitions, postulate, properties and theorems helpful in writing proofs?Objective(s):Students will use algebra to write two – column proofs.Students will use properties of equality to write geometric proofs.Lesson 2.6 – Algebraic Proof, pp. 134-141VocabularyAlgebraic proof, two-column proof, formal proofWriting in MathCompare and contrast informal or paragraph proofs with formal or two-column proofs. Which type of proof do you find easier to write? Justify your answer.Transformations and Congruence; Transformations and Symmetry (Allow approximately 3 weeks for instruction, review, and assessment) Domain: G-CO Congruence Cluster: Understand congruence in terms of rigid motion 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.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically Essential Question(s)How do you identify corresponding parts of congruent triangles?How do you show that two triangles are congruent?Objective(s):Students will identify corresponding sides and corresponding triangles of congruent triangles.Students will explain that in a pair of congruent triangles, corresponding sides are congruent (distance is preserved) and corresponding angles are congruent (angle measure is preserved).Lesson 4.3 – Congruent Triangles, pp. 253 – 261 Teaching Resource for this section (Lesson1.2 in document)Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s) HYPERLINK "" TN Geometry Instructional Task- Comparing ShapesVocabularyCongruent, congruent polygons, corresponding partsWriting in MathDetermine whether the following statement is always, sometimes, or never true. Explain your reasoning.Equilateral triangles are congruent.Domain: G-CO CongruenceCluster: Experiment with transformations in the planeG.CO.A.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically Essential Question(s)What are rigid motions and how can they be defined? Objective(s):Students will identify reflections, translations, and rotations.Students will define rigid motions as reflections, rotations, translations, and combinations of these, all of which preserve distance and angle measure.Students will define congruent figures as figures that have the same shape and size and state that a composition of rigid motions will map one congruent figure onto the other.Lesson 4.7 –Congruence Transformations, pp. 294 – 295Use 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):HYPERLINK ""Engageny Geometry Module 1, Topic C, Lesson 12 – Transformations—The Next Level Engageny Geometry Module 1, Topic C, Lesson 16 – TranslationsVocabularyTransformation, preimage, image, congruence transformation, isometry, reflection, translation, rotationWriting in MathExplain the prefix pre- when discussing pre- image.Explain, give an example and write the rules for the translations and nonrigid motion transformation on a coordinate plane of a reflection, a translation, a rotation and a nonrigid motion transformation.Domain: G-CO CongruenceCluster: Experiment with transformations in the planeG-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)How can you represent a transformation in the coordinate plane?Objective(s):Students will construct the reflection definition by connecting any point on the pre-image to is corresponding parts on the reflected image and describe the line segment’s relationship to the line of reflection (i.e., the line of reflection is the perpendicular bisector of the segment).Lessons 9.1 –Reflections, pp. 615 – 623Use 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)HYPERLINK ""Engageny Geometry Module 1, Topic C, Lesson 14 – Reflections Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s) HYPERLINK "" TN Task Arc, Geometry -Investigating Congruence in Terms of Rigid MotionTask 3 – Reflect on This(Use patty paper to differentiate for struggling learners.)Task: Introduction to Reflections, Translations, and RotationsTranslations, Reflections and RotationsVocabularyLine of reflectionWriting in MathDescribe how to reflect a coordinate figure not on a plane across a line.Domain: G-CO CongruenceCluster: Experiment with transformations in the planeG-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)How can you represent a transformation in the coordinate plane? Objective(s):Students will construct the translation definition by connecting any point on the pre-image to its corresponding point on the translated image, and connecting a second point on the pre-image to its corresponding point on the translated image, and describe how the two segments are equal in length, point in the same direction, and are parallel.Lesson 9.2 –Translations, pp. 624 – 631Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsVocabularyTranslation vectorWriting in MathCompare and contrast a translation and a reflection.Describe what a vector is and how it is used to define a translation.Describe any similarities between the meaning of translation as it us used in geometry and the word’s