A1: Algebra I

A1.1: Students simplify and compare expressions. They use rational exponents and simplify square roots.

A1.1.2: Simplify square roots using factors.

Square Roots

A1.2: Students solve linear equations and inequalities in one variable. They solve word problems that involve linear equations, inequalities, or formulas.

A1.2.1: Solve linear equations.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

A1.2.2: Solve equations and formulas for a specified variable.

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

A1.2.3: Find solution sets of linear inequalities when possible numbers are given for the variable.

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

A1.2.4: Solve linear inequalities using properties of order.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

A1.2.5: Solve combined linear inequalities.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

A1.3: Students sketch and interpret graphs representing given situations. They understand the concept of a function and analyze the graphs of functions.

A1.3.1: Sketch a reasonable graph for a given relationship.

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

A1.3.3: Understand the concept of a function, decide if a given relation is a function, and link equations to functions.

Introduction to Functions
Linear Functions
Using Algebraic Equations

A1.3.4: Find the domain and range of a relation.

Introduction to Functions

A1.4: Students graph linear equations and inequalities in two variables. They write equations of lines and find and use the slope and y-intercept of lines. They use linear equations to model real data.

A1.4.1: Graph a linear equation.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Standard Form of a Line

A1.4.2: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line.

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

A1.4.3: Write the equation of a line in slope-intercept form. Understand how the slope and y-intercept of the graph are related to the equation.

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
Using Tables, Rules and Graphs

A1.4.4: Write the equation of a line given appropriate information.

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

A1.4.5: Write the equation of a line that models a data set and use the equation (or the graph of the equation) to make predictions. Describe the slope of the line in terms of the data, recognizing that the slope is the rate of change.

Defining a Line with Two Points
Direct Variation
Direct and Inverse Variation
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

A1.4.6: Graph a linear inequality in two variables.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

A1.5: Students solve pairs of linear equations using graphs and using algebra. They solve pairs of linear inequalities using graphs. They solve word problems involving pairs of linear equations.

A1.5.1: Use a graph to estimate the solution of a pair of linear equations in two variables.

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

A1.5.2: Use a graph to find the solution set of a pair of linear inequalities in two variables.

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

A1.5.4: Understand and use the addition or subtraction method to solve a pair of linear equations in two variables.

Special Types of Solutions to Linear Systems

A1.5.5: Understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables.

Special Types of Solutions to Linear Systems

A1.5.6: Use pairs of linear equations to solve word problems.

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

A1.6: Students add, subtract, multiply, and divide polynomials. They factor quadratics.

A1.6.1: Add and subtract polynomials.

Addition of Polynomials - Activity A

A1.6.2: Multiply and divide monomials.

Dividing Exponential Expressions
Multiplying Exponential Expressions
Simplifying Radicals - Activity A

A1.6.4: Multiply polynomials.

Polynomials and Linear Factors

A1.6.5: Divide polynomials by monomials.

Dividing Polynomials Using Synthetic Division

A1.6.6: Find a common monomial factor in a polynomial.

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

A1.6.7: Factor the difference of two squares and other quadratics.

Factoring Special Products

A1.6.8: Understand and describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression.

Modeling the Factorization of x²+bx+c
Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations

A1.7: Students simplify algebraic ratios and solve algebraic proportions.

A1.7.1: Simplify algebraic ratios.

Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood

A1.7.2: Solve algebraic proportions.

Estimating Population Size

A1.8: Students graph and solve quadratic and radical equations. They graph cubic equations.

A1.8.1: Graph quadratic, cubic, and radical equations.

Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

A1.8.2: Solve quadratic equations by factoring.

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

A1.8.3: Solve quadratic equations in which a perfect square equals a constant.

Roots of a Quadratic

A1.8.5: Derive the quadratic formula by completing the square.

Roots of a Quadratic

A1.8.6: Solve quadratic equations by using the quadratic formula.

Roots of a Quadratic

A1.8.8: Solve equations that contain radical expressions.

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

A2: Algebra II

A2.1: Students graph relations and functions and find zeros. They use function notation and combine functions by composition. They interpret functions in given situations.

A2.1.1: Recognize and graph various types of functions, including polynomial, rational, and algebraic functions.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Rational Functions

A2.1.2: Use function notation. Add, subtract, multiply, and divide pairs of functions.

Addition and Subtraction of Polynomials

A2.1.4: Graph relations and functions with and without graphing technology.

Exponential Functions - Activity A
Introduction to Functions
Linear Functions
Logarithmic Functions: Translating and Scaling

A2.1.5: Find the zeros of a function.

Polynomials and Linear Factors

A2.1.6: Solve an inequality by examining the graph.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

A2.1.8: Interpret given situations as functions in graphs, formulas, and words.

Cosine Function
Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Introduction to Functions
Linear Functions
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Sine Function
Tangent Function
Using Tables, Rules and Graphs

A2.2: Students solve systems of linear equations and inequalities and use them to solve word problems. They model data with linear equations.

A2.2.1: Graph absolute value equations and inequalities.

