1: Number and Operations

1.1: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.

1.1.1: Solve problems and equations that require the number system to be extended from real to complex numbers.

Points in the Complex Plane

1.1.2: Convert between radical and exponential forms of numerical expressions.

Operations with Radical Expressions
Simplifying Radical Expressions

2: Data Analysis, Probability, and Discrete Mathematics

2.1: Understand and apply data collection, organization, and representation to analyze and sort data.

2.1.2: Compare data sets using graphs and summary statistics, including variance and standard deviation, with or without technology.

Polling: City
Real-Time Histogram

2.1.3: Compute and explain summary statistics for distributions of data including measures of center and spread, including variance and standard deviation.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

2.1.7: Determine when arguments based on data mistake correlation for causation.

Correlation

2.1.8: Draw a line of best fit for a scatterplot with or without technology, describe how the correlation coefficient relates to fit, and explain when it is appropriate to use the regression equation to make predictions.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

2.2: Understand and apply the basic concepts of probability.

2.2.1: Apply probability concepts to calculate the probability of events and to make informed decisions in practical situations.

Binomial Probabilities
Independent and Dependent Events
Theoretical and Experimental Probability

2.2.2: Use the principal characteristics of the normal distribution to estimate probabilities.

Polling: City

2.2.3: Estimate probabilities and predict outcomes using one- and two-variable data.

Polling: Neighborhood

2.3: Understand and demonstrate the systematic listing and counting of possible outcomes.

2.3.1: Use the binomial theorem and Pascal's Triangle to solve problems.

Binomial Probabilities

2.3.2: Demonstrate the connections between the binomial coefficients, entries of Pascal's triangle, and combinations.

Binomial Probabilities

3: Patterns, Algebra, and Functions

3.1: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

3.1.1: Analyze sequences and series and use them in modeling, including

3.1.1.a: explicit formulas for nth terms,

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

3.1.2: Apply recursive formulas for arithmetic and geometric sequences to solve problems.

Arithmetic Sequences
Geometric Sequences

3.1.4: Solve problems involving recursion.

Arithmetic Sequences
Geometric Sequences

3.2: Describe and model functions and their relationships.

3.2.1: Express and solve problems that can be modeled using linear, quadratic, logarithmic, exponential, cubic, reciprocal, absolute value, and step and other piecewise-defined functions; interpret their solutions in terms of the context.

Arithmetic Sequences
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Quadratics in Polynomial Form
Slope-Intercept Form of a Line

3.2.3: Graph absolute value, and step and other piecewise-defined functions identifying their key characteristics.

Absolute Value with Linear Functions
Translating and Scaling Functions

3.2.4: Graph exponential functions identifying their key characteristics.

Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

3.2.6: Graph polynomial functions identifying their key characteristics.

Graphs of Polynomial Functions
Polynomials and Linear Factors
Quadratics in Factored Form

3.2.7: Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions.

Exponential Functions
General Form of a Rational Function
Hyperbolas
Introduction to Exponential Functions
Logarithmic Functions
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors
Radical Functions
Rational Functions
Roots of a Quadratic

3.2.8: Find the major and minor axes, intercepts and asymptotes of conic sections.

Hyperbolas
Parabolas

3.2.9: Find domain, range, intercepts, period, amplitude, and asymptotes of trigonometric functions.

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

3.2.10: Given a function

3.2.10.a: find the inverse of the function,

Logarithmic Functions

3.2.12: Use theorems of polynomial behavior (including but not limited to the Fundamental Theorem of Algebra, Remainder Theorem, the Rational Root Theorem, Descartes Rule of Signs, the Conjugate Root Theorem) to find the zeros of a polynomial function.

Graphs of Polynomial Functions

3.2.14: Combine functions by composition, as well as by addition, subtraction, multiplication, and division including any necessary restrictions on the domain.

Addition and Subtraction of Functions

3.2.16: Identify the degree of a given polynomial function and write a polynomial function of a given degree.

Graphs of Polynomial Functions
Polynomials and Linear Factors

3.3: Represent and analyze mathematical situations and structures using algebraic representations.

3.3.1: Rewrite and describe the need for equivalent forms of algebraic expressions.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Modeling the Factorization of ax²+bx+c
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

3.3.2: Apply the laws of exponents including rational and negative exponents to rewrite expressions in alternative forms.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

3.3.4: Use matrices to represent everyday problems that involve systems of linear equations.

Solving Linear Systems (Matrices and Special Solutions)

3.3.5: Simplify radical expressions by performing operations on them.

Operations with Radical Expressions
Simplifying Radical Expressions

3.3.6: Divide a polynomial by a lower degree polynomial.

Dividing Polynomials Using Synthetic Division

3.3.7: Find complex solutions for quadratic equations.

Roots of a Quadratic

3.3.8: Describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression with and without technology.

Logarithmic Functions
Modeling the Factorization of x²+bx+c
Polynomials and Linear Factors
Roots of a Quadratic

3.3.11: Add, subtract, and compute the dot product of two-dimensional vectors; multiply a two-dimensional vector by a scalar.

Adding Vectors
Vectors

3.4: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

3.4.5: Solve problems involving compound interest.

Compound Interest

3.4.6: Demonstrate the relationship between

3.4.6.a: simple interest and linear growth

Compound Interest

3.4.6.b: compound interest and exponential growth.

Compound Interest

4: Geometry and Measurement

4.1: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

4.1.1: Perform basic geometric constructions using a variety of methods, including

4.1.1.a: perpendicular bisector of a line segment,

Concurrent Lines, Medians, and Altitudes
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

4.1.1.b: bisector of an angle

Concurrent Lines, Medians, and Altitudes
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

4.1.1.c: perpendicular or parallel lines.

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Parallel, Intersecting, and Skew Lines

4.2: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

4.2.1: Describe how changing the parameters of a quadratic function affects the shape and position of its graph (f(x) = a(x-h)²+k).

Graphs of Polynomial Functions
Zap It! Game

4.2.2: Describe how changing the parameters of an exponential function affects the shape and position of its graph (f(x) = ab to the x power).

Introduction to Exponential Functions

4.3: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.

4.3.2: Determine an equation of a circle given its center and radius; given an equation of a circle, find its center and radius.

Circles

4.3.3: Graph equations of conic sections explaining the relationship between their algebraic form and key characteristics of the graph.

Circles
Ellipses
Hyperbolas
Parabolas

4.3.4: Graph all six trigonometric functions identifying their key characteristics.

Translating and Scaling Functions

4.3.5: Evaluate all six trigonometric functions at angles between (0 degrees and 360 degrees, 0 and 2π radians) using the unit circle in the coordinate plane.

Cosine Function
Sine Function
Tangent Function

4.4: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.4.1: Explain, use, and convert between degree and radian measures for angles.

Cosine Function
Sine Function
Tangent Function