GA--CCGPS Frameworks

1.MCC9-12.G.GPE.3: Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

1.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.

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

2.MCC9-12.F.BF.4: Find inverse functions.

2.MCC9-12.F.BF.4d: Produce an invertible function from a non‐invertible function by restricting the domain.

2.MCC9-12.F.TF.3: Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π - x in terms of their values for x, where x is any real number.

Cosine Function

Sine Function

Sum and Difference Identities for Sine and Cosine

Tangent Function

Translating and Scaling Sine and Cosine Functions

2.MCC9-12.F.TF.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

2.MCC9-12.F.TF.7: Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

2.MCC9-12.F.TF.7e: Graph trigonometric functions showing period, midline, and amplitude

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

2.MCC9-12.F.TF.2: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers interpreted as radian measures of angles traversed counterclockwise around the unit circle.

Cosine Function

Sine Function

Tangent Function

2.MCC9-12.F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

3.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

3.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

4.MCC9-12.F.TF.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Sum and Difference Identities for Sine and Cosine

5.MCC9-12.N.VM.8: Add, sub tract, and multiply matrices of appropriate dimensions.

5.MCC9-12.N.VM.12: Work with 2 X 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

5.MCC9-12.A.REI.8: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

5.MCC9-12.A.REI.9: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

Solving Linear Systems (Matrices and Special Solutions)

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

Points in the Complex Plane

Roots of a Quadratic

6.MCC9-12.N.CN.4: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

6.MCC9-12.N.CN.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

6.MCC9-12.N.VM.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||,v).

6.MCC9-12.N.VM.4: Add and subtract vectors.

6.MCC9-12.N.VM.4a: Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

6.MCC9-12.N.VM.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

6.MCC9-12.N.VM.4c: Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.

7.MCC9-12.CP.8: Apply the general Multiplication Rule in a uniform probability model, P(A and B)=[P(A)] x [P(B│ A)] = [P(B)] x [P(A│B)], and interpret the answer in terms of the model.

Independent and Dependent Events

7.MCC9-12.CP.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

Binomial Probabilities

Permutations and Combinations

7.MCC9-12.S.MD.1: Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

7.MCC9-12.S.MD.2: Calculate the expected value of a random variable; interpret it as the mean of a probability distribution.

7.MCC9-12.S.MD.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value

Binomial Probabilities

Geometric Probability

Probability Simulations

Theoretical and Experimental Probability

7.MCC9-12.S.MD.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value

Geometric Probability

Probability Simulations

Theoretical and Experimental Probability

7.MCC9-12.S.MD.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

Binomial Probabilities

Independent and Dependent Events

7.MCC9-12.S.MD.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Probability Simulations

Theoretical and Experimental Probability

7.MCC9-12.S.MD.7: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Estimating Population Size

Probability Simulations

Theoretical and Experimental Probability

7.MCC7.SP.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Binomial Probabilities

Independent and Dependent Events

Permutations and Combinations

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.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

Correlation last revised: 5/10/2018