High School Math Missouri Standards

Arithmetic with Polynomials and Rational Expressions

Perform operations on polynomials.

Add, subtract and multiply polynomials, and understand that polynomials follow the same general rules of arithmetic and are closed under these operations.

add polynomials

subtract polynomials

multiply polynomials

given a context, determine whether to add, subtract, or multiply polynomials

understand that polynomials follow the general rules of arithmetic

understand that polynomials are closed under the operation of addition

understand that polynomials are closed under the operation of subtraction

understand that polynomials are closed under the operation of multiplication

Divide polynomials by monomials.

divide polynomials by monomials

given a context, determine when to divide polynomials by monomials

Building Functions

Build new functions from existing functions (limited to linear, quadratic and exponential).

Analyze the effect of translations and scale changes on functions.

analyze the effect of translations on linear functions

analyze the effect of translations on quadratic functions

analyze the effect of translations on exponential functions

analyze the effect of scale changes on linear functions

analyze the effect of scale changes on quadratic functions

analyze the effect of scale changes on exponential functions

find the specific value of change (k) given before and after graphs of a translation

find the specific value of change (k) given before and after graphs of a scale change

Creating Equations

Create equations that describe linear, quadratic and exponential relationships.

Create equations and inequalities in one variable and use them to model and/or solve problems.

create linear equations in one variable

create linear inequalities in one variable

use linear equations in one variable to model problems

use linear equations in one variable to solve problems

use linear inequalities in one variable to model problems

use linear inequalities in one variable to solve problems

create quadratic equations in one variable

use quadratic equations in one variable to model problems

use quadratic equations in one variable to solve problems

create exponential equations in one variable

use exponential equations in one variable to model problems

use exponential equations in one variable to solve problems

Create and graph linear, quadratic and exponential equations in two variables.

create linear equations in two variables

create quadratic equations in two variables

create exponential equations in two variables

graph linear equations in two variables with labels and scales

graph quadratic equations in two variables with labels and scales

graph exponential equations in two variables with labels and scales

Represent constraints by equations or inequalities and by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context.

identify a system of equations

identify a system of inequalities

identify a system of mixed equations and inequalities

represent constraints by equations

represent constraints by inequalities

represent constraints by systems of equations

represent constraints by systems of inequalities

interpret data points as a solution to an equation in a modeling context

interpret data points as a solution to an inequality in a modeling context

interpret data points as a solution to a system of equations in a modeling context

interpret data points as a solution to a system of inequalities in a modeling context

interpret data points as a non-solution to an equation in a modeling context

interpret data points as a non-solution to an inequality in a modeling context

interpret data points as a non-solution to a system of equations in a modeling context

interpret data points as a non-solution to a system of inequalities in a modeling context

Solve literal equations and formulas for a specified variable that highlights a quantity of interest.

solve literal equations for a specified variable

solve literal formulas for a specified variable

in literal equations, determine which variable highlights a quantity of interest

in literal formulas, determine which variable highlights a quantity of interest

Data and Statistical Analysis

Summarize, represent and interpret data.

Analyze and interpret graphical displays of data.

analyze a dot plot

interpret a dot plot

analyze a histogram

interpret a histogram

analyze a box plot

interpret a box plot

Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.

determine statistics appropriate to the shape of a data distribution

use statistics appropriate to the shape of a data distribution to compare median of two or more different data sets

use statistics appropriate to the shape of a data distribution to compare mean of two or more different data sets

use statistics appropriate to the shape of a data distribution to compare mode of two or more different data sets

use statistics appropriate to the shape of a data distribution to compare interquartile range of two or more different data sets

use statistics appropriate to the shape of a data distribution to compare standard deviation of two or more different data sets

calculate statistics appropriate to the shape of a data distribution to compare standard deviation of two or more different data sets

Interpret differences in shape, center and spreads in the context of the data sets, accounting for possible effects of outliers.

identify differences in shape of up to three data sets

identify differences in center of up to three data sets

identify differences in spreads of up to three data sets

interpret differences in shape in the context of the data sets, accounting for possible effects of outliers

interpret differences in center in the context of the data sets, accounting for possible effects of outliers

interpret differences in spreads in the context of the data sets, accounting for possible effects of outliers

Summarize data in two-way frequency tables.

identify frequencies in the data in two-way frequency tables

interpret relative frequencies in the context of the data in a two-way frequency table

recognize possible associations in the data in a two-way frequency table

recognize possible trends in the data in a two-way frequency table

Construct a scatter plot of bivariate quantitative data describing how the variables are related; determine and use a function that models the relationship.

