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

(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
 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): 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
 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
 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.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
 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.)

 Introduction to Functions
 Logarithmic Functions
 Radical 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
 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
 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
 Introduction to Exponential 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
 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
 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.

 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
 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
 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

Correlation last revised: 4/4/2018

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