Reveal Math Integrated I-III Table of Contents

[Pages:8]Reveal MathTM Integrated I-III Table of Contents

INTEGRATED I

Module 1 Expressions

1-1

Numerical Expressions Explore: Order of Operations

1-2

Algebraic Expressions Explore: Using Algebraic Expressions in the Real World

1-3

Properties of Real Numbers Explore: Testing the Associative Property

Distributive Property 1-4 Explore: Using Rectangles with the Distributive Property

Explore: Modeling the Distributive Property

1-5

Expressions Involving Absolute Value Explore: Distance Between Points on a Number Line

1-6 Descriptive Modeling and Accuracy

Module 2 Equations in One Variable

2-1

Writing and Interpreting Equations Explore: Writing Equations by Modeling a Real-World Situation

Solving One-Step Equations

2-2

Explore: Using Algebra Tiles to Solve One-Step Equations Involving Addition or Subtraction

Explore: Using Algebra Tiles to Solve One-Step Equations Involving Multiplication

2-3

Solving Multi-Step Equations Explore: Using Algebra Tiles to Model Multi-Step Equations

2-4

Solving Equations with the Variable on Each Side Explore: Modeling Equations with the Variable on Each Side

2-5

Solving Equations Involving Absolute Value Explore: Modeling Absolute Value

2-6

Solving Proportions Explore: Comparing Two Quantities

Using Formulas

2-7 Explore: Centripetal Force

Explore: Using Dimensional Analysis

Module 3 Relations and Functions

3-1

Representing Relations Explore: Choosing Scales

3-2

Functions Explore: Vertical Line Test

3-3

Linearity and Continuity of Graphs Explore: Representing Discrete and Continuous Functions

3-4 Intercepts of Graphs

Shapes of Graphs 3-5 Explore: Line Symmetry

Explore: Relative High and Low Points

3-6

Sketching Graphs and Comparing Functions Explore: Modeling Relationships by Using Functions

Module 4 Linear and Nonlinear Functions

Graphing Linear Functions

4-1 Explore: Points on a Line

Explore: Lines Through Two Points

4-2

Rate of Change and Slope Explore: Investigating Slope

Expand 4-2 Proving the Slope Criteria

Slope-Intercept Form 4-3 Explore: Graphing Linear Equations by Using the

Slope-Intercept Form

Expand 4-3 Linear Growth Patterns

4-4

Transformations of Linear Functions Explore: Transforming Linear Functions

4-5

Arithmetic Sequences Explore: Common Differences

4-6

Piecewise and Step Functions Explore: Age as a Function

4-7

Absolute Value Functions Explore: Parameters of an Absolute Value Function

Module 5 Creating Linear Equations

5-1

Writing Equations in Slope-Intercept Form Explore: Slope-Intercept Form

5-2

Writing Equations in Standard and Point-Slope Forms Explore: Forms of Linear Equations

5-3

Scatter Plots and Lines of Fit Explore: Making Predictions by Using a Scatter Plot

5-4

Correlation and Causation Explore: Collecting Data to Determine Correlation and Causation

5-5 Linear Regression

5-6

Inverses of Linear Functions Explore: Comparing a Function and its Inverse

Module 6 Linear Inequalities

Solving One-Step Inequalities 6-1 Explore: Graphing Inequalities

Explore: Properties of Inequalities

6-2

Solving Multi-Step Inequalities Explore: Modeling Multi-Step Inequalities

6-3

Solving Compound Inequalities Explore: Guess the Range

6-4

Solving Absolute Value Inequalities Explore: Solving Absolute Value Inequalities

6-5

Graphing Inequalities in Two Variables Explore: Graphing Linear Inequalities on the Coordinate Plane

Integrated I Integrated II Integrated III

INTEGRATED I CONTINUED

Module 7 Systems of Linear Equations and Inequalities

7-1

Graphing Systems of Equations Explore: Intersections of Graphs

7-2

Substitution Explore: Using Substitution

7-3 Elimination Using Addition and Subtraction

7-4

Elimination Using Multiplication Explore: Graphing and Elimination Using Multiplication

7-5

Systems of Inequalities Explore: Solutions of Systems of Inequalities

Module 8 Exponential Functions

Exponential Functions

8-1 Explore: Exponential Behavior

Explore: Restrictions on Exponential Functions

Transformations of Exponential Functions

8-2

Explore: Translating Exponential Functions Explore: Dilating Exponential Functions

