Foundations of Mathematics
A Quantitative Reasoning Approach
by Robin Hendrix and Barbara Miller
The Foundations of Mathematics workbook focuses on ensuring students' conceptual understanding and ability to apply their mathematical knowledge. Providing conceptual and application exercises for discovery, study skills, group and chapter projects, and much more, it is the perfect complement to Hawkes software mastery approach to problemsolving skills!
Formats: Software, Workbook
Product  13 Digit ISBN 

Courseware + Developmental Mathematics eBook^{*}  9781944894764 
Courseware + Developmental Mathematics eBook^{*} + Workbook  9781941552360 
* Included eBook can only be accessed online through the courseware. 
Video
Watch the video below for more information.
Table of Contents

Chapter 1: Whole Numbers
 Math@Work: Introduction
 Study Skills
 1.1 Reading and Writing Whole Numbers
 1.2 Addition and Subtraction with Whole Numbers
 1.3 Multiplication with Whole Numbers
 1.4 Division with Whole Numbers
 1.5 Rounding and Estimating with Whole Numbers
 1.6 Exponents and Order of Operations
 1.7 Problem Solving with Whole Numbers
 1.8 Tests for Divisibility (2, 3, 4, 5, 6, 9 and 10)
 1.9 Prime Numbers and Prime Factorizations
 Chapter 1 Projects
 Math@Work
 Foundations Skill Check for Chapter 2

Chapter 2: Fractions and Mixed Numbers
 Math@Work: Introduction
 Study Skills
 2.1 Introduction to Fractions and Mixed Numbers
 2.2 Multiplication and Division with Fractions and Mixed Numbers
 2.3 Least Common Multiple (LCM)
 2.4 Addition and Subtraction with Fractions
 2.5 Addition and Subtraction with Mixed Numbers
 2.6 Order of Operations with Fractions and Mixed Numbers
 Chapter 2 Projects
 Math@Work
 Foundations Skill Check for Chapter 3

Chapter 3: Decimal Numbers
 Math@Work: Introduction
 Study Skills
 3.1 Introduction to Decimal Numbers
 3.2 Addition and Subtraction with Decimal Numbers
 3.3 Multiplication with Decimal Numbers
 3.4 Division with Decimal Numbers
 3.5 Decimal Numbers and Fractions
 Chapter 3 Projects
 Math@Work
 Foundations Skill Check for Chapter 4

Chapter 4: Ratios and Proportions, Percent, and Applications
 Math@Work: Introduction
 Study Skills
 4.1 Ratios and Proportions
 4.2 Solving Proportions
 4.3 Decimals Numbers and Percents
 4.4 Fractions and Percents
 4.5 Solving Percent Problems Using Proportions
 4.6 Solving Percent Problems Using Equations
 4.7 Applications: Discount, Sales Tax, Commission, and Percent Increase/Decrease
 4.8 Applications: Profit, Simple Interest, and Compound Interest
 Chapter 4 Projects
 Math@Work
 Foundations Skill Check for Chapter 5

Chapter 5: Geometry
 Math@Work: Introduction
 Study Skills
 5.1 Angles
 5.2 Perimeter
 5.3 Area
 5.4 Circles
 5.5 Volume and Surface Area
 5.6 Triangles
 5.7 Square Roots and the Pythagorean Theorem
 Chapter 5 Projects
 Math@Work
 Foundations Skill Check for Chapter 6

Chapter 6: Statistics, Graphs, and Probability
 Math@Work: Introduction
 Study Skills
 6.1 Statistics: Mean, Median, Mode, and Range
 6.2 Reading Graphs
 6.3 Constructing Graphs from Databases
 6.4 Probability
 Chapter 6 Projects
 Math@Work
 Foundations Skill Check for Chapter 7

Chapter 7: Introduction to Algebra
 Math@Work: Introduction
 Study Skills
 7.1 The Real Number Line and Absolute Value
 7.2 Addition with Real Numbers
 7.3 Subtraction with Real Numbers
 7.4 Multiplication and Division with Real Numbers
 7.5 Order of Operations with Real Numbers
 7.6 roperties of Real Numbers
 7.7 Simplifying and Evaluating Algebraic Expressions
 7.8 Translating English Phrases and Algebraic Expressions
 Chapter 7 Projects
 Math@Work
 Foundations Skill Check for Chapter 8

Chapter 8: Solving Linear Equalities and Inequalities
 Math@Work: Introduction
 Study Skills
 8.1 Solving Linear Equations: x + b = c and ax = c
 8.2 Solving Linear Equations: ax + b = c
 8.3 Solving Linear Equations: ax + b = cx + d
 8.4 Applications: Number Problems and Consecutive Integers
 8.5 Working with Formulas
 8.6 Applications: DistanceRateTime, Interest, Average
 8.7 Linear Inequalities
 Chapter 8 Projects
 Math@Work
 Foundations Skill Check for Chapter 9

