MM1A1: Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MM1A1.b: Graph the basic functions f(x) = x to the n power, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

Functions Involving Square Roots
General Form of a Rational Function
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Roots of a Quadratic
Translating and Scaling Functions

MM1A1.c: Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

Absolute Value with Linear Functions - Activity B
Functions Involving Square Roots
Logarithmic Functions: Translating and Scaling
Reflections of a Linear Function
Reflections of a Quadratic Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

MM1A1.d: Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
Introduction to Functions
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

MM1A1.e: Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Roots of a Quadratic
Sine Function
Slope-Intercept Form of a Line - Activity A
Tangent Function
Translating and Scaling Functions
Using Tables, Rules and Graphs

MM1A1.f: Recognize sequences as functions with domains that are whole numbers.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MM1A1.g: Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Functions Involving Square Roots
Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Roots of a Quadratic
Slope - Activity B
Slope-Intercept Form of a Line - Activity A

MM1A1.h: Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

Cosine Function
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Sine Function
Tangent Function

MM1A1.i: Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

Solving Equations By Graphing Each Side

MM1A2: Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MM1A2.a: Simplify algebraic and numeric expressions involving square root.

Operations with Radical Expressions
Simplifying Radicals - Activity A
Square Roots

MM1A2.b: Perform operations with square roots.

Operations with Radical Expressions
Simplifying Radicals - Activity A
Square Roots

MM1A2.c: Add, subtract, multiply, and divide polynomials.

Addition of Polynomials - Activity A
Dividing Polynomials Using Synthetic Division

MM1A2.e: Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below.

MM1A2.e.1: (x + y)² = x² + 2xy + y²

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MM1A2.e.2: (x - y)² = x² - 2xy + y²

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MM1A2.e.3: (x + y)(x - y) = x² - y²

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MM1A2.e.4: (x + a)(x + b) = x² + (a + b)x + ab

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MM1A2.e.5: (x + y)³ = x³ +3x²y + 3xy² + y³

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MM1A2.e.6: (x – y)³ = x³ –3x²y + 3xy² - y

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MM1A2.f: Use area and volume models for polynomial arithmetic.

Addition of Polynomials - Activity A

MM1A3: Students will solve simple equations.

MM1A3.a: Solve quadratic equations in the form ax² + bx + c = 0 where a = 1 by using factorization and finding square roots where applicable.

Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Roots of a Quadratic

MM1A3.b: Solve equations involving radicals such as square root of x + b = c, using algebraic techniques.

Square Roots

MM1A3.c: Use a variety of techniques, including technology, tables and graphs to solve equations resulting from the investigation of x² + bx + c = 0.

Roots of a Quadratic

MM1G1: Students will investigate properties of geometric figures in the coordinate plane.

MM1G1.a: Determine the distance between two points.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

MM1G1.b: Determine the distance between a point and a line.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

MM1G1.d: Understand the distance formula as an application of the Pythagorean theorem.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

MM1G1.e: Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.

Area of Parallelograms - Activity A

MM1G3: Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MM1G3.a: Determine the sum of interior and exterior angles in a polygon.

Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

MM1G3.b: Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

Classifying Triangles
Triangle Angle Sum - Activity A
Triangle Inequalities

MM1G3.c: Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

Congruence in Right Triangles
Proving Triangles Congruent

MM1G3.d: Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

MM1G3.e: Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

Concurrent Lines, Medians, and Altitudes

MM1D1: Students will determine the number of outcomes related to a given event

MM1D1.b: Calculate and use simple permutations and combinations.

Binomial Probabilities
Permutations
Permutations and Combinations

MM1D2: Students will use the basic laws of probability

MM1D2.b: Find the probabilities of dependent events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

MM1D3: Students will relate samples to a population.

MM1D3.a: Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

Box-and-Whisker Plots
Line Plots
Mean, Median and Mode
Populations and Samples

MM1D3.b: Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

Line Plots
Mean, Median and Mode
Polling: City

MM1D3.c: Understand that a random sample is used to improve the chance of selecting a representative sample.

Polling: Neighborhood

MM1D4: Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations.)

Line Plots

MM2N1: Students will represent and operate with complex numbers.

MM2N1.b: Write complex numbers in the form a + bi.

Points in the Complex Plane - Activity A

MM2A1: Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MM2A1.a: Write absolute value functions as piecewise functions.

