Wiggins question #6

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 31 \frac{3}{8}. 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:

  1. Allow/force students to interpret their computational results in light of the context (there is a CCSS Mathematical Practice standard about this), and
  2. 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.
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8 responses to “Wiggins question #6

  1. Michael Paul Goldenberg

    Isn’t 243 / 8 = 30 3/8 so that the integer answer is 31?

  2. 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.

    • Michael Paul Goldenberg

      You don’t recall the now-infamous soldiers/bus problem that was used on some big national test (NAEP?) and subsequently made the rounds of all the “The Sky Is Falling!” pundits to demonstrate how US math education, education in general, and “our youth” were all failing?

      • Yes, I know of that problem. And if the intention of this problem was to describe understanding of the mistake so many students made, then that intention should be made clear.

  3. 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.

  4. 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… ;)

  5. 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… ;)

  6. 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…

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