Cost of paint … priceless!

Today’s class assignment…

How much will it cost to paint this room?

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Each wall: 13’ x 13’
Right window: 5’ x 7’
Left window: 6’ x 9’
Door (do not paint): 7’ x 3’
Cost of paint: $71.20 / gallon
Spread rate: 400 sq ft / gallon

That’s it. Pretty easy, right? Figure out the area of the walls, minus door and windows. Decide how many gallons of paint you need. Figure out the price of that much paint. Done.

Except! I didn’t give them the givens — none of them. I made them work in groups to develop their own questions, write them down, and hand them to me for answering. They had to decide for themselves what information they needed, and since my time was a limited resource, they had to try to do the whole thing efficiently. They found that sometimes their questions were too vague or general and I wouldn’t answer them. Sometimes they asked questions whose answers didn’t help. Sometimes I gave them answers that they decided were incomplete, and then they had to rephrase their questions.

It was incredible. Students were engaged. They were arguing with each other. The groups were being quiet because they were competing against each other.

Actual questions:
  • How big is the room? (No answer.)
  • What color is the rug? (No answer.)
  • What city is the room in? (Really?)
  • Do we have to paint the ceiling? (No.)
  • How tall is the room? (13′) How wide is the room? (13′ — two questions where one would do)
  • What are the dimensions of the windows? (5’ x 7’ and 6’ x 9’)
  • What is the cost of the paint? ($71.20 / gallon)
  • What is the cost to paint one wall? (Pick another question you can use to answer that yourself.)
  • How much wall does one gallon of paint cover? (400 sqft)

The coverage question usually appeared during the second wave of questions, after the students began to get a feel for the exercise. Students started by asking one or two questions, and then picked up momentum. One group of football players (who challenge my biases every day) came up with the most succinct list of questions the quickest, a list which nearly matched my list above.

I did not use the word area myself, but some teams discovered it and used it. I believe there was some learning there as the stronger players in the team helped the weaker players discover and adopt the word. (It’s much more intimate to use the word in the small-group context than to read it in a question that asks, “What is the area of a floor that is 8′ x 12′?”)

I reminded my students that “be less helpful” is my motto this year. This exercise was an example of that. It was wildly popular, and of course time flew.

This lesson and the phrase “be less helpful” were massively inspired by the great Dan Meyer.

Optional additions next time:

  1. Students pay for questions. Give out ten tickets to each team. Each question costs one ticket. At the end of the exercise, redeem tickets for points. (Give points for accuracy and speed as well.)
  2. Be sure to let teams announce their own results.
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2 responses to “Cost of paint … priceless!

  1. Love the task, Bruce. A lot of information and abstraction to think about and solicit in act two there. Strong work.

  2. Thanks. Of course I’ll be stealing from you this year when we get to the surface-area/volume part of Geometry. Octagonal prisms!

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