IM: Introductory Mathematics

IM.1: The learner will understand and compute with real numbers.

IM.1.01: Develop number sense for the real numbers.

IM.1.01.b: Compare and order.

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers

IM.2: The learner will use properties and relationships in geometry and measurement concepts to solve problems.

IM.2.01: Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.

Area of Parallelograms - Activity A
Minimize Perimeter
Prisms and Cylinders - Activity A

IM.2.04: Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

IM.2.05: Identify, predict, and describe dilations in the coordinate plane.

Dilations

IM.3: The learner will understand and use graphs and data analysis.

IM.3.01: Collect, organize, analyze, and display data (including scatterplots) to solve problems.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

IM.3.02: Approximate a line of best fit for a given scatterplot; explain the meaning of the line as it relates to the problem and make predictions.

Correlation
Lines of Best Fit Using Least Squares - Activity A
Scatter Plots - Activity A
Solving Using Trend Lines

IM.4: The learner will understand and use linear relations and functions.

IM.4.01: Develop an understanding of function.

IM.4.01.a: Translate among verbal, tabular, graphic, and algebraic representations of functions.

Exponential Functions - Activity A
Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs

IM.4.01.b: Identify relations and functions as linear or nonlinear.

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Using Tables, Rules and Graphs

IM.4.01.c: Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.

Direct Variation
Direct and Inverse Variation
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Slope-Intercept Form of a Line - Activity A

IM.4.01.d: Interpret and compare properties of linear functions from tables, graphs, or equations.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

IM.4.02: Write an equation of a linear relationship given: two points, the slope and one point on the line, or the slope and y-intercept.

Defining a Line with Two Points
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Using Tables, Rules and Graphs

IM.4.03: Solve problems using linear equations and inequalities; justify symbolically and graphically.

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
Systems of Linear Inequalities (Slope-intercept form) - Activity A

IM.4.04: Solve problems using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots.

Function Machines 3 (Functions and Problem Solving)
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations
Square Roots

A1: Algebra 1

A1.1: The learner will perform operations with numbers and expressions to solve problems.

A1.1.01: Write equivalent forms of algebraic expressions to solve problems.

A1.1.01.a: Apply the laws of exponents.

Dividing Exponential Expressions
Exponents and Power Rules

A1.1.01.b: Operate with polynomials.

Addition of Polynomials - Activity A

A1.1.01.c: Factor polynomials.

Dividing Polynomials Using Synthetic Division
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

A1.1.03: Model and solve problems using direct variation.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

A1.2: The learner will describe geometric figures in the coordinate plane algebraically.

A1.2.01: Find the lengths and midpoints of segments to solve problems.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

A1.2.02: Use the parallelism or perpendicularity of lines and segments to solve problems.

Construct Parallel and Perpendicular Lines

A1.4: The learner will use relations and functions to solve problems.

A1.4.01: Use linear functions or inequalities to model and solve problems; justify results.

A1.4.01.a: Solve using tables, graphs, and algebraic properties.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations
Using Tables, Rules and Graphs

A1.4.01.b: Interpret constants and coefficients in the context of the problem.

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

A1.4.02: Graph, factor, and evaluate quadratic functions to solve problems.

Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

A1.4.03: Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify results.

Modeling Linear Systems - Activity A
Special Types of Solutions to Linear Systems
Systems of Linear Inequalities (Slope-intercept form) - Activity A

A1.4.04: Graph and evaluate exponential functions to solve problems.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Function Machines 2 (Functions, Tables, and Graphs)

GE: Geometry

GE.1: The learner will perform operations with real numbers to solve problems.

GE.1.01: Use the trigonometric ratios to model and solve problems involving right triangles.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio

GE.1.02: Use length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

GE.1.03: Use length, area, and volume to model and solve problems involving probability.

Geometric Probability - Activity A
Prisms and Cylinders - Activity A

GE.2: The learner will use geometric and algebraic properties of figures to solve problems and write proofs.

GE.2.02: Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.

Investigating Angle Theorems - Activity A

GE.2.03: Apply properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:

GE.2.03.a: Triangles.

Classifying Triangles

GE.2.03.b: Quadrilaterals.

Classifying Quadrilaterals - Activity B

GE.2.04: Develop and apply properties of solids to solve problems.

Classifying Triangles
Prisms and Cylinders - Activity A

GE.3: The learner will transform geometric figures in the coordinate plane algebraically.

GE.3.01: Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

A2: Algebra 2

A2.1: The learner will perform operations with complex numbers, matrices, and polynomials.

