80% of Our Students Will Graduate from High School College Or Career Ready s9

Curriculum and Instruction – Mathematics Quarter 3 Advanced Algebra & Trigonometry

Introduction

In 2014, the Shelby County Schools Board of Education adopted a set of ambitious, yet attainable goals for school and student performance. The District is committed to these goals, as further described in our strategic plan, Destination2025. By 2025,  80% of our students will graduate from high school college or career ready  90% of students will graduate on time  100% of our students who graduate college or career ready will enroll in a post-secondary opportunity

In order to achieve these ambitious goals, we must collectively work to provide our students with high quality, college and career ready aligned instruction. The Tennessee State Standards provide a common set of expectations for what students will know and be able to do at the end of a grade. College and career readiness is rooted in the knowledge and skills students need to succeed in post-secondary study or careers. The TN State Standards represent three fundamental shifts in mathematics instruction: focus, coherence and rigor.

The Standards for Mathematical Practice describe varieties of expertise, habits of minds and productive dispositions that mathematics educators at all levels should seek to develop in their students. These practices rest on important National Council of Teachers of Mathematics (NCTM) “processes and proficiencies” with longstanding importance in mathematics education. Throughout the year, students should continue to develop proficiency with the eight Standards for Mathematical Practice.

This curriculum map is designed to help teachers make effective decisions about what mathematical content to teach so that, ultimately our students, can reach Destination 2025. To reach our collective student achievement goals, we know that teachers must change their practice so that it is in alignment with the three mathematics instructional shifts.

Throughout this curriculum map, you will see resources as well as links to tasks that will support you in ensuring that students are able to reach the demands of the standards in your classroom. In addition to the resources embedded in the map, there are some Shelby County Schools 2016/2017 1 of 19 high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:

The TN Mathematics Standards The Tennessee Mathematics Standards: Teachers can access the Tennessee State standards, which https://www.tn.gov/education/article/mathematics- are featured throughout this curriculum map and represent standards college and career ready learning at reach respective grade level. Standards for Mathematical Practice Mathematical Practice Standards Teachers can access the Mathematical Practice Standards, https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1 which are featured throughout this curriculum map. This link pGdEJTYkE/view contains more a more detailed explanation of each practice along with implications for instructions.

Purpose of the Mathematics Curriculum Maps

This 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- 2 Curriculum and Instruction – Mathematics Quarter 3 Advanced Algebra & Trigonometry 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 Support Shelby 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 Maps

Overview An 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 Standards Shelby County Schools 2016/2017 3 of 19 The 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.

Content Teachers 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 Resources District 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.

4 Curriculum and Instruction – Mathematics Quarter 3 Advanced Algebra & Trigonometry

Topics Addressed in Quarter

 Applications of Trigonometry  Systems of Equations and Inequalities

Overview In the third quarter students extend their knowledge of finding inverses to doing so for trigonometric functions, and use them in a wide range of application problems. The relationships of general triangles using appropriate auxiliary lines result in the Laws of Sines and Cosines in general cases and they connect the relationships described to the geometry of vectors. Students investigate the geometry of the complex numbers more fully and connect it to operations with complex numbers. In addition, students develop the notion of a vector and connect operations with vectors and matrices to transformations of the plane. Students use systems of equations and inequalities to solve real-world problems algebraically, graphically, and with matrices.

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.