Chapter 9: Linear Equalities and Inequalities in Two Variables
 Math@Work: Introduction
 Study Skills
 9.1 The Cartesian Coordinate System
 9.2 Graphing Linear Equations in Two Varibles: Ax + By = C
 9.3 The SlopeIntercept Form: y = mx + b
 9.4 The PointSlope Form: y  y_{1} = m(x  x_{1})
 9.5 Introduction to Functions and Function Notation
 9.6 Graphing Linear Equalities in Two Variables
 Chapter 9 Projects
 Math@Work
 Foundations Skill Check for Chapter 10

Chapter 10: Systems of Linear Equations
 Math@Work: Introduction
 Study Skills
 10.1 Systems of Linear Equations: Solutions by Graphing
 10.2 Systems of Linear Equations: Solutions by Substitution
 10.3 Systems of Linear Equations: Solutions by Addition
 10.4 Applications: DistanceRateTime, Number Problems, Amounts, and Costs
 10.5 Applications: Interest and Mixture
 Chapter 10 Projects
 Math@Work
 Foundations Skill Check for Chapter 11

Chapter 11: Exponents and Polynomials
 Math@Work: Introduction
 Study Skills
 11.1 Exponents
 11.2 Exponents and Scientific Notation
 11.3 Introduction to Polynomials
 11.4 Addition and Subtraction with Polynomials
 11.5 Multiplication with Polynomials
 11.6 Special Products of Binomials
 11.7 Division with Polynomials
 Chapter 11 Projects
 Math@Work
 Foundations Skill Check for Chapter 12

Chapter 12: Factoring Polynomials and Solving Quadratic Equations
 Math@Work: Introduction
 Study Skills
 12.1 Greatest Common Factor and Factoring by Grouping
 12.2 Factoring Trinomials: x^{2} + bx + c
 12.3 Factoring Trinomials: ax^{2} + bx + c
 12.4 Special Factoring Techniques
 12.5 Additional Factoring Practice
 12.6 Solving Quadratic Equations by Factoring
 12.7 Applicatinos of Quadratic Equations
 Chapter 12 Projects
 Math@Work
 Foundations Skill Check for Chapter 13

Chapter 13: Rational Expressions
 Math@Work: Introduction
 Study Skills
 13.1 Multiplication and Division with Rational Expressions
 13.2 Addition and Subtraction with Rational Expressions
 13.3 Complex Fractions
 13.4 Solving Equations with Rational Expressions
 13.5 Applications
 13.6 Variation
 Chapter 13 Projects
 Math@Work
 Foundations Skill Check for Chapter 14

Chapter 14: Radicals
 Math@Work: Introduction
 Study Skills
 14.1 Roots and Radicals
 14.2 Simplifying Radicals
 14.3 Addition, Subtraction, and Multiplication with Radicals
 14.4 Rationalizing Denominators
 14.5 Equations with Radicals
 14.6 Radical Exponents
 14.7 Functions with Radicals
 Chapter 14 Projects
 Math@Work
 Foundations Skill Check for Chapter 15

Chapter 15: Quadratic Equations
 Math@Work: Introduction
 Study Skills
 15.1 Quadratic Equations: The Square Root Method
 15.2 Quadratic Equations: Completing the Square
 15.3 Quadratic Equations: The Quadratic Formula
 15.4 Applications
 15.5 Quadratic Functions: y = ax^{2} + bx + c
 Chapter 15 Projects
 Math@Work

Appendices: Further Topics in Algebra
 A.1 U.S. Measurements
 A.2 The Metric System
 A.3 U.S. to Metric Conversions
 A.4 Absolute Value Equations and Inequalities
 A.5 Synthetic Division and the Remainder Theorem
 A.6 Graphing Systems of Linear Inequalities
 A.7 Systems of Linear Equations: Three Variables
 A.8 Introduction to Complex Numbers
 A.9 Multiplication and Division with Complex Numbers
 Additional Projects
Frequently Asked Instructor Questions

What does the workbook offer my students?
The workbook builds students' understanding of the mathematical content and develops students' problemsolving skills through:
 Conceptual exercises to extend understanding
 Application exercises with real life contexts
 Study Skills to improve student success
 Group or individual chapter discovery projects
 Quick Tips to provide helpful problemsolving hints
 Lesson Links – A connection of current topics to previously learned topics or future topics
 Math@Work – A connection of the skills learned to career contexts
 Foundations Skill Check – A chapter selftest for knowledge of previously learned skills needed for the next chapter