Inequalities Involving Absolute Values
Quadratic and Absolute Value Functions

MM2A1.c: Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MM2A2: Students will explore exponential functions.

MM2A2.a: Extend properties of exponents to include all integer exponents.

Dividing Exponential Expressions
Exponents and Power Rules

MM2A2.b: Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B

MM2A2.c: Graph functions as transformations of f(x) = a to the x power.

Exponential Functions - Activity A
Translating and Scaling Functions

MM2A2.d: Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MM2A2.e: Understand and use basic exponential functions as models of real phenomena.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life

MM2A2.f: Understand and recognize geometric sequences as exponential functions with domains that are whole numbers.

Arithmetic and Geometric Sequences
Exponential Functions - Activity A
Geometric Sequences

MM2A2.g: Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

Arithmetic and Geometric Sequences
Exponential Functions - Activity A
Geometric Sequences

MM2A3: Students will analyze quadratic functions in the forms f(x) = ax² + bx + c and f(x) = a(x - h)² + k.

MM2A3.a: Convert between standard and vertex form.

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

MM2A3.b: Graph quadratic functions as transformations of the function f(x) = x².

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Translating and Scaling Functions

MM2A3.c: Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

MM2A3.d: Explore arithmetic series and various ways of computing their sums.

Arithmetic Sequences
Arithmetic and Geometric Sequences

MM2A3.e: Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

MM2A4: Students will solve quadratic equations and inequalities in one variable.

MM2A4.a: Solve equations graphically using appropriate technology.

Quadratic Inequalities - Activity A
Roots of a Quadratic

MM2A4.b: Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Roots of a Quadratic

MM2A4.c: Analyze the nature of roots using technology and using the discriminant.

Roots of a Quadratic

MM2A4.d: Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Quadratic Inequalities - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MM2A5: Students will explore inverses of functions.

MM2A5.a: Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

Functions Involving Square Roots
Logarithmic Functions - Activity A

MM2A5.b: Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

General Form of a Rational Function
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Roots of a Quadratic

MM2A5.c: Explore the graphs of functions and their inverses.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

MM2G2: Students will define and apply sine, cosine, and tangent ratios to right triangles.

MM2G2.a: Discover the relationship of the trigonometric ratios for similar triangles.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

MM2G2.b: Explain the relationship between the trigonometric ratios of complementary angles.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

MM2G2.c: Solve application problems using the trigonometric ratios.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

MM2G3: Students will understand the properties of circles.

MM2G3.a: Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

Chords and Arcs

MM2G3.b: Understand and use properties of central, inscribed and related angles.

Chords and Arcs
Inscribing Angles

MM2G3.c: Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

MM2G3.d: Justify measurements and relationships in circles using geometric and algebraic properties.

Circles

MM2D1: Using sample data, students will make informal inferences about population means and standard deviations.

MM2D1.b: Understand and calculate the means and standard deviations of sets of data.

Line Plots

MM2D1.c: Use the means and standard deviations to compare data sets.

Line Plots
Populations and Samples

MM2D1.d: Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

Polling: City
Polling: Neighborhood

MM2D2: Students will determine an algebraic model to quantify the association between two quantitative variables.

MM2D2.a: Gather and plot data that can be modeled with linear and quadratic functions.

Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

MM2D2.b: Examine the issues of curve fitting by finding good linear fits to data using simple methods such as the median-median line and “eyeballing”.

Mean, Median and Mode

MM3A1: Students will analyze graphs of polynomial functions of higher degree.

MM3A1.a: Graph simple polynomial functions as translations of the function f(x) = ax to the n power.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Translating and Scaling Functions

MM3A1.b: Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Translating and Scaling Functions

MM3A1.c: Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A

MM3A1.d: Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A

MM3A2: Students will explore logarithmic functions as inverses of exponential functions.

MM3A2.c: Define logarithmic functions as inverses of exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

MM3A2.e: Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

MM3A2.f: Graph functions as transformations of f(x) = a to the x power, f(x) = log of a(x), f(x) = e to the x power, f(x) = ln x.

Exponential Functions - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Translating and Scaling Functions

MM3A2.g: Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

MM3A3: Students will solve a variety of equations and inequalities.

MM3A3.a: Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and the fundamental theorem of algebra, incorporating the role of complex and radical conjugates.

