Curriculum Framework

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

A.SSE.2: Use the structure of an expression to identify ways to rewrite it.

Equivalent Algebraic Expressions II

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations II

A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A.SSE.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

A.SSE.3.c: Use the properties of exponents to transform expressions for exponential functions.

A.APR.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

A.APR.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Polynomials and Linear Factors

Quadratics in Factored Form

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.

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.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

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

A.REI.4: Solve quadratic equations in one variable.

A.REI.4.b: Solve quadratic equations by inspection (e.g., for 𝘹² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as 𝘢 ± 𝘣𝘪 for real numbers 𝘢 and 𝘣.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

Roots of a Quadratic

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)

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

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

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

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

F.IF.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions

Radical Functions

F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.8.a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

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.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

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.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.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

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)

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.

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

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 last revised: 1/19/2017