Foundational Mathematics for Corequisite Courses: Succeeding at College Mathematics

Section 6 Alignment with Precalculus Courses

This textbook was organized with precalculus in mind. While precalculus textbooks vary somewhat, they mostly fit the same basic pattern. This means that this textbook should work well with most standard first semester precalculus courses. We wanted to create a rough alignment between this material and the basic structure those courses. Specifically, there were three major touch points that we wanted to have:

• Discuss the coordinate plane and graphing lines around the same time students are studying the general properties of functions.

• Discuss of fractions before introducing of rational functions to remind students of the underlying manipulations before they need it.

• Discuss scientific notation around the time as logarithmic functions to create the opportunity to connect the two ideas.

The suggested course alignment below is based on having extra contact time with students for the corequisite content, which allows for the extra time up front to set the stage with the Main Branch of this book. (I don't know how you would try to teach both the support material and the core content without extra contact time!) It's possible to use this material without it, but students may not adopt the mindset and writing habits if those sections are not treated as the primary learning outcomes. After the Main Branch, very little in-class time is spent directly teaching the Foundations content. Students are expected to read the book, and only a small portion of the class time is dedicated to completing the worksheets and discussing the ideas directly.