Find the size of the smallest square that will enclose five non-overlapping unit squares. This is approachable by an able 7th grade math student. Let’s look the solving process in the following steps:
- By playing around, one can guess the best situation that leads to the desired minimum;
- With a bit more skills, one can find the answer;
- Prove your method is indeed the best;
- Extend this question.
We would say that step (2) will be helpful for MATHCOUNTS/AMC8, 10, 12/AIME. Working out (3) will be helpful for USAMO/IMO. On the other hand, (1) and (4) develop students’ appreciation for the problem-solving strategies that transcend mathematics and apply to any fields they might choose to pursue.