MGSE9-12.N.CN: The Complex Number System

1.1: Use properties of rational and irrational numbers.

MGSE9-12.N.CN.3: Find the conjugate of a complex number; use the conjugate to find the absolute value (modulus) and quotient of complex numbers.

 Points in the Complex Plane
 Roots of a Quadratic

1.2: Represent complex numbers and their operations on the complex plane.

MGSE9-12.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.

 Points in the Complex Plane

MGSE9-12.N.VM: Vector and Matrix Quantities

2.1: Represent and model with vector quantities.

MGSE9-12.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).

 Vectors

MGSE9-12.N.VM.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

 Vectors

MGSE9-12.N.VM.3: Solve problems involving velocity and other quantities that can be represented by vectors.

 2D Collisions
 Golf Range

2.2: Perform operations on vectors.

MGSE9-12.N.VM.4: Add and subtract vectors.

MGSE9-12.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.

 Adding Vectors
 Vectors

MGSE9-12.N.VM.4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

 Adding Vectors
 Vectors

MGSE9-12.N.VM.5: Multiply a vector by a scalar.

MGSE9-12.N.VM.5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as 𝘤(𝘷ₓ, 𝘷 subscript 𝘺) = (𝘤𝘷ₓ, 𝘤𝘷 subscript 𝘺).

 Dilations

MGSE9-12.A.REI: Reasoning with Equations and Inequalities

3.1: Solve systems of equations

MGSE9-12.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)

MGSE9-12.F.IF: Interpreting Functions

4.1: Interpret functions that arise in applications in terms of the context

MGSE9-12.F.IF.4: Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval 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
 Introduction to Exponential Functions
 Linear Functions
 Logarithmic Functions
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Radical Functions
 Slope-Intercept Form of a Line

4.2: Analyze functions using different representations

MGSE9-12.F.IF.7: Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.

MGSE9-12.F.IF.7e: Graph trigonometric functions, showing period, midline, and amplitude.

 Cosine Function
 Sine Function
 Tangent Function
 Translating and Scaling Sine and Cosine Functions

MGSE9-12.F.TF: Trigonometric Functions

6.2: Model periodic phenomena with trigonometric functions

MGSE9-12.F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

 Sound Beats and Sine Waves

6.3: Prove and apply trigonometric identities

MGSE9-12.F.TF.8: Prove the Pythagorean identity (sin A)² + (cos A)² = 1 and use it to find sin A, cos A, or tan A, given sin A, cos A, or tan A, and the quadrant of the angle.

 Simplifying Trigonometric Expressions
 Sine, Cosine, and Tangent Ratios

MGSE9-12.F.TF.9: Prove addition, subtraction, double, and half-angle formulas for sine, cosine, and tangent and use them to solve problems.

 Sum and Difference Identities for Sine and Cosine

MGSE9-12.G.GPE: Expressing Geometric Properties with Equations

8.1: Translate between the geometric description and the equation for a conic section

MGSE9-12.G.GPE.2: Derive the equation of a parabola given a focus and directrix.

 Parabolas

MGSE9-12.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.

 Ellipses
 Hyperbolas

MGSE9-12.S.CP: Conditional Probability and the Rules of Probability

9.1: Use the rules of probability to compute probabilities of compound events in a uniform probability model

MGSE9-12.S.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

MGSE9-12.S.CP.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

 Binomial Probabilities
 Permutations and Combinations

MGSE9-12.S.MD: Use Probability to Make Decisions

10.1: Calculate expected values and use them to solve problems

MGSE9-12.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.

 Independent and Dependent Events
 Probability Simulations
 Theoretical and Experimental Probability

MGSE9-12.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
 Independent and Dependent Events
 Probability Simulations
 Theoretical and Experimental Probability

Correlation last revised: 1/19/2017

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