A.1: Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots, radical form, or decimal approximations.

A.1.1: Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents

Dividing Exponential Expressions
Exponents and Power Rules

A.2: Analyze linear functions from their equations, slopes, and intercepts.

A.2.1: Finding the slope of a line from its equation or by applying the slope formula

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

A.2.2: Determining the equations of linear functions given two points, a point and the slope, tables of values, graphs, or ordered pairs

Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

A.2.3: Graphing two-variable linear equations and inequalities on the Cartesian plane

Defining a Line with Two Points
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form) - Activity A

A.3: Determine characteristics of a relation, including its domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs.

A.3.1: Finding the range of a function when given its domain

Functions Involving Square Roots

A.4: Represent graphically common relations, including x = constant, y = constant, y = x, y = square root of x , y = x² , and y = |x|.

A.4.1: Identifying situations that are modeled by common relations, including x = constant, y = constant, y = x, y = square root of x , y = x², and y = |x|

Functions Involving Square Roots
Introduction to Functions
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Roots of a Quadratic

A.5: Perform operations of addition, subtraction, and multiplication on polynomial expressions.

A.5.1: Dividing by a monomial

Dividing Polynomials Using Synthetic Division

A.6: Factor binomials, trinomials, and other polynomials using GCF, difference of squares, perfect square trinomials, and grouping.

Factoring Special Products

A.7: Solve multistep equations and inequalities including linear, radical, absolute value, and literal equations.

A.7.1: Writing the solution of an equation or inequality in set notation

Inequalities Involving Absolute Values
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

A.7.2: Graphing the solution of an equation or inequality

Defining a Line with Two Points
Ellipse - Activity A
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Standard Form of a Line
Systems of Linear Inequalities (Slope-intercept form) - Activity A

A.7.3: Modeling real-world problems by developing and solving equations and inequalities, including those involving direct and inverse variation

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation
Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations

A.8: Solve systems of linear equations and inequalities in two variables graphically or algebraically.

A.8.1: Modeling real-world problems by developing and solving systems of linear equations and inequalities

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

A.9: Solve quadratic equations using the zero product property.

A.9.1: Approximating solutions graphically and numerically

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

A.10: Calculate length, midpoint, and slope of a line segment when given coordinates of its endpoints on the Cartesian plane.

A.10.1: Deriving the distance, midpoint, and slope formulas

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

A.14: Use a scatterplot and its line of best fit or a specific line graph to determine the relationship existing between two sets of data, including positive, negative, or no relationship.

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

A.15: Estimate probabilities given data in lists or graphs.

A.15.1: Comparing theoretical and experimental probabilities

Compound Independent Events
Compound Independent and Dependent Events
Geometric Probability - Activity A
Independent and Dependent Events
Polling: City
Probability Simulations
Theoretical and Experimental Probability

G.1: Determine the equation of a line parallel or perpendicular to a second line through a given point.

Point-Slope Form of a Line - Activity A

G.2: Justify theorems related to pairs of angles, including angles formed by parallel and perpendicular lines, vertical angles, adjacent angles, complementary angles, and supplementary angles.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation
Investigating Angle Theorems - Activity A

G.3: Verify the relationships among different classes of polygons by using their properties.

G.3.1: Determining the missing lengths of sides or measures of angles in similar polygons

Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

G.4: Determine the measure of interior and exterior angles associated with polygons.

G.4.1: Verifying the formulas for the measures of interior and exterior angles of polygons inductively and deductively

Biconditional Statement
Conditional Statement
Triangle Angle Sum - Activity A

G.5: Solve real-life and mathematical problems using properties and theorems related to circles, quadrilaterals, and other geometric shapes.

G.5.1: Determining the equation of a circle given its center and radius

Circles
Defining a Line with Two Points
Ellipse - Activity A
Percent of Change
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

G.6: Apply the Pythagorean Theorem to solve application problems, expressing answers in simplified radical form or as decimal approximations, using Pythagorean triples when applicable.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Parabolas - Activity A
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Simplifying Radicals - Activity A

G.7: Use the ratios of the sides of special right triangles to find lengths of missing sides.

