I am looking at a lesson research proposal for grade 5 on division of decimal values by a whole number. The problem the team plans to use is 4.26 ÷ 3, and their goal is for students to discover that the same processes they use to model division with whole numbers (e.g. with base-10 blocks) also apply to division involving a decimal.

For the moment, let’s think about these numbers, 4.26 and 3. Given that this is the first time students are dividing a decimal by a whole number, is 4.26÷3 the right problem? One might argue, for example, that 6.45 ÷ 3 would be better, because the students wouldn’t have to regroup across the decimal point. Or how about 6.28 ÷ 2, where no regrouping is necessary? (But maybe division by 2 is a special case, and not difficult enough to make students think about the process?) Or 9.6 ÷ 3? or 4.2 ÷ 3?

In planning a lesson, it is important to think about how the choice of numbers will shape what students end up doing and thinking, and whether those numbers are the best choice for accomplishing the lesson goals. The lesson research proposal should probably explain this choice of numbers in the section about the design of the unit and lesson, and certainly the team should anticipate it as a topic of discussion after the lesson.