One of Chicago’s Lesson Study Leaders, Joshua Lerner, wrote a terrific article in NCTM’s journal Mathematics Teacher: Learning and Teaching in PK-12. It is titled, “Recommendations for Teaching Division with Remainders.”
From the introduction:
Recently our team of third- and fourth-grade teachers tested instructional ideas on the topic of division with remainders (DWR) using lesson study (for more on lesson study, see Lewis and Hurd 2011; Takahashi and Yoshida 2004). In our case, third-grade teachers wanted to know how to best prepare students for this topic, whereas fourth-grade teachers felt that their curriculum’s approach to DWR had not been effective. From our work together, we developed a deeper understanding for ourselves of DWR and discovered an effective way to help our students master the concept.
…
On the basis of our lesson study work, we make 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.
NCTM members can access the article here. (Regrettably, we cannot legally share it on our site.)
You can access the research lesson report on which the article is based in our database. Search for grade 3 and key word “remainder”.