construct a scatter plot of bivariate quantitative data

use the scatter plot to determine the type of function that models the relationship

construct a linear function to model bivariate data on a scatter plot

minimize residuals using calculation

minimize residuals using technology

construct an exponential function to model bivariate data on a scatter plot

minimize residuals using calculation

minimize residuals using technology

Interpret the slope (rate of change) and the y-intercept (constant term) of a linear model in the context of the data.

identify the slope of a linear model

interpret the slope of a linear model as rate of change

interpret the slope of a linear model in the context of the data

identify the y-intercept of a linear model

interpret the y-intercept of a linear model as a constant term

interpret the y-intercept of a linear model in the context of the data

Determine and interpret the correlation coefficient for a linear association.

determine the correlation coefficient for a linear association

interpret the correlation coefficient for a linear association

Distinguish between correlation and causation.

distinguish between correlation and causation

distinguish between strong correlation and causation

Interpreting Functions

Understand the concept of a function and use function notation.

Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range.

understand domain

understand range

understand that a function assigns to each element of the domain exactly one element of the range

understand that f(x) denotes the elements of the range of a function f that correspond to the elements of the domain (x).

identify function notation

represent a function using function notation

understand that the input and output values of a function correspond to (x,y) values on the Cartesian coordinate plane

understand that the graph of a function labeled 𝑓 is the set of all ordered pairs (𝑥, y) that satisfy the equation 𝑦=f(𝑥)

graph an equation presented using functional notation

Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

use function notation to evaluate functions for inputs in their domains

interpret statements that use function notation in terms of a context

interpret statements involving inputs of a function in terms of a context

interpret statements involving outputs of a function in terms of context

solve problems presented in function notation

Interpret linear, quadratic and exponential functions in terms of the context.

Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities.

using tables, interpret key characteristics of a linear function that models the relationship between two quantities

using graphs, interpret key characteristics of a linear function that models the relationship between two quantities

using verbal descriptions, interpret key characteristics of a linear function that models the relationship between two quantities

using tables, interpret key characteristics of a quadratic function that models the relationship between two quantities

using graphs, interpret key characteristics of a quadratic function that models the relationship between two quantities

using verbal descriptions, interpret key characteristics of a quadratic function that models the relationship between two quantities

using tables, interpret key characteristics of an exponential function that models the relationship between two quantities

using graphs, interpret key characteristics of an exponential function that models the relationship between two quantities

using verbal descriptions, interpret key characteristics of an exponential function that models the relationship between two quantities

Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.

relate the domain of a linear function to its graph

relate the range of a linear function to its graph

describe how, within the context of a situation, the domain and range of a linear function affect the characteristics of the graph of the function

relate the domain of a quadratic function to its graph

relate the range of a quadratic function to its graph

describe how, within the context of a situation, the domain and range of a quadratic function affect the characteristics of the graph of the function

relate the domain of an exponential function to its graph

relate the range of an exponential function to its graph

describe how, within the context of a situation, the domain and range of an exponential function affect the characteristics of the graph of the function

Determine the average rate of change of a function over a specified interval and interpret the meaning.

determine the average rate of change of a linear function over a specified interval

interpret the meaning of the average rate of change of a linear function over a specified interval in a given context

determine the average rate of change of a quadratic function over a specified interval

interpret the meaning of the average rate of change of a quadratic function over a specified interval in a given context

determine the average rate of change of an exponential function over a specified interval

interpret the meaning of the average rate of change of an exponential function over a specified interval in a given context

Interpret the parameters of a linear or exponential function in terms of the context.

identify the parameters of a linear function

identify the parameters of an exponential function

interpret the parameters of a linear function in terms of the context

interpret the parameters of an exponential function in terms of the context

Analyze linear, quadratic and exponential functions using different representations.

Graph functions expressed symbolically and identify and interpret key features of the graph.

by hand, graph linear equations expressed symbolically

by hand, identify key features of the graph of a linear function

by hand, interpret key features of the graph of a linear function

by hand, graph quadratic equations expressed symbolically

by hand, identify key features of the graph of a quadratic function

by hand, interpret key features of the graph of a quadratic function

by hand, graph exponential equations expressed symbolically

by hand, identify key features of the graph of an exponential function

by hand, interpret key features of the graph of an exponential function

by hand, graph simple piecewise functions expressed symbolically

by hand, identify key features of the graph of a simple piecewise function

by hand, interpret key features of the graph of a simple piecewise function

using technology, graph linear equations expressed symbolically

using technology, identify key features of the graph of a linear function

using technology, interpret key features of the graph of a linear function

using technology, graph quadratic equations expressed symbolically

using technology, identify key features of the graph of a quadratic function

using technology, interpret key features of the graph of a quadratic function

using technology, graph exponential equations expressed symbolically

using technology, identify key features of the graph of an exponential function

using technology, interpret key features of the graph of an exponential function

using technology, graph simple piecewise functions expressed symbolically

using technology, identify key features of the graph of a simple piecewise function

using technology, interpret key features of the graph of a simple piecewise function

