Where? And Up or Down?
Some problems prove more interesting to students, and I am rarely sure why. The following problem is one that students (and math teachers) have enjoyed exploring.
Assume the pattern continues...
One nice observation is that numerous students, without being prompted, have solved this extension of the problem:
- Where would 125 be located?
- Is 125 on a triangle that points up or down?
- Where would 457 be located?
- Is 457 on a triangle that points up or down?
Answers to these extensions requires multiple cases, and considerable thought!
- Where would the positive integer N be located?
- Is the positive integer N on a triangle that points up or down?
Source: Wish I could remember so I could thank the person!
Hint: Write out some more cases....Look for patterns.
Do not waste your time (and thinking ability) by extending the pattern visually to 125, or evebn worse, 457!
Solution Commentary: Share your answers, observations, and conclusions with others exploring the problem. You can be referees for each other.