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 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 judgment 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 9-12 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 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 QuarterSimilarity and TransformationsUsing Similar TrianglesRight Triangles with TrigonometryProperties of Angles and Segments in CirclesOverviewDuring the third quarter students formalize their understanding of similarity, which was informally studied prior to geometry. Similarity of polygons and triangles is explored and triangle similarity postulates and theorems are formally proven. The proportionality of corresponding sides of similar figures is applied. Similarity is extended to the side-splitting, proportional medians, altitudes, angle bisectors, and segments theorems. The geometric mean is defined and related to the arithmetic mean. The special right triangles of 30-60-90 and 45-45-90 are also studied. Students are introduced to the right-triangle trigonometric ratios of sine, cosine, and tangent, and their applications. Angles and the sine, cosine, and tangent functions are defined in terms of a rotation of a point on the unit circle. Students will end the quarter by starting their study of circles. They will quickly review circumference and then identify central angles, major and minor arcs, semicircles and find their measures. They will finish the quarter studying inscribed angles and intercepted arcs.HYPERLINK ""Year at a Glance DocumentContent StandardType of RigorFoundational StandardsSample Assessment Items**G-SRT.A.2Procedural Skill and Fluency , Conceptual Understanding 8.G.A.1, 2,3, 4,5Illustrative: Are They Similar; Illustrative: Congruent and Similar Triangles; Illustrative: Similar TrianglesG-SRT.B.4, 5Procedural Skill and Fluency , Conceptual Understanding & Application8.G.A.1, 2,3, 4,5Illustrative: Joining Two Midpoints of Sides of a Triangle; Illustrative: Pythagorean Theorem; Illustrative: Bank Shot; Illustrative: Points From DirectionsG-SRT.C.6, 7, 8Procedural Skill and Fluency , Conceptual Understanding & Application8.G.A.1, 2,3, 4,5Math shell: Hopewell GeometryG-C.A.1, 2Procedural Skill and Fluency , Conceptual Understanding & Application8.G.A.5; 8.G.B.7Illustrative: Similar Circles; Illustrative: Neglecting the Curvature of the EarthG-MG.A.3Procedural Skill and Fluency , Conceptual Understanding & Application8.G.A.5; 8.G.B.7Illustrative: Ice Cream Cone; Illustrative: Satellite** 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 & RESOURCESSimilarity and Transformations (Allow approximately 3 weeks for instruction, review, and assessment)Domain: G-MG Modeling with GeometryCluster: Apply geometric concept 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)Polygons are similar if and only if corresponding angles are congruent and corresponding sides are proportional.Essential Question(s)What is the difference between a ratio and a proportion?What operations are used to solve a proportion?Objective(s):Write ratiosWrite and solve proportionsUse the following lesson(s) first to introduce concepts/build conceptual understanding. Better Lesson: Comparing SequencesUse the textbook resources to address procedural skill and fluency.Lesson 7.1 Ratios and Proportions pp. 457 - 464 Graphing Technology Lab - Fibonacci Sequence and Ratios p. 464VocabularyRatio, extended ratios, proportion, extremes, means, cross productsActivity with DiscussionResearch and Report- The Fibonacci Sequence and the Golden Ratio - what are they, why are they important, and how are they related.Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Understand similarity in terms?? of similarity transformationsG-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.Enduring Understanding(s)Polygons are similar if and only if corresponding angles are congruent and corresponding sides are proportional.Essential Question(s)How do you use proportions to find side lengths in similar polygons?How do you identify corresponding parts of similar triangles?Objective(s):Use proportions to Identify similar polygonsSolve problems using the properties of similar polygonsUse the following lesson(s) first to introduce concepts/build conceptual understanding. engageny Geometry Module 2, Topic C, Lesson 12 – Similarity TransformationsUse the textbook resources to address procedural skill and fluency.Lesson 7.2 Similar Polygons pp.465-473Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each Standard(Designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)VocabularySimilar polygons, similarity ratio, scale factorActivity with Discussionp. 472 #54 Draw two regular pentagons that are different sizes. Are the pentagon’s similar? Will any two regular polygons with the same number of sides be similar? ExplainWriting in Math/Discussionp. 472 #55 Compare and contrast congruent, similar, and equal figures.Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Understand similarity in terms?? of similarity transformationsG-SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Define trigonometric ratios?and solve problems involving?right trianglesG-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.Enduring Understanding(s)Geometric figures can change size and/or position while maintaining proportional attributes.Essential Question(s)How do you show two triangles are similar?Objective(s):Identify similarity transformationsVerify similarity after a similarity transformationUse the following lesson(s) first to introduce concepts/build conceptual understanding. engageny Geometry Module 2, Topic A, Lesson 2 – Scale Drawings by Ratio Methodengageny Geometry Module 2, Topic A, Lesson 3 – Scale Drawings by the Parallel Methodengageny Geometry Module 2, Topic B Lesson 6 – Dilationsengageny Geometry Module 2, Topic B, Lesson 7 – Do Dilations Map Segments?Use the textbook resources to address procedural skill and fluency.Lesson 7.6 Similarity Transformations pp. 505-511Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardVocabularydilation, similarity transformation, center of dilation, scale factor of a dilation, enlargement, reductionActivity with DiscussionExplain how you can use scale factor to determine whether a transformation is an enlargement, a reduction, or a congruence transformation.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)Geometric figures can change size and/or position while maintaining proportional attributes.Essential Question(s)How do you use proportions to find side lengths in similar polygons?Objective(s):Interpret scale modelsUse scale factors to solve problemsUse the following lesson(s) first to introduce concepts/build conceptual understanding. engageny Geometry Module 2, Topic A, Lesson 1 – Scale DrawingsUse the textbook resources to address procedural skill and fluency.Lesson 7.7 Scale Drawings and Scale Models pp. 512-517VocabularyScale model, scale drawing, scaleWriting in Math/DiscussionCompare and contrast scale and scale factor.You can produce a scale model of a certain object by extending each dimension by a constant. What must be true of the shape of the object? Explain your reasoning.Using Similar Triangles (Allow approximately 3 weeks for instruction, review, and assessment)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)Polygons are similar if and only if corresponding angles are congruent and corresponding sides are proportional.Essential Question(s)How do you use proportions to find side lengths in similar polygons? How do you show two triangles are similar?Objective(s):Identify and prove similar triangles using the AA Similarity Postulate and the SSS and SAS similarity TheoremsUse similar triangles to solve problemsUse the following lesson(s) first to introduce concepts/build conceptual understanding. engageny Geometry Module 2, Topic C, Lesson 14 – Similarityengageny Geometry Module 2, Topic C, Lesson 15 – AA Similarityengageny Geometry Module 2, Topic C, Lesson 17 – SSS & SAS Similarityengageny Geometry Module 2, Topic C, Lesson 16 – Applying Similar TrianglesUse the textbook resources to address procedural skill and fluency.Lesson 7.3 Similar Triangles pp. 474-483Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardWriting in Math/DiscussionContrast and compare the triangle congruence theorems with the triangle similarity theorems.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)Polygons are similar if and only if corresponding angles are congruent and corresponding sides are proportional.Essential Question(s)How do you use proportions to find side lengths in similar polygons?Objective(s):Use proportional parts within trianglesUse proportional parts with parallel linesUse the following lesson(s) first to introduce concepts/build conceptual understanding. engageny Geometry Module 2, Topic A, Lesson 4 – Triangle Side Splitter Theoremengageny Geometry Module 2, Topic B, Lesson 10 – Dividing a Line Segment into Equal Partsengageny Geometry Module 2, Topic C, Lesson 19 – Parallel Lines and Proportional SegmentsUse the textbook resources to address procedural skill and fluency.Lesson 7.4 Parallel Lines and Proportional Parts (midsegments was previously covered in unit 2) pp. 484-492Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardTask(s)See Mathematics, Instructional Resources, Geometry, Task Arc: Investigating Coordinate GeometryPartitioning However You Want to Slice It Comparing ShapesUse the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each Standard (Designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)VocabularyMid-segment of a triangleActivity with DiscussionUse multiple representations to explore angle bisectors and proportions. See p. 492, #47Domain: 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)Similar figures map one shape proportionally onto another through non-rigid motions. Congruence and similarity criteria for triangles are used to solve problems and prove relationships of geometric figures. Essential Question(s)Can the geometric mean be used in any triangle?Why does geometric mean help us to find the missing sides in a right triangle?Objective(s):Find the geometric mean between two numbersSolve problems involving relationships between parts of a right triangle and the altitude to its hypotenuseUse the following lesson(s) first to introduce concepts/build conceptual understanding. engageny Geometry Module 2, Topic D, Lesson 21 – Special Relationships within Right Trainglesengageny Geometry Module 2, Topic D, Lesson 24 – Prove the Pythagorean Theorem Using SimilarityUse the textbook resources to address procedural skill and fluency.Lesson 8.1 Geometric Mean pp.531-539Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardVocabularyGeometric meanWriting in Math/DiscussionWhat is an arithmetic mean and a geometric mean of two numbers? Are they ever equal? Justify your answer.