This month, some of my Twitter Math Camp friends are hosting a fun, month-long event called “Explore the MathTwitterBlogoSphere”. You can check out the website for more details, and each week promises a new task designed to encourage math teachers to reach out via blogs and twitter.
For the first weekly challenge, Sam Shah has asked participants to share their favorite rich task. Even with having taught for 17 years, it was not easy to come up with one task which I felt summarized my philosophies, but here is what I feel is my best question. It is one I have given many times in algebra 2, and our freshman-year prob/stat course:
How many zeroes are there at the end of 200! (200 factorial)?
Here’s why I like this problem, and why I enjoy giving it:
- It’s has a simple premise. Sometimes I need to embellish with “think about multiplying out 200! It would be a really long number. That number has a lot of zeroes at the end. How many are there?” But besides having to know what factorial does, it is plain and simple in premise.
- It requires thinking about the nature of numbers. Brute force doesn’t work well here. When I first started giving this problem, I think I used 25 factorial, but then technology started to catch up with me. One year, a few students used Excel, which gave a wrong answer, as it began to konk out at bigger numbers. Even if students can now find an “answer” through some tech means, the challenge to explain the “why” remains.
- The answer is secondary. Communicating your reasoning is king. This problem present great opportunities to utilize math vocabulary: factors, commutative property, grouping, etc. I grade this task almost exclusively on communication, and students are often surprised to find that a math task can require such a level of revision and reflection.
- I can move towards a generalization if I need to put my foot on the gas more. If a few students seem to have the answer and communicate a solution, I can challenge them to develop a formula which works for any number factorialed (is this a word?).
Rich problem solving experiences have always been a part of my classroom culture. This problem is one of my favorites.