The first part of the article focuses on deriving the essential properties of arithmetic sequences by appealing to students' sense making and reasoning. The second part describes how to guide students to translate their knowledge of arithmetic sequences into an understanding of linear equations. Ryota Matsuura originally wrote these lessons for his mathematics course for preservice elementary teachers. Patrick Harless used the lessons and the described approach with his eighth-grade algebra students and experienced success. The anecdotes drawn from Harless's experience provide insight into how teachers can implement these ideas and how his students made sense of arithmetic sequences and linear equations. (Contains 11 figures.)