Grade 8 - Shelby County Schools

?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 MapsThe 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 MapsTennessee 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.Instructional Support and ResourcesDistrict 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 ics Addressed in QuarterTriangle Congruence with ApplicationsProperties of TrianglesSpecial Segments in TrianglesProperties of Quadrilaterals with Coordinate ProofOverviewDuring 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 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 & RESOURCESProperties of Triangles and Triangle Congruence with Applications (Allow 3 weeks for instruction, review, and assessment)Domain: G-CO CongruenceCluster: Prove geometric theoremsG-CO.C.10 Prove theorems about triangles. 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)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 measureStudents will identify and classify triangles by side measureLesson 4.1 Classifying Triangles, pp.235-242Vocabularyacute triangle, equiangular triangle, obtuse triangle, right triangle, equilateral triangle isosceles triangle, scalene triangleActivity 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 CongruenceCluster: Prove geometric theoremsG-CO.C.10 Prove theorems about triangles. 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)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?Objective(s):Students will apply the Triangle Angle Sum TheoremStudents will prove the measures of interior angles of a triangle have a sum of 180?. Lesson 4.2 Angles of Triangles, pp. 243-252Choose 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. 243VocabularyAuxiliary line, exterior angle, remote interior angles, flow proof, corollaryWriting 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 who has never taken geometry before.)Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Prove theorems involving similarityG-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.Domain: G-CO CongruenceCluster: Understand congruence in terms of rigid motionsG-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 CongruenceCluster: Understand congruence in terms of rigid motionsG-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 CongruenceCluster: Make geometric constructionsG-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circleEnduring 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. 271Choose 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 ProofsInvestigating 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):HYPERLINK ""Engageny 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 SAS congruence criter. 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)Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Prove theorems involving similarityG-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.Domain: G-CO CongruenceCluster: Understand congruence in terms of rigid motionsG-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 CongruenceCluster: Understand congruence in terms of rigid motionsG-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 CongruenceCluster: Make geometric constructionsG-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circleEnduring 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 ProofsAnalyzing Congruency ProofsAre the Triangles Congruent?VocabularyIncluded sideWriting 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 CongruenceCluster: Prove geometric theoremsG-CO.C.10 Prove theorems about triangles. 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-SRT Similarity, Right Triangles and TrigonometryCluster: Prove theorems involving similarityG-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 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. Lesson 4.6 Isosceles and Equilateral Triangles, pp. 283-291Choose 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):HYPERLINK ""Engageny Geometry Module 1, Topic D, Lesson 23 – Isosceles Triangles VocabularyPythagorean tripleWriting 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 CongruenceCluster: Prove geometric theoremsG-CO.C.10 Prove theorems about triangles. Domain: G-MG Modeling with GeometryCluster: Apply geometric concepts?? in modeling situationsG-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 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?Objective(s):Students will identify and use perpendicular bisectors in trianglesStudents 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.Lesson 5.1 Bisectors of Triangles pp. 321-331Choose 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)HYPERLINK ""Centers of Triangles HYPERLINK "" Centers of Triangles SolutionsHospital LocatorDividing a Town into Pizza Delivery RegionsGeometry Lab - Constructing Bisectors p. 321VocabularyPerpendicular bisector, concurrent lines, point of concurrency, circumcenter, incenterWriting 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?Domain: G-MG Modeling with GeometryCluster: Apply geometric concepts?? in modeling situationsG-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 trianglesStudents 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):HYPERLINK ""Engageny Geometry Module 1, Topic E, Lesson 30 – Medians of TrianglesChoose 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 TriangleBalancing ActExploring the Centroid of a TriangleVocabularyMedian, centroid, altitude, orthocenterWriting in MathSummarize the special segments of a triangle including their names, properties and diagrams into a chart or booklet.Domain: G-CO CongruenceCluster: Prove geometric theoremsG-CO.C.10 Prove theorems about triangles. Domain: G-MG Modeling with GeometryCluster: Apply geometric concepts?? in modeling situationsG-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.359-366Choose 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 InequalitiesWriting in Mathp. 