I'm taking this week's textbook challenge on directly. Here is the original problem Dan posed yesterday:
Immediately, I notice that they're getting cute with units. I find it distracts from the task at hand. Stronger math students may not get tripped up but from experience, the whole meters, yards, and feet thing would create an unnecessary hurdle. First, we're tossing out the units and I hand out this diagram and some rolls of tape (masking, electrical, painter's, whatever).
A challenge is posed: Carpet your room. Use the least amount of tape. Go.
- Do we have a winner?
- How many unique carpeting methods did we have?
- Did we get similar results from multiple methods?
- Pretend that tape represents a 12ft wide roll of carpet, what's the square footage of your room?
- Would you want a hired carpet installer to experiment like this?
- Wait, they should have a plan ahead of time?
- How can we plan ahead of time for the amount of carpet we need?
- Ok, area of the room, what are we missing?
Now we try again.
I would give them a few minutes to determine the area of the room. I would guess this would be done in the middle of a unit on compound area. Subdividing the shape into two rectangles shouldn't be a problem.
Next, let's determine the remodeling cost based on some choices:
This points out an issue with the original problem. Stating the carpet prices in square yards is simply a unit conversion for the sake of unit conversions. Real, live carpet is not sold that way. If we were going to coat the floor in denim we might use square yards. Stop lying about the real world. Rolls of carpet being 12ft wide, however, is accurate. At this point I would introduce the bit about the seaming tape.
Now, if everyone is feeling comfortable, we can start messing around with units. I would present these three different rooms and have them determine the installation cost for each type of floor.
The original problem would be great as a concluding activity. As an opener, there's way too much going on, primarily because of the different units. If the goal is to use the problem to discuss compound area, remove the hurdles to compound area. There is no need to derail your goal because you have to answer the same question about meters and yards over and over again. Once you've had the time to address compound area, you can let the unit conversions add a level of depth to later work.