A2.1.02: Define and compute with complex numbers.

Points in the Complex Plane - Activity A

A2.1.05: Model and solve problems using direct, inverse, combined and joint variation.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

A2.2: The learner will use relations and functions to solve problems.

A2.2.01: Use the composition and inverse of functions to model and solve problems; justify results.

Function Machines 3 (Functions and Problem Solving)

A2.2.02: Use quadratic functions and inequalities to model and solve problems; justify results.

A2.2.02.a: Solve using tables, graphs, and algebraic properties.

Modeling and Solving Two-Step Equations
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Solving Two-Step Equations

A2.2.02.b: Interpret the constants and coefficients in the context of the problem.

Correlation
Parabolas - Activity A
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

A2.2.03: Use exponential functions to model and solve problems; justify results.

A2.2.03.a: Solve using tables, graphs, and algebraic properties.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

A2.2.03.b: Interpret the constants, coefficients, and bases in the context of the problem.

Correlation
Exponential Functions - Activity A

A2.2.04: Create and use best-fit mathematical models of linear, exponential, and quadratic functions to solve problems involving sets of data.

A2.2.04.a: Interpret the constants, coefficients, and bases in the context of the data.

Correlation
Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Roots of a Quadratic

A2.2.04.b: Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Roots of a Quadratic

A2.2.05: Use rational equations to model and solve problems; justify results.

A2.2.05.b: Interpret the constants and coefficients in the context of the problem.

Correlation

A2.2.05.c: Identify the asymptotes and intercepts graphically and algebraically.

Distance-Time Graphs
Hyperbola - Activity A

A2.2.06: Use cubic equations to model and solve problems.

A2.2.06.a: Solve using tables and graphs.

Cubic Function Activity
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

A2.2.06.b: Interpret constants and coefficients in the context of the problem.

Correlation
Cubic Function Activity

A2.2.07: Use equations with radical expressions to model and solve problems; justify results.

A2.2.07.a: Solve using tables, graphs, and algebraic properties.

Functions Involving Square Roots
Radical Functions
Simplifying Radicals - Activity A

A2.2.07.b: Interpret the degree, constants, and coefficients in the context of the problem.

Correlation
Functions Involving Square Roots
Radical Functions
Simplifying Radicals - Activity A

A2.2.08: Use equations and inequalities with absolute value to model and solve problems; justify results.

A2.2.08.a: Solve using tables, graphs, and algebraic properties.

Inequalities Involving Absolute Values

A2.2.08.b: Interpret the constants and coefficients in the context of the problem.

Correlation
Inequalities Involving Absolute Values

A2.2.09: Use the equations of parabolas and circles to model and solve problems; justify results.

A2.2.09.a: Solve using tables, graphs, and algebraic properties.

Circles
Modeling and Solving Two-Step Equations
Parabolas - Activity A
Solving Two-Step Equations

A2.2.09.b: Interpret the constants and coefficients in the context of the problem.

Circles
Correlation
Parabolas - Activity A

A2.2.10: Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties.

Modeling Linear Systems - Activity A
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

T1: Technical Mathematics 1

T1.1: The learner will apply various strategies to solve problems.

T1.1.01: Apply various techniques and strategies to solve problems.

T1.1.01.b: Identify and represent patterns using appropriate algebraic notation.

Arithmetic and Geometric Sequences
Finding Patterns

T1.2: The learner will measure and apply geometric concepts to solve problems.

T1.2.01: Select and use appropriate tools to measure two- and three-dimensional figures; interpret and communicate results with regard to precision.

Prisms and Cylinders - Activity A
Triple Beam Balance

T1.2.03: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

T1.2.04: Use the trigonometric ratios to model and solve problems involving right triangles.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio

T1.3: The learner will describe the transformation of polygons in the coordinate plane algebraically.

T1.3.02: Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

T2: Technical Mathematics 2

T2.1: The learner will use properties of geometric figures to solve problems.

T2.1.02: Apply the properties and definitions of plane figures to model and solve problems:

T2.1.02.a: Triangles.

Classifying Triangles

T2.1.02.b: Quadrilaterals.

Classifying Quadrilaterals - Activity B

T2.2: The learner will use relations and functions to solve problems.

T2.2.02: Use exponential functions to model and solve problems; justify results.

T2.2.02.a: Solve using tables, graphs, and algebraic properties.

Distance-Time Graphs

T2.2.02.b: Interpret the constants, coefficients, and bases in the context of the problem.

