RQ: Relationships between Quantities and Reasoning with Equations

(Framing Text): Interpret the structure of expressions.

RQ.M.A1HS.4: Interpret expressions that represent a quantity in terms of its context.

RQ.M.A1HS.4.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Compound Interest
Exponential Growth and Decay
Unit Conversions

RQ.M.A1HS.4.b: Interpret complicated expressions by viewing one or more of their parts as a single entity. (e.g., Interpret P(1 + r)ⁿ as the product of P and a factor not depending on P.

Compound Interest
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Translating and Scaling Functions
Using Algebraic Expressions

(Framing Text): Create equations that describe numbers or relationships.

RQ.M.A1HS.5: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Exponential Functions
General Form of a Rational Function
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
Quadratic Inequalities
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Rational Functions
Slope-Intercept Form of a Line
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Translating and Scaling Functions
Using Algebraic Equations

RQ.M.A1HS.6: 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

RQ.M.A1HS.7: 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. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.)

Linear Inequalities in Two Variables
Linear Programming
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

RQ.M.A1HS.8: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.)

Area of Triangles
Solving Formulas for any Variable

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

RQ.M.A1HS.9: 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

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

RQ.M.A1HS.10: 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

LER: Linear and Exponential Relationships

(Framing Text): Extend the properties of exponents to rational exponents.

LER.M.A1HS.11: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. (e.g., We define 5¹/³ to be the cube root of 5 because we want (5¹/³)³ = 5(¹/³)³ to hold, so (5¹/³)³ must equal 5.)

Exponents and Power Rules

(Framing Text): Solve systems of equations.

LER.M.A1HS.13: 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)

LER.M.A1HS.14: 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)

(Framing Text): Represent and solve equations and inequalities graphically.

LER.M.A1HS.15: Recognize 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).

Absolute Value Equations and Inequalities
Circles
Ellipses
Hyperbolas
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Standard Form of a Line

LER.M.A1HS.16: 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.

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

LER.M.A1HS.17: 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

(Framing Text): Understand the concept of a function and use function notation.

LER.M.A1HS.18: Recognize 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 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
Quadratics in Vertex Form
Radical Functions
Standard Form of a Line

LER.M.A1HS.19: 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

LER.M.A1HS.20: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (e.g., The Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n)+ f(n-1) for n ≥ 1.

Arithmetic Sequences
Geometric Sequences

(Framing Text): Interpret functions that arise in applications in terms of a context.

LER.M.A1HS.21: 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; end behavior; and periodicity.

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
Quadratics in Vertex Form
Radical Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Sine and Cosine Functions

LER.M.A1HS.22: Relate the domain of a function to its graph and where applicable, to the quantitative relationship it describes. (e.g., If the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.)

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

LER.M.A1HS.23: 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 functions using different representations.

LER.M.A1HS.24: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

LER.M.A1HS.24.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

LER.M.A1HS.24.b: Graph exponential and logarithmic functions, showing intercepts and end behavior and trigonometric functions, showing period, midline and amplitude.

Cosine Function
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

LER.M.A1HS.25: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.)

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

(Framing Text): Build a function that models a relationship between two quantities.

LER.M.A1HS.26: Write a function that describes a relationship between two quantities.

LER.M.A1HS.26.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences
Geometric Sequences

LER.M.A1HS.26.b: Combine standard function types using arithmetic operations. (e.g., Build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.)

Addition and Subtraction of Functions

LER.M.A1HS.27: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

Arithmetic Sequences
Geometric Sequences

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

LER.M.A1HS.28: 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Vertex Form
Radical Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

(Framing Text): Construct and compare linear, quadratic, and exponential models and solve problems.

LER.M.A1HS.29: Distinguish between situations that can be modeled with linear functions and with exponential functions.

LER.M.A1HS.29.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
Exponential Growth and Decay
Introduction to Exponential Functions
Linear Functions
Slope-Intercept Form of a Line

LER.M.A1HS.29.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

LER.M.A1HS.29.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

LER.M.A1HS.30: 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).

