Gizmos for Texas - Mathematics: Algebraic Reasoning (Essential Knowledge and Skills adopted 2015)

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

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

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

AR.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;

AR.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;

AR.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;

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

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

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

AR.2: : Patterns and structure. The student applies mathematical processes to connect finite differences or common ratios to attributes of functions.

AR.2.A: : The student is expected to: determine the patterns that identify the relationship between a function and its common ratio or related finite differences as appropriate, including linear, quadratic, cubic, and exponential functions;

AR.2.B: : The student is expected to: classify a function as linear, quadratic, cubic, and exponential when a function is represented tabularly using finite differences or common ratios as appropriate;

AR.2.C: : The student is expected to: determine the function that models a given table of related values using finite differences and its restricted domain and range.

AR.3: : Patterns and structure. The student applies mathematical processes to understand the connections among representations of functions and combinations of functions, including the constant function, f(x) = x, f(x) = x^2, f(x) = the square root of x, f(x) = 1/x, f(x) = x^3, f(x) = the cube root of x, f(x) = b to the x power, f(x) = |x|, and f(x)= log to the base b of x where b is 2, 10 or e; functions and their inverses; and key attributes of these functions.

AR.3.B: : The student is expected to: compare and contrast the key attributes of a function and its inverse when it exists, including domain, range, maxima, minima, and intercepts, tabularly, graphically, and symbolically;

AR.3.C: : The student is expected to: verify that two functions are inverses of each other tabularly and graphically such as situations involving compound interest and interest rate, velocity and braking distance, and Fahrenheit-Celsius conversions;

AR.3.D: : The student is expected to: represent a resulting function tabularly, graphically, and symbolically when functions are combined or separated using arithmetic operations such as combining a 20% discount and a 6% sales tax on a sale to determine h(x), the total sale, f(x) = 0.8x, g(x) = 0.06(0.8x), and h(x) = f(x) + g(x);

AR.3.F: : The student is expected to: compare and contrast a function and possible functions that can be used to build it tabularly, graphically, and symbolically such as a quadratic function that results from multiplying two linear functions.

AR.4: : Number and algebraic methods. The student applies mathematical processes to simplify and perform operations on functions represented in a variety of ways, including real-world situations.

AR.4.A: : The student is expected to: connect tabular representations to symbolic representations when adding, subtracting, and multiplying polynomial functions arising from mathematical and real-world situations such as applications involving surface area and volume;

AR.4.D: : The student is expected to: determine the linear factors of a polynomial function of degree two and of degree three when represented symbolically and tabularly and graphically where appropriate.

AR.5: : Number and algebraic methods. The student applies mathematical processes to represent, simplify, and perform operations on matrices and to solve systems of equations using matrices.

AR.5.A: : The student is expected to: add and subtract matrices;

AR.5.C: : The student is expected to: multiply matrices by a scalar;

AR.5.D: : The student is expected to: represent and solve systems of two linear equations arising from mathematical and real-world situations using matrices.

AR.6: : Number and algebraic methods. The student applies mathematical processes to estimate and determine solutions to equations resulting from functions and real-world applications with fluency.

AR.6.A: : The student is expected to: estimate a reasonable input value that results in a given output value for a given function, including quadratic, rational, and exponential functions;

AR.6.B: : The student is expected to: solve equations arising from questions asked about functions that model real-world applications, including linear and quadratic functions, tabularly, graphically, and symbolically; and

AR.6.C: : The student is expected to: approximate solutions to equations arising from questions asked about exponential, logarithmic, square root, and cubic functions that model real-world applications tabularly and graphically.

AR.7: : Modeling from data. The student applies mathematical processes to analyze and model data based on real-world situations with corresponding functions.

AR.7.D: : The student is expected to: determine an appropriate function model, including linear, quadratic, and exponential functions, for a set of data arising from real-world situations using finite differences and average rates of change; and

AR.7.E: : The student is expected to: determine if a given linear function is a reasonable model for a set of data arising from a real-world situation.

Correlation last revised: 2/10/2025

Texas - Mathematics: Algebraic Reasoning

Essential Knowledge and Skills | Adopted: 2015