Introduction to patterns in Algebra I. Students were exploring the number of toothpicks needed to make certain patterns and then were asked to predict/calculate/explain how many toothpicks would be needed for the 50th iteration.

To the students, math should be more than, as Conrad Wolfram says, "applying procedures to problems they don't really understand for reasons they don't get". Math needs to be so much more than that, and it takes a good teacher to realize that exploration is as important as any step in the learning process.