9. Four Fours

Play 9

I meant to blog about this problem about 10 months ago, but better late than never.

Highlight: We got student-supplied answers for 1-100.

Lowlight: Those 100 answers did not come from 100 different students. In fact, one student was able to come up with about a third of them himself. We got some but not nearly enough female representation. There was no faculty representation.

Highlight: For the first few days, students were really excited and interested. Their submissions were a bit overwhelming to keep track of.

Lowlight: That engagement level disappeared entirely after a few days. We had 30 or 40 left to figure out, and only 1-2 students were working on it.

Highlight: The leaderboard. Some students really took pride in having their name publicly displayed.

Lowlight: The start of the school year was so crazy that this was the only problem that we had up for the first month.

Highlight: There was a nice unintentional synchronicity between this task and my class. In precalculus, we covered piecewise and step functions, and a couple students noticed that this allowed for crazy new opportunities in this problem. Now they could write 0 or 1 with only one 4 using decimals and the floor/ceiling function.

Lowlight: It was unclear whether or not using e was a violation of the rules. Generally, I like this ambiguity – it allows me to ask the student what they think it fair. Unfortunately, they decided it was fair, and they used it over and over again with the floor function, making things just a bit too easy. In hindsight, I should have pushed him to realize that this shouldn’t count in the hopes he would persist and find a more interesting solution.

The final product (click to enlarge):09-Solutions

What would we change for next time?? Maybe it would be more interesting to focus on a smaller batch of numbers and try to find as many ways to write them? Perhaps that would lead into questions about what makes two equations “different” or not? Maybe a leaderboard with a bigger font so student names are even more public? We definitely need some new ways to publicize our problems and offer different ways for submissions …


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