1: Number and Operations

1.1: Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems.In

1.1.1: Justify with examples the relation between the number system being used (natural numbers, whole numbers, integers, rational numbers and irrational numbers) and the question of whether or not an equation has a solution in that number system.

Solving Algebraic Equations II
Solving Equations on the Number Line

1.1.3: Express that the distance between two numbers is the absolute value of their difference.

Absolute Value Equations and Inequalities

1.2: Understand and apply numerical operations and their relationship to one another.

1.2.2: Summarize the properties of and connections between real number operations; justify manipulations of expressions using the properties of real number operations.

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

1.2.3: Calculate powers and roots of rational and irrational numbers.

Square Roots

1.2.4: Compute using scientific notation.

Unit Conversions

2: Data Analysis, Probability, and Discrete Mathematics

2.1: Understand and apply data collection, organization, and representation to analyze and sort data.

2.1.2: Organize collected data into an appropriate graphical representation with or without technology.

Box-and-Whisker Plots
Correlation
Stem-and-Leaf Plots

2.1.3: Display data, including paired data, as lists, tables, matrices, and plots with or without technology; make predictions and observations about patterns or departures from patterns.

Box-and-Whisker Plots
Stem-and-Leaf Plots

2.1.5: Determine which measure of center is most appropriate in a given situation and explain why.

Box-and-Whisker Plots
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Stem-and-Leaf Plots

2.1.6: Evaluate the reasonableness of conclusions drawn from data analysis.

Polling: City

2.1.7: Identify misrepresentations and distortions in displays of data and explain why they are misrepresentations or distortions.

Polling: City

2.1.8: Design simple experiments or investigations and collect data to answer questions.

Describing Data Using Statistics
Real-Time Histogram

2.2: Understand and apply the basic concepts of probability.

2.2.1: Make predictions and solve problems based on theoretical probability models.

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

2.2.2: Determine the theoretical probability of events, estimate probabilities using experiments, and compare the two.

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

2.2.3: Use simulations to model situations involving independent and dependent events.

Independent and Dependent Events

2.2.4: Explain and use the law of large numbers (that experimental results tend to approach theoretical probabilities after a large number of trials).

Theoretical and Experimental Probability

2.2.5: Use concepts and formulas of area to calculate geometric probabilities.

Geometric Probability

2.3: Understand and demonstrate the systematic listing and counting of possible outcomes.

2.3.1: Apply the addition and multiplication principles of counting, representing these principles algebraically using factorial notation.

Binomial Probabilities
Permutations and Combinations

2.3.2: Apply appropriate means of computing the number of possible arrangements of items using permutations where order matters, and combinations where order does not matter.

Binomial Probabilities
Permutations and Combinations

2.3.3: Determine the number of possible outcomes of an event.

Binomial Probabilities

3: Patterns, Algebra, and Functions

3.1: Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands.

3.1.1: Recognize, describe, and analyze sequences using tables, graphs, words, or symbols; use sequences in modeling.

Arithmetic Sequences
Geometric Sequences

3.1.2: Determine a specific term of a sequence.

Arithmetic Sequences
Geometric Sequences

3.1.3: Create sequences using explicit and recursive formulas involving both subscripts and function notation.

Arithmetic Sequences
Geometric Sequences

3.2: Describe and model functions and their relationships.

3.2.2: Determine if a relationship represented by an equation, graph, table, description, or set of ordered pairs is a function.

Introduction to Functions
Linear Functions
Points, Lines, and Equations

3.2.4: Use equations, graphs, tables, descriptions, or sets of ordered pairs to express a relationship between two variables.

Absolute Value with Linear Functions

3.2.5: Recognize and solve problems that can be modeled using a system of two equations in two variables.

Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)

3.2.6: Recognize and solve problems that can be modeled using a quadratic function.

Quadratics in Polynomial Form

3.2.7: Determine domain and range of a function from an equation, graph, table, description, or set of ordered pairs.

Exponential Functions
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Logarithmic Functions
Radical Functions

3.3: Represent and analyze mathematical situations and structures using algebraic representations.

3.3.2: Solve formulas for specified variables.

Solving Formulas for any Variable

3.3.3: Write an equation given a table of values, two points on the line, the slope and a point on the line, or the graph of the line.

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

3.3.5: Solve linear equations and equations involving absolute value, with one variable.

