Grade 8 - Shelby County Schools Alg _ Trig Q3 16-1… · Web viewIn 2014, the Shelby County...

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.

Shelby County Schools 2016/20171 of 16

Focus

The Standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, the Standards require us to significantly narrow and deepen the way time and energy is spent in the math classroom. We focus deeply on the major concepts of each subject so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom.

Coherence

Thinking across grades:The Standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding on to foundations built in previous years. Each standard is not a new event, but an extension of previous learning. Linking to major topics:Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems.

Rigor

Conceptual understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures. Procedural skill and fluency: The Standards call for speed and accuracy in calculation. While high school standards for math do not list high school fluencies, there are fluency standards for algebra 1, geometry, and algebra 2..Application: The Standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.



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 high-leverage resources around the content standards and mathematical practice standards that teachers should consistently access:




The TN Mathematics StandardsThe Tennessee Mathematics Standards:https://www.tn.gov/education/article/mathematics-standards

Teachers 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 PracticeMathematical Practice Standardshttps://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

Teachers 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 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-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


https://drive.google.com/file/d/0B926oAMrdzI4RUpMd1pGdEJTYkE/view

https://www.tn.gov/education/article/mathematics-standards



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

OverviewAn overview is provided for each quarter. The information given is intended to aid teachers, coaches and administrators develop an understanding of the content the students will learn in the quarter, how the content addresses prior knowledge and future learning, and may provide some non-summative assessment items.

Tennessee State StandardsThe TN State Standards are located in the left column. Each content standard is identified as the following: Major Work, Supporting Content or Additional Content.; a key can be found at the bottom of the map. The major work of the grade should comprise 65-85% of your instructional time. Supporting Content are standards that supports student’s learning of the major work. Therefore, you will see supporting and additional standards taught in conjunction with major work. It is the teacher’s responsibility to examine the standards and skills needed in order to ensure student mastery of the indicated standard.

ContentTeachers are expected to carefully craft weekly and daily learning objectives/ based on their knowledge of TEM Teach 1. In addition, teachers should include related best practices based upon the TN State Standards, related shifts, and knowledge of students from a variety of sources (e.g., student work samples, MAP, etc.). Support for the development of these lesson objectives can be found under the column titled ‘Content’. The enduring understandings will help clarify the “big picture” of the standard. The essential questions break that picture down into smaller questions and the objectives provide specific outcomes for that standard(s). Best practices tell us that clearly communicating and making objectives measureable leads to greater student mastery.

Instructional Support and ResourcesDistrict and web-based resources have been provided in the Instructional Resources column. Throughout the map you will find instructional/performance tasks, i-Ready lessons and additional resources that align with the standards in that module. The additional resources provided are supplementary and should be used as needed for content support and differentiation.




Topics Addressed in Quarter

Applications of Trigonometry Systems of Equations and Inequalities

OverviewIn 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/ http://edutoobox.org

TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESApplications of Trigonometry


http://edutoobox.org/

http://achievethecore.org/

http://www.nctm.org/Standards-and-Positions/Position-Statements/Procedural-Fluency-in-Mathematics/

http://www.corestandards.org/

https://www.engageny.org/



TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES(Allow approximately 3 weeks for instruction, assessment, and review)

Domain: Applied TrigonometryCluster: Use trigonometry to solve problemsG-AT5. 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)

Enduring Understanding(s) Trigonometric relationships and functions

could be used to model real-world phenomenon.

Indirect measurements of lengths and angles can be used to solve a variety of problems.

Essential Question(s):How do you use the Law of Sines and Law of Cosines to solve oblique triangles?

Objective(s):Students will: develop the law of sines, and use it to

solve ASA and AAS triangles solve SSA triangles (the ambiguous case)

using the law of sines use the law of sines to solve applications

7.1 Oblique Triangles and Law of Sines (Coburn)

Additional Resource(s)Algebra & Trigonometry (Coburn), 2nd Edition(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)

Visu a l P roof of A mb i g u o us C a se Ambiguous Case for the Law of SinesOn - l i ne L a w o f Sin e s P ra c t i c e Khan Academy: The Law of Sines

Task(s)Proving the Law of Sines Task, p.25 (GSE Pre-Calculus Unit 3: Trigonometry of General Triangles)

VocabularyOblique triangle, Law of Sines, ambiguous case,

Writing in MathWhat is an oblique triangle?

Without using symbols, state the Law of Sines in your own words.

Why is SSA called the ambiguous case?

If you are given two sides of a triangle and their included angle, you can find the triangle’s area. Can the Law of Sines be used to solve the triangle with this given information? Explain your answer.

