How I use Open Middle Problems in the Classroom

I love talking about OM problems, and when I do I always send the message that OM problems can fit into almost any aspect of your lesson- that you can decide when or where. I always assumed that people understood what I meant- now I realize I was being that teacher! I have had many people come to me after talks saying how they would like to know how I use it within my classroom. Before I forget to address this and give another presentation, I want to have an outline in my blog.

My daily routine typically looks like this: Bellwork -> Lesson ->Exit Reflection.

OK, this looks pretty simplistic, but I try to keep it that way. When I first started teaching, my school implemented the Developmental Design for Middle School and in their training, they had a lesson template that really connected to me for how I wanted my day to progress. I have been using the Origins Lesson Plan Template ever since (and each new Administrator asks me about it- but has always seen the value of it to me and my classroom). It looks like this:


As you can see, even though I go through 3 transitions in my classroom, how they look and feel can vary. It gives my students the safety of knowing what the daily routine is, but give them the variety to keep things fresh, new, engaging.  So my

Bellwork -> Lesson -> Exit Reflection  translates to:

Plan & Prepare -> Options & Work -> Exhibit & Reflect on the lesson plan.

Now, in my talks I say that OM problems can be used at any point in this, so let’s look at how that could happen.

1)   Bellwork OR Plan & Prepare

Everything I use in class has a purpose, it’s never time-filler.  As such, I make sure to pick bellwork that will get students thinking of the upcoming lesson OR use concepts we talked about yesterday so that we can build upon them in the lesson for today.  So one OM problem I like using for bellwork when we talk about functions in 8th grade is this:


I like this problem because even though it seems too open-ended, it can generate a lot of good discussions.  Unlike a lot of other OM problems, it doesn’t provide students with a “fill in the box” format but it allows students to generate as many (or as little) points in the table as they want. I typically have students write their tables on the board and as a class we discuss whether they are a function or not.  There are times I have DESMOS on the SMARTBoard and I enter the table when we are unsure. In 8th grade my students have an idea of what functions are or are not, and this sparks a lot of prior understanding and learning which primes them for the lesson.

2)  Lesson OR Options & Work

I will keep with the functions theme through this example, but I will not use an OM problem more than once in any part of my day. It’s good to use them to challenge students, but if I am throwing too many/too often at students it looses its effectiveness.  Let’s say I get done with a great lesson on functions and want to assign practice problems for students to explore, solidify and demonstrate their understanding. I do not believe in the “Do 1-60 odds” philosophy of homework, I did not benefit from this practice as a student and do not believe in it as a teacher. I do believe in providing students with a homework assignment that is manageable and have them thinking of math outside the classroom for 15-20 minutes of their day.  As such, I like OM problems for this reason. Consider this problem:


Consider working on this problem as a 8th grade student.  Will they get a lot of practice? How many problems were assigned? Do they know what rate of change is and how it effects the points that lie on the line?  Will they have understanding of a function if they solve this problem? How can they demonstrate this? I believe they will have a solid understanding of functions and are ready to continue their learning of functions.

3)  Exit Reflection OR Exibit & Reflect

I’ve had a great lesson on linear functions, and I am positive all of my students understand what we covered. How can I be sure? Well I give them an Exit Ticket OM problem to check that understanding and provide data for tomorrow’s lesson. remember when I had the OM bellwork to tell me what a function wasn’t? Well I could give them that problem again with a few more constraints (limited number set, minimum number of points, etc) or I could give them something like this:


I would like you to reflect on this. If your students can correctly answer this, was it a good learning experience?

Those are they ways OM problems would appear in my classroom, implemented in any of the 3 transitions of my classroom. I hope this helps you envision how you can use OM in your classroom to make homework problems more challenging and interesting.


My Biggest Fail…

First off, I would like to really say thank you to Annie (@Annieperkins) for being bold and posting her failure this week.  It was a great story, reminder, and way to cope with what we do on a daily basis.  Read her awesome post here.


This is why I really appreciate the MTBoS, there is no way I could have these discussions and reflections without it.  It is a conversation I could have with my close colleagues (CLOSE colleagues, you don’t want everyone in the building knowing this), and even then when you are the only math teacher in the building it makes it hard to really connect with any condolences you may receive (because you know, our profession is SO much different than anyone else’s).  It is comforting to know that others experience the same struggles that I do.

