Shelby County Schools’ mathematics instructional maps are ...



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 standards-aligned instruction. Acknowledging the need to develop competence in literacy and language as the foundation for all learning, Shelby County Schools developed the Comprehensive Literacy Improvement Plan (CLIP). The CLIP ensures a quality balanced literacy approach to instruction that results in high levels of literacy learning for all students across content areas. Destination 2025 and the CLIP establish common goals and expectations for student learning across schools. CLIP connections are evident throughout the mathematics curriculum maps.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 Ready Standards are rooted in the knowledge and skills students need to succeed in post-secondary study or careers. While the academic standards establish desired learning outcomes, the curriculum provides instructional planning designed to help students reach these outcomes. Educators will use this guide and the standards as a roadmap for curriculum and instruction. The sequence of learning is strategically positioned so that necessary foundational skills are spiraled in order to facilitate student mastery of the standards.These standards emphasize thinking, problem-solving and creativity through next generation assessments that go beyond multiple-choice tests to increase college and career readiness among Tennessee students. In addition, assessment blueprints ( ) have been designed to show educators a summary of what will be assessed in each grade, including the approximate number of items that will address each standard. Blueprints also detail which standards will be assessed on Part I of TNReady and which will be assessed on Part II.4363085-2222500Our collective goal is to ensure our students graduate ready for college and career. The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation and connections.-406408064500The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations) procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics and sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy). Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.How to Use the Mathematic Curriculum MapsThis 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 instructional practice in alignment with the three College and Career Ready shifts in instruction for Mathematics. We should see these shifts in all classrooms:FocusCoherenceRigorThroughout 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 each of the three shifts that teachers should consistently access:The TNCore 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.Mathematical ShiftsFocus standards are focused on fewer topics so students can learn moreCoherence within a grade are connected to support focus, and learning is built on understandings from previous gradesRigor standards set expectations for a balanced approach to pursuing conceptual understanding, procedural fluency, and application and modelingCurriculum Maps:Locate the TDOE Standards in the left column. Analyze the language of the standards and match each standard to a learning target in the second column. Consult your McGraw-Hill Algebra and Trigonometry 2nd edition by John W. Coburn or Pearson Algebra and Trigonometry 4th editionby Robert Blitzer Teachers’ Edition (TE) and other cited references to map out your week(s) of instruction.Plan your weekly and daily objectives, using the standards' explanations provided in the second column. Best practices tell us that making objectives measureable increases student mastery.Carefully review the web-based resources provided in the 'Content and Tasks' column and use them as you introduce or assess a particular standard or set of standards.Review the CLIP Connections found in the right column. Make plans to address the content vocabulary, utilizing the suggested literacy strategies, in your instruction.Examine the other standards and skills you will need to address in order to ensure mastery of the indicated standard.Using your McGraw-Hill or Pearson TE and other resources cited in the curriculum map, plan your week using the SCS lesson plan template. Remember to include differentiated activities for small-group instruction and math stations.TN State StandardsEssential UnderstandingsContent & TasksCLIP ConnectionsApplications of Trigonometry(3 Weeks)HYPERLINK ""G-AT – Applied TrigonometryUse trigonometry to solve problems. 5. Understand and apply the Law of Sines (including the ambiguous case and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces)7.1 Oblique Triangles and Law of Sines (Coburn)Visual Proof of Ambiguous CaseOn-line Law of Sines PracticeResources in the TextMcGraw-Hill (Coburn)Chapter ConnectionsReal-world ConnectionsExercises – ApplicationsExtending the ConceptHYPERLINK ""G-AT – Applied TrigonometryUse trigonometry to solve problems. 3. Derive and apply the formulas for the area of a sector of a circle. 4. Calculate the arc length of a circle subtended by a central angle.7.2 Law of Cosines and Area of a Triangle (Coburn)On-Line Law of Cosines PracticeHYPERLINK ""N-VM – Vector and Matrix QuantitiesRepresent and model with vector quantities. Understand the graphic representation of vectors and vector quantities. 1. Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g. v, │v│, ││v││, v). 4. Add and subtract vectors. a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. c. Understand vector subtraction v-w as v+(-w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. 