Explore: Reflecting Exponential Functions

8-3

Writing Exponential Functions Explore: Writing an Exponential Function to Model Population Growth

8-4 Transforming Exponential Expressions

8-5

Geometric Sequences Explore: Modeling Geometric Sequences

Expand 8-5 Exponential Growth Patterns

8-6

Recursive Formulas Explore Writing Recursive Formulas from Sequences

Module 9 Statistics

9-1

Measures of Center Explore: Finding Percentiles

9-2 Representing Data

9-3

Using Data Explore: Phrasing Questions

9-4

Measures of Spread Explore: Using Measures of Spread to Describe Data

9-5 Distributions of Data

Comparing Sets of Data 9-6 Explore: Transforming Sets of Data by Using Addition

Explore: Transforming Sets of Data by Using Multiplication

9-7

Summarizing Categorical Data Explore: Categorical Data

9-8 Normal Distributions

Module 10 Tools of Geometry

10-1

The Geometric System Explore: Using a Game to Explore Axiomatic Systems

10-2

Points, Lines, and Planes Explore: Intersections of Three Planes

10-3

Line Segments Explore: Using Tools to Determine Betweenness of Points

10-4

Distance Explore: Using the Pythagorean Theorem to Find Distances

10-5

Locating Points on a Number Line Explore: Locating Points on a Number Line with Fractional Distance

10-6

Locating Points on a Coordinate Plane Explore: Applying Fractional Distance

10-7

Midpoints and Bisectors Explore: Midpoints

Module 11 Angles and Geometric Figures

11-1

Angles and Congruence Explore: Angles Formed by Intersecting Lines

Angle Relationships

11-2 Explore: Complementary and Supplementary Angles Explore: Interpreting Diagrams

11-3

Two-Dimensional Figures Explore: Modeling Objects by Using Two-Dimensional Figures

11-4

Transformations in the Plane Explore: Introducing Transformations

11-5

Three-Dimensional Figures Explore: Measuring Real-World Objects

11-6

Two-Dimensional Representations of Three-Dimensional Figures Explore: Representing Three-Dimensional Figures

11-7

Precision and Accuracy Explore: Precision and Accuracy in Basketball

11-8

Representing Measurements Explore: Significant Figures

Integrated I Integrated II Integrated III

INTEGRATED I CONTINUED

Module 12 Logical Arguments and Line Relationships

12-1

Conjectures and Counterexamples Explore: Using Inductive Reasoning to Make Conjectures

12-2

Statements, Conditionals, and Biconditionals Explore: Truth Values

12-3

Deductive Reasoning Explore: Applying Laws of Deductive Reasoning by Using Venn Diagrams

12-4

Writing Proofs Explore: Algebraic Proof

12-5

Proving Segment Relationships Explore: Segment Relationships

12-6

Proving Angle Relationships Explore: Angle Relationships

12-7

Parallel Lines and Transversals Explore: Relationships Between Angles and Parallel Lines

12-8

Slope and Equations of Lines Explore: Equations of Lines

12-9

Proving Lines Parallel Explore: Intersecting Lines

12-10

Perpendiculars and Distance Explore: Distance from a Point to a Line

Module 13 Transformations and Symmetry

13-1

Reflections Explore: Developing the Definition of Reflection

13-2

Translations Explore: Developing the Definition of Translation

13-3

Rotations Explore: Developing the Definition of Rotation

13-4

Compositions of Transformations Explore: Reflections in Two Lines

13-5

Tessellations Explore: Creating Tessellations

13-6

Symmetry Explore: Symmetry in Figures

Module 14 Triangles and Congruence

14-1

Angles of Triangles Explore: Triangle Angle Sums

14-2

Congruent Triangles Explore: Relationships in Congruent Triangles

14-3

Proving Triangles Congruent: SSS, SAS Explore: Conditions That Prove Triangles Congruent

14-4 Proving Triangles Congruent: ASA, AAS

14-5

Proving Right Triangles Congruent Explore: Congruence Theorems and Right Triangles

Isosceles and Equilateral Triangles

14-6 Explore: Properties of Equilateral, Isosceles, and Scalene Triangles

Explore: Isosceles and Equilateral Triangles

14-7

Triangles and Coordinate Proofs Explore: Triangles and Coordinate Proofs

Integrated I Integrated II Integrated III

Reveal MathTM Integrated I-III Table of Contents

INTEGRATED II

Module 1 Relationships in Triangles

1-1

Perpendicular Bisectors Explore: Relationships Formed by Perpendicular Bisectors

1-2

Angle Bisectors Explore: Relationships Formed by Angle Bisectors

1-3

Medians and Altitudes of Triangles Explore: Centroid of a Triangle

1-4

Inequalities in One Triangle Explore: Angle and Angle-Side Inequalities in Triangles