I can totally relate to Annie’s initial fears of “airing out” her failure.  When I started blogging, I wrote one post to begin with, and didn’t post another for 6 months.  Why was this?  Feeling of failure and insecurity.  I started blogging because I wanted a way to have reflections and records of what I did through the years, but I will be honest in the fact that “putting yourself out there” is very hard and immensely daunting.  I mean, anyone can access my blog and read what I post, how will I be viewed as a person, teacher or presenter when I write about all of my shortcomings?  Even now, I rarely tell anyone about my blog in district- I still have that fear.  I’m getting better, and presenting at NCTM San Antonio was a huge breakthrough for me in this.  I am far from where I feel I need to go, but I am a lot more accepting of what I do here on my blog and twitter.

MCTM Pic.png

(Like this Pic, I love that I’m presenting- but I’m like “My eyes are closed!  Thanks Nicole, I look like a dumb-___!”)

So, off to my biggest fail- and I really have to thank Annie for making me revisit this blast from the past.  It was a turning point in my teaching career, and it started me down this path to seeking people, research and resources to make myself into the teacher I wish I had (yea, here’s also to you Tracy!).

It was early in my teaching career, and I had gone through 4 administrators in the first 3 years of teaching.  This year was proving no different, this was my second administrator for the year (the first had gotten into a car accident and passed away, so our middle school administrator started servicing both buildings) I was in my final year of administrator observations.  Trying to lesson plan for that many different administrators and being a new teacher is a HUGE stress factor, I was used to test-taking for that many professors- having to focus on what they deemed important and be evaluated by their exams- but when it was the determining factor for my JOB it was a whole different level.  Every administrator has a different focus and what they deem is important to teaching in “their” building.  This administrator was a traditionalist, so I tried to “please” him for my observation.

The lesson was an exercise in boring.  We had “student note” workbooks, which meant I spent the hour in direct lecture, drawing beautiful diagrams and defining vocabulary for students to then copy in their workbooks.  This was one of the most difficult lessons I did (for me personally as a teacher, this wasn’t my style), it felt wrong- and there was a particular student who felt that way as well.  I noticed him right after defining the term polynomial- he had his head propped up on his hand and had is eyes closed.  This particular student was one who was “at-risk”: he rarely attended class, he had numerous discipline problems, a challenging home life, and he was behind on credits- but he was extremely smart.  It took me a while to catch a hook on this student, and typically we had a good working relationship for class.  He liked the way I typically approached class, and could not do “traditional.”  His current status for this lesson wasn’t a surprise, and I tried to gather his attention by allowing students near him to share with the class, I taught from his general area instead of by the board- but I knew that if I called him out directly in front of his peers and in front of the principal there would be a problem.  It was a tough choice to make since I was being observed, but since he was seated off to the side and towards the back of the room, I allowed him some space and continued with class.


The principal left during our “direct lesson note-taking” and when that was done, I followed through with the schema and assigned practice problems.  Once I had this done, I approached my student and quietly talked with him in class about what he was doing, what we had covered and what would happen next.  He told me he had a really tough night, there was a fight at his home and he stayed up most of the night protecting his siblings.  He stated that no one ever came to the back of the trailer to their room, but he was afraid to sleep.  He also told me he was sorry because he knew the principal was there, but he couldn’t stay awake.  I quickly reviewed what we had went over, and he found a partner to work with and catch up on his notes.  Not a major deal breaker in the least- as far as I was concerned.

The next day, I had a follow up with my administrator.  That is where I found out that for the first time since I had been teaching, I failed.  He did not have any sort of rapport with the student who was sleeping in class, and once he had come to the principal’s attention, everything I had done in class after that was forgotten.  I was supposed to confront the student, get them awake and attentive- or send him to the ISS room to “rethink” his actions.  This was a very hard observation meeting for me to attend, this was my last year of mandatory assessments, my last year of probationary teaching, and this man held the power to end my career at the school.  Instead of sticking up for myself and my student, I shouldered the burden of being a bad teacher and was referred to a “master teacher” with which to work and council.  I received an hour long “in-house PD” lesson on the fine arts of classroom management and student behavior from him.  I had an extra observation that year from him as well as three more that was required from my co-operating teacher.  At the end of the year, on the last day of school, I was called into his office (in the middle school building no less) to be told that I was no longer a high school teacher and I was moved to the middle school.  I was to have another year of probation where I could be overseen by him personally.  I won’t go into that next stress-filled year but all I could think about was that I was the worst teacher ever.  I even actively sought out new positions in my area because I felt so much shame that I wasn’t sure I could work in the district anymore.


I was a bad teacher, so bad I had to move to a different school, teach a different grade, have a mentor and be personally watched over by the principal

It was difficult for me that summer, my teaching self-esteem was shattered.  There wasn’t any local teaching jobs open in my area and although I applied for any other related type of field I didn’t get any calls for interviews.  This left me in a low that I had never really felt before- I even almost went back to bartending just so I didn’t have to work another year for a man I was sure was using me for another year before sending me on my way.

I can’t thank my wife and friends enough that summer, they kept me doing things and always were great ears for me.  They convinced me to keep moving forward, to prove who I was and to take this new challenge and make the best of it I could.  Standing outside my car, outside that building and taking that first step into the middle school, his place of power, was a very difficult step to take.  Although I never gave into his vision of what kind of teacher I should be, the whole experience did shape me into the teacher I now am.

Wow, I can’t believe I actually just typed all of this and am going to put it out there on the web- but I do realize that now that I have I can start being more accepting of the smaller failures I have along the path of teaching.

Teaching students is the biggest act of being human.  I hated that most instructors feel they have to come from a place of absolute power and certainty.  I knew this was never the truth because all through school I thought about Math differently than it was presented to me, I played the game however and on tests I would replicate the work they wanted me to do.  There were times I forgot and I had many long talks with the teacher explaining my work.  As teachers we can’t be afraid to show students that we too struggle with work, make mistakes and feel like failures.  Students need to know that it’s OK for that to happen, but it doesn’t have to shape who you are.  We also have to teach them how to get back up from failure and keep going, no matter how hard it seems.  This is what being a teacher truly is.


I failed myself that day, and I failed my students- not because of my lack of content knowledge but because I was afraid to show an outsider who I really was and how I used that to create a learning environment where all of my students have the opportunity to be successful.  If you see me in class, you will see one of these being used by me, in a way I feel comfortable with that allows my students to own their own mathematical ability- not mine.


What did I realize a few years later (well, actually 3 years later when that Administrator also left the district)?  I was a good teacher, I made the right call for all of my students at the time, and no one in that room (other than my administrator) thought I was not doing my job or supporting them to my fullest.

Sometimes, being a “failure” is actually the best thing that can happen to you.  Thanks Annie for inspiring me to share this story and many more in years to come.

The Struggle is Real

If you have been following me on this blog or on twitter, you have noticed a change of tone in my posts.  I have been delving into issues concerning special education more and more.  This shouldn’t come as a surprise for those who know me, since I have had to pursue my special education license with the acceptance of my “new” job here at the juvenile center.  This has been a struggle for me, my journey in education was never intended to take this path- and I still want to cling to my title of mathematics teacher rather than special education teacher.  I continue to struggle with this difference daily, but one thing I am grateful for is the fact that since I have taken this journey it has caused me to question a great many things.


The first nagging question for me was the concept of an inclusive classroom.  From the reading I have done lately, there is a heavy emphasis on what we do with students with learning disabilities.  At the same time, the types of strategies and accommodations they suggest are such that would benefit all learners in the classroom, not just those identified as needing special services (and I blogged about some of this here).  Personally I can tell you that while I do have students with IEPs in my classroom, I know of many students who should qualify, but do not have a big enough discrepancy between IQ and performance.  With this knowledge, how can I lie to myself by thinking I am providing the best education for my students without changing my classroom practices?  The hardest thing for any of us is change, and many of us fear it.  We need to quit justifying what we are doing in the classroom and know is wrong- we are not doing what is best for the students, we are doing what is best for ourselves.  The last time I checked, I wasn’t doing this for the fame or money- I am doing this because of the kids.  Remember that when you are faced with new programs, curriculum, or assignments.  There will always be a lot of work up front, but once you get that accomplished you will find that you are enjoying what you are doing more and students are learning and having fun.


The second question that has come up is how general education teachers do not want to talk about how they purposefully design lessons for students with disabilities.  I co-moderate #msmathchat on Monday nights, 9EST, and while it gave me a wealth of things to think about- there were a lot of voices who remained quiet or provided “safe” answers.  I love msmathchat because its a fluid conversation, where we can throw out ideas and talk about them in a safe environment.  It has been the best PD I have found for a long time.  The past two weeks were different, and that could be my fault as a moderator but I also have a feeling that it was because of the topic.  We need to start purposefully designing lessons with these students in mind, and it can be used for any class.  Don’t run the same subject class two different ways because of the presence or absence of students with learning disabilities, always run them as if you do have them!  I have yet to come across research that proves students are hindered with these accommodations, yet I continually find research that says these interventions provide positive learning opportunities for all students.

I would like to hear of what teachers are doing to provide these positive experiences in their classroom, please send me links or comments!


The struggle is real, for me to define what kind of teacher I really am as well as how I haven’t purposefully designed my class with these interventions as a norm.  Time to make that struggle an accomplishment.

My plan for next year….

Sorry for the reblogged posts of late.  I am researching what kind of practices I want to incorporate into my classroom for next year and am “compiling” blogs about the pieces I need. 

As I work more and more with my 8th graders, I am of the same mind as Jim Scammell.  The students who are taking homework home and bringing it completed the next day are the ones who are good students and driven by grades.  Those students who truly need the practice leave their materials at school because they either go out and hang with their friends all night, or go home and take care of their siblings because their parents are going out and hanging with their friends all night.  Our district uses a Developmental Design behavioral strategy, and with that is a lesson plan layout of Spark/Lesson/Reflect- which is similar to Jim’s model of class.  I have 60 minute classes so my breakdown is normally 15/30/15 (For 3Acts, my time is typically 15 Act1, 30 Act2, 15 Act3).  During this time, I try to allow for as much in-class work as possible.

With that, formal Direct Instruction has gone out the door for me.  Typically I present student with some type of problem, or more recently a picture or video (in a 3Acts format).  I allow students to work on the problem, walk around and check in on students, and offer quick help.  One thing that my students are not used to when they first enter my class is the type of help I provide them.  I ask questions (normally those I listed in my previous blog), I never give answers and that throws students for a loop.  After a few minutes of good student struggle, I discuss things about the problem as a class.  We list strategies to try, and work through them.  One thing I don’t do during this is erase any strategy, just because it didn’t work the way the class is progressing through this problem doesn’t mean it won’t be helpful in future problems.  We get a problem done, and they are given another that becomes student led.


When that problem is finished, we hit the 30 minutes of practice and this is where I would look at splitting students into either similar solver or mixed skill level groups- depending on what activity I had planned for the day.  This is my time to give differentiated instruction to my similar solver students, and to support student discourse in the mixed level groups, similar to what was posted on the Life of Mrs. Rilley.  Which group students would be placed in would depend on whether it was a discovery day or practice/application day.  I really want to be careful of creating a “tracked” theme with myself or the students as evidenced by Fawn Nguyen.  There will be days where I will utilize both groupings.  When students are discovering or applying mathematical skills I want a mixed group so students approach the problem from all angles.  This also provides the opportunity for a lot of mathematical conversations about what method students should implement and whether their answer is correct.  During practice time I want to correct student mistakes or misconceptions and would provide work appropriate to their challenges with the mathematical concept (group students with a similar misconception, group by a missing skill, group students who have a great handle of the topic and provide them with enrichment activities).  With Ashli’s approach to grading, students would not see this as any type of leveling of “smartness”- and would realize the grouping as a result of need.

After we have the problem worked out, students would get either the big reveal or an exit pass.  When students receive the big reveal they would be expected to discuss the similarities or differences in their work and answer.  Students would show their work (via a doc-cam) and work through how they solved it and what troubles they encountered (if any).  Since I would have them in groups, there would be 4-5 presentations and students would share out reporting duties.  Before students left class in this scenario, they would be expected to complete an exit reflection form- giving me information on how they perceived the activity, what things were good/bad about it, and what they now know and still need help with.  This will help me “tweak” the activity to my student’s needs.

Reflection form

If my class is comprised of practice/application then all I really want to do is give them an Exit Pass that has problems from the practice on it, as well as 3 Reflection questions so that I can better address these problems for the next class period.  The problems on the Exit Pass/Reflection form would be graded in my gradebook, but not for students.  Instead, questions about their work will greet students to create conversations about what they need to correct.

Exit Pass

Using these forms will allow me to differentiate instruction for the next day, which will improve student performance in class.  I am still thinking out formal end-of-unit assessment, but this plan is really taking shape in my mind and I am excited to implement it for the upcoming year.