Exponential Functions - Activity A

T2.2.03: Create, interpret, and analyze best-fit models of linear, exponential, and quadratic functions to solve problems.

T2.2.03.a: Interpret the constants, coefficients, and bases in the context of the data.

Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Roots of a Quadratic

T2.2.04: Use systems of equations and inequalities to model and solve problems using tables, graphs, matrix operations, and algebraic properties; justify results.

Modeling Linear Systems - Activity A
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AF: Advanced Functions and Modeling

AF.1: The learner will analyze data and apply probability concepts to solve problems.

AF.1.01: Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, and logarithmic functions of bivariate data to solve problems.

AF.1.01.a: Interpret the constants, coefficients, and bases in the context of the data.

Correlation
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function

AF.1.01.b: Check models for goodness-of-fit; use the most appropriate model to draw conclusions and make predictions.

Correlation
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function

AF.1.02: Summarize and analyze univariate data to solve problems.

AF.1.02.c: Determine measures of central tendency and spread.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

AF.1.02.e: Interpret graphical displays of univariate data.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

AF.1.02.f: Compare distributions of univariate data.

Populations and Samples

AF.1.03: Use theoretical and experimental probability to model and solve problems.

AF.1.03.b: Calculate and apply permutations and combinations.

Binomial Probabilities
Permutations
Permutations and Combinations

AF.1.03.c: Create and use simulations for probability models.

Probability Simulations

AF.1.03.f: Apply the Binomial Theorem.

Binomial Probabilities

AF.2: The learner will use functions to solve problems.

AF.2.01: Use logarithmic (common, natural) functions to model and solve problems; justify results.

AF.2.01.a: Solve using tables, graphs, and algebraic properties.

Distance-Time Graphs
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

AF.2.01.b: Interpret the constants, coefficients, and bases in the context of the problem.

Correlation
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

AF.2.02: Use piecewise-defined functions to model and solve problems; justify results.

AF.2.02.a: Solve using tables, graphs, and algebraic properties.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

AF.2.02.b: Interpret the constants, coefficients, and bases in the context of the problem.

Correlation

AF.2.03: Use power functions to model and solve problems; justify results.

AF.2.03.a: Solve using tables, graphs, and algebraic properties.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

AF.2.03.b: Interpret the constants, coefficients, and bases in the context of the problem.

Correlation

AF.2.04: Use trigonometric (sine, cosine) functions to model and solve problems; justify results.

AF.2.04.a: Solve using tables, graphs, and algebraic properties.

Cosine Function
Distance-Time Graphs
Sine Function
Tangent Function
Unit Circle

AF.2.04.b: Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

AF.2.04.c: Develop and use the law of sines and the law of cosines.

Cosine Function
Sine Function
Unit Circle

AF.2.05: Use recursively-defined functions to model and solve problems.

AF.2.05.d: Translate between recursive and explicit representations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

DM: Discrete Mathematics

DM.1: The learner will use matrices and graphs to model relationships and solve problems.

DM.1.01: Use matrices to model and solve problems.

DM.1.01.a: Display and interpret data.

Box-and-Whisker Plots
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

DM.2: The learner will analyze data and apply probability concepts to solve problems.

DM.2.01: Describe data to solve problems.

DM.2.01.c: Determine measures of central tendency and spread.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

DM.2.01.e: Interpret graphical displays of data.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

DM.2.01.f: Compare distributions of data.

Populations and Samples

DM.2.02: Use theoretical and experimental probability to model and solve problems.

DM.2.02.b: Calculate and apply permutations and combinations.

Binomial Probabilities
Permutations
Permutations and Combinations

DM.2.02.c: Create and use simulations for probability models.

Probability Simulations

DM.2.02.f: Apply the Binomial Theorem.

Binomial Probabilities

DM.3: The learner will describe and use recursively-defined relationships to solve problems.

DM.3.01: Use recursion to model and solve problems.

DM.3.01.d: Write explicit definitions using iterative processes, including finite differences and arithmetic and geometric formulas.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

PC: Pre-Calculus

PC.1: The learner will describe geometric figures in the coordinate plane algebraically.

PC.1.01: Transform relations in two dimensions; describe the results algebraically and geometrically.

Translating and Scaling Functions

PC.1.02: Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results.

PC.1.02.a: Solve using tables, graphs, and algebraic properties.

Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

PC.1.02.b: Interpret the constants and coefficients in the context of the problem.

Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

PC.2: The learner will use relations and functions to solve problems.

