1: Similarity, Congruence, and Proofs

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.

 Dilations

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.

 Dilations
 Similar Figures

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.

 Similar Figures

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: Right Triangle Trigonometry

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: Circles and Volume

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: Extending the Number System

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 x2+bx+c

5: Quadratic Functions

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.

 Compound Interest

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 ax2+bx+c
 Modeling the Factorization of x2+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 x2+bx+c
 Quadratics in Factored Form

5.MCC9-12.A.SSE.3b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

 Quadratics in Vertex 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
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 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.

 Roots of a Quadratic

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 x2+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
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Logarithmic Functions
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex 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
 General Form of a Rational Function
 Graphs of Polynomial Functions
 Introduction to Exponential Functions
 Logarithmic Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex 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
 Quadratics in Vertex 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 x2+bx+c
 Quadratics in Factored Form
 Quadratics in Vertex 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
 Quadratics in Vertex Form

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

 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: Modeling Geometry

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.

 Circles

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

 Parabolas

7: Applications of Probability

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.

 Histograms

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: 4/4/2018

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