1: Number, Number Sense and Operations

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

1.B.2: Determine what properties hold for vector addition and multiplication, and for scalar multiplication.

Adding Vectors
Vectors

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

1.C.8: Use fractional and negative exponents as optional ways of representing and finding solutions for problem situations; e.g., 27 ^{[27 and two-thirds]} = (27 ^{[27 and one-third]} )² = 9.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

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.

1.D.6: Compute sums, differences and products of matrices using paper and pencil calculations for simple cases, and technology for more complicated cases.

Translations

1.D.9: Use vector addition and scalar multiplication to solve problems.

Adding Vectors
Vectors

1.E: Represent and compute with complex numbers.

1.E.3: Represent complex numbers on the complex plane.

Points in the Complex Plane

3: Geometry and Spatial Sense

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

3.A.4: Use trigonometric relationships to determine lengths and angle measures; i.e., Law of Sines and Law of Cosines.

Sine, Cosine, and Tangent Ratios

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

3.B.3: Describe multiplication of a vector and a scalar graphically and algebraically, and apply to problem situations.

Adding Vectors
Vectors

4: Patterns, Functions and Algebra

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

4.A.3: Describe and compare the characteristics of the following families of functions: quadratics with complex roots, polynomials of any degree, logarithms, and rational functions; e.g., general shape, number of roots, domain and range, asymptotic behavior.

General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions: Translating and Scaling
Polynomials and Linear Factors
Quadratics in Factored Form
Rational Functions
Roots of a Quadratic

4.A.4: Identify the maximum and minimum points of polynomial, rational and trigonometric functions graphically and with technology.

Graphs of Polynomial Functions
Quadratics in Factored Form

4.A.5: Identify families of functions with graphs that have rotation symmetry or reflection symmetry about the y-axis, x-axis or y = x.

Absolute Value with Linear Functions
Translating and Scaling Functions

4.A.10: Describe the characteristics of the graphs of conic sections.

Circles
Ellipses
Hyperbolas
Parabolas

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

4.B.8: Solve equations involving radical expressions and complex roots.

Operations with Radical Expressions
Radical Functions

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

4.C.1: Identify and describe problem situations involving an iterative process that can be represented as a recursive function; e.g., compound interest.

Arithmetic Sequences
Geometric Sequences

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

4.D.7: Model and solve problems with matrices and vectors.

Adding Vectors
Dilations

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: Create a scatterplot of bivariate data, identify trends, and find a function to model the data.

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

5.A.5: Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

5.A.7: Describe the standard normal curve and its general properties, and answer questions dealing with data assumed to be normal.

Polling: City
Populations and Samples
Real-Time Histogram
Sight vs. Sound Reactions

5.A.8: Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions.

Box-and-Whisker Plots
Conditional Statements
Correlation
Real-Time Histogram
Solving Using Trend Lines
Trends in Scatter Plots

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

5.B.5: Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

5.B.6: Use technology to compute the standard deviation for a set of data, and interpret standard deviation in relation to the context or problem situation.

Polling: City
Real-Time Histogram

5.B.8: Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions.

Box-and-Whisker Plots
Conditional Statements
Correlation
Real-Time Histogram
Solving Using Trend Lines
Trends in Scatter 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: Design a statistical experiment, survey or study for a problem; collect data for the problem; and interpret the data with appropriate graphical displays, descriptive statistics, concepts of variability, causation, correlation and standard deviation.

Correlation
Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Real-Time Histogram

5.C.2: Describe the role of randomization in a well-designed study, especially as compared to a convenience sample, and the generalization of results from each.

Polling: City
Polling: Neighborhood
Populations and Samples

5.C.9: Evaluate validity of results of a study based on characteristics of the study design, including sampling method, summary statistics and data analysis techniques.

Box-and-Whisker Plots
Polling: City
Populations and Samples

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

5.D.1: Design a statistical experiment, survey or study for a problem; collect data for the problem; and interpret the data with appropriate graphical displays, descriptive statistics, concepts of variability, causation, correlation and standard deviation.

Correlation
Describing Data Using Statistics
Polling: City
Polling: Neighborhood
Real-Time Histogram

5.D.2: Describe the role of randomization in a well-designed study, especially as compared to a convenience sample, and the generalization of results from each.

Polling: City
Polling: Neighborhood
Populations and Samples

5.D.9: Evaluate validity of results of a study based on characteristics of the study design, including sampling method, summary statistics and data analysis techniques.

Box-and-Whisker Plots
Polling: City
Populations and Samples

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
Percent of Change