Alabama Common Core
N.CN.2: 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.
Complex Numbers in Polar Form
Points in the Complex Plane - Activity A
N.CN.3: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
Points in the Complex Plane - Activity A
N.CN.4: 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.
Absolute Value of a Complex Number
Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Points in the Complex Plane - Activity A
Pythagorean Theorem - Activity A
N.VM.6: 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.7: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
N.VM.9: Add and subtract vectors.
N.VM.9.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.9.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
N.VM.9.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.16: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
Dilations
Reflections
Rotations, Reflections and Translations
N.VM.17: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
Area of Parallelograms - Activity B
Dilations
Real Number Line - Activity B
Reflections
Rotations, Reflections and Translations
A.REI.19: 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).
Systems of Linear Equations - Activity A
F.CS.20: Create graphs of conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.
F.CS.20.a: Formulate equations of conic sections from their determining characteristics.
F.IF.21: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
Function Machines 2 (Functions, Tables, and Graphs)
General Form of a Rational Function
Polynomials and Linear Factors
Rational Functions
F.BF.22: Compose functions.
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
F.BF.23: Determine the inverse of a function and a relation.
Function Machines 3 (Functions and Problem Solving)
F.BF.25: Read values of an inverse function from a graph or a table, given that the function has an inverse.
Function Machines 2 (Functions, Tables, and Graphs)
F.BF.26: Produce an invertible function from a non-invertible function by restricting the domain.
Function Machines 3 (Functions and Problem Solving)
F.BF.27: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Function Machines 3 (Functions and Problem Solving)
F.BF.28: Compare effects of parameter changes on graphs of transcendental functions.
Slope-Intercept Form of a Line - Activity B
Translating and Scaling Functions
F.TF.29: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses.
Cosine Function
Function Machines 3 (Functions and Problem Solving)
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
F.TF.30: Use the sum, difference, and half-angle identities to find the exact value of a trigonometric function.
Cosine Function
Sine Function
Sum and Difference Identities for Sine and Cosine
Tangent Function
F.TF.31: Utilize parametric equations by graphing and by converting to rectangular form.
F.TF.31.b: Solve applied problems that include sequences with recurrence relations.
Percent of Change
Road Trip (Problem Solving)
F.TF.32: Use special triangles to determine geometrically the values of sine, cosine, 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 and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle
F.TF.33: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Cosine Function
Sine Function
Tangent Function
Unit Circle
F.TF.34: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
Cosine Function
Sine Function
Tangent Function
F.TF.36: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Sum and Difference Identities for Sine and Cosine
Tangent Function
Tangent Ratio
Unit Circle
G.GPE.37: Derive the equation of a parabola given a focus and directrix.
G.GPE.38: 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.
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A
S.MD.40: 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.
Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots
S.MD.41: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
S.MD.42: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
Probability Simulations
Theoretical and Experimental Probability
S.MD.43: 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 - Activity A
Probability Simulations
Theoretical and Experimental Probability
S.MD.44: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
S.MD.44.a: Find the expected payoff for a game of chance.
Binomial Probabilities
Geometric Probability - Activity A
Correlation last revised: 3/17/2015