Defining a Line with Two Points
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

A2.2.2: Use substitution, elimination, and matrices to solve systems of two or three linear equations in two or three variables.

Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

A2.2.3: Use systems of linear equations and inequalities to solve word problems.

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

A2.3: Students solve quadratic equations, including the use of complex numbers. They interpret maximum and minimum values of quadratic functions. They solve equations that contain square roots.

A2.3.2: Understand how real and complex numbers are related, including plotting complex numbers as points in the plane.

Points in the Complex Plane - Activity A

A2.3.3: Solve quadratic equations in the complex number system.

Roots of a Quadratic

A2.3.4: Graph quadratic functions. Apply transformations to quadratic functions. Find and interpret the zeros and maximum or minimum value of quadratic functions.

Parabolas - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Reflections of a Quadratic Function
Roots of a Quadratic
Translating and Scaling Functions

A2.3.6: Solve equations that contain radical expressions.

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

A2.3.7: Solve pairs of equations, one quadratic and one linear, or both quadratic.

Modeling and Solving Two-Step Equations
Roots of a Quadratic
Solving Equations By Graphing Each Side
Solving Two-Step Equations

A2.4: Students write equations of conic sections and draw their graphs.

A2.4.1: Write the equations of conic sections (circle, ellipse, parabola, and hyperbola).

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

A2.4.2: Graph conic sections.

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

A2.5: Students use the binomial theorem, divide and factor polynomials, and solve polynomial equations.

A2.5.2: Divide polynomials by others of lower degree.

Dividing Polynomials Using Synthetic Division

A2.5.3: Factor polynomials completely and solve polynomial equations by factoring.

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

A2.5.7: Understand and describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression.

Modeling the Factorization of x²+bx+c
Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations

A2.6: Students use negative and fractional exponents. They simplify algebraic fractions and solve equations involving algebraic fractions. They solve problems of direct, inverse, and joint variation.

A2.6.2: Add, subtract, multiply, divide, and simplify algebraic fractions.

Fractions with Unlike Denominators

A2.6.4: Solve equations involving algebraic fractions.

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

A2.6.5: Solve word problems involving fractional equations.

Using Algebraic Equations

A2.6.6: Solve problems of direct, inverse, and joint variation.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

A2.7: Students graph exponential functions and relate them to logarithms. They solve logarithmic and exponential equations and inequalities. They solve word problems using exponential functions.

A2.7.1: Graph exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B

A2.7.4: Solve logarithmic and exponential equations and inequalities.

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

A2.7.8: Solve word problems involving applications of exponential functions to growth and decay.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life

A2.8: Students define and use arithmetic and geometric sequences and series.

A2.8.1: Define arithmetic and geometric sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A2.8.2: Find specified terms of arithmetic and geometric sequences.

Arithmetic Sequences

A2.8.4: Solve word problems involving applications of sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A2.9: Students use fundamental counting principles to compute combinations, permutations, and probabilities.

A2.9.1: Understand and apply counting principles to compute combinations and permutations.

Binomial Probabilities
Permutations
Permutations and Combinations

A2.9.2: Use the basic counting principle, combinations, and permutations to compute probabilities.

Binomial Probabilities
Permutations
Permutations and Combinations

C: Calculus, Advanced Placement

C.1: Students understand the concept of limit, find limits of functions at points and at infinity, decide if a function is continuous, and use continuity theorems.

C.1.1: Understand the concept of limit and estimate limits from graphs and tables of values.

Using Tables, Rules and Graphs

C.1.4: Find limits of rational functions that are undefined at a point.

General Form of a Rational Function
Rational Functions

C.1.11: Find the types of discontinuities of a function.

Functions Involving Square Roots

C.3: Students find slopes and tangents, maximum and minimum points, and points of inflection. They solve optimization problems and find rates of change.

C.3.10: Find average and instantaneous rates of change. Understand the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed, and acceleration.

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

C.3.11: Find the velocity and acceleration of a particle moving in a straight line.

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

C.4: Students define integrals using Riemann Sums, use the Fundamental Theorem of Calculus to find integrals, and use basic properties of integrals. They integrate by substitution and find approximate integrals.

C.4.2: Calculate the values of Riemann Sums over equal subdivisions using left, right, and midpoint evaluation points.

Riemann Sum

C.4.3: Interpret a definite integral as a limit of Riemann Sums.

Riemann Sum

C.4.8: Understand and use Riemann Sums, the Trapezoidal Rule, and technology to approximate definite integrals of functions represented algebraically, geometrically, and by tables of values.

Riemann Sum

C.5: Students find velocity functions and position functions from their derivatives, solve separable differential equations, and use definite integrals to find areas and volumes.

C.5.1: Find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions, and applications to motion along a line.

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

C.5.7: Apply integration to model and solve problems in physics, biology, economics, etc., using the integral as a rate of change to give accumulated change and using the method of setting up an approximating Riemann Sum and representing its limit as a definite integral.

Riemann Sum

DM: Discrete Mathematics

DM.1: Students use counting techniques.

