Grade 8 Math IAS Standards

Data Analysis, Statistics, and Probability

Geometry and Measurement

Algebra and Functions

Number Sense

Mathematics Process Standards

Students understand the formal definition of a function, analyze linear functions in multiple representations, and differentiate between linear and nonlinear functions. Students also solve a system of linear equations in two unknowns.

Solve linear equations and inequalities with rational number coefficients fluently, including those whose solutions require expanding expressions using the distributive property and collecting like terms. Represent real-world problems using linear equations and inequalities in one variable and solve such problems.

Solve linear equations and inequalities with rational number coefficients fluently, including those whose solutions require expanding expressions using the distributive property and collecting like terms. Represent real-world problems using linear equations and inequalities in one variable and solve such problems. (E)

Solve two- or three-step one-variable linear equations and inequalities. Limit to combining like terms or variables on both sides (e.g., 4x+3=2x+11 or 2x+4x+5=23).

Generate linear equations in one variable with one solution, infinitely many solutions, or no solutions. Justify the classification given.

Generate linear equations in one variable with one solution, infinitely many solutions, or no solutions. Justify the classification given.

Identify when the solution set to a linear equation has one solution, infinitely many solutions, or no solutions.

Understand that a function assigns to each x-value (independent variable) exactly one y-value (dependent variable), and that the graph of a function is the set of ordered pairs <em>(x,y)</em>.

Understand that a function assigns to each x-value (independent variable) exactly one y-value (dependent variable), and that the graph of a function is the set of ordered pairs (x,y).

Identify if a relation represented in a table or graph is a function or not a function based on the independent (x-values) and dependent (y-values) variables.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative features of a function that has been verbally described.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative features of a function that has been verbally described. (E)

Given a graph of a function, identify where the function is increasing or decreasing, if it is linear or nonlinear, and identify a maximum or minimum value. Given a verbal description of a situation, sketch the graph that could represent the situation.

Interpret the equation <em>y = mx + b</em> as defining a linear function whose graph is a straight line; give examples of functions that are not linear. Describe similarities and differences between linear and nonlinear functions from tables, graphs, verbal descriptions, and equations.

Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. Describe similarities and differences between linear and nonlinear functions from tables, graphs, verbal descriptions, and equations.

Given a table or a graph identify a situation as linear or nonlinear. Describe similarities and differences between linear and nonlinear graphs. (E)

Construct a function to model a linear relationship between two quantities given a verbal description, table of values, or graph. Within the context of a problem, describe the meaning of m (rate of change) and <em>b (y</em>-intercept) in <em>y = mx + b</em>.

Construct a function to model a linear relationship between two quantities given a verbal description, table of values, or graph. Within the context of a problem, describe the meaning of m (rate of change) and b (y-intercept) in y = mx + b. (E)

Identify the slope (rate of change) and y-intercept (initial value), and the linear equation in the form of y = mx + b from a graph of a realistic situation. Within the context of a problem, describe the meaning of m (rate of change) and b (y-intercept). (E)

Compare properties of two linear functions given in different forms, such as a table of values, equation, verbal description, and graph (e.g., compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed).

Compare properties of two linear functions given in different forms, such as a table of values, equation, verbal description, and graph (e.g., compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed).

Given a table, graph, or equation compare two linear functions by using the slope (rate of change). (E)

Approximate the solution of a system of equations by graphing and interpreting the reasonableness of the approximation.

Approximate the solution of a system of equations by graphing and interpreting the reasonableness of the approximation. (E)

Identify the solution to a system of linear equations by graphing. (E)

Students begin to investigate and represent bivariate data using scatter plots.They build on their experience with univariate data. Students also build on the probability work in grade seven to examine and represent the probability and compound events.

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantitative variables. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantitative variables. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Graph bivariate data using a scatter plot. Given a scatter plot identify a positive or negative association, clustering and points that are outliers.

Write and use equations that model linear relationships to make predictions, including interpolation and extrapolation, in real-world situations involving bivariate measurement data. Interpret the slope and y-intercept in context.

