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1 Statewide Framework Document for: Standards may be added to this document prior to submission, but may not be removed from the framework to meet state credit equivalency requirements. Performance assessments may be developed at the local level. In order to earn state approval, performance assessments must be submitted within this framework. This course is eligible for 1 credit of Algebra II. Washington Mathematics Standards (Common Core State Standards) support foundational mathematical knowledge and reasoning. While it is important to develop a conceptual understanding of mathematical topics and fluency in numeracy and procedural skills, teachers should focus on the application of mathematics to career fields to support the three (3) key shifts of CCSS. The Standards for Mathematical Practice develop mathematical habits of mind and are to be modeled and integrated throughout the course. Applied Algebra II Course Title: Applied Algebra II Total Framework Hours: 180 CIP Code: Exploratory Preparatory Date Last Modified: Career Cluster: Science, Technology, Engineering and Math Cluster Pathway: Science and Math Eligible for Equivalent Credit in: Math Science Total Number of Units: 13 Course Overview Summary: Applied Algebra II focuses on the application of mathematics and statistics to the solution of functional problems in fields such as engineering and the applied sciences. The course includes practical application of mathematical concepts such as exponents and systems of equations and inequalities. Students will learn about functions, quadratic equations, conic sections, exponential and logarithmic functions, polynomials, rational functions, sequences and series, probability, and trigonometric functions and identities. Unit 1: Fundamentals of Algebra Total Learning Hours for Unit: 8 Unit Summary: In this unit, students will: Identify natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Understand identity properties and inverse properties. Solving equations and inequalities. Understand the properties of inequalities. Course : Applied Algebra II 1

2 Solve absolute value equations and inequalities. Graph linear equations and inequalities using y-intercept, slope intercept form, and point slope form. Graph scatter plots. Performance Assessments: Performance assessments may be developed at the local level. In order to earn approval at the state level, performance assessments must be submitted within this framework. Each unit has assessment resources that may include hands-on practice, group projects, applied problem-solving tasks, unit quizzes, and preand post-tests for understanding. It is expected that students will: Synthesize information from a variety of instructional and technological sources by using real numbers, equations, and inequalities. Leadership Alignment: Leadership activities should include 21st Century Skills embedded in curriculum and instruction for this unit of instruction. Include leadership skills that are being taught and assessed within the class for all students. The event, activity, or project and the associated 21st Century Skill should be clearly articulated. Example: Students will demonstrate the ability to communicate clearly through their group project presentation. Aligned Washington State Standards Standards for Mathematical Practice (Common Core State Standards): Practice 1: Make sense of problems and persevere in solving them. Practice 2: Reason abstractly and quantitatively. Practice 3: Construct viable arguments and critique the reasoning of others. Practice 4: Model with mathematics. Practice 5: Use appropriate tools strategically. Practice 6: Attend to precision. Practice 7: Look for and make use of structure. Practice 8: Look for and express regularity in repeated reasoning. Washington Mathematical Standards (Common Core State Standards): Cluster: Reason quantitatively and use units to solve problems. N.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Cluster: Interpret the structure of expressions. A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context. 1a Interpret part of an expression, such as terms, factors, and coefficients. 1b Interpret complicated expressions by viewing one or more of their parts as a single entity. A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it. Cluster: Create equations that describe numbers or relationships. A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Course : Applied Algebra II 2

4 SL Present information, findings, and supporting evidence, conveying a clear and distinct perspective, such that listeners can follow the line of reasoning, alternative or opposing perspectives are addressed, and the organization, development, substance, and style are appropriate to purpose, audience, and a range of formal and informal tasks. Washington English Language Arts Standards (Common Core State Standards) - Language Standards (Grades 11-12): L Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. L Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. L Apply knowledge of language to understand how language functions in different context, to make effective choices for meaning or style, and to comprehend more fully when reading or listening. Educational Technology: Communicate and collaborate to learn with others Locate and organize information from a variety of sources and media Develop skills to use technology effectively. Unit 2: Systems of Equations and Inequalities Total Learning Hours for Unit: 10 Unit Summary: In this unit, students will: Solve systems of equations by graphing. Solve systems of equations using substitution. Solve systems of equations using elimination. Solve systems of equations in three variables. Solve systems of linear inequalities. Performance Assessments: Performance assessments may be developed at the local level. In order to earn approval at the state level, performance assessments must be submitted within this framework. It is expected that students will: Engage in a variety of mechanisms to identify the function of the mathematical computation. Leadership Alignment: Leadership activities should include 21st Century Skills embedded in curriculum and instruction for this unit of instruction. Include leadership skills that are being taught and assessed within the class for all students. The event, activity, or project and the associated 21st Century Skill should be clearly articulated. Example: Students will demonstrate the ability to communicate clearly through their group project presentation. Aligned Washington State Standards Standards for Mathematical Practice (Common Core State Standards): Practice 1: Make sense of problems and persevere in solving them. Practice 2: Reason abstractly and quantitatively. Practice 3: Construct viable arguments and critique the reasoning of others. Course : Applied Algebra II 4

5 Practice 4: Model with mathematics. Practice 5: Use appropriate tools strategically. Practice 6: Attend to precision. Practice 7: Look for and make use of structure. Practice 8: Look for and express regularity in repeated reasoning. Washington Mathematical Standards (Common Core State Standards): Cluster: Reason quantitatively and use units to solve problems. N.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Cluster: Perform operations on matrices and use matrices in applications. N.VM.C.6 Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. N.VM.C.7 Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. N.VM.C.8 Add, subtract, and multiply matrices of appropriate dimensions. N.VM.C.9 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. N.VM.C.10 Understand that the zero and identity 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. N.VM.C.11 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. N.VM.C.12 Work with 2 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. Cluster: Interpret the structure of expressions. A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context. 1a Interpret part of an expression, such as terms, factors, and coefficients. 1b Interpret complicated expressions by viewing one or more of their parts as a single entity. A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it. Cluster: Create equations that describe numbers or relationships. A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Cluster: Understand solving equations as a process of reasoning and explain the reasoning. A.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Cluster: Solve systems of equations. A.REI.C.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A.REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x 2 + y 2 = 3. Course : Applied Algebra II 5