Dividing Polynomials Using Synthetic Division
Factoring Special Products
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors
Roots of a Quadratic

MM3A3.c: Solve polynomial, exponential and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MM3A3.d: Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

MM3A5: Students will use matrices to formulate and solve problems.

MM3A5.c: Represent and solve realistic problems using systems of linear equations.

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

MM3A6: Students will solve linear programming problems in two variables.

MM3A6.a: Solve systems of inequalities in two variables, showing the solutions graphically.

Linear Programming - Activity A
Modeling Linear Systems - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

MM3A6.b: Represent and solve realistic problems using linear programming.

Linear Programming - Activity A

MM3G1: Students will investigate the relationships between lines and circles.

MM3G1.a: Find equations of circles.

Circles

MM3G1.b: Graph a circle given an equation in general form.

Circles

MM3G1.d: Solve a system of equations involving a circle and a line.

Circles

MM3G1.e: Solve a system of equations involving two circles.

Circles

MM3G2: Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MM3G2.b: Graph conic sections, identifying fundamental characteristics.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

MM3G2.c: Write equations of conic sections given appropriate information.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

MM3G3: Students will investigate planes and spheres.

MM3G3.a: Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

Prisms and Cylinders - Activity A

MM3G3.b: Apply the distance formula in 3-space.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

MM3D1: Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Histograms
Independent and Dependent Events
Populations and Samples
Probability Simulations
Theoretical and Experimental Probability

MM4A1: Students will explore rational functions.

MM4A1.a: Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

General Form of a Rational Function
Rational Functions

MM4A1.b: Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

General Form of a Rational Function
Rational Functions

MM4A1.c: Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MM4A2: Students will use the circle to define the trigonometric functions.

MM4A2.a: Define and understand angles measured in degrees and radians, including but not limited to 0°, 30°, 45°, 60°, 90°, their multiples, and equivalences.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MM4A2.b: Understand and apply the six trigonometric functions as functions of general angles in standard position.

Cosine Function
Sine Function
Tangent Function

MM4A2.c: Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

Cosine Function
Sine Function
Tangent Function

MM4A2.d: Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MM4A2.e: Find values of trigonometric functions using the unit circle.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MM4A3: Students will investigate and use the graphs of the six trigonometric functions.

MM4A3.a: Understand and apply the six basic trigonometric functions as functions of real numbers.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MM4A3.b: Determine the characteristics of the graphs of the six basic trigonometric functions.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

MM4A3.c: Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

MM4A3.d: Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

MM4A4: Students will investigate functions.

MM4A4.a: Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Roots of a Quadratic
Sine Function
Tangent Function

MM4A4.b: Investigate transformations of functions.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

MM4A4.c: Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

Addition and Subtraction of Polynomials

MM4A5: Students will establish the identities below and use them to simplify trigonometric expressions and verify equivalence statements.

MM4A5.a: tan theta = sin theta/cos theta

Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle

MM4A5.c: sec theta = 1/cos theta

Simplifying Trigonometric Expressions

MM4A5.d: csc theta = 1/sin theta

Simplifying Trigonometric Expressions

MM4A5.e: sin² theta + cos² theta = 1

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

MM4A5.f: cot² + 1 = csc² theta

Simplifying Trigonometric Expressions

MM4A5.g: sin (alpha ± beta)= sin alpha cos beta ± cos alpha sin beta

Sum and Difference Identities for Sine and Cosine

MM4A5.h: cos (alpha ± beta) = cos alpha cos beta ± sin alpha sin beta

Sum and Difference Identities for Sine and Cosine

MM4A5.i: sin (2 theta) = 2 sin theta cos theta

Sum and Difference Identities for Sine and Cosine

MM4A5.j: cos (2 theta) = cos² theta - sin² theta

Sum and Difference Identities for Sine and Cosine

MM4A6: Students will solve trigonometric equations both graphically and algebraically.

MM4A6.b: Use the coordinates of a point on the terminal side of an angle to express x as r cos theta and y as r sin theta.

Points in Polar Coordinates

MM4A9: Students will use sequences and series

MM4A9.a: Use and find recursive and explicit formulae for the terms of sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MM4A9.b: Recognize and use simple arithmetic and geometric sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MM4A10: Students will understand and use vectors.

MM4A10.a: Represent vectors algebraically and geometrically.

