The Bridge Between Arithmetic and Algebra
Edition: 9
Copyright: 2017
Edition: 9
Copyright: 2017
Pages: 506
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$133.12
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$126.78
Instead of overwhelming students with many new abstract concepts, The Bridge Between Arithmetic and Algebra is limited to six topics (six chapters) which serve as pillars on which an introductory algebra class is structured. These topics are equations, inequalities, translations, word puzzles that use charts, factoring, and graphing.
Initially, concrete arithmetic methods are used to help students make connections to abstract concepts within the selected topics. After connections are made, alternative algebraic strategies are introduced.
Now available in print and eBook formats, The Bridge Between Arithmetic and Algebra:
- Promotes acceleration! After using this book, increasing numbers of students are able to skip Introductory Algebra, immediately enroll in Intermediate Algebra, and earn "A's" and "B's".
- Is proven! A five-year study of 9418 college algebra students revealed that 75% of the students who used this publication in their prealgebra course went on to be successful in introductory algebra. This is 20% higher than for the other algebra students.
- Reduces math anxiety and promotes retention! The carefully chosen topics and the consistency of methods used give students the feeling that each day is a review with a little "twist". This “refuge of familiarity” reduces the anxiety often resulting from a common attitude that algebra is an endless bombardment of unrelated, useless ideas. Familiarity and consistency also promote retention.
- Integrates problem-solving skills! Drawing pictures, making charts, and making lists are emphasized throughout the book.
- Teaches math like a language! It emphasizes the vocabulary, punctuation, and syntax of math. It uses a step-by-step approach to word puzzles that appeal to verbal learners and students whose first language is NOT English.
- Offers encouragement and hope for students who have struggled! Students will see a variety of short, motivational biographies in which struggles became successes because determined people did NOT give up. Short encouraging quotes (often humorous) appear throughout the answer keys.
- Is student friendly! Common misunderstandings are explained and mnemonics are used. Explanations and analogies help students relate math concepts to common life experiences.
- Is flexible! A three-hole binder format is utilized so that students can easily remove and place practice pages next to the appropriate explanation in the text.
- Is instructor friendly! Ancillary materials are available for adopting instructors.
PART I, The Text: Explanations, and Examples
Chapter 1. Signed Numbers and Equations
Something to Think About: The Human Brain
What Is Algebra?
Basic Vocabulary
The Number Line
The Horizontal Number Line and Signed Numbers
Symbols Used for Multiplication
Using the Order of Operations
Making Addition and Subtraction of Integers Easier
Additive Inverses
Using the Multiplicative Identity of “1”
Identifying Clusters of Multiplication
Nested (or Embedded) Grouping Symbols
Substitution
Getting Ready to Solve Equations
Punctuation Symbols in Mathematics
Misunderstandings in Mathematics
Using Inverses to Solve Equations
Phrases, Sentences, and Verbs in Algebra
Solving Algebraic Equations That Contain Fractions
Chapter 1 Review
Chapter 2. Multiple Step Equations and Inequalities
Someone to Think About: Maxcy Filer
Solving Multiple Step Equations
Exponents and Combining Like Terms
Solving Equations That Contain Like Terms
The Distributive Property of Multiplication
Identity and No Solution Puzzles
Embedded Grouping Symbols
Graphing Equalities and Inequalities
Solving and Graphing Inequalities
Chapter 2 Review
Someone to Think About: Tom Monaghan
Chapter 3. Translations, Pictures, and Charts
Someone to Think About: Helen Keller
Introduction to Word Puzzles
From Arithmetic to Algebra
Steps to Use When Translating
The Syntax of Mathematics
Translating and Solving Multiple Operation Word Puzzles
Translating Multiple Operation Word Puzzles
Consecutive Integers
Pythagorus and Right Angles
Puzzles with One Known and One Unknown
Using One Variable to Find Multiple Unknowns
Formulas, Multiple Unknowns, and One Variable
Working with Conditional Statements
Chapter 3 Review
Chapter 4. Charts and Rates
Someone to Think About: Jaime Escalante
Using a Chart to Organize Information
Using a Chart to Organize a Coin Mixture Puzzle
Solution Puzzles
Understanding and Solving Proportions
Using a Chart to Solve a Distance Puzzle
Chapter 4 Review