DM.1.1: Use networks, traceable paths, tree diagrams, Venn diagrams, and other pictorial representations to find the number of outcomes in a problem situation.

Binomial Probabilities
Permutations
Permutations and Combinations

DM.1.3: Use combinatorial reasoning to solve problems.

Binomial Probabilities
Permutations and Combinations

DM1.5: Use simulations to solve counting and probability problems.

Binomial Probabilities
Geometric Probability - Activity A
Probability Simulations

DM.2: Students use matrices.

DM.2.1: Use matrices to organize and store data.

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

DM.3: Students use recursive techniques.

DM.3.1: Use recursive thinking to solve problems.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

DM.3.2: Use finite differences to solve problems.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

G: Geometry

G.1: Students find lengths and midpoints of line segments. They describe and use parallel and perpendicular lines. They find slopes and equations of lines.

G.1.1: Find the lengths and midpoints of line segments in one- or two-dimensional coordinate systems.

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

G.1.2: Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass, explaining and justifying the process used.

Construct Parallel and Perpendicular Lines

G.1.3: Understand and use the relationships between special pairs of angles formed by parallel lines and transversals.

Investigating Angle Theorems - Activity A

G.1.4: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

Point-Slope Form of a Line - Activity A
Slope - Activity B

G.2: Students identify and describe polygons and measure interior and exterior angles. They use congruence, similarity, symmetry, tessellations, and transformations. They find measures of sides, perimeters, and areas.

G.2.2: Find measures of interior and exterior angles of polygons, justifying the method used.

Triangle Angle Sum - Activity A

G.2.3: Use properties of congruent and similar polygons to solve problems.

Classifying Triangles
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

G.2.4: Apply transformations (slides, flips, turns, expansions, and contractions) to polygons in order to determine congruence, similarity, symmetry, and tessellations. Know that images formed by slides, flips and turns are congruent to the original shape.

Dilations
Holiday Snowflake Designer
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons
Translations

G.2.5: Find and use measures of sides, perimeters, and areas of polygons, and relate these measures to each other using formulas.

Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

G.2.6: Use coordinate geometry to prove properties of polygons such as regularity, congruence, and similarity.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

G.3: Students identify and describe simple quadrilaterals. They use congruence and similarity. They find measures of sides, perimeters, and areas.

G.3.1: Describe, classify, and understand relationships among the quadrilaterals square, rectangle, rhombus, parallelogram, trapezoid, and kite.

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

G.3.2: Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas.

Area of Parallelograms - Activity A
Classifying Quadrilaterals - Activity B
Congruence in Right Triangles
Perimeter, Circumference, and Area - Activity B
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

G.3.3: Find and use measures of sides, perimeters, and areas of quadrilaterals, and relate these measures to each other using formulas.

Area of Parallelograms - Activity A
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

G.3.4: Use coordinate geometry to prove properties of quadrilaterals such as regularity, congruence, and similarity.

Classifying Quadrilaterals - Activity B
Congruence in Right Triangles
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
Special Quadrilaterals

G.4: Students identify and describe types of triangles. They identify and draw altitudes, medians, and angle bisectors. They use congruence and similarity. They find measures of sides, perimeters, and areas. They apply inequality theorems.

G.4.1: Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.

Classifying Triangles
Isosceles and Equilateral Triangles
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity A

G.4.2: Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors.

Concurrent Lines, Medians, and Altitudes

G.4.3: Construct triangles congruent to given triangles.

Congruence in Right Triangles
Proving Triangles Congruent

G.4.4: Use properties of congruent and similar triangles to solve problems involving lengths and areas.

Congruence in Right Triangles
Perimeter, Circumference, and Area - Activity B
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

G.4.5: Prove and apply theorems involving segments divided proportionally.

Estimating Population Size
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Similar Figures - Activity A
Similar Polygons

G.4.6: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

G.4.7: Find and use measures of sides, perimeters, and areas of triangles, and relate these measures to each other using formulas.

Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

G.4.8: Prove, understand, and apply the inequality theorems: triangle inequality, inequality in one triangle, and hinge theorem.

Triangle Inequalities

G.4.9: Use coordinate geometry to prove properties of triangles such as regularity, congruence, and similarity.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

G.5: Students prove the Pythagorean Theorem and use it to solve problems. They define and apply the trigonometric relations sine, cosine, and tangent.

G.5.1: Prove and use the Pythagorean Theorem.

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

G.5.2: State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.

Similarity in Right Triangles

G.5.4: Define and use the trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) in terms of angles of right triangles.

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

G.5.5: Know and use the relationship sin²x + cos²x = 1.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

G.5.6: Solve word problems involving right triangles.

Classifying Triangles

G.6: Students define ideas related to circles: e.g., radius, tangent. They find measures of angles, lengths, and areas. They prove theorems about circles. They find equations of circles.

G.6.2: Define and identify relationships among: radius, diameter, arc, measure of an arc, chord, secant, and tangent.

Chords and Arcs

G.6.3: Prove theorems related to circles.

Chords and Arcs
Inscribing Angles

G.6.5: Define, find, and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).

