1: Number, Number Sense and Operations

1.B: Develop an understanding of properties of and representations for addition and multiplication of vectors and matrices.

Adding Vectors
Dilations
Translations
Vectors

1.C: Apply factorials and exponents, including fractional exponents, to solve practical problems.

1.C.2: Apply combinations as a method to create coefficients for the Binomial Theorem, and make connections to everyday and workplace problem situations.

Binomial Probabilities

1.D: Demonstrate fluency in operations with real numbers, vectors and matrices, using mental computation or paper and pencil calculations for simple cases and technology for more complicated cases.

Adding Vectors

3: Geometry and Spatial Sense

3.A: Use trigonometric relationships to verify and determine solutions in problem situations.

3.A.3: Relate graphical and algebraic representations of lines, simple curves and conic sections.

Slope

3.B: Represent transformations within a coordinate system using vectors and matrices.

3.B.1: Use matrices to represent translations, reflections, rotations, dilations and their compositions.

Dilations
Translations

4: Patterns, Functions and Algebra

4.A: Analyze functions by investigating rates of change, intercepts, zeros, asymptoes, and local and global behavior.

4.A.1: Analyze the behavior of arithmetic and geometric sequences and series as the number of terms increases.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

4.A.3: Describe and compare the characteristics of transcendental and periodic functions; e.g., general shape, number of roots, domain and range, asymptotic behavior, extrema, local and global behavior.

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

4.A.4: Represent the inverse of a transcendental function symbolically.

Cosine Function
Logarithmic Functions

4.B: Use the quadratic formula to solve quadratic equations that have complex roots.

Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic

4.C: Use recursive functions to model and solve problems; e.g., home mortgages, annuities.

4.C.8: Compare estimates of the area under a curve over a bounded interval by partitioning the region with rectangles; e.g., make successive estimates using progressively smaller rectangles.

Riemann Sum

4.D: Apply algebraic methods to represent and generalize problem situations involving vectors and matrices.

4.D.5: Set up and solve systems of equations using matrices and graphs, with and without technology.

Cat and Mouse (Modeling with Linear Systems)
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

5: Data Analysis and Probability

5.A: Create and analyze tabular and graphical displays of data using appropriate tools, including spreadsheets and graphing calculators.

5.A.4: Apply the concept of a random variable to generate and interpret probability distributions, including binomial, normal and uniform.

Polling: City

5.B: Use descriptive statistics to analyze and summarize data, including measures of center, dispersion, correlation and variability.

5.B.3: Describe the shape and find all summary statistics for a set of univariate data, and describe how a linear transformation affects shape, center and spread.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Real-Time Histogram
Stem-and-Leaf Plots

5.C: Design and perform a statistical experiment, simulation or study; collect and interpret data; and use descriptive statistics to communicate and support predictions and conclusions.

5.C.1: Identify and use various sampling methods (voluntary response, convenience sample, random sample, stratified random sample, census) in a study.

Polling: City
Polling: Neighborhood
Populations and Samples

5.C.5: Use sampling distributions as the basis for informal inference.

Polling: City
Populations and Samples

5.D: Connect statistical techniques to applications in workplace and consumer situations.

5.D.6: Use theoretical or experimental probability, including simulations, to determine probabilities in real-world problem situations involving uncertainty, such as mutually exclusive events, complementary events and conditional probability.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

6: Mathematical Processes

6.B: Construct logical verifications or counter-examples to test conjectures and to justify or refute algorithms and solutions to problems.

Biconditional Statements
Conditional Statements

6.D: Select and use various types of reasoning and methods of proof.

Biconditional Statements

6.H: Use formal mathematical language and notation to represent ideas, to demonstrate relationships within and among representation systems, and to formulate generalizations.

Using Algebraic Expressions

6.J: Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation.

Estimating Population Size