RQ: Relationships between Quantities

(Framing Text): Interpret the structure of expressions.

RQ.M.1HS.4: Interpret expressions that represent a quantity in terms of its context.

RQ.M.1HS.4.a: Interpret parts of an expression, such as terms, factors, and coefficients.

 Compound Interest
 Exponential Growth and Decay
 Unit Conversions

RQ.M.1HS.4.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

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

RQ.M.1HS.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
 Function Machines 2 (Functions, Tables, and Graphs)
 Function Machines 3 (Functions and Problem Solving)
 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
 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.1HS.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.1HS.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.1HS.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

LER: Linear and Exponential Relationships

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

LER.M.1HS.9: 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

LER.M.1HS.10: 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.1HS.11: 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
 Linear Programming
 Systems of Linear Inequalities (Slope-intercept form)

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

LER.M.1HS.12: 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

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

LER.M.1HS.15: 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
 Radical Functions
 Roots of a Quadratic
 Slope-Intercept Form of a Line
 Translating and Scaling Sine and Cosine Functions

LER.M.1HS.16: 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.1HS.17: 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.1HS.18: 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.1HS.18.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.1HS.18.b: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

 Cosine Function
 Exponential Functions
 Exponential Growth and Decay
 Logarithmic Functions
 Logarithmic Functions: Translating and Scaling
 Sine Function
 Tangent Function

LER.M.1HS.19: 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

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

LER.M.1HS.20: Write a function that describes a relationship between two quantities.

LER.M.1HS.20.a: Determine an explicit expression, a recursive process or steps for calculation from a context.

 Arithmetic Sequences
 Arithmetic and Geometric Sequences
 Geometric Sequences

LER.M.1HS.20.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.1HS.21: 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.1HS.22: 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.1HS.23: Distinguish between situations that can be modeled with linear functions and with exponential functions.

LER.M.1HS.23.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.1HS.23.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.1HS.23.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.1HS.24: 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

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

LER.M.1HS.26: 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

RE: Reasoning with Equations

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

RE.M.1HS.27: 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.

RE.M.1HS.28: 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

(Framing Text): Solve systems of equations.

RE.M.1HS.29: 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)

RE.M.1HS.30: 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)

DS: Descriptive Statistics

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

DS.M.1HS.31: 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.1HS.32: 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.1HS.33: Interpret differences in shape, center and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

 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.

DS.M.1HS.34: 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.1HS.35: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

DS.M.1HS.35.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.1HS.35.b: Informally assess the fit of a function by plotting and analyzing residuals. (Focus should be on situations for which linear models are appropriate.)

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

DS.M.1HS.35.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.1HS.36: 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.1HS.37: Compute (using technology) and interpret the correlation coefficient of a linear fit.

 Correlation

CPC: Congruence, Proof, and Constructions

(Framing Text): Experiment with transformations in the plane.

CPC.M.1HS.39: 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
 Inscribed Angles
 Parallel, Intersecting, and Skew Lines

CPC.M.1HS.40: 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

CPC.M.1HS.41: Given a rectangle, parallelogram, trapezoid or regular polygon, describe the rotations and reflections that carry it onto itself.

 Reflections
 Rotations, Reflections, and Translations
 Similar Figures

CPC.M.1HS.42: Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.

 Circles
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

CPC.M.1HS.43: Given a geometric figure and a rotation, reflection or translation draw the transformed figure using, e.g., graph paper, tracing paper or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

 Reflections
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

(Framing Text): Understand congruence in terms of rigid motions.

CPC.M.1HS.44: 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 if they are congruent.

 Proving Triangles Congruent
 Reflections
 Rotations, Reflections, and Translations
 Translations

CPC.M.1HS.46: 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.

CPC.M.1HS.47: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

 Concurrent Lines, Medians, and Altitudes
 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines
 Parallel, Intersecting, and Skew Lines
 Segment and Angle Bisectors

CPC.M.1HS.48: Construct an equilateral triangle, a square and a regular hexagon inscribed in a circle.

 Concurrent Lines, Medians, and Altitudes
 Inscribed Angles

Correlation last revised: 4/7/2017

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