Vectors

MM4A10.b: Convert between vectors expressed using rectangular coordinates and expressed using magnitude and direction.

Vectors

MM4A10.c: Add, subtract, and compute scalar multiples of vectors.

Vectors

MM4A10.d: Use vectors to solve realistic problems.

Vectors

MM4D1: Using simulation, students will develop the idea of the central limit theorem.

Probability Simulations

MM4D2: Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

Polling: Neighborhood

MA1N1: Students will represent and operate with complex numbers.

MA1N1.a: Write square roots of negative numbers in imaginary form.

Square Roots

MA1N1.b: Write complex numbers in the form a + bi.

Points in the Complex Plane - Activity A

MA1A1: Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.

MA1A1.b: Graph the basic functions f(x) = x to the power n, where n = 1 to 3, f(x) = square root of x, f(x) = |x|, and f(x) = 1/x.

Functions Involving Square Roots
General Form of a Rational Function
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Roots of a Quadratic

MA1A1.c: Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axes.

Absolute Value with Linear Functions - Activity B
Logarithmic Functions: Translating and Scaling
Reflections of a Linear Function
Reflections of a Quadratic Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

MA1A1.d: Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.

Functions Involving Square Roots
Introduction to Functions
Parabolas - Activity A
Polynomials and Linear Factors
Roots of a Quadratic

MA1A1.e: Relate to a given context the characteristics of a function, and use graphs and tables to investigate its behavior.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Tangent Function
Using Tables, Rules and Graphs

MA1A1.f: Recognize sequences as functions with domains that are sets of whole numbers.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
Linear Functions

MA1A1.g: Explore rates of change, comparing constant rates of change (i.e., slope) versus variable rates of change. Compare rates of change of linear, quadratic, square root, and other function families.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Functions Involving Square Roots
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Roots of a Quadratic
Slope - Activity B

MA1A1.h: Determine graphically and algebraically whether a function has symmetry and whether it is even, odd, or neither.

Cosine Function
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Sine Function
Tangent Function

MA1A1.i: Understand that any equation in x can be interpreted as the equation f(x) = g(x), and interpret the solutions of the equation as the x-value(s) of the intersection point(s) of the graphs of y = f(x) and y = g(x).

Ellipse - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side

MA1A2: Students will simplify and operate with radical expressions, polynomials, and rational expressions.

MA1A2.a: Simplify algebraic and numeric expressions involving square root.

Operations with Radical Expressions
Simplifying Radicals - Activity A
Square Roots

MA1A2.b: Perform operations with square roots.

Operations with Radical Expressions
Simplifying Radicals - Activity A
Square Roots

MA1A2.c: Add, subtract, multiply, and divide polynomials.

Addition of Polynomials - Activity A
Dividing Polynomials Using Synthetic Division

MA1A2.e: Factor expressions by greatest common factor, grouping, trial and error, and special products limited to the formulas below.

MA1A2.e.1: (x + y)² = x² + 2xy + y²

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MA1A2.e.2: (x – y)² = x² – 2xy + y²

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MA1A2.e.3: (x + y)(x – y) = x² – y²

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MA1A2.e.4: (x + a)(x + b) = x² + (a + b)x + ab

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MA1A2.e.5: (x + y)³ = x³ + 3x²y + 3xy² + y³

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MA1A2.e.6: (x – y)³ = x³ – 3x²y + 3xy² – y³

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

MA1A2.f: Use area and volume models for polynomial arithmetic.

Addition of Polynomials - Activity A

MA1A3: Students will analyze quadratic functions in the forms f(x) = ax² + bx + c and f(x) = a(x - h)² + k.

MA1A3.a: Convert between standard and vertex form.

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

MA1A3.b: Graph quadratic functions as transformations of the function f(x) = x².

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Translating and Scaling Functions

MA1A3.c: Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change.

Holiday Snowflake Designer
Parabolas - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

MA1A3.d: Explore arithmetic series and various ways of computing their sums.

Arithmetic Sequences
Arithmetic and Geometric Sequences

MA1A3.e: Explore sequences of partial sums of arithmetic series as examples of quadratic functions.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

MA1A4: Students will solve quadratic equations and inequalities in one variable.

MA1A4.a: Solve equations graphically using appropriate technology.

