Find resources aligned to Texas Essential Knowledge and Skills (TEKS)

Bivariate data. The student applies the mathematical process standards to analyze relationships among bivariate quantitative data. The student is expected to:

analyze scatterplots for patterns, linearity, outliers, and influential points;

transform a linear parent function to determine a line of best fit;

compare different linear models for the same set of data to determine best fit, including discussions about error;

compare different methods for determining best fit, including median-median and absolute value;

describe the relationship between influential points and lines of best fit using dynamic graphing technology; and

identify and interpret the reasonableness of attributes of lines of best fit within the context, including slope and y-intercept.

Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

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

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;

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;

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

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

analyze mathematical relationships to connect and communicate mathematical ideas; and

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

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

classify a function as linear, quadratic, cubic, and exponential when a function is represented tabularly using finite differences or common ratios as appropriate;

determine the function that models a given table of related values using finite differences and its restricted domain and range; and

determine a function that models real-world data and mathematical contexts using finite differences such as the age of a tree and its circumference, figurative numbers, average velocity, and average acceleration.

Patterns and structure. The student applies mathematical processes to understand the connections among representations of functions and combinations of functions, including the constant function, \(f(x) = x\), \(f(x) = x^2\), \(f(x) = \sqrt{x}\), \(f(x) = 1/x\), \(f(x) = x^3\), \(f(x) = \sqrt[3]{x}\), \(f(x) = bx\), \(f(x) = |x|\), and \(f(x) = log_b (x)\) where \(b\) is 10 or \(e\); functions and their inverses; and key attributes of these functions. The student is expected to:

compare and contrast the key attributes, including domain, range, maxima, minima, and intercepts, of a set of functions such as a set comprised of a linear, a quadratic, and an exponential function or a set comprised of an absolute value, a quadratic, and a square root function tabularly, graphically, and symbolically;

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;

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;

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 \(h(x) = f(x) + g(x)\);

model a situation using function notation when the output of one function is the input of a second function such as determining a function \(h(x) = g(f(x)) = 1.06(0.8x)\) for the final purchase price, \(h(x)\) of an item with price \(x\) dollars representing a 20% discount, \(f(x) = 0.8x\) followed by a 6% sales tax, \(g(x) = 1.06x\); and

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.

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. 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;

compare and contrast the results when adding two linear functions and multiplying two linear functions that are represented tabularly, graphically, and symbolically;

determine the quotient of a polynomial function of degree three and of degree four when divided by a polynomial function of degree one and of degree two when represented tabularly and symbolically; and

determine the linear factors of a polynomial function of degree two and of degree three when represented symbolically and tabularly and graphically where appropriate.

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. The student is expected to:

add and subtract matrices;

multiply matrices;

multiply matrices by a scalar;

represent and solve systems of two linear equations arising from mathematical and real-world situations using matrices; and

represent and solve systems of three linear equations arising from mathematical and real-world situations using matrices and technology.

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. 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;

solve equations arising from questions asked about functions that model real-world applications, including linear and quadratic functions, tabularly, graphically, and symbolically; and

approximate solutions to equations arising from questions asked about exponential, logarithmic, square root, and cubic functions that model real-world applications tabularly and graphically.

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

represent domain and range of a function using interval notation, inequalities, and set (builder) notation;

compare and contrast between the mathematical and reasonable domain and range of functions modeling real-world situations, including linear, quadratic, exponential, and rational functions;

determine the accuracy of a prediction from a function that models a set of data compared to the actual data using comparisons between average rates of change and finite differences such as gathering data from an emptying tank and comparing the average rate of change of the volume or the second differences in the volume to key attributes of the given model;

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

determine if a given linear function is a reasonable model for a set of data arising from a real-world situation.

History. The student understands the development of the field of psychology. The student is expected to:

identify characteristics that differentiate the field of psychology from other related social sciences;