1: Number, Number Sense and Operations

1.A: Demonstrate that vectors and matrices are systems having some of the same properties of the real number system.

Vectors

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

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
Permutations and Combinations

2: Measurement

2.A: Explain differences among accuracy, precision and error, and describe how each of those can affect solutions in measurement situations.

Triple Beam Balance

2.B: Apply various measurement scales to describe phenomena and solve problems.

Dilations
Similar Figures - Activity A
Similar Polygons

2.C: Estimate and compute areas and volume in increasingly complex problem situations.

2.C.3: Apply informal concepts of successive approximation, upper and lower bounds, and limits in measurement situations; e.g., measurement of some quantities, such as volume of a cone, can be determined by sequences of increasingly accurate approximations.

Pyramids and Cones - Activity A

3: Geometry and Spatial Sense

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

3.A.2: Derive and apply the basic trigonometric identities; i.e., angle addition, angle subtraction, and double angle.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

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

Circles
Ellipse - Activity A
Hyperbola - Activity A

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
Reflections
Rotations, Reflections and Translations
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
Geometric Sequences

4.A.2: Translate between the numeric and symbolic form of a sequence or series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
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 - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions - Activity A

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

Cosine Function
Exponential Functions - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function

4.A.9: Translate freely between polar and Cartesian coordinate systems.

Points in Polar Coordinates

4.A.10: Use the concept of limit to find instantaneous rate of change for a point on a graph as the slope of a tangent at a point.

Tangent Ratio

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

Roots of a Quadratic

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.

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

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.

Binomial Probabilities

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: Neighborhood

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

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.

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

6: Mathematical Processes

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

Proving Triangles Congruent

6.G: Understand the difference between a statement that is verified by mathematical proof, such as a theorem, and one that is verified empirically using examples or data.

Conditional Statement
Proving Triangles Congruent
Sum and Difference Identities for Sine and Cosine

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.

Percent of Change