Roots of a Quadratic

MA1A4.b: Find real and complex solutions of equations by factoring, taking square roots, and applying the quadratic formula.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Roots of a Quadratic

MA1A4.c: Analyze the nature of roots using technology and using the discriminant.

Roots of a Quadratic

MA1A4.d: Solve quadratic inequalities both graphically and algebraically, and describe the solutions using linear inequalities.

Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Quadratic Inequalities - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MA1A5: Students will investigate step and piecewise functions, including greatest integer and absolute value functions.

MA1A5.a: Write absolute value functions as piecewise functions.

Inequalities Involving Absolute Values
Quadratic and Absolute Value Functions

MA1A5.b: Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

Holiday Snowflake Designer
Polynomials and Linear Factors

MA1A5.c: Solve absolute value equations and inequalities analytically, graphically, and by using appropriate technology.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MA1G1: Students will investigate properties of geometric figures in the coordinate plane.

MA1G1.a: Determine the distance between two points.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

MA1G1.b: Determine the distance between a point and a line.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A

MA1G1.d: Understand the distance formula as an application of the Pythagorean theorem.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

MA1G3: Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.

MA1G3.a: Determine the sum of interior and exterior angles in a polygon.

Polygon Angle Sum - Activity A
Triangle Angle Sum - Activity A

MA1G3.b: Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.

Triangle Inequalities

MA1G3.c: Understand and use congruence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).

Congruence in Right Triangles
Proving Triangles Congruent

MA1G3.d: Understand, use, and prove properties of and relationships among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

MA1G3.e: Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.

Concurrent Lines, Medians, and Altitudes

MA1G4: Students will understand the properties of circles.

MA1G4.a: Understand and use properties of chords, tangents, and secants as an application of triangle similarity.

Chords and Arcs

MA1G4.b: Understand and use properties of central, inscribed, and related angles.

Chords and Arcs
Inscribing Angles

MA1G4.c: Use the properties of circles to solve problems involving the length of an arc and the area of a sector.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

MA1G4.d: Justify measurements and relationships in circles using geometric and algebraic properties.

Circles

MA1D1: Students will determine the number of outcomes related to a given event.

MA1D1.b: Calculate and use simple permutations and combinations.

Binomial Probabilities
Permutations
Permutations and Combinations

MA1D2: Students will use the basic laws of probability.

MA1D2.b: Find the probabilities of dependent events.

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

MA1D3: Students will relate samples to a population.

MA1D3.a: Compare summary statistics (mean, median, quartiles, and interquartile range) from one sample data distribution to another sample data distribution in describing center and variability of the data distributions.

Box-and-Whisker Plots
Line Plots
Mean, Median and Mode
Populations and Samples

MA1D3.b: Compare the averages of the summary statistics from a large number of samples to the corresponding population parameters.

Line Plots
Mean, Median and Mode
Polling: City

MA1D3.c: Understand that a random sample is used to improve the chance of selecting a representative sample.

Polling: Neighborhood

MA1D4: Students will explore variability of data by determining the mean absolute deviation (the average of the absolute values of the deviations).

Line Plots

MA1D5: Students will determine an algebraic model to quantify the association between two quantitative variables.

MA1D5.a: Gather and plot data that can be modeled with linear and quadratic functions.

Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

MA2A1: Students will explore exponential functions.

MA2A1.a: Extend properties of exponents to include all integer exponents.

Dividing Exponential Expressions
Exponents and Power Rules

MA2A1.b: Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B

MA2A1.c: Graph functions as transformations of f(x) = a to the x power.

Exponential Functions - Activity A
Translating and Scaling Functions

MA2A1.d: Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MA2A1.e: Understand and use basic exponential functions as models of real phenomena.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life

MA2A1.f: Understand and recognize geometric sequences as exponential functions with domains that are sets of whole numbers.

Arithmetic and Geometric Sequences
Exponential Functions - Activity A
Geometric Sequences

MA2A1.g: Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.

Arithmetic and Geometric Sequences
Exponential Functions - Activity A
Geometric Sequences

MA2A2: Students will explore inverses of functions.

MA2A2.a: Discuss the characteristics of functions and their inverses, including one-to-oneness, domain, and range.

Functions Involving Square Roots
Logarithmic Functions - Activity A

MA2A2.b: Determine inverses of linear, quadratic, and power functions and functions of the form f(x) = a/x, including the use of restricted domains.