Chords and Arcs
Inscribing Angles

G.6.6: Define and identify congruent and concentric circles.

Congruence in Right Triangles
Proving Triangles Congruent

G.6.7: Define, find, and use measures of circumference, arc length, and areas of circles and sectors. Use these measures to solve problems.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

G.6.8: Find the equation of a circle in the coordinate plane in terms of its center and radius.

Circles

G.7: Students describe and make polyhedra and other solids. They describe relationships and symmetries, and use congruence and similarity.

G.7.2: Describe the polyhedron that can be made from a given net (or pattern). Describe the net for a given polyhedron.

Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

G.7.4: Describe symmetries of geometric solids.

Holiday Snowflake Designer
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

G.7.5: Describe sets of points on spheres: chords, tangents, and great circles.

Chords and Arcs

G.7.6: Identify and know properties of congruent and similar solids.

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Proving Triangles Congruent

G.7.7: Find and use measures of sides, volumes of solids, and surface areas of solids, and relate these measures to each other using formulas.

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

PC: Pre-Calculus/Trigonometry

PC.1: Students use polynomial, rational, and algebraic functions to write functions and draw graphs to solve word problems, to find composite and inverse functions, and to analyze functions and graphs. They analyze and graph circles, ellipses, parabolas, and hyperbolas.

PC.1.1: Recognize and graph various types of functions, including polynomial, rational, algebraic, and absolute value functions. Use paper and pencil methods and graphing calculators.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Quadratic and Absolute Value Functions
Rational Functions
Translating and Scaling Functions

PC.1.2: Find domain, range, intercepts, zeros, asymptotes, and points of discontinuity of functions. Use paper and pencil methods and graphing calculators.

Functions Involving Square Roots
Introduction to Functions
Polynomials and Linear Factors

PC.1.3: Model and solve word problems using functions and equations.

Linear Functions
Using Algebraic Equations

PC.1.5: Describe the symmetry of the graph of a function.

Cosine Function
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Sine Function
Tangent Function

PC.1.7: Apply transformations to functions.

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

PC.1.10: Write the equations of conic sections in standard form (completing the square and using translations as necessary), in order to find the type of conic section and to find its geometric properties (foci, asymptotes, eccentricity, etc.).

Circles
Ellipse - Activity A
Hyperbola - Activity A
Parabolas - Activity A
Rotations, Reflections and Translations
Translations

PC.2: Students solve word problems involving logarithmic and exponential functions. They draw and analyze graphs and find inverse functions.

PC.2.1: Solve word problems involving applications of logarithmic and exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

PC.2.2: Find the domain, range, intercepts, and asymptotes of logarithmic and exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

PC.2.3: Draw and analyze graphs of logarithmic and exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

PC.2.4: Define, find, and check inverse functions of logarithmic and exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling

PC.3: Students define trigonometric functions using right triangles. They solve word problems and apply the laws of sines and cosines.

PC.3.1: Solve word problems involving right and oblique triangles.

Classifying Triangles

PC.3.3: Find the area of a triangle given two sides and the angle between them.

Isosceles and Equilateral Triangles
Perimeter, Circumference, and Area - Activity B
Triangle Angle Sum - Activity A

PC.4: Students define trigonometric functions using the unit circle and use degrees and radians. They draw and analyze graphs, find inverse functions, and solve word problems.

PC.4.1: Define sine and cosine using the unit circle.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Unit Circle

PC.4.3: Learn exact sine, cosine, and tangent values for 0, pi/2, pi/3, pi/4, pi/6, and multiples of pi. Use those values to find other trigonometric values.

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

PC.4.4: Solve word problems involving applications of trigonometric functions.

Cosine Function
Sine Function
Tangent Function
Unit Circle

PC.4.5: Define and graph trigonometric functions (i.e., sine, cosine, tangent, cosecant, secant, cotangent).

Cosine Function
Sine Function
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Translating and Scaling Functions
Unit Circle

PC.4.6: Find domain, range, intercepts, periods, amplitudes, and asymptotes of trigonometric functions.

Functions Involving Square Roots

PC.4.7: Draw and analyze graphs of translations of trigonometric functions, including period, amplitude, and phase shift.

Functions Involving Square Roots
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A

PC.4.9: Find values of trigonometric and inverse trigonometric functions.

Cosine Function
Sine Function
Tangent Function

PC.4.10: Know that the tangent of the angle that a line makes with the x-axis is equal to the slope of the line.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope - Activity B
Tangent Function
Tangent Ratio

PC.4.11: Make connections between right triangle ratios, trigonometric functions, and circular functions.

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

PC.5: Students prove trigonometric identities, solve trigonometric equations, and solve word problems.

PC.5.1: Know the basic trigonometric identity cos²x + sin²x = 1 and prove that it is equivalent to the Pythagorean Theorem.

Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity B
Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

PC.5.2: Use basic trigonometric identities to verify other identities and simplify expressions.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

PC.5.3: Understand and use the addition formulas for sines, cosines, and tangents.

