This is my first attempt at a #MakeoverMonday problem that Dan Meyer has been leading. However, I want to put my own spin on it and try to use the concepts from Stephen Brown & Marion Walter’s book, The Art of Problem Posing, 3rd ed. (BN.com or Amazon.com) I am also going to be posting it early because I am traveling for the next 6 days and want to get it out there instead of forgetting.
Here is the problem that needs a makeover:
— Dan Meyer (@ddmeyer) July 4, 2013
It is a pretty typical problem from any number of Algebra 1 books I have seen. A psuedo-context of two internet café’s (presumably) and we are asked some standard questions that leave nothing to chance or to think about. It has to be psuedo-context because no company except cafés would charge by the hour.
Here is my reworking of the problem using the “What-If-Not” problem posing strategy.
The initial set-up:
As you know, I take a lot of trips to conventions during the summer. During one convention week the hotel did not offer internet in room (I know, right!) but across the street were two competing internet cafés. Tell me which I should have decided to use and justify your answer.
What: [Brown suggests we first write out all the “whats” or the attributes of the problem]
- One café has a flat fee of $9.95 each month
- That same café has a per hour fee of $2.25
- The second café has no base fee at all
- The second café has a per hour fee of $2.95
These are the attributes of the problem, so AFTER the learners have figured out the initial problem, then we go into the “What – If – Not” extensions.
- What if the first café did not have a flat fee? What would change in our answer?
- What if the first café had a flat fee of $4.95 per month, what would change in our answer?
- What if the first café did not have a $2.25 per hour fee but had a $1.95 per hour fee?
- What if the second café did not have a $2.95 per hour fee but had a $4.95 per hour fee?
- What if the second café had a base fee of x?
That is the most simple explanation / demonstration of the “What-If-Not” model I can do. It essentially is take a problem or situation you know the solution to, list all the attributes you can, and then play with them. You may do one, or you may do all of them.
If you are attending TMC13, this is what my presentation is about. Asking better questions and problem posing in math class. I chose this approach because it does not require the graduate level creativity that Dan and others demonstrate all the time. This method is approachable enough I can teach my department to do it.