Amarillo ISD Math Curriculum

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1 Amarillo Independent School District follows the Texas Essential Knowledge and Skills (TEKS). All of AISD curriculum and documents and resources are aligned to the TEKS. The State of Texas State Board of Education has defined the focal points for Algebra II in mathematics in the first paragraph of the introduction to the Texas Essential Knowledge and Skills. Foundation concepts for high school mathematics. As presented in Grades K-8, the basic understandings of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics are essential foundations for all work in high school mathematics. Students will continue to build on this foundation as they expand their understanding through other mathematical experiences Unit 1 Parent Functions, Absolute Value, Equations Unit 2 Quadratics Unit 3 Systems of Equations and Inequalities Unit 4 Square Root Functions Unit 5 Exponents and Logarithms Unit 6 Rational Functions Unit 7 Conics Page 1 of 8

2 Second Semester ONLY Unit 4 Square Root Functions 3 Weeks 2A.02 Foundations for functions. The student understands the importance of the skills required to manipulate symbols in order to solve problems and uses the necessary algebraic skills required to simplify algebraic expressions and solve equations and inequalities in problem situations. The student is expected to: 2A.04 Algebra and geometry. The student connects algebraic and geometric representations of functions. The student is expected to: 2A.09 Quadratic and square root functions. The student formulates equations and inequalities based on square root functions, use a variety of methods to solve them, and analyze the solutions in terms of the situation. The student is expected to: (A) use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations; (A) identify and sketch graphs of parent functions, including linear (f (x) = x), quadratic (f (x) = x 2 ), exponential (f (x) = a x ), and logarithmic (f (x) = log a x) functions, absolute value of x (f (x) = x ), square root of x (f (x) = Öx), and reciprocal of x (f (x) = 1/x); (B) extend parent functions with parameters such as a in f (x) = a/x and describe the effects of the parameter changes on the graph of parent functions; and (C) describe and analyze the relationship between a function and its inverse (A) use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges; (B) relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions; (C) determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities; (D) determine solutions of square root equations using graphs, tables, and algebraic Page 2 of 8

3 methods; (E) determine solutions of square root inequalities using graphs and tables; (F) analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems; and (G) connect inverses of square root functions with quadratic functions New TEKS to Bridge for Unit 4 2A.02 Attributes of functions and their inverses. The student applies mathematical processes to understand that functions have distinct key attributes and understand the relationship between a function and its inverse. The student is expected to: 2A.04 Quadratic and square root functions, equations, and inequalities. The student applies mathematical processes to understand that quadratic and square root functions, equations, and quadratic inequalities can be used to model situations, solve problems, and make predictions. The student is expected to: 2A.06 Cubic, cube root, absolute value and rational functions, equations, and inequalities. The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to: (A) graph the functions f(x)= x, f(x)=1/x, f(x)=x 3, f(x)= 3 x, f(x)=b x, f(x)= x, and f(x)=log b (x) where b is 2, 10, and e, and, when applicable, analyze the key attributes such as domain, range, intercepts, symmetries, asymptotic behavior, and maximum and minimum given an interval; (B) graph and write the inverse of a function using notation such as f -1 (x); (C) describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range; and (D) use the composition of two functions, including the necessary restrictions on the domain, to determine if the functions are inverses of each other. (C) determine the effect on the graph of f(x) = x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative values of a, b, c, and d; (E) formulate quadratic and square root equations using technology given a table of data; (F) solve quadratic and square root equations; (G) identify extraneous solutions of square root equations; and (A) analyze the effect on the graphs of f(x) = x 3 and f(x) = 3 x when f(x) is replaced by af(x), f(bx), f(x - c), and f(x) + d for specific positive and negative real values of a, b, c, and d; (B) solve cube root equations that have real roots; Page 3 of 8

4 Unit 5 Exponents and Logarithms 5 Weeks 2A.04 Algebra and geometry. The student connects algebraic and geometric representations of functions. The student is expected to: 2A.11 Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (A) identify and sketch graphs of parent functions, including linear (f (x) = x), quadratic (f (x) = x 2 ), exponential (f (x) = a x ), and logarithmic (f (x) = log a x) functions, absolute value of x (f (x) = x ), square root of x (f (x) = Öx), and reciprocal of x (f (x) = 1/x); (B) extend parent functions with parameters such as a in f (x) = a/x and describe the effects of the parameter changes on the graph of parent functions; and (C) describe and analyze the relationship between a function and its inverse (A) develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses; (B) use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior; (C) determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities; (D) determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods; (E) determine solutions of exponential and logarithmic inequalities using graphs and tables; and (F) analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem New TEKS to Bridge for Unit 5 2A.02 Attributes of functions and their inverses. The student applies mathematical processes to understand that functions have distinct key attributes and understand the (C) describe and analyze the relationship between a function and its inverse (quadratic and square root, logarithmic and exponential), including the restriction(s) on domain, which will restrict its range; and Page 4 of 8