References:  https://www.engageny.org/  http://www.corestandards.org/  http://www.nctm.org/  http://achievethecore.org/

Shelby County Schools 2016/2017 5 of 19  http://edutoobox.org

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Applications of Trigonometry (Allow approximately 3 weeks for instruction, assessment, and review) Domain: Applied Trigonometry Enduring Understanding(s) 7.1 Oblique Triangles and Law of Vocabulary Sines (Coburn) Cluster: Use trigonometry to solve  Trigonometric relationships and Oblique triangle, Law of Sines, problems functions could be used to model ambiguous case, G-AT real-world phenomenon. Additional Resource(s) 5. Understand and apply the Law of  Indirect measurements of lengths Algebra & Trigonometry (Coburn), Writing in Math Sines (including the ambiguous case and angles can be used to solve 2nd Edition What is an oblique triangle? and the Law of Cosines to find a variety of problems. (Exercise Videos, Lecture Videos, unknown measurements in right and Graphing Calculator Videos, non-right triangles (e.g., surveying PowerPoint Presentations) Without using symbols, state the Essential Question(s): Law of Sines in your own words. problems, resultant forces) How do you use the Law of Sines and Visu a l P roof of A mb i g u o us C a se Law of Cosines to solve oblique Ambiguous Case for the Law of Sines Why is SSA called the ambiguous triangles? On - l i ne L a w o f Sin e s P ra c t i c e case? Objective(s): Khan Academy: The Law of Sines Students will: If you are given two sides of a Task(s) triangle and their included angle,  develop the law of sines, and use you can find the triangle’s area. Can Proving the Law of Sines Task, p.25 it to solve ASA and AAS triangles the Law of Sines be used to solve the (GSE Pre-Calculus Unit 3: triangle with this given information?  solve SSA triangles (the Trigonometry of General Triangles) Explain your answer. ambiguous case) using the law of sines

 use the law of sines to solve applications

7.2 Law of Cosines and Area of a Domain: Applied Trigonometry Enduring Understanding(s): Vocabulary Triangle (Coburn) Cluster: Use trigonometry to solve  Understand and verify the Law of Law of Cosines Additional Resource(s) problems Sines and the Law of Cosines for 6 Curriculum and Instruction – Mathematics Quarter 3 Advanced Algebra & Trigonometry

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES G-AT a general triangle. Algebra & Trigonometry (Coburn), Writing in Math 3. Derive and apply the formulas for 2nd Edition  The application of the Law of Without using symbols, state the the area of a sector of a circle. (Exercise Videos, Lecture Sines and the Law of Cosines to Law of Cosines in your own words. 4. Calculate the arc length of a circle Videos, Graphing Calculator solve problems. subtended by a central angle. Videos, PowerPoint Essential Question(s): Presentations) Why can’t the Law of Sines be used in the first step solve an SAS  How can I calculate the area of Khan Academy: The Law of Cosines triangle? any triangle given only two sides On - L i n e L a w of Cosines P r a c t i c e and a non-included angle? Describe a strategy for solving an Task(s) SAS triangle.  How can I apply trigonometric Proving the Law of Cosines Task, relationships to non-right p.16 triangles? Describe a strategy for solving an (GSE Pre-Calculus Unit 3: SSS triangle.  What is the least amount of Trigonometry of General Triangles) information that is sufficient to find all six parts of a triangle? Proving the Hinge Theorem Task, Objective(s): p.33 Students will: (GSE Pre-Calculus Unit 3:  apply the law of cosines when Trigonometry of General Triangles) two sides and an included angle are known (SAS) Culminating Task; Combining Lots, p.40  apply the law of cosines when (GSE Pre-Calculus Unit 3: three sides are known (SSS) Trigonometry of General Triangles)

 solve applications using the law of cosines

 use trigonometry to find the area of a triangle

Domain: Vector and Matrix Enduring Understanding(s): 7.3 Vectors and Vector Diagrams Vocabulary

