Math = Love: Absolute Value Graphs and Inequalities Interactive Notebook Pages

## Saturday, January 21, 2017

### Absolute Value Graphs and Inequalities Interactive Notebook Pages

Thursday, my Algebra 1 students finished our unit on Absolute Value Graphs and Inequalities.  On Friday, I had a large percentage of my students gone due to both a basketball tournament and a powerlifting tournament.  Classes that normally have 22 had 6 or 7.  My trig class consisted of 2 students.  This meant that my students who were there got time to retake quizzes and get their notebooks up to date.  If they were caught up, I taught them how to play Farkle (affiliate link).  When I wasn't grading retakes or teaching kids to play Farkle, I used this extra time to update my interactive notebooks.  I do notebooks with three of my classes: Algebra 1, Trig, and Physical Science.  I was able to get Algebra 1 and Physical Science fully updated!

Here's a peek at our notebook pages for this unit.

Unit Divider:

Skill List for this Unit:

Can you catch my mistake?  I was SO aggravated with myself when I saw my goof.  Only one student noticed it, though.

My first goal was to get students to graph absolute value functions by making an input/output table and make connections between the numbers in the equation/inequality and the slopes, vertex, and orientation.

My students had already graphed absolute value functions earlier in the unit in our relations and functions unit.  So, the graphing part wasn't new.  The looking for patterns for vertex, slopes, and orientation was definitely new.

Students took turns picking x-values for us to plug into the equation/inequality.  We had already learned that absolute value graphs are always "v-shaped," so students knew that we had to keep plugging in values until our graph made a "v."

When I was teaching this lesson during the first period of the day, I kept finding myself frustrated that my students didn't seem to be looking for patterns between the slopes, vertex, and orientation.  Instead, they seemed plenty happy with just plugging in value after value to make every single graph.

I teach three periods of Algebra 1 each day.  1st period, 5th period, and 6th period.  This meant I had plenty of time to think about how to salvage this lesson that did not go as planned during 1st period.

When 5th period rolled around, we did the first problem the same way we had done it first period.  Students gave us x-values.  We plugged each value in and graphed the resulting ordered pair.  Repeat until the graph made a "v."  After we had found the slopes, vertex, and orientation, I told my students that my goal for this lesson was that they would be able to figure out the slopes, vertex, and orientation without doing ANY graphing by the time the bell rang.

Of course, they told me this was impossible.  There's no way that you can tell those things without making a graph.  Next, I made a slight change that did get my students looking for patterns.  It was such a simple idea, but it worked like a charm!

Before I let students give me x-values to plug into the next problem, I asked students to make predictions about what the slopes, vertex, and orientation were going to be.  I wrote these guesses on the board, but I warned my students to NOT write them down until we had made the graph and verified them.

After my students made random, off the wall guesses, we plugged in values and made a graph.  Then, we examined if our guesses were correct.  All of a sudden, students were making much more informed guesses and sharing their theories with their classmates.  Many of their theories were later disproven, but I felt like my students learned SO much from these false theories.

So, I guess I learned an important lesson.  I shouldn't just expect that my students will discover patterns on their own.  I need to explicitly encourage them to look for patterns.

After spending a day working on our theories, we made a foldable to summarize our findings.

I had students take a colored sheet of paper, fold it in half hamburger style, cut it in half, and give give half to their neighbor.  We used colored markers to write out the general form of an absolute value equation.  Then, we took our scissors and cut the flaps.

Under each flap, we recorded our observations about the impact of each variable on the graph.

We also took notes over what to do if a, h, or k was missing.  This wasn't originally in my plans, but some of my students became frustrated that their notes didn't tell them what to do if one of the variables was missing.  I told them that instead of getting mad at me for leaving something out of their notes that we should just add it to our notes!

Next, we did lots of practice using Desmos.  Students would predict the slopes, vertex, and orientation.  Then, I would display the graph on Desmos.  Students were always eager to ask what would happen if we did x, y, or z.  I love how Desmos let us see instantly what happened when we made tiny changes!

Next, we changed things up.  I gave my students a graph of an absolute value relation.  Students had to identify the slopes, vertex, and orientation.  Then, we wrote the equation or inequality.  I think in the past, I would have expected students to jump straight from the graph to the equation.  But, I had already made a nifty slopes, vertex, and orientation table from the previous foldable.

I love how little of the work I actually had to do during this lesson.  Students were offering answers.  Other students were asking questions.  And, more students were answering those questions.  It was a beautiful!

Our last skill of the unit was to predict transformations of absolute value relations.

My students were a bit frustrated with me because I only put the list of 5 things that could be changed on the front.  They got tired of flipping back and forth.

I loved hearing my students argue about whether the slopes change when we go from y = |x + 2| - 3 to y = -|x + 2| - 2.  Some students were adamant that the slope changed from positive 1 to negative 1.  When the rest of the class heard this, most agreed.  But, there was always a student or two who remembered that an absolute value function always has a positive slope AND a negative slope.

And, that was our absolute value unit.  Many of my students are convinced this is the easiest thing we have done all year.  I find that very interesting.  Absolute value has always been something in the past that I kinda rushed through and my students never really got a strong grasp of.

Files are uploaded here.  Okay, as of 1/21/17, only one of the three file is uploaded.  The other two files are on my school computer, so I will upload them to BOX on Monday!