G.7.1: Deriving the ratios of the sides of 30-60-90 and 45-45-90 triangles

Perimeters and Areas of Similar Figures

G.8: Deduce relationships between two triangles, including proving congruence or similarity of the triangles from given information, using them to solve problems and to establish other relationships.

G.8.1: Determining the geometric mean to find missing lengths in right triangles

Similarity in Right Triangles

G.10: Find the missing measures of sides and angles in right triangles by applying the right triangle definitions of sine, cosine, and tangent.

Circle: Circumference and Area
Classifying Triangles
Cosine Function
Perimeter, Circumference, and Area - Activity B
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle

G.11: Determine the areas and perimeters of regular polygons, including inscribed or circumscribed polygons, given the coordinates of vertices or other characteristics.

Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area
Triple Beam Balance

G.12: Apply distance, midpoint, and slope formulas to solve problems and to confirm properties of polygons.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Perimeter, Circumference, and Area - Activity B
Perimeters and Areas of Similar Figures
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Similar Figures - Activity A
Similar Polygons
Slope - Activity B

G.13: Identify the coordinates of the vertices of the image of a given polygon that is translated, rotated, reflected, or dilated.

Dilations
Reflections
Rotations, Reflections and Translations
Translations
Using Tables, Rules and Graphs

G.14: Classify polyhedrons according to their properties, including the number of faces.

G.14.1: Identifying Euclidean solids

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

G.16: Calculate surface areas and volumes of solid figures, including spheres, cones, and pyramids.

G.16.1: Developing formulas for surface area and volume of spheres, cones, and pyramids

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Pyramids and Cones

G.16.2: Calculating specific missing dimensions of solid figures from surface area or volume

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

G.16.3: Determining the relationship between the surface areas of similar figures and volumes of similar figures

Perimeters and Areas of Similar Figures
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

G.17: Analyze sets of data from geometric contexts to determine what, if any, relationships exist.

G.17.1: Distinguishing between conclusions drawn when using deductive and statistical reasoning

Biconditional Statement
Conditional Statement

G.17.2: Calculating probabilities arising in geometric contexts

Geometric Probability - Activity A

G.18: Construct with precision a circle graph to represent data from given tables or classroom experiments.

Geometric Probability - Activity A
Probability Simulations

G.1.1: Generating, manually or with technological tools, graphs and tables related to personal finance and economics

Percent of Change

G.9: Use inductive reasoning to make conjectures and deductive reasoning to justify conclusions.

Holiday Snowflake Designer
Reflections
Rotations, Reflections and Translations

AII.1: Determine the relationships among the subsets of complex numbers.

Points in the Complex Plane - Activity A

AII.2: Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value.

Absolute Value of a Complex Number
Points in the Complex Plane - Activity A

AII.3: Analyze families of functions, including shifts, reflections, and dilations of y = k/x (inverse variation), y = kx (direct variation/linear), y = x² (quadratic), y = a to the x power (exponential), and y = log to base a of x (logarithmic).

AII.3.1: Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Functions Involving Square Roots
Introduction to Functions
Logarithmic Functions: Translating and Scaling
Using Tables, Rules and Graphs

AII.4: Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions.

AII.4.1: Using completing the square, the zero product property, and the quadratic formula

Roots of a Quadratic

AII.5: Identify the characteristics of quadratic functions from their roots, graphs, or equations.

AII.5.1: Writing an equation when given its roots or graph

Ellipse - Activity A
Polynomials and Linear Factors
Roots of a Quadratic

AII.5.3: Determining the nature of the solutions of a quadratic equation

Roots of a Quadratic

AII.5.4: Determining the maximum or minimum values of quadratic functions both graphically and algebraically

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

AII.6: Perform operations on functions, including addition, subtraction, multiplication, division, and composition.

AII.6.2: Performing operations on polynomial and rational expressions containing variables

Addition of Polynomials - Activity A
Dividing Exponential Expressions

AII.7: Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as exponential and logarithmic functions.

