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).


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.


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

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

Adding Vectors

MGSE9-12.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.

Adding 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).


2.3: Perform operations on matrices and use matrices in applications.

MGSE9-12.N.VM.7: Multiply matrices by scalars to produce new matrices.


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
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex 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
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
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.

Simplifying Trigonometric Expressions
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.


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.


MGSE9-12.S.ID: Interpreting Categorical and Quantitative Data

9.1: Summarize, represent, and interpret data on a single count or measurement variable

MGSE9-12.S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

Box-and-Whisker Plots
Describing Data Using Statistics
Real-Time Histogram
Sight vs. Sound Reactions

MGSE9-12.S.IC: Making Inferences and Justifying Conclusions

10.2: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

MGSE9-12.S.IC.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Estimating Population Size
Polling: City
Polling: Neighborhood

MGSE9-12.S.IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Real-Time Histogram
Sight vs. Sound Reactions

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

11.1: 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: Using Probability to Make Decisions

12.1: Calculate expected values and use them to solve problems

MGSE9-12.S.MD.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

Lucky Duck (Expected Value)

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
Lucky Duck (Expected Value)
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
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability

12.2: Use probability to evaluate outcomes of decisions

MGSE9-12.S.MD.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

MGSE9-12.S.MD.5a: Find the expected payoff for a game of chance.

Lucky Duck (Expected Value)

MGSE9-12.S.MD.5b: Evaluate and compare strategies on the basis of expected values.

Lucky Duck (Expected Value)

MGSE9-12.S.MD.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

Lucky Duck (Expected Value)

MGSE9-12.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).

Lucky Duck (Expected Value)

Correlation last revised: 9/16/2020

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