Absolute Value with Linear Functions
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line

3.3.6: Solve linear inequalities in one variable.

Compound Inequalities
Solving Linear Inequalities in One Variable
Systems of Linear Inequalities (Slope-intercept form)

3.3.7: Solve systems of two linear equations in two variables.

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

3.3.8: Simplify and evaluate polynomials, rational expressions, expressions containing absolute value, and radicals.

Compound Interest
Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Radical Expressions
Solving Equations by Graphing Each Side
Solving Equations on the Number Line

3.3.9: Multiply and divide monomial expressions with integer exponents.

Dividing Exponential Expressions
Multiplying Exponential Expressions

3.3.10: Add, subtract, and multiply polynomial and rational expressions.

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of x²+bx+c

3.3.11: Solve square root equations involving only one radical.

Operations with Radical Expressions
Radical Functions

3.3.12: Factor quadratic polynomials in the form of ax² + bx + c where a, b, and c are integers.

Dividing Polynomials Using Synthetic Division
Factoring Special Products

3.3.13: Solve quadratic equations.

Roots of a Quadratic

3.3.14: Factor higher order polynomials.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

3.4: Analyze how changing the values of one quantity corresponds to change in the values of another quantity.

3.4.2: Solve problems involving rate of change.

Translating and Scaling Functions

3.4.3: Solve interest problems.

Compound Interest

4: Geometry and Measurement

4.1: Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships.

4.1.1: Use the basic properties of a circle (relationships between angles, radii, intercepted arcs, chords, tangents, and secants) to prove basic theorems and solve problems.

Chords and Arcs
Circles
Inscribed Angles

4.1.2: Visualize solids and surfaces in 3-dimensional space when given 2-dimensional representations and create 2-dimensional representations for the surfaces of 3-dimensional objects.

Surface and Lateral Areas of Prisms and Cylinders

4.1.4: Apply properties, theorems, and constructions about parallel lines, perpendicular lines, and angles to prove theorems.

Investigating Angle Theorems

4.1.7: Use the hierarchy of quadrilaterals in deductive reasoning.

Classifying Quadrilaterals

4.1.8: Prove similarity and congruence of triangles.

Congruence in Right Triangles
Proving Triangles Congruent
Similar Figures

4.1.9: Solve problems using the triangle inequality property.

Triangle Inequalities

4.1.10: Solve problems using right triangles, including special triangles.

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

4.1.11: Solve problems using the sine, cosine, and tangent ratios of the acute angles of a right triangle.

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

4.2: Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations.

4.2.1: Determine whether a transformation of a 2-dimensional figure on a coordinate plane represents a translation, reflection, rotation, or dilation and whether congruence is preserved.

Circles
Dilations
Rotations, Reflections, and Translations
Translations

4.2.2: Determine the new coordinates of a point when a single transformation is performed on a 2-dimensional figure.

Dilations
Rotations, Reflections, and Translations
Translations

4.2.4: Determine the effects of a single transformation on linear or area measurements of a 2-dimensional figure.

Dilations

4.3: Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands.

4.3.2: Illustrate the connection between the distance formula and the Pythagorean Theorem.

Circles
Distance Formula

4.3.3: Determine the distance between two points in the coordinate plane.

Points in the Coordinate Plane

4.3.5: Graph a linear equation or linear inequality in two variables.

Absolute Value with Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Solving Linear Inequalities in One Variable
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form)

4.3.6: Describe how changing the parameters of a linear function affect the shape and position of its graph.

Absolute Value with Linear Functions
Slope-Intercept Form of a Line

4.3.7: Determine the solution to a system of linear equations in two variables from the graphs of the equations.

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

4.4: Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements.

4.4.1: Use dimensional analysis to keep track of units of measure when converting.

Unit Conversions

4.4.2: Find the length of a circular arc; find the area of a sector of a circle.

Inscribed Angles

4.4.3: Determine the effect that changing dimensions has on the perimeter, area, or volume of a figure.

Perimeter and Area of Rectangles

4.4.4: Solve problems involving similar figures using ratios and proportions.

Beam to Moon (Ratios and Proportions)
Perimeters and Areas of Similar Figures
Similar Figures

4.4.5: Calculate the surface area and volume of 3-dimensional figures and solve for missing measures.

Surface and Lateral Areas of Prisms and Cylinders