## Question 6

### 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.

I’m not sure why this one is in the list (I have the same feeling about #4 and #8). Mr. Wiggins provides no support for what needs to be explained.

Is it that a common wrong answer is 30, and that we should explain why that is wrong? Or is it that various assumptions might give a different answer than 31, as you detail? Or is it intentionally left open-ended? If it is, then that should be spelled out. Even if the intent was just to explain why division is appropriate, a simple “motivate your choice of computation for solving the problem” would be a helpful prompt.

I sometimes ask my students to explain even very computational work, but I always lay out for them before this what I expect.

I appreciate the fact that this Q with its comments encourages practical thinking and questing for knowledge. Unfortunately something that is often discouraged or at least (as a 63 yr old) that has been my experience.

I would love it if my students came up with reasoning behind getting any answer between 30 and 35…I’d be happy with any reasoning at all…period… ;)

Reblogged this on Pretend to be Nice and commented:

I think everyone has lost sight of the big picture when it comes to teaching/helping/explaining/experiencing math. I would love it if my students came up with reasoning behind getting any answer between 30 and 35…I’d be happy with any reasoning at all…period… ;)

Barry, I put it here for all the reasons listed: the famous NAEP bus problem, the fact that, as in most things, the right answer is: “it depends” and because most kids STILL get variants of this wrong – look at recent NAEP results. Clearly, they are unthinkingly rounding down in vast numbers 25 years after the army bus problem…