SI.MP: Mathematical Practices

(Framing Text): Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes.

SI.MP.1: Make sense of problems and persevere in solving them.

SI.MP.1.a: Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, “Does this make sense?” Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.

 Biconditional Statements
 Estimating Population Size
 Linear Inequalities in Two Variables
 Modeling One-Step Equations
 Solving Equations on the Number Line
 Using Algebraic Equations
 Using Algebraic Expressions

SI.MP.3: Construct viable arguments and critique the reasoning of others.

SI.MP.3.a: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

 Biconditional Statements

SI.MP.4: Model with mathematics.

SI.MP.4.a: Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

 Determining a Spring Constant
 Estimating Population Size

SI.MP.7: Look for and make use of structure.

SI.MP.7.a: Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.

 Arithmetic Sequences
 Finding Patterns
 Function Machines 2 (Functions, Tables, and Graphs)
 Geometric Sequences

SI.MP.8: Look for and express regularity in repeated reasoning.

SI.MP.8.a: Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

A: Algebra

A.SSE: Seeing Structure in Expressions

(Framing Text): Interpret the structure of expressions.

A.SSE.1: Interpret linear expressions and exponential expressions with integer exponents 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

A.CED: Creating Equations

(Framing Text): Create equations that describe numbers or relationships. Limit these to linear equations and inequalities, and exponential equations. In the case of exponential equations, limit to situations requiring evaluation of exponential functions at integer inputs.

A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and simple exponential functions.

 Absolute Value Equations and Inequalities
 Absolute Value with Linear Functions
 Arithmetic Sequences
 Compound Interest
 Exploring Linear Inequalities in One Variable
 Exponential Functions
 Function Machines 2 (Functions, Tables, and Graphs)
 Function Machines 3 (Functions and Problem Solving)
 Geometric Sequences
 Introduction to Exponential Functions
 Linear Functions
 Linear Inequalities in Two Variables
 Logarithmic Functions
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Slope-Intercept Form of a Line
 Solving Equations on the Number Line
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations
 Using Algebraic 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 Inequalities in Two Variables
 Linear Programming
 Solving Linear Systems (Standard Form)
 Systems of Linear Inequalities (Slope-intercept form)

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

 Solving Formulas for any Variable

A.REI: Reasoning With Equations and Inequalities

(Framing Text): Understand solving equations as a process of reasoning and explain the reasoning.

A.REI.1: Explain each step in solving a linear 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. Students will solve exponential equations with logarithms in Secondary Mathematics III.

 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Equations on the Number Line
 Solving Two-Step Equations

(Framing Text): Solve equations and inequalities in one variable.

A.REI.3: Solve equations and inequalities in one variable.

A.REI.3.a: Solve one-variable equations and literal equations to highlight a variable of interest.

 Absolute Value Equations and Inequalities
 Area of Triangles
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Equations on the Number Line
 Solving Formulas for any Variable
 Solving Two-Step Equations

A.REI.3.b: Solve compound inequalities in one variable, including absolute value inequalities.

 Absolute Value Equations and Inequalities
 Compound Inequalities
 Solving Linear Inequalities in One Variable

A.REI.3.c: Solve simple exponential equations that rely only on application of the laws of exponents (limit solving exponential equations to those that can be solved without logarithms). For example, 5ˣ = 125 or 2ˣ = 1/16.

 Exponential Functions

(Framing Text): Solve systems of equations. Build on student experiences graphing and solving systems of linear equations from middle school. Include cases where the two equations describe the same line—yielding infinitely many solutions—and cases where two equations describe parallel lines—yielding no solution; connect to GPE.5, which requires students to prove the slope criteria for parallel lines.

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 (numerically, algebraically, graphically), focusing on pairs of linear equations in two variables.

 Cat and Mouse (Modeling with Linear Systems)
 Solving Equations by Graphing Each Side
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Slope-Intercept Form)
 Solving Linear Systems (Standard Form)

(Framing Text): 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 and exponential functions.

 Cat and Mouse (Modeling with Linear Systems)
 Solving Equations by Graphing Each Side
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Slope-Intercept Form)

A.REI.12: Graph the solutions to a linear inequality in two variables as a halfplane (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
 Linear Programming
 Systems of Linear Inequalities (Slope-intercept form)

F: Functions

F.IF: Interpreting Linear and Exponential Functions

(Framing Text): Understand the concept of a linear or exponential function and use function notation. Recognize arithmetic and geometric sequences as examples of linear and exponential functions.

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).