General Form of a Rational Function
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Roots of a Quadratic

MA2A2.c: Explore the graphs of functions and their inverses.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Functions Involving Square Roots
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

MA2A3: Students will analyze graphs of polynomial functions of higher degree.

MA2A3.a: Graph simple polynomial functions as translations of the function f(x) = ax to the n power.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Translating and Scaling Functions

MA2A3.b: Understand the effects of the following on the graph of a polynomial function: degree, lead coefficient, and multiplicity of real zeros.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Translating and Scaling Functions

MA2A3.c: Determine whether a polynomial function has symmetry and whether it is even, odd, or neither.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A

MA2A3.d: Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors

MA2A4: Students will explore logarithmic functions as inverses of exponential functions.

MA2A4.c: Define logarithmic functions as inverses of exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

MA2A4.e: Investigate and explain characteristics of exponential and logarithmic functions including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, and rate of change.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

MA2A4.f: Graph functions as transformations of f(x) = a to the x power, f(x) = log a to the x power, f(x) = e to the x power, f(x) = ln x.

Exponential Functions - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Translating and Scaling Functions

MA2A4.g: Explore real phenomena related to exponential and logarithmic functions including half-life and doubling time.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

MA2A5: Students will solve a variety of equations and inequalities.

MA2A5.a: Find real and complex roots of higher degree polynomial equations using the factor theorem, remainder theorem, rational root theorem, and fundamental theorem of algebra, incorporating complex and radical conjugates.

Dividing Polynomials Using Synthetic Division
Polynomials and Linear Factors
Roots of a Quadratic

MA2A5.c: Solve polynomial, exponential, and logarithmic inequalities analytically, graphically, and using appropriate technology. Represent solution sets of inequalities using interval notation.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MA2A5.d: Solve a variety of types of equations by appropriate means choosing among mental calculation, pencil and paper, or appropriate technology.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

MA2A7: Students will use matrices to formulate and solve problems.

MA2A7.c: Represent and solve realistic problems using systems of linear equations.

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

MA2A8: Students will solve linear programming problems in two variables.

MA2A8.a: Solve systems of inequalities in two variables, showing the solutions graphically.

Linear Programming - Activity A
Modeling Linear Systems - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

MA2A8.b: Represent and solve realistic problems using linear programming.

Linear Programming - Activity A

MA2G2: Students will define and apply sine, cosine, and tangent ratios to right triangles.

MA2G2.a: Discover the relationship of the trigonometric ratios for similar triangles.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

MA2G2.b: Explain the relationship between the trigonometric ratios of complementary angles.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

MA2G2.c: Solve application problems using the trigonometric ratios.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

MA2G3: Students will investigate the relationships between lines and circles.

MA2G3.a: Find equations of circles.

Circles

MA2G3.b: Graph a circle given an equation in general form.

Circles

MA2G3.d: Solve a system of equations involving a circle and a line.

Circles

MA2G3.e: Solve a system of equations involving two circles.

Circles

MA2G4: Students will recognize, analyze, and graph the equations of the conic sections (parabolas, circles, ellipses, and hyperbolas).

MA2G4.b: Graph conic sections, identifying fundamental characteristics.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

MA2G4.c: Write equations of conic sections given appropriate information.

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

MA2G5: Students will investigate planes and spheres.

MA2G5.a: Plot the point (x, y, z) and understand it as a vertex of a rectangular prism.

Prisms and Cylinders - Activity A

MA2G5.b: Apply the distance formula in 3-space.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

MA2D1: Using sample data, students will make informal inferences about population means and standard deviations.

MA2D1.b: Understand and calculate the means and standard deviations of sets of data.

Line Plots

MA2D1.c: Use means and standard deviations to compare data sets.

Line Plots
Populations and Samples

MA2D1.d: Compare the means and standard deviations of random samples with the corresponding population parameters. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.

Polling: City
Polling: Neighborhood

MA2D2: Students will create probability histograms of discrete random variables, using both experimental and theoretical probabilities.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Histograms
Independent and Dependent Events
Populations and Samples
Probability Simulations
Theoretical and Experimental Probability

MA3A1: Students will explore rational functions.

MA3A1.a: Investigate and explain characteristics of rational functions, including domain, range, zeros, points of discontinuity, intervals of increase and decrease, rates of change, local and absolute extrema, symmetry, asymptotes, and end behavior.

