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
Translating and Scaling Functions
Using Algebraic Expressions

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
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Trigonometric Expressions
Solving Algebraic Equations II
Using Algebraic Expressions

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

Factoring Special Products
Modeling the Factorization of ax²+bx+c
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
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

MGSE9-12.A.CED.2: Create quadratic 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 on the Number Line
Standard Form of a Line
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).

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Points in the Complex Plane
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
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

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).

Absolute Value with Linear Functions
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.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
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

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.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

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
Similarity in Right Triangles

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
Prisms and Cylinders
Pyramids and Cones

MGSE9-12.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

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
Probability Simulations
Theoretical and Experimental Probability

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