PC.2.01: Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise-defined, and greatest integer) to model and solve problems; justify results.

PC.2.01.a: Solve using graphs and algebraic properties.

Distance-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions

PC.2.01.b: Interpret the constants, coefficients, and bases in the context of the problem.

Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions

PC.2.02: Use trigonometric and inverse trigonometric functions to model and solve problems; justify results.

PC.2.02.a: Solve using graphs and algebraic properties.

Cosine Function
Distance-Time Graphs
Sine Function
Tangent Function

PC.2.02.b: Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

PC.2.03: For sets of data, create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions.

PC.2.03.a: Interpret the constants, coefficients, and bases in the context of the data.

Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function

PC.2.04: Use the composition and inverse of functions to model and solve problems.

Function Machines 3 (Functions and Problem Solving)

PC.2.05: Use polar equations to model and solve problems.

PC.2.05.a: Solve using graphs and algebraic properties.

Distance-Time Graphs

PC.2.06: Use parametric equations to model and solve problems.

Modeling and Solving Two-Step Equations

PC.2.07: Use recursively-defined functions to model and solve problems.

PC.2.07.d: Translate between recursive and explicit representations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

I1: Integrated Mathematics 1

I1.1: The learner will perform operations with numbers and expressions to solve problems.

I1.1.01: Write equivalent forms of algebraic expressions to solve problems.

I1.1.01.a: Apply the laws of exponents.

Dividing Exponential Expressions
Exponents and Power Rules

I1.1.01.b: Operate with polynomials.

Addition of Polynomials - Activity A

I1.1.01.c: Factor polynomials.

Dividing Polynomials Using Synthetic Division

I1.1.02: Use algebraic expressions, including iterative and recursive forms, to model and solve problems.

Arithmetic and Geometric Sequences

I1.2: The learner will use properties of geometric figures to solve problems.

I1.2.01: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

I1.2.02: Develop and apply properties of solids to solve problems.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

I1.3: The learner will analyze data and apply probability concepts to solve problems.

I1.3.02: Use theoretical and experimental probability to model and solve problems.

I1.3.02.b: Calculate and apply permutations and combinations.

Binomial Probabilities
Permutations
Permutations and Combinations

I1.3.02.c: Create and use simulations for probability models.

Probability Simulations

I1.3.03: Create linear and exponential models, for sets of data, to solve problems.

I1.3.03.a: Interpret the constants, coefficients, and bases in the context of the data.

Correlation
Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)

I1.3.03.b: Check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

Correlation
Exponential Functions - Activity A
Function Machines 2 (Functions, Tables, and Graphs)

I1.4: The learner will use relations and functions to solve problems.

I1.4.01: Use linear functions or inequalities to model and solve problems; justify results.

I1.4.01.a: Solve using tables, graphs, and algebraic properties.

Modeling and Solving Two-Step Equations
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

I1.4.01.b: Interpret the constants and coefficients in the context of the problem.

Correlation
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

I1.4.02: Use exponential functions to model and solve problems; justify results.

I1.4.02.a: Solve using tables, graphs, and algebraic properties.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

I1.4.02.b: Interpret the constants, coefficients, and bases in the context of the problem.

Correlation
Exponential Functions - Activity A

I1.4.03: Use systems of linear equations or inequalities in two variables to model problems and solve graphically.

Modeling Linear Systems - Activity A
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

I2: Integrated Mathematics 2

I2.1: The learner will perform operations with numbers, algebraic expressions, and matrices to solve problems.

I2.1.03: Model and solve problems using direct variation.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

I2.2: The learner will describe geometric figures in the coordinate plane algebraically.

I2.2.01: Find the lengths and midpoints of segments to solve problems.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

I2.2.03: Use the trigonometric ratios to model and solve problems.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio

I2.2.04: Describe the transformation (translation, reflection, rotation, dilation) of polygons in the coordinate plane in simple algebraic terms.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

I2.3: The learner will collect, organize, and interpret data to solve problems.

I2.3.01: Describe data to solve problems.

I2.3.01.c: Determine measures of central tendency and spread.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

I2.3.01.f: Compare distributions of data.

Populations and Samples

I2.3.02: Create and use, for sets of data, calculator-generated models of linear, exponential, and quadratic functions to solve problems.

I2.3.02.a: Interpret the constants, coefficients, and bases in the context of the data.

Correlation

I2.4: The learner will use relations and functions to solve problems.