1-5

Indirect Proof Explore: Applying Indirect Reasoning

1-6

The Triangle Inequality Explore: Relationships Among Triangle Side Lengths

1-7

Inequalities in Two Triangles Explore: Analyzing Inequalities in Two Triangles

Module 2 Quadrilaterals

2-1

Angles of Polygons Explore: Angles of Polygons

2-2

Parallelograms Explore: Properties of Parallelograms

2-3

Tests for Parallelograms Explore: Constructing Parallelograms

2-4

Rectangles Explore: Properties of Rectangles

2-5

Rhombi and Squares Explore: Properties of Rhombi and Squares

2-6

Trapezoids and Kites Explore: Properties of Trapezoids and Kites

Module 3 Similarity

3-1

Dilations Explore: Verifying the Properties of Dilations

3-2

Similar Polygons Explore: Similarity in Polygons

Similar Triangles: AA Similarity 3-3 Explore: Similarity Transformations and Triangles

Explore: Conditions that Prove Triangles Similar

3-4

Similar Triangles: SSS and SAS Similarity Explore: Similarity Criteria: SSS, SAS, and SSA

3-5

Triangle Proportionality Explore: Proportions in Triangles

3-6

Parts of Similar Triangles Explore: Special Segments in Triangles

Module 4 Right Triangles and Trigonometry

4-1

Geometric Means Explore: Relationships in Right Triangles

4-2

Pythagorean Theorem and Its Converse Explore: Proving the Pythagorean Theorem

4-3

Coordinates in Space Explore: Proving the Distance Formula in Space

4-4

Special Right Triangles Explore: Properties of Special Right Triangles

Trigonometry 4-5 Explore: Sine and Cosine of Complementary Angles

Explore: Trigonometry and Similarity

Applying Trigonometry 4-6 Explore: Angles of Elevation and Depression

Explore: Measuring Angles of Elevation

4-7

The Law of Sines Explore: Trigonometric Ratios in Nonright Triangles

4-8

The Law of Cosines Explore: Trigonometric Relationships in Nonright Triangles

Module 5 Circles

5-1

Circles and Circumference Explore: Discovering the Formula for Circumference

5-2

Measuring Angles and Arcs Explore: Relationships Between Arc Lengths and Radii

5-3

Arcs and Chords Explore: Chords in Circles

5-4

Inscribed Angles Explore: Angles Inscribed in Circles

5-5

Tangents Explore: Tangents and Circumscribed Angles

5-6

Tangents, Secants, and Angle Measures Explore: Relationships Between Tangents and Secants

Equations of Circles

5-7 Explore: Deriving Equations of Circles

Explore: Exploring Equations of Circles

5-8

Equations of Parabolas Explore: Focus and Directrix of a Parabola

5-9 Equations of Ellipses and Hyperbolas

Integrated I Integrated II Integrated III

INTEGRATED II continued

Module 6 Measurement

6-1

Areas of Quadrilaterals Explore: Deriving the Area Formulas

6-2

Areas of Regular Polygons Explore: Regular Polygons

6-3

Areas of Circles and Sectors Explore: Areas of Circles

6-4

Surface Area Explore: Cone Patterns

6-5

Cross Sections and Solids of Revolution Explore: Cross Sections

6-6

Volumes of Prisms and Pyramids Explore: Volumes of Square Pyramids

6-7

Volumes of Cylinders, Cones, and Spheres Explore: Volumes of Spheres

6-8

Applying Similarity to Solid Figures Explore: Similar Solids

6-9

Density Explore: Strategies Based on Density

Module 7 Probability

7-1 Sample Spaces

7-2

Probability and Counting Explore: Venn Diagrams

Geometric Probability

7-3 Explore: Probability Using Lengths of Segments

Explore: Probability and Decision Making

Expand 7-3 Making Fair Decisions

7-4

Probability with Permutations and Combinations Explore: Permutations and Combinations

7-5

Probability and the Multiplication Rule Explore: Independent and Dependent Events

