Texas homeschool hubGrade 8 · Mathematics
Grade 8 MathematicsTEKS Scope & Sequence
The Texas Essential Knowledge and Skills your grade 8 student covers in mathematics — the same standards state assessments and Texas curricula are built on.
TEKS scope & sequence
171 standardsStandards are ordered by STAAR priority — Readiness standards first, then Supporting, then the rest. Readiness standards carry the most weight on the state assessment.
ReadinessSupportingSTAAR-tested
| TEKS | Standard | STAAR |
|---|---|---|
| 8.10C | 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; | Readiness |
| 8.12D | write a formula for the nᵗʰ term of arithmetic and geometric sequences, given the value of several of their terms; and | Readiness |
| 8.2D | write and solve equations involving direct variation; | Readiness |
| 8.3C | 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 - y1 = m(x - x1); | Readiness |
| 8.4B | compare and contrast association and causation in real-world problems; and | Readiness |
| 8.4C | write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems. | Readiness |
| 8.5I | write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations. | Readiness |
| 8.7A | 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; | Readiness |
| 8.7B | describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions; and | Readiness |
| 8.7C | 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), and f(bx) for specific values of a, b, c, and d. | Readiness |
| 8.8C | model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants; | Readiness |
| 8.10A | add and subtract polynomials of degree one and degree two; | Supporting |
| 8.10B | multiply polynomials of degree one and degree two; | Supporting |
| 8.10D | rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property; | Supporting |
| 8.11A | simplify numerical radical expressions involving square roots; | Supporting |
| 8.11B | simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents. | Supporting |
| 8.12A | decide whether relations represented verbally, tabularly, graphically, and symbolically define a function; | Supporting |
| 8.12C | evaluate functions, expressed in function notation, given one or more elements in their domains; | Supporting |
| 8.12G | estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college. | Supporting |
| 8.2A | extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers; | Supporting |
| 8.2B | 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; | Supporting |
| 8.2C | write linear equations in two variables given a table of values, a graph, and a verbal description; | Supporting |
| 8.3A | use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line; | Supporting |
| 8.3B | graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; | Supporting |
| 8.4A | calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association; | Supporting |
| 8.5A | 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; | Supporting |
| 8.5B | 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; | Supporting |
| 8.5C | solve systems of two linear equations with two variables for mathematical and real-world problems. | Supporting |
| 8.5E | solve problems involving direct variation; | Supporting |
| 8.5H | identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; | Supporting |
| 8.6A | determine the domain and range of quadratic functions and represent the domain and range using inequalities; | Supporting |
| 8.6C | write quadratic functions when given real solutions and graphs of their related equations. | Supporting |
| 8.7D | determine the distance between two points on a coordinate plane using the Pythagorean Theorem. | Supporting |
| 8.8A | solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula; and | Supporting |
| 8.8B | write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems. | Supporting |
| 8.8D | use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. | Supporting |
| 8.9A | determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities; | Supporting |
| 8.1 | Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to: (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. | — |
| 8.10 | 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. The student is expected to: (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; (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. | — |
| 8.10 | 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. The student is expected to: (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. | — |
| 8.10 | Two-dimensional shapes. The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to: (A) generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane; (B) differentiate between transformations that preserve congruence and those that do not; (C) explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation; (D) model the effect on linear and area measurements of dilated two-dimensional shapes. | — |
| 8.10A | add and subtract polynomials of degree one and degree two; | — |
| 8.10A | generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane; | — |
| 8.10B | multiply polynomials of degree one and degree two; | — |
| 8.10B | differentiate between transformations that preserve congruence and those that do not; | — |
| 8.10C | 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; | — |
| 8.10D | rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property; | — |
| 8.10D | model the effect on linear and area measurements of dilated two-dimensional shapes. | — |
| 8.10E | factor, if possible, trinomials with real factors in the form ax² + bx + c, including perfect square trinomials of degree two; and | — |
| 8.10E | factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two; | — |
| 8.10F | 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. | — |
| 8.10F | 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. | — |
| 8.11 | Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to: (A) simplify numerical radical expressions involving square roots; (B) simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents. | — |
| 8.11 | Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms. The student is expected to: (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. | — |
| 8.11A | simplify numerical radical expressions involving square roots; and | — |
| 8.11B | simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents. | — |
| 8.11C | simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected. | — |
| 8.12 | Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to: (A) identify functions using sets of ordered pairs and mappings; (B) decide whether relations represented verbally, tabularly, graphically, and symbolically define a function; (C) evaluate functions, expressed in function notation, given one or more elements in their domains; (D) identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes; (E) write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms; (F) solve mathematic and scientific formulas, and other literal equations, for a specified variable. | — |
| 8.12 | Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions. The student is expected to: (A) decide whether relations represented verbally, tabularly, graphically, and symbolically define a function; (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 (E) solve mathematic and scientific formulas, and other literal equations, for a specified variable. | — |
