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# Foundations of MathematicsA 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 problem-solving skills!

Formats: Software, Workbook

Product 13 Digit ISBN
Courseware + Developmental Mathematics eBook 978-1-944894-76-4
Courseware + Developmental Mathematics eBook + Workbook 978-1-941552-36-0

### Video

1. Chapter 1: Whole Numbers
1. Math@Work: Introduction
2. Study Skills
3. 1.1 Reading and Writing Whole Numbers
4. 1.2 Addition and Subtraction with Whole Numbers
5. 1.3 Multiplication with Whole Numbers
6. 1.4 Division with Whole Numbers
7. 1.5 Rounding and Estimating with Whole Numbers
8. 1.6 Exponents and Order of Operations
9. 1.7 Problem Solving with Whole Numbers
10. 1.8 Tests for Divisibility (2, 3, 4, 5, 6, 9 and 10)
11. 1.9 Prime Numbers and Prime Factorizations
12. Chapter 1 Projects
13. Math@Work
14. Foundations Skill Check for Chapter 2
2. Chapter 2: Fractions and Mixed Numbers
1. Math@Work: Introduction
2. Study Skills
3. 2.1 Introduction to Fractions and Mixed Numbers
4. 2.2 Multiplication and Division with Fractions and Mixed Numbers
5. 2.3 Least Common Multiple (LCM)
6. 2.4 Addition and Subtraction with Fractions
7. 2.5 Addition and Subtraction with Mixed Numbers
8. 2.6 Order of Operations with Fractions and Mixed Numbers
9. Chapter 2 Projects
10. Math@Work
11. Foundations Skill Check for Chapter 3
3. Chapter 3: Decimal Numbers
1. Math@Work: Introduction
2. Study Skills
3. 3.1 Introduction to Decimal Numbers
4. 3.2 Addition and Subtraction with Decimal Numbers
5. 3.3 Multiplication with Decimal Numbers
6. 3.4 Division with Decimal Numbers
7. 3.5 Decimal Numbers and Fractions
8. Chapter 3 Projects
9. Math@Work
10. Foundations Skill Check for Chapter 4
4. Chapter 4: Ratios and Proportions, Percent, and Applications
1. Math@Work: Introduction
2. Study Skills
3. 4.1 Ratios and Proportions
4. 4.2 Solving Proportions
5. 4.3 Decimals Numbers and Percents
6. 4.4 Fractions and Percents
7. 4.5 Solving Percent Problems Using Proportions
8. 4.6 Solving Percent Problems Using Equations
9. 4.7 Applications: Discount, Sales Tax, Commission, and Percent Increase/Decrease
10. 4.8 Applications: Profit, Simple Interest, and Compound Interest
11. Chapter 4 Projects
12. Math@Work
13. Foundations Skill Check for Chapter 5
5. Chapter 5: Geometry
1. Math@Work: Introduction
2. Study Skills
3. 5.1 Angles
4. 5.2 Perimeter
5. 5.3 Area
6. 5.4 Circles
7. 5.5 Volume and Surface Area
8. 5.6 Triangles
9. 5.7 Square Roots and the Pythagorean Theorem
10. Chapter 5 Projects
11. Math@Work
12. Foundations Skill Check for Chapter 6
6. Chapter 6: Statistics, Graphs, and Probability
1. Math@Work: Introduction
2. Study Skills
3. 6.1 Statistics: Mean, Median, Mode, and Range
5. 6.3 Constructing Graphs from Databases
6. 6.4 Probability
7. Chapter 6 Projects
8. Math@Work
9. Foundations Skill Check for Chapter 7
7. Chapter 7: Introduction to Algebra
1. Math@Work: Introduction
2. Study Skills
3. 7.1 The Real Number Line and Absolute Value
4. 7.2 Addition with Real Numbers
5. 7.3 Subtraction with Real Numbers
6. 7.4 Multiplication and Division with Real Numbers
7. 7.5 Order of Operations with Real Numbers
8. 7.6 roperties of Real Numbers
9. 7.7 Simplifying and Evaluating Algebraic Expressions
10. 7.8 Translating English Phrases and Algebraic Expressions
11. Chapter 7 Projects
12. Math@Work
13. Foundations Skill Check for Chapter 8
8. Chapter 8: Solving Linear Equalities and Inequalities
1. Math@Work: Introduction
2. Study Skills
3. 8.1 Solving Linear Equations: x + b = c and ax = c
4. 8.2 Solving Linear Equations: ax + b = c
5. 8.3 Solving Linear Equations: ax + b = cx + d
6. 8.4 Applications: Number Problems and Consecutive Integers
7. 8.5 Working with Formulas
8. 8.6 Applications: Distance-Rate-Time, Interest, Average
9. 8.7 Linear Inequalities
10. Chapter 8 Projects
11. Math@Work
12. Foundations Skill Check for Chapter 9
9. Chapter 9: Linear Equalities and Inequalities in Two Variables
1. Math@Work: Introduction
2. Study Skills
3. 9.1 The Cartesian Coordinate System
4. 9.2 Graphing Linear Equations in Two Varibles: Ax + By = C
5. 9.3 The Slope-Intercept Form: y = mx + b
6. 9.4 The Point-Slope Form: y - y1 = m(x - x1)
7. 9.5 Introduction to Functions and Function Notation
8. 9.6 Graphing Linear Equalities in Two Variables
9. Chapter 9 Projects
10. Math@Work
11. Foundations Skill Check for Chapter 10
10. Chapter 10: Systems of Linear Equations
