Don't Break the Product Rule or you'll be Slathered in Butter and Grilled!

My Pre-algebra class is reaching the end of their exponent unit.  I blogged about this unit before, but it was one of my first posts so I'm sorry about the roughness (I was also a little scribd happy because I was excited by how easy it was to throw documents right into my post.  It's magical!) I still feel like this unit is really important because really internalizing the exponent rules makes for a much smoother transition into algebra 2 and beyond, but after reading around a lot on other people's blogs, I'm not sure that stomping along through all the rules in order is the best way to teach them.  I also am aware that in the real world students will never have to simplify these ridiculous exponent problems. Though I still think that understanding these rules is necessary in creating a foundation for high school math and is a good way to introduce the logical system of math, I'm a little uncomfortable with how hard it is to tie them to the real world.  I ended the unit with exponential growth and decay and scientific notation which use the exponent rules in context, but I still wish I had a more concrete way to make these rules relevant to students.

I've been trying to think of a way to review what we learned throughout the whole unit.  Last year, I had the students just do a poster project where they had to neatly and creatively demonstrate all the rules, but I think that was just a desperate attempt on my part to have them review the material without adding a whole bunch more prep work on my part because I was swamped.  This year I created this review activity for them:

Exponent Unit 'Going on Vacation' Review Project After reading around so many blogs and seeing what the larger teaching community is doing, I've realized that even the activities I'm most proud of are lacking the real world context that has been stressed by so many other bloggers.  I've stressed teaching the logic of mathematics to my students because that is what is beautiful about math to me, but my students probably need more context driven activities and examples.  The problem is that my education in mathematics has been entirely traditional (i.e. contextless) and I don't think about applications and I don't interpret the "real world" through math.  I don't know how to see math in the world around me.  Yet I guess, just as we tend to repeat our parent's mistakes, it's so easy to teach the way I was taught and to focus strictly on logic.  I've realized that this is a grave deficiency in my teaching that I need to learn to correct, but changing the way I think about mathematics is going take a lot of time.  At least I'm pretty good at making fun and silly math assignments, even if they're not tied to context.  Two months ago when I came up with the idea for this project I was pretty proud of it.  Now I realize that it doesn't give students any deeper insights into math.  It will be silly and engaging I think, but I need to do better.