Gizmos for Texas - Mathematics: Algebra I (Essential Knowledge and Skills adopted 2012)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

A1.1: : Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding.

A1.1.A: : The student is expected to: apply mathematics to problems arising in everyday life, society, and the workplace;

A1.1.B: : The student is expected to: 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;

A1.1.C: : The student is expected to: 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;

A1.1.D: : The student is expected to: communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate;

A1.1.E: : The student is expected to: create and use representations to organize, record, and communicate mathematical ideas;

A1.1.F: : The student is expected to: analyze mathematical relationships to connect and communicate mathematical ideas; and

A1.1.G: : The student is expected to: display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

A1.2: : Linear functions, equations, and inequalities. 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.

A1.2.A: : The student is expected to: 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;

A1.2.B: : The student is expected to: write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y sub 1 = m(x - x sub 1), given one point and the slope and given two points;

A1.2.C: : The student is expected to: write linear equations in two variables given a table of values, a graph, and a verbal description;

A1.2.D: : The student is expected to: write and solve equations involving direct variation;

A1.2.G: : The student is expected to: 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;

A1.2.H: : The student is expected to: write linear inequalities in two variables given a table of values, a graph, and a verbal description; and

A1.2.I: : The student is expected to: write systems of two linear equations given a table of values, a graph, and a verbal description.

A1.3: : Linear functions, equations, and inequalities. 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.

A1.3.A: : The student is expected to: 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 = C, and y - y sub 1 = m(x - x sub 1);

A1.3.B: : The student is expected to: calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems;

A1.3.C: : The student is expected to: 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;

A1.3.D: : The student is expected to: graph the solution set of linear inequalities in two variables on the coordinate plane;

A1.3.E: : The student is expected to: 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;

A1.3.F: : The student is expected to: graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist;

A1.3.G: : The student is expected to: estimate graphically the solutions to systems of two linear equations with two variables in real-world problems; and

A1.3.H: : The student is expected to: graph the solution set of systems of two linear inequalities in two variables on the coordinate plane.

A1.4: : Linear functions, equations, and inequalities. The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data.

A1.4.A: : The student is expected to: calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association;

A1.4.B: : The student is expected to: compare and contrast association and causation in real-world problems; and

A1.4.C: : The student is expected to: write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.

A1.5: : Linear functions, equations, and inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.

A1.5.A: : The student is expected to: 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;

A1.5.B: : The student is expected to: 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

A1.5.C: : The student is expected to: solve systems of two linear equations with two variables for mathematical and real-world problems.

A1.6: : Quadratic functions and equations. 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.

A1.6.B: : The student is expected to: 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

A1.6.C: : The student is expected to: write quadratic functions when given real solutions and graphs of their related equations.

A1.7: : Quadratic functions and equations. 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.

A1.7.A: : The student is expected to: 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;

A1.7.B: : The student is expected to: describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions; and

A1.7.C: : The student is expected to: 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.

A1.8: : Quadratic functions and equations. 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.

A1.8.A: : The student is expected to: solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula.

A1.9: : Exponential functions and equations. 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.

A1.9.B: : The student is expected to: interpret the meaning of the values of a and b in exponential functions of the form f(x) = a(b to the x power) in real-world problems;

A1.9.C: : The student is expected to: write exponential functions in the form f(x) = a(b to the x power) (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay;

A1.9.D: : The student is expected to: graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems.

A1.10: : Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.

A1.10.A: : The student is expected to: add and subtract polynomials of degree one and degree two;

A1.10.B: : The student is expected to: multiply polynomials of degree one and degree two;

A1.10.C: : The student is expected to: 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;

A1.10.D: : The student is expected to: rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property;

A1.10.E: : The student is expected to: factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two; and

A1.10.F: : The student is expected to: 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.

A1.11: : Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.

A1.11.A: : The student is expected to: simplify numerical radical expressions involving square roots; and

A1.11.B: : The student is expected to: simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.

A1.12: : Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.

A1.12.A: : The student is expected to: decide whether relations represented verbally, tabularly, graphically, and symbolically define a function;

A1.12.D: : The student is expected to: write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms; and

A1.12.E: : The student is expected to: solve mathematic and scientific formulas, and other literal equations, for a specified variable.

Correlation last revised: 2/11/2025

Texas - Mathematics: Algebra I

Essential Knowledge and Skills | Adopted: 2012