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.

**The Problem**

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.

So, we visited the U.S. Census Bureau website and got this.

We found that the “average children under 18 per family” was 0.90. And, that the “average children under 18 per family with children” was 1.86.

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
- bias
- 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)

Thoughts?

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*Related*

This is really interesting, seems like a good thing to try for teaching basisc stats. I would also like to look up the census data for the age distribution and average family size, and see how well these data match. And it’s also interesting to see that in this example how those non-math factors(langage in this case) affect the reality that math could reveal. The biggest problem of the census data presented is the lack of clarification. The data just show the current and sorta instanious situation, and it won’t help much with the birthrate-related questions.

A trivial thought, aren’t your second and fourth thoughts the same thing? You feel the numbers are too low because the typical american family in your mind says otherwise? It does seems to me that you missed a big hint “under 18” there. Well I don’t know I’m trying to say, it’s just kinda funny. And thanks for sharing, as always.

There’s so much data available in the world these days! I’d love to teach a unit on statistics and use some real-world “noisy” data. I think census data could be engaging because it is supposed to represent communities in which students live. Well, at the very least, it’s engaging to me :P. And, if the teacher is not engaged by the problems he or she gives, what chance do the students have of being engaged?

With regards to your thoughts on bias, I think the only reason I separate them as two separate thoughts is because a lot of questions on standardized tests ask students to identify studies that are biased, but rarely ask them to design for themselves data collection methods that minimize bias.