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

1.1.1: Demonstrate an understanding of numbers as rational or irrational

Rational Numbers, Opposites, and Absolute Values

1.1.2: Compare relative sizes of real numbers

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

1.1.3: Estimate square roots

Square Roots

1.2: Operations

1.2.2: Extend the ?order of operations? to include absolute value

Rational Numbers, Opposites, and Absolute Values

1.2.4: Use properties of the real number system to simplify expressions (Associative, Commutative, Identity, Inverse, and Distributive)

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Algebraic Equations II

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

2.1.2: Understand and compare the graphs, tables, and equations within linear contexts that are direct variations (proportional) and those that are not

Absolute Value with Linear Functions
Arithmetic Sequences
Compound Interest
Direct and Inverse Variation
Exponential Functions
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

2.1.3: Describe the effect of parameter changes on linear and exponential functions within a context, table, graph, and equation

Absolute Value with Linear Functions
Introduction to Exponential Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line

2.1.4: Compare linear with exponential functions using, the context, table, graph, or equation

Absolute Value with Linear Functions
Exponential Functions
Linear Functions
Logarithmic Functions

2.2: Representations

2.2.1: Model and solve real-world linear situations, including linear inequalities, using tables, graphs, and symbols

Slope-Intercept Form of a Line
Systems of Linear Inequalities (Slope-intercept form)
Using Algebraic Expressions

2.2.2: Model and solve situations involving systems of equations with tables or graphs using technology

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

2.2.3: Analyze data sets using technology to find an appropriate linear or exponential mathematical model

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

2.2.6: Analyze the interrelationship among the table, graph and equation of both linear and exponential functions paying particular attention to the meaning of intercept and slope in the context of the problem

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Logarithmic Functions
Slope-Intercept Form of a Line

2.3: Symbols

2.3.1: Determine symbolically the equation of a line given combinations of point, slope, and intercept information

Linear Inequalities in Two Variables
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

2.3.2: Convert between equivalent forms of linear functions

Linear Functions
Points, Lines, and Equations

2.3.3: Solve single variable equations and inequalities algebraically

Absolute Value Equations and Inequalities
Compound Inequalities
Linear Inequalities in Two Variables
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

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.

3.3: Measurement

3.3.1: Demonstrate an understanding of and apply formulas for area, surface area, and volume of geometric figures including pyramids, cones, spheres, and cylinders

Area of Parallelograms
Area of Triangles
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

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: Describe and explain how the validity of predictions are affected by number of trials, sample size, and the population

Polling: City

4.2: Represent

4.2.1: Select and interpret the most appropriate display for a given purpose and set(s) of data (e.g., histograms, parallel box plots, stem-and-leaf plots, scatter plots)

Box-and-Whisker Plots
Correlation
Histograms
Least-Squares Best Fit Lines
Real-Time Histogram
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

4.3: Analyze

4.3.2: Describe the effect of outliers in both one-variable and two-variable contexts

Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode

4.4: Probability

4.4.1: Use and design simulations or experiments to determine probabilities of independent and dependent events

Binomial Probabilities
Independent and Dependent Events

4.4.3: Compare event experimental probability with theoretical probability (Law of Large Numbers)

Theoretical and Experimental Probability