Translate between different but equivalent forms of a function to reveal and explain properties of the function and interpret these in terms of a context.

translate between different but equivalent forms of a linear function

use equivalent forms of a linear function to reveal properties of the function

use equivalent forms of a linear function to explain properties of the function

interpret different but equivalent forms of a linear function in terms of a context

translate between different but equivalent forms of a quadratic function

use equivalent forms of a quadratic function to reveal properties of the function

use equivalent forms of a quadratic function to explain properties of the function

interpret different but equivalent forms of a quadratic function in terms of a context

translate between different but equivalent forms of an exponential function

use equivalent forms of an exponential function to reveal properties of the function

use equivalent forms of an exponential function to explain properties of the function

interpret different but equivalent of an exponential function in terms of a context

Compare the properties of two functions given different representations.

compare the properties of two linear functions given different representations

compare the properties of two quadratic functions given different representations

compare the properties of two exponential functions given different representations

possible representations

function table

graph

equations in various forms

possible properties of linear functions

graph is a straight line

graph is not vertical

variables are raised to the 1st power

rate of change is constant

possible properties of quadratic functions

graph is a parabola

parabola opens up if coefficient a> 0

parabola opens down if coefficient a<0

coefficient a cannot be 0

coefficients a, b, and c are real numbers

the discriminant is b^2-4ac

variable is raised to the 2nd power

possible properties of exponential functions

graph crosses the y-axis at (0,1)

when b > 1, the graph increases

when 0 < b < 1, the graph decreases

the domain is all real numbers

the range is all positive real numbers

graph is asymptotic to the x-axis

compare the properties of a quadratic and an exponential function given different representations

compare the properties of a linear and an exponential function given different representations

compare the properties of a linear and a quadratic function given different representations

Linear, Quadratic, and Exponential Models

Construct and compare linear, quadratic and exponential models and solve problems.

Distinguish between situations that can be modeled with linear or exponential functions.

determine that linear functions change by equal differences over equal intervals

identify situations that can be modeled with linear functions

determine that exponential functions change by equal factors over equal intervals

determine that situations in which a quantity grows by a constant percent rate per unit interval are exponential functions

determine that situations in which a quantity decays by a constant percent rate per unit interval are exponential functions

identify situations that can be modeled with exponential functions

distinguish between situations that can be modeled with linear or exponential functions

Describe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

using a graph, describe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly

using a graph, describe that a quantity increasing exponentially eventually exceeds a quantity increasing quadratically

using a table, describe that a quantity increasing exponentially eventually exceeds a quantity increasing linearly

using a table, describe that a quantity increasing exponentially eventually exceeds a quantity increasing quadratically

Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.

construct a linear equation given a graph

construct a linear equation given a verbal description

construct a linear equation given a table

construct a quadratic equation given a graph

construct a quadratic equation given a verbal description

construct a quadratic equation given a table

construct an exponential equation given a graph

construct an exponential equation given a verbal description

construct an exponential equation given a table

given a graph, determine whether to construct a linear, quadratic, or exponential equation

given a verbal description, determine whether to construct a linear, quadratic, or exponential equation

given a table, determine whether to construct a linear, quadratic, or exponential equation

Use arithmetic and geometric sequences.

Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms.

determine whether a sequence is arithmetic or geometric

use arithmetic sequences in recursive form

use arithmetic sequences in explicit form

connect arithmetic sequences to linear functions

use geometric sequences in recursive form

use geometric sequences in explicit form

connect geometric sequences to exponential functions

write recursive form of an arithmetic sequence to model a situation given graphically

write recursive form of an arithmetic sequence to model a situation given by verbal description

write recursive form of an arithmetic sequence to model a situation given in a table

write explicit form of an arithmetic sequence to model a situation given graphically

write explicit form of an arithmetic sequence to model a situation given by verbal description

write explicit form of an arithmetic sequence to model a situation given in a table

write recursive form of a geometric sequence to model a situation given graphically

write recursive form of a geometric sequence to model a situation given by verbal description

write recursive form of a geometric sequence to model a situation given in a table

write explicit form of a geometric sequence to model a situation given graphically

write explicit form of a geometric sequence to model a situation given by verbal description

write explicit form of a geometric sequence to model a situation given in a table

translate between recursive and explicit forms of arithmetic sequences

translate between recursive and explicit forms of geometric sequences

model situations with arithmetic sequences

recognize

generate

model situations with geometric sequences

recognize

generate

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the set of integers.

