6A: Students who meet the standard can demonstrate knowledge and use of numbers and their many representations in a broad range of theoretical and practical settings. (Representations)

6A.1: Represent numbers in equivalent forms (e.g., exponential/logarithmic, radical/rational exponents).

Part-to-part and Part-to-whole Ratios

6A.2: Graph or interpret the graph of a complex number in rectangular and vector forms.

Points in the Complex Plane

6B: Students who meet the standard can investigate, represent and solve problems using number facts, operations, and their properties, algorithms, and relationships. (Operations and properties)

6B.1: Compare and contrast the properties of numbers and number systems, including the complex numbers as solutions to quadratic equations that do not have real solutions.

Solving Algebraic Equations I
Solving Algebraic Equations II

6B.2: Simplify expressions using the field properties, order properties, and properties of equality for the set of real numbers.

Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

6B.4: Determine the opposite, reciprocal, absolute values, and positive integral powers of a complex number.

Points in the Complex Plane

6B.9: Solve problems using matrices.

Dilations

7A: Students who meet the standard can measure and compare quantities using appropriate units, instruments, and methods. (Performance and conversion of measurements)

7A.1: Convert angle measures between degrees and radians.

Cosine Function
Sine Function
Tangent Function

7B: Students who meet the standard can estimate measurements and determine acceptable levels of accuracy. (Estimation)

7B.3: Solve problems to a desired interval of accuracy.

Polling: Neighborhood

8A: Students who meet the standard can describe numerical relationships using variables and patterns. (Representations and algebraic manipulations)

8A.1: Generalize patterns using explicitly-defined and recursively-defined sequences.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

8A.2: Translate between explicit and recursive forms of sequences where possible.

Arithmetic Sequences
Geometric Sequences

8A.5: Explain the differences and similarities of different forms of growth formulas.

Compound Interest

8A.7: Simplify algebraic expressions using exponential, logarithmic, and rational number techniques, including more advanced factoring.

Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Factoring Special Products
Multiplying Exponential Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

8B: Students who meet the standard can interpret and describe numerical relationships using tables, graphs, and symbols. (Connections of representations including the rate of change)

8B.3: Relate the effect of transformations on graphs and equations.

Absolute Value with Linear Functions
Dilations
Introduction to Exponential Functions
Rotations, Reflections, and Translations
Translating and Scaling Sine and Cosine Functions
Translations

8B.4: Analyze functions by investigating domain, range, rates of change, intercepts, zeros, asymptotes, and local and global behavior.

Exponential Functions
General Form of a Rational Function
Radical Functions
Slope

8B.5: Describe the properties and features of any non-degenerate conic section from an equation or graph.

Addition and Subtraction of Functions
Circles
Ellipses
Hyperbolas
Parabolas

8B.9: Write an equation for conic sections from a graph.

Ellipses
Hyperbolas

8C: Students who meet the standard can solve problems using systems of numbers and their properties. (Problem solving)

8C.1: Describe and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions.

Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions

8C.2: Identify and explain the relationship between arithmetic/geometric sequences and linear/exponential functions.

Arithmetic and Geometric Sequences
Compound Interest
Exponential Functions

8C.5: Model and solve real problems using mathematical functions and relations.

Linear Functions

8C.6: Identify essential quantitative relationships in a situation and determine the class or classes of functions (e.g., power, exponential, logarithmic) that might model the relationships.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

8D: Students who meet the standard can use algebraic concepts and procedures to represent and solve problems. (Connection of 8A, 8B, and 8C to solve problems)

8D.1: Solve problems using linear programming.

Linear Programming

8D.2: Solve problems using equations of exponential and logarithmic growth.

Compound Interest

8D.3: Solve problems using direct, inverse, and mixed variation.

Determining a Spring Constant
Direct and Inverse Variation

8D.5: Solve problems using rational equations and inequalities.

Circles
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Rational Functions
Solving Equations on the Number Line

8D.6: Set up and solve problems of non-linear growth.

Compound Interest

9A: Students who meet the standard can demonstrate and apply geometric concepts involving points, lines, planes, and space. (Properties of single figures, coordinate geometry and constructions)

9A.1: Analyze geometric situations using Cartesian coordinates and other coordinate systems such as navigational, polar, or spherical systems.

Points in the Coordinate Plane

9A.2: Represent transformations of an object in the plane using function notation and matrices.

Dilations
Translations

9A.3: Represent and describe with the language of geometry real-life objects, paths and regions in space.

Parallel, Intersecting, and Skew Lines

9A.4: Apply properties of two- and three-dimensional models to solve problems.

Classifying Quadrilaterals

9D: Students who meet the standard can use trigonometric ratios and circular functions to solve problems.

9D.4: Relate circular functions, arcs, and radian measure to triangle trigonometry and degree measure.

Chords and Arcs
Inscribed Angles

9D.5: Simplify expressions and solve problems using trigonometric identities.

Simplifying Trigonometric Expressions
Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine

9D.8: Identify key characteristics of graphs of trigonometric functions and their inverses.

Translating and Scaling Functions

9D.9: Graph trigonometric functions using translations and dilations.

Translating and Scaling Sine and Cosine Functions

9D.10: Graph a given trigonometric function using its characteristics (e.g., period, amplitude).

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

10A: Students who meet the standard can organize, describe and make predictions from existing data. (Data analysis)

10A.1: Describe the differences among various kinds of studies and which types of inferences can legitimately be drawn from each.

Polling: City
Populations and Samples

10A.3: Describe how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference.

Polling: City
Polling: Neighborhood
Populations and Samples

10A.4: Present results and conclusions from given data using basic statistics (e.g., measures of central tendencies, standard deviation).

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

10A.6: Evaluate survey results for conformity to simple distributions.

Polling: City

10B: Students who meet the standard can formulate questions, design data collection methods, gather and analyze data and communicate findings. (Data Collection)

10B.1: Explore the variability of sample statistics from a known population and construct sampling distributions using simulations.

Polling: City
Populations and Samples

10B.2: Describe how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference.

Polling: City
Polling: Neighborhood
Populations and Samples

10B.3: Create a survey from a critical question and decide which sampling technique to use for the survey.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood

10B.4: Evaluate surveys for clarity, bias, return rate, and specialized audiences.

Describing Data Using Statistics
Polling: City
Polling: Neighborhood

10C: Students who meet the standard can determine, describe and apply the probabilities of events. (Probability including counting techniques)

10C.2: Describe the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed.

Polling: City
Populations and Samples
Sight vs. Sound Reactions

10C.4: Describe a simulation for a more advanced experiment.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

10C.5: Carry out a simulation to estimate probabilities, and if possible, compare it to the theoretical probability.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

10C.6: Compute and interpret the expected value of random variables in simple cases.

Probability Simulations
Theoretical and Experimental Probability

10C.7: Apply advanced counting techniques to determine probability.

Probability Simulations