Shelby County Schools 2016/2017 7 of 19 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES Quantities (Coburn)  Complex numbers can be Vector quantities (vectors), scalar 7.6 Vectors (Blitzer) Cluster: Represent and model with represented as points in the quantities (scalar), directed line vector quantities. complex plane, with operations segment, initial point, terminal point, N-VM (+, –, ×, ÷, conjugate) and 7.4 Vector Applications and the Dot magnitude, scalar multiplication, Product (Coburn) resultant vector, unit vectors, dot 1. Recognize vector quantities as properties (modulus, distance, 7.7 The Dot Product (Blitzer) products, orthogonal having both magnitude and direction. average) having geometric Represent vector quantities by representations. Additional Resource(s) directed line segments, and use  Operations on vectors (addition, Writing in Math appropriate symbols for vectors and subtraction, scalar multiplication, Algebra & Trigonometry (Coburn), What is a directed line segment? their magnitudes (e.g. v, │v│, ││v││, and multiplying by a 2nd Edition v). transformation matrix) have (Exercise Videos, Lecture If v is represented by an arrow, how geometric representations. Videos, Graphing Calculator 3. Solve problems involving velocity Videos, PowerPoint is -3v represented? and other quantities that can be  Vectors can be represented in Presentations) component or direction- represented by vectors. Describe one similarity between the magnitude form. E x plan a t i ons of Vec tors Khan Academy: Vectors zero vector and the number zero. Domain: Vector and Matrix  Complex numbers can be Quantities represented in rectangular or Compare and contrast a vector and a Cluster: Understand the graphic polar form. Task(s) coordinate. Explore and emphasize representation of vectors and vector V ec tors a nd S ca l a rs Ac t i vi t y quantities.  Geometric interpretations of the differences and similarities operations on complex numbers between them. N-VM and vectors can make GSE Pre-Calculus Unit 7: Vectors computations easier. 4. Add and subtract vectors. Walking and Flying Around Explain in a paragraph why the dot a. Add vectors end-to-end,  Problems involving quantities Hogsmeade, p. 13 product is so useful. What is component-wise, and by the that have both magnitude and A Delicate Operation, p. 25 eliminated by using the dot product? parallelogram rule. Understand that direction, such as velocity or Hedwig and Errol, p. 33 the magnitude of a sum of two displacement, can be modeled Putting Vectors to Use, p.47 What are parallel vectors? vectors is typically not the sum of the and solved using vectors. He Who Must Not Be Named p.54 magnitudes. Essential Question(s): b. Given two vectors in magnitude What are orthogonal vectors? and direction form, determine the  How can I represent complex magnitude and direction of their numbers graphically? sum. c. Understand vector subtraction v-w  How does the complex plane as v+(-w), where –w is the additive show addition, subtraction, inverse of w, with the same multiplication, and conjugation of magnitude as w and pointing in the complex numbers? opposite direction. Represent vector  What are two ways to represent a subtraction graphically by connecting complex number, and what are 8 Curriculum and Instruction – Mathematics Quarter 3 Advanced Algebra & Trigonometry

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES the tips in the appropriate order, and the advantages of each form? perform vector subtraction component-wise.  How are operations on real numbers represented in the 5. Multiply a vector by a scalar. complex plane? a. Represent scalar multiplication  When given two points on the graphically by scaling vectors and complex plane, what does it possibly reversing their direction; mean to find the distance perform scalar multiplication between them and the midpoint component-wise, e.g. as of the segment connecting them? c(vx,vy)=(cvx,cvy). b. Compute the magnitude of a  How are vectors and scalars scalar multiple cv using ││cv││= similar and different? │c│v. Compute the direction of cv  How can I use vector operations knowing that when │c│v≠0, the to model, solve, and interpret direction of cv is either along v (for real-world problems? c›0) or against v (for c ‹0).  How can I represent addition, 6. Calculate and interpret the dot subtraction, and scalar product of two vectors. multiplication of vectors geometrically?  How do geometric interpretations of addition, subtraction, and scalar multiplication of vectors help me perform computations efficiently?  What are some different ways to add two vectors, and how are these representations related?  In what ways can matrices transform vectors? Objective(s): Students will:

