In my capstone class for future secondary math teachers, I ask my students to come up with ideas for *engaging* their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Alyssa Mendez. Her topic, from Precalculus: exponential growth and decay.

In July 2002, National Geographic had an article about how America faces a rapid growth of nuclear waste. This is a great example to bring into as an engaging topic by allowing students to think about social issues that have been plaguing societies. We talk about recycling and learning how to reuse old materials. This topic is very well talked about in the media, as recycling is becoming very important and well advertised. I can pose a question to students about how they feel if we never were able to break down all the trash that we expel, including the nuclear waste that builds up, and other toxins. This will lead into the topic of exponential decay. I can also pose a question about how bacteria multiply at an exponential rate. As bacteria grow, there might not eventually be room or nutrients for bacteria. This is what exponential growth would be used for when we have a discussion.

http://math.ucsd.edu/~wgarner/math4c/textbook/chapter4/expgrowthdecay.htm

There are many ways to express exponential growth and decay. The world population has continuously grown at an exponential rate. As an engage, 1 could ask students how they think the rate of births and deaths grow. How could we gather the information? How do we plot the information? I would like the students to make predictions before we plot data. They could plot this on a hand drawn graph. Then once data is gathered, they could plot an “actual” graph that will show this data, and compare to what they had predicted. We could look at certain points in time, and I could pose questions such as why the graph dips or grows quicker at certain points in time. Time periods such as the plague, people moving to the Americas, and the baby boom.

Ms. Collier gave us a really great activity for exponential growth, and possibly decay. I could use M&Ms, and have the students shake them in boxes. When they open the box, then I they will count all the ones that show an “M” on them. They will tally all the M&Ms that they find, and will notice an exponential pattern. The students could possibly find this activity really fun and exciting. Especially since they can eat the M&Ms afterwards. This will show students what exponential decay and growth would look like. Again I can have them make predictions, before they open the box after one or two shakes.