recognize that arithmetic sequences are functions

recognize that arithmetic sequences are sometimes defined recursively

recognize that the domain of an arithmetic sequence is a subset of the set of integers

recognize that geometric sequences are functions

recognize that geometric sequences are sometimes defined recursively

recognize that the domain of a geometric sequence is a subset of the set of integers

Find the terms of sequences given an explicit or recursive formula.

find the terms of an arithmetic sequence given an explicit formula

find the terms of an arithmetic sequence given a recursive formula

find the terms of a geometric sequence given an explicit formula

find the terms of a geometric sequence given a recursive formula

Number and Quantity

Extend and use properties of rational exponents.

Explain how the meaning of rational exponents extends from the properties of integer exponents.

explain the meaning of rational exponents

identify the properties of integer exponents

product of powers property

power of a power property

power of a product property

quotient of powers property

power of a quotient property

zero power property

negative power property

explain how the meaning of rational exponents extends from the properties of integer exponents

Rewrite expressions involving radicals and rational exponents using the properties of exponents. Limit to rational exponents with a numerator of 1.

identify the properties of exponents

rewrite expressions involving radicals using the properties of exponents

rewrite expressions involving rational exponents (limit to a numerator of 1) using the properties of exponents

Use units to solve problems.

Use units of measure as a way to understand and solve problems involving quantities.

use units of measure as a way to understand problems involving quantities

use units of measure as a way to solve problems involving quantities

identify appropriate units of measure within a problem

label appropriate units of measure within a problem

use appropriate units of measure within a problem

convert units

convert rates

use units with problems

choose a scale in a graph

interpret the scale in a graph

choose an origin in a graph

interpret an origin in a graph

choose a scale in a data display

interpret the scale in a data display

choose an origin in a data display

interpret an origin in a data display

Define and use appropriate quantities for representing a given context or problem.

define appropriate quantities for representing a given context

define appropriate quantities for representing a given problem

use appropriate quantities for representing a given context

use appropriate quantities for representing a given problem

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

choose a level of accuracy appropriate to limitations on measurement when reporting quantities

Reasoning with Equations and Inequalities

Understand solving equations as a process, and solve equations and inequalities in one variable.

Explain how each step taken when solving an equation or inequality in one variable creates an equivalent equation or inequality that has the same solution(s) as the original.

explain how each step taken when solving an equation in one variable creates an equivalent equation that has the same solution(s) as the original

explain how each step taken when solving an inequality in one variable creates an equivalent inequality that has the same solution(s) as the original

Solve problems involving quadratic equations.

identify a quadratic equation

identify a quadratic expression

use the method of completing the square to create an equivalent quadratic equation

solve a standard quadratic equation for a certain value using the completing the square method

derive the quadratic formula from the standard quadratic equation

explain the relationship between the quadratic formula and the standard quadratic equation

analyze the factoring method of solving quadratic equations

solve quadratic equations using the factoring method

analyze the completing the square method of solving quadratic equations

solve quadratic equations using the completing the square method

analyze the quadratic formula method of solving quadratic equations

solve quadratic equations using the quadratic formula method

analyze the graphing method of solving quadratic equations

solve quadratic equations using the graphing method

determine when a quadratic equation has no real solution

determine the most efficient way to solve a given quadratic equation

Solve systems of equations.

Solve a system of linear equations algebraically and/or graphically.

identify a system of linear equations

solve a system of linear equations algebraically

solve a system of linear equations graphically

Solve a system consisting of a linear equation and a quadratic equation algebraically and/or graphically.

identify a system consisting of a linear equation and a quadratic equation

solve a system consisting of a linear equation and a quadratic equation algebraically

solve a system consisting of a linear equation and a quadratic equation graphically

Justify that the technique of linear combination produces an equivalent system of equations.

justify that the technique of linear combination produces an equivalent system of equations

identify when to use linear combination

Represent and solve linear and exponential equations and inequalities graphically

Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane.

