MCC9-12.N.Q.1b: Convert units and rates using dimensional analysis (English-to-English and Metric-to-Metric without conversion factor provided and between English and Metric with conversion factor);

Unit Conversions

MCC9-12.A.SSE.1a: Interpret parts of an expression, such as terms, factors, and coefficients, in context.

Compound Interest
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

MCC9-12.A.SSE.1b: Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.

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

MCC9-12.A.APR.1: Add, subtract, and multiply polynomials; understand that polynomials form a system analogous to the integers in that they are closed under these operations.

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

MCC9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, and exponential functions (integer inputs only).

Absolute Value Equations and Inequalities
Arithmetic Sequences
Compound Interest
Exploring Linear Inequalities in One Variable
Geometric Sequences
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations
Using Algebraic Equations

MCC9-12.A.CED.2: Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (The phrase “in two or more variables” refers to formulas like the compound interest formula, in which A = P(1 + r/n)nt has multiple variables.)

Absolute Value Equations and Inequalities
Circles
Compound Interest
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Standard Form of a Line
Using Algebraic Equations

MCC9-12.A.CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.

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

MCC9-12.A.CED.4: Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations.

Area of Triangles
Solving Formulas for any Variable

MCC9-12.A.REI.1: Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next using properties.

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Formulas for any Variable
Solving Two-Step Equations

MCC9-12.A.REI.3: Solve linear equations and inequalities in one variable including equations with coefficients represented by letters.

Area of Triangles
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations I
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Formulas for any Variable
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

MCC9-12.A.REI.5: Show and explain why the elimination method works to solve a system of two-variable equations.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

MCC9-12.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)

MCC9-12.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.

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

MCC9-12.A.REI.11: Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.

Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Circles
Exponential Functions
Parabolas
Point-Slope Form of a Line
Points, Lines, and Equations
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Standard Form of a Line

MCC9-12.A.REI.12: Graph the solution set to a linear inequality in two variables.

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

MCC9-12.F.IF.1: Understand that a function from one set (the input, called the domain) to another set (the output, called the range) assigns to each element of the domain exactly one element of the range, i.e. each input value maps to exactly one output value. If f is a function, x is the input (an element of the domain), and f(x) is the output (an element of the range). Graphically, the graph is 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

MCC9-12.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

MCC9-12.F.IF.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. (Generally, the scope of high school math defines this subset as the set of natural numbers 1,2,3,4...) By graphing or calculating terms, students should be able to show how the recursive sequence a₁=7, aₙ=a ₙ₋₁ +2; the sequence sₙ = 2(n-1) + 7; and the function f(x) = 2x + 5 (when x is a natural number) all define the same sequence.

Arithmetic Sequences
Geometric Sequences

MCC9-12.F.IF.4: Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; end behavior.

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
Introduction to Exponential Functions
Linear Functions
Logarithmic Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Radical Functions
Slope-Intercept Form of a Line

MCC9-12.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

MCC9-12.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

MCC9-12.F.IF.7a: Graph linear functions and show intercepts, maxima, and minima (as determined by the function or by context).

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Exponential Functions
Graphs of Polynomial Functions
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Slope-Intercept Form of a Line
Standard Form of a Line
Zap It! Game

MCC9-12.F.IF.7e: Graph exponential functions, showing intercepts and end behavior.

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

MCC9-12.F.BF.1a: Determine an explicit expression and the recursive process (steps for calculation) from context.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MCC9-12.F.BF.2: Write arithmetic and geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect arithmetic sequences to linear functions and geometric sequences to exponential functions.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MCC9-12.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.

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

MCC9-12.F.LE.1b: 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

MCC9-12.F.LE.1c: 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

MCC9-12.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

MCC9-12.F.LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly.

Compound Interest
Introduction to Exponential Functions

MCC9-12.F.LE.5: Interpret the parameters in a linear (f(x) = mx + b) and exponential (f(x) = a•dˣ) function in terms of context. (In the functions above, “m” and “b” are the parameters of the linear function, and “a” and “d” are the parameters of the exponential function.) In context, students should describe what these parameters mean in terms of change and starting value.

Arithmetic Sequences
Compound Interest
Exponential Growth and Decay
Introduction to Exponential Functions

MCC9-12.G.CO.1: 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
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines

MCC9-12.G.CO.2: Represent transformations in the plane using, e.g., 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
Reflections
Rotations, Reflections, and Translations
Translations

MCC9-12.G.CO.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

Dilations
Reflections
Rotations, Reflections, and Translations
Translations

MCC9-12.G.CO.5: 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.

Dilations
Reflections
Rotations, Reflections, and Translations
Translations

MCC9-12.G.CO.6: 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

MCC9-12.G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (Extend to include HL and AAS.)

Proving Triangles Congruent

MCC9-12.G.CO.13: Construct an equilateral triangle, a square, and a regular hexagon, each inscribed in a circle.

Concurrent Lines, Medians, and Altitudes
Inscribed Angles

MCC9-12.G.SRT.1a: The dilation of a line not passing through the center of the dilation results in a parallel line and leaves a line passing through the center unchanged.

Dilations

MCC9-12.G.SRT.1b: The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.

Dilations
Similar Figures

MCC9-12.G.SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain, using similarity transformations, the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Circles
Dilations
Similar Figures
Similarity in Right Triangles

MCC9-12.G.SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Dilations
Perimeters and Areas of Similar Figures
Similarity in Right Triangles

MCC9-12.G.SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Sine, Cosine, and Tangent Ratios

MCC9-12.G.SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine, Cosine, and Tangent Ratios

MCC9-12.G.C.1: Understand that all circles are similar.

Circles

MCC9-12.G.C.2: Identify and describe relationships among inscribed angles, radii, chords, tangents, and secants. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Chords and Arcs
Circumference and Area of Circles
Inscribed Angles

MCC9-12.G.C.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Chords and Arcs

MCC9-12.G.GPE.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

Distance Formula

MCC9-12.G.GMD.1a: Give informal arguments for the formulas of the circumference of a circle and area of a circle using dissection arguments and informal limit arguments.

Circumference and Area of Circles
Prisms and Cylinders
Pyramids and Cones

MCC9-12.G.GMD.1b: Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

Circumference and Area of Circles
Prisms and Cylinders
Pyramids and Cones

MCC9-12.G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Prisms and Cylinders
Pyramids and Cones

MCC9-12.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

MCC9-12.S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, mean absolute deviation) of two or more different data sets.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions

MCC9-12.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)

MCC9-12.S.ID.6a: Decide which type of function is most appropriate by observing graphed data, charted data, or by analysis of context to generate a viable (rough) function of best fit. Use this function to solve problems in context. Emphasize linear and exponential models.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
Zap It! Game

MCC9-12.S.ID.6c: Using given or collected bivariate data, fit a linear function for a scatter plot that suggests a linear association.

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

MCC9-12.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)

MCC9-12.S.ID.8: Compute (using technology) and interpret the correlation coefficient “r” of a linear fit. (For instance, by looking at a scatterplot, students should be able to tell if the correlation coefficient is positive or negative and give a reasonable estimate of the “r” value.) After calculating the line of best fit using technology, students should be able to describe how strong the goodness of fit of the regression is, using “r”.

Correlation