meaning when used to describe the process of converting words from one language to another.Domain: G-CO CongruenceCluster: Experiment with transformations in the planeG-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)How can you represent a transformation in the coordinate plane? Objective(s):Students will construct rotation definition by connecting the center of rotation to any point on the pre-image and to its corresponding point on the rotated image, and describe the measure of the angle formed and the equal measures of the segments that formed the angles part of the definition.Lesson 9.3 – Rotations, pp. 632 - 638Lesson 9.3 Explore – Geometry Lab: Rotations p. 631Use 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)Engageny Geometry Module 1, Topic C, Lesson 13 – RotationsUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s) HYPERLINK "" TN Task Arc, Geometry -Investigating Congruence in Terms of Rigid Motion Task 2: Twisting Triangles (Use patty paper to differentiate for struggling learners.)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsVocabularyCenter of rotation, angle of rotationWriting in MathUse a graphic organizer to keep track of the types of transformations and their properties in a sequence of transformations.Domain: G-CO CongruenceCluster: Experiment with transformations in the planeG-CO.A.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)How can you represent a transformation in the coordinate plane?Objective(s):Students will draw a specific transformation given a geometric figure and a rotation.Students will predict and verify the sequence of transformations (a composition) that will map a figure onto another.Lesson 9.4 – Compositions of Transformations, pp. 641 - 649Lesson 9.4 Explore – Geometry Software Lab: Compositions of Transformations, p. 640Use 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)Engageny Geometry Module 1, Topic C, Lesson 13 – RotationsVocabularyComposition of transformations, glide reflectionWriting in MathExplain how the Latin word for rigid helps to understand nonrigid pare and contrast the methods learned for combining rigid transformations and nonrigid transformations in the coordinate plane.Domain: G-CO CongruenceCluster: Experiment with transformations in the planeG.CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)How can you identify the type of symmetry that a figure has? Objective(s):Students will identify line and rotational symmetries in two-dimensional figures.Lesson 9.5 – Symmetry, pp. 653 - 659 Transforming 2-D FiguresUse 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) HYPERLINK "" Engageny Geometry Module 1, Topic C, Lesson 15 – Rotations, Reflections, and SymmetryVocabularySymmetry, line symmetry, line of symmetry, rotational symmetry, center of symmetry, order of symmetry, magnitude of symmetry, plane symmetry, axis symmetryWriting in MathConnect the idea of a reflection to a figure with line symmetry.Domain: G-CO CongruenceCluster: Understand congruence in terms of rigid motion G-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)How do you define congruence in terms of rigid motion? Objective(s):Students will predict the composition of transformations that will map a figure onto a congruent figure.Students will determine if two figures are congruent by determining if rigid motions will turn one figure into the other.Additional Lesson(s)Extra lesson – Congruence TransformationRigid Motions and Congruence Activity (just the activity page)Congruence and Triangles Lesson (Lesson 3.1)Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s)TN Task Arc, Geometry -Investigating Congruence in Terms of Rigid Motion Task 4 -Looks Can Be Deceiving Writing in MathDefine congruent. Relate the word to the terms equal and equivalent.Lines, Angles and Triangles’ Lines and Angles (Allow approximately 2 weeks for instruction, review, and assessment) Domain: G-CO Congruence Cluster: Prove geometric theorems G-CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)How can you identify relationships between two lines or two planes?Objective(s):Students will identify the relationships between two lines.Students will name angle pairs formed by parallel lines and transversals.Lesson 3.1 – Parallel Lines and Transversals, pp. 171 – 176Use the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s)Parallel Lines and Transversals(Interactive Notebook/Foldables)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsVocabularyParallel lines, skew lines, parallel planes, transversal, interior angles, exterior angles, consecutive interior angles, alternate interior angles, alternate exterior angles, corresponding anglesWriting in MathDetermine what the term alternate means and demonstrate its using a series of figures. Domain: G-CO Congruence Cluster: Prove geometric theorems G-CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)How are the angles formed by two parallel