| 8.12 | Personal financial literacy. The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor. The student is expected to: (A) solve real-world problems comparing how interest rate and loan length affect the cost of credit; (B) calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator; (C) explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time; (D) calculate and compare simple interest and compound interest earnings; (E) identify and explain the advantages and disadvantages of different payment methods; (F) analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility; (G) estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college. | — |
| 8.12A | identify functions using sets of ordered pairs and mappings; | — |
| 8.12B | decide whether relations represented verbally, tabularly, graphically, and symbolically define a function; | — |
| 8.12B | evaluate functions, expressed in function notation, given one or more elements in their domains; | — |
| 8.12C | identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes; | — |
| 8.12D | calculate and compare simple interest and compound interest earnings; | — |
| 8.12D | identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes; | — |
| 8.12E | solve mathematic and scientific formulas, and other literal equations, for a specified variable. | — |
| 8.12E | identify and explain the advantages and disadvantages of different payment methods; | — |
| 8.12E | write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms; | — |
| 8.12F | analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility; | — |
| 8.12F | solve mathematic and scientific formulas, and other literal equations, for a specified variable. | — |
| 8.1A | apply mathematics to problems arising in everyday life, society, and the workplace; | — |
| 8.1A | apply mathematics to problems arising in everyday life, society, and the workplace; | — |
| 8.1B | 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; | — |
| 8.1C | 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; | — |
| 8.1C | 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; | — |
| 8.1D | communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; | — |
| 8.1D | communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate; | — |
| 8.1E | create and use representations to organize, record, and communicate mathematical ideas; | — |
| 8.1E | create and use representations to organize, record, and communicate mathematical ideas; | — |
| 8.1F | analyze mathematical relationships to connect and communicate mathematical ideas; | — |
| 8.1F | analyze mathematical relationships to connect and communicate mathematical ideas; and | — |
| 8.1G | display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. | — |
| 8.1G | display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication. | — |
| 8.2 | Number and operations. The student applies mathematical process standards to represent and use real numbers in a variety of forms. The student is expected to: (A) extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers; (B) approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line; (C) convert between standard decimal notation and scientific notation; (D) order a set of real numbers arising from mathematical and real-world contexts. | — |
| 8.2 | 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. The student is expected to: (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. | — |
| 8.2 | 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. The student is expected to: (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; (I) write systems of two linear equations given a table of values, a graph, and a verbal description. | — |
| 8.2A | 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; | — |
| 8.2A | 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; | — |
| 8.2B | 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; | — |
| 8.2B | approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line; | — |
| 8.2C | write linear equations in two variables given a table of values, a graph, and a verbal description; | — |
| 8.2D | write and solve equations involving direct variation; | — |
| 8.2E | write the equation of a line that contains a given point and is parallel to a given line; | — |
| 8.2E | write the equation of a line that contains a given point and is parallel to a given line; | — |
| 8.2F | write the equation of a line that contains a given point and is perpendicular to a given line; | — |
| 8.2F | write the equation of a line that contains a given point and is perpendicular to a given line; | — |
| 8.2G | 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; | — |
| 8.2G | 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; | — |
| 8.2H | write linear inequalities in two variables given a table of values, a graph, and a verbal description; | — |
| 8.2H | write linear inequalities in two variables given a table of values, a graph, and a verbal description; and | — |
| 8.2I | write systems of two linear equations given a table of values, a graph, and a verbal description. | — |
| 8.2I | write systems of two linear equations given a table of values, a graph, and a verbal description. | — |
| 8.3 | 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. The student is expected to: (A) use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line; (B) graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; (C) 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 - y1 = m(x - x1); (D) calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems; (E) use data from a table or graph to determine the rate of change or slope and y -intercept in mathematical and real-world problems; (F) 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; (G) graph the solution set of linear inequalities in two variables on the coordinate plane; (H) 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), and f(bx) for specific values of a, b, c, and d; (I) graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist; (J) estimate graphically the solutions to systems of two linear equations with two variables in real-world problems; (K) graph the solution set of systems of two linear inequalities in two variables on the coordinate plane. | — |
| 8.3 | 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. The student is expected to: (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 = C, 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. | — |
| 8.3A | generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation; | — |
| 8.3A | 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 - y₁ = m(x - x₁); | — |
| 8.3B | calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems; | — |
| 8.3B | compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; | — |
| 8.3C | 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; | — |
| 8.3D | graph the solution set of linear inequalities in two variables on the coordinate plane; | — |
| 8.3D | calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems; | — |
| 8.3E | use data from a table or graph to determine the rate of change or slope and y -intercept in mathematical and real-world problems; | — |
| 8.3E | 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; | — |
| 8.3F | 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; | — |
| 8.3F | graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist; | — |
| 8.3G | graph the solution set of linear inequalities in two variables on the coordinate plane; | — |
| 8.3G | estimate graphically the solutions to systems of two linear equations with two variables in real-world problems; and | — |
| 8.3H | 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), and f(bx) for specific values of a, b, c, and d; | — |