Someone to Think About: Jackie Nink Pflug
Chapter 5. Polynomials, Lists, Factoring, and Quadratic Equations
Someone to Think About: Thomas Edison
Squares and Square Roots
Exponents and Powers
Polynomials
Vertical Method of Multiplying Polynomials
Horizontal Method of Multiplying Two Binomials
Factoring and the Distributive Property
Factoring Concepts and Methods:
- Extracting the Greatest Common Factor
- The Sum and Difference of Two Squares
- Perfect Square Trinomials
- Making Organized Lists to Sort Information
- Factoring Trinomials That Have “1” as the Leading Coefficient
- “Creating” Common Factors
- Factoring by Grouping
- Master Product
- Using More Than One Factoring Method
- Summary of Basic Factoring Methods
An Introduction to Basic Algebraic Fractions
Zero Factor Property
Types of Polynomial Equations
Missing Numbers in Quadratic Equations
The Quadratic Formula
When a Solution CanNOT Be Determined
Chapter 5 Review
Someone to Think About: Mary McCloud Bethune
Walt Disney
Chapter 6. Using Formulas and Graphing Lines
Someone to Think About: Albert Einstein
The Cartesian Coordinate System
The Graph
Determining Slope:
- Using Inspection
- Zero Slope and No Slope
- The Slope Formula
X and Y Intercepts
The Uniqueness of a Line
Different Ways of Writing the Same Slope
Equations of Lines
- Slope Intercept Form Equation of a Line
- Graphing a Line When the Slope Intercept Form of Its Equation is Given
- Solutions to Equations of Lines
- Writing the Slope-Intercept Form of the Equation of a Line When a Graph Is Given
- Standard Equation of a Line
- Converting Equations to Slope-Intercept Form of an Equation of a Line
- Converting Equations to Standard Form of an Equation of a Line
- What to Do When Information Seems to Be Missing
- A System of Equations
Chapter 6 Review
Index
References
PART II, Practice Puzzles:
Practice Puzzles
Table of Contents for Quizzes, Reviews and Check Tests
Chapter 1: Signed Numbers and Equations
Chapter 2: Solving and Graphing Equations and Inequalities
Chapter 3: Translations, Pictures, and Charts
Chapter 4: Charts and Rates
Chapter 5: Polynomials, Lists, Factoring, and Quadratic Equations
Chapter 6: Using Formulas and Graphing Lines
PART III, ANSWERS to Puzzles:
Many People, Many Obstacles, Many Successes
Someone to Think About: Joseph Horswill
Rosemarie Bezerra-Nader was raised on a dairy farm in rural Lemoore, California. Although neither parent ever attended high school, James and Mary Bezerra placed a high value on education as a means of improving one’s quality of life; they instilled a very strong ambition and work ethic in each of their four children. Rosemarie is married to Fareed Nader, a Geomatics engineering Professor Emeritus at California State University, Fresno (CSUF). They support and encourage each other’s passion for teaching.
Rosemarie has had a wide variety of teaching experiences:
5 summers
as a K-3 teacher in dairy-farming communities
5 years
as a 4th and 5th grade teacher in a Central California community where children were members of
multigenerational dairy-farming families, migrant families, and military families.
12 years
as a 7th-9th grade teacher in large urban and suburban communities where she taught math, English, critical
thinking, and peer counseling.
25 years
as an adjunct instructor at California State University, Fresno where she taught professional development
and test prep classes for teachers in math, critical thinking, and English. At CSUF, she also taught bulletin
board classes for teachers and beginning guitar.
1990 - the present
as a developmental math instructor at Fresno City College in Fresno, California where she also taught
reading, critical thinking, and decision-making classes.
In a fast-paced, ever-changing world, Rosemarie is committed to teaching people to “learn how to learn.” Math is the subject she enjoys using to do this. Rosemarie enjoys the challenge and rewards in teaching people who doubt their abilities. Developmental math is the subject she enjoys teaching most.
Throughout her varied teaching experience, Rosemarie has integrated the development of critical thinking skills and problem-solving strategies. She strongly feels these are the keys that unlock the doors to learning retention, and transfer across the curriculum for all age groups.
Rosemarie traveled widely within the United States as a consultant in how to integrate critical thinking into an existing curriculum.
She has written three developmental books:
Arithmetic For Success
The Bridge Between Arithmetic and Algebra
Mastering Whole Numbers, the Express Way
In her “spare time”, Rosemarie enjoys singing, playing piano, ballroom dancing, sewing, and spending time playing with her two canine “kids.”
