Grade 8 Math GSE Standards

Number and algebraic methods

Exponential functions and equations

Quadratic functions and equations

Linear functions, equations, and inequalities

Mathematical process standards.

The student uses mathematical processes to acquire and demonstrate mathematical understanding

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

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

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

add and subtract polynomials of degree one and degree two

multiply polynomials of degree one and degree two

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

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

factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two

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

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

simplify numerical radical expressions involving square roots

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

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

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

evaluate functions, expressed in function notation, given one or more elements in their domains

identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes

write a formula for the nth term of arithmetic and geometric sequences, given the value of several of their terms

solve mathematic and scientific formulas, and other literal equations, for a specified variable

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

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

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

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

write and solve equations involving direct variation

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

compare and contrast association and causation in real-world problems

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

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

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

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

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

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

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

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)

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

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

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

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

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

solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula

write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems

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

determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities

interpret the meaning of the values of a and b in exponential functions of the form f(x) = abx in real-world problems

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

graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems;

write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems

Personal financial literacy

Measurement and data

Two-dimensional shapes

Expressions, equations, and relationships

Proportionality

Mathematical process standards

The student uses mathematical processes to acquire and demonstrate mathematical understanding

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

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

The student applies mathematical process standards to develop transformational geometry concepts

generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane

differentiate between transformations that preserve congruence and those that do not

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

model the effect on linear and area measurements of dilated two-dimensional shapes

The student applies mathematical process standards to use statistical procedures to describe data

construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data

determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points

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

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

solve real-world problems comparing how interest rate and loan length affect the cost of credit

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

explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time

calculate and compare simple interest and compound interest earnings

identify and explain the advantages and disadvantages of different payment methods

analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility

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

The student applies mathematical process standards to represent and use real numbers in a variety of forms

Number and operations

extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers

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

convert between standard decimal notation and scientific notation

order a set of real numbers arising from mathematical and real-world contexts

The student applies mathematical process standards to use proportional relationships to describe dilations

generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation

compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane

use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation

The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope

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

graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship

use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems

The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions

represent linear proportional situations with tables, graphs, and equations in the form of y = kx

represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

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

use a trend line that approximates the linear relationship between bivariate sets of data to make predictions

solve problems involving direct variation

distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0

identify functions using sets of ordered pairs, tables, mappings, and graphs

identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems

write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations

The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas

describe the volume formula V = Bh of a cylinder in terms of its base area and its height

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

use models and diagrams to explain the Pythagorean theorem

The student applies mathematical process standards to use geometry to solve problems

solve problems involving the volume of cylinders, cones, and spheres

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

use the Pythagorean Theorem and its converse to solve problems

determine the distance between two points on a coordinate plane using the Pythagorean Theorem

The student applies mathematical process standards to use one-variable equations or inequalities in problem situations

write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants

write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants

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

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

The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations. The student is expected to 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