5 relationship between a function and its inverse. The student is expected to: 2A.05 Exponential and logarithmic functions and equations. The student applies mathematical processes to understand that exponential and logarithmic functions can be used to model situations and solve problems. The student is expected to: Amarillo ISD Algebra II Standards (A) determine the effects on the key attributes on the graphs of f(x) = b x and f(x) = log b (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d; (B) formulate exponential and logarithmic equations that model real-world situations, including exponential relationships written in recursive notation; (C) rewrite exponential equations as their corresponding logarithmic equations and logarithmic equations as their corresponding exponential equations; (D) solve exponential equations of the form y = ab x where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions; and (E) determine the reasonableness of a solution to a logarithmic equation. Unit 6 Rational Functions 7 Weeks 2A.04 Algebra and geometry. The student connects algebraic and geometric representations of functions. The student is expected to: 2A.10 Rational functions. The student formulates equations and inequalities based on rational functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (A) identify and sketch graphs of parent functions, including linear (f (x) = x), quadratic (f (x) = x 2 ), exponential (f (x) = a x ), and logarithmic (f (x) = log a x) functions, absolute value of x (f (x) = x ), square root of x (f (x) = x), and reciprocal of x (f (x) = 1/x); (B) extend parent functions with parameters such as a in f (x) = a/x and describe the effects of the parameter changes on the graph of parent functions; (A) use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior; (B) analyze various representations of rational functions with respect to problem situations; (C) determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities; (D) determine the solutions of rational equations using graphs, tables, and algebraic Page 5 of 8

6 methods; (E) determine solutions of rational inequalities using graphs and tables; (F) analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem; and (G) use functions to model and make predictions in problem situations involving direct and inverse variation New TEKS to Bridge for Unit 6 2A.06 Cubic, cube root, absolute value and rational functions, equations, and inequalities. The student applies mathematical processes to understand that cubic, cube root, absolute value and rational functions, equations, and inequalities can be used to model situations, solve problems, and make predictions. The student is expected to: (G) analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d; (H) formulate rational equations that model real-world situations; (I) solve rational equations that have real solutions; (J) determine the reasonableness of a solution to a rational equation; (K) determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation; and (L) formulate and solve equations involving inverse variation. Unit 7 Conics 5 Weeks 2A.05 Algebra and geometry. The student knows the relationship between the geometric and algebraic descriptions of conic sections. The student is expected to: (A) describe a conic section as the intersection of a plane and a cone; (B) sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph; (C) identify symmetries from graphs of conic sections; (D) identify the conic section from a given equation; and (E) use the method of completing the square New TEKS to Bridge for Unit 7 2A.07 Number and algebraic methods. The student applies mathematical processes to simplify and perform operations on expressions and to solve equations. The (A) add, subtract, and multiply complex numbers; (B) add, subtract, and multiply polynomials; (C) determine the quotient of a polynomial of degree three and of degree four when divided by a polynomial of degree one and of degree two; Page 6 of 8

7 student is expected to: Amarillo ISD Algebra II Standards (D) determine the linear factors of a polynomial function of degree three and of degree four using algebraic methods; (E) determine linear and quadratic factors of a polynomial expression of degree three and of degree four, including factoring the sum and difference of two cubes and factoring by grouping; (F) determine the sum, difference, product, and quotient of rational expressions with integral exponents of degree one and of degree two; (G) rewrite radical expressions that contain variables to equivalent forms; (H) solve equations involving rational exponents; and (I) write the domain and range of a function in interval notation, inequalities, and set notation. Page 7 of 8

8 To ensure that every student has an opportunity to learn, understand and demonstrate the Texas Essential Knowledge and Skills. Amarillo Independent has adopted the following protocols for teachers, curriculum and others to use in reference to Curriculum, Instruction and Assessment. Curriculum 1) Prioritize essential learning based on AISD written curriculum and adhere to the scope and sequence. 2) Develop deep understandings of the AISD written curriculum with an emphasis on the essential learning outcomes. 3) Create relevant learning environments in every classroom using the AISD written curriculum. 4) Analyze vertical and horizontal alignment to ensure grade level curriculum is being taught. Instruction 1) Common lessons are developed based on strategically selected grade level TEKS and include learning opportunities for students that: are at the expected level of thinking and rigor utilize research based instructional strategies are actively engaging have real world applications 2) Collaboratively align instruction to assessment. 3) Individual student instructional needs are considered and addressed in the lessons. 4) Strategic re-teaching when students do not understand. 5) Common lessons are analyzed and strengthened through a continuous improvement process such as the Professional Teaching Model, Lesson Study or other method for collaborative study and sharing. Assessment 1) Collaboratively align all assessment to the AISD written curriculum and reflect appropriate rigor. 2) Collaboratively engage in purposeful dialogue about assessment tied to clearly defined essential learning outcomes. 3) Continuously improve and adjust instruction based on common assessment results and student work. 4) Provide feedback to the annual curriculum feedback and revision process. Page 8 of 8

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