Wednesday, March 11, 2015

Absolute Value Functions Part 2

After a few days of working on absolute value functions, I wanted my students to apply it to something concrete.  They had the transformations and graphing down pretty well and had done creative assignments to demonstrate their understanding.  I found a "Fire House" problem that seemed like a good fit.

My mistake: I used the problem after my students knew too much about writing absolute value functions, so going back to linear functions seemed odd to my students.

I did like the problem; they got right into modeling.  The biggest discussion was how you count blocks.  Culturally, I could have guessed that this would be hard for my kids to get.  I live in a rural area and most students don't live in an area where they can walk "a block" to get somewhere.  I saw the lightbulbs go off as I explained how houses are numbered by blocks.  The 100s, 200s, and 300s are separated by cross streets.  Many didn't know this or had never realized it. 

We got through parts I and II today.  Tomorrow we'll tackle the graphing calculator-heavy extension. 

If I use this problem set again, I will reword a few questions to make it more clear what is being asked.  I had a few questions come up over and over as I moved from group to group. 

What's your favorite way to teach absolute value functions?

Mathematically yours,
Miss B

Wednesday, March 4, 2015

Absolute Value Functions

I taught a lesson I really liked today because my kids were into it, even after a very long session of PARCC testing.  It's bringing me back to blogging after a very quiet school year.  :)

Earlier this year, my Algebra I students learned about exponential functions.  We've been asked to follow the sequencing of EngageNY and I'm not a huge fan of the program.  For whatever reason, that meant that my treatment of absolute value functions came after exponentials.  This makes little sense to me, but it meant that absolute value functions seemed very obvious to my classes, which I expected.

I made a set of 12 graphs using, took screenshots, and printed them as cards for each student.  The students cut the cards apart and we got to work sorting the cards after a short reminder of what absolute value means and a sketch of the parent function using a table of values.  For each round of the sort, I had students keep the parent function separate from the other graphs so they would have it as a point of reference from which to make comparisons.

The sorting rounds each worked like this:
  • I told students what characteristic they should sort by (orientation, stretch/shrink, horizontal shift, vertical shift).
  • Students sorted the cards by themselves.
  • At their tables, students discussed the answers to three questions:
  1. How many piles did you make?
  2. What did you label the piles? 
  3. Which cards belonged in each pile and why?
  • Following a brief team discussion, we had a whole class discussion of the sorting methods and the cards that they selected to put in each pile.  
In the sorting, we were able to develop the vocabulary word "vertex" as well as further clarify the difference between a vertical stretch and a vertical shrink.  Speaking of stretch or shrink, the BEST tip I have on teaching that (and what I would share as a "my favorite" if I were going to TMC15) is that I have taught my students to take out "imaginary silly putty" and stretch it out.  I've taught them that in math class we only stretch silly putty vertically.  If I say "get out your silly putty" they all mime stretching silly putty vertically.  It's cleared up SO much confusion compared to previous years and none of them are really confused by it like I can remember in the past. 

After sorting, students glued the cards into their ISNs, and wrote notes under each graph describing any differences from the parent function.  We did the first few together and they did the rest in their groups.  Then, as groups finished, I distributed lists of equations that matched each graph.  Students matched the graphs and equations using their prior knowledge of transformations on exponential functions.  This part took so little time and students were overall confident in their answers.

With the hard work done, we just needed to formalize our notes with a summary page. 

The document I'm sharing contains the graphs, equations, and sorting questions.

This document was our pre- and post- notes.

Mathematically yours,
Miss B