### 3: Seeing Structure in Expressions

#### 3: Interpret the structure of expressions

A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

A.SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.

A.SSE.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

### 4: Creating Equations

#### 4: Create equations that describe numbers or relationships

A.CED.1: Create equations and inequalities in one variable and use them to solve problems.

A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

### 5: Reasoning with Equations and Inequalities

#### 5: Understand solving equations as a process of reasoning and explain the reasoning

A.REI.1: Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

#### 6: Solve equations and inequalities in one variable

A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

#### 7: Solve systems of equations

A.REI.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

#### 8: Represent and solve equations and inequalities graphically

A.REI.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A.REI.11: Explain why the 𝘹-coordinates of the points where the graphs of the equations 𝘺 = 𝘧(𝘹) and 𝘺 = 𝑔(𝘹) intersect are the solutions of the equation 𝘧(𝘹) = 𝑔(𝘹); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝘧(𝘹) and/or 𝑔(𝘹) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

A.REI.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

### 6: Interpreting Functions

#### 9: Understand the concept of a function and use function notation

F.IF.1: Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝘧 is a function and 𝘹 is an element of its domain, then 𝘧(𝘹) denotes the output of 𝘧 corresponding to the input 𝘹. The graph of 𝘧 is the graph of the equation 𝘺 = 𝘧(𝘹).

F.IF.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

#### 10: Interpret functions that arise in applications in terms of the context

F.IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F.IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

#### 11: Analyze functions using different representations

F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.7.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

### 7: Building Functions

#### 12: Build a function that models a relationship between two quantities

F.BF.1: Write a function that describes a relationship between two quantities.

F.BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

#### 13: Build new functions from existing functions

F.BF.3: Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

### 8: Linear, Quadratic, and Exponential Models

#### 14: Construct and compare linear, quadratic, and exponential models and solve problems

F.LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

F.LE.1.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

F.LE.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

F.LE.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

#### 15: Interpret expressions for functions in terms of the situation they model

F.LE.5: Interpret the parameters in a linear or exponential function in terms of a context.

### 9: Interpreting Categorical and Quantitative Data

#### 16: Summarize, represent, and interpret data on a single count or measurement variable

S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).

S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

S.ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

#### 17: Summarize, represent, and interpret data on two categorical and quantitative variables

S.ID.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S.ID.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

S.ID.6.b: Informally assess the fit of a function by plotting and analyzing residuals.

S.ID.6.c: Fit a linear function for a scatter plot that suggests a linear association.

#### 18: Interpret linear models

S.ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

S.ID.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.

Correlation last revised: 5/8/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.