I2.4.01: Use systems of linear equations or inequalities in two variables to model and solve problems. Solve using tables, graphs, and algebraic properties; justify steps used.

Linear Programming - Activity A
Modeling Linear Systems - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Special Types of Solutions to Linear Systems
Systems of Linear Inequalities (Slope-intercept form) - Activity A

I2.4.02: Use quadratic functions to model and solve problems; justify results.

I2.4.02.a: Solve using tables, graphs, and algebraic properties.

Linear Inequalities in Two Variables - Activity A

I2.4.02.b: Interpret the constants and coefficients in the context of the problem.

Parabolas - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

I2.4.03: Use power models to solve problems.

I2.4.03.a: Solve using tables, graphs, and algebraic properties.

Distance-Time Graphs
Linear Inequalities in Two Variables - Activity A

I3: Integrated Mathematics 3

I3.1: The learner will perform operations with numbers and algebraic expressions to solve problems.

I3.1.02: Use algebraic expressions, including iterative and recursive forms, to model and solve problems.

Arithmetic and Geometric Sequences

I3.1.04: Model and solve problems using direct, inverse, combined and joint variation.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

I3.2: The learner will use properties of geometric figures to solve problems.

I3.2.02: Apply the properties, definitions, and theorems of angles and lines to solve problems and write proofs.

Investigating Angle Theorems - Activity A

I3.2.03: Apply the properties, definitions, and theorems of two-dimensional figures to solve problems and write proofs:

I3.2.03.a: Triangles.

Classifying Triangles
Simplifying Trigonometric Expressions

I3.2.03.b: Quadrilaterals.

Parallelogram Conditions
Simplifying Trigonometric Expressions

I3.2.03.c: Other polygons.

Simplifying Trigonometric Expressions

I3.2.03.d: Circles.

Chords and Arcs
Inscribing Angles
Simplifying Trigonometric Expressions

I3.2.04: Use the law of sines and law of cosines to solve problems.

Cosine Function
Sine Function
Unit Circle

I3.3: The learner will use relations and functions to solve problems.

I3.3.01: Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties.

Modeling Linear Systems - Activity A
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

I3.3.02: Use quadratic functions and inequalities to model and solve problems; justify results.

I3.3.02.a: Solve using tables, graphs, and algebraic properties.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Parabolas - Activity A
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

I3.3.02.b: Interpret the constants and coefficients in the context of the problem.

Correlation
Parabolas - Activity A
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

I3.3.03: Use rational equations to model and solve problems; justify results.

I3.3.03.a: Solve using tables, graphs, and algebraic properties.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

I3.3.03.b: Interpret the constants and coefficients in the context of the problem.

Correlation

I3.3.03.c: Identify the asymptotes and intercepts graphically and algebraically.

Distance-Time Graphs
Hyperbola - Activity A

I3.3.04: Use equations and inequalities with absolute value to model and solve problems; justify results.

I3.3.04.a: Solve using tables, graphs, and algebraic properties.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Inequalities Involving Absolute Values

I3.3.04.b: Interpret the constants and coefficients in the context of the problem.

Correlation
Inequalities Involving Absolute Values

I3.3.05: Transform functions in two dimensions; describe the results algebraically and geometrically.

Translating and Scaling Functions

I4: Integrated Mathematics 4

I4.1: The learner will operate with complex numbers and vectors to solve problems.

I4.1.02: Define and compute with complex numbers.

Points in the Complex Plane - Activity A

I4.2: The learner will describe geometric figures in the coordinate plane algebraically.

I4.2.01: Use the quadratic relations (parabola, circle, ellipse, hyperbola) to model and solve problems; justify results.

I4.2.01.a: Solve using tables, graphs, and algebraic properties.

Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

I4.2.01.b: Interpret the constants and coefficients in the context of the problem.

Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A

I4.2.02: Estimate the area and volume of continuously varying quantities.

Prisms and Cylinders - Activity A

I4.3: The learner will analyze data to solve problems.

I4.3.01: Analyze univariate data to solve problems.

I4.3.01.c: Determine measures of central tendency and spread.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

I4.3.01.e: Interpret graphical displays of distributions of univariate data.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

I4.3.01.f: Compare distributions of univariate data.

Populations and Samples

I4.3.02: Create and use calculator-generated models of linear, polynomial, exponential, trigonometric, power, logistic, and logarithmic functions of bivariate data to solve problems.

I4.3.02.a: Interpret the constants, coefficients, and bases in the context of the data.

Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Sine Function
Tangent Function

I4.4: The learner will use relations and functions to solve problems.

I4.4.01: Use functions (polynomial, power, rational, exponential, logarithmic, logistic, piecewise-defined, and greatest integer) to model and solve problems; justify results.

I4.4.01.a: Solve using graphs and algebraic properties.

Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions

I4.4.01.b: Interpret the constants, coefficients, and bases in the context of the problem.

Exponential Functions - Activity A
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Rational Functions

I4.4.02: Use recursively-defined functions to model and solve problems.

I4.4.02.d: Translate between recursive and explicit representations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

I4.4.03: Use the composition and inverse of functions to model and solve problems.

Function Machines 3 (Functions and Problem Solving)

I4.4.04: Use trigonometric and inverse trigonometric functions to model and solve problems.

I4.4.04.a: Solve using graphs and algebraic properties.

Cosine Function
Sine Function
Tangent Function

I4.4.04.b: Create and identify transformations with respect to period, amplitude, and vertical and horizontal shifts.

Dilations
Reflections
Rotations, Reflections and Translations
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

I4.4.05: Use polar equations to model and solve problems.

I4.4.05.a: Solve using graphs and algebraic properties.

Defining a Line with Two Points
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

I4.4.06: Use parametric equations to model and solve problems.

Modeling and Solving Two-Step Equations

I4.4.07: Find the rate of change at any point of a function.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

AS: Advanced Placement Statistics

AS.1: The learner will analyze univariate data to solve problems.

AS.1.01: Summarize distributions of univariate data by determining and interpreting measures of center, spread, position, boxplots, and effects of changing units on summary measures.

Box-and-Whisker Plots
Describing Data Using Statistics
Line Plots
Mean, Median and Mode

AS.2: The learner will construct and interpret displays of univariate data to solve problems.

AS.2.01: Construct and interpret graphical displays of univariate data.

Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Line Plots
Scatter Plots - Activity A
Stem-and-Leaf Plots

AS.2.02: Compare distributions among sets of univariate data.

Populations and Samples

AS.3: The learner will collect and analyze date to solve problems.

AS.3.07: Simulate sampling distributions.

Populations and Samples
Probability Simulations

AS.3.08: Use simulations to develop an understanding of the Central Limit Theorem and its importance in confidence intervals and tests of significance.

Probability Simulations

AS.4: The learner will analyze bivariate data to solve problems.

AS.4.01: Analyze bivariate data.

AS.4.01.a: Recognize and analyze correlation and linearity.

Correlation

AC: Advanced Placement Calculus

AC.1: The learner will demonstrate an understanding of the behavior of functions.

AC.1.02: Recognize and describe the nature of aberrant behavior caused by asymptotes and unboundedness.

AC.1.02.c: Compare relative magnitudes of functions and their rates of change.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

AC.1.03: Identify and demonstrate an understanding of continuity of functions.

AC.1.03.a: Develop an intuitive understanding of continuity. (Close values of the domain lead to close values of the range.)

Functions Involving Square Roots

AC.2: The learner will use derivatives to solve problems.

AC.2.02: Apply the concept of the derivative at a point.

AC.2.02.c: Find the instantaneous rate of change as the limit of average rate of change.

Distance-Time Graphs

AC.2.02.d: Approximate a rate of change from graphs and tables of values.

Distance-Time Graphs

AC.2.03: Interpret the derivative as a function.

AC.2.03.d: Translate between verbal and algebraic descriptions of equations involving derivatives.

Using Algebraic Equations
Using Algebraic Expressions

AC.2.06: Apply the derivative in graphing and modeling contexts.

AC.2.06.d: Use implicit differentiation to find the derivative of an inverse function.

Function Machines 3 (Functions and Problem Solving)

AC.2.06.e: Interpret the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.

Distance-Time Graphs

AC.3: The learner will use integrals to solve problems.

AC.3.01: Explore and interpret the concept of the definite integral.

AC.3.01.a: Compute Riemann sums using left, right, and midpoint evaluation points.

Riemann Sum

AC.3.01.b: Find the definite integral as a limit of Riemann sums over equal subdivisions.

Riemann Sum

AC.3.04: Define and use appropriate integrals in a variety of applications.

AC.3.04.c: Set up and use an approximating Riemann sum or trapezoidal sum and represent its limit as a definite integral.

Riemann Sum

AC.3.04.d: Find the area of a region.

Riemann Sum

AC.3.04.g: Find the distance traveled by a particle along a line.

Distance-Time Graphs