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If you are obliged to follow a mandated math curriculum at your school, then I suggest you read no further because this site is probably not suitable for you. However, if you are looking for something that is different, yet might spark an interest in either you or your students, then it might be worthwhile for you to continue reading.
In 1992 I wrote an alternative curriculum for Pre Calculus students who enjoyed mathematics, but not the rigor of mathematics. I named the course Mathematical Investigations and it soon became recognized as the most enjoyable math course at our school for many of our students. One of topics that we delved into was titled Calculator Limitations and Extensions. The students’ reactions were so positive that I made a similar presentation with the same title at the Wisconsin Mathematics Council Annual Meeting to 60 math educators. Of the five problems that were examined, none could be solved directly by use of a calculator without applying the appropriate mathematical concepts. Interestingly, many of the math teachers struggled with the problems as much as my students did.
Eventually, I wrote an enrichment booklet series called Ten Plus One for American Educational Products that contained similar type problems. Of the original six booklets, four remain in their catalog for sale, but the other two have been discontinued so I am free to sell them myself through TpT. This booklet is titled as Calculator Investigations.