explain that the graph of a linear equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane

explain that the graph of an exponential equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane

explain that any point not on the graph of a linear equation in the Cartesian coordinate plane is not a solution

explain that any point not on the graph of an exponential equation in the Cartesian coordinate plane is not a solution

Graph the solution to a linear inequality in two variables.

find the solution to a linear inequality in two variables

graph the solution to a linear inequality in two variables

Solve problems involving a system of linear inequalities.

identify a system of linear inequalities

solve problems involving a system of linear inequalities

given a context, interpret the solution to a system of linear inequalities

Seeing Structure in Expressions

Interpret and use structure

Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions.

interpret the contextual meaning of individual terms from a given problem that utilizes formulas

interpret the contextual meaning of individual factors from a given problem that utilizes formulas

interpret the contextual meaning of individual terms from a given problem that utilizes expressions

interpret the contextual meaning of individual factors from a given problem that utilizes expressions

interpret the meaning of individual terms based on the mathematics structures of a given problem that utilizes formulas

interpret the meaning of individual factors based on the mathematics structures of a given problem that utilizes formulas

interpret the meaning of individual terms based on the mathematics structures of a given problem that utilizes expressions

interpret the meaning of individual factors based on the mathematics structures of a given problem that utilizes expressions

Analyze the structure of polynomials to create equivalent expressions or equations.

identify a polynomial

analyze the structures of polynomials

factor a polynomial expression

factor a polynomial equation

analyze the structure of polynomials to determine an appropriate method for decomposing and composing to create equivalent expressions

analyze the structure of polynomials to determine an appropriate method for decomposing and composing to create equivalent equations

Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties.

identify a quadratic expression

identify a quadratic equation

choose equivalent forms of a quadratic expression to reveal properties

choose equivalent forms of a quadratic expression to explain properties

choose equivalent forms of a quadratic equation to reveal properties

choose equivalent forms of a quadratic equation to explain properties

produce equivalent forms of a quadratic expression to reveal properties

produce equivalent forms of a quadratic expression to explain properties

produce equivalent forms of a quadratic equation to reveal properties

produce equivalent forms of a quadratic equation to explain properties

factor a quadratic function

find the zeros of a quadratic function by rewriting it in factored form

find the maximum value of a quadratic function by completing the square

find the minimum value of a quadratic function by completing the square

understand that the vertex of an equation in the form y=a(x-h)2 + k is (h,k).

Arithmetic with Polynomials and Rational Expressions

Perform operations on polynomials and rational expressions.

Extend the knowledge of factoring to include factors with complex coefficients.

Understand the Remainder Theorem and use it to solve problems.

Find the least common multiple of two or more polynomials.

Add, subtract, multiply and divide rational expressions.

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.

Building Functions

Create new functions from existing functions.

Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).

Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.

Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections and dilations (expansions/compressions) for linear, quadratic, cubic, square and cube root, absolute value, exponential and logarithmic functions.

Data and Statistical Analysis

Make inferences and justify conclusions.

Analyze how random sampling could be used to make inferences about population parameters.

Determine whether a specified model is consistent with a given data set.

Describe and explain the purposes, relationship to randomization and differences among sample surveys, experiments and observational studies.

Use data from a sample to estimate characteristics of the population and recognize the meaning of the margin of error in these estimates.

Describe and explain how the relative sizes of a sample and the population affect the margin of error of predictions.

Analyze decisions and strategies using probability concepts.

Evaluate reports based on data.

Fit a data set to a normal distribution.

Know and use the characteristics of normally distributed data sets; predict what percentage of the data will be above or below a given value that is a multiple of standard deviations above or below the mean.

Fit a data set to a distribution using its mean and standard deviation to determine whether the data is approximately normally distributed.

Interpreting Functions

Use and interpret functions.

Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.

Translate between equivalent forms of functions.

Modeling

Use functions to model real-world problems.

Create functions and use them to solve applications of quadratic and exponential function model problems.

Number and Quantity

Extend and use the relationship between rational exponents and radicals.

Extend the system of powers and roots to include rational exponents.

Create and recognize equivalent expressions involving radical and exponential forms of expressions.

Add, subtract, multiply and divide radical expressions.

Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.

Use complex numbers.

Represent complex numbers.

Add, subtract, multiply and divide complex numbers.

Know and apply the Fundamental Theorem of Algebra.

Reasoning with Equations and Inequalities

Solve equations and inequalities.

Create and solve equations and inequalities, including those that involve absolute value.

Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result.

Solve general systems of equations and inequalities.

Create and solve systems of equations that may include non-linear equations and inequalities.

