I hope to use this website as a filing cabinet for ideas I have about engaging math problems. Some of these problem ideas will be developed to the point where I will create a lesson plan around them. Other ideas will not be fully developed at all. This one is somewhere in between. I invite anyone to discuss similar ideas for making mathematical problems more engaging for students. To me, Dan Meyer still provides the gold standard for crafting engaging, challenging problems around interesting ideas.
My girlfriend and I were discussing the affect of the birth rate on various social problems including, rising health care and pension costs and global warming. Specifically, we started talking about if the Chinese one-child policy would have positive or negative affects on these social problems. This led us to want to know how many children the typical American family has.
These statistics immediately flabbergasted me. First of all, they made me say, “What the hell does `average children per family with children’ mean?” Second, the numbers seemed WAY too low to me. Third, these seem to be numbers that politicians can easily LIE with. Fourth, these numbers don’t represent any family that I know. I did become slightly less horrified after some research led me to figure out that the category “average children under 18 per family” counts parents, whose children have already past their 18th birthday, as having 0 children. Thus, lots of families are counted as having 0 children, even though they might have had many more children at some point in their lifetime.
I foresee an engaging classroom activity where we explore how representative these census numbers are of the families of the students that I am teaching. My students can collect data about their own family sizes, and we explore topics such as
- measures of central tendency
- interpreting data and backwards engineering to better understand data that is being reported as “fact”
- discussing ideas for collecting data to answer a specific question (the census data that I present here answers a question, just not the question I meant to be answering)