### 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.

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.

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.

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

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.

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.

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.

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.

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.

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

### 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.

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

### 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.

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.

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.

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.

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

### 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.

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

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.

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

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.

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

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

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.

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

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.

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.

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.

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

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.

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.

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

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.

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

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

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.

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).

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

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

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

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.

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.

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

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.

### 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.

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

### 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”).

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.

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.

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.

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.

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

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.

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

Correlation last revised: 5/10/2018

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