Cosine Function
Sine Function
Sine, Cosine and Tangent
Sum and Difference Identities for Sine and Cosine
Tangent Function
Tangent Ratio
Unit Circle

PC.5.4: Understand and use the half-angle and double-angle formulas for sines, cosines, and tangents.

Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Sum and Difference Identities for Sine and Cosine
Tangent Function
Tangent Ratio
Unit Circle

PC.6: Students define polar coordinates and complex numbers and understand their connection with trigonometric functions.

PC.6.1: Define polar coordinates and relate polar coordinates to Cartesian coordinates.

Points in Polar Coordinates

PC.6.2: Represent equations given in rectangular coordinates in terms of polar coordinates.

Points in Polar Coordinates

PC.6.3: Graph equations in the polar coordinate plane.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Points in Polar Coordinates
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

PC.6.4: Define complex numbers, convert complex numbers to trigonometric form, and multiply complex numbers in trigonometric form.

Complex Numbers in Polar Form

PC.7: Students define and use arithmetic and geometric sequences and series, understand the concept of a limit, and solve word problems.

PC.7.3: Prove and use the sum formulas for arithmetic series and for finite and infinite geometric series.

Arithmetic Sequences
Arithmetic and Geometric Sequences

PC.7.4: Use recursion to describe a sequence.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

PC.7.6: Solve word problems involving applications of sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

PC.8: Students model data with linear and nonlinear functions.

PC.8.1: Find linear models using the median fit and least squares regression methods. Decide which model gives a better fit.

Correlation
Solving Using Trend Lines

PC.8.2: Calculate and interpret the correlation coefficient. Use the correlation coefficient and residuals to evaluate a “best-fit” line.

Correlation

PC.8.3: Find a quadratic, exponential, logarithmic, power, or sinusoidal function to model a data set and explain the parameters of the model.

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

PS: Probability and Statistics

PS.1: Students gather and display data and use measures of central tendency and variability.

PS.1.1: Create, compare, and evaluate different graphic displays of the same data, using histograms, frequency polygons, cumulative distribution functions, pie charts, scatter plots, stem-and-leaf plots, and box-and-whisker plots. Draw these by hand or use a computer spreadsheet program.

Box-and-Whisker Plots
Correlation
Histograms
Populations and Samples
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

PS. 1.2: Compute and use mean, median, mode, weighted mean, geometric mean, harmonic mean, range, quartiles, variance, and standard deviation.

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

PS.2: Students solve problems involving the use of probability and probability distributions.

PS.2.1: Understand the counting principle, permutations, and combinations, and use them to solve problems.

Binomial Probabilities
Permutations
Permutations and Combinations

PS.2.3: Understand and use the multiplication rule to calculate probabilities for independent and dependent events.

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

PS.2.6: Use discrete random variables and probability distributions, including the binomial and geometric distributions.

Binomial Probabilities

PS.2.7: Compute and interpret the mean and variance of a probability distribution.

Binomial Probabilities
Line Plots
Mean, Median and Mode
Populations and Samples

PS.2.10: Use other continuous random variables and probability distributions to solve problems.

Binomial Probabilities

PS.3: Students use confidence intervals and hypothesis tests, fit curves to data, and calculate correlation coefficients.

PS.3.2: Understand hypothesis tests of means and differences between means and use them to reach conclusions.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

PS.3.4: Calculate and interpret the correlation coefficient of a set of data.

Correlation

IM1: Integrated Mathematics I

IM1.1: Students simplify and compare expressions. They use rational exponents and simplify square roots.

IM1.1.1: Compare real number expressions.

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

IM1.1.2: Simplify square roots using factors.

Square Roots

IM1.2: Students solve linear equations and inequalities in one variable. They write equations of lines and find and use the slope and y-intercept of lines. Students solve pairs of linear equations using graphs and algebra. Students add, subtract, multiply, and divide polynomials and solve word problems using exponential functions.

IM1.2.1: Solve linear equations.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

IM1.2.2: Solve equations and formulas for a specific variable.

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

IM1.2.3: Find solution sets of linear inequalities when possible numbers are given for the variable.

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

IM1.2.4: Solve linear inequalities using properties of order.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

IM1.2.6: Sketch a reasonable graph for a given relationship.

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

IM1.2.8: Understand the concept of a function, decide if a given relation is a function and link equations to functions.

Introduction to Functions
Linear Functions
Using Algebraic Equations

IM1.2.9: Find the domain and range of a relation.

Introduction to Functions

IM1.2.10: Graph a linear equation.

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Standard Form of a Line

IM1.2.11: Find the slope, x-intercept and y-intercept of a line given its graph, its equation, or two points on the line.

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

IM1.2.12: Write the equation of a line in slope-intercept form. Understand how the slope and y-intercept are related to the equation.

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
Using Tables, Rules and Graphs

IM1.2.13: Write the equation of a line given appropriate information.

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

IM1.2.14: Write the equation of a line that models a given situation and use (or the graph of the line) to make predictions. Describe the slope of the line in terms of the given situation, recognizing that the slope is the rate of change.