Domain: Applied TrigonometryCluster: Use trigonometry to solve problemsG-AT3. 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.

Enduring Understanding(s): Understand and verify the Law of Sines

and the Law of Cosines for a general triangle.

The application of the Law of Sines and the Law of Cosines to solve problems.

Essential Question(s): How can I calculate the area of any

triangle given only two sides and a non-included angle?

How can I apply trigonometric relationships to non-right triangles?

What is the least amount of information

7.2 Law of Cosines and Area of a Triangle (Coburn)

Additional Resource(s)Algebra & Trigonometry (Coburn), 2nd Edition

(Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations)

Khan Academy: The Law of Cosines On - L i n e L a w of Cosines P r a c t i c e Task(s)Proving the Law of Cosines Task, p.16 (GSE Pre-Calculus Unit 3: Trigonometry of General Triangles)

VocabularyLaw of Cosines

Writing in MathWithout using symbols, state the Law of Cosines in your own words.

Why can’t the Law of Sines be used in the first step solve an SAS triangle?Describe a strategy for solving an SAS triangle.


https://www.georgiastandards.org/Georgia-Standards/Frameworks/Pre-Calculus-Unit-3.pdf



https://www.khanacademy.org/math/geometry-home/right-triangles-topic/law-of-cosines-geo/v/law-of-cosines-example

http://glencoe.mheducation.com/sites/0003112010/index.html




http://www.tn.gov/assets/entities/education/attachments/std_math_adv_alg_trig.pdf




https://www.khanacademy.org/math/geometry-home/right-triangles-topic#law-of-sines-geo

https://www.youtube.com/watch?v=FtYbQ8X7U_w







TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES

that is sufficient to find all six parts of a triangle?

Objective(s):Students will: apply the law of cosines when two sides

and an included angle are known (SAS) apply the law of cosines when three sides

are known (SSS) solve applications using the law of

cosines use trigonometry to find the area of a

triangle

Proving the Hinge Theorem Task, p.33 (GSE Pre-Calculus Unit 3: Trigonometry of General Triangles)

Culminating Task; Combining Lots, p.40 (GSE Pre-Calculus Unit 3: Trigonometry of General Triangles)

Describe a strategy for solving an SSS triangle.

Domain: Vector and Matrix QuantitiesCluster: Represent and model with vector quantities.N-VM1. 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).

3. Solve problems involving velocity and other quantities that can be represented by vectors.

Domain: Vector and Matrix QuantitiesCluster: Understand the graphic representation of vectors and vector quantities.

N-VM4. 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

Enduring Understanding(s): Complex numbers can be represented as

points in the complex plane, with operations (+, –, ×, ÷, conjugate) and properties (modulus, distance, average) having geometric representations.

Operations on vectors (addition, subtraction, scalar multiplication, and multiplying by a transformation matrix) have geometric representations.

Vectors can be represented in component or direction-magnitude form.

Complex numbers can be represented in rectangular or polar form.

Geometric interpretations of operations on complex numbers and vectors can make computations easier.

Problems involving quantities that have both magnitude and direction, such as velocity or displacement, can be modeled and solved using vectors.

Essential Question(s):

7.3 Vectors and Vector Diagrams (Coburn)7.6 Vectors (Blitzer)

7.4 Vector Applications and the Dot Product (Coburn)7.7 The Dot Product (Blitzer)



E x plan a t i ons of Vec tors Khan Academy: Vectors

Task(s)V ec tors a nd S ca l a rs Ac t i vi t y

GSE Pre-Calculus Unit 7: VectorsWalking and Flying Around Hogsmeade, p. 13A Delicate Operation, p. 25

VocabularyVector quantities (vectors), scalar quantities (scalar), directed line segment, initial point, terminal point, magnitude, scalar multiplication, resultant vector, unit vectors, dot products, orthogonal

Writing in MathWhat is a directed line segment?

If v is represented by an arrow, how is -3v represented?

Describe one similarity between the zero vector and the number zero.

Compare and contrast a vector and a coordinate. Explore and emphasize the differences and similarities between them.

Explain in a paragraph why the dot product is



https://www.khanacademy.org/math/precalculus/vectors-precalc

















TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESdirection 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.

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.

How can I represent complex numbers graphically?

How does the complex plane show addition, subtraction, multiplication, and conjugation of complex numbers?

What are two ways to represent a complex number, and what are the advantages of each form?

How are operations on real numbers represented in the complex plane?

When given two points on the complex plane, what does it mean to find the distance between them and the midpoint of the segment connecting them?

How are vectors and scalars similar and different?

