Common Core Georgia Performance Standards

MCC9-12.N.RN.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

MCC9-12.N.CN.1: Know there is a complex number ?? such that ??² = ?1, and every complex number has the form ?? + ???? with ?? and ?? real.

MCC9-12.N.CN.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

MCC9-12.N.CN.7: Solve quadratic equations with real coefficients that have complex solutions.

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

Compound Interest

Exponential Growth and Decay

Unit Conversions

MCC9-12.A.SSE.1b: 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

MCC9-12.A.SSE.2: Use the structure of an expression to identify ways to rewrite it.

Equivalent Algebraic Expressions II

Factoring Special Products

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

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

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations II

MCC9-12.A.SSE.3a: Factor a quadratic expression to reveal the zeros of the function it defines.

Factoring Special Products

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

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

MCC9-12.A.APR.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

MCC9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems.

Absolute Value Equations and Inequalities

Arithmetic Sequences

Compound Interest

Exploring Linear Inequalities in One Variable

Exponential Growth and Decay

Geometric Sequences

Modeling and Solving Two-Step Equations

Quadratic Inequalities

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

MCC9-12.A.CED.2: 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

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

Solving Formulas for any Variable

MCC9-12.A.REI.4b: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??.

Factoring Special Products

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

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

Roots of a Quadratic

MCC9-12.F.IF.4: 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.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

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 quadratic functions and show intercepts, maxima, and minima.

Exponential Functions

Quadratics in Factored Form

Quadratics in Polynomial Form

Roots of a Quadratic

Zap It! Game

MCC9-12.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*

MCC9-12.F.BF.1a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences

Geometric Sequences

MCC9-12.F.BF.3: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Exponential Functions

Logarithmic Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Zap It! Game

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.

MCC9-12.G.CO.9: Prove theorems about lines and angles.

MCC9-12.G.CO.10: Prove theorems about triangles.

Pythagorean Theorem

Triangle Angle Sum

Triangle Inequalities

MCC9-12.G.CO.11: Prove theorems about parallelograms.

Parallelogram Conditions

Special Parallelograms

MCC9-12.G.CO.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

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

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.

MCC9-12.G.SRT.4: Prove theorems about triangles.

Pythagorean Theorem

Similar Figures

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.2: Identify and describe relationships among inscribed angles, radii, and chords.

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.

MCC9-12.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

MCC9-12.G.GPE.2: Derive the equation of a parabola given a focus and directrix.

MCC9-12.G.GMD.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

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.6a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

Least-Squares Best Fit Lines

Solving Using Trend Lines

Zap It! Game

MCC9-12.S.CP.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (?or,? ?and,? ?not?).

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

MCC9-12.S.CP.2: Understand that two events ?? and ?? are independent if the probability of ?? and ?? occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Independent and Dependent Events

MCC9-12.S.CP.3: Understand the conditional probability of ?? given ?? as ??(?? and ??)/??(??), and interpret independence of ?? and ?? as saying that the conditional probability of ?? given ?? is the same as the probability of ??, and the conditional probability of ?? given ?? is the same as the probability of ??.

Independent and Dependent Events

Correlation last revised: 3/7/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.