# Teaching Textbooks

Teaching Textbooks Algebra 1

#### operations with rational numbers (addition, subtraction, multiplication, division, and order of operations)

Chapter 3: Order of Operations

Lesson 20—Order of Operations

Lesson 21—Equations Too

Lesson 22—Help from the Fraction Bar

Lesson 23—Undoing In Reverse Order

Lesson 24—Undoing with Division

Lesson 25—More than Two Operations

Lesson 26—Using the Associative Property

Lesson 27—More on the Associative Property

Chapter 7: Rational Expressions

Lesson 47—Reducing Fractions

Lesson 48—Factoring into Prime Numbers

Lesson 49—Reducing Rational Expressions

Lesson 50—Rational Expressions and Parentheses

Lesson 51—Distributing in Reverse (Part 1)

Lesson 52—Distributing in Reverse (Part 2)

Lesson 53—Multiplying Rational Expressions

Lesson 54—Dividing Rational Expressions

Lesson 56—Subtracting Rational Expressions

Chapter 8: Solving Rational Equations

Lesson 57—Rational Equations

Lesson 58—More than x in the Bottom

Lesson 59—Ratios and Proportions

Lesson 60—Clearing More than One Fraction

Lesson 61—When the Denominators are Different

Lesson 62—Finding the Lowest Common Denominator

Lesson 63—Rational Equations with Complicated Denominators

#### exponents and exponent laws with whole-number exponents

Chapter 9: Powers and Exponents

Lesson 64—Raising a Number to a Power

Lesson 65—Scientific Notation

Lesson 66—Order of Operations and Powers

Lesson 67—Combining Powers

Lesson 68—Multiplying Powers

Lesson 70—Dividing Powers

Lesson 71—More Scientific Notation

Lesson 72—Harder Rational Expressions

Lesson 73—Combining Harder Rational Expressions

#### operations with polynomials, of degree less than or equal to 2

Chapter 12: Powers, Polynomials, and Radicals

Lesson 87—Relations, Functions, and Equations

Lesson 88—Solving for the Other Variable

Lesson 89—Calculating Profits

Lesson 90—Galileo Analyzes Motion

Lesson 91—Kepler Tracks the Planets

Lesson 92—Equations with Several Variables

Lesson 93—Newton’s Equation of the Universe

Chapter 13: More on Polynomials and Rational Expressions

Lesson 94—Adding and Subtracting with Several Variables

Lesson 95—Multiplying with Several Variables

Lesson 96—Distributing with Several Variables

Lesson 97—Reducing Rational Expressions with Several Variables

Lesson 98—More Reducing with Several Variables

Lesson 99—Finding the Right Pair with Several Variables

Lesson 100—Difference of Two Squares

Lesson 101—Multiplying and Dividing Rational Expressions with Several Variables

Lesson 102—Adding and Subtracting Rational Expressions with Several Variables

Lesson 103—Equation-Solving Strategies

Chapter 15: Rate of Change and Slope

Lesson 109—Change in y over Change in x

Lesson 110—Different Kinds of Slopes

Lesson 111—Horizontal and Vertical Lines

Lesson 112—Slope Intercept Form

Lesson 113—Point-Slope Form

Chapter 16: Systems of Equations

Lesson 114—Solving Systems

Lesson 115—Solving Systems by Subtraction

Lesson 116—More on the Addition and Subtraction Methods

Lesson 117—Solving Systems by Substitution

Lesson 118—Graphing Systems

Lesson 119—Inconsistent and Dependent Systems

#### two-variable linear relations, using graphing, interpolation, and extrapolation

Chapter 14: Graphing Functions and Slope

Lesson 105—Drawing a Picture

Lesson 106—Graphing Linear Equations

Lesson 107—Graphing Higher-Degree Equations

Lesson 108—Graphing Shortcuts

Lesson 118—Graphing Systems

#### multi-step one-variable linear equations

Chapter 4: Combining Like Terms

Lesson 28—Combining x’s

Lesson 29—More on Rates

Lesson 30—Invisible Coefficients

Lesson 31—Getting Bigger/Getting Smaller

Lesson 32—Two Unknowns

Lesson 92—Equations with Several Variables

Chapter 15: Rate of Change and Slope

Lesson 109—Change in y over Change in x

Lesson 110—Different Kinds of Slopes

Lesson 111—Horizontal and Vertical Lines

Lesson 112—Slope Intercept Form

Lesson 113—Point-Slope Form

#### spatial proportional reasoning

Geometry Teaching Textbooks:

