Analyzing Shapes- Open Middle Problem

Directions: Using the diagram, fill in the blanks with the names of the shapes to make each statement true.


__________ has more sides than __________

__________ has the same sides as __________

__________ has more vertices than __________


Note: you can choose to have students reuse shapes or use them only once.


Describing Shapes- Open Middle Problem

Directions: Using the following picture, complete the following sentences (using the phrases: above, below, beside, in front of, behind, and next to)

Shapes with  no names.jpg


The cube is ___________ the sphere and ___________ the triangle.

The hexagon is