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Section 36.1 Yet Another Pause for Reflection

Congratulations! You are at the end of this book. As you have worked your way through these materials, we hope that you've started to really embrace the idea that thinking mathematically is both important and useful. We've covered a lot of material, and even though many of the concepts were simple, that doesn't mean that this was an easy journey.

And now that we are at the very end, we're going to look back over the scope of topics that we covered.

The main trunk of this book focused on making sure that you had an understanding of the core algebraic manipulations that you will need to be successful in a college level math course:

  • Basic Algebraic Presentation

  • Variables in Expressions and Equations

  • Like and Unlike Terms

  • Simplifying Expressions and Solving Equations

  • Variables and Substitutions

  • The Properties of Exponents

  • Common Factors

  • Factoring Quadratic Polynomials

  • Reading Mathematical Expressions

The first branch covered linear equations and coordinate plane:

  • Lines and the Coordinate Plane

  • Slope-Intercept Form

  • Solving Systems of Equations by Substitution

  • Solving Systems of Equations by Elimination

The second branch covered fractions and decimals:

  • Fraction Basics

  • Fraction Addition and Subtraction

  • Fraction Multiplication

  • Fraction Division

  • Decimal Addition and Subtraction

  • Multiplying Decimals and Percents

The third branch covered the underlying concepts that we use in arithmetic:

  • The Number Line and Base-10 blocks as Visualizations of the Integers

  • Visualizations of Addition and the Addition Algorithm

  • Visualizations of Subtraction and the Subtraction Algorithm

  • Integer Chips as a Representation of Negative Numbers in Addition and Subtraction Calculations

  • Movement on the Number Line for Negative Numbers in Addition and Subtraction Calculations

  • Visualizations of Multiplication as "A Groups of B" and Area

  • Visualizations of Division as Making Groupings and Equal Distribution

The fourth branch covered a few key application ideas:

  • General Word Problems and Avoiding the Trap of Key Words

  • Scientific Notation

  • Unit Conversions

If you worked your way through all of these topics, you should feel very confident that you have the basic foundation you need to be successful at your introductory college level mathematics course. You may not consider yourself a "math person" (yet), but you are well on your way for having completed this book.