7.3 Vectors and Vector Diagrams (Coburn)7.6 Vectors (Blitzer)Explanations of VectorsCompare/Contrast a vector and a coordinate. Explore and emphasize the differences and similarities between them.Resources in the TextMcGraw-Hill (Coburn)Chapter ConnectionsReal-world ConnectionsExercises – Applications Extending the Concept HYPERLINK ""N-VM – Vector and Matrix QuantitiesRepresent and model with vector quantities. Understand the graphic representation of vectors and vector quantities.3. Solve problems involving velocity and other quantities that can be represented by vectors. 5. Multiply a vector by a scalar.a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g. as c(vx,vy)=(cvx,cvy). b. Compute the magnitude of a scalar multiple cv using ││cv││= │c│v. Compute the direction of cv knowing that when │c│v≠0, the direction of cv is either along v (for c?0) or against v (for c ?0). 6. Calculate and interpret the dot product of two vectors. 7.4 Vector Applications and the Dot Product (Coburn)7.7 The Dot Product (Blitzer)Task - Vectors and Scalars Activity:Resultant-Vector Worksheet:Explain in a paragraph why the dot product is so useful. What is eliminated by using the dot product?HYPERLINK ""N-CN – Complex NumbersPerform complex number arithmetic and understand the representation on the complex plane. 1. Perform arithmetic operations with complex numbers expressing answers in the form a+bi.2. Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. 3. Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. 4. Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example (-1+√3i) has modulus 2 and argument 120 degrees.5. Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. 7.5 Complex Numbers in Trigonometric Form (Coburn)7.5 Complex numbers in Polar Form; DeMoivre’s Theorem (Blitzer)Resources in the TextMcGraw-Hill (Coburn)Chapter ConnectionsReal-world ConnectionsExercises – Applications Extending the Concept7.6 DeMoivre’s Theorem and the Theorem on nth Root(Coburn)7.5 Complex numbers in Polar Form; DeMoivre’s Theorem (Blitzer)Systems of Equations and Inequalities(3 Weeks )HYPERLINK ""A-REI – Solve Equations and InequalitiesSolve systems of equations and nonlinear inequalities 8.1 Linear Systems in Two Variables with Applications (Coburn)8.1 Systems of Linear Equations in Two Variables (Blitzer)Task – Supply and DemandWhat are some of the real life applications of two-variable linear systems? HYPERLINK ""A-REI – Solve Equations and InequalitiesSolve systems of equations and nonlinear inequalities8.2 Linear Systems in Three Variables with Applications (Coburn)8.2 Systems of Linear Equations in Three Variables (Blitzer)Using Excel to Solve Systems of Linear EquationsResources in the TextMcGraw-Hill (Coburn)Chapter ConnectionsReal-world ConnectionsExercises – Applications Extending the ConceptHYPERLINK ""A-REI – Solve Equations and InequalitiesSolve systems of equations and nonlinear inequalities4. Solve systems of nonlinear inequalities by graphing.8.3 Non-Linear Systems of Equations and Inequalities (Coburn)8.4 Systems of Nonlinear Equations in Two Variables (Blitzer)Examples of Non-Linear SystemsHYPERLINK ""A-REI – Solve Equations and InequalitiesSolve systems of equations and nonlinear inequalities4. Solve systems of nonlinear inequalities by graphing.8.4 Systems of Inequalities and Linear Programming (Coburn)8.5 Systems of Inequalities (Blitzer)8.6 Linear Programming (Blitzer)HYPERLINK ""A-REI – Solve Equations and InequalitiesSolve systems of equations and nonlinear inequalities1. Represent a system of linear equations as a single matrix equation in a vector variable.9.1 Solving Linear Systems Using Matrices and Row Operations (Coburn)9.1 Matrix Solutions to Linear Systems (Blitzer)9.2 Inconsistent and Dependent Systems and Their Applications (Blitzer)List some operations that are best suited for matricies. HYPERLINK ""N-VM – Vector and Matrix QuantitiesPerform operations on matrices and use materials in applications. 8. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.9. Add, subtract, and multiply matrices of appropriate dimensions. 10. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. 11. Understand that the zero and identify matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.9.2 The Algebra of Matrices (Coburn)9.3 Matrix Operations and Their Applications (Blitzer)Resources in the TextMcGraw-Hill (Coburn)Chapter ConnectionsReal-world ConnectionsExercises – Applications Extending the ConceptHYPERLINK ""A-REI – Solve Equations and InequalitiesSolve systems of equations and nonlinear inequalities 2. Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3x3 or greater).9.3 Solving Linear Systems Using Matrix Equations (Coburn)9.4 Multiplicative Inverses of Matrices and Matrix Equations (Blitzer)Task -Matrix Solutions to Linear Systems:HYPERLINK ""N-VM – Vector and Matrix QuantitiesPerform operations on matrices and use materials in applications. 13. Work with 2x2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. 9.4 Applications of Matrices and Determinants: Cramer’s Rule, Partial Fractions, and More (Coburn)9.5 Determinant and Cramer’s Rule HYPERLINK "" Video of Determinatants and Cramer’s Rule for3 x 3RESOURCE TOOLBOXTextbook Resources Core Standards - MathematicsCommon Core Standards - Mathematics Appendix A TN Core Core LessonsTennessee's State Mathematics Standards HYPERLINK "" TN Advanced Algebra & Trigonometry StandardsVideosBrightstormTeacher TubeThe Futures ChannelKhan AcademyMath TVLamar University TutorialCalculator Interactive Manipulatives Sites Math Tasks (Advanced Algebra & Trigonometry)CLIPGlencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12) ................
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