Write and use equations that model linear relationships to make predictions, including interpolation and extrapolation, in real-world situations involving bivariate measurement data. Interpret the slope and y-intercept in context. (E)

Make predictions in real-world situations involving bivariate data when provided the line of best fit. (E)

Represent sample spaces and find probabilities of compound events (independent and dependent) using organized lists, tables, and tree diagrams.

Represent sample spaces and find probabilities of compound events (independent and dependent) using organized lists, tables, and tree diagrams.(E)

Determine the theoretical probability of a two-stage compound event (e.g., one roll of a die, one spin of a spinner)

Define the probability of a compound event, just as with simple events, as the fraction of outcomes in the sample space for which the compound event occurs. Use appropriate terminology to describe independent, dependent, complementary, and mutually exclusive events.

Define the probability of a compound event, just as with simple events, as the fraction of outcomes in the sample space for which the compound event occurs. Use appropriate terminology to describe independent, dependent, complementary, and mutually exclusive events. (E)

Determine if a compound probability event is dependent or independent. (E)

For events with a large number of outcomes, understand the use of the multiplication counting principle. Develop the multiplication counting principle, and apply it to situations with a large number of outcomes.

For events with a large number of outcomes, understand the use of the multiplication counting principle. Develop the multiplication counting principle, and apply it to situations with a large number of outcomes.

Determine the total number of outcomes by using the multiplication counting principle. (E)

Students explore transformations in the coordinate plane and are also expected to understand and explain the Pythagorean Theorem, its converse, and to use this relationship to solve problems and find distance on the coordinate plane.

Explore dilations, translations, rotations, and reflections on two-dimensional figures in the coordinate plane.

Explore dilations, translations, rotations, and reflections on two-dimensional figures in the coordinate plane. (E)

Given a graph of a two-dimensional figure that has undergone a single transformation in the coordinate plane, identify if the transformation is an example of a dilation, rotation, translation, and/or reflection.

Solve real-world and other mathematical problems involving volume of cones, spheres, and pyramids and surface area of spheres.

Solve real-world and other mathematical problems involving volume of cones, spheres, and pyramids and surface area of spheres. (E)

Find the volume of cones, spheres, and pyramids given the formulas for volume, a model, and all required measurements. (E)

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and other mathematical problems in two dimensions.

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and other mathematical problems in two dimensions. (E)

Apply the Pythagorean Theorem to find the hypotenuse of a right triangle. (E)

Students continue to deepen their understanding of rational and irrational numbers by explaining the differences between them and solving real-world problems.

Give examples of rational and irrational numbers, and explain the difference between them. State decimal equivalents for any number. For rational numbers, show that the decimal equivalent terminates or repeats, and convert a repeating decimal into a rational number.

Give examples of rational and irrational numbers, and explain the difference between them. State decimal equivalents for any number. For rational numbers, show that the decimal equivalent terminates or repeats, and convert a repeating decimal into a rational number.

Identify numbers as rational or irrational and explain the difference between them. (E)

Use rational approximations of irrational numbers to compare the size of irrational numbers, plot them approximately on a number line, and estimate the value of expressions involving irrational numbers.

Use rational approximations of irrational numbers to compare the size of irrational numbers, plot them approximately on a number line, and estimate the value of expressions involving irrational numbers.

Compare the value of two irrational numbers by plotting the rational approximate location on a number line.

Given a numeric expression with common rational number bases and integer exponents, apply the properties of exponents to generate equivalent expressions.

Given a numeric expression with common rational number bases and integer exponents, apply the properties of exponents to generate equivalent expressions. (E)

Use the property of exponents to create equivalent expressions with common integer bases and integer exponents limited to 5.

Solve real-world problems with rational numbers by using multiple operations.

Solve real-world problems with rational numbers by using multiple operations. (E)

Solve two-step real-world problems with positive rational numbers.(E)

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

Algebra and Functions

Data Analysis, Statistics, and Probability

Geometry and Measurement

Number Sense