348 #43 & 48 (H.O.T. Problems)p. 365 #45 & 48 (H.O.T. Problems)Domain: G-CO CongruenceCluster: Prove geometric theoremsG-CO.C.10 Prove theorems about triangles. Domain: G-MG Modeling with GeometryCluster: Apply geometric concepts?? in modeling situationsG-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)In what ways can congruence be useful?Objective(s):Students will apply the Hinge Theorem or its converse to make comparisons in two trianglesProve triangle relationships using the hinge theorem or its converseLesson 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 ActivityWriting in MathCompare and contrast the Hinge Theorem to the SAS Postulate for Triangle Congruence.Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Prove theorems involving similarityG-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 similarityG-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. 484-493Choose 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):HYPERLINK ""Engageny Geometry Module 1, Topic E, Lesson 29 – Mid-segments of TrianglesVocabularymid-segment of a triangleWriting 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 triangleProperties of Quadrilaterals and Coordinate Proof (Allow 2.5 weeks for instruction, review, and assessment)Domain: G-MG Modeling with GeometryCluster: Apply geometric concepts?? in modeling situationsG-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?Objective(s):Students will find and use the sum of the measures of the interior angles of a polygonFind and use the sum of the measures of the exterior angles of a polygonLesson 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 SumsSpreadsheet Lab p. 398VocabularydiagonalWriting 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 interior angles sum have? Justify your answerDomain: G-CO CongruenceCluster: Prove geometric theoremsG-CO.C.11 Prove theorems about parallelograms. Domain: G-GPE Expressing Geometric Properties with Equations Cluster: Use coordinates to prove simple geometric theorems algebraicallyG-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 parallelogramsStudents will recognize and apply properties of parallelogramsLesson 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: ParallelogramsUse 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 E, Lesson 28 – Properties of ParallelogramsVocabularyparallelogramWriting 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 CongruenceCluster: Prove geometric theoremsG-CO.C.11 Prove theorems about parallelograms. Domain: G-GPE Expressing Geometric Properties with Equations Cluster: Use coordinates to prove simple geometric theorems algebraicallyG-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 quadrilateralsEssential 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.Lesson 6.3 Tests for Parallelograms pp.409-417Choose 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. 408 HYPERLINK "" Whitebeard's Treasure Task HYPERLINK "" TN Task: Park CitySimilarity, Congruence & ProofsUse 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 4, Topic D, Lesson 13 – Coordinate ProofWriting in MathJournal Question: Are two parallelograms congruent if they both have four congruent angles? Justify your answerDomain: G-CO CongruenceCluster: Prove geometric theoremsG-CO.C.11 Prove theorems about parallelograms. Domain: G-GPE Expressing Geometric Properties with Equations Cluster: Use coordinates to prove simple geometric theorems algebraicallyG-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 quadrilateralsEssential 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? Objective(s):Students will recognize and use the properties of rectanglesStudents will determine whether parallelograms are rectanglesStudents will recognize and apply the properties of rhombi and squares.Students will determine whether quadrilaterals are rectangles, rhombi, or squares. Lesson 6.4 RectanglesLesson 6.5 Rhombi and SquaresChoose 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) HYPERLINK "" TN Task: Getting in ShapeTN Task: Lucio’s RideUse 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 D, Lesson 33 – Review of the Assumptions 1 HYPERLINK "" Engageny Geometry Module 1, Topic D, Lesson 34– Review of the Assumptions 2Vocabularyrectangle, rhombi, and square.Writing in MathSee Engageny lessonsDomain: G-MG Modeling with GeometryCluster: Apply geometric concepts?? in modeling situationsG-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 quadrilateralsEssential Question(s)What are the properties of kites and trapezoids?Objective(s):Students will apply properties of trapezoidsStudents will apply properties of kitesLesson 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 Vocabulary trapezoid, bases, legs of a trapezoid, base angles, isosceles trapezoid, midsegment of a trapezoidGraphic OrganizerUse a Venn Diagram to show the relationship of the quadrilaterals you studied in Chapter 6RESOURCE 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 SCS Math Tasks 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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