1.
Were there any topics that you had seen before, but you understand better as a result of working through it again?
Chapter 36 Reflection
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.
Section 36.2 Worksheets
PDF Version of these Worksheets
1
external/worksheets/36-Worksheets.pdfWorksheet Worksheet 1: Questions about the Content
2.
Were there any ideas that you had never seen before?
3.
Based on your experience, which of these ideas seems the most important to understand well?
4.
Did any part of the presentation make you curious about math in a way that went beyond the material? Are there questions or ideas that you would like to explore?
Worksheet Worksheet 2: Questions about You
1.
How has your mathematical writing continued to evolve from the previous pause for reflection? Do you find yourself thinking in different ways?
2.
Did you have any "Aha!" moments where you had an insight into something that you had not noticed before?
3.
What is the biggest mathematical connection that you made?
4.
How is your mathematical confidence coming out of these book? Do you feel more or less confident in your mathematical knowledge than before the book? Explain why you think you feel the way you do.
