Grades
Standard
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units [...]
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their [...]
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases [...]
Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs [...]
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such [...]
Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a [...]
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope [...]
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in [...]
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function [...]
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [...]
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give [...]
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of [...]
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, [...]
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those [...]
Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a [...]
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when [...]
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and [...]
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for [...]
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line [...]
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^(–5) = 3^(–3) [...]
Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 [...]
Verify experimentally the properties of rotations, reflections, and translations:
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large [...]
Lines are taken to lines, and line segments to line segments of the same length.
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific [...]
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in [...]
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical [...]
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a [...]
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the [...]
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about [...]
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of [...]
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its [...]
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; [...]
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of [...]
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For [...]
Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for [...]
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the [...]
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how [...]
Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described [...]
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and [...]
Grades
Standard
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units [...]
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their [...]
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases [...]
Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs [...]
Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such [...]
Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a [...]
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope [...]
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in [...]
Understand that a function is a rule that assigns to each input exactly one output. The graph of a function [...]
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [...]
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give [...]
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of [...]
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, [...]
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those [...]
Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a [...]
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when [...]
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and [...]
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Know the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for [...]
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line [...]
Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3^2 × 3^(–5) = 3^(–3) [...]
Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 [...]
Verify experimentally the properties of rotations, reflections, and translations:
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large [...]
Lines are taken to lines, and line segments to line segments of the same length.
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific [...]
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in [...]
Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical [...]
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a [...]
Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the [...]
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about [...]
Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of [...]
Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its [...]
Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; [...]
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of [...]
Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For [...]
Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for [...]
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the [...]
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how [...]
Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described [...]
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and [...]