Defining a Line with Two Points
Direct Variation
Direct and Inverse Variation
Modeling Linear Systems - Activity A
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

IM1.2.15: Use the graph to estimate the solution of a pair of linear equations in two variables.

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

IM1.2.17: Understand and use the addition or subtraction method to solve a pair of linear equations in two variables.

Special Types of Solutions to Linear Systems

IM1.2.18: Understand and use multiplication with the addition or subtraction method to solve a pair of linear equations in two variables.

Special Types of Solutions to Linear Systems

IM1.2.19: Use pairs of linear equations to solve word problems.

Modeling Linear Systems - Activity A
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

IM1.2.20: Add and subtract polynomials.

Addition of Polynomials - Activity A

IM1.2.21: Multiple and divide monomials.

Dividing Exponential Expressions
Multiplying Exponential Expressions
Simplifying Radicals - Activity A

IM1.2.22: Find powers and roots of monomials (only when the answer has an integer exponent).

Dividing Exponential Expressions
Multiplying Exponential Expressions

IM1.2.23: Multiply polynomials.

Polynomials and Linear Factors

IM1.2.24: Divide polynomials by monomials.

Dividing Polynomials Using Synthetic Division

IM1.2.25: Understand and describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression.

Modeling the Factorization of x²+bx+c
Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations

IM1.2.26: Graph quadratic, cubic, and radical equations.

Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A

IM1.2.27: Solve quadratic equations by using the quadratic formula.

Roots of a Quadratic

IM1.2.30: Graph exponential functions.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B

IM1.2.31: Solve word problems involving applications of exponential functions to growth and decay.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Simple and Compound Interest

IM1.3: Students identify and describe polygons, including finding measures of sides, perimeters, and areas. They use congruence, similarity, symmetry, tessellations, and transformations. Students understand the Pythagorean Theorem and use it to solve problems. They describe relationships and symmetries in geometric solids.

IM1.3.2: Apply transformations (slides, flips, turns, expansions, and contractions) to polygons to determine congruence, similarity, symmetry, and tessellations. Know that images formed by slides, flips, and turns are congruent to the original shape.

Dilations
Holiday Snowflake Designer
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons
Translations

IM1.3.3: Find and use measures of sides, perimeter, and areas of polygons, and relate these measures to each other using formulas.

Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

IM1.3.4: Use properties of congruent and similar quadrilaterals to solve problems involving lengths and areas.

Area of Parallelograms - Activity A
Classifying Quadrilaterals - Activity B
Perimeter, Circumference, and Area - Activity B
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

IM1.3.5: Find and use measures of sides, perimeters, and areas of quadrilaterals, and relate these measures to each other using formulas.

Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

IM1.3.6: Prove and use the Pythagorean Theorem.

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

IM1.3.8: Describe symmetries of geometric solids.

Holiday Snowflake Designer
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

IM1.4: Students find measures of the center and variability of a set of data, as well as construct and analyze data displays and plot least square regression lines.

IM1.4.1: Construct a line plot.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

IM1.4.2: Find measures of central tendency for a set of data.

Describing Data Using Statistics
Line Plots
Mean, Median and Mode

IM1.4.4: Construct a histogram using a graphing calculator.

Histograms
Populations and Samples

IM1.4.6: Find a linear transformation.

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

IM1.4.7: Construct a stem-and-leaf plot using a graphing calculator.

Stem-and-Leaf Plots

IM1.4.12: Construct a scatterplot from a set of data.

Box-and-Whisker Plots
Correlation
Histograms
Line Plots
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots

IM1.4.15: Compare sets of data using scatterplots and the line y = x, and interpret these comparisons for real-world data.

Correlation
Populations and Samples
Scatter Plots - Activity A
Solving Using Trend Lines

IM1.4.16: Recognize patterns in tables and graphs that are modeled by linear equations.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences

IM1.5: Students use simulations, find probabilities, and use the Law of Large Numbers.

IM1.5.1: Design and use simulations in order to estimate answers related to probability.

Probability Simulations

IM1.5.2: Use empirical (experimental) and theoretical 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

IM1.5.3: Understand independent events.

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

IM1.5.4: Use the Law of Large Numbers to understand situations involving chance.

Geometric Probability - Activity A
Polling: City

IM1.5.5: Understand the concept of a probability distribution. Understand how an approximate probability can be constructed using simulation involving chance.

Binomial Probabilities

IM1.6: Students construct graphs, explore algorithms, and use recursion equations and matrices.

IM1.6.5: Use a recursion function to describe an exponential function.

Exponential Functions - Activity A

IM2: Integrated Mathematics II

IM2.1: Students graph linear inequalities in two variables and quadratics. They model data with linear equations.

IM2.1.1: Graph a linear inequality in two variables.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

IM2.1.2: Interpret given situations as functions in graphs, formulas, and words.

Linear Functions

IM2.1.4: Graph quadratic functions. Show and explain the effects on the graph of changing a coefficient in a quadratic function. Find and interpret the zeros and maximum or minimum value of quadratic functions.

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

IM2.2: Students identify and describe types of triangles. They define and apply the trigonometric relations. Students apply theorems to triangles and circles.