How can I use vector operations to model, solve, and interpret real-world problems?

How can I represent addition, subtraction, and scalar 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: represent a vector quantity geometrically represent a vector quantity graphically perform defined vector operations

Hedwig and Errol, p. 33Putting Vectors to Use, p.47He Who Must Not Be Named p.54

so useful. What is eliminated by using the dot product?

What are parallel vectors?

What are orthogonal vectors?




TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES 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 NumbersCluster: Perform complex number arithmetic and understand the representation on the complex plane.N-CN1. 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)³ = 8 because (–1 + 3i ) has modulus 2 and argument 120º.5. Calculate the distance between numbers in

Objective(s):Students will: Solve logarithmic equations using the

fundamental properties of logarithms Apply the product, quotient, and power

properties of logarithms Solve general logarithmic and exponential

equations Solve applications involving logistic,

exponential, and logarithmic functions

7.5 Complex Numbers in Trigonometric Form (Coburn)7.6 DeMoivre’s Theorem and the Theorem on nth Root(Coburn)7.5 Complex Numbers in Polar Form; DeMoivre’s Theorem (Blitzer)



Khan Academy: Complex Numbers Khan Academy: The Complex Plane Khan Academy: Polar and Rectangular Forms of Complex Numbers

Task(s)GSE Pre-Calculus Unit 7: VectorsIt’s Not That Complex, p. 62

VocabularyReal axis, imaginary axis, complex plane, polar form, rectangular form, trigonometric form , modulus, argument, DeMoivre’s Theorem, complex roots

Writing in MathExplain how to plot a complex number in the complex plane. Provide an example with your explanation.

What is the polar form of a complex number?

If you are given a complex number in rectangular form, how do you write it in polar form?

If you are given a complex number in polar form, how do you write it in rectangular form?



https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/polar-form-of-complex-numbers/v/polar-form-complex-number

https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/polar-form-of-complex-numbers/v/polar-form-complex-number

https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/the-complex-plane/v/plotting-complex-numbers-on-the-complex-plane

https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/the-complex-numbers/v/complex-number-intro








TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCESthe complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

A Plane You Can Fly, p. 66Complex Operations, p. 76How Far and Halfway in Hogsmeade, p.94Culminating Task: Putting It All Together p.104

Explain how to find the product of two complex numbers in polar form.

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 InequalitiesCluster: Solve systems of equations and nonlinear inequalitiesA-REI

(Review)

Enduring Understanding(s):A system models, represents and solves real-world problems with multiple variables.

Essential Question(s): What is a system of equations and

inequalities and how can they be used to model real-life situations?

How can a system of equations or inequalities be solved algebraically and graphically?

What does it mean to look for a solution(s) of a system of equations or inequalities?

Objective(s):Students will: verify ordered pair solutions solve linear systems by graphing solve linear systems by substitution solve linear systems by elimination recognize inconsistent systems and

dependent systems use a system of equations to model and

solve applications

8.1 Linear Systems in Two Variables with Applications (Coburn)8.2 Linear Systems in Three Variables with Applications (Coburn)8.1 Systems of Linear Equations in Two Variables (Blitzer)8.2 Systems of Linear Equations in Three Variables (Blitzer)

Additional Resources:Algebra & Trigonometry (Coburn), 2nd Edition


Khan Academy: Systems of Equations Khan Academy: Systems of Inequalities

Task(s)Mathematics Vision Project; Module 1- Systems of Equations & Inequalities

(Choose from the twelve tasks)S upp l y a nd D e mand Using E x ce l t o S olve S y s tems of L in e a r

Vocabularysystem of equations, simultaneous equations, standard form of a line, y-intercept, slope form, point of intersection, infinitely many solutions, no solution, solution set, parallel lines, perpendicular lines, linear system, solve by substitution, solve by elimination

Writing in MathWhat is a system of linear equations? Provide an example with your description.

When is it easier to use the addition method rather than the substitution method to solve a system of equations?

When using the addition or substitution method, how can you tell if a system of linear equations has no solution?

What are some of the real life applications of two-variable linear systems?


http://www.mathematicsvisionproject.org/uploads/1/1/6/3/11636986/sec1_mod1_systems_se_90312.pdf


https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphical-system-of-inequalities

https://www.khanacademy.org/math/algebra-basics/alg-basics-systems-of-equations








TN STATE STANDARDS CONTENT INSTRUCTIONAL SUPPORT & RESOURCES 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

Equ a t i ons

Domain: Solve Equations and InequalitiesCluster: Solve systems of equations and nonlinear inequalitiesA-REI4. Solve systems of nonlinear inequalities by graphing.

