Wednesday, February 13, 2013

Absolute Value Foldables and a 3-Hole Punch Story

[If you're not interested in absolute value, there is a pretty funny story about a 3-hole punch at the very end.  Or, maybe it's not funny.  Maybe it's sad.  Either way, it was a memorable experience.]

This week, I started introducing the concept of absolute value to my Algebra 1 students.  Our Algebra 1 textbooks introduce the concept of absolute value in Algebra 1.  It introduces graphing absolute value equations in the same chapter where graphing linear equations is taught.  Of course, I don't use the textbooks.  I keep one by my desk as a reference, but the rest of the books are collecting dust on my shelves.

This summer, I had planned to introduce absolute value using the textbook sequence.  I even created some pages for my students' interactive notebooks.

I never used this page, though.  Actually, I decided it was in the best interest of my students to postpone discussing absolute value until later in the school year.  When I started working with my students at the beginning of the year, I realized just how low many of them were.  There were a lot of middle school math topics that I had to reteach.  So, I made the decision to take certain concepts and postpone them until later in the school year.  I was hoping that if I refined my focus I could build up my students' math levels and make them more confident.  Then, with more confidence, we could start looking at concepts such as fractions, absolute value, probability, etc.

So, Monday was my students' first experience with absolute value in Algebra 1.  A few students who took Algebra last year knew what absolute value was.  A few others wrongly described absolute value as meaning the opposite.  They thought it meant that you just changed the sign.

My students had been working really hard at multiplying binomials and factoring quadratics for the past two weeks.  Test scores were not exactly where I had wanted them, but at the same time I was proud of my students because I have seen them grown an incredible amount since meeting them in August.  In August, I would not have thought that my students would be factoring quadratics with a leading term greater than one.  But, we've gotten here.  We still need some more practice with factoring, but we will continue reviewing it and practicing it for the remainder of the semester.  And, it was a Monday.  So, I decided to kinda ease into our absolute value unit using the Estimating Age activity from Dan Meyer's Algebra Curriculum (Week 3.)

Estimating Ages Chart
I picked 15 of the celebrities from his file.  I used their birthdays to calculate their current age.  I typed up a half-sheet of paper for students to record their guesses.  It's not perfect.  After using it once, I realized that I should have added a fourth column for students to record the difference between the actual age and their guess.  I don't know if it would be of use to anyone, but I have uploaded my file below.

We went through each celebrity.  As a class, the students tried to guess who the celebrity was.  This led to some very enlightening conversations.  My students didn't know who Natalie Portman was.  They didn't recognize Penelope Cruz.  I thought for sure that the would recognize Julia Roberts.  No, they thought she was a character off of Sex and the City.  We had arguments over whether Tobey Maguire's real name was Tobey Maguire or Peter Parker.  I was shocked to learn that one of my students thought Judi Dench was James Bond's mother.  But, my other classes didn't even know that she had played M in the James Bond movies.  Somehow, Ronald Reagan got brought up in my 8th grade Algebra class, and I learned that two of my 8th graders had no clue who Ronald Reagan was.  One student told me that they thought Morgan Freeman looked like the president of Africa.  But, others tried to convince me that Morgan Freeman looked the exact same as Samuel Jackson and Denzel Washington.  Another student was convinced that Will Smith was only 21.  

After my students had recorded their guesses for the age of each celebrity, I revealed the correct ages.  They  wrote down in the margin how far off they were.  Then, we totaled this column.  The student with the lowest total won.  And, I didn't realize how much of a controversy my award would cause.  Up for grabs was a much-coveted "Super Student Award."  I picked these up at Dollar General during a 75% off school supplies clearance sale.  So, I picked up a few packs of awards.  At 25 cents for 24 awards, it was too good of a deal to pass up.  I thought my students might consider them childish, but I was wrong...  

Super Student Award
One student was so mad when he didn't win the award that he crumpled up his paper, tossed it across the room, and pouted for the rest of the class period.  He tried every way he could to get me to just write him a certificate, too.  I told him that I couldn't do that; he would have to find a way to earn one.  Now, he asks every day if we are going to play the game again so he can win an award.

After playing the celebrity age guessing game, I started to transition to absolute value by asking my students to consider a scenario where a celebrity was actually 55.  If one person guessed 51 and another person guessed 59, who would win?  One of my classes was convinced that the person who guessed 51 would win because it just had to be like the Price is Right where you automatically lose if you guess too high of a number.  I assured them that we weren't following the rules of the Price is Right.  Finally, we agreed that it was a tie because both guesses were the same distance from the true celebrity age.

In math, we aren't worried about how close a number is to a celebrity's age.  Instead, we want to know how close a number is to zero on the number line.  We filled out a Frayer Model on absolute value to glue in our interactive notebooks.

