Patterns and inductive reasoning (informal reasoning where students use the process of using patterns to make a conjecture such as "what comes next" or stating what relationship holds) are stepping stones that students can use for improving their understanding of mathematical principles, problems solving, and algebraic thinking. Yogi Berra once said, "You can observe a lot just by watching." In that spirit, you can learn a lot just by observing. Searching for patterns is a problem solving strategy. Students like being detectives and looking for patterns or relationships. Inductive reasoning is an accessible and informal form of justification. It makes mathematics more engaging and fascinating, and it gives students the power to learn new mathematical ideas and solve problems.
This activity includes an example where students learn that inductive reasoning (make a conjecture based on a few examples) is an imperfect form of reasoning because sometimes the patterns in the observations lead you to an incorrect prediction or conclusion. However, this limitation of inductive reasoning does not make it a poor method. Scientists, mathematicians, and teachers use it frequently to discover patterns that help them recognize relationships, group objects, acquire understanding, and experience some exciting "aha" moments while learning.