Winston Churchill is her favorite character in history. Rosemarie ends every motivational biography with a message to students: This message is Churchill's famous quote to:
“Never, never, never give up!”
“A five-year study of 9,418 students indicated that those who successfully completed the pre algebra class for which The Bridge was written averaged a 75% passing rate in Introductory Algebra. This is a 20% higher success rate than the other algebra students in the study.”
Director of Institutional Research,
Assessment, and Planning
Fresno City College
“The carefully chosen topics, the clarity of the presentation, and the consistency of methods used in The Bridge have elevated the confidence levels, success rates, and attitudes of students when they go on to take Introductory Algebra.”
“The style of writing in The Bridge Between Arithmetic and Algebra is very easy to understand. Each topic is specific and clear. The approach is consistent and spirals into the depth of the topic. Students feel like they are reading a book that is ‘talking’ to them instead of a dry text book.”
“The book’s straightforward, no-distraction presentation enables students to focus on a single concept one page at a time. The consistency of the format and methodology cause mastered concepts to link to new steps, providing reinforcement and relevance. Because the practice work is well-coordinated with the narrative, anxiety is reduced and student success is increased.”
“Because of the thoroughness and simplicity of The Bridge, I spend less time lecturing and more time helping students individually.”
“The Bridge Between Arithmetic and Algebra is skillfully sequenced so that students quickly feel every day is a review with a “little twist.” With two entire chapters dedicated to word problems, students quickly realize there is no escape from learning how to solve them. Arrows and dialogue boxes guide students in the development of critical thinking skills and problem-solving techniques. Students quickly gain confidence in their ability to transfer, integrate, and retain skills and concepts.”
“I am an immigrant who always had difficulty with math. The Bridge Between Arithmetic and Algebra was an eye-opener that helped me look at math and learn it like another language. When I became a tutor, I emphasized this to struggling students. I also shared my discovery that the step-by-step methods used in the book laid a solid foundation that made higher math classes easier for me than classmates who did not know them. The methods in the book helped the rest of math unfold like a domino effect.”
Find Student Testimonials Featured in JOURNAL OF THE FACULTY ASSOCIATION OF CALIFORNIA COMMUNITY COLLEGES | FALL 2019
Instead of overwhelming students with many new abstract concepts, The Bridge Between Arithmetic and Algebra is limited to six topics (six chapters) which serve as pillars on which an introductory algebra class is structured. These topics are equations, inequalities, translations, word puzzles that use charts, factoring, and graphing.
Initially, concrete arithmetic methods are used to help students make connections to abstract concepts within the selected topics. After connections are made, alternative algebraic strategies are introduced.
Now available in print and eBook formats, The Bridge Between Arithmetic and Algebra:
- Promotes acceleration! After using this book, increasing numbers of students are able to skip Introductory Algebra, immediately enroll in Intermediate Algebra, and earn "A's" and "B's".
- Is proven! A five-year study of 9418 college algebra students revealed that 75% of the students who used this publication in their prealgebra course went on to be successful in introductory algebra. This is 20% higher than for the other algebra students.
- Reduces math anxiety and promotes retention! The carefully chosen topics and the consistency of methods used give students the feeling that each day is a review with a little "twist". This “refuge of familiarity” reduces the anxiety often resulting from a common attitude that algebra is an endless bombardment of unrelated, useless ideas. Familiarity and consistency also promote retention.
- Integrates problem-solving skills! Drawing pictures, making charts, and making lists are emphasized throughout the book.
- Teaches math like a language! It emphasizes the vocabulary, punctuation, and syntax of math. It uses a step-by-step approach to word puzzles that appeal to verbal learners and students whose first language is NOT English.
- Offers encouragement and hope for students who have struggled! Students will see a variety of short, motivational biographies in which struggles became successes because determined people did NOT give up. Short encouraging quotes (often humorous) appear throughout the answer keys.
- Is student friendly! Common misunderstandings are explained and mnemonics are used. Explanations and analogies help students relate math concepts to common life experiences.
- Is flexible! A three-hole binder format is utilized so that students can easily remove and place practice pages next to the appropriate explanation in the text.
- Is instructor friendly! Ancillary materials are available for adopting instructors.
PART I, The Text: Explanations, and Examples
Chapter 1. Signed Numbers and Equations
Something to Think About: The Human Brain
What Is Algebra?
