Recently a team of third- and fourth-grade teachers tested instructional ideas on the topic of division with remainders (DWR) using lesson study. The Common Core State Standards for Mathematics give little attention to the concept of the remainder, specifying only that students are to solve problems for which remainders must be interpreted (NGA Center and CCSSO 2010). Furthermore, the American textbooks studied spent only one or two lessons on DWR. The team looked at a unit from a popular Japanese curriculum (Fujii and Iitaka 2011). This third-grade unit devoted eight lessons to the topic, using simple numbers and problem contexts. The team decided to teach the lessons in the Japanese unit, focusing the research lesson on why the remainder must be smaller than the divisor. The unit and research lesson provided rich learning experiences that successfully led students to a deep understanding of this topic. On the basis of this lesson study work, the team makes the following recommendations for high-quality instruction of DWR: (1) strategically use quotative division contexts; (2) help students understand why the remainder must be smaller than the divisor; and (3) teach how to interpret the meaning of remainders in context only after students have achieved some fluency.