Grades
Standard
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 [...]
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an [...]
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units [...]
Verify experimentally the properties of rotations, reflections, and translations:
Lines are taken to lines, and line segments to line segments of the same length.
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a [...]
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 [...]
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large [...]
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 [...]
Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for [...]
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how [...]
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and [...]
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems [...]
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, [...]
Solve word problems leading to inequalities of the form px + q > r or px + q < r, [...]
Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations [...]
Use random sampling to draw inferences about a population. Use data from a random sample to draw inferences about 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; [...]
Grades
Standard
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 [...]
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Explain why the sum or product of rational numbers is rational; that the sum of a rational number and an [...]
Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units [...]
Verify experimentally the properties of rotations, reflections, and translations:
Lines are taken to lines, and line segments to line segments of the same length.
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a [...]
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 [...]
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large [...]
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 [...]
Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for [...]
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how [...]
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and [...]
Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems [...]
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, [...]
Solve word problems leading to inequalities of the form px + q > r or px + q < r, [...]
Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations [...]
Use random sampling to draw inferences about a population. Use data from a random sample to draw inferences about 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; [...]