lines cut by a transversal related?Objective(s):Students will use theorems to determine the relationship[s between specific pairs of angels.Students will use algebra to find angle measurements.Lesson 3.2 – Angles and Parallel Lines, pp. 178 - 184Lesson 3.2 Explore – Geometry SoftwareLab: Angles and Parallel Lines p. 177Writing in MathExplain how to construct parallel lines using one of the postulates or theorems.Define converse using the Latin meaning. Connect converse to the word conversation. Domain: G-CO Congruence Cluster: Prove geometric theorems G-CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.Enduring Understanding(s)Proving and applying congruence provides a basis for modeling situations geometrically.Essential Question(s)How can coordinates and the coordinate plane be used to prove theorems algebraically? Objective(s):Students will determine if lines are parallel using their slopes.Students will recognize angle pairs that occur with parallel lines.Students will prove that two lines are parallelLesson 3.5 – Proving Lines Parallel, pp. 205 - 212 Constructing Parallel LinesUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s)Select appropriate tasks from GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsWriting in MathWrite and solve a problem involving finding the equation of a line that is parallel to a given line.Domain: G-GPE Expressing Geometric Properties with EquationsCluster: Use coordinates to prove simple geometric theorems algebraically G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).Enduring Understanding(s)Algebra can be used to efficiently and effectively describe and apply geometric properties.Essential Question(s)How can algebra be useful when expressing geometric properties?Objective(s):Students will find slopes of lines and use the slope of a line to identify parallel and perpendicular lines.Lesson 3.3 – Slopes of Lines, pp. 186 – 194VocabularySlope, rate of changeWriting in MathA classmate says that all lines have positive or negative slope. Write a question that would challenge her conjecture.Domain: G-GPE Expressing Geometric Properties with EquationsCluster: Use coordinates to prove simple geometric theorems algebraically G-GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).Enduring Understanding(s)Algebra can be used to efficiently and effectively describe and apply geometric properties.Essential Question(s)How can algebra be useful when expressing geometric properties?Objective(s):Students will write an equation of a line given information about the graph.Students will solve problems by writing equations.Lesson 3.4 – Equations of Lines, pp. 196 - 203Constructing Perpendicular Lines and Perpendicular Bisectors p. 55Lesson 3.4 Extension – Geometry Lab: Equations of Perpendicular Bisectors p. 204Use 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)Select additional lessons as appropriate from Engageny Geometry Module 1, Topics A -GUse the following resources to ensure that the intended outcome and level of rigor of the standards are met.Task(s)Finding Equations of Parallel and Perpendicular LinesConstruction of a Perpendicular BisectorVocabularySlope-intercept form, point-slope formWriting in MathCreate a graphic organizer that shows how some of the properties, postulates and theorems build upon one another.RESOURCE TOOLBOXTextbook ResourcesConnectED Site - Textbook and Resources Glencoe Video LessonsHotmath - solutions to odd problemsComprehensive Geometry Help: Online Math Learning (Geometry)I LOVE MATHNCTM IlluminationsNew Jersey Center for Teaching & Learning (Geometry)CalculatorFinding Your Way Around TI-83+ & TI-84+ ()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 downloadsTasksEdutoolbox (formerly TNCore) Tasks Inside Math Tasks Mars Tasks Dan Meyer's Three-Act Math Tasks NYC tasks Illustrative Math TasksUT Dana Center GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsStandardsCommon Core Standards - MathematicsCommon Core Standards - Mathematics Appendix A TN CoreCCSS Flip Book with Examples of each StandardGeometry Model Curriculum North Carolina – Unpacking Common Core geometry.htmlUtah Electronic School - Geometry Ohio Common Core ResourcesChicago Public Schools Framework and Tasks Mathy McMatherson Blog - Geometry in Common CoreVideos Math TV VideosThe Teaching ChannelKhan Academy Videos (Geometry)NWEA MAP Resources: 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) These Khan Academy lessons are aligned to RIT scores. ?Interactive ManipulativesGeoGebra – Free software for dynamic math and science learningNCTM Core Math Tools (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 HYPERLINK "" TN Ready Geometry BlueprintState ACT ResourcesLiteracy Resources Literacy Skills and Strategies for Content Area Teachers (Math, p. 22)Glencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12) () ................
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