Shelby County Schools 2016/2017 9 of 19 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES  represent a vector quantity geometrically  represent a vector quantity graphically  perform defined vector operations  represent a vector quantity algebraically and find unity vectors  use vector diagrams to solve applications  use vectors to investigate forces in equilibrium  find the components of one vector along another  solve applications involving work  compute dot products and the angle between two vectors  find the projection of one vector along another and resolve a vector into orthogonal components  use vectors for nonvertical projectile motion, and solve related applications Domain: Complex Numbers Objective(s): 7.5 Complex Numbers in Vocabulary Cluster: Perform complex number Trigonometric Form (Coburn) Students will: Real axis, imaginary axis, complex arithmetic and understand the 7.6 DeMoivre’s Theorem and the plane, polar form, rectangular form, representation on the complex plane.  Solve logarithmic equations Theorem on nth Root(Coburn) trigonometric form , modulus, N-CN 7.5 Complex Numbers in Polar Form; using the fundamental properties argument, DeMoivre’s Theorem, 1. Perform arithmetic operations DeMoivre’s Theorem (Blitzer) of logarithms complex roots with complex numbers expressing answers in the form a+bi.  Apply the product, quotient, and 2. Find the conjugate of a complex power properties of logarithms Additional Resource(s) number; use conjugates to find  Solve general logarithmic and Writing in Math moduli and quotients of complex Algebra & Trigonometry (Coburn), 10 Curriculum and Instruction – Mathematics Quarter 3 Advanced Algebra & Trigonometry

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES numbers. exponential equations 2nd Edition Explain how to plot a complex 3. Represent complex numbers on  Solve applications involving (Exercise Videos, Lecture number in the complex plane. the complex plane in rectangular and logistic, exponential, and Videos, Graphing Calculator Provide an example with your polar form (including real and Videos, PowerPoint explanation. logarithmic functions imaginary numbers), and explain Presentations) why the rectangular and polar forms Khan Academy: Complex Numbers of a given complex number represent What is the polar form of a complex the same number. Khan Academy: The Complex Plane number? 4. Represent addition, subtraction, Khan Academy: Polar and multiplication, and conjugation of Rectangular Forms of Complex If you are given a complex number in complex numbers geometrically on Numbers rectangular form, how do you write it the complex plane; use properties of in polar form? this representation for computation. Task(s) For example (-1+√3i)³ = 8 because (– 1 + 3i ) has modulus 2 and argument GSE Pre-Calculus Unit 7: Vectors If you are given a complex number in 120º. It’s Not That Complex, p. 62 polar form, how do you write it in 5. Calculate the distance between A Plane You Can Fly, p. 66 rectangular form? numbers in the complex plane as the Complex Operations, p. 76 modulus of the difference, and the How Far and Halfway in Hogsmeade, Explain how to find the product of midpoint of a segment as the p.94 two complex numbers in polar form. average of the numbers at its Culminating Task: Putting It All endpoints. Together p.104 Explain how to find the quotient of two complex numbers in polar form.

Explain how to use DeMoivre’s Theorem for finding complex roots to find the two square roots of 9. Systems of Equations and Inequalities (Allow approximately 3 weeks for instruction, assessment, and review) Domain: Solve Equations and  Enduring Understanding(s): 8.1 Linear Systems in Two Variables Vocabulary with Applications (Coburn) Inequalities A system models, represents and system of equations, simultaneous 8.2 Linear Systems in Three Cluster: Solve systems of equations solves real-world problems with equations, standard form of a line, y- Variables with Applications (Coburn) and nonlinear inequalities multiple variables. intercept, slope form, point of Shelby County Schools 2016/2017 11 of 19 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES A-REI 8.1 Systems of Linear Equations in intersection, infinitely many (Review) Essential Question(s): Two Variables (Blitzer) solutions, no solution, solution set,  What is a system of equations 8.2 Systems of Linear Equations in parallel lines, perpendicular lines, and inequalities and how can Three Variables (Blitzer) linear system, solve by substitution, they be used to model real-life Additional Resources: solve by elimination situations? Algebra & Trigonometry (Coburn),  How can a system of equations or 2nd Edition Writing in Math inequalities be solved (Exercise Videos, Lecture What is a system of linear algebraically and graphically? Videos, Graphing Calculator equations? Provide an example with  What does it mean to look for a Videos, PowerPoint your description. solution(s) of a system of Presentations) equations or inequalities? Khan Academy: Systems of When is it easier to use the addition Equations method rather than the substitution Objective(s): Khan Academy: Systems of method to solve a system of Students will: Inequalities equations?  verify ordered pair solutions Task(s) When using the addition or  solve linear systems by graphing Mathematics Vision Project; substitution method, how can you solve linear systems by  Module 1- Systems of Equations & tell if a system of linear equations substitution Inequalities has no solution? solve linear systems by  (Choose from the twelve tasks) elimination S upp l y a nd D e mand What are some of the real life  recognize inconsistent systems applications of two-variable linear Using E x ce l t o S olve S y s tems of and dependent systems systems? L in e a r Equ a t i ons  use a system of equations to model and solve applications  visualize a solution in three dimensions  check ordered triple solutions  solve linear systems in three variables  recognize inconsistent and dependent systems  use a system of three equations in three variables to solve applications