IM2.2.2: Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass, explaining and justifying the process used.

Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles

IM2.2.3: Find the measures of interior and exterior angles of polygons, justifying the method used.

Triangle Angle Sum - Activity A

IM2.2.4: Identify and describe triangles that are right, acute, obtuse, scalene, isosceles, equilateral, and equiangular.

Classifying Triangles
Isosceles and Equilateral Triangles
Pythagorean Theorem - Activity B
Triangle Angle Sum - Activity A

IM2.2.5: Define, identify, and construct altitudes, medians, angle bisectors, and perpendicular bisectors.

Concurrent Lines, Medians, and Altitudes

IM2.2.6: Use properties of congruent and similar triangles to solve problems involving lengths and areas.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

IM2.2.7: Find measures of sides, perimeters, and areas of triangles, and relate these measures to each other using formulas.

Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

IM2.2.8: Prove, understand, and apply the inequality theorems: triangle inequality, inequality in one triangle, and the hinge theorem.

Triangle Inequalities

IM2.2.9: State and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle.

Similarity in Right Triangles

IM2.2.11: Define and apply the trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant) defined by angles of right triangles.

Cosine Function
Sine Function
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle

IM2.2.12: Know and use the relationship sin²x + cos²x = 1.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

IM2.2.13: Solve word problems involving right triangles.

Classifying Triangles

IM2.2.15: Define and identify relationships among: radius, diameter, arc, measure of an arc, chord, secant, and tangent.

Chords and Arcs

IM2.2.16: Prove theorems related to circles.

Chords and Arcs
Inscribing Angles

IM2.2.18: Define, find, and use measures of arcs and related angles (central, inscribed, and intersections of secants and tangents).

Chords and Arcs
Inscribing Angles

IM2.2.20: Define, find, and use measures of circumference, arc length, and areas of circles and sectors. Use these measures to solve problems.

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

IM2.2.21: Describe sets of points on spheres: chords, tangents, and great circles.

Chords and Arcs

IM2.3: Students interpret scatterplots and analyze correlation.

IM2.3.1: Describe the association between two variables by interpreting a scatterplot.

Correlation
Scatter Plots - Activity A
Solving Using Trend Lines

IM2.3.2: Interpret correlation coefficients.

Correlation

IM2.3.4: Understand that a correlation between two variables does not necessarily imply one directly causes the other.

Correlation
Solving Using Trend Lines

IM2.3.5: Understand the effects of outliers on correlation coefficients, on the least squares regression line, and on the interpretations of correlation coefficients and regression lines in real-life contexts.

Correlation
Solving Using Trend Lines

IM2.4: Students construct probability distributions, understand fundamental probability concepts, and use counting principles.

IM2.4.1: Construct a probability distribution by simulation and use it to understand and analyze the probabilistic situation.

Binomial Probabilities
Probability Simulations

IM2.4.2: Explore the geometric, or waiting-time, distribution.

Geometric Probability - Activity A

IM2.4.3: Understand fundamental concepts of probability (i.e., independent events, multiplication rule, expected value).

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

IM2.4.4: Understand and apply counting principles to compute combinations and permutations.

Binomial Probabilities
Permutations
Permutations and Combinations

IM2.4.5: Use the basic counting principle, combinations, and permutations to compute probabilities.

Binomial Probabilities
Permutations
Permutations and Combinations

IM2.6: Students apply trigonometric ratios to right triangles.

IM2.6.1: Explore properties and applications of the sine, cosine, and tangent ratios for the lengths of sides of right triangles.

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

IM3: Integrated Mathematics III

IM3.1: Students solve inequalities, quadratic equations, and systems of equations. They graph polynomial, rational, algebraic, and piece-wise defined functions. They graph and write the equations of conic sections and compute with and factor polynomials and algebraic fractions. They solve problems involving exponential and logarithmic expressions, as well as define and use arithmetic and geometric sequences and series.

IM3.1.1: Solve combined linear inequalities.

Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

IM3.1.2: Use a graph to find the solution set of a pair of linear inequalities in two variables.

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

IM3.1.3: Find a common monomial factor in a polynomial.

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

IM3.1.4: Factor the difference of two squares and other quadratics.

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

IM3.1.5: Simplify algebraic ratios.

Similar Figures - Activity A
Similar Polygons

IM3.1.6: Solve algebraic proportions.

Estimating Population Size
Polling: Neighborhood
Similar Figures - Activity A
Similar Polygons

IM3.1.7: Solve quadratic equations by factoring.

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

IM3.1.8: Solve quadratic equations in which a perfect square equals a constant.

Roots of a Quadratic

IM3.1.10: Derive the quadratic formula by completing the square.

Roots of a Quadratic

IM3.1.12: Recognize and graph various types of functions, including polynomials, rational, and algebraic functions.

Cubic Function Activity
Fourth-Degree Polynomials - Activity A
General Form of a Rational Function
Rational Functions

IM3.1.13: Use function notation. Add, subtract, multiply, and divide pairs of functions.

