To focus on mathematical reasoning and what makes a good argument, the authors developed an assignment that requires college students to submit a book of mathematical reasoning as an assessment during the semester. To begin, the authors looked for questions and tasks that lend themselves to developing mathematical arguments and justifications and that reflected important ideas they had explored in class. They also searched for questions that were accessible to a variety of solution methods and multiple representations. The students' mathematical reasoning books include solutions to six open-ended problem-solving questions that required students to apply ideas that had been investigated in class to a new situation. Solutions are evaluated both on the quality of students' mathematical reasoning and their ability to communicate clearly. The problem solutions are submitted as a book titled "My Mathematical Reasoning Book." In this article, the authors present the typical student solutions to one of the problems from the book, their reflections about students' thinking, and suggestions for how others might get started on a similar project. (Contains 5 figures.) [Additional problems are appended online.]