1. Math@Work: Introduction
2. Study Skills
3. 10.1 Systems of Linear Equations: Solutions by Graphing
4. 10.2 Systems of Linear Equations: Solutions by Substitution
5. 10.3 Systems of Linear Equations: Solutions by Addition
6. 10.4 Applications: Distance-Rate-Time, Number Problems, Amounts, and Costs
7. 10.5 Applications: Interest and Mixture
8. Chapter 10 Projects
9. Math@Work
10. Foundations Skill Check for Chapter 11
11. Chapter 11: Exponents and Polynomials
1. Math@Work: Introduction
2. Study Skills
3. 11.1 Exponents
4. 11.2 Exponents and Scientific Notation
5. 11.3 Introduction to Polynomials
6. 11.4 Addition and Subtraction with Polynomials
7. 11.5 Multiplication with Polynomials
8. 11.6 Special Products of Binomials
9. 11.7 Division with Polynomials
10. Chapter 11 Projects
11. Math@Work
12. Foundations Skill Check for Chapter 12
12. Chapter 12: Factoring Polynomials and Solving Quadratic Equations
1. Math@Work: Introduction
2. Study Skills
3. 12.1 Greatest Common Factor and Factoring by Grouping
4. 12.2 Factoring Trinomials: x2 + bx + c
5. 12.3 Factoring Trinomials: ax2 + bx + c
6. 12.4 Special Factoring Techniques
8. 12.6 Solving Quadratic Equations by Factoring
9. 12.7 Applicatinos of Quadratic Equations
10. Chapter 12 Projects
11. Math@Work
12. Foundations Skill Check for Chapter 13
13. Chapter 13: Rational Expressions
1. Math@Work: Introduction
2. Study Skills
3. 13.1 Multiplication and Division with Rational Expressions
4. 13.2 Addition and Subtraction with Rational Expressions
5. 13.3 Complex Fractions
6. 13.4 Solving Equations with Rational Expressions
7. 13.5 Applications
8. 13.6 Variation
9. Chapter 13 Projects
10. Math@Work
11. Foundations Skill Check for Chapter 14
1. Math@Work: Introduction
2. Study Skills
6. 14.4 Rationalizing Denominators
10. Chapter 14 Projects
11. Math@Work
12. Foundations Skill Check for Chapter 15
1. Math@Work: Introduction
2. Study Skills
3. 15.1 Quadratic Equations: The Square Root Method
4. 15.2 Quadratic Equations: Completing the Square
6. 15.4 Applications
7. 15.5 Quadratic Functions: y = ax2 + bx + c
8. Chapter 15 Projects
9. Math@Work
16. Appendices: Further Topics in Algebra
1. A.1 U.S. Measurements
2. A.2 The Metric System
3. A.3 U.S. to Metric Conversions
4. A.4 Absolute Value Equations and Inequalities
5. A.5 Synthetic Division and the Remainder Theorem
6. A.6 Graphing Systems of Linear Inequalities
7. A.7 Systems of Linear Equations: Three Variables
8. A.8 Introduction to Complex Numbers
9. A.9 Multiplication and Division with Complex Numbers

• #### What does the workbook offer my students?

The workbook builds students' understanding of the mathematical content and develops students' problem-solving 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 problem-solving 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 self-test 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 college-level 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 real-life contexts and in a variety of career paths.

By focusing on concepts, we aim to build understanding. By emphasizing problem-solving 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 1-15: For students who need an intensive two-course sequence in foundational mathematics.

• Chapters 4-9: For students with a strong pre-algebra background that are proceeding to a non-STEM curriculum math course like Math for Liberal Arts, Statistics or Quantitative Reasoning.

• Chapters 1-9: For students at institutions desiring an alternate pathway to achieve mathematical literacy or reasoning skills as a precursor to a curriculum-level course in Quantitative Reasoning or Statistics.

• Chapters 10-15: For students with a solid algebra background who plan to follow a STEM pathway and proceed to College Algebra, Pre-calculus, and Calculus. (Material from Chapters 1-9 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 in-class 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.

• Co-requisite or Blended Model (Remediation + Curriculum-level Math Course)

The accompanying software can be used for remediation of math skills needed for the curriculum-level math course. The exercises and projects in the Foundations of Mathematics workbook can be used to ensure conceptual understanding, assist in developing problem-solving skills, provide real-world applications of the concepts studied, and provide the necessary study skills for student success.