7-6

Probability and the Addition Rule Explore: Mutually Exclusive Events

7-7

Conditional Probability Explore: Conditional Probability

7-8

Two-Way Frequency Tables Explore: Two-Way Frequency Tables

Module 8 Relations and Functions

Functions and Continuity 8-1 Explore: Analyzing Functions Graphically

Explore: Defining and Analyzing Variables

8-2

Linearity, Intercepts, and Symmetry Explore: Symmetry and Functions

8-3

Extrema and End Behavior Explore: End Behavior of Linear and Quadratic Functions

8-4

Sketching Graphs and Comparing Functions Explore: Using Technology to Examine Key Features of Graphs

8-5

Graphing Linear Functions and Inequalities Explore: Shading Graphs of Linear Inequalities

8-6

Special Functions Explore: Using Tables to Graph Piecewise Functions

8-7

Transformations of Functions Explore: Using Technology to Transform Functions

Module 9 Linear Equations, Inequaltities, and Systems

9-1

Solving Linear Equations and Inequalities Explore: Comparing Linear Equations and Inequalities

9-2 Solving Absolute Value Equations and Inequalities

9-3

Equations of Linear Functions Explore: Arithmetic Sequences

9-4

Solving Systems of Equations Graphically Explore: Solutions of a System of Equations

9-5 Solving Systems of Equations Algebraically

9-6

Solving Systems of Inequalities Explore: Solutions of Systems of Inequalities

9-7

Optimization with Linear Programming Explore: Using Technology with Linear Programming

9-8

Systems of Equations in Three Variables Explore: Systems of Equations Represented as Lines and Planes

9-9 Solving Absolute Value Equations and Inequalities by Graphing

Module 10 Exponents and Roots

10-1

Multiplication Properties of Exponents Explore: Products of Powers

10-2

Division Properties of Exponents Explore: Quotients of Powers

10-3

Negative Exponents Explore: Simplifying Expressions with Negative Exponents

10-4

Rational Exponents Explore: Expressions with Rational Exponents

10-5

Simplifying Radical Expressions Explore: Square Roots and Negative Numbers

10-6 Operations with Radical Expressions

Expand 10-6 Operations with Rational Numbers

Expand 10-6 Sums and Products of Rational and Irrational Numbers

10-7

Exponential Equations Explore: Solving Exponential Equations

Integrated I Integrated II Integrated III

INTEGRATED II continued

Module 11 Polynomials

11-1

Adding and Subtracting Polynomials Explore: Using Algebra Tiles to Add and Subtract Polynomials

11-2

Multiplying a Polynomial by a Monomial Explore: Using Algebra Tiles to Find Products of Polynomials and Monomials

11-3

Multiplying Polynomials Explore: Using Algebra Tiles to Find Products of Two Binomials

Special Products

11-4

Explore: Using Algebra Tiles to Find the Squares of Sums Explore: Using Algebra Tiles to Find the Squares of Differences

Explore: Using Algebra Tiles to Find Products of Sums and Differences

11-5

Using the Distributive Property Explore: Using Algebra Tiles to Factor Polynomials

Expand 11-5 Proving the Elimination Method

11-6

Factoring Quadratic Trinomials Explore: Using Algebra Tiles to Factor Trinomials

11-7

Factoring Special Products Explore: Using Algebra Tiles to Factor Differences of Squares

Module 12 Quadratic Functions

12-1

Graphing Quadratic Functions Explore: Graphing Parabolas

12-2

Transformations of Quadratic Functions Explore: Transforming Quadratic Functions

12-3

Solving Quadratic Equations by Graphing Explore: Roots and Zeros of Quadratics

12-4

Solving Quadratic Equations by Factoring Explore: Using Factors to Solve Quadratic Equations

12-5

Solving Quadratic Equations by Completing the Square Explore: Using Algebra Tiles to Complete the Square

Solving Quadratic Equations by Using the Quadratic Formula

12-6 Explore: Deriving the Quadratic Formula Algebraically

Explore: Deriving the Quadratic Formula Visually

12-7

Solving Systems of Linear and Quadratic Equations Explore: Using Algebra Tiles to Solve Systems of Linear and Quadratic Equations

12-8

Modeling and Curve Fitting Explore: Using Differences and Ratios to Model Data

12-9

Combining Functions Explore: Using Graphs to Combine Functions

12-10 Inverses of Quadratic Functions

Module 13 Trigonometric Identities and Equations

Trigonometric Identities 13-1 Explore: Pythagorean Identity

Explore: Negative-Angle Identity

13-2 Verifying Trigonometric Identities

13-3 Sum and Difference Identities

13-4

Double-Angle and Half-Angle Identities Explore: Proving the Double-Angle Identity for Cosine

