When I originally created this activity more than a decade ago, I intended to provide meaningful measurement practice for high school students who were in the non-accelerated mathematics track and not proficient in measuring skills. It was my further intention to illustrate to these students the importance of mathematics reasoning, which in these problems saves time as well as providing more accurate responses.
Because my students’ positive responses and enthusiasm to the mathematical concepts of these four problems exceeded my expectations, I decided to offer this same set of four challenging problems to my calculus students. Their reaction was even more amazing so I now regularly offer this activity to my advanced math classes during the first day of school while I hand out text books, assign seating arrangements, and take care of other first day tasks.
By application of insight, these four challenges can be solved accurately by use of simple mathematical concepts in less than 15 minutes. Yet most students struggle to successfully complete two of these problems during the allotted 30-minute time limit.
Near the end of the period as I discuss the various solutions and insights necessary to solve these problems efficiently, I also explain how seemingly unrelated math concepts can be applied to solve a variety of problems. I conclude this explanation with my hope that students will recognize that applying mathematics that they have previously learned will enable them to solve many of the mathematical challenges they will encounter throughout the school year.
Although I teach at a high school, I do believe that comparable results would be obtained if this activity were presented to gifted and talented classes at the elementary or middle school levels.