1: Students will develop Numeric Reasoning and an understanding of Number and Operations by solving problems in which there is a need to represent and model real numbers verbally, physically, and symbolically; to explain the relationship between numbers; to determine the relative magnitude of real numbers; to use operations with understanding; and to select appropriate methods of calculations from among mental math, paper-and-pencil, calculators, or computers.

1.1: Number sense

1.1.2: Simplify expressions with negative and fractional exponents

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

1.2: Operations

1.2.2: Perform addition, subtraction, and multiplication on polynomial expressions

Addition and Subtraction of Functions
Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c

1.2.3: Perform addition, subtraction, and multiplication on irrational expressions

Operations with Radical Expressions
Simplifying Radical Expressions

1.2.4: Recognize and use inverse operations to solve equations, powers, and their corresponding roots

Solving Two-Step Equations
Square Roots

2: Students will develop Algebraic Reasoning and an understanding of Patterns and Functions by solving problems in which there is a need to recognize and extend a variety of patterns; to progress from the concrete to the abstract using physical models, equations, and graphs; to describe, represent, and analyze relationships among variable quantities; and to analyze, represent, model, and describe real-world functional relationships.

2.1: Patterns and change

2.1.3: Develop the conceptual understanding that logarithmic and exponential functions are inverse functions

Logarithmic Functions

2.2: Representations

2.2.1: Model constraints to solve linear programming problems

Linear Programming

2.2.2: Analyze linear, quadratic, exponential, periodic, trigonometric, or inverse relationships in graphs using best fit lines and curves (regression lines and curve fitting)

Zap It! Game

2.3: Symbols

2.3.2: Write equivalent symbolic forms of linear, quadratic, or exponential functions

Slope-Intercept Form of a Line

2.3.3: Use geometric models and/or algebraic symbols to multiply binomials and complete the square

Circles

2.3.4: Use algebraic techniques to identify the vertex and intercepts for quadratic functions

Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Zap It! Game

2.3.5: Apply the quadratic formula and/or factor to solve problems

Modeling the Factorization of x²+bx+c
Roots of a Quadratic

2.3.6: Use expressions or equations to describe arithmetic and geometric sequences (nth term) and series (using sigma notation) to represent the sum

Arithmetic Sequences
Geometric Sequences

3: Students will develop Geometric Reasoning and an understanding of Geometry and Measurement by solving problems in which there is a need to recognize, construct, transform, analyze properties of, and discover relationships among geometric figures; and to measure to a required degree of accuracy by selecting appropriate tools and units.

3.1: Classification

3.1.2: Use Sine and Cosine functions to explore periodic real world phenomena

Translating and Scaling Sine and Cosine Functions

3.1.3: Identify and apply the properties of circles as they relate to central angles, inscribed angles, and tangents

Chords and Arcs
Inscribed Angles

3.2: Location and transformation

3.2.1: Stretch and shrink periodic functions by changing parameters

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

3.3: Measurement

3.3.2: Understand the relationship between degree measures and radian measures of benchmark angles such as 0°, 30°, 45°, 60°, 90°, and multiples of these angles

Cosine Function
Sine Function
Tangent Function

3.3.3: Use trigonometric relationships to determine side lengths and angle measures of any triangle

Sine, Cosine, and Tangent Ratios

4: Students will develop Quantitative Reasoning and an understanding of Data Analysis and Probability by solving problems in which there is a need to collect, appropriately represent, and interpret data; to make inferences or predictions and to present convincing arguments; and to model mathematical situations to determine the probability.

4.1: Collect

4.1.1: Understand the differences among the various kinds of studies (e.g., survey, controlled experiment)

Correlation
Polling: City
Polling: Neighborhood

4.1.2: Determine factors which may affect the outcome of a survey

Polling: City
Polling: Neighborhood

4.2: Represent

4.2.1: Interpret least squares regression line as the line that minimizes the sum of the squared errors

Correlation

4.3: Analyze

4.3.1: Compute and use standard deviation to analyze data variability

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

4.3.2: Apply benchmark percents described by the ?empirical rule? (68%-95%-99.7% rule) in a normal distribution

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

4.3.3: Recognize approximate norm distributions

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

4.4: Probability

4.4.1: Understand and use the addition rule to calculate probabilities for mutually exclusive and non-mutually exclusive events

Binomial Probabilities
Theoretical and Experimental Probability