12 Curriculum and Instruction – Mathematics Quarter 3 Advanced Algebra & Trigonometry

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES 8.3 Non-Linear Systems of Domain: Solve Equations and  Enduring Understanding(s): Writing in Math Equations and Inequalities (Coburn) Inequalities What is a system of nonlinear A system models, represents and 8.4 Systems of Nonlinear Equations equations? Provide an example with Cluster: Solve systems of equations solves real-world problems with in Two Variables (Blitzer) and nonlinear inequalities multiple variables. your description. A-REI Essential Question(s): Additional Resource(s) 4. Solve systems of nonlinear Explain how to solve a nonlinear Algebra & Trigonometry (Coburn), inequalities by graphing.  What is a nonlinear system of system using the substitution 2nd Edition 2 2 equations and inequalities and method. Use x + y = 9 and 2x – y how can they be used to model (Exercise Videos, Lecture =3 to illustrate your explanation. real-life situations? Videos, Graphing Calculator Videos, PowerPoint  How can a nonlinear system of Presentations) equations or inequalities be solved algebraically and Khan Academy: Nonlinear graphically? Systems of Equations  What does it mean to look for a solution(s) of a system of E x a mp l e s of N o n - L in e a r S y stems nonlinear equations or inequalities? Objective(s): Students will:  visualize possible solutions  solve nonlinear systems using substitution  solve nonlinear systems using elimination  solve nonlinear systems of inequalities  solve applications of nonlinear systems 8.4 Systems of Inequalities and Domain: Solve Equations and Objective(s): Writing in Math Linear Programming (Coburn) Inequalities Students will: Explain how to graph 2x – 3y < 6. 8.5 Systems of Inequalities (Blitzer) Shelby County Schools 2016/2017 13 of 19 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