Why the Quantitative Reasoning Approach?
As an instructor, you are probably asking yourself if this workbook is the right choice for your developmental math students. In combination with Hawkes' software, the Foundations of Mathematics: A Quantitative Reasoning Approach workbook was developed for instructors like yourself, who are looking for a better way to teach developmental students the vital foundational topics in mathematics that students need to progress to collegelevel mathematics courses such as Math for Liberal Arts, College Algebra, Statistics, and Quantitative Reasoning. Instead of focusing on rote memorization of procedures, which are soon forgotten once the class is over, this workbook takes a different approach than most developmental texts. Our workbook focuses more on the thorough understanding of concepts and the use of reasoning skills to solve problems. We have also attempted to answer the frequently asked question, "When will I ever use this? " by showing students where the mathematics they are learning can be applied in reallife contexts and in a variety of career paths.
By focusing on concepts, we aim to build understanding. By emphasizing problemsolving and applications, we aim to better prepare students for the demands of today's job market. By integrating technology, we aim to actively engage students in their own learning. Our vision while creating this workbook was to more efficiently and effectively prepare students for the mathematics courses they will take in college and to hopefully change their perspective and way of thinking about mathematics as a whole. In addition, we hope that students who complete this workbook will no longer think of mathematics as something they must endure in order to reach their educational goals, but instead as a subject they need to master in order to make their lives and careers more productive and rewarding.

How do I use this workbook?
The Foundations of Mathematics workbook, in conjunction with Hawkes' software, can be used for a variety of course structures.

Chapters 115: For students who need an intensive twocourse sequence in foundational mathematics.

Chapters 49: For students with a strong prealgebra background that are proceeding to a nonSTEM curriculum math course like Math for Liberal Arts, Statistics or Quantitative Reasoning.

Chapters 19: For students at institutions desiring an alternate pathway to achieve mathematical literacy or reasoning skills as a precursor to a curriculumlevel course in Quantitative Reasoning or Statistics.

Chapters 1015: For students with a solid algebra background who plan to follow a STEM pathway and proceed to College Algebra, Precalculus, and Calculus. (Material from Chapters 19 can be used for review purposes.)
The combination of the workbook and software is flexible enough to accommodate a variety of instructor teaching styles and institutional course offerings:

Flipped Classroom
Students read through the Learn portion on their own. In the classroom students ask questions about the material they didn't understand and the instructor answers their questions and provides further instruction if needed. The remaining class time can be used to work collaboratively or individually on the workbook exercises and/or projects. The instructor floats around the room offering guidance as needed. Class time can also be used to discuss the Math@Work career connections to explore your students' career interests. Additional practice in the software can be done outside of class.

Traditional Lecture or Interactive Classroom
Students should preview the Learn portion in the software before the material is presented in class to provide a foundation for the lecture. The instructor presents material with an emphasis on more difficult concepts, leaving time in class for students to ask questions and work on exercises and/or projects in the workbook either in groups or individually. The amount of time spent lecturing versus inclass work time is up to the individual instructor.

Emporium Model
Students should read through the Learn portion of the software on their own. In the math lab setting the student should be prepared to ask the instructor or tutor questions about the material they didn't understand. Students can use class time to work particular sections of the workbook or complete the Practice mode of the software while they have someone to assist them. If an instructor requires the student to complete Certify mode, we recommend that this be completed in a supervised lab setting or testing center.

Hybrid (Online + Classroom)
Students read through the Learn portion of the software on their own and come to class prepared to ask questions about the material they didn't understand. The instructor answers their questions and provides further instruction if needed. The remaining class time can be used to work collaboratively or individually on the workbook exercises and/or projects. The instructor floats around the room offering guidance as needed. Class time can also be used to discuss the Math@Work career connections to explore your students' career interests. Additional practice in the software can be done outside of class. An instructor who chooses to use Certify mode can allow students to complete it at home or require them to complete it in a supervised lab setting or at a testing center on campus. Additional materials or resources needed by students can be posted online.

Entirely Online
Students would complete the Learn and Practice modes online. Particular sections or exercises from the workbook can be used for additional assignments or discussion forums. Information in the study skills pages can also be used for discussion forums and written assignments. The material presented in the Math@Work career connections could also be used to explore students' career interests through discussion forum questions. Students could be asked to write a paper discussing their chosen career path and how mathematics might be used in their chosen career. It is left up to the instructor whether they want to use Certify mode and how they would use it in the online environment.

Corequisite or Blended Model (Remediation + Curriculumlevel Math Course)
The accompanying software can be used for remediation of math skills needed for the curriculumlevel math course. The exercises and projects in the Foundations of Mathematics workbook can be used to ensure conceptual understanding, assist in developing problemsolving skills, provide realworld applications of the concepts studied, and provide the necessary study skills for student success.
