Tuesday, November 24, 2015

How I Taught Absolute Value Equations This Year.

I'd like to share with you how my students learned about Absolute Value Equations this year.


...we started by playing The Absolute Value Equation game as a whole class.  This worked out well, because the students started class by taking a test on the previous topic and once they were all finished we played a few rounds as a whole class.  I split the class into 4-5 teams and they worked together on their turn.  This was a great way to explain the rules to the whole class at once.
Now that they know the rules, the next day I split the students into groups to play the game as a tabletop version.  This way, instead of teams, each person was playing against all the others at his table.

This is the first year the students played the game individually at tables rather than as a whole class.  They loved it.  Everyday since we played the game, they've been asking to play again.  I'm thrilled that they enjoyed the game so much.


...I lectured.  Yup, that's still important.  We talked about distance, absolute value, and subtraction.  I connected absolute value equations to the game and then connected it all to the solutions.  We solved absolute value equations algebraically AND graphically and compared the two methods.  


...we practiced.  I created 6 different stations for the students to work through. 

  • Card Sort
  • Worksheets
  • Challenge problems
  • Error Analysis
  • Educreations video
  • Play Absolute Value Equation game (optional)

To begin, I gave each student a copy of the stations/activities they needed to complete.  Click here for that.  

Card Sort:

For the card sort, I made 4 copies of them in 4 different colors, so that more than one person could be at this station at a time.  Click here for that.
I do give the answer key as well.  I found that most students are more interested in doing it themselves than cheating.


I created 3 different versions of the worksheet on math-aids.com.  Here is a link to that website.
Level 1 included "Monomial Expressions" and "Polynomial Expressions (no coefficients)".
Level 2 included all of Level 1 plus "Polynomial Expressions (with coefficients)".
Level 3 included all check boxes.

I included an answer key for all three levels at the station as well.

Surprisingly, the worksheet station was the most popular.  I guess that's what is most familiar to the students.

Challenge Problems:

I gave four challenging problems for the students to work through.  They are problems that we have not covered in class and asked students to dig a little deeper.  Click here for those.

I found that students were more willing to attempt and not give up on these challenging problems because there would be no punishment for being wrong.  And the reward was intrinsic.  I did include and answer key for all four problems at the station.  Most students did attempt the problem before looking and the answers.  Most.

Error Analysis:

This seemed to be new to students.  They wanted to just solve the problems on their own and then say, "The person should have done it like this."  They really struggled to find the error.  Click here for that.

Absolute Value Equation Game:

This station was optional since they have played this previously.  But, since the students enjoyed the game so much, why not?  You can read more about the game here.


We had some issues with the filter in my district, so we put off this station until after the test.  The requirements were that the video had to be under 5 minutes in length and it had to include solving simple absolute value equations by graphing, solving simple absolute value equations algebraically, and solving complex absolute value equation algebraically.    Below are some of examples of their work.

Here's an example of student work.  Absolute Value Equations.

The Exam:

Once I gave the students the exam it was just all too easy.  After the game, the lecture, the stations, the students were more than ready for this exam and it showed.  I had more students pass this year than in previous years.

What I Would Change:

  • I would change the worksheet.  I was running out of time and used a worksheet generator rather than creating my own problems.  Next year, I will create my own problems and worked-out solutions.  
  • The card sort was way too easy.  I would like to make one (or two) that are a little more challenging.  Such as blank cards that the students have to fill in.
  • I feel that I need to make the students more accountable during the stations.  A few students skipped some stations because they "didn't feel like doing them".  And those were the students who didn't pass the exam.  

Monday, November 2, 2015

Collaborative Teaching

I have this idea, but it requires my district to spend money.  Like hiring-an-additional-math-teacher kind of money.  So, I had better come up with a convincing argument to see my idea come to fruition.

My idea:
I have this idea to change the way we schedule and group students in math class.  I would like to try a pilot program with CP Algebra 1 (they are the students who have to take our state exams).  The students would have their Algebra class all scheduled at the same time.  This way we could easily switch up classes, groups, activities, lessons, etc.

For example, all the CP Algebra 1 students take a pre-test on a certain topic.  From there the teachers can plan how to proceed.  They could regroup the students homogeneously.  One teacher could take the students who scored low on the topic and need more assistance, another teacher could take the 'middle students' and work with them, and another teacher could take the students who seem to know what they're doing and work on enrichment.  They could also regroup the students heterogeneously.  The teachers could groups students so that there is one strong student in each group.

Assuming the total amount of students isn't too large, we could hold a whole group lesson/activity in the LGI room (Large Group Instruction).  I see review games like kahoot or socrative taking place and each teacher could play a role during these activities.

We have SBG and RTI in our district and I believe this model would integrate seamlessly with these two initiatives.  Those students who are not successful on a topic could be grouped together and provided more support.  Those who are successful can work on a project or activity to gain a deeper understanding.

There's also the option for research.  Teachers could regroup students as evenly as possible and complete different lessons/activities on the topic and compare results to see which method was most successful.

We know that students are more engaged in their education when they have more control over it.  The teacher could create lessons/activities and allow students to pick which one(s) that want to participate in.

Why an Additional Math Teacher?

If this were to be done correctly, the teachers involved would need time to collaborate.  Usually, when we ask for something like this we are told that we could be scheduled the same prep period.  It sound greedy when we say that we can't give up our prep period every day to collaborate with each other, but it's true that we some individual time too.  We need our prep periods to call parents, make copies, talk with other colleagues, attend meetings, grade papers, create lessons for our other classes, and attend to other paperwork.  I also use my prep period to stay connected to other teachers online through twitter, blogs, and other online PD.

In my district, we teach 6 classes and have 1 prep.  I'm proposing 5 classes, 1 prep, and 1 collaborative period for the teachers involved in this program.  Out of those 5 classes, 1 is the collaborative class.  Then of course, since there are multiple teachers teaching 1 less class, there is a need for another teacher to pick up those classes.

The question begs, "What will the teachers do during this collaborative period?"
The teachers will create lesson plans, activities, and projects.  They will review benchmark exams, pre-tests, exams, and other formative assessments.  They will share successes and failures in order to move forward.  They will work together to create dynamic students groups.  They will hold parent-teacher conferences together.  Notice the common denominator here: TOGETHER!!

Have any of you participated in something like this?  Can you poke some holes for me?