 Absolute Value with Linear Functions
 Exponential Functions
 Function Machines 1 (Functions and Tables)
 Function Machines 2 (Functions, Tables, and Graphs)
 Function Machines 3 (Functions and Problem Solving)
 Introduction to Exponential Functions
 Introduction to Functions
 Linear Functions
 Logarithmic Functions
 Parabolas
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Radical Functions
 Standard Form of a Line

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

F.IF.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Recognize arithmetic and geometric sequences as examples of linear and exponential functions.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

(Framing Text): Interpret linear or exponential functions that arise in applications in terms of a 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. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; and end behavior.

 Absolute Value with Linear Functions
 Cat and Mouse (Modeling with Linear Systems)
 Exponential Functions
 Function Machines 3 (Functions and Problem Solving)
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Logarithmic Functions
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Radical Functions
 Roots of a Quadratic
 Slope-Intercept Form of a Line

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

(Framing Text): Analyze linear or exponential 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 functions and show intercepts.

 Absolute Value with Linear Functions
 Cat and Mouse (Modeling with Linear Systems)
 Exponential Functions
 Linear Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Standard Form of a Line

F.IF.9: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, compare the growth of two linear functions, or two exponential functions such as y=3ⁿ and y=100×2ⁿ.

 General Form of a Rational Function
 Graphs of Polynomial Functions
 Linear Functions
 Logarithmic Functions
 Quadratics in Polynomial Form

F.BF: Building Linear or Exponential Functions

(Framing Text): Build a linear or exponential 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

F.BF.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Limit F.BF.1a, 1b, and 2 to linear and exponential functions. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

(Framing Text): Build new functions from existing functions.

F.BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, for specific values of k (both positive and negative); find the value of k given the graphs. Relate the vertical translation of a linear function to its y-intercept. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

 Absolute Value with Linear Functions
 Exponential Functions
 Introduction to Exponential Functions
 Rational Functions
 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions
 Translations
 Zap It! Game

F.LE: Linear and Exponential

(Framing Text): Construct and compare linear 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; exponential functions grow by equal factors over equal intervals.

 Compound Interest
 Direct and Inverse Variation
 Exponential Functions
 Introduction to Exponential Functions
 Slope-Intercept Form of a Line

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.1.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

 Drug Dosage
 Exponential Growth and Decay
 Half-life

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

F.LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.

 Compound Interest
 Introduction to Exponential Functions

(Framing Text): 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. Limit exponential functions to those of the form f(x) = bˣ + k.

 Arithmetic Sequences
 Compound Interest
 Introduction to Exponential Functions

G: Geometry

G.CO: Congruence

(Framing Text): Build on student experience with rigid motions from earlier grades.

G.CO.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

 Circles
 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines

G.CO.2: Represent transformations in the plane using, for example, transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

 Dilations
 Rotations, Reflections, and Translations
 Translations

G.CO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

 Dilations
 Reflections
 Rotations, Reflections, and Translations
 Translations

G.CO.5: Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, for example, graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Point out the basis of rigid motions in geometric concepts, for example, translations move points a specified distance along a line parallel to a specified line; rotations move objects along a circular arc with a specified center through a specified angle.

 Reflections
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

(Framing Text): Understand congruence in terms of rigid motions. Rigid motions are at the foundation of the definition of congruence. Reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems.

G.CO.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide whether they are congruent.

 Absolute Value with Linear Functions
 Circles
 Dilations
 Holiday Snowflake Designer
 Reflections
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

 Proving Triangles Congruent

(Framing Text): Make geometric constructions.

G.CO.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Emphasize the ability to formalize and defend how these constructions result in the desired objects.

 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines
 Segment and Angle Bisectors

G.CO.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Emphasize the ability to formalize and defend how these constructions result in the desired objects.

 Concurrent Lines, Medians, and Altitudes
 Inscribed Angles

G.GPE: Expressing Geometric Properties With Equations

(Framing Text): Use coordinates to prove simple geometric theorems algebraically.

G.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles; e.g., connect with The Pythagorean Theorem and the distance formula.

 Circles
 Distance Formula

S: Statistics and Probability

S.ID: Interpreting Categorical and Quantitative Data

(Framing Text): 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). Calculate the weighted average of a distribution and interpret it as a measure of center.

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Least-Squares Best Fit Lines
 Mean, Median, and Mode
 Populations and Samples
 Reaction Time 1 (Graphs and Statistics)
 Real-Time Histogram
 Stem-and-Leaf Plots

(Framing Text): 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 linear function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions, or choose a function suggested by the context. Emphasize linear and exponential models.

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots
 Zap It! Game

S.ID.6.b: Informally assess the fit of a function by plotting and analyzing residuals. Focus on situations for which linear models are appropriate.

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots

S.ID.6.c: Fit a linear function for scatter plots that suggest a linear association.

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots

(Framing Text): Interpret linear models building on students’ work with linear relationships, and introduce the correlation coefficient.

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

Correlation last revised: 1/19/2017

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