#### MCC9-12.N: High School---Number and Quantity

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 i such that i² = -1, and every complex number has the form a + bi with a and b 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: High School---Algebra

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

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

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

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

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.

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.

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

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.

#### MCC9-12.F: High School---Functions

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.

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

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.

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

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.

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

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.

#### MCC9-12.G: High School---Geometry

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.

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

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.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

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.

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

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.

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.

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

#### MCC9-12.S: High School---Statistics and Probability

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.

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').

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.

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.

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.