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.

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
Function Machines 2 (Functions, Tables, and Graphs)
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
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
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.

Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Reflections of a Quadratic Function
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
Quadratics in Factored Form
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

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
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.

Function Machines 3 (Functions and Problem Solving)

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.

Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
General Form of a Rational Function
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

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

Cosine Function
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Translating and Scaling Functions

MM2A5.d: Use composition to verify that functions are inverses of each other.

Function Machines 3 (Functions and Problem Solving)

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

MM2G4: Students will find and compare the measures of spheres.

MM2G4.a: Use and apply surface area and volume of a sphere.

Surface and Lateral Area of Pyramids and Cones

MM2G4.b: Determine the effect on surface area and volume of changing the radius or diameter of a sphere.

Surface and Lateral Area of Pyramids and Cones

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 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.

Function Machines 2 (Functions, Tables, and Graphs)
Quadratics in Factored Form
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

MM2D2.d: Investigate issues that arise when using data to explore the relationship between two variables, including confusion between correlation and causation.

Correlation