WV--College- and Career-Readiness Standards

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

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

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

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.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.)

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)

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

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

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

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

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

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

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

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.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)

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.

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.

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

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.

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 *ax*^{2}+*bx*+*c*

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

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations II

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 *ax*^{2}+*bx*+*c*

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

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

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 *x*^{2}+*bx*+*c*

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

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.

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 *ax*^{2}+*bx*+*c*

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

Points in the Complex Plane

Roots of a Quadratic

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

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 *ax*^{2}+*bx*+*c*

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

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

Compound Interest

Exponential Growth and Decay

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

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.

Correlation last revised: 9/16/2020