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 x2+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.

 Quadratics in Vertex Form

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 x2+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 quadratic functions.

 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.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.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.

 Roots of a Quadratic

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 x2+bx+c
 Roots of a Quadratic

MGSE9-12.F.IF: Interpreting Functions

MGSE9-12.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; relative maximums and minimums; symmetries; end behavior.

 Absolute Value with Linear Functions
 Cat and Mouse (Modeling with Linear Systems)
 Exponential Functions
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Introduction to Exponential Functions
 Linear Functions
 Logarithmic Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Radical Functions
 Slope-Intercept Form of a Line

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 quadratic functions and show intercepts, maxima, and minima (as determined by the function or by context).

 Exponential Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Roots of a Quadratic
 Zap It! Game

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 ax2+bx+c
 Modeling the Factorization of x2+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.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
 Rational Functions
 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions
 Translations
 Zap It! Game

MGSE9-12.G.CO: Congruence

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.9: Prove theorems about lines and angles.

 Investigating Angle Theorems

MGSE9-12.G.CO.10: Prove theorems about triangles.

 Pythagorean Theorem
 Triangle Angle Sum
 Triangle Inequalities

MGSE9-12.G.CO.11: Prove theorems about parallelograms.

 Parallelogram Conditions
 Special Parallelograms

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.

 Dilations

MGSE9-12.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

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

MGSE9-12.G.SRT.4: Prove theorems about triangles.

 Pythagorean Theorem
 Similar Figures

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.G.C: Circles

MGSE9-12.G.C.1: Understand that all circles are similar.

 Circles

MGSE9-12.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

MGSE9-12.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

MGSE9-12.G.GPE: Expressing Geometric Properties with Equations

MGSE9-12.G.GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

 Circles
 Distance Formula
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard

MGSE9-12.G.GMD: Geometric Measurement and Dimension

MGSE9-12.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

MGSE9-12.G.GMD.1b: Give informal arguments for the formula of the volume of a cylinder, pyramid, and cone using Cavalieri’s principle.

 Prisms and Cylinders
 Pyramids and Cones

MGSE9-12.G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

 Prisms and Cylinders
 Pyramids and Cones

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

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 quadratic models.

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

MGSE9-12.S.CP: Conditional Probability and the Rules of Probability

MGSE9-12.S.CP.1: Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events (or, and, not).

 Independent and Dependent Events

MGSE9-12.S.CP.2: Understand that if two events A and B are independent, the probability of A and B occurring together is the product of their probabilities, and that if the probability of two events A and B occurring together is the product of their probabilities, the two events are independent.

 Independent and Dependent Events

MGSE9-12.S.CP.3: Understand the conditional probability of A given B as P (A and B)/P(B). Interpret independence of A and B in terms of conditional probability; that is, the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

 Independent and Dependent Events

MGSE9-12.S.CP.6: Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in context.

 Independent and Dependent Events

Correlation last revised: 4/4/2018

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