Seeing Structure in Expressions

Define and use logarithms.

Develop the definition of logarithms based on properties of exponents.

Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic equations.

Use properties of logarithms to solve equations or find equivalent expressions.

Understand why logarithmic scales are used, and use them to solve problems.

Data and Statistics

Linear, Quadratic and Exponential Models

Building Functions

Interpreting Functions

Reasoning with Equations and Inequalities

Creating Equations

Seeing Structure in Expressions

Build new functions from existing functions (limited to linear, quadratic and exponential).

Analyze the effect of translations and scale changes on functions.

Create equations that describe linear, quadratic and exponential relationships.

Create equations and inequalities in one variable and use them to model and/or solve problems.

Summarize, represent and interpret data.

Analyze and interpret graphical displays of data.

Interpret linear, quadratic and exponential functions in terms of the context.

Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities.

Analyze linear, quadratic and exponential functions using different representations.

Graph functions expressed symbolically and identify and interpret key features of the graph.

Construct and compare linear, quadratic and exponential models and solve problems.

Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.

Use arithmetic and geometric sequences.

Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms.

Understand solving equations as a process, and solve equations and inequalities in one variable.

Analyze different methods of solving quadratic equations.

Represent and solve linear and exponential equations and inequalities graphically.

Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane.

Solve problems involving a system of linear inequalities.

Interpret and use structure.

Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions.

Analyze the structure of polynomials to create equivalent expressions or equations.

Data and Statistics

Function Modeling

Building Functions

Interpreting Functions

Arithmetic with Polynomials and Rationals

Reasoning with Equations and Inequalities

Seeing Structure in Expressions

Number and Quantity

Perform operations on polynomials and rational expressions.

Understand the Remainder Theorem and use it to solve problems.

Create new functions from existing functions.

Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).

Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections and dilations (expansions/compressions) for linear, quadratic, cubic, square and cube root, absolute value, exponential and logarithmic functions.

Make inferences and justify conclusions.

Determine whether a specified model is consistent with a given data set.

Use data from a sample to estimate characteristics of the population and recognize the meaning of the margin of error in these estimates.

Fit a data set to a normal distribution.

Know and use the characteristics of normally distributed data sets; predict what percentage of the data will be above or below a given value that is a multiple of standard deviations above or below the mean.

Use functions to model real-world problems.

Create functions and use them to solve applications of quadratic and exponential function model problems.

Use and interpret functions.

Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.

Use complex numbers.

Know and apply the Fundamental Theorem of Algebra.

Solve equations and inequalities.

Create and solve equations and inequalities, including those that involve absolute value.

Solve general systems of equations and inequalities.

Create and solve systems of equations that may include non-linear equations and inequalities.

Define and use logarithms.

Understand why logarithmic scales are used, and use them to solve problems.

Conditional Probability and the Rules of Probability

Modeling with Geometry

Geometric Measurement and Dimension

Expressing Geometric Properties with Equations

Similarity, Right Triangles, and Trigonometry

Congruence

Experiment with transformations in the plane.

Demonstrate the ability to rotate, reflect or translate a figure, and determine a possible sequence of transformations between two congruent figures.

Understand congruence in terms of rigid motions.

Develop the definition of congruence in terms of rigid motions.

Prove geometric theorems.

Prove theorems about polygons.

Make geometric constructions.

Construct geometric figures using various tools and methods.

Understand independence and conditional probability and use them to interpret data.

Understand the definition of independent events and use it to solve problems.

Recognize and explain the concepts of conditional probability and independence in a context.

Explain volume formulas and use them to solve problems.

Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems.

Use coordinates to prove geometric theorems algebraically.

Use coordinates to prove geometric theorems algebraically.

Apply geometric concepts in modeling situations.

Apply geometric methods to solve design mathematical modeling problems.

Prove theorems involving similarity.

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Define trigonometric ratios, solve problems involving right triangles.

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles.

Conditional Probability and Rules of Probability

Modeling with Geometry

Geometric Measurement and Dimension

Exploring Geometric Properties with Equations

Circles

Similarity, Right Triangles, and Trigonometry

Congruence

Geometry

Data and Statistical Analysis

Modeling

Building Functions

Interpreting Functions

Arithmetic with Polynomials and Rational Expressions

Reasoning with Equations and Inequalities

Seeing Structure in Expressions

Number and Quantity

Algebra II

Data and Statistical Analysis

Linear, Quadratic and Exponential Models

Building Functions

Interpreting Functions

Arithmetic with Polynomials and Rational Expressions

Reasoning with Equations and Inequalities

Creating Equations

Seeing Structure in Expressions

Number and Quantity

Algebra I

Perform operations on polynomials.

