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

1.1.3: Simplify numeric and symbolic expressions involving absolute value, square roots, and exponents

Dividing Exponential Expressions
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Radical Expressions

1.2: Operations

1.2.1: Use technology to add, subtract, and multiply with matrices in problem solving situations

Translations

1.2.2: Solve problems that involve using inverse operations including powers and roots

Logarithmic Functions
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

2.1.4: Use a variety of strategies to write expressions that generate the nth term of linear, exponential, and quadratic functions

Slope-Intercept Form of a Line

2.1.5: Distinguish between situations involving direct and inverse variations

Direct and Inverse Variation

2.2: Representations

2.2.1: Model and solve situations involving systems of equations and inequalities

Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Linear Programming
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

2.2.2: Determine the appropriateness of linear, exponential or quadratic models given a real-world situation

Arithmetic Sequences
Compound Interest
Quadratics in Polynomial Form

2.3: Symbols

2.3.1: Solve systems of linear equations and inequalities both algebraically and using technology

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

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

3.1.1: Determine whether a triangle is a right triangle (e.g., Converse of Pythagorean Theorem, slopes of adjacent sides)

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Cosine Function
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Similarity in Right Triangles
Sine Function
Tangent Function

3.1.2: Identify necessary and sufficient conditions that define parallelograms or triangles

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

3.1.3: Justify whether two figures are similar or congruent

Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

3.1.4: Use and justify angle relationships created by intersecting and parallel lines

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Triangle Angle Sum

3.2: Location and transformation

3.2.2: Use appropriate technologies to model geometric figures and to develop conjectures about them

Segment and Angle Bisectors

3.3: Measurement

3.3.1: Apply trigonometric relationships to determine side lengths and angle measures of right triangle

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

3.3.3: Find missing dimensions of a shape given the area, volume, or surface area

Area of Triangles
Perimeter and Area of Rectangles
Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

3.3.4: Apply the Pythagorean Theorem and its converse

Circles
Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Surface and Lateral Areas of Pyramids and Cones
Tangent Function

3.3.5: Develop and apply the distance and midpoint formulas

Circles
Distance Formula

3.3.7: Demonstrate the effects of scaling on volume and surface area of three-dimensional solids

Surface and Lateral Areas of Prisms and Cylinders

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: Use permutations and combinations as counting techniques

Binomial Probabilities
Permutations and Combinations

4.4: Probability

4.4.1: Compute and interpret expected value

Binomial Probabilities

4.4.2: Compute the probability of both independent and dependent events

Binomial Probabilities
Independent and Dependent Events