7 Educational Technology: Communicate and collaborate to learn with others Locate and organize information from a variety of sources and media Develop skills to use technology effectively. Unit 3: Functions Total Learning Hours for Unit: 15 Unit Summary: In this unit, students will: Identify functions using the vertical line test. Identify a relation. Identify the domain and range of a function. Identify the domain and range of a data set. Use and evaluate function notation. Perform operations of addition and subtraction in functions. Identify constant and inverse functions. Perform transformations of functions. Performance Assessments: Performance assessments may be developed at the local level. In order to earn approval at the state level, performance assessments must be submitted within this framework. It is expected that students will: Engage in a variety of mechanisms to identify and use functions and function notation to solve problems. Leadership Alignment: Leadership activities should include 21st Century Skills embedded in curriculum and instruction for this unit of instruction. Include leadership skills that are being taught and assessed within the class for all students. The event, activity, or project and the associated 21st Century Skill should be clearly articulated. Example: Students will demonstrate the ability to communicate clearly through their group project presentation. Aligned Washington State Standards Standards for Mathematical Practice (Common Core State Standards): Practice 1: Make sense of problems and persevere in solving them. Practice 2: Reason abstractly and quantitatively. Practice 3: Construct viable arguments and critique the reasoning of others. Practice 4: Model with mathematics. Practice 5: Use appropriate tools strategically. Practice 6: Attend to precision. Practice 7: Look for and make use of structure. Practice 8: Look for and express regularity in repeated reasoning. Course : Applied Algebra II 7

8 Washington Mathematical Standards (Common Core State Standards): Cluster: Reason quantitatively and use units to solve problems. N.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Cluster: Interpret the structure of expressions. A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context. 1a Interpret part of an expression, such as terms, factors, and coefficients. 1b Interpret complicated expressions by viewing one or more of their parts as a single entity. A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it. Cluster: Create equations that describe numbers or relationships. A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Cluster: Understand solving equations as a process of reasoning and explain the reasoning. A.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Cluster: Solve equations and inequalities in one variable. A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Cluster: Represent and solve equations and inequalities graphically. A.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. A.REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Cluster: Understand the concept of a function and use function notation. F.IF.A.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F.IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Cluster: Interpret functions that arise in applications in terms of the context. F.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. F.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Cluster: Analyze functions using different representations. F.IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Course : Applied Algebra II 8

11 Leadership Alignment: Leadership activities should include 21st Century Skills embedded in curriculum and instruction for this unit of instruction. Include leadership skills that are being taught and assessed within the class for all students. The event, activity, or project and the associated 21st Century Skill should be clearly articulated. Example: Students will demonstrate the ability to communicate clearly through their group project presentation. Aligned Washington State Standards Standards for Mathematical Practice (Common Core State Standards): Practice 1: Make sense of problems and persevere in solving them. Practice 2: Reason abstractly and quantitatively. Practice 3: Construct viable arguments and critique the reasoning of others. Practice 4: Model with mathematics. Practice 5: Use appropriate tools strategically. Practice 6: Attend to precision. Practice 7: Look for and make use of structure. Practice 8: Look for and express regularity in repeated reasoning. Washington Mathematical Standards (Common Core State Standards): Cluster: Extend the properties of exponents to rational exponents. N.RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. N.RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Cluster: Reason quantitatively and use units to solve problems. N.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Cluster: Perform arithmetic operations with complex numbers. N.CN.A.1 Know that there is a complex number i such that i 2 = -1, and every complex number has the form a+bi with a and b real. N.CN.A.2 Use the relation i 2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. N.CN.A.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. Cluster: Interpret the structure of expressions. A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context. 1a Interpret part of an expression, such as terms, factors, and coefficients. 1b Interpret complicated expressions by viewing one or more of their parts as a single entity. A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it. Cluster: Write expressions in equivalent forms to solve problems. A.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. 3a Factor a quadratic expression to reveal the zeros of the function it defines. 3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 3c Use the properties of exponents to transform expressions for exponential functions. Course : Applied Algebra II 11

14 N.CN.C.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Cluster: Interpret the structure of expressions. A.SSE.A.1 Interpret expressions that represent a quantity in terms of its context. 1a Interpret part of an expression, such as terms, factors, and coefficients. 1b Interpret complicated expressions by viewing one or more of their parts as a single entity. A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it. Cluster: Write expressions in equivalent forms to solve problems. A.SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. 3a Factor a quadratic expression to reveal the zeros of the function it defines. 3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. 3c Use the properties of exponents to transform expressions for exponential functions. Cluster: Create equations that describe numbers or relationships. A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A.CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Cluster: Understand solving equations as a process of reasoning and explain the reasoning. A.REI.A.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Cluster: Solve equations and inequalities in one variable. A.REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Cluster: Solve systems of equations. A.REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x 2 + y 2 = 3. Cluster: Represent and solve equations and inequalities graphically. A.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A.REI.D.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Cluster: Analyze functions using different representations. F.IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. 8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. 8b Use the properties of exponents to interpret expressions for exponential functions. F.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). Washington English Language Arts Standards (Common Core State Standards) - Science and Technology Literacy Standards (Grades 11-12): RST Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. RST Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms. Course : Applied Algebra II 14

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