Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals.
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.
| Standard | Definition | Code |
|---|---|---|
| Display perseverance and patience in problem-solving | Display perseverance and patience in problem-solving. Demonstrate skills and strategies needed to succeed in mathematics, including critical thinking, reasoning, and effective collaboration and expression. Seek help and apply feedback. Set and monitor goals. | 8.MP |
| Make sense of problems and persevere in solving them | Make sense of problems and persevere in solving them. | 8.MP.1 |
| Reason abstractly and quantitatively | Reason abstractly and quantitatively. | 8.MP.2 |
| Construct viable arguments and critique the reasoning of others | Construct viable arguments and critique the reasoning of others. | 8.MP.3 |
| Model with mathematics | Model with mathematics. | 8.MP.4 |
| Use appropriate tools strategically | Use appropriate tools strategically. | 8.MP.5 |
| Attend to precision | Attend to precision. | 8.MP.6 |
| Look for and make use of structure | Look for and make use of structure. | 8.MP.7 |
| Look for and express regularity in repeated reasoning | Look for and express regularity in repeated reasoning. | 8.MP.8 |
All rational numbers
Scientific notation
Numerical expressions with integer exponents
Use appropriate counting strategies to approximate rational and irrational numbers (radicals) on a number line
Operations with scientific notation
Scientific notation in real situations seen in everyday life
Expressions with integer exponents
Rational and irrational numbers (radicals)
Compare proportional relationships presented in different ways
Integer exponents
Perfect squares and perfect cubes
Expressions with integer exponents
Linear expressions
Operations with algebraic expressions
Analyze and solve linear equations and inequalities
Interpret unit rate as the slope of a graph
Linear functions
Comparing linear and non-linear functions
Systems of linear equations (including parallel and perpendicular)
Linear inequalities
Analyze data distributions
Linear functions
Line of best fit
Introduction to Pythagorean Theorem and the converse
Pythagorean Theorem to determine distance between two points
Volume of cones, cylinders, and spheres
| Standard | Definition | Code |
|---|---|---|
| All rational numbers | All rational numbers | 8.LP5.1.1 |
| Scientific notation | Scientific notation | 8.LP5.1.2 |
| Numerical expressions with integer exponents | Numerical expressions with integer exponents | 8.LP5.1.3 |
| Use appropriate counting strategies to approximate rational and irrational… | Use appropriate counting strategies to approximate rational and irrational numbers (radicals) on a number line | 8.LP5.1.4 |
| Operations with scientific notation | Operations with scientific notation | 8.LP5.2.1 |
| Scientific notation in real situations seen in everyday life | Scientific notation in real situations seen in everyday life | 8.LP5.2.2 |
| Expressions with integer exponents | Expressions with integer exponents | 8.LP5.2.3 |
| Rational and irrational numbers | Rational and irrational numbers (radicals) | 8.LP5.3.1 |
| Compare proportional relationships presented in different ways | Compare proportional relationships presented in different ways | 8.LP5.3.2 |
| Integer exponents | Integer exponents | 8.LP6.1.1 |
| Perfect squares and perfect cubes | Perfect squares and perfect cubes | 8.LP6.1.2 |
| Expressions with integer exponents | Expressions with integer exponents | 8.LP6.2.1 |
| Linear expressions | Linear expressions | 8.LP6.2.2 |
| Operations with algebraic expressions | Operations with algebraic expressions | 8.LP6.2.3 |
| Analyze and solve linear equations and inequalities | Analyze and solve linear equations and inequalities | 8.LP6.3.1 |
| Interpret unit rate as the slope of a graph | Interpret unit rate as the slope of a graph | 8.LP6.4.1 |
| Linear functions | Linear functions | 8.LP6.6.1 |
| Comparing linear and non-linear functions | Comparing linear and non-linear functions | 8.LP6.6.2 |
| Systems of linear equations | Systems of linear equations (including parallel and perpendicular) | 8.LP6.6.3 |
| Linear inequalities | Linear inequalities | 8.LP6.6.4 |
| Analyze data distributions | Analyze data distributions | 8.LP6.6.5 |
| Linear functions | Linear functions | 8.LP7.1.1 |
| Line of best fit | Line of best fit | 8.LP7.1.2 |
| Introduction to Pythagorean Theorem and the converse | Introduction to Pythagorean Theorem and the converse | 8.LP8.1.1 |
| Pythagorean Theorem to determine distance between two points | Pythagorean Theorem to determine distance between two points | 8.LP8.2.1 |
| Volume of cones, cylinders | Volume of cones, cylinders, and spheres | 8.LP8.2.2 |
Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.
Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.
Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.
Solve problems involving radicals and integer exponents including relevant application situations; apply place value understanding with scientific notation and use scientific notation to explain real phenomena.
Apply the properties of integer exponents to generate equivalent numerical expressions.
Use square root and cube root symbols to represent solutions to equations. Recognize that x^ 2 = p (where p is a positive rational number and |x| ≤ 25) has two solutions and x^3 = p (where p is a negative or positive rational number and |x| ≤ 10) has one solution. Evaluate square roots of perfect squares ≤ 625 and cube roots of perfect cubes ≥ -1000 and ≤ 1000.
Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other.
Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology (e.g., calculators or online technology tools).
| Standard | Definition | Code |
|---|---|---|
| Solve problems involving irrational numbers and rational approximations of… | Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications. | 8.NR.1 |
| Distinguish between rational and irrational numbers using decimal expansion | Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number. | 8.NR.1.1 |
| Approximate irrational numbers to compare the size of irrational numbers… | Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions. | 8.NR.1.2 |
| Solve problems involving radicals and integer exponents including relevant… | Solve problems involving radicals and integer exponents including relevant application situations; apply place value understanding with scientific notation and use scientific notation to explain real phenomena. | 8.NR.2 |
| Apply the properties of integer exponents to generate equivalent numerical… | Apply the properties of integer exponents to generate equivalent numerical expressions. | 8.NR.2.1 |
| Use square root and cube root symbols to represent solutions to equations | Use square root and cube root symbols to represent solutions to equations. Recognize that x^ 2 = p (where p is a positive rational number and |x| ≤ 25) has two solutions and x^3 = p (where p is a negative or positive rational number and |x| ≤ 10) has one solution. Evaluate square roots of perfect squares ≤ 625 and cube roots of perfect cubes ≥ -1000 and ≤ 1000. | 8.NR.2.2 |
| Use numbers expressed in scientific notation to estimate very large or very… | Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other. | 8.NR.2.3 |
| Add, subtract, multiply and divide numbers expressed in scientific notation… | Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology (e.g., calculators or online technology tools). | 8.NR.2.4 |
Create and interpret expressions within relevant situations. Create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real phenomena.
Interpret expressions and parts of an expression, in context, by utilizing formulas or expressions with multiple terms and/or factors.
Describe and solve linear equations in one variable with one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b). Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Create and solve linear equations and inequalities in one variable within a relevant application.
Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.
Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solution based on the contextual, mathematical situation.
Use algebraic reasoning to fluently manipulate linear and literal equations expressed in various forms to solve relevant, mathematical problems.
Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph.
Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for a line intersecting the vertical axis at b.
Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane.
Create and solve linear equations and inequalities in one variable within a relevant application.
| Standard | Definition | Code |
|---|---|---|
| Create and interpret expressions within relevant situations | Create and interpret expressions within relevant situations. Create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real phenomena. | 8.PAR.3 |
| Interpret expressions and parts of an expression, in context, by utilizing… | Interpret expressions and parts of an expression, in context, by utilizing formulas or expressions with multiple terms and/or factors. | 8.PAR.3.1 |
| Describe and solve linear equations in one variable with one solution | Describe and solve linear equations in one variable with one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b). Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers). | 8.PAR.3.2 |
| Create and solve linear equations and inequalities in one variable within a… | Create and solve linear equations and inequalities in one variable within a relevant application. | 8.PAR.3..3 |
| Using algebraic properties and the properties of real numbers, justify the… | Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality. | 8.PAR.3.4 |
| Solve linear equations and inequalities in one variable with coefficients… | Solve linear equations and inequalities in one variable with coefficients represented by letters and explain the solution based on the contextual, mathematical situation. | 8.PAR.3.5 |
| Use algebraic reasoning to fluently manipulate linear and literal equations… | Use algebraic reasoning to fluently manipulate linear and literal equations expressed in various forms to solve relevant, mathematical problems. | 8.PAR.3.6 |
| Show and explain the connections between proportional and non-proportional… | Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph. | 8.PAR.4 |
| Use the equation y = mx | Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for a line intersecting the vertical axis at b. | 8.PAR.4.1 |
| Show and explain that the graph of an equation representing an applicable… | Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane. | 8.PAR.4.2 |
| Create and solve linear equations and inequalities in one variable within a… | Create and solve linear equations and inequalities in one variable within a relevant application. | 8.PAR.3.3 |
Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.