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)Similar figures map one shape proportionally onto another through non-rigid motions. Congruence and similarity criteria for triangles are used to solve problems and prove relationships of geometric figures. .Essential Question(s)How might the features of one figure be useful when solving problems about a similar figure?Objective(s):Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar trianglesUse the Triangle Angle Bisector TheoremUse the following lesson(s) first to introduce concepts/build conceptual understanding. engageny Geometry Module 2, Topic C, Lesson 18 – Triangle Angles Bisector TheoremUse the textbook resources to address procedural skill and fluency.Lesson 7.5 Parts of Similar Triangles pp.495-503Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardACT Practice (sample problems to prepare for the ACT)Glencoe, pp.456-457Activity with DiscussionFind a counterexample: If the measure of an altitude and side of a triangle are proportional to the corresponding altitude and corresponding side of another triangle, then the triangles are similarRight Triangles and Trigonometry (Allow approximately 1.5 weeks for instruction, review, and assessment)t)Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Define trigonometric ratios?and solve problems involving?right trianglesG-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.Enduring Understanding(s)Trigonometry can be used to measure sides and angles indirectly in right triangles.Essential Question(s)How do you find a side length or angle measure in a right triangle?Objective(s):Identify and apply side ratios in 45-45-90 right triangles.Identify and apply side ratios in 30-60-90 right trianglesUse the following lesson(s) first to introduce concepts/build conceptual understanding. HYPERLINK "" engageny Geometry Module 2, Topic D, Lesson 24 - Prove the Pythagorean Theorem Using SimilarityUse the textbook resources to address procedural skill and fluency.Lesson 8.3 Special Right Triangles pp.552-559Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardTask(s)Discovering Special Right Triangles Learning TaskFinding Right Triangles in your Environment Learning Task Create your own triangles Learning TaskActivity with Discussionp.559 #50Explain how you can find the lengths of two legs of a 30-60-90 triangle in radical form if you are given the length of the hypotenuse.Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Define trigonometric ratios?and solve problems involving?right trianglesG-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Define trigonometric ratios?and solve problems involving?right trianglesG-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Define trigonometric ratios?and solve problems involving?right trianglesG-SRT.C.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.Enduring Understanding(s)Trigonometry can be used to measure sides and angles indirectly in right triangles.Essential Question(s)How do you find a side length or angle measure in a right triangle?How do trigonometric ratios relate to similar right triangles?Objective(s):Define trigonometric ratios for acute angles in right trianglesUse trigonometric rations and Pythagorean Theorem to solve right trianglesUse the relationship between the sine and cosine of complementary angles.Use the following lesson(s) first to introduce concepts/build conceptual understanding. HYPERLINK "" engageny Geometry Module 2, Topic ELesson 25: Incredibly Useful Ratios Lesson 26: The Definition of Sine, Cosine, and Tangent Lesson 27: Sine and Cosine of Complementary Angles and Special Angles Lesson 28: Solving Problems Using Sine and Cosine Lesson 29: Applying Tangents Lesson 30: Trigonometry and the Pythagorean Theorem Use the textbook resources to address procedural skill and fluency.Lesson 8.4 Trigonometry pp.562-271Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardTask(s)Discovering Trigonometric Ratio Relationships learning task p.22VocabularyTrigonometry, trigonometry ratio, sine, cosine, tangent, inverse sine, inverse cosine, inverse tangentActivity with Discussionp.570 #65Explain how you can use ratios of the side lengths to find the angle measures of the acute angles in a right triangle.Domain: G-SRT Similarity, Right Triangles and TrigonometryCluster: Define trigonometric ratios?and solve problems involving?right trianglesG-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★Enduring Understanding(s)Trigonometry can be used to measure sides and angles indirectly in right triangles.Essential Question(s)How do you find a side length or angle measure in a right triangle?How do trigonometric ratios relate to similar right triangles?Objective(s):Solve problems involving angles of elevation. Solve problems involving angles of depression.Use the following lesson(s) first to introduce concepts/build conceptual understanding. HYPERLINK "" engageny Geometry Module 2, Topic D, Lesson Lesson 31: Using Trigonometry to Determine Area Lesson 32: Using Trigonometry to Find Side Lengths of an Acute TriangleLesson 33: Applying the Laws of Sines and Cosines Lesson 34: Unknown AnglesUse the textbook resources to address procedural skill and fluency.Lesson 8.5 – Angles of Elevation and Depression pp.574-581Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardTask(s)Find that Side or Angle TaskEdutoolbox: Interstate TaskACT Practice (sample problems to prepare for the ACT)Glencoe, pp.618-619VocabularyAngle of elevation, angle of depressionWriting in Math/Discussionp.580 #25Classify the statement below as true or false. Explain. “As a person moves closer to an object he or she is sighting, the angle of elevation increases”Properties of Angles and Segments in Circles (Allow approximately 1.5 weeks for instruction, review, and assessment)t)Domain: G-C CirclesCluster: Understand and apply theorems about circlesG-C.A.1 Prove that all circles are similar.