Basic Vocabulary
The Number Line
The Horizontal Number Line and Signed Numbers
Symbols Used for Multiplication
Using the Order of Operations
Making Addition and Subtraction of Integers Easier
Additive Inverses
Using the Multiplicative Identity of “1”
Identifying Clusters of Multiplication
Nested (or Embedded) Grouping Symbols
Substitution
Getting Ready to Solve Equations
Punctuation Symbols in Mathematics
Misunderstandings in Mathematics
Using Inverses to Solve Equations
Phrases, Sentences, and Verbs in Algebra
Solving Algebraic Equations That Contain Fractions
Chapter 1 Review
Chapter 2. Multiple Step Equations and Inequalities
Someone to Think About: Maxcy Filer
Solving Multiple Step Equations
Exponents and Combining Like Terms
Solving Equations That Contain Like Terms
The Distributive Property of Multiplication
Identity and No Solution Puzzles
Embedded Grouping Symbols
Graphing Equalities and Inequalities
Solving and Graphing Inequalities
Chapter 2 Review
Someone to Think About: Tom Monaghan
Chapter 3. Translations, Pictures, and Charts
Someone to Think About: Helen Keller
Introduction to Word Puzzles
From Arithmetic to Algebra
Steps to Use When Translating
The Syntax of Mathematics
Translating and Solving Multiple Operation Word Puzzles
Translating Multiple Operation Word Puzzles
Consecutive Integers
Pythagorus and Right Angles
Puzzles with One Known and One Unknown
Using One Variable to Find Multiple Unknowns
Formulas, Multiple Unknowns, and One Variable
Working with Conditional Statements
Chapter 3 Review
Chapter 4. Charts and Rates
Someone to Think About: Jaime Escalante
Using a Chart to Organize Information
Using a Chart to Organize a Coin Mixture Puzzle
Solution Puzzles
Understanding and Solving Proportions
Using a Chart to Solve a Distance Puzzle
Chapter 4 Review
Someone to Think About: Jackie Nink Pflug
Chapter 5. Polynomials, Lists, Factoring, and Quadratic Equations
Someone to Think About: Thomas Edison
Squares and Square Roots
Exponents and Powers
Polynomials
Vertical Method of Multiplying Polynomials
Horizontal Method of Multiplying Two Binomials
Factoring and the Distributive Property
Factoring Concepts and Methods:
- Extracting the Greatest Common Factor
- The Sum and Difference of Two Squares
- Perfect Square Trinomials
- Making Organized Lists to Sort Information
- Factoring Trinomials That Have “1” as the Leading Coefficient
- “Creating” Common Factors
- Factoring by Grouping
- Master Product
- Using More Than One Factoring Method
- Summary of Basic Factoring Methods
An Introduction to Basic Algebraic Fractions
Zero Factor Property
Types of Polynomial Equations
Missing Numbers in Quadratic Equations
The Quadratic Formula
When a Solution CanNOT Be Determined
Chapter 5 Review
Someone to Think About: Mary McCloud Bethune
Walt Disney
Chapter 6. Using Formulas and Graphing Lines
Someone to Think About: Albert Einstein
The Cartesian Coordinate System
The Graph
Determining Slope:
- Using Inspection
- Zero Slope and No Slope
- The Slope Formula
X and Y Intercepts
The Uniqueness of a Line
Different Ways of Writing the Same Slope
Equations of Lines
- Slope Intercept Form Equation of a Line
- Graphing a Line When the Slope Intercept Form of Its Equation is Given
- Solutions to Equations of Lines
- Writing the Slope-Intercept Form of the Equation of a Line When a Graph Is Given
- Standard Equation of a Line
- Converting Equations to Slope-Intercept Form of an Equation of a Line
- Converting Equations to Standard Form of an Equation of a Line
- What to Do When Information Seems to Be Missing
- A System of Equations
Chapter 6 Review
Index
References
PART II, Practice Puzzles:
Practice Puzzles
Table of Contents for Quizzes, Reviews and Check Tests
Chapter 1: Signed Numbers and Equations
Chapter 2: Solving and Graphing Equations and Inequalities
Chapter 3: Translations, Pictures, and Charts
Chapter 4: Charts and Rates
Chapter 5: Polynomials, Lists, Factoring, and Quadratic Equations
Chapter 6: Using Formulas and Graphing Lines
PART III, ANSWERS to Puzzles:
Many People, Many Obstacles, Many Successes
Someone to Think About: Joseph Horswill
Rosemarie Bezerra-Nader was raised on a dairy farm in rural Lemoore, California. Although neither parent ever attended high school, James and Mary Bezerra placed a high value on education as a means of improving one’s quality of life; they instilled a very strong ambition and work ethic in each of their four children. Rosemarie is married to Fareed Nader, a Geomatics engineering Professor Emeritus at California State University, Fresno (CSUF). They support and encourage each other’s passion for teaching.