13-5 Solving Trigonometric Equations

Integrated I Integrated II Integrated III

Reveal MathTM Integrated I-III Table of Contents

INTEGRATED III

Module 1 Quadratic Functions

1-1

Graphing Quadratic Functions Explore: Transforming Quadratic Functions

1-2

Solving Quadratic Equations by Graphing Explore: Roots of Quadratic Equations

1-3

Complex Numbers Explore: Factoring Prime Polynomials

1-4

Solving Quadratic Equations by Factoring Explore: Finding the Solutions of Quadratic Equations by Factoring

1-5

Solving Quadratic Equations by Completing the Square Explore: Using Algebra Tiles to Complete the Square

1-6

Using the Quadratic Formula and the Discriminant Explore: The Discriminant

1-7

Quadratic Inequalities Explore: Graphing Quadratic Inequalities

1-8

Solving Linear-Nonlinear Systems Explore: Linear-Quadratic Systems

Module 2 Polynomials and Polynomial Functions

Polynomial Functions 2-1 Explore: Power Functions

Explore: Polynomial Functions

2-2 Analyzing Graphs of Polynomial Functions

2-3

Operations with Polynomials Explore: Multiplying Polynomials

2-4

Dividing Polynomials Explore: Using Algebra Tiles to Divide Polynomials

2-5

Powers of Binomials Explore: Expanding Binomials

Module 3 Polynomial Equations

3-1

Solving Polynomial Equations by Graphing Explore: Solutions of Polynomial Equations

3-2 Solving Polynomial Equations Algebraically

3-3

Proving Polynomial Identities Explore: Polynomial Identities

3-4

The Remainder and Factor Theorems Explore: Remainders

3-5

Roots and Zeros Explore: Roots of Quadratic Polynomials

Module 4 Inverses and Radical Functions

4-1

Operations on Functions Explore: Adding Functions

4-2

Inverse Relations and Functions Explore: Inverse Functions

4-3

nth Roots and Rational Exponents Explore: Inverses of Power Functions

4-4

Graphing Radical Functions Explore: Using Technology to Analyze Square Root Functions

4-5 Operations with Radical Expressions

4-6

Solving Radical Equations Explore: Solutions of Radical Equations

Module 5 Exponential Functions

5-1

Graphing Exponential Functions Explore: Using Technology to Analyze Graphs of Exponential Functions

5-2

Solving Exponential Equations and Inequalities Explore: Solving Exponential Equations

5-3

Special Exponential Functions Explore: Finding the Value of e

5-4

Geometric Sequences and Series Explore: Explicit and Recursive Formulas

Expand 5-4 Sum of a Finite Geometric Series

5-5

Modeling Data Explore: Modeling Exponential Decay

Integrated I Integrated II Integrated III

INTEGRATED III continued

Module 6 Logarithmic Functions

6-1

Logarithms and Logarithmic Functions Explore: Transforming Logarithmic Functions

6-2

Properties of Logarithms Explore: Logarithmic Expressions and Equations

6-3 Common Logarithms

6-4

Natural Logarithms Explore: Using a Scatter Plot to Analyze Data

6-5 Using Exponential and Logarithmic Functions

Module 7 Rational Functions

7-1

Multiplying and Dividing Rational Expressions Explore: Simplifying Complex Fractions

7-2

Adding and Subtracting Rational Expressions Explore: Closure of Rational Expressions

7-3

Graphing Reciprocal Functions Explore: Transforming Reciprocal Functions

7-4

Graphing Rational Functions Explore: Analyzing Rational Functions

7-5

Variation Explore: Variation

7-6

Solving Rational Equations and Inequalities Explore: Solving Rational Equations

Module 8 Inferential Statistics

8-1 Random Sampling

Using Statistical Experiments 8-2 Explore: Simulations and Experiments

Explore: Fair Decisions

8-3 Analyzing Population Data

8-4

Normal Distributions Explore: Probability Distributions

8-5 Estimating Population Parameters

Module 9 Trigonometric Functions

9-1

Angles and Angle Measure Explore: Arc Length

9-2 Trigonometric Functions of General Angles

9-3

Circular and Periodic Functions Explore: Trigonometric Functions of Special Angles

9-4 Graphing Sine and Cosine Functions

9-5 Graphing Other Trigonometric Functions

9-6

Translations of Trigonometric Graphs Explore: Analyzing Graphs of Trigonometric Functions by Using Technology

9-7 Inverse Trigonometric Functions

MA19M17183 Integrated I Integrated II Integrated III

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