General Form of a Rational Function
Rational Functions

MA3A1.b: Find inverses of rational functions, discussing domain and range, symmetry, and function composition.

General Form of a Rational Function
Rational Functions

MA3A1.c: Solve rational equations and inequalities analytically, graphically, and by using appropriate technology.

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

MA3A2: Students will use the circle to define the trigonometric functions.

MA3A2.c: Find values of trigonometric functions using points on the terminal sides of angles in the standard position.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MA3A2.d: Understand and apply the six trigonometric functions as functions of arc length on the unit circle.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MA3A2.e: Find values of trigonometric functions using the unit circle.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MA3A3: Students will investigate and use the graphs of the six trigonometric functions.

MA3A3.a: Understand and apply the six basic trigonometric functions as functions of real numbers.

Cosine Function
Sine Function
Tangent Function
Unit Circle

MA3A3.b: Determine the characteristics of the graphs of the six basic trigonometric functions.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

MA3A3.c: Graph transformations of trigonometric functions including changing period, amplitude, phase shift, and vertical shift.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

MA3A3.d: Apply graphs of trigonometric functions in realistic contexts involving periodic phenomena.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions - Activity A
Unit Circle

MA3A4: Students will investigate functions.

MA3A4.a: Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Roots of a Quadratic
Sine Function
Tangent Function

MA3A4.b: Investigate transformations of functions.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

MA3A4.c: Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

Addition and Subtraction of Polynomials

MA3A5: Students will establish the identities below and use them to simplify trigonometric expressions and verify equivalence statements.

MA3A5.a: tan theta = sin theta/cos theta

Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle

MA3A5.c: sec theta = 1/cos theta

Simplifying Trigonometric Expressions

MA3A5.d: csc theta = 1/sin theta

Simplifying Trigonometric Expressions

MA3A5.e: sin² theta + cos² theta = 1

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

MA3A5.f: cot² theta + 1 = csc² theta

Simplifying Trigonometric Expressions

MA3A5.g: sin (alpha ± beta) = sin alpha cos beta ± cos alpha sin beta

Sum and Difference Identities for Sine and Cosine

MA3A5.h: cos (alpha ± beta) = cos alpha cos beta ± sin alpha sin beta

Sum and Difference Identities for Sine and Cosine

MA3A5.i: sin (2 theta) = 2 sin theta cos theta

Sum and Difference Identities for Sine and Cosine

MA3A5.j: cos (2 theta) = cos² theta - sin² theta

Sum and Difference Identities for Sine and Cosine

MA3A6: Students will solve trigonometric equations both graphically and algebraically.

MA3A6.b: Use the coordinates of a point on the terminal side of an angle to express x as r cos theta and y as r sin theta.

Points in Polar Coordinates

MA3A9: Students will use sequences and series

MA3A9.a: Use and find recursive and explicit formulae for the terms of sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MA3A9.b: Recognize and use simple arithmetic and geometric sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

MA3A9.g: Determine geometric series and their limits.

Arithmetic and Geometric Sequences
Geometric Sequences

MA3A10: Students will understand and use vectors.

MA3A10.a: Represent vectors algebraically and geometrically.

Vectors

MA3A10.b: Convert between vectors expressed using rectangular coordinates and vectors expressed using magnitude and direction.

Vectors

MA3A10.c: Add and subtract vectors and compute scalar multiples of vectors.

Vectors

MA3A10.d: Use vectors to solve realistic problems.

Vectors

MA3A11: Students will use complex numbers in trigonometric form.

MA3A11.a: Represent complex numbers in trigonometric form.

Complex Numbers in Polar Form

MA3A11.b: Find products, quotients, powers, and roots of complex numbers in trigonometric form.

Complex Numbers in Polar Form

MA3A13: Students will explore polar equations.

MA3A13.a: Express coordinates of points in rectangular and polar form.

Points in Polar Coordinates

MA3A13.b: Graph and identify characteristics of simple polar equations including lines, circles, cardioids, limaòons, and roses.

Circles

MA3D1: Using simulation, students will develop the idea of the central limit theorem.

Probability Simulations

MA3D2: Using student-generated data from random samples of at least 30 members, students will determine the margin of error and confidence interval for a specified level of confidence.

Polling: Neighborhood