Cluster: Solve systems of equations  solve a linear inequality in two 8.6 Linear Programming (Blitzer) and nonlinear inequalities variables Additional Resource(s) What does it mean if a system of A-REI linear inequalities has no solution?  solve a system of linear Algebra & Trigonometry (Coburn), 4. Solve systems of nonlinear inequalities 2nd Edition inequalities by graphing. (Exercise Videos, Lecture What kinds of problems are solved  solve applications using a system Videos, Graphing Calculator using the linear programming of linear inequalities Videos, PowerPoint method?  solve applications using linear Presentations) programming Khan Academy: Modeling with In your own words, describe how to Systems of Inequalities solve a linear programming problem. Math Vision Project: Systems of Equations and Inequalities pp.123- 131 9.1 Solving Linear Systems Using Domain: Solve Equations and Enduring Understanding(s) Vocabulary Matrices and Row Operations Inequalities Matrix/matrices, elements,  Matrices provide an (Coburn) augmented matrix, row-echelon Cluster: Solve systems of equations organizational structure in which 9.1 Matrix Solutions to Linear form, row operations, Gaussian and nonlinear inequalities to represent and solve complex Systems (Blitzer) elimination, Gauss-Jordan A-REI problems. 9.2 Inconsistent and Dependent elimination, reduced row-echelon 1. Represent a system of linear  The commutative property Systems and Their Applications form equations as a single matrix equation applies to matrix addition but (Blitzer) in a vector variable. does not extend to matrix Additional Resource(s) multiplication. Algebra & Trigonometry (Coburn), Writing in Math  A zero matrix behaves in 2nd Edition What is a matrix? addition, subtraction, and (Exercise Videos, Lecture multiplication much like 0 in the Videos, Graphing Calculator real number system. Videos, PowerPoint Describe what is meant by the  An identity matrix behaves much Presentations) augmented matrix of a system of like the number 1 in the real Task(s) linear equations. number system. GSE Pre-Calculus: Unit 5- Matrices  The determinant of a matrix is Central High Booster Club, p.10 In your own words, describe each of the three matrix row operations. nonzero if and only if the matrix Walk Like a Mathematician, p.25 has an inverse. Give an example with each of the Candy? What Candy? p.38 operations.  2 X 2 matrices can be written as An Okefenokee Food Web, p.48 transformations of the plane and Culminating Task: Vacationing in can be interpreted as absolute Georgia, p.60 14 Curriculum and Instruction – Mathematics Quarter 3 Advanced Algebra & Trigonometry

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES value of the determinant in terms of area.  Solving systems of linear equations can be extended to matrices and the methods we use can be justified. Essential Question(s)  How can we represent data in matrix form?  How do we add and subtract matrices and when are these operations defined?  How do we perform scalar multiplication on matrices?  How do we multiply matrices and when is this operation defined?  How do the commutative, associative, and distributive properties apply to matrices?  What is a zero matrix and how does it behave?  What is an identity matrix and how does it behave?  How do we find the determinant of a matrix and when is it nonzero?  How do we find the inverse of a matrix and when does a matrix not have an inverse defined?

Shelby County Schools 2016/2017 15 of 19 TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

 How do we solve systems of equations using inverse matrices?  How do we find the area of a plane using matrices? Objective(s): Students will:  state the size of a matrix and identify its entries  form the augmented matrix of a system of equations  solve a system of equations using row operations  recognize inconsistent and dependent systems  solve applications using linear systems Domain: Vector and Matrix Objective(s): 9.2 The Algebra of Matrices Vocabulary Quantities Students will: (Coburn) Square matrix, scalar Cluster: Perform operations on 9.3 Matrix Operations and Their  determine if two matrices are matrices and use materials in Applications (Blitzer) applications. equal Writing in Math N-VM What is meant by the order of a Additional Resource(s) 8. Multiply matrices by scalars to  add and subtract matrices matrix? Give an example with your explanation. produce new matrices, e.g., as when Algebra & Trigonometry (Coburn), 2nd Edition all of the payoffs in a game are  compute the product of two doubled. matrices (Exercise Videos, Lecture Describe how to perform scalar Videos, Graphing Calculator 9. Add, subtract, and multiply multiplication. Provide an example Videos, PowerPoint with your description. matrices of appropriate dimensions. Presentations) 10. Understand that, unlike multiplication of numbers, matrix Task(s) multiplication for square matrices is Matrix Solutions to Linear Systems not a commutative operation, but still satisfies the associative and GSE Pre-Calculus: Unit 5- Matrices 16 Curriculum and Instruction – Mathematics Quarter 3 Advanced Algebra & Trigonometry

