GA--CCGPS Frameworks

1.MCC9-12.G.SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:

1.MCC9-12.G.SRT.1.a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

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

1.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

1.MCC9-12.G.SRT.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

1.MCC9-12.G.SRT.4: Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Similar Figures

1.9-12.G.SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Congruence in Right Triangles

Constructing Congruent Segments and Angles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures

Similarity in Right Triangles

1.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.

Dilations

Reflections

Rotations, Reflections, and Translations

Translations

1.MCC9-12.G.CO.9: Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Congruence in Right Triangles

Investigating Angle Theorems

Proving Triangles Congruent

Similar Figures

1.MCC9-12.G.CO.10: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Isosceles and Equilateral Triangles

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Triangle Angle Sum

Triangle Inequalities

1.MCC9-12.G.CO.11: Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Parallelogram Conditions

Special Parallelograms

1.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.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Concurrent Lines, Medians, and Altitudes

Constructing Congruent Segments and Angles

Constructing Parallel and Perpendicular Lines

Segment and Angle Bisectors

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

Concurrent Lines, Medians, and Altitudes

Inscribed Angles

2.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

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

Cosine Function

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

3.MCC9-12.G.C.2: Identify and describe relationships among inscribed angles, radii, and chords. 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

Inscribed Angles

3.MCC9-12.G.C.3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Concurrent Lines, Medians, and Altitudes

Inscribed Angles

3.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. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

Circumference and Area of Circles

Prisms and Cylinders

Pyramids and Cones

3.MCC9-12.G.GMD.2: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

Prisms and Cylinders

Pyramids and Cones

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

Prisms and Cylinders

Pyramids and Cones

4.MCC9-12.N.CN.1: Know there is a complex number i such that i²= −1, and every complex number has the form a + bi with a and b real.

Points in the Complex Plane

Roots of a Quadratic

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

Points in the Complex Plane

Roots of a Quadratic

4.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.

Addition and Subtraction of Functions

Addition of Polynomials

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

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

Points in the Complex Plane

Roots of a Quadratic

5.MCC9-12.A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

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

Compound Interest

Operations with Radical Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

5.MCC9-12.A.SSE.1b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

Compound Interest

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

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

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Exponents and Power Rules

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

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

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

5.MCC9-12.A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Solving Algebraic Equations II

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

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

Quadratics in Factored Form

5.MCC9-12.A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential 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

5.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.

Absolute Value Equations and Inequalities

Circles

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Solving Equations on the Number Line

Standard Form of a Line

Using Algebraic Equations

5.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

5.MCC9-12.A.REI.4: Solve quadratic equations in one variable.

5.MCC9-12.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 this form.

5.MCC9-12.A.REI.4b: Solve quadratic equations by inspection (e.g., for x² = 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 a ± bi for real numbers a and b.

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

Points in the Complex Plane

Roots of a Quadratic

5.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

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

Logarithmic Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Radical Functions

Rational Functions

Roots of a Quadratic

Slope-Intercept Form of a Line

Translating and Scaling Sine and Cosine Functions

5.MCC9-12.F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

Introduction to Functions

Logarithmic Functions

Radical Functions

5.MCC9-12.F.IF.6: Calculate and interpret the average r ate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Cat and Mouse (Modeling with Linear Systems)

Slope

5.MCC9-12.F.IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated case

Absolute Value with Linear Functions

Exponential Functions

Function Machines 3 (Functions and Problem Solving)

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Quadratics in Factored Form

Quadratics in Polynomial Form

Radical Functions

5.MCC9-12.F.IF.7a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

Absolute Value with Linear Functions

Cat and Mouse (Modeling with Linear Systems)

Exponential Functions

Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Roots of a Quadratic

Slope-Intercept Form of a Line

Standard Form of a Line

Zap It! Game

5.MCC9-12.F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

5.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.

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

Quadratics in Factored Form

Roots of a Quadratic

5.MCC9-12.F.IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

General Form of a Rational Function

Graphs of Polynomial Functions

Linear Functions

Logarithmic Functions

Quadratics in Polynomial Form

5.MCC9-12.F.BF.1: Write a function that describes a relationship between two quantities.

Function Machines 1 (Functions and Tables)

Points, Lines, and Equations

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

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

5.MCC9-12.F.BF.1b: Combine standard function types using arithmetic operations.

Addition and Subtraction of Functions

5.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. 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

5.MCC9-12.F.LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Compound Interest

Introduction to Exponential Functions

5.MCC9-12.S.ID.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

5.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. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

Zap It! Game

6.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.

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

7.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

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

Independent and Dependent Events

7.MCC9-12.S.CP.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that 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

7.MCC9-12.S.CP.4: Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.

7.MCC9-12.S.CP.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

Independent and Dependent Events

7.MCC9-12.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 terms of the model.

Independent and Dependent Events

7.MCC7.SP.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event

Geometric Probability

Probability Simulations

Theoretical and Experimental Probability

7.MCC7.SP.8a: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Independent and Dependent Events

Theoretical and Experimental Probability

7.MCC7.SP.8b: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event

Binomial Probabilities

Permutations and Combinations

Correlation last revised: 1/19/2017