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.

Compound Interest
Exponential Growth and Decay
Unit Conversions

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

Compound Interest
Exponential Growth and Decay
Translating and Scaling Functions
Using Algebraic Expressions

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.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Exponential Growth and Decay
Geometric Sequences
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

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

2D Collisions
Air Track
Compound Interest
Determining a Spring Constant
Golf Range
Points, Lines, and Equations
Slope-Intercept Form of a Line

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.

Linear Programming

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

Solving Formulas for any Variable

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.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Formulas for any Variable

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.

Exploring Linear Inequalities in One Variable
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Linear Inequalities in One Variable

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.

Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

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

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)

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).

Circles
Ellipses
Hyperbolas
Parabolas
Points, Lines, and Equations

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.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)

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.

Linear Inequalities in Two Variables

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).

Introduction to Functions
Points, Lines, and Equations

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.

Absolute Value with Linear Functions
Translating and Scaling Functions

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.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

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

General Form of a Rational Function
Introduction to Functions
Radical Functions
Rational Functions

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.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

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.

Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Zap It! Game

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.

Arithmetic Sequences
Geometric Sequences

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.

Exponential Functions
Logarithmic Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Zap It! Game

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.

Compound Interest
Linear Functions

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

Arithmetic Sequences
Compound Interest
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Linear Functions

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).

Compound Interest
Exponential Functions
Exponential Growth and Decay
Point-Slope Form of a Line
Slope-Intercept Form of a Line

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.

Arithmetic Sequences
Compound Interest
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Growth and Decay

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).

Box-and-Whisker Plots
Histograms
Mean, Median, and Mode

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.

Box-and-Whisker Plots
Describing Data Using Statistics
Real-Time Histogram
Sight vs. Sound Reactions

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).

Mean, Median, and Mode
Reaction Time 2 (Graphs and Statistics)

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.

Least-Squares Best Fit Lines
Solving Using Trend Lines
Zap It! Game

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

Least-Squares Best Fit Lines

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

Least-Squares Best Fit Lines

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.

Cat and Mouse (Modeling with Linear Systems)

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

Correlation