Enduring Understanding(s):A system models, represents and solves real-world problems with multiple variables.

Essential Question(s): What is a nonlinear system of equations

and inequalities and how can they be used to model real-life situations?

How can a nonlinear system of equations or inequalities be solved algebraically and graphically?

What does it mean to look for a solution(s) of a system of 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

8.3 Non-Linear Systems of Equations and Inequalities (Coburn)8.4 Systems of Nonlinear Equations in Two Variables (Blitzer)



Khan Academy: Nonlinear Systems of Equations

E x a mp l e s of N o n - L in e a r S y stems

Writing in MathWhat is a system of nonlinear equations? Provide an example with your description.

Explain how to solve a nonlinear system using the substitution method. Use x2 + y2 = 9 and 2x – y =3 to illustrate your explanation.

Domain: Solve Equations and InequalitiesCluster: Solve systems of equations and nonlinear inequalitiesA-REI4. Solve systems of nonlinear inequalities by graphing.

Objective(s):Students will: solve a linear inequality in two variables solve a system of linear inequalities solve applications using a system of

linear inequalities solve applications using linear

8.4 Systems of Inequalities and Linear Programming (Coburn)8.5 Systems of Inequalities (Blitzer)8.6 Linear Programming (Blitzer)


(Exercise Videos, Lecture Videos, Graphing Calculator Videos,

Writing in MathExplain how to graph 2x – 3y < 6.

What does it mean if a system of linear inequalities has no solution?

What kinds of problems are solved using the linear programming method?






https://www.khanacademy.org/math/algebra/quadratics/systems-of-quadratic-equations/v/non-linear-systems-of-equations-1

https://www.khanacademy.org/math/algebra/quadratics/systems-of-quadratic-equations/v/non-linear-systems-of-equations-1









programming PowerPoint Presentations)Khan Academy: Modeling with Systems of InequalitiesMath Vision Project: Systems of Equations and Inequalities pp.123-131

In your own words, describe how to solve a linear programming problem.

Domain: Solve Equations and InequalitiesCluster: Solve systems of equations and nonlinear inequalitiesA-REI1. Represent a system of linear equations as a single matrix equation in a vector variable.

Enduring Understanding(s) Matrices provide an organizational

structure in which to represent and solve complex problems.

The commutative property applies to matrix addition but does not extend to matrix multiplication.

A zero matrix behaves in addition, subtraction, and multiplication much like 0 in the real number system.

An identity matrix behaves much like the number 1 in the real number system.

The determinant of a matrix is nonzero if and only if the matrix has an inverse.

2 X 2 matrices can be written as transformations of the plane and can be interpreted as absolute 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?

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)Additional Resource(s)Algebra & Trigonometry (Coburn), 2nd Edition


Task(s)GSE Pre-Calculus: Unit 5- MatricesCentral High Booster Club, p.10Walk Like a Mathematician, p.25Candy? What Candy? p.38An Okefenokee Food Web, p.48Culminating Task: Vacationing in Georgia, p.60

VocabularyMatrix/matrices, elements, augmented matrix, row-echelon form, row operations, Gaussian elimination, Gauss-Jordan elimination, reduced row-echelon form

Writing in MathWhat is a matrix?

Describe what is meant by the augmented matrix of a system of linear equations.

In your own words, describe each of the three matrix row operations. Give an example with each of the operations.


https://www.georgiastandards.org/Archives/Documents/CCGPS-Math-9-12-Pre-Calculus-Unit-2.pdf








https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/modeling-with-linear-inequalities/v/u06-l3-t1-we3-graphing-systems-of-inequalities

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/modeling-with-linear-inequalities/v/u06-l3-t1-we3-graphing-systems-of-inequalities






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?

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 QuantitiesCluster: Perform operations on matrices and use materials in applications.N-VM8. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

Objective(s):Students will: determine if two matrices are equal add and subtract matrices compute the product of two matrices

9.2 The Algebra of Matrices (Coburn)9.3 Matrix Operations and Their Applications (Blitzer)


(Exercise Videos, Lecture Videos,

VocabularySquare matrix, scalar

Writing in Math What is meant by the order of a matrix? Give an example with your explanation.









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.

Graphing Calculator Videos, PowerPoint Presentations)

Task(s)Matrix Solutions to Linear SystemsGSE Pre-Calculus: Unit 5- Matrices (from 9.1 above)Central High Booster Club, p.10Walk Like a Mathematician, p.25Candy? What Candy? p.38An Okefenokee Food Web, p.48Culminating Task: Vacationing in Georgia, p.60

Describe how to perform scalar multiplication. Provide an example with your description.