Addition and Subtraction of Polynomials

IM3.1.16: Find the zeros of a function.

Polynomials and Linear Factors

IM3.1.17: Solve an inequality by examining the graph.

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

IM3.1.19: Graph absolute value equations and inequalities.

Defining a Line with Two Points
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

IM3.1.20: Use substitution, elimination, and matrices to solve systems of two or three equations in two or three variables.

Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A

IM3.1.21: Use system of equations and inequalities to solve word problems.

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

IM3.1.23: Understand how real and complex numbers are related, including plotting complex numbers as points in the plane.

Points in the Complex Plane - Activity A

IM3.1.24: Solve quadratic equations in the complex number system.

Roots of a Quadratic

IM3.1.27: Solve pairs of equations, one quadratic and one linear, or both quadratic.

Roots of a Quadratic
Solving Equations By Graphing Each Side

IM3.1.28: Write the equations of conic sections (circle, ellipse, parabola, and hyperbola).

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

IM3.1.29: Graph conic sections.

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

IM3.1.31: Divide polynomials by others of lower degree.

Dividing Polynomials Using Synthetic Division

IM3.1.32: Factor polynomials completely and solve polynomial equations by factoring.

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

IM3.1.36: Understand and describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of the graph, and the factors of a polynomial expression.

Modeling the Factorization of x²+bx+c
Point-Slope Form of a Line - Activity A
Polynomials and Linear Factors
Slope-Intercept Form of a Line - Activity A
Using Algebraic Equations

IM3.1.38: Add, subtract, multiply, divide, and simplify algebraic fractions.

Fractions with Unlike Denominators

IM3.1.40: Solve equations involving algebraic fractions.

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

IM3.1.41: Solve word problems involving fractional equations.

Using Algebraic Equations

IM3.1.42: Solve problems of direct, inverse, and joint variation.

Determining a Spring Constant
Direct Variation
Direct and Inverse Variation

IM3.1.49: Solve word problems involving applications of exponential functions to growth and decay.

Exponential Functions - Activity A
Exponential Growth and Decay - Activity B
Half-life
Simple and Compound Interest

IM3.1.50: Define arithmetic and geometric sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

IM3.1.51: Find specified terms of arithmetic and geometric sequences.

Arithmetic Sequences

IM3.1.53: Solve word problems involving applications of sequences and series.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

IM3.2: Students describe and use parallel and perpendicular lines. They use coordinate geometry and prove that triangles are congruent or similar. They find the equation of a circle in the coordinate plane and describe and use properties of solids.

IM3.2.1: Understand and use the relationships between special pairs of angles formed by parallel lines and transversals.

Investigating Angle Theorems - Activity A

IM3.2.2: Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines.

Construct Parallel and Perpendicular Lines
Point-Slope Form of a Line - Activity A
Slope - Activity B

IM3.2.3: Use properties of congruent and similar polygons to solve problems.

Classifying Triangles
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

IM3.2.4: Use coordinate geometry to prove properties of polygons such as regularity, congruence, and similarity.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

IM3.2.5: Describe, classify, and understand relationships among quadrilaterals square, rectangles, rhombus, parallelogram, trapezoid, and kite.

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

IM3.2.6: Use coordinate geometry to prove properties of quadrilaterals such as regularity, congruence, and similarity.

Classifying Quadrilaterals - Activity B
Perimeters and Areas of Similar Figures

IM3.2.7: Construct triangles congruent to given triangles.

Congruence in Right Triangles
Proving Triangles Congruent

IM3.2.9: Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

IM3.2.10: Use coordinate geometry to prove properties of triangles such as regularity, congruence, and similarity.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

IM3.2.11: Find the equation of a circle in the coordinate plane in terms of its center and radius.

Circles

IM3.2.13: Describe the polyhedron that can be made from a given net (or pattern). Describe the net for a given polygon.

Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

IM3.2.14: Identify and know properties of congruent and similar solids.

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Proving Triangles Congruent

IM3.2.15: Find and use measures of sides, volumes of solids, and surface areas of solids. Relate these measures to each other using formulas.

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

IM3.3: Students design and interpret surveys, use sampling distributions, and understand standard deviation.

IM3.3.1: Understand and apply basic ideas related to the design and interpretation of surveys, such as background information, random sampling, and bias.

Polling: Neighborhood

IM3.3.2: Construct simulated sampling distributions of sample proportions and use sampling distributions to identify which proportions are likely to be found in a sample of a given size.

Populations and Samples
Probability Simulations

IM3.6: Students use the Law of Sines and the Law of Cosines to solve problems. They analyze families of trigonometric functions.

IM3.6.1: Find the measures of sides and angles in triangles using the Law of Sines.

Classifying Triangles
Isosceles and Equilateral Triangles
Triangle Angle Sum - Activity A

IM3.6.2: Find the measures of sides and angles in triangles using the Law of Cosines.

Classifying Triangles
Isosceles and Equilateral Triangles
Triangle Angle Sum - Activity A

IM3.6.3: Compare and contrast families of trigonometric functions.

Cosine Function
Sine Function
Tangent Function
Unit Circle