A catering company rents out tables for big parties. 8 people can sit around a table. A school is giving a party for parents, siblings, students and teachers. The guest list totals 243. How many tables should the school rent?
This is a classic example demonstrating the danger of applying procedures without thinking. The quotient can be expressed either as 31, remainder 3; or as . Neither of these answers the question, though. According to unspoken principles of table renting, we will probably need 32 tables.
Of course, I can imagine a student thinking like a caterer and building any of the following arguments:
- We need 31 tables (or fewer) because 5% of people on a typical guest list do not show up.
- We need 31 tables because if everyone comes, several will be young children who will sit in their parents’ laps.
- We need 31 tables—if everyone shows up, we can just stick an extra chair at each of three tables.
- We need at least 35 tables: No one wants to sit on the side where they can’t see the band playing at the front of the room, so we need to allow for fewer than 8 people at each table.
- Et cetera.
I would argue that we need to teach in ways that do two things:
- Allow/force students to interpret their computational results in light of the context (there is a CCSS Mathematical Practice standard about this), and
- Focus students’ attention on the role the computation plays in answering this kind of question. Why are we dividing? and What does the quotient mean? are the kinds of questions I have in mind here.