Domain: Solve Equations and InequalitiesCluster: Solve systems of equations and nonlinear inequalitiesA-REI2. 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).

Objective(s):Students will: recognize the identity matrix for

multiplication find the inverse of a square matrix solve systems using matrix equations use determinants to find whether a matrix

is invertible

9.3 Solving Linear Systems Using Matrix Equations (Coburn)9.4 Multiplicative Inverses of Matrices and Matrix Equations (Blitzer)

VocabularyMultiplicative inverse of a matrix,

Writing in MathIf you are given two matrices, A and B, explain how to determine if B is the multiplicative inverse of A.

Explain why a matrix that does not have the same number of rows and columns cannot have a multiplicative inverse.



https://www.georgiastandards.org/Archives/Documents/CCGPS-Math-9-12-Pre-Calculus-Unit-2.pdf

https://www.scribd.com/document/15806638/A2T-MatrixTransforms





RESOURCE TOOLBOX

Textbook Resourceshttp://glencoe.mcgraw-hill.com/sites/0003112010/

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/instructor_s_solutions_manual.htm

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/preformatted_tests.htm

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/powerpoint_presentations.html

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/computerized_testing.htm

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/additional_topics.html

http://highered.mcgrawhill.com/sites/0003112010/instructor_view0/modeling_with_technology.html

StandardsCom m on Core S tand a rds - Math e matics

Com m on Core S tand a rds - Math e matics A pp e ndix A

http://www.edutoolbox.org/tntools (formerly tncore.org) ht t p: / /ww w . cc ss t oolbo x . o r g /

Common Core Lessons

Tennessee's State Mathematics Standards

TN Advanced Algebra & Trigonometry Standards

CCSS Flip Book (with Examples of each standard )

VideosBrightstorm

Teacher Tube

The Futures Channel

Khan Academy

Math TV

Lamar University Tutorial

Calculator

ht t p: / /ww w .t i -m athnspir e d. c om

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 g e / a c t i vi t y

ht t p: / /ww w . ca sioedu ca t i on. c om / e du ca tors

Interactive Manipulatives

ht t p: / /ww w .i l ov e math.o r g / i nd e x .ph p ? opt i on =c om_docm a n

http://www.mathopenref.com

Edugoodies

Additional Sitesht 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 ht t p: / /ww w .kutaso f tw a r e . c om / f ree .ht m ht t p: / / i l lu m inations.n c t m . o r g / ht t p: / /ww w .stemr e sour c e s.com/ https://compasslearning.com/www.explorelearning.comht 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 SheetOnline Algebra and Trigonometry Tutorial

Literacy

Glencoe Reading & Writing in the Mathematics ClassroomGraphic Organizers (9-12)Literacy Skills and Strategies for Content Area Teachers

ACTTN ACT Information & ResourcesACT College & Career Readiness Mathematics Standards

Tasks/LessonsUT Dana CenterMars TasksInside Math Tasks


http://www.insidemathematics.org/performance-assessment-tasks

http://map.mathshell.org/materials/tasks.php

http://www.utdanacenter.org/k12mathbenchmarks/secondary/index.php

http://www.act.org/content/dam/act/unsecured/documents/CCRS-MathStandards.pdf

http://www.tn.gov/education/topic/act-sat

http://www.valrc.org/resources/docs/MHS_Literacy_Strategy_Book.pdf

https://www.teachervision.com/tv/tvsearch/site=TV&lowest_grade=109&highest_grade=112&type=graphic-organizer

http://www.glencoe.com/sec/teachingtoday/downloads/pdf/ReadingWritingMathClass.pdf

http://tutorial.math.lamar.edu/Extras/AlgebraTrigReview/AlgebraTrigIntro.aspx

http://www.math.uci.edu/sites/math.uci.edu/files/trig.pdf

http://www.explorelearning.com/

https://compasslearning.com/

http://edugoodies.com/scs/

http://tutorial.math.lamar.edu/

http://www.mathtv.com/

https://www.khanacademy.org/

http://thefutureschannel.com/#loaded

http://www.teachertube.com/

http://www.brightstorm.com/

http://www.azed.gov/azccrs/files/2013/11/high-school-ccss-flip-book-usd-259-2012.pdf

http://tn.gov/assets/entities/education/attachments/std_math_adv_alg_trig.pdf

http://state.tn.us/education/standards/math.shtml

http://www.edutoolbox.org/tntools



RESOURCE TOOLBOX(Math, p. 22) Math Vision Project Tasks

Better Lesson


http://betterlesson.com/common_core

http://www.mathematicsvisionproject.org/secondary-mathematics-i.html

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