Algebra I

one credit course

Introduction

Unit 01: Linear Expressions, Equations, and Inequalities (one variable)

Unit 02: Introduction to Functions

Unit 03: Investigation of Linear Functions and Inequalities (two variables)

Unit 04: Application of Linear Functions

Unit 05: Systems of Linear Equations and Inequalities

Unit 06: Laws of Exponents, Expressions, and Factoring

Unit 07: Quadratic Equations, including Simplification of Numerical Radical Expressions

Unit 08: Investigation and Application of Quadratic Functions

Unit 09: Investigation and Application of Exponential Functions

Unit 10: Arithmetic and Geometric Sequences

Unit 11: Making Connections

Unit 12: Cost Comparison Analysis

Texas Essential Knowledge & Skills (TEKS)

Introduction

(1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while focusing on fluency and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.

(2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental math, estimation, and number sense to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language. Students will use mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

(3) In Algebra I, students will build on the knowledge and skills for mathematics in Grades 6-8, which provide a foundation in linear relationships, number and operations, and proportionality. Students will study linear, quadratic, and exponential functions and their related transformations, equations, and associated solutions. Students will connect functions and their associated solutions in both mathematical and real-world situations. Students will use technology to collect and explore data and analyze statistical relationships. In addition, students will study polynomials of degree one and two, radical expressions, sequences, and laws of exponents. Students will generate and solve linear systems with two equations and two variables and will create new functions through transformations.

Unit 01: Linear Expressions, Equations, and Inequalities (one variable)

(15 classes for the entire unit)

Students define polynomial expressions and perform operations (addition, subtraction, scalar multiplication) with polynomials of degree one, including rewriting a polynomial to an equivalent form when distributing by a rational scale factor. Students determine the quotient of a polynomial of degree one divided by a polynomial of degree one. Students make connections between expressions and equations, and solve linear equations in one variable, including variables on both sides and the application of the distributive property. Students model both mathematical and real-world problem situations using equations. Students solve linear inequalities in one variable, including variables on both sides and the application of the distributive property. Students model both mathematical and real-world problem situations using inequalities. Students solve mathematical formulas (including solving for y), scientific formulas, and other literal equations for a specified variable.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.5A, A.5B, A.10A, A.10C, A.10D, A.12E

Unit 02: Introduction to Functions

(10 classes for the entire unit)

Students identify relations and determine if relations represented verbally, tabularly, graphically, and symbolically define a function. Students identify domain and range (continuous and discrete) of functions and represent the domain and range using inequality notation and verbal descriptions. Students express functions in function notation. Students evaluate functions in function notation given one or more elements in their domains. Students explore real-world problem situations, identify the domain and range of problem situations, express representative functions for problem situations using function notation, and evaluate functions for specified domains in problem situations. Problems in this unit incorporate linear, quadratic, and exponential functions, since those are the functions studied in Algebra I.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.2A, A.6A, A.9A, A.12A, A.12B

Unit 03: Investigation of Linear Functions and Inequalities (two variables)

(10 classes for the entire unit)

Students graph linear functions on the coordinate plane given tables, verbal descriptions, and algebraic generalizations. Students determine domain (continuous and discrete) and range of linear functions representing domain and range using inequality notation and verbal descriptions for mathematical problems. Students determine the reasonableness of domain (continuous and discrete) and range in real-world situations. Students also calculate rate of change for a linear function in mathematical and real world problems from tables, graphs, and algebraic methods. Students determine the slope of a line given a table, graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1). Students make connections between rate of change and slope of the line. Students determine the rate of change for various intervals on a given graph of a piecewise function. Students write linear equations in two variables given a table of values, a graph, and a verbal description. Students write an equation of a line that is parallel or perpendicular to the x- or y-axis and determine whether the slope of the line is zero or undefined. Students graph linear functions in two variables, identifying key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems. Students determine the effects on the graph of the parent function f(x) = x 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, including multiple parameter changes within one linear function. Students write linear inequalities in two variables given a table of values, a graph, and a verbal description; and graph the solution set of linear inequalities in two variables on the coordinate plane.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.2A, A.2C, A.2G, A.2H, A.3A, A.3B, A.3C, A.3D, A.3E

Unit 04: Application of Linear Functions

(15 classes for the entire unit)

Students write linear equations in two variables from given information, including a table of values, a graph, a verbal description, one point and the slope, two points, a point and parallel to a given line, a point and perpendicular to a given line, or a line parallel or perpendicular to the x- or y-axis, and represent the linear equations in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1). Students calculate the rate of change or slope as needed from a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y – y1 = m(x – x1). Students write linear functions for real-world situations, and model the linear functions using various representations. Students identify domain (continuous or discrete), range, x-intercept, y-intercept, zeros, and slope and the meaning of the key attributes in terms of the situation. Students make predictions and critical judgments, and justify the solution in terms of the problem situation, including writing and solving problems involving direct variation. Students write, with and without technology, linear functions, analyze the strength of the linear function using scatterplots and linear correlations, compare association and causation between the variables, and estimate solutions and make predictions in terms of the problem situation.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.2A, A.2B, A.2C, A.2D, A.2E, A.2F, A.2G, A.3A, A.3B, A.3C, A.4A, A.4B, A.4C

Unit 05: Systems of Linear Equations and Inequalities

(10 classes for the entire unit)

