Math = Love: Algebra 2 INB Pages - Function Transformations and Linear Functions

## Saturday, November 23, 2013

### Algebra 2 INB Pages - Function Transformations and Linear Functions

We have been busy, busy, busy this year in Algebra 2!  Now that we're on Unit 4, I decided it was time that I get our pages from Unit 2 and Unit 3 posted!  Our first unit of the year covered the basics of functions.  I posted the pictures of the rest of Unit 1's material here.  But, I had yet to finish or take a picture of our function transformations foldable at that time.  This foldable was created after students had explored function transformations using an activity I learned about this summer called Move the Monster.  I got a paper copy of the handout at the OGAP Common Core Workshop I attended this summer.  But, I found an answer key to the activity online that someone else had posted if you want to see what the activity is all about.

My goal was for students to discover the transformations for themselves.  Then, we summarized these findings in a foldable for future reference.  I'll be honest.  My Algebra 2 kiddos struggled a lot with this activity.  But, I would like to think that it was a productive struggle.

 Function Transformations Foldable - Outside

 Function Transformations Foldable - Inside
Unit 2 was a review of linear functions.  Since linear functions are an Algebra 1 topic, we went through this very quickly.  I covered rate of change, graphing linear functions, graphing linear inequalities, and graphing systems of equations and inequalities.  We didn't create any INB pages over systems.  Due to time constraints, I only reviewed how to solve systems graphically.  Time will tell if that was a smart decision or not.

 Rate of Change Graphic Organizer
This year, I emphasized rate of change much more than I did last year.  I used this as an opportunity to constantly review the difference between dependent and independent variables.  Whenever students would struggle with interpreting the rate of change, I would direct them to this page a lot.

I also made the decision to teach my students about linear functions in the form y = a+bx instead of the typical y = mx+b.  Let me tell you, this is a hard thing to do.  First off, I've always taught y=mx+b before.  When I took Algebra 1, I was taught y=mx+b.  My Algebra 2 students who paid attention in Algebra 1 love y=mx+b.  Okay, maybe they don't love it.  But, the idea of changing from y=mx+b to y=a+bx did not set well with them at all.

I was told, however, at two separate conferences this summer that my students would do better with exponential functions of the form y=a(b)^x if I taught them linear functions in the form y=a+bx.  We will see.  We will definitely see.

There are some things I like about teaching y=a+bx.  It does make more sense to tell students that we always graph the y-intercept first when it comes first in the equation.  However, standardized test questions seem to always write linear functions in the form y=mx+b.  This does give me an opportunity to remind students that it doesn't really matter what order we write the equation in as long as we make sure that the signs are correct and that the slope is the coefficient of the x.
 Slope and Linear Functions INB Page

 Outside of y=a+bx Foldable

 Inside of y=a+bx Foldable
I am still in love with Slope Dude.  I thought that I wouldn't need to show Slope Dude to my Algebra 2 students.  But, my students who had me last year in Algebra 1 insisted that we HAD to watch it again.  It was kinda funny.  They talked up Slope Dude like crazy to their fellow students.  "This is the best video ever."  "It's so funny."  Then, they kept making cryptic comments like "Puff Puff Positive" and "This is Zero Fun."  Their classmates were SO confused and intrigued at the same time.  So, I pulled up the video on YouTube.  The audio isn't the loudest, so I made everyone stop talking.  I started the video.  The kids who had seen it before were cracking up.  The kids who had never seen it before had a look on their faces that was priceless.

Seriously, if you haven't watched Slope Dude, it will be the best 2 minutes and 36 seconds of your day.  I promise.  I don't know what it is about this video, but every time I have ever showed it, my students were narrating Slope Dude's adventures by the end of the video.  Be forewarned:  your students will also never refer to the slope as positive again.  It will be "Puff Puff Positive."  And, there may be an audible gasp whenever you say the word "Undefined."  After all, it is the worst curse word ever in mathematics.

Months later, my students still are talking about Slope Dude.  Last week, our Geometry classes started reviewing linear functions.  Some of my Algebra 1 students from last year came by to tell me about it.  When the Geometry teacher reviewed the four types of slope, the students insisted on calling the slopes by their Slope Dude names.  I hear that the Geometry teacher was not impressed...

 Slope Foldable (When Closed)
 Slope Foldable (When Open)
I used our lesson over linear vs non-linear graphs as graphing calculator practice.  Students rearranged each equation to get y by itself and entered it in their graphing calculator.  I downloaded this activity for free from TpT.
 Linear / Nonlinear Card Sort
I also can't teach horizontal and vertical lines with HOYVUX!
 HOYVUX - Outside of Foldable
I made a slight change this year.  I added O/K to the horizontal lines slope and N/O to the vertical lines slope to emphasize that it is okay to have a zero in the numerator.  The slope is just zero.  But, you cannot have a zero in the denominator.  Then, the slope is UNDEFINED!  (And, yes, I apologize for my cursing.)

 HOYVUX - Inside of Foldable
After making this foldable for the second time, I had an epiphany.  I should have made this into two separate foldables.  The HOY section should glue on the page horizontally.  The VUX section should glue on the page vertically.  I'll definitely be trying this out when I get to this topic with my Algebra 1 students!

 Graphing Linear Inequalities

Many of my Algebra 2 students were very nervous about graphing linear inequalities.  It was a topic that they hadn't really understood in Algebra 1, and they did not think they would be able to understand it.  This was a lesson where my principal just decided to pop in for a formal observation.  It ended up going well, though.  I was worried at first.  The students were telling me that this was going to be hard and that they wouldn't be able to get it.

Once we had worked through 3 problems together, one of my students announced to me, her fellow students, and the principal that "You have shown me the light!"  Graphing linear inequalities quickly became one of my students' favorite parts of this unit.

We concluded our INB pages for Unit 2 by gluing in our two linear regression labs: Bouncing Tennis Ballas and Twizzlers.  I posted about these two labs here.
 Bouncing Tennis Balls Lab

 Twizzlers Lab