GA--Standards of Excellence

MGSE9-12.N.Q: Quantities

MGSE9-12.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);

MGSE9-12.A.SSE: Seeing Structure in Expressions

MGSE9-12.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

MGSE9-12.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

MGSE9-12.A.SSE.2: Use the structure of an expression to rewrite it in different equivalent forms.

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Using Algebraic Expressions

MGSE9-12.A.SSE.3a: Factor any quadratic expression to reveal the zeros of the function defined by the expression.

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

Quadratics in Factored Form

MGSE9-12.A.SSE.3b: Complete the square in a quadratic expression to reveal the maximum and minimum value of the function defined by the expression.

MGSE9-12.A.APR: Arithmetic with Polynomials and Rational Expressions

MGSE9-12.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 *x*^{2}+*bx*+*c*

MGSE9-12.A.CED: Creating Equations

MGSE9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions (integer inputs only).

Absolute Value Equations and Inequalities

Arithmetic Sequences

Exploring Linear Inequalities in One Variable

Geometric Sequences

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Equations on the Number Line

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Using Algebraic Equations

MGSE9-12.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

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Solving Equations by Graphing Each Side

Standard Form of a Line

MGSE9-12.A.CED.3: Represent constraints by equations or inequalities, and by systems of equation 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)

MGSE9-12.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

MGSE9-12.A.REI: Reasoning with Equations and Inequalities

MGSE9-12.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 Two-Step Equations

MGSE9-12.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

MGSE9-12.A.REI.4a: 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 ax² + bx + c = 0.

MGSE9-12.A.REI.4b: Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, factoring, completing the square, and the quadratic formula, as appropriate to the initial form of the equation (limit to real number solutions).

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

Roots of a Quadratic

MGSE9-12.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 (Standard Form)

MGSE9-12.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)

MGSE9-12.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

Parabolas

Point-Slope Form of a Line

Points, Lines, and Equations

Standard Form of a Line

MGSE9-12.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

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

Standard Form of a Line

MGSE9-12.A.REI.12: Graph the solution set to a linear inequality in two variables.

Linear Inequalities in Two Variables

Systems of Linear Inequalities (Slope-intercept form)

MGSE9-12.F.IF: Interpreting Functions

MGSE9-12.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

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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.F.IF.7a: Graph linear and quadratic 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

MGSE9-12.F.IF.7e: Graph exponential functions, showing intercepts and end behavior.

MGSE9-12.F.IF.8a: 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*

MGSE9-12.F.BF: Building Functions

MGSE9-12.F.BF.1a: Determine an explicit expression and the recursive process (steps for calculation) from context.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

MGSE9-12.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

MGSE9-12.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. 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

Radical Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

MGSE9-12.F.LE: Linear, Quadratic, and Exponential Models

MGSE9-12.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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.G.CO: Congruence

MGSE9-12.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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.G.SRT: Similarity, Right Triangles, and Trigonometry

MGSE9-12.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.

MGSE9-12.G.SRT.1b: The dilation of a line segment is longer or shorter according to the ratio given by the scale factor.

MGSE9-12.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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.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

MGSE9-12.S.ID: Interpreting Categorical and Quantitative Data

MGSE9-12.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

MGSE9-12.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)

MGSE9-12.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, quadratic and exponential models.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

Zap It! Game

MGSE9-12.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

MGSE9-12.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)

MGSE9-12.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 last revised: 1/22/2020