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:

Submit your posts for Math Teachers at Play #54!

Bloggers--

The September 2012 issue of Math Teachers at Play is just around the corner! Please submit your posts (old  or new) through the MTaP Submission Form or send them directly to me via my Contact Page.  If you send them to me, include the following:

• Submission URL
• Submission title
• Email address

In addition, feel free to include your name and any comments you may have about the post.  You're encouraged to submit either your own posts or others' posts you've come across recently that deserve more attention!

Tune back here next week for the 54th Carnival!

The MTaP is a monthly blogging round-up shared at a different blog each month. We welcome posts from parents, teachers, homeschoolers, and students -- anyone who is interested in playing around with school-level (preschool to pre-college) or recreational math. Each of us can help others learn, so in a sense we are all teachers. --Let's Play Math

Week 3 :: A math quote I love

A prompt for this week's New Blogger Initiation was to pick one of our favorite math quotes and write about it.

I just got done with Open House at our school, and I shared a slide with the following to my parents:

In mathematics, the art of proposing a question must be held of higher value than solving it.

Georg Cantor, 1867

I asked them if they were ok with a brief math history lesson.  They said yes as long as there wouldn't be a test afterwards (I like this group).  I gave them a few tidbits that I find really fascinating about Mr. Cantor:  he was one of the forerunners to formalize the rigorous definitions we use in calculus; he classified the levels of infinity (WHOA); people thought he was so crazy, he got thrown into an insane asylum.

So a genius beyond genius, if you ask me.

But one of the things I love most about Cantor is the quote from above.  Because it summarizes my thoughts not just on mathematics but on teaching mathematics so beautifully.

I told the parents, as a teacher, I'm much more interested in developing students who can ask deep questions, than students who know how to take a multiple-choice test.  I'm interested in helping students learn when to ask, "Mrs. Peterson...why do we do it this way?" or "What if we considered this case instead?"  I want to help develop curious students; and central to curiosity is the desire to ask good questions.

One challenge that I face, however, is that my students are used to their curiosity being satiated so quickly and easily.  If they want to know the answer to something, they can just Google it.  On their phone.  Right there.

Don't get me wrong, I love that we have access to so much knowledge.  The downside is...many of us are not used to really, truly working hard to find a satisfying answer.

And the downside to that?  We never experience the joy of a hard-fought discovery.

And that's one of the coolest things in life.

Hence, my love of this quote.

Best. Co-workers. Ever.

Yesterday was my birthday, and my fellow math teachers brought me this:

Why the question mark?  I think because many of them are over a half a century... ;)

Being just two weeks into a new job, one of the best feelings in the world is to know that you have co-workers who are going to work beside you and support you.  I completely lucked out with these people.  They really are the best.

Week 2 :: A Warm Up I'm proud of

One of Week 2's prompts for the New Blogger Initiation is to pick something--anything--that we've created that we're proud of.  If I read it correctly, it can even be just a problem.

So, here goes: a Warm Up/Bell Ringer/Do Now that I'm quite proud of.  It's the pre-cursor to a lesson on transformations for Pre-Calculus:

WARM UP (Do Now)

1. Write f(1)=2 as an ordered pair.
2. If you know the point (1,2) is on the graph of y=f(x), what point do you know has to be on the graph of y=f(x)+3?  Why?  (Hint: What is f(1) equal to?)
3. What about on the graph of y=f(x+3)?

Plotting these transformations gets us thinking about translations and (I think) reveals the "opposite" behavior of the "inside" transformations.  (Though it's really not opposite at all, is it?!  Yay for math!)

That's all I have for this week!  Thanks to the wonderful people at the blogging initiative for encouraging continued writing.