Here are the problem-solving techniques we teach in 4 through 6th grades:
- Reasoning using logic
- Reasoning using patterns
- Reasoning by trial and error
- Reasoning by asking questions
- Reasoning using a possibility chart
- Reasoning by process of elimination
- Solving problems using deductive reasoning
- Estimating which answer is most reasonable
- Reasoning by examining evidence and making notes
- Reasoning by working backwards from a given solution
- Determining if there is enough information to solve a problem
Re-read the list, then keep them in mind as we review some real flat tire incidents. I will code these 4 different solutions red (useless), black (not sure) and green (helpful):
A. My vehicle has a mini-spare tire. Driving across the desert on paved roads, I hit a small rock and cracked my alloy wheel. The impact damaged the tire irreparably. I changed the wheel, put on the mini-spare and drove home. It took 10 days to get a new wheel and tire.
RUN-FLAT - wouldn't have helped if the rim was broken.
TIRE INFLATOR - wouldn't have helped if the rim was broken.
ROADSIDE SERVICE - the rim was ruined so my spare was essential. There was no mobile phone signal for 50 miles.
TPMS - it would have warned me that the tire lost air (but I learned that as soon as I hit the rock).
B. In the morning my tire was flat. I put on the spare. I could see a huge screw sticking out of the middle of the tread of the flat tire. I marked the spot, pulled out the screw and went to the store to have the flat fixed.
RUN-FLAT - the screw probably wouldn't have mattered to a run-flat tire; it would have held air.
TIRE INFLATOR - would have re-inflated the tire after removing the screw (or I could leave it in).
ROADSIDE SERVICE - someone could have changed my tire for me.
TPMS - it would have warned me that the tire lost air (but I could easily see it).
C. My wife was driving down the street. She realized a rear tire was flat when someone honked and pointed. She limped the car 2 blocks to a parking lot and called me to come and change the tire. The sidewall had been damaged by a pothole.
RUN-FLAT - probably wouldn't have prevented the sidewall damage.
TIRE INFLATOR - it wouldn't have worked on the sidewall damage.
ROADSIDE SERVICE - someone DID change her tire. Me. This worked!
TPMS - it would have warned her when the tire was damaged.
D. I was about to depart on a cross-country trip when I saw my front tire was low. I pulled out a screw sticking out from the corner of the tread, and the tire went flat. No tire stores in town had a new tire, and they wouldn't repair mine. Rather than continue without a spare, I bought an inflator and filled the tire. It's been holding air for 9 years (now as a spare).
RUN-FLAT - none available on my elderly car and wheel.
TIRE INFLATOR - it DID work on the sidewall / tread puncture.
ROADSIDE SERVICE - someone could have changed my tire, but I would still have had to inflate it.
TPMS - it would have warned me that the tire was leaking.
Don't worry right now about choosing the best solution of the 4 solutions. The question is Which of the 11 math reasoning methods are we using?
[Click here for my answer]