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 I 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 Functions and Expressions Using Functions / Solving Linear Equations / Inequalities Unit 2 Linear Patterns Unit 3 Linear Functions Unit 4 Investigating Real World Situations / Scatterplots Unit 5 Systems of Equations Unit 6 Investigating and Solving Quadratics Unit 7 Simplifying Polynomials Unit 8 Exploring Non-Linear Functions Page 1 of 6
2 Second Semester ONLY Unit 5 Systems of Equations 5 Weeks 1A.08 Linear functions. The student formulates systems of linear equations from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (A) analyze situations and formulate systems of linear equations in two unknowns to solve problems; (B) solve systems of linear equations using concrete models, graphs, tables, and algebraic methods; and (C) interpret and determine the reasonableness of solutions to systems of linear equations Unit 6 Investigating and Solving Quadratics 6 Weeks 1A.02 Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: 1A.09 Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student is expected to: 1A.10 Quadratic and other nonlinear functions. The student understands there is more than one way to solve a quadratic equation and solves them using appropriate methods. The student is expected to: (A) describe independent and dependent quantities in functional relationships; (A) determine the domain and range for quadratic functions in given situations; (B) investigate, describe, and predict the effects of changes in a on the graph of y = ax 2 + c; (C) investigate, describe, and predict the effects of changes in c on the graph of y = ax 2 + c; and (D) analyze graphs of quadratic functions and draw conclusions. (A) solve quadratic equations using concrete models, tables, graphs, and algebraic methods; and (B) make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function. New TEKS to Bridge for Unit 6 Page 2 of 6
3 1A.06 Quadratic functions and equations. The standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations. The student is expected to: 1A.07 Quadratic functions and equations. The standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations. The student is expected to: 1A.08 Quadratic functions and equations. The standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data. The student is expected to: 1A.10 Number and algebraic methods. The standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions. The student is expected to: 1A.11 Number and algebraic methods. The standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to: Amarillo ISD Algebra I Standards (B) write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x - h) 2 + k), and rewrite the equation from vertex form to standard form (f(x) = ax 2 + bx + c); and (C) write quadratic functions when given real solutions and graphs of their related equations. (C) determine the effects on the graph of the parent function f(x) = x 2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d. (A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula; and (B) write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems. (E) factor, if possible, trinomials with real factors in the form ax 2 + bx + c, including perfect square trinomials of degree two; and (F) decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial. (A) simplify numerical radical expressions involving square roots; and Page 3 of 6
4 Unit 7 Simplifying Polynomials 2 Weeks 1A.04 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: 1A.11 Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to: (A) find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations; (A) use patterns to generate the laws of exponents and apply them in problem-solving situations; New TEKS to Bridge for Unit 7 1A.10 Number and algebraic methods. The standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions. The student is expected to: 1A.11 Number and algebraic methods. The standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to: (C) determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend; (B) simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents. Unit 8 Exploring Non-Linear Functions 3 weeks Page 4 of 6
5 1A.11 Quadratic and other nonlinear functions. The student understands there are situations modeled by functions that are neither linear nor quadratic and models the situations. The student is expected to: New TEKS to Bridge for Unit 8 Amarillo ISD Algebra I Standards (B) analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods; and (C) analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods. 1A.09 Exponential functions and equations. The standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on realworld data. The student is expected to: 1A. 12 Number and algebraic methods. The standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to: (A) determine the domain and range of exponential functions of the form f(x) = ab x and represent the domain and range using inequalities; (D) graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems; and (E) write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems. (C) identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes; (D) write a formula for the n th term of arithmetic and geometric sequences, given the value of several of their terms; and Page 5 of 6
6 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 6 of 6
Amarillo ISD Math Curriculum
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
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