Chapter 2: Lines and Angles

Lesson 6—Too Simple to Define

Lesson 7—Some Definitions and Postulates

Lesson 8—Line Segments

Lesson 9—Rays and Angles

Lesson 10—Measuring Angles

Lesson 11—Kinds of Angles

Lesson 12—Midpoints and Bisectors

Lesson 13—Properties of Equality

Chapter 3: Angle Pairs & Perpendicular Lines

Lesson 14—Formal (and Informal) Proofs

Lesson 15—Complementary Angle Pairs

Lesson 16—Supplementary Angle Pairs

Lesson 18—Vertical Angles

Lesson 19—Right Angles and Perpendicular Lines

Lesson 20—Drawing Perpendicular Lines through Points

Lesson 21—Measuring Distances

Chapter 4: Parallel Lines

Lesson 22—Lines That Never Meet

Lesson 23—Parallel Lines and Angles

Lesson 24—More on Parallel Lines

Lesson 25—Measuring the Earth

Lesson 26—Converse Statements

Lesson 27— Proving Lines are Parallel

Chapter 5: Triangles

Lesson 28—A Triangle and its Parts

Lesson 29—Kinds of Triangles

Lesson 31—Exterior Angles

Lesson 32—Congruent Triangles

Lesson 33—Side-Angle-Side

Lesson 34—Angle-Side-Angle and Angle-Angle-Side

Lesson 35—Hypotenuse-Leg

Lesson 36—Side-Side-Side

Lesson 37—Overlapping Triangles

Chapter 6: Using Congruent Triangles

Lesson 38—Proving Corresponding Parts are Congruent

Lesson 39—Proving Bisectors

Lesson 40—Proving Lines Parallel or Perpendicular

Lesson 41—Altitudes and Medians of Triangles

Lesson 42—Base Angles of an Isosceles Triangle

Lesson 43—Proving That a Triangle is Isosceles

#### statistics in society

Chapter 19: Statistics and Probability

Lesson 136—Statistics

Lesson 137—Measures of Dispersion

Lesson 138—More Measures of Dispersion

Lesson 139—Probability

Lesson 140—Probability Shortcuts

#### financial literacy — simple budgets and transactions

Lesson 89—Calculating Profits

## Curricular Competencies

### Reasoning/Analyzing

#### Use logic and patterns to solve puzzles and play games

Supplementation Required

#### Use reasoning and logic to explore, analyze, and apply mathematical ideas

Lesson 9—Moon Vacation

Lesson 10—Extending the Concept of Speed

Lesson 86—Building a Pool Deck

Lesson 90—Galileo Analyzes Motion

Lesson 91—Kepler Tracks the Planets

Lesson 92—Equations with Several Variables

Lesson 93—Newton’s Equation of the Universe

#### Estimate reasonably

Supplementation Required

#### Demonstrate and apply mental math strategies

Supplementation Required

#### Use tools or technology to explore and create patterns and relationships, and test conjectures

Lesson 142—Using a Graphing Calculator

May require the further support of a teacher

Supplementation Required

#### Model mathematics in contextualized experiences

Supplementation Required

### Understanding/Solving

#### Apply multiple strategies to solve problems in both abstract and contextualized situations

Lesson 9—Moon Vacation

Lesson 10—Extending the Concept of Speed

Lesson 86—Building a Pool Deck

Lesson 90—Galileo Analyzes Motion

Lesson 91—Kepler Tracks the Planets

Lesson 92—Equations with Several Variables

Lesson 93—Newton’s Equation of the Universe

#### Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

Lesson 86—Building a Pool Deck

Lesson 90—Galileo Analyzes Motion

Lesson 91—Kepler Tracks the Planets

Lesson 92—Equations with Several Variables

Lesson 93—Newton’s Equation of the Universe

#### Visualize to explore mathematical concepts

Lesson 90—Galileo Analyzes Motion

Lesson 91—Kepler Tracks the Planets

Lesson 92—Equations with Several Variables

Lesson 93—Newton’s Equation of the Universe

May require the further support of a teacher

Supplementation Required

#### Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

Lesson 90—Galileo Analyzes Motion

Lesson 91—Kepler Tracks the Planets

Lesson 92—Equations with Several Variables

Lesson 93—Newton’s Equation of the Universe

### Communicating/Representing

#### Use mathematical vocabulary and language to contribute to mathematical discussions

Lesson 90—Galileo Analyzes Motion

Lesson 91—Kepler Tracks the Planets

Lesson 92—Equations with Several Variables

Lesson 93—Newton’s Equation of the Universe

May require the further support of a teacher

Supplementation Required

#### Explain and justify mathematical ideas and decisions

Supplementation Required

#### Communicate mathematical thinking in many ways

Supplementation Required

#### Represent mathematical ideas in concrete, pictorial, and symbolic forms

Lesson 90—Galileo Analyzes Motion

Lesson 91—Kepler Tracks the Planets

Lesson 92—Equations with Several Variables

Lesson 93—Newton’s Equation of the Universe

### Connecting/Reflecting

#### Reflect on mathematical thinking

Supplementation Required

#### Connect mathematical concepts to each other and to other areas and personal interests

Lesson 86—Building a Pool Deck

Lesson 90—Galileo Analyzes Motion

Lesson 91—Kepler Tracks the Planets

Lesson 92—Equations with Several Variables

Lesson 93—Newton’s Equation of the Universe

#### Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts

Supplementation Required