AII.7.2: Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation

Compound Inequalities
Inequalities Involving Absolute Values
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

AII.11: Determine an equation of linear regression from a set of data.

AII.11.1: Examining data to determine if a linear or quadratic relationship exists and to predict outcomes

Linear Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

AII.12: Calculate probabilities of events using the laws of probability.

AII.12.1: Using permutations and combinations to calculate probabilities

Binomial Probabilities
Permutations
Permutations and Combinations

AII.12.3: Calculating probabilities of mutually exclusive events, independent events, and dependent events

Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

AIIT.1: Determine the relationships of subsets of complex numbers.

Points in the Complex Plane - Activity A

AIIT.2: Simplify expressions involving complex numbers, using order of operations and including conjugate and absolute value.

Absolute Value of a Complex Number
Points in the Complex Plane - Activity A

AIIT.3: Analyze families of functions, including shifts, reflections, and dilations of y = k/x (inverse variation), y = kx (direct variation/linear), y = [x] (greatest integer), y = x² (quadratic), y = a to the x power (exponential), and y = log to the base a of x (logarithmic).

AIIT.3.1: Identifying the domain and range of a relation given its graph, a table of values, or its equation, including those with restricted domains

Cosine Function
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Functions Involving Square Roots
General Form of a Rational Function
Introduction to Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Radical Functions
Rational Functions
Sine Function
Tangent Function
Using Tables, Rules and Graphs

AIIT.4: Determine approximate real zeros of functions graphically and numerically and exact real zeros of polynomial functions.

AIIT.4.1: Using the zero product property, completing the square, and the quadratic formula

Polynomials and Linear Factors
Roots of a Quadratic

AIIT.4.2: Deriving the quadratic formula

Roots of a Quadratic

AIIT.5: Identify the characteristics of quadratic functions from their roots, graphs, or equations.

AIIT.5.1: Generating an equation when given its roots or graph

Circles
Ellipse - Activity A
Hyperbola - Activity A
Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side

AIIT.5.3: Determining the maximum or minimum values of quadratic functions both graphically and algebraically

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

AIIT.6: Perform operations on functions, including addition, subtraction, multiplication, division, and composition.

AIIT.6.2: Performing operations on polynomial and rational expressions containing variables

Addition of Polynomials - Activity A
Dividing Exponential Expressions

AIIT.6.3: Constructing graphs by analyzing their functions as sums, differences, or products

Addition and Subtraction of Polynomials
Exponential Functions - Activity A
Introduction to Functions
Linear Functions
Logarithmic Functions: Translating and Scaling
Using Tables, Rules and Graphs

AIIT.7: Solve equations, inequalities, and applied problems involving absolute values, radicals, and quadratics over the complex numbers, as well as simple trigonometric, exponential, and logarithmic functions.

AIIT.7.1: Solving equations using laws of exponents, including rational and irrational exponents

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

AIIT.7.2: Expressing the solution of an equation, inequality, or applied problem as a graph on a number line or by using set or interval notation

Compound Inequalities
Inequalities Involving Absolute Values
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

AIIT.9: Graph trigonometric functions of the form y=a sin(bx), y=a cos(bx), and y=a tan(bx).

AIIT.9.1: Determining period and amplitude of sine, cosine, and tangent functions from graphs or basic equations

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

AIIT.9.2: Determining specific unit circle coordinates associated with special angles

Cosine Function
Sine Function
Tangent Function
Unit Circle

AIIT.10: Solve general triangles, mathematical problems, and real-world applications using the Law of Sines and the Law of Cosines.

AIIT.10.2: Determining area of oblique triangles

Classifying Triangles

AIIT.11: Define the six trigonometric functions using ratios of the sides of a right triangle, coordinates on the unit circle, and the reciprocal of other functions.

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

AIIT.12: Verify simple trigonometric identities using Pythagorean and/or reciprocal identities.

Simplifying Trigonometric Expressions

AIIT.14: Determine an equation of linear regression from a set of data.