Add, subtract and multiply polynomials, and understand that polynomials follow the same general rules of arithmetic and are closed under these operations.

Divide polynomials by monomials.

Build new functions from existing functions (limited to linear, quadratic and exponential).

Analyze the effect of translations and scale changes on functions.

Create equations that describe linear, quadratic and exponential relationships.

Create equations and inequalities in one variable and use them to model and/or solve problems.

Create and graph linear, quadratic and exponential equations in two variables.

Represent constraints by equations or inequalities and by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context.

Solve literal equations and formulas for a specified variable that highlights a quantity of interest.

Summarize, represent and interpret data.

Analyze and interpret graphical displays of data.

Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.

Interpret differences in shape, center and spreads in the context of the data sets, accounting for possible effects of outliers.

Summarize data in two-way frequency tables.

Interpret relative frequencies in the context of the data.

Recognize possible associations and trends in the data.

Construct a scatter plot of bivariate quantitative data describing how the variables are related; determine and use a function that models the relationship.

Construct a linear function to model bivariate data represented on a scatter plot that minimizes residuals.

Construct an exponential function to model bivariate data represented on a scatter plot that minimizes residuals.

Interpret the slope (rate of change) and the y-intercept (constant term) of a linear model in the context of the data.

Determine and interpret the correlation coefficient for a linear association.

Distinguish between correlation and causation.

Understand the concept of a function and use function notation.

Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range.

Represent a function using function notation.

Understand that the graph of a function labeled f

Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Interpret linear, quadratic and exponential functions in terms of the context.

Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities.

Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.

Determine the average rate of change of a function over a specified interval and interpret the meaning.

Interpret the parameters of a linear or exponential function in terms of the context.

Analyze linear, quadratic and exponential functions using different representations.

Graph functions expressed symbolically and identify and interpret key features of the graph.

Translate between different but equivalent forms of a function to reveal and explain properties of the function and interpret these in terms of a context.

Compare the properties of two functions given different representations.

Construct and compare linear, quadratic and exponential models and solve problems.

Distinguish between situations that can be modeled with linear or exponential functions.

Determine that linear functions change by equal differences over equal intervals.

Recognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval.

Describe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.

Use arithmetic and geometric sequences.

Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms.

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the set of integers.

Find the terms of sequences given an explicit or recursive formula.

Extend and use properties of rational exponents.

Explain how the meaning of rational exponents extends from the properties of integer exponents.

Rewrite expressions involving radicals and rational exponents using the properties of exponents. Limit to rational exponents with a numerator of 1.

Use units to solve problems.

Use units of measure as a way to understand and solve problems involving quantities.

Identify, label and use appropriate units of measure within a problem.

Convert units and rates.

Use units within problems.

Choose and interpret the scale and the origin in graphs and data displays.

Define and use appropriate quantities for representing a given context or problem.

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Understand solving equations as a process, and solve equations and inequalities in one variable.

Explain how each step taken when solving an equation or inequality in one variable creates an equivalent equation or inequality that has the same solution(s) as the original.

Solve problems involving quadratic equations.

Use the method of completing the square to create an equivalent quadratic equation.

Derive the quadratic formula.

Analyze different methods of solving quadratic equations.

Solve systems of equations.

Solve a system of linear equations algebraically and/or graphically.

Solve a system consisting of a linear equation and a quadratic equation algebraically and/or graphically.

Justify that the technique of linear combination produces an equivalent system of equations.

Represent and solve linear and exponential equations and inequalities graphically.

Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane.

Graph the solution to a linear inequality in two variables.

Solve problems involving a system of linear inequalities.

Interpret and use structure.

Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions.

Analyze the structure of polynomials to create equivalent expressions or equations.

Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties.

Find the zeros of a quadratic function by rewriting it in factored form.

Find the maximum or minimum value of a quadratic function by completing the square.

Perform operations on polynomials and rational expressions.

Extend the knowledge of factoring to include factors with complex coefficients.

Understand the Remainder Theorem and use it to solve problems.

Find the least common multiple of two or more polynomials.

Add, subtract, multiply and divide rational expressions.

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.

Create new functions from existing functions.

Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).

Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.

Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections and dilations (expansions/compressions) for linear, quadratic, cubic, square and cube root, absolute value, exponential and logarithmic functions.

Make inferences and justify conclusions.

