The book is designed to give students not only the “hows” but also an understanding of the “whys” of the basic math processes they may be reviewing and those they are learning for the first time. The first information the student encounters in each activity is a real-life application of the skills and techniques covered by that activity.

This portion of the activity clearly states the target proficiencies that the student should gain over the course of the activity.

Each module provides a terminology checkpoint, listing previously used terms relevant to the new topic as well as the new terms to be introduced, giving students a "heads up" on the vocabulary they should have already learned before going on.

A Building Mathematical Language section focuses on the specific and well-defined vocabulary of mathematics as well as commonly used notation and translation. This section does more than teach students to "speak math"; it teaches them how to think through and talk about math.

Math processes that require more than three steps are presented in table form as Methodologies, which break the processes down to their fundamental steps. Techniques are presented for one or two-step processes, translations, and conversions.

In a step, when a particular mathematical property is applied for the first time, a Why can you do this? or “Why do you do this?” is inserted and footnoted for the student who desires to understand the process, not just memorize a set of steps.
 

The commonly used shortcuts to computation and notation are footnoted as such and presented in models, which follow the methodologies.
 

Special cases, for which the student might ask, “This doesn’t fit the original example, so what do I do now?” are also footnoted and presented as separate models.
 

Students are occasionally prompted with a Think graphic to draw their attention to an otherwise easily missed step or procedure.

Models for the special cases and shortcuts are presented in step-by-step format. As students work through the models, they are cued with the special case and shortcut instructions. In chapters 4 through 6, specifically chosen models also serve as opportunities for review by incorporating computations with decimals and fractions.

When appropriate for the section, estimation techniques are presented with examples as additional (optional) tools the student can use to verify the answer to a problem.
 

Gleaned from the observations of Basic Mathematics instructors as to what mathematical errors students are most likely to make, a table-format section called Addressing Common Errors lists and gives the student an example of each of those problematic areas. Most importantly, however, it provides resolution for each common pitfall—how to avoid this—and the correct process for each example.
 

The Pre-Activity section ends with a Preparation Inventory which provides students with an actual checklist of critical skills and understandings they need to have before proceeding to the Activity section.

In this section, students are given concrete guidelines as to the criteria against which their performance is measured, as well as guidelines for presentation of their responses to questions and exercises.

This section presents a set of Critical Thinking Questions, encouraging the student to articulate in writing what he or she has learned thus far. The first few questions are direct, followed by those convergent questions that require the students to tie in previously learned knowledge with the topic at hand. Finally, a question is posed to challenge the student to explore the topic further. The convergent Critical Thinking Questions are especially suitable for small group discussion, and may be worth revisiting once the students have demonstrated that they have mastered the processes.

This section provides important suggestions for successfully performing the skills and solving the problems posed in the Activity. Suggestions include the use of a horizontal bar in fractions, as opposed to a diagonal bar, which can easily interfere with correct alignment in the problem, careful use of the original problem rather than an intermediate step when validating a final answer, and so forth.

When an answer does not validate, many students first instinct is to erase the entire problem and begin again. An Identify and Correct section presents actual student-written work for the students to first validate for accuracy, and then analyze to detect the error(s) made.
 

Foundations of Math also provides additional student
support tools at the back of the book: