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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  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?

Thursday, October 15, 2015

Slope-Intercept Card Sort - Google Drawing

Click here for a link to a copy of the card sort.

The link above is a copy of the drawing, so feel free to change (and use) it how you like, it will not effect mine. :)

I was creating a notes template on google drawing when it occurred to me that google drawing can replace my card sorts.  Yes!!  No more paper to print, copy, cut, and laminate!!

Students simply open the copy of this google drawing, click and drag each equation on to the corresponding graph and submit their work.

Tuesday, October 13, 2015


This is my school district's first year in their 1-to-1 initiative called Project OLE (Olympian Learning Environment).  Our mascot is an olympian.

Because we are 1-to-1, I think it's time I try a learning management system in my classroom.  At first I assumed that Google Classroom was the way to go.  My IT showed me how to use Google Classroom and then mentioned Schoology.  I know very little about either one, but decided to try Schoology because I hear it has more bells and whistles.  

So, without any training or anytime to play around with it, I jumped in.  Honestly, what's the worst that can happen?  (<-- That is not foreshadowing)  I created an account, gave the students the class code and POOF, I now have a learning management system.  Yay!  It's so easy.  

You hear this all the time but it's true:  You don't have to be an expert in technology to use it in your classroom.  The students are very knowledgeable with technology and are eager to help.  I started the class by being open and honest with the students and told them it was new to me and I wanted their help.  

My favorite feature so far: grading.  This is wonderful.  No papers to collect, no papers to carry back and forth to grade, and students can submit from home.  

Anyone else use schoology?

Wednesday, October 7, 2015

Expression Polygons

In the August 2015 issue of Mathematics Teacher the article Expression Polygons by Colin Foster caught my attention.  A quick google search lead me to a PDF of the article if you'd like to read it.

Just this morning my colleagues and I were talking about the struggle that students have when faced with an expression.  They are programmed to solve, so they insert an equal sign where ever they can.  Even Algebra II students.  I feel that this activity is a great way to help students understand the difference between expressions and equations.

In a nutshell, the students create 4 expressions and set each one equal to the others, so that there are a total of 6 equations:

Try it myself:

Before I try a new activity with students I like to try the activity for myself.  Here are the requirements I'd like to give the students:

  • Create 4 expressions where the 6 solutions will all be different integers.
  • Two of the expressions are of the form __x +- ___.
  • One of the expressions is of the form x +-____.
  • One of the expressions is a constant. 
It took me 6 minutes to come up with this, so I think it's a reasonable assignment for my students.  

For the Students:

I introduced the project to the students, put them into groups of 2 or 3 students, and gave them this link for a copy of the template.  Click here for template.  

I gave each student a copy of the rubric.  Click here for the rubric.

There was a lot of productive struggle going on in my classes.  One thing many groups were doing was not getting an integer answer, so they erased the entire equation rather than working backwards for a solution.  

Many times I hear the students say that the assignment was hard (not as a complaint though) and I was ready for them to give up and say that it was impossible.  But, this assignment must have had the right amount of flow to keep them going because not one group of students gave up.  

I also like all the bonus stuff we got to talk about other than solving equations.  First was vocabulary: expressions, equations, vertex, and polygon.  Students had many questions as to what an integer was since all the solutions had to be an integer.  And believe it or not, in high school the students wanted to know if there was a difference between 5 divided by 1 and 1 divided by 5.  

Action Shots:


Here are some of the students' work ,worts and all.

I found this one interesting with all the same solution of 5.  

Monday, October 5, 2015

How to Implement Games in the Classroom

Since playing more games in my classroom, I've been stumbling though the implementation part of it.  Trial and error really.  My hope with this post is two-fold.  For one, I want to reflect on my lesson/game planning.  And two, if any of you are considering using games in the classroom perhaps you can learn from my trials (and errors).

This is a little tricky, since different games have different objectives.  For instance, some games are created to introduce a topic and should be played before the lesson.  However, other games are meant as more of a review or reinforcement and would be played after the lesson.  Here is my flowchart of a unit of study.


The idea of previewing a topic before pre-testing is new to me.  Typically I would start by giving students a pre-test.  I read about previews in the book Mindsets in the Classroom by Mary Cay Ricci.  The book suggests that before giving a pre-assessment, to quickly preview the material.  It even states that 5 minutes or less will do.  We could show a few examples on the board, watch a short video clip, or have a class discussion.


I teach Algebra 1 and most of the material that I cover has already been touched in to some degree in previous courses.  But how much was covered and how much do they remember?  You won't know unless you pre-test them.  Remember to share the results with the students, but be careful with their egos the first time.  I seem to get students who are not accustomed to pre-assessments.  They often tell me they feel stupid.  Once they become familiar with pre-assessments they understand that they will feel better once they have the chance to compare the pre- and post- test results.

Play the Game:

Most of the games that I play with the students introduce the topic so I'm going to focus on game play that takes place before the lesson.  I generally don't tie the game to curriculum with introductory games until after game play.  Every once in a while a students will say something like, "I enjoy playing this game, but shouldn't we be learning some math?"  Ah, but you are.  I like this element of surprise when I show them how the game is actually teaching some math concept or at least a connection to a math concept.  I think this sudden and surprising learning experience is effective.

Teach the Lesson:

When game play is over and it's time to teach the lesson, I often refer back to the game.
"What numbers would you use to capture this city?"
"Pretend this ordered pair is one of the character in the game.  How would you get him to this ordered pair?"
Just as it is important to help student make connections between topics in our curriculum, it's also important to help them make connections between the game and the topic it covers.

Post Test:

Once I feel that almost everybody will be successful, I give the post-test.  However, once in a while I will give the students a test even when I know they're not ready.  I use it as formative assessment to see what areas still need reinforcement.  Sometimes this includes the game and sometimes it doesn't.

Repeat as Necessary:

I feel it's important for students to know that the teacher will work at their pace.  If a class is struggling with a topic, the teacher will go back and help them.

There you have it.  This is my general guideline for playing games in the classroom.

Thursday, September 24, 2015

Hidden Squares Activity Goes Digital

Remember my hidden squares activity that I wrote about last year.

Click here to read about that.  You won't be sorry, it's a great activity.

We just finished this activity with 3 of my classes, roughly 65 students.  As much as I enjoy this activity, I do not enjoy the little scraps of paper all over the floor, the students who still cut paper as skillfully as a Kindergartener, and the  s l o w n e s s  of the students' pace with just creating the posters.  Not to mention the grading.  I don't mind the grading, it's just that I'm not willing to drag them all home to grade, I try to get them done at school.  Oh and I almost forgot to complain about buying the supplies.

Then I received an email from our tech coach about making virtual posters with Google Drawing.  If only she had sent this one week sooner.  Better yet:  why didn't I think of this?

4(x + 2) + 3x + 5 = 34
4x + 8 + 3x + 5 = 34
7x + 13 = 34
7x = 21
x = 3

Here is a link for you.