Analyze how random sampling could be used to make inferences about population parameters.

Determine whether a specified model is consistent with a given data set.

Describe and explain the purposes, relationship to randomization and differences, among sample surveys, experiments and observational studies.

Use data from a sample to estimate characteristics of the population and recognize the meaning of the margin of error in these estimates.

Describe and explain how the relative sizes of a sample and the population affect the margin of error of predictions.

Analyze decisions and strategies using probability concepts.

Evaluate reports based on data.

Fit a data set to a normal distribution.

Know and use the characteristics of normally distributed data sets; predict what percentage of the data will be above or below a given value that is a multiple of standard deviations above or below the mean.

Fit a data set to a distribution using its mean and standard deviation to determine whether the data is approximately normally distributed.

Use functions to model real-world problems.

Create functions and use them to solve applications of quadratic and exponential function modeling problems.

Use and interpret functions.

Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.

Translate between equivalent forms of functions.

Extend and use the relationship between rational exponents and radicals.

Extend the system of powers and roots to include rational exponents.

Create and recognize equivalent expressions involving radical and exponential forms of expressions.

Add, subtract, multiply and divide radical expressions.

Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.

Use complex numbers.

Represent complex numbers.

Add, subtract, multiply and divide complex numbers.

Know and apply the Fundamental Theorem of Algebra.

Solve equations and inequalities.

Create and solve equations and inequalities, including those that involve absolute value.

Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result.

Solve general systems of equations and inequalities.

Create and solve systems of equations that may include nonlinear equations and inequalities.

Define and use logarithms.

Develop the definition of logarithms based on properties of exponents.

Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic equations.

Use properties of logarithms to solve equations or find equivalent expressions.

Understand why logarithmic scales are used, and use them to solve problems.

Understand and apply theorems about circles.

Prove that all circles are similar using similarity transformations.

Identify and describe relationships among inscribed angles, radii and chords of circles.

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Find arc lengths and areas of sectors of circles.

Derive the formula for the length of an arc of a circle.

Derive the formula for the area of a sector of a circle.

Experiment with transformations in the plane.

Define angle, circle, perpendicular line, parallel line, line segment and ray based on the undefined notions of point, line, distance along a line and distance around a circular arc.

Represent transformations in the plane, and describe them as functions that take points in the plane as inputs and give other points as outputs.

Describe the rotational symmetry and lines of symmetry of two-dimensional figures.

Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.

Demonstrate the ability to rotate, reflect or translate a figure, and determine a possible sequence of transformations between two congruent figures.

Understand congruence in terms of rigid motions.

Develop the definition of congruence in terms of rigid motions.

Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions.

Prove geometric theorems.

Prove theorems about polygons.

Prove theorems about lines and angles.

Prove theorems about triangles.

Make geometric constructions.

Construct geometric figures using various tools and methods.

Understand independence and conditional probability and use them to interpret data.

Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections or complements of other events.

Understand the definition of independent events and use it to solve problems.

Calculate conditional probabilities of events.

Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

Recognize and explain the concepts of conditional probability and independence in a context.

Apply and interpret the Addition Rule for calculating probabilities.

Apply and Interpret the general Multiplication Rule in a uniform probability model.

Use permutations and combinations to solve problems.

Explain volume formulas and use them to solve problems.

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid and cone.

Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems.

Visualize relationships between two-dimensional and three-dimensional objects.

Identify the shapes of two-dimensional cross-sections of three-dimensional objects.

Identify three-dimensional objects generated by transformations of two-dimensional objects.

Translate between the geometric description and the equation for a conic section.

Derive the equation of a circle.

Derive the equation of a parabola given a focus and directrix.

Use coordinates to prove geometric theorems algebraically.

Use coordinates to prove geometric theorems algebraically.

Prove the slope criteria for parallel and perpendicular lines and use them to solve problems.

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

Apply geometric concepts in modeling situations.

Use geometric shapes, their measures and their properties to describe objects.

Apply concepts of density based on area and volume in modeling situations.

Apply geometric methods to solve design mathematical modeling problems.

Understand similarity in terms of similarity transformations.

Construct and analyze scale changes of geometric figures.

Use the definition of similarity to decide if figures are similar and to solve problems involving similar figures.

Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Prove theorems involving similarity.

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Define trigonometric ratios, and solve problems involving right triangles.

Understand that side ratios in right triangles define the trigonometric ratios for acute angles.

Explain and use the relationship between the sine and cosine of complementary angles.

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles.

Derive the formula A = ½ ab sin(C) for the area of a triangle.