Students analyze a table of values representing a system of two linear equations in two variables and determine the solutions, if they exist. Students graph systems of two linear equations in two variables on the coordinate plane and determine the solutions, if they exist. Students solve systems of two linear equations with two variables for mathematical problems, including substitution and elimination methods. Students formulate, estimate, and solve systems of equations in real-world problem situations and justify the solutions in terms of the situation. Students also graph the solution set of systems of two linear inequalities in two variables on the coordinate plane, and formulate and solve graphically two linear inequalities in two variables in real-world problem situations and justify the solution.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.2I, A.3F, A.3G, A.3H, A.5C

Unit 06: Laws of Exponents, Expressions, and Factoring

(10 classes for the entire unit)

Students simplify numeric and algebraic expressions and solve equations using the laws of exponents, including integral and rational exponents. Students perform operations (addition, subtraction, multiplication) with polynomials of degree one and degree two, including rewriting a polynomial to an equivalent form using the distributive property. Students 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, and justify the answer by multiplication. Students apply the distributive property to factor out the greatest common factor of the terms in a polynomial expression. Students also factor binomials (difference of two squares) and factor trinomials (ax^2 + bx + c) having real roots, including perfect square trinomials of degree two, and justify the results by multiplication.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.10A, A.10B, A.10C, A.10D, A.10E, A.10F, A.11B

Unit 07: Quadratic Equations, including Simplification of Numerical Radical Expressions

(10 classes for the entire unit)

Students solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula. Students simplify numerical radical expressions involving square roots and apply this concept when solving quadratic equations. Students formulate quadratic equations for problem situations, solve the quadratic equation, and justify the solution(s) in terms of the problem situation. Students also solve for specified variables in literal equations, including solving for variables in mathematical and scientific formulas involving square variables.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.8A, A.11A, A.12E

Unit 08: Investigation and Application of Quadratic Functions

(15 classes for the entire unit)

Students graph quadratic functions on the coordinate plane identifying key attributes, including y-intercept, x-intercept(s), zeros, maximum value, minimum value, vertex, and the equation of the axis of symmetry, when applicable. Students determine the domain and range, representing the domain and range using inequality notation and verbal descriptions. Students describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions and write quadratic functions when given real solutions and graphs of their related equations. Students 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. Students formulate quadratic functions for real-world problem situations over an appropriate domain and range given various attributes, identify key attributes in terms of the problem situation, and justify the meaning of key attributes in terms of the problem situation. Students 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 and identify effects of parameter changes of quadratic functions in terms of the problem situation.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.6A, A.6B, A.6C, A.7A, A.7B, A.7C, A.8B

Unit 09: Investigation and Application of Exponential Functions

(10 classes for the entire unit)

Students graph exponential functions that model growth and decay. Students identify key features, including y-intercept and asymptote, and determine the domain and range of exponential functions in the form f(x) = ab^x, representing the domain and range using inequality notation and verbal descriptions. Students interpret the effects of the values of a and b in exponential functions in the form f(x) = ab^x and write exponential functions in the form f(x) = ab^x (where b is a rational number greater than 0) to describe problems arising from mathematical and real-world situations, including growth and decay. Students use technology to write exponential functions that provide a reasonable fit to data to estimate solutions, make predictions, and justify solutions in terms of the problem situation for real-world problems and data collection activities.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.9A, A.9B, A.9C, A.9D, A.9E

Unit 10: Arithmetic and Geometric Sequences

(15 classes for the entire unit)

Students define and identify terms of arithmetic and geometric sequences when sequences are given in recursive, explicit, and function notation using recursive processes. Students write a formula for the nth term of arithmetic and geometric sequences in recursive, explicit, and function notation, given the value of several of their terms. Students connect arithmetic sequences to linear functions, graph sequences on the coordinate plane, and compare key attributes of the representative function and sequence in mathematical and real-world problems. Students connect geometric sequences to exponential functions, graph sequences on the coordinate plane, and compare key attributes of the representative function and sequence in mathematical and real-world problems. Students compare and contrast arithmetic and geometric sequences in real-world problems and data collections.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.3C, A.9D, A.12C, A.12D

Unit 11: Making Connections

(10 classes for the entire unit)

Students review solving linear equations, inequalities, and systems of linear equations and inequalities. Students review writing linear equations and inequalities from given criteria and graphs. Students review application of linear functions to model real-world problem situations. Students review solving quadratic equations (taking square roots, factoring, quadratic formula, completing the square) and exponential equations (graphically). Students review writing and graphing quadratic and exponential functions from given criteria, including comparing the quadratic parent function with another function that undergoes parameter changes. Students review application of quadratic and exponential functions to model real-world problem situations.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.2A, A.2C, A.2E, A.2F, A.2G, A.2H, A.2I, A.3B, A.3C, A.3D, A.3H, A.4C, A.5A, A.5B, A.5C, A.6A, A.6B, A.6C, A.7A, A.7C, A.8A, A.8B, A.9C, A.9D, A.9E, A.10E, A.10F, A.11B

Unit 12: Cost Comparison Analysis

(10 classes for the entire unit)

Students apply prior knowledge to compare products or services for two companies. Student groups formulate a real-world problem design to conduct a cost comparison analysis that can be modeled by linear functions. Students collect and analyze data for the two companies, make predictions and draw conclusions, and justify conclusions about the cost comparisons. Students present a written report and an oral presentation both including displays of project data, representations, analysis, equations/inequalities and systems of equations/inequalities, calculations, summary of predictions and conclusions, and justification in terms of their problem situation.

TEKS in this unit: A.1A, A.1B, A.1C, A.1D, A.1E, A.1F, A.1G, A.2A, A.2C, A.2H, A.2I, A.3B, A.3C, A.3H, A.4C, A.5A, A.5C

Texas Essential Knowledge & Skills (TEKS)

TEKS - Math - A1.pdf

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