Course of Study

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

N-CN.1: Students will: 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.

N-CN.2: Students will: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

N-CN.3: Students will: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

1.5.1: Represent and model with vector quantities.

N-VM.5: Students will: 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).

N-VM.6: Students will: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

N-VM.7: Students will: Solve problems involving velocity and other quantities that can be represented by vectors.

2D Collisions

Adding Vectors

Golf Range

Vectors

1.5.2: Perform operations on vectors.

N-VM.8: Students will: Add and subtract vectors.

N-VM.8.a: 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.

N-VM.8.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

N-VM.8.c: 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.

N-VM.9: Students will: Multiply a vector by a scalar.

N-VM.9.a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as ??(???, ?? subscript ??) = (?????, ???? subscript ??).

N-VM.9.b: Compute the magnitude of a scalar multiple ???? using ||????|| = |??|??. Compute the direction of ???? knowing that when |??|?? ? 0, the direction of ???? is either along ?? (for ?? > 0) or against ?? (for ?? < 0).

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

N-VM.11: Students will: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

2.2.1: Use polynomial identities to solve problems.

A-APR.13: Students will: Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined, for example, by Pascal’s Triangle.

2.3.1: Solve systems of equations.

A-REI.14: Students will: Represent a system of linear equations as a single matrix equation in a vector variable.

Solving Linear Systems (Matrices and Special Solutions)

2.4.1: Understand the graphs and equations of conic sections.

A-CS.15: Students will: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.

A-CS.15.a: Formulate equations of conic sections from their determining characteristics.

Addition and Subtraction of Functions

Circles

Ellipses

Hyperbolas

Parabolas

3.1.1: Interpret functions that arise in applications in terms of the context.

F-IF.16: Students will: 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.

Absolute Value with Linear Functions

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Exponential Functions

Function Machines 3 (Functions and Problem Solving)

General Form of a Rational Function

Graphs of Polynomial Functions

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

Rational Functions

Standard Form of a Line

F-IF.17: Students will: 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.

Cat and Mouse (Modeling with Linear Systems)

Graphs of Derivative Functions

Slope

3.1.2: Analyze functions using different representations.

F-IF.18: Students will: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.18.a: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

Radical Functions

Translating and Scaling Functions

F-IF.18.b: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Graphs of Polynomial Functions

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Vertex Form

Roots of a Quadratic

Zap It! Game

F-IF.18.c: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

General Form of a Rational Function

Rational Functions

F-IF.18.d: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Cosine Function

Exponential Functions

Exponential Growth and Decay

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

3.2.1: Build a function that models a relationship between two quantities.

F-BF.19: Students will: Compose functions.

Function Machines 1 (Functions and Tables)

3.2.2: Build new functions from existing functions.

F-BF.20: Students will: Determine the inverse of a function and a relation.

F-BF.21: Students will: Verify by composition that one function is the inverse of another.

F-BF.22: Students will: Read values of an inverse function from a graph or a table, given that the function has an inverse.

Function Machines 3 (Functions and Problem Solving)

Logarithmic Functions

F-BF.23: Students will: Produce an invertible function from a non-invertible function by restricting the domain.

F-BF.24: Students will: Understand the inverse relationship between exponents and logarithms, and use this relationship to solve problems involving logarithms and exponents.

F-BF.25: Students will: Compare effects of parameter changes on graphs of transcendental functions.

Exponential Functions

Exponential Growth and Decay

Introduction to Exponential Functions

Logarithmic Functions

Logarithmic Functions: Translating and Scaling

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

3.3.1: Recognize attributes of trigonometric functions and solve problems involving trigonometry.

F-TF.26: Students will: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

F-TF.27: Students will: Use the sum, difference, and half-angle identities to find the exact value of a trigonometric function.

Sum and Difference Identities for Sine and Cosine

F-TF.28: Students will: Utilize parametric equations by graphing and by converting to rectangular form.

F-TF.28.b: Solve applied problems that include sequences with recurrence relations.

Arithmetic Sequences

Geometric Sequences

3.3.2: Extend the domain of trigonometric functions using the unit circle.

F-TF.29: Students will: Use special triangles to determine geometrically the values of sine, cosine, and tangent for pi/3, pi/4, and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi – x, pi + x, and 2pi – x in terms of their values for x, where x is any real number.

Cosine Function

Sine Function

Sine, Cosine, and Tangent Ratios

Sum and Difference Identities for Sine and Cosine

Tangent Function

Translating and Scaling Sine and Cosine Functions

F-TF.30: Students will: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions

3.3.4: Prove and apply trigonometric identities.

F-TF.33: Students will: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1, and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

Cosine Function

Simplifying Trigonometric Expressions

Sine Function

Sine, Cosine, and Tangent Ratios

F-TF.34: Students will: Prove the addition and subtraction formulas for sine, cosine, and tangent, and use them to solve problems.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

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

G-GPE.36: Students will: Derive the equation of a parabola given a focus and directrix.

G-GPE.37: Students will: 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.

4.2.2: Explain volume formulas and use them to solve problems.

G-GPE.38: Students will: Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.

Prisms and Cylinders

Pyramids and Cones

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

S-ID.39: Students will: 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

Logarithmic Functions: Translating and Scaling

Mean, Median, and Mode

Polling: City

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Real-Time Histogram

Sight vs. Sound Reactions

S-ID.40: Students will: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Box-and-Whisker Plots

Describing Data Using Statistics

Least-Squares Best Fit Lines

Mean, Median, and Mode

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Reaction Time 2 (Graphs and Statistics)

Real-Time Histogram

Stem-and-Leaf Plots

S-ID.41: Students will: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Polling: City

Populations and Samples

Real-Time Histogram

Sight vs. Sound Reactions

5.1.2: Interpret linear models.

S-ID.42: Students will: Compute (using technology) and interpret the correlation coefficient of a linear fit.

S-ID.43: Students will: Distinguish between correlation and causation.

5.2.1: Understand and evaluate random processes underlying statistical experiments.

S-IC.44: Students will: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Polling: City

Polling: Neighborhood

Populations and Samples

S-IC.45: Students will: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

Polling: City

Polling: Neighborhood

Populations and Samples

Probability Simulations

Theoretical and Experimental Probability

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

S-IC.46: Students will: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

Polling: City

Polling: Neighborhood

Sight vs. Sound Reactions

Time Estimation

S-IC.47: Students will: 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.

Polling: City

Polling: Neighborhood

Populations and Samples

S-IC.48: Students will: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Polling: City

Polling: Neighborhood

Populations and Samples

S-IC.49: Students will: Evaluate reports based on data.

Describing Data Using Statistics

Polling: City

Polling: Neighborhood

Real-Time Histogram

5.3.1: Calculate expected values and use them to solve problems.

S-MD.50: Students will: 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.

Lucky Duck (Expected Value)

Polling: City

S-MD.51: Students will: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

Lucky Duck (Expected Value)

Polling: City

S-MD.52: Students will: 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

Independent and Dependent Events

Lucky Duck (Expected Value)

Probability Simulations

Theoretical and Experimental Probability

S-MD.53: Students will: 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

5.3.2: Use probability to evaluate outcomes of decisions.

S-MD.54: Students will: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

S-MD.54.a: Find the expected payoff for a game of chance.

S-MD.54.b: Evaluate and compare strategies on the basis of expected values.

Correlation last revised: 9/15/2020

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