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.


Teacher Reflection 180: Day 14

Day 14:

Summarize today’s lesson in just one sentence.

When I first started asking this question, it was a way for me to get quick student feedback without it seeming too in-depth for students.  The first few times I ask this exit question, I am just looking for the quick and slick points from the day.  After I get student’s feet wet, I take a little more time at the end of class for this activity.  Much like I do when I work with the 3 Acts lesson, I collect student responses and start writing them on the board.  This allows students to see everyone’s thoughts from the class so they can make further connections to the concept (note: before responses get posted on the board, I always go through a check-in process with students where I read their response and ask questions for further clarification or details).  As a class we then go through all the responses and create one sentence that is a collection of student thoughts.  Typically I will leave these up on the board for a few days for student reference.

Things I think of when I read student responses are:

Do students accurately know the objective of the day?

As many can relate to, students can take a vastly different version of the lesson than what you intend.  I always think of this when I look at student reflections, am I doing a good job creating a learning opportunity that clearly projects the objective I am wanting it to?  If not, what message am I providing?  What changes can I make so that students create the connection I am intending them to?

How well can they describe it?  Do they have a strong or weak understanding of the concept?

Just because students can tell you what we did that day does not mean it sticks with them or that they even understand it.  A classic example is my son.  He will be watching TV while I am talking to him.  When he doesn’t break eye contact with the TV, I will ask him to restate what information I told him.  He can do so without any problems.  When the time comes for him to use that information however, he can’t remember it- or if he does he can’t remember why he needed it or what it was for.  Many of my students have this ability- they remember things very clearly in the short term.  The next day or even the next week however is a totally different matter.  They have not learned how to make connections to their long term memory- which creates “learning gaps” that many in the education field refer to.  When I look at student responses, it becomes fairly clear which students are making either short term or long term connections to the concept.  My next step is to engage student’s brains so that they can make the transition from short to long term memory input and access.  Currently this is where I am working, and hoping that these student reflection are impacting student’s long term memories.

What points do you need to review with the class to strengthen this understanding?

I like reflections, they give me a map to how tomorrow’s lesson should unfold.  I will typically use them to create warm-ups for the next day.  I also typically modify the lesson to reach back into yesterday’s concepts instead of assuming that it is mastered.  If there is a small number of students who are struggling with the concept, I will create a time in class to pull them into small group work where we can remediate and correct misconceptions from the previous day.  I hope that student reflections lead me to this scenario, that means that I am hitting the class as a whole (for the most part) and it allows me to provide quick, easy intervention in a small group instead of having to plan for large group review.

Overall, this is my go-to question for reflection.  It is short and quick but also provides a great basis on which to judge student knowledge of the concept.  I hope it works as well for you.

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.