Absolute Value with Linear Functions
Arithmetic Sequences
Arithmetic and Geometric Sequences
Compound Interest
Exponential Functions
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

(Framing Text): Interpret expressions for functions in terms of the situation they model.

LER.M.A1HS.32: 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

DS: Descriptive Statistics

(Framing Text): Summarize, represent, and interpret data on a single count or measurement variable.

DS.M.A1HS.33: Represent data with plots on the real number line (dot plots, histograms, and box plots).

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

DS.M.A1HS.34: 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

DS.M.A1HS.35: 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)

(Framing Text): Summarize, represent, and interpret data on two categorical and quantitative variables.

DS.M.A1HS.36: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal and conditional relative frequencies). Recognize possible associations and trends in the data.

Histograms

DS.M.A1HS.37: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

DS.M.A1HS.37.a: Fit a 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

DS.M.A1HS.37.b: Informally assess the fit of a function by plotting and analyzing residuals.

Least-Squares Best Fit Lines

DS.M.A1HS.37.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.

DS.M.A1HS.38: 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)

DS.M.A1HS.39: Compute (using technology) and interpret the correlation coefficient of a linear fit.

Correlation

EE: Expressions and Equations

(Framing Text): Interpret the structure of equations.

EE.M.A1HS.41: Interpret expressions that represent a quantity in terms of its context.

EE.M.A1HS.41.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Compound Interest
Exponential Growth and Decay
Unit Conversions

EE.M.A1HS.41.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

EE.M.A1HS.42: Use the structure of an expression to identify ways to rewrite it.

Equivalent Algebraic Expressions II
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II

(Framing Text): Write expressions in equivalent forms to solve problems.

EE.M.A1HS.43: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

EE.M.A1HS.43.a: Factor a quadratic expression to reveal the zeros of the function it defines.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

EE.M.A1HS.43.c: Use the properties of exponents to transform expressions for exponential functions.

Exponents and Power Rules

(Framing Text): Perform arithmetic operations on polynomials.

EE.M.A1HS.44: Recognize 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.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

(Framing Text): Create equations that describe numbers or relationships.

EE.M.A1HS.45: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Exponential Functions
General Form of a Rational Function
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
Quadratic Inequalities
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Rational Functions
Slope-Intercept Form of a Line
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Translating and Scaling Functions
Using Algebraic Equations

EE.M.A1HS.46: 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

EE.M.A1HS.47: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (e.g., Rearrange Ohm’s law V = IR to highlight resistance R.

Area of Triangles
Solving Formulas for any Variable

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

EE.M.A1HS.48: Solve quadratic equations in one variable.

EE.M.A1HS.48.a: Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.

Roots of a Quadratic

EE.M.A1HS.48.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 ax²+bx+c
Modeling the Factorization of x²+bx+c
Points in the Complex Plane
Roots of a Quadratic

QFM: Quadratic Functions and Modeling

(Framing Text): Interpret functions that arise in applications in terms of a context.

QFM.M.A1HS.51: 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; end behavior; and periodicity.

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
Quadratics in Vertex Form
Radical Functions
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Sine and Cosine Functions

QFM.M.A1HS.52: 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

QFM.M.A1HS.53: 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 functions using different representations.

QFM.M.A1HS.54: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

QFM.M.A1HS.54.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

QFM.M.A1HS.54.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions

QFM.M.A1HS.55: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

QFM.M.A1HS.55.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 ax²+bx+c
Modeling the Factorization of x²+bx+c

QFM.M.A1HS.55.b: Use the properties of exponents to interpret expressions for exponential functions.

Compound Interest
Exponential Growth and Decay

(Framing Text): Build a function that models a relationship between two quantities.

QFM.M.A1HS.57: Write a function that describes a relationship between two quantities.

QFM.M.A1HS.57.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences
Geometric Sequences

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

QFM.M.A1HS.58: 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
Quadratics in Vertex Form
Radical Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

QFM.M.A1HS.59: Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.

Logarithmic Functions