As a foundational evolutionary concept, the Hardy-Weinberg principle should be taught enthusiastically in introductory biology courses. In a companion Perspectives paper, I made the case that students are often given limited or incorrect information on the HW principle due to a lack of mastery or confidence on the part of their teachers. The purpose of this Innovations paper is to identify where errors are most-often made in the set-up and solutions of HW problems. The centerpiece of this paper is a set of six biological scenarios to which students need to apply the HW principle to answer interesting evolutionary questions. I provide explanations for solving the problems (including Excel instructions with formulas to perform chi-square tests), and I identify several teachable moments that are likely to arise in the discussion of the solutions. The use of this problem set and the pedagogical strategy described in this paper significantly improved students' performance on HW problems in my introductory biology class, and I expect that they can benefit other teachers at least as much. [For the companion paper, see EJ1186047.]