| 8.3H | graph the solution set of systems of two linear inequalities in two variables on the coordinate plane. | — |
| 8.3I | graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist; | — |
| 8.3J | estimate graphically the solutions to systems of two linear equations with two variables in real-world problems; | — |
| 8.3K | graph the solution set of systems of two linear inequalities in two variables on the coordinate plane. | — |
| 8.4 | 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. The student is expected to: (A) construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data; (B) contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation; (C) use a trend line that approximates the linear relationship between bivariate sets of data to make predictions; (D) calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association; (E) compare and contrast association and causation in real-world problems; (F) write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems. | — |
| 8.4 | 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. The student is expected to: (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. | — |
| 8.4A | construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data; | — |
| 8.4B | graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; | — |
| 8.4B | contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation; | — |
| 8.4C | use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems. | — |
| 8.4C | use a trend line that approximates the linear relationship between bivariate sets of data to make predictions; | — |
| 8.4D | calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association; | — |
| 8.4E | compare and contrast association and causation in real-world problems; | — |
| 8.4F | write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems. | — |
| 8.5 | 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. The student is expected to: (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; (C) solve systems of two linear equations with two variables for mathematical and real -world problems. | — |
| 8.5 | 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. The student is expected to: (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. | — |
| 8.5A | 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; | — |
| 8.5B | 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 | — |
| 8.5C | solve systems of two linear equations with two variables for mathematical and real -world problems. | — |
| 8.5C | contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation; | — |
| 8.6 | 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. The student is expected to: (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. | — |
| 8.6 | 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. The student is expected to: (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); (C) write quadratic functions when given real solutions and graphs of their related equations. | — |
| 8.6 | Expressions, equations, and relationships. The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas. The student is expected to: (A) describe the volume formula V = Bh of a cylinder in terms of its base area and its height; (B) model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas; (C) use models and diagrams to explain the Pythagorean theorem. | — |
| 8.6A | determine the domain and range of quadratic functions and represent the domain and range using inequalities; | — |
| 8.6B | 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 | — |
| 8.6B | 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); | — |
| 8.6C | write quadratic functions when given real solutions and graphs of their related equations. | — |
| 8.7 | Expressions, equations, and relationships. The student applies mathematical process standards to use geometry to solve problems. The student is expected to: (A) solve problems involving the volume of cylinders, cones, and spheres; (B) use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders; (C) use the Pythagorean Theorem and its converse to solve problems; (D) determine the distance between two points on a coordinate plane using the Pythagorean Theorem. | — |
| 8.7 | 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. The student is expected to: (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; (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), and f(bx) for specific values of a, b, c, and d. | — |
| 8.7 | 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. The student is expected to: (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. | — |
| 8.7A | 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; | — |
| 8.7B | describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions; | — |
| 8.7C | 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. | — |
| 8.7C | use the Pythagorean Theorem and its converse to solve problems; | — |
| 8.8 | 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. The student is expected to: (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. | — |
| 8.8 | 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. The student is expected to: (A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula; (B) write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems. | — |
| 8.8A | write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants; | — |
| 8.8A | solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula; | — |
| 8.8B | write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems. | — |
| 8.9 | 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. The student is expected to: (A) determine the domain and range of exponential functions of the form f(x) = abˣ 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) = abˣ in real-world problems; (C) write exponential functions in the form f(x) = abˣ (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. | — |
| 8.9 | Expressions, equations, and relationships. The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to: (A) identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations. | — |
| 8.9 | 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. The student is expected to: (A) determine the domain and range of exponential functions of the form f(x) = abx 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) = abx in real-world problems; (C) write exponential functions in the form f(x) = abx (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; (E) write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems. | — |
| 8.9A | identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations. | — |
| 8.9A | determine the domain and range of exponential functions of the form f(x) = abˣ and represent the domain and range using inequalities; | — |
| 8.9B | interpret the meaning of the values of a and b in exponential functions of the form f (x) = abx in real-world problems; | — |
| 8.9B | interpret the meaning of the values of a and b in exponential functions of the form f(x) = abˣ in real-world problems; | — |
| 8.9C | write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay; | — |
| 8.9C | write exponential functions in the form f(x) = abˣ (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay; | — |
| 8.9D | graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems; and | — |
| 8.9D | graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems; | — |
| 8.9E | write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems. | — |
| 8.9E | write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems. | — |