Monday, September 10, 2012

Week 4 :: Writing Piece-wise Functions

A prompt for the final week of the New Blogger Initiation was to write about another new blogger's post.

Maggie (@pitoinfinity8) posted an awesome activity for piece-wise functions in which students literally cut up the different pieces of a given function and then puzzle them together.  Brilliant.  In response, Bowman Dickson mentioned that it might be useful to go the other way, too; in other words, give the students the graph and have them write the equation.

I love both these ideas:  the first gets the students to read; the latter gets them to write.  I didn't read Maggie's post until after I introduced piece-wise functions this year in Pre-Calc, but I did read it in time for our first test review.

So, here's what we did...


I gave them a few minutes to answer these questions and then we used their answers along with the restrictions to write the function.

Onto another one:

They were rockin and rollin, so I asked them...


This time, I gave them the problem in the traditional manner:


Success!  Finally!  Many thanks to Maggie and Bowman.  What a great way to review both piece-wise functions and function transformations.

Speaking of function transformations, a twitter conversation in which I laughed out loud:


3 comments:

  1. I'm trying to get somewhat caught up on reader (between the new blogger initiative and school starting I'm extremely far behind) - this morning I read all your posts so far. I liked several of them, so the least I can do is leave you one comment. Several things you've talked about really resonated with me. I also emphasize functions and use piecewise as a continuation of parent functions and transformations (not that this is uncommon among us math teachers). I also found it interesting that you had been teaching at the college level and switched 'down' - one of the reasons I pursued a MS in Mathematics was to be able to possibly teach at the college-level one day if I wanted. I've wondered if it's different in a good way, but I think that's mostly a "grass is greener" sort of idea. Finally, I also really like to share the basics of Cantor's life with students - I feel that he's a mathematician who was recent enough that students can relate to his personal life yet not very mainstream at the high school level. It'd be nice if even high school students had heard of Gauss, Euler, Cantor, etc. in addition to the really dead guys like Euclid and Pythagoras. My students express frustration and wonder (some just one, others both) at the idea of empty sets and levels of infinity. Keep up the good work, I plan to keep reading as best I can!

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    1. My apologies for just now responding! I'm extremely behind, too. I've gotten to peruse your blog, and I'm really excited to read more! Great stuff.

      There are days I wonder why in the world I left college teaching. It's a piece of cake compared to HS teaching. But I wanted to see what the system was like so I could better understand the types of students we get at the college level. I sure hope it turns out to be a worthwhile experiment... :)

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  2. I happen to be teaching piecewise right now in Algebra 2, so great timing for me! Thanks for sharing :)

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