AIIT.14.1: Examining data to determine if a linear, quadratic, or exponential relationship exists and to predict outcomes

Exponential Functions - Activity A
Linear Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic

AIIT.15: Calculate probabilities of events using the laws of probability.

AIIT.15.1: Using permutations and combinations to calculate probabilities

Binomial Probabilities
Permutations
Permutations and Combinations

AIIT.15.2: Calculating conditional probability

Binomial Probabilities

AIIT.15.3: Calculating probabilities of mutually exclusive events, independent events, and dependent events

Binomial Probabilities
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events

AIII.2: Solve problems involving maximum or minimum values of functions by using linear programming procedures.

Linear Programming - Activity A

AIII.3: Graph conic sections, centered at and rotated about the origin, given the equations.

AIII.3.1: Determining equations of conic sections from their graphs

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A
Quadratics in Factored Form

AIII.4: Graph polynomial functions.

AIII.4.1: Approximating zeros using Descartes’ Rule of Signs and the bisection method

Polynomials and Linear Factors

AIII.4.2: Describing the end behavior of a polynomial function given its degree and leading coefficient

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A

AIII.5: Solve systems of linear and quadratic equations and inequalities.

Linear Programming - Activity A
Systems of Linear Inequalities (Slope-intercept form) - Activity A

AIII.8: Plot points in a polar coordinate system given their coordinates in polar form, a table of values, or an equation.

Complex Numbers in Polar Form
Points in Polar Coordinates
Using Tables, Rules and Graphs

AIII.9: Compare summary statistics for sets of data represented in a graph, a stem-and-leaf chart, a box-and-whisker graph, a histogram, a linear or quadratic equation of best fit of a scatterplot, and a frequency distribution.

Box-and-Whisker Plots
Correlation
Histograms
Lines of Best Fit Using Least Squares - Activity A
Populations and Samples
Solving Using Trend Lines
Stem-and-Leaf Plots

AIII.10: Calculate descriptive statistics of univariate data, including measures of central tendency, measures of dispersion, and measures of position.

AIII.10.1: Defining vocabulary associated with probability and statistics, including descriptive and inferential statistics

Binomial Probabilities
Geometric Probability - Activity A

AIII.10.2: Comparing descriptive statistics for samples of varying sizes generated by simulation

Populations and Samples
Probability Simulations

AIII.11: Interpret relationships of bivariate data using linear or quadratic regression and linear correlation.

AIII.11.1: Testing a hypothesis by displaying a scatterplot of experimental data, determining the regression coefficient and equation, and determining the correlation coefficient

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

AIII.14: Determine the probability of an event using a frequency distribution curve.

AIII.14.1: Comparing the terms of a binomial expansion to the terms of a binomial probability distribution

Binomial Probabilities

P.3: Graph conic sections, including parabolas, hyperbolas, ellipses, circles, and degenerate conics, from second-degree equations.

P.3.1: Formulating equations of conic sections from their determining characteristics

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

P.5: Analyze the effects of parameter changes on the graphs of trigonometric, logarithmic, and exponential functions.

P.5.1: Determining the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Functions

P.7: Solve trigonometric equations and inequalities using sum, difference, and half-and double-angle identities.

P.7.1: Verifying trigonometric identities

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

P.9: Solve applied problems involving sequences with recurrence relations.

P.9.1: Determining characteristics of arithmetic and geometric sequences and series, including those defined with recurrence relations, first terms, common differences or ratios, n th terms, limits, or statements of convergence or divergence

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

P.11: Convert coordinates, equations, and complex numbers in Cartesian form to polar form and from polar form to Cartesian form.

P.11.1: Graphing simple polar equations in the polar coordinate plane

Complex Numbers in Polar Form
Points in Polar Coordinates

P.11.2: Graphing polar coordinates and complex numbers

Complex Numbers in Polar Form
Points in Polar Coordinates

P.12: Determine the equation of a curve of best fit from a set of data by using exponential, quadratic, or logarithmic functions.

Exponential Functions - Activity A
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic