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Skills available for Texas high school math standards

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College and Career Readiness Standards College and Career Readiness Standards
Texas Essential Knowledge and Skills (TEKS): 111.47 Statistics Texas Essential Knowledge and Skills (TEKS): 111.47 Statistics
Texas Essential Knowledge and Skills (TEKS): 111.48 Algebraic Reasoning Texas Essential Knowledge and Skills (TEKS): 111.48 Algebraic Reasoning
State of Texas Assessments of Academic Readiness (STAAR) State of Texas Assessments of Academic Readiness (STAAR)
Texas Essential Knowledge and Skills (TEKS): Algebra 1 Texas Essential Knowledge and Skills (TEKS): Algebra 1
Texas Essential Knowledge and Skills (TEKS): Algebra 2 Texas Essential Knowledge and Skills (TEKS): Algebra 2
Texas Essential Knowledge and Skills (TEKS): Algebraic Reasoning Texas Essential Knowledge and Skills (TEKS): Algebraic Reasoning
Texas Essential Knowledge and Skills (TEKS): Geometry Texas Essential Knowledge and Skills (TEKS): Geometry
Texas Essential Knowledge and Skills (TEKS): Precalculus Texas Essential Knowledge and Skills (TEKS): Precalculus
Texas College and Career Readiness Standards: Grades: 9-12 Texas College and Career Readiness Standards: Grades: 9-12

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1 Mathematical process standards

1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.
- A apply mathematics to problems arising in everyday life, society, and the workplace;
- B 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;
- C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;
- D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;
- E create and use representations to organize, record, and communicate mathematical ideas;
- F analyze mathematical relationships to connect and communicate mathematical ideas; and
- G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

2-5 Linear functions, equations, and inequalities

2 The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations.
- A determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities;
- B write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y₁ = m(x - x₁), given one point and the slope and given two points;
- C write linear equations in two variables given a table of values, a graph, and a verbal description;
- D write and solve equations involving direct variation;
- E write the equation of a line that contains a given point and is parallel to a given line;
  - Slopes of parallel and perpendicular lines (A1-L.18)
  - Write an equation for a parallel or perpendicular line (A1-L.19)
- F write the equation of a line that contains a given point and is perpendicular to a given line;
  - Slopes of parallel and perpendicular lines (A1-L.18)
  - Write an equation for a parallel or perpendicular line (A1-L.19)
- G 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;
  - Equations of horizontal and vertical lines (A1-L.12)
- H write linear inequalities in two variables given a table of values, a graph, and a verbal description; and
  - Write a linear inequality from a graph (A1-P.4)
  - Write two-variable inequalities: word problems (A1-P.5)
- I write systems of two linear equations given a table of values, a graph, and a verbal description.
- Checkpoint opportunity
  - Checkpoint: Linear equations (A1)
  - Checkpoint: Parallel and perpendicular lines (A1)
3 The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations.
- A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C₁ and y - y₁ = m(x - x₁);
- B calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems;
- C graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems;
- D graph the solution set of linear inequalities in two variables on the coordinate plane;
  - Does (x, y) satisfy the inequality? (A1-P.1)
  - Graph a two-variable linear inequality (A1-P.3)
- E 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;
  - Transformations of linear functions (A1-N.13)
- F graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist;
  - Solve a system of equations by graphing (A1-O.2)
  - Find the number of solutions to a system of equations by graphing (A1-O.4)
- G estimate graphically the solutions to systems of two linear equations with two variables in real-world problems; and
  - Solve a system of equations by graphing: word problems (A1-O.3)
- H graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.
  - Is (x, y) a solution to the system of linear inequalities? (A1-P.6)
  - Solve systems of linear inequalities by graphing (A1-P.7)
- Checkpoint opportunity
4 The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.
- A calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association;
  - Match correlation coefficients to scatter plots (A1-JJ.3)
  - Calculate correlation coefficients (A1-JJ.4)
- B compare and contrast association and causation in real-world problems; and
  - Correlation and causation (A1-JJ.11)
- C write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
- Checkpoint opportunity
  - Checkpoint: Linear modeling (A1)
5 The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.
- A solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides;
- B solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides; and
- C solve systems of two linear equations with two variables for mathematical and real-world problems.
- Checkpoint opportunity
  - Checkpoint: Solve linear equations and inequalities (A1)
  - Checkpoint: Systems of equations and inequalities (A1)

6-8 Quadratic functions and equations

6 The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations.
- A determine the domain and range of quadratic functions and represent the domain and range using inequalities;
  - Domain and range of quadratic functions: graphs (A1-Y.9)
  - Domain and range of quadratic functions: equations (A1-Y.10)
- 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) = ax²+ bx + c); and
  - Write a quadratic function in vertex form from its vertex and another point (A1-Y.11)
- C write quadratic functions when given real solutions and graphs of their related equations.
  - Match quadratic functions and graphs (A1-Y.8)
  - Write a quadratic function in factored form from its x-intercepts and another point (A1-Y.12)
7 The student applies the mathematical process 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.
- A graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry;
- B describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions; and
  - Solve a quadratic equation using the zero product property (A1-Z.2)
  - Solve a quadratic equation by factoring (A1-Z.3)
- C determine the effects on the graph of the parent function f(x) = x² 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.
  - Transformations of quadratic functions (A1-Y.4)
- Checkpoint opportunity
  - Checkpoint: Graphs and transformations of quadratic functions (A1)
8 The student applies the mathematical process 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.
- 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.
- Checkpoint opportunity
  - Checkpoint: Write quadratic functions (A1)
  - Checkpoint: Solve quadratic equations (A1)

