1: Number and Operations

1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

1.1.C: Compose and decompose numbers

1.1.C.1: use vectors and matrices as systems and compare their properties to the real-number system

Vectors

1.3: Compute fluently and make reasonable estimates

1.3.E: Use proportional reasoning

1.3.E.1: solve problems involving proportions

Estimating Population Size

2: Algebraic Relationships

2.1: Understand patterns, relations, and functions

2.1.B: Create and analyze patterns

2.1.B.1: generalize patterns using explicitly or recursively defined functions

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

2.1.D: Identify and compare functions

2.1.D.1: understand and compare the properties of exponential, polynomial, rational, logarithmic, and periodic functions

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions - Activity A

2.1.E: Describe the effects of parameter changes

2.1.E.1: describe the effects of parameter changes on polynomial and periodic function

Cosine Function
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Parabolas - Activity A
Roots of a Quadratic
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

2.2: Represent and analyze mathematical situations and structures using algebraic symbols

2.2.A: Represent mathematical situations

2.2.A.1: use symbolic algebra to represent and solve problems that involve periodic relationships, including recursive and parametric relationships

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

2.2.B: Describe and use mathematical manipulation

2.2.B.1: describe and use algebraic manipulations, including inverse of functions, composition of functions

Addition and Subtraction of Polynomials

2.2.C: Utilize equivalent forms

2.2.C.1: use and solve equivalent forms of equations and inequalities (polynomial and trigonometric)

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

2.2.D: Utilize systems

2.2.D.1: use and solve systems of equations or inequalities

Linear Programming - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Special Types of Solutions to Linear Systems
Systems of Linear Inequalities (Slope-intercept form) - Activity A

2.3: Use mathematical models to represent and understand quantitative relationships

2.3.A: Use mathematical models

2.3.A.1: identify quantitative relationships and determine the type(s) of functions that might model the situation to solve the problem (including recursive forms)

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions: Translating and Scaling

2.4: Analyze change in various contexts

2.4.A: Analyze change

2.4.A.1: analyze rational, polynomial and periodic functions by investigating rates of change, intercepts and asymptotes

Cosine Function
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Rational Functions
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions - Activity A

3: Geometric and Spatial Relationships

3.1: Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships

3.1.A: Describe and use geometric relationships

3.1.A.1: use trigonometric relationships to determine lengths and angle measures in all types of triangles

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio

3.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems

3.2.A: Use coordinate systems

3.2.A.1: use Cartesian coordinates and other coordinate systems to analyze geometric situations, such as navigational, polar or spherical systems

Points in Polar Coordinates

3.3: Apply transformations and use symmetry to analyze mathematical situations

3.3.B: Use transformations on functions

3.3.B.1: perform simple transformations and their compositions on linear, quadratic, logarithmic, exponential, rational and periodic functions

Exponential Functions - Activity A
General Form of a Rational Function
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Reflections of a Linear Function
Reflections of a Quadratic Function
Roots of a Quadratic
Translating and Scaling Functions

5: Data and Probability

5.2: Select and use appropriate statistical methods to analyze data

5.2.C: Represent data algebraically

5.2.C.1: create a scatterplot, describe its shape, determine and analyze regression equations using technological tools

Correlation
Lines of Best Fit Using Least Squares - Activity A
Scatter Plots - Activity A
Solving Using Trend Lines

5.4: Understand and apply basic concepts of probability

5.4.A: Apply basic concepts of probability

5.4.A.1: use simulations to construct empirical probability distributions

Binomial Probabilities