Absolute Value Frayer Model
 We ended up Day 1 of the unit by practicing some order of operation problems that involved absolute value.  This was a great way to review absolute value without feeling like I was losing valuable class time.  A lot of my students left my class this day feeling more confident about math than I had seen them all semester. Our two previous units on exponent rules and polynomials have left some of my students with lower grades than last semester.  I hope my students realize that I am pushing them because I care for them.  We have made great strides this school year!

Day 1 of the Unit - Interactive Notebook Entry
On Day 2 of the unit, we started graphing absolute value equations.  I had my students do this using a t-chart.  I created a booklet foldable to guide our in-class practice time.  As a class, we graphed 5 absolute value equations together.  Then, I gave them 6 more to complete in-class on their own.

Graphing Absolute Value Equations Booklet Foldable - Outside

Graphing Absolute Value Equations Booklet Foldable - Inside
We had some great conversations while graphing these.  It was exciting to see them discover that absolute value equations form a "V" when graphed.  I intentionally had them graph y = |x| and see the shape for themselves before writing the definition of absolute value equations on the cover.  Initially, some students assumed that they must have did something wrong since the graph wasn't a straight line.

We talked a lot about why the y-values for some graphs could be negative.  Eventually they realized that it made a big difference whether the subtraction happened inside the absolute value bars or outside the absolute value bars.  I've been trying to incorporate more foldables into this semester.  Last semester, I did a ton of foldables.  I kind of stopped for a few weeks this semester.  I think it was a mixture of feeling uninspired / rushed.  I think all of my students love foldables, but they are really crucial to the success of my IEP students.  These students need examples to look out.  They need a reference to remind them what steps to take.

I've embedded my absolute value foldable below.  I think next time I teach this unit, I want to have my students write out more of the steps that you go through to take your input x to reach the output y.  Because this doesn't capture that process, it is not an amazing resource for my IEP students or students who were absent the day we went over this lesson.

Day 3 of our unit focused on graphing absolute value transformations.  In Oklahoma, Algebra 1 students are only tested on horizontal and vertical translations.  I used the same graphic organizer that I used with my Algebra 2 students at the beginning of the school year.  I'm more worried about my students realizing that changing the equation will shift the graph than making them memorize what aspect of the equation creates what shift.  That will come in Algebra 2.

Absolute Value Transformations
In one class, one of my students wanted to write "It went jogging" or "It went on a diet" to describe the transformation of number 5 above.  My students definitely know how to make me smile!  Life is definitely never dull around them.

To illustrate that last statement, I have a story to tell.  One of my students borrowed my three-hole punch today.  She was taking colored paper and using it to create dividers in her binder.  Instead of returning it to my desk when the bell rang, she left it on her desk.  The next hour, my 8th graders arrive and start working on their bellwork.  After completing our "Beat the School" problem, I hear one of my students saying "What in the world is that?"  When I look at him, he is frantically pointing at something in front of him.  I'm imagining all kinds of terrible creepy, crawly, or yucky things that could be causing this response.  No, he is pointing at the three-hole punch.  He's never seen one before in his life.  I thought he was exaggerating.  No, he was telling the truth.  I tried my best to explain the foreign concept of a three-hole punch.  Other students started confessing that they didn't know what it did either.  Finally, another student demonstrates the three-hole punch.

Instead of amazement, the questioning student responds with confusion.  Why would you need something to punch three holes into your paper?  Realizing that I can't assume anything, I asked the class if anyone else knew what a three-hole punch was.  3 hands.  Out of 9.  Two-thirds of my class has never used a three-hole punch.  Oh my goodness.  I attempted another explanation.  Do you know what a binder is?  It has three metal rings.  We use the three-hole punch to punch the holes in the paper so we can put it in the rings.  To this, I was told that it was really unnecessary.  Instead, my students thought that notebook paper was meant to go in the rings.  That's why notebook paper comes with the holes.  Any paper that doesn't come with the holes is meant to go in the pockets of the binder.  Some days I wonder what this world is coming to...      


  1. Sarah - the Graphing Absolute Value booklet was exactly what I needed!! Thanks so much for sharing your experience. This is my 13th year teaching middle school math, but my first teaching Algebra, and your blog has really been an inspiration as well as a great resource.

  2. y 13th year teaching middle school math, but my first teaching Algebra, and your blog has really been an inspiration as well as a great resource.

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  5. LOVE the activities, especially the age guessing game. I'll bet they will remember it for sure. And the award story is pretty funny (yet, sad...). And WOW--how do they not know what a 3-hole punch is??!! Great post! :)

    Tales of Frogs and Cupcakes