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-GMD Geometric Measurement and DimensionCluster: Explain volume formulas and use them to solve problems G-GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.Enduring Understanding(s)The concept of similarity as it relates to circles can be extended with proof. Essential Question(s)What role do circles play in modeling the word around us?Objective(s):Give an argument to justify the formula for the circumference of a circle.Prove that all circles are similar.Use the following lesson(s) first to introduce concepts/build conceptual understanding. engageny Geometry Module 3, Topic A, Lesson 4 – Proving the Area of a DiskUse the textbook resources to address procedural skill and fluency.Lesson 10.1 – Circles and Circumference pp.683-691Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardTask(s)Illustrative Math: Similar Circles TaskAll Circles are Similar TaskVocabularyCircle, center, radius, chord, diameter, congruent circles, concentric circles, circumference, pi, inscribed, circumscribedWriting in Math/Discussionp.690 #54Research and write about the history of pi and its importance to the study of geometry.Domain: G-C CirclesCluster: Understand and apply theorems about circlesG-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Enduring Understanding(s)Relationships between angles, radii and chords will be investigated. Similarities will be applied to derive an arc length and a sector area. Essential Question(s)When lines intersect a circle, or within a circle, how do you find the measures of resulting angles, arcs, and segments?Objective(s):Identify central angles, major arcs, minor arcs, and semicircles and find their measures.Use the following lesson(s) first to introduce concepts/build conceptual understanding. . engageny Geometry Module 5, Topic A, Lesson 4 – Explore Relationships between Inscribed Angles, Central Angles and their Intercepted ArcsUse the textbook resources to address procedural skill and fluency.Lesson 10.2 Measuring Angles and Arcs pp.692-700Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardTask(s) HYPERLINK "" Circles and their Relationships among Central Angles, Arcs and Chords (p. 15)Investigating Angle Relationships in Circles (pp. 46 & 52)VocabularyCentral angle, arc, minor arc, major arc, semicircle, congruent arcs, adjacent arcs, arc lengthWriting in Math/Discussionp.699 #62Describe the three different types of arcs in a circle and the method for finding the measure of each one.Domain: G-C CirclesCluster: Understand and apply theorems about circlesG-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Enduring Understanding(s)Relationships between angles, radii and chords will be investigated. Similarities will be applied to derive an arc length and a sector area. Essential Question(s)When lines intersect a circle, or within a circle, how do you find the measures of resulting angles, arcs, and segments?Objective(s):Identify and describe relationships involving inscribed angles.Prove properties of angles for a quadrilateral inscribed in a circle.Use the following lesson(s) first to introduce concepts/build conceptual understanding. Engageny Geometry Module 5, Topic A, Lesson 5 – Prove Inscribed Angle TheoremUse the textbook resources to address procedural skill and fluency.Lesson 10.4 Inscribed Angles pp.709-716Use the following resources to deepen students' conceptual understanding of mathematical content and develop their ability to apply that knowledge to non-routine problems.HS Flip Book with examples of each StandardTask(s)Illustrative Math: Opposite angles in a cyclic quadrilateralVocabularyInscribed angle, intercepted arcWriting in Math/Discussionp.715 #50Compare and contrast inscribed angles and central angles of a circle. If they intercept the same arc, how are they related?RESOURCE TOOLBOXThe Resource Toolbox provides additional support for comprehension and mastery of subject-level skills and concepts. While some of these resources are embedded in the map, the use of these categorized materials can assist educators with maximizing their instructional practices to meet the needs of all students.?Textbook 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)StandardsCommon Core Standards - MathematicsCommon Core Standards - Mathematics Appendix A TN CoreHS Flip Book with Examples of each Standard(The Flip Book is designed as a resource tool to assist teachers in deepening their understanding of what each standard means in terms of what students must know and be able to do. It outlines only a sample of instructional strategies and examples. Links to conceptual categories and specific standards in the document can be accessed from page 5 Mathematics Standards for High School.)Geometry Model Curriculum Utah Electronic School - Geometry Ohio Common Core ResourcesChicago Public Schools Framework and Tasks ACT TN ACT Information & ResourcesACT College & Career Readiness Mathematics StandardsVideos Math TV VideosThe Teaching ChannelKhan Academy Videos (Geometry)TasksEdutoolbox (formerly TNCore) Tasks Inside Math Tasks Mars Tasks Dan Meyer's Three- NYC tasks Illustrative Math TasksUT Dana Center GSE Analytic Geometry Unit 1: Similarity, Congruence and ProofsCalculatorFinding 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 downloadsNWEA 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.Literacy 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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