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES distributive properties. (from 9.1 above) 11. Understand that the zero and Central High Booster Club, p.10 identify matrices play a role in matrix addition and multiplication Walk Like a Mathematician, p.25 similar to the role of 0 and 1 in the Candy? What Candy? p.38 real numbers. The determinant of a An Okefenokee Food Web, p.48 square matrix is nonzero if and only Culminating Task: Vacationing in if the matrix has a multiplicative Georgia, p.60 inverse. Domain: Solve Equations and Objective(s): 9.3 Solving Linear Systems Using Vocabulary Inequalities Students will: Matrix Equations (Coburn) Multiplicative inverse of a matrix, 9.4 Multiplicative Inverses of Cluster: Solve systems of equations  recognize the identity matrix for Matrices and Matrix Equations and nonlinear inequalities multiplication Writing in Math A-REI (Blitzer)  find the inverse of a square If you are given two matrices, A and 2. Find the inverse of a matrix if it matrix B, explain how to determine if B is exists and use it to solve systems of the multiplicative inverse of A. linear equations (using technology  solve systems using matrix equations for matrices of dimension 3x3 or Explain why a matrix that does not greater).  use determinants to find whether have the same number of rows and a matrix is invertible columns cannot have a multiplicative inverse.

Shelby County Schools 2016/2017 17 of 19 RESOURCE TOOLBOX Textbook Resources Standards Videos http://glencoe.mcgraw- Com m on Core S tand a rds - Math e matics Brightstorm hill.com/sites/0003112010/ Com m on Core S tand a rds - Math e matics A pp e ndix Teacher Tube http://highered.mcgrawhill.com/sites/000311201 A The Futures Channel 0/instructor_view0/instructor_s_solutions_manual. http://www.edutoolbox.org/tntools (formerly htm Khan Academy tncore.org) http://highered.mcgrawhill.com/sites/000311201 ht t p: / /ww w . cc ss t oolbo x . o r g / Math TV 0/instructor_view0/preformatted_tests.htm Common Core Lessons Lamar University Tutorial http://highered.mcgrawhill.com/sites/000311201 0/instructor_view0/powerpoint_presentations.htm Tennessee's State Mathematics Standards l TN Advanced Algebra & Trigonometry Standards http://highered.mcgrawhill.com/sites/000311201 CCSS Flip Book (with Examples of each standard) 0/instructor_view0/computerized_testing.htm http://highered.mcgrawhill.com/sites/000311201 0/instructor_view0/additional_topics.html http://highered.mcgrawhill.com/sites/000311201 0/instructor_view0/modeling_with_technology.ht ml Calculator Interactive Manipulatives Additional Sites ht t p: / /ww w .t i -m athnspir e d. c om ht t p: / /ww w .i l ov e math.o r g / i nd e x .ph p ? ht t p: / /ww w .in t e rn e t4cl a s srooms. c om / g a t e w a y _ a l g e b ra .htm opt i on =c om_docm a n ht t p: / /ww w .kutaso f tw a r e . c om / f ree .ht m ht t p: / /edu ca t i on.t i . c om / e du ca t i onpo r tal/a c t i vi t y e x c h a n ht t p: / / i l lu m inations.n c t m . o r g / g e / a c t i vi t y http://www.mathopenref.com ht t p: / /ww w .stemr e sour c e s.com/ ht t p: / /ww w . ca sioedu ca t i on. c om / e du ca tors Edugoodies https://compasslearning.com/ www.explorelearning.com ht t p: / / j c - s c hools.n e t / d y n a m i c / m a th / math12.ht m l Trigonometry Cheat Sheet Online Algebra and Trigonometry Tutorial Literacy ACT Tasks/Lessons Glencoe Reading & Writing in the Mathematics TN ACT Information & Resources UT Dana Center 18 Curriculum and Instruction – Mathematics Quarter 3 Advanced Algebra & Trigonometry

RESOURCE TOOLBOX Classroom ACT College & Career Readiness Mathematics Mars Tasks Graphic Organizers (9-12) Standards Inside Math Tasks Literacy Skills and Strategies for Content Area Math Vision Project Tasks Teachers Better Lesson (Math, p. 22)

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