Rosemarie has had a wide variety of teaching experiences:
5 summers
as a K-3 teacher in dairy-farming communities
5 years
as a 4th and 5th grade teacher in a Central California community where children were members of
multigenerational dairy-farming families, migrant families, and military families.
12 years
as a 7th-9th grade teacher in large urban and suburban communities where she taught math, English, critical
thinking, and peer counseling.
25 years
as an adjunct instructor at California State University, Fresno where she taught professional development
and test prep classes for teachers in math, critical thinking, and English. At CSUF, she also taught bulletin
board classes for teachers and beginning guitar.
1990 - the present
as a developmental math instructor at Fresno City College in Fresno, California where she also taught
reading, critical thinking, and decision-making classes.
In a fast-paced, ever-changing world, Rosemarie is committed to teaching people to “learn how to learn.” Math is the subject she enjoys using to do this. Rosemarie enjoys the challenge and rewards in teaching people who doubt their abilities. Developmental math is the subject she enjoys teaching most.
Throughout her varied teaching experience, Rosemarie has integrated the development of critical thinking skills and problem-solving strategies. She strongly feels these are the keys that unlock the doors to learning retention, and transfer across the curriculum for all age groups.
Rosemarie traveled widely within the United States as a consultant in how to integrate critical thinking into an existing curriculum.
She has written three developmental books:
Arithmetic For Success
The Bridge Between Arithmetic and Algebra
Mastering Whole Numbers, the Express Way
In her “spare time”, Rosemarie enjoys singing, playing piano, ballroom dancing, sewing, and spending time playing with her two canine “kids.”
Winston Churchill is her favorite character in history. Rosemarie ends every motivational biography with a message to students: This message is Churchill's famous quote to:
“Never, never, never give up!”
“A five-year study of 9,418 students indicated that those who successfully completed the pre algebra class for which The Bridge was written averaged a 75% passing rate in Introductory Algebra. This is a 20% higher success rate than the other algebra students in the study.”
Director of Institutional Research,
Assessment, and Planning
Fresno City College
“The carefully chosen topics, the clarity of the presentation, and the consistency of methods used in The Bridge have elevated the confidence levels, success rates, and attitudes of students when they go on to take Introductory Algebra.”
“The style of writing in The Bridge Between Arithmetic and Algebra is very easy to understand. Each topic is specific and clear. The approach is consistent and spirals into the depth of the topic. Students feel like they are reading a book that is ‘talking’ to them instead of a dry text book.”
“The book’s straightforward, no-distraction presentation enables students to focus on a single concept one page at a time. The consistency of the format and methodology cause mastered concepts to link to new steps, providing reinforcement and relevance. Because the practice work is well-coordinated with the narrative, anxiety is reduced and student success is increased.”
“Because of the thoroughness and simplicity of The Bridge, I spend less time lecturing and more time helping students individually.”
“The Bridge Between Arithmetic and Algebra is skillfully sequenced so that students quickly feel every day is a review with a “little twist.” With two entire chapters dedicated to word problems, students quickly realize there is no escape from learning how to solve them. Arrows and dialogue boxes guide students in the development of critical thinking skills and problem-solving techniques. Students quickly gain confidence in their ability to transfer, integrate, and retain skills and concepts.”
“I am an immigrant who always had difficulty with math. The Bridge Between Arithmetic and Algebra was an eye-opener that helped me look at math and learn it like another language. When I became a tutor, I emphasized this to struggling students. I also shared my discovery that the step-by-step methods used in the book laid a solid foundation that made higher math classes easier for me than classmates who did not know them. The methods in the book helped the rest of math unfold like a domino effect.”
Find Student Testimonials Featured in JOURNAL OF THE FACULTY ASSOCIATION OF CALIFORNIA COMMUNITY COLLEGES | FALL 2019