9 Exponential functions and equations

9 The student applies the mathematical process 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 real-world data.
- A determine the domain and range of exponential functions of the form f(x) = ab to the x power and represent the domain and range using inequalities;
  - Domain and range of exponential functions: graphs (A1)
  - Domain and range of exponential functions: equations (A1)
- B interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab to the x power in real-world problems;
  - Exponential growth and decay: word problems (A1-V.9)
- C write exponential functions in the form f(x) = ab to the x power (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay;
- 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.
  - Exponential regression (A1-JJ.10)
- Checkpoint opportunity
  - Checkpoint: Exponential functions (A1)

10-12 Number and algebraic methods

10 The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.
- A add and subtract polynomials of degree one and degree two;
- B multiply polynomials of degree one and degree two;
- 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;
  - Divide polynomials by monomials (A1)
  - Divide polynomials using long division (A1)
- D rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property;
  - Distributive property (A1-B.6)
- E factor, if possible, trinomials with real factors in the form ax² + 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.
  - Factor quadratics: special cases (A1-X.7)
- Checkpoint opportunity
  - Checkpoint: Polynomial operations (A1)
11 The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.
- A simplify numerical radical expressions involving square roots; and
- B simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
- Checkpoint opportunity
  - Checkpoint: Exponents and radicals (A1)
12 The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.
- A decide whether relations represented verbally, tabularly, graphically, and symbolically define a function;
  - Identify functions (A1-M.4)
  - Identify functions: vertical line test (A1-M.5)
- B evaluate functions, expressed in function notation, given one or more elements in their domains;
- 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 nth term of arithmetic and geometric sequences, given the value of several of their terms; and
  - Write variable expressions for arithmetic sequences (A1-U.7)
  - Write variable expressions for geometric sequences (A1-U.8)
- E solve mathematic and scientific formulas, and other literal equations, for a specified variable.
  - Rearrange multi-variable equations (A1-C.18)
  - Linear equations: solve for y (A1-L.8)
- Checkpoint opportunity
  - Checkpoint: Sequences (A1)
  - Checkpoint: Function concepts (A1)

Texas

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Actions

1 Mathematical process standards

1 The student uses mathematical processes to acquire and demonstrate mathematical understanding.

A apply mathematics to problems arising in everyday life, society, and the workplace;

B 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;

C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems;

D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

E create and use representations to organize, record, and communicate mathematical ideas;

F analyze mathematical relationships to connect and communicate mathematical ideas; and

G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

2-5 Linear functions, equations, and inequalities

2 The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations.

A determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities;

B write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points;

C write linear equations in two variables given a table of values, a graph, and a verbal description;

D write and solve equations involving direct variation;

E write the equation of a line that contains a given point and is parallel to a given line;

F write the equation of a line that contains a given point and is perpendicular to a given line;

G 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;

H write linear inequalities in two variables given a table of values, a graph, and a verbal description; and

I write systems of two linear equations given a table of values, a graph, and a verbal description.

Checkpoint opportunity

3 The student applies the mathematical process standards when using graphs of linear functions, key features, and related transformations to represent in multiple ways and solve, with and without technology, equations, inequalities, and systems of equations.

A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C1 and y - y1 = m(x - x1);

B calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems;

C graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems;

D graph the solution set of linear inequalities in two variables on the coordinate plane;

E 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;

F graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist;

G estimate graphically the solutions to systems of two linear equations with two variables in real-world problems; and

H graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.

Checkpoint opportunity

4 The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.

A calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association;

B compare and contrast association and causation in real-world problems; and

C write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

Checkpoint opportunity

5 The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.

A solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides;

B solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides; and

C solve systems of two linear equations with two variables for mathematical and real-world problems.

Checkpoint opportunity

6-8 Quadratic functions and equations

6 The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations.

A determine the domain and range of quadratic functions and represent the domain and range using inequalities;

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) = ax²+ bx + c); and

C write quadratic functions when given real solutions and graphs of their related equations.

7 The student applies the mathematical process 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.

A graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry;

B describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions; and

C determine the effects on the graph of the parent function f(x) = x² 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.

Checkpoint opportunity

8 The student applies the mathematical process 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.

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.

Checkpoint opportunity

9 Exponential functions and equations

A determine the domain and range of exponential functions of the form f(x) = ab to the x power and represent the domain and range using inequalities;

B interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab to the x power in real-world problems;

C write exponential functions in the form f(x) = ab to the x power (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay;

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.

Checkpoint opportunity

10-12 Number and algebraic methods

10 The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.

A add and subtract polynomials of degree one and degree two;

B multiply polynomials of degree one and degree two;

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;

D rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property;

E factor, if possible, trinomials with real factors in the form ax² + 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.

Checkpoint opportunity

11 The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.

A simplify numerical radical expressions involving square roots; and

B simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.

Checkpoint opportunity

12 The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.

A decide whether relations represented verbally, tabularly, graphically, and symbolically define a function;

B write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y₁ = m(x - x₁), given one point and the slope and given two points;

A determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C₁ and y - y₁ = m(x - x₁);