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Foundations of Mathematics

Thinkwell's Foundations of Mathematics offers a focused approach to our Pre-algebra curriculum. With its emphasis on such basics as integers, fractions, decimals, and percents, it's the perfect resource for students wanting a fundamentals-based approach to mathematics.

Foundations of Mathematics is customized specifically for the Technical Colleges of Georgia.

Our complete Foundations of Mathematics package includes:
  • 12-month Online Subscription to our complete Foundations of Mathematics course with video lessons, automatically graded exercises, and much more.
  • Workbook (optional) with lecture notes, sample problems, and exercises so that you can study even when away from the computer.

Workbook requires the purchase of an online subscription.

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Foundations of Mathematics Materials

Online Subscription, 12-month access

Access to a complete online package that includes everything you need:

  • High quality video lessons explain all of the Foundations of Mathematics concepts
  • Automatically graded exercises with immediate feedback allow you to track your progress
  • Printable full-color illustrated notes help you review what you've learned in the video lesson
  • Subscriptions start when you are ready. Buy now and activate your course anytime you like. Wait up to one year to activate your subscription; your 12-month subscription doesn't begin until you say so!

Workbook, Notes, sample problems, exercises, and practice problems

Study without a computer. Our workbook companion contains the same lecture notes and sample problems that are delivered online, as well as some additional exercises, all in a convenient print format. Answers to the odd-numbered exercises are in the back of the book. Online Subscription is required; workbook not sold separately.

Foundations of Mathematics Details

Thinkwell's Foundations of Mathematics includes all of these features for your student:

  • More than 100 video tutorials (see sample)
  • 1000+ automatically graded Pre-Algebra problems (see sample)
  • Real-world application examples in both lectures and exercises
  • Printable illustrated notes for each topic
  • Searchable glossary of mathematical terms
  • Engaging content to help students advance their mathematical knowledge:
    • Operations with whole numbers, integers, decimals, and fractions
    • Variables and expressions
    • One-step, two-step, and multi-step equations and inequalities
    • Ratios, proportions, and percents
    • Simple and compound interest
    • Customary and metric units of measurement
    • Organizing, displaying, and interpreting data
    • Graphing equations and slopes
    • Polygons and solids
    • The Pythagorean theorem
    • Exponents
    • Polynomials
    • Probability

Table of Contents

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1. Integers

  • 1.1 Introduction to Integers
    • 1.1.1 Integers and the Number Line
  • 1.2 Operations with Integers
    • 1.2.1 Addition of Integers
    • 1.2.2 Subtraction of Integers
    • 1.2.3 Multiplication and Division of Integers
    • 1.2.4 Introduction to Exponents
    • 1.2.5 Using the Order of Operations

2. Fractions

  • 2.1 Introduction to Fractions
    • 2.1.1 Factors, Multiples, and Equivalent Fractions
  • 2.2 Operations with Fractions
    • 2.2.1 Multiplying Fractions and Mixed Numbers
    • 2.2.2 Dividing Fractions and Mixed Numbers
    • 2.2.3 Adding and Subtracting Fractions and Mixed Numbers

3. Decimals

  • 3.1 Introduction to Decimals
    • 3.1.1 Representing, Comparing, and Ordering Decimals
    • 3.1.2 Rounding and Estimating Decimals
  • 3.2 Operations with Decimals
    • 3.2.1 Adding and Subtracting Decimals
    • 3.2.2 Multiplying Decimals
    • 3.2.3 Dividing Decimals
  • 3.3 Fractions and Decimals
    • 3.3.1 Converting between Fractions and Decimals
    • 3.3.2 The Order of Operations with Fractions and Decimals

4. Ratios, Proportions, and Percents

  • 4.1 Ratios and Proportions
    • 4.1.1 Ratios and Rates
    • 4.1.2 Proportions
    • 4.1.3 Finding an Unknown Value in a Proportion
    • 4.1.4 Applications of Proportions
  • 4.2 Percents
    • 4.2.1 Introduction to Percents
    • 4.2.2 Percents
    • 4.2.3 Relating Percents, Decimals, and Fractions
    • 4.2.4 Estimating with Percents
    • 4.2.5 Finding and Using Percents

5. Variables, Expressions, and Equations

  • 5.1 Introduction to Equations
    • 5.1.1 Variables and Expressions
    • 5.1.2 Translating Between Words and Math
    • 5.1.3 Simplifying Algebraic Expressions
    • 5.1.4 Translating Between Tables and Expressions
    • 5.1.5 Equations and Their Solutions
  • 5.2 Introduction to Solving Equations
    • 5.2.1 Solving Addition Equations
    • 5.2.2 Solving Subtraction Equations
    • 5.2.3 Solving Multiplication Equations
    • 5.2.4 Solving Division Equations
  • 5.3 Solving Equations
    • 5.3.1 Solving Equations Containing Integers
    • 5.3.2 Writing and Solving Two-Step Equations
    • 5.3.3 Writing and Solving Multi-Step Equations
    • 5.3.4 Solving Equations with Variables on Both Sides
    • 5.3.5 Solving Literal Equations

6. Measurement

  • 6.1 Measurement
    • 6.1.1 Understanding Customary Units of Measurement
    • 6.1.2 Understanding Metric Units of Measurement
    • 6.1.3 Converting Customary Units
    • 6.1.4 Converting Metric Units
    • 6.1.5 Converting between Customary and Metric Units
    • 6.1.6 Time and Temperature

7. Geometry

  • 7.1 Polygons
    • 7.1.1 Triangles
    • 7.1.2 Quadrilaterals
    • 7.1.3 Finding Angles in Polygons
  • 7.2 Area, Perimeter, and Circumference
    • 7.2.1 Perimeter
    • 7.2.2 Area of Rectangles and Parallelograms
    • 7.2.3 Circles and Circumference
    • 7.2.4 Area of Circles
  • 7.3 Solids
    • 7.3.1 Introduction to Three-Dimensional Figures
    • 7.3.2 Volume of Prisms and Cylinders

8. Statistics and Graphs

  • 8.1 Organizing, Displaying, and Interpreting Data
    • 8.1.1 Organizing Data
    • 8.1.2 Bar Graphs and Histograms
    • 8.1.3 Line Graphs
    • 8.1.4 Reading and Interpreting Circle Graphs
    • 8.1.5 Measures of Central Tendency

About the Author

Author BUR

Edward Burger
Williams College

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest listed him in the "100 Best of America". After completing his tenure as Gaudino Scholar at Williams, he was named Lissack Professor for Social Responsibility and Personal Ethics.

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Foundations of Mathematics Video lessons

Video Lessons

Foundations of Mathematics Interactive Exercises

Interactive Exercises

Foundations of Mathematics Illustrated Notes

Illustrated Notes

Using Thinkwell has helped me to become more prepared and better able to answer teachers' questions during lectures.