Show and explain that a function is a rule that assigns to each input exactly one output.
Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.
Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y − y1 ) = m(x − x1 ) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.
Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph.
Explain the meaning of the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.
Solve practical, linear problems involving situations using bivariate quantitative data.
Show that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, visually fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line of best fit.
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercepts.
Explain the meaning of the predicted slope (rate of change) and the predicted intercept (constant term) of a linear model in the context of the data.
Use appropriate graphical displays from data distributions involving lines of best fit to draw informal inferences and answer the statistical investigative question posed in an unbiased statistical study.
Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena.
Interpret and solve relevant mathematical problems leading to two linear equations in two variables.
Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of intersection satisfy both equations simultaneously.
Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.
Create and compare the equations of two lines that are either parallel to each other, perpendicular to each other, or neither parallel nor perpendicular.
Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection
| Standard | Definition | Code |
|---|---|---|
| Describe the properties of functions to define, evaluate | Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena. | 8.FGR.5 |
| Show and explain that a function is a rule that assigns to each input exactly… | Show and explain that a function is a rule that assigns to each input exactly one output. | 8.FGR.5.1 |
| Within realistic situations, identify and describe examples of functions that… | Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally. | 8.FGR.5.2 |
| Relate the domain of a linear function to its graph and where applicable to the… | Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes. | 8.FGR.5.3 |
| Compare properties (rate of change and initial value) of two functions used to… | Compare properties (rate of change and initial value) of two functions used to model an authentic situation each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). | 8.FGR.5.4 |
| Write and explain the equations y = mx + b | Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y − y1 ) = m(x − x1 ) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function. | 8.FGR.5.5 |
| Write a linear function defined by an expression in different but equivalent… | Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. | 8.FGR.5.6 |
| Construct a function to model a linear relationship between two quantities | Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. | 8.FGR.5.7 |
| Explain the meaning of the rate of change and initial value of a linear… | Explain the meaning of the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. | 8.FGR.5.8 |
| Graph and analyze linear functions expressed in various algebraic forms and… | Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations. | 8.FGR.5.9 |
| Solve practical, linear problems involving situations using bivariate… | Solve practical, linear problems involving situations using bivariate quantitative data. | 8.FGR.6 |
| Show that straight lines are widely used to model relationships between two… | Show that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, visually fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line of best fit. | 8.FGR.6.1 |
| Use the equation of a linear model to solve problems in the context of… | Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercepts. | 8.FGR.6.2 |
| Explain the meaning of the predicted slope | Explain the meaning of the predicted slope (rate of change) and the predicted intercept (constant term) of a linear model in the context of the data. | 8.FGR.6.3 |
| Use appropriate graphical displays from data distributions involving lines of… | Use appropriate graphical displays from data distributions involving lines of best fit to draw informal inferences and answer the statistical investigative question posed in an unbiased statistical study. | 8.FGR.6.4 |
| Justify and use various strategies to solve systems of linear equations to… | Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena. | 8.FGR.7 |
| Interpret and solve relevant mathematical problems leading to two linear… | Interpret and solve relevant mathematical problems leading to two linear equations in two variables. | 8.FGR.7.1 |
| Show and explain that solutions to a system of two linear equations in two… | Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of intersection satisfy both equations simultaneously. | 8.FGR.7.2 |
| Analyze and solve systems of two linear equations in two variables… | Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions. | 8.FGR.7.4 |
| Create and compare the equations of two lines that are either parallel to each… | Create and compare the equations of two lines that are either parallel to each other, perpendicular to each other, or neither parallel nor perpendicular. | 8.FGR.7.5 |
| Approximate solutions of two linear equations in two variables by graphing the… | Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection | 8.FGR.7.3 |
Solve contextual, geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena.
Explain a proof of the Pythagorean Theorem and its converse using visual models.
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions.
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems.
Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.
| Standard | Definition | Code |
|---|---|---|
| Solve contextual, geometric problems involving the Pythagorean Theorem and the… | Solve contextual, geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena. | 8.GSR.8 |
| Explain a proof of the Pythagorean Theorem and its converse using visual models | Explain a proof of the Pythagorean Theorem and its converse using visual models. | 8.GSR.8.1 |
| Apply the Pythagorean Theorem to determine unknown side lengths in right… | Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions. | 8.GSR.8.2 |
| Apply the Pythagorean Theorem to find the distance between two points in a… | Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems. | 8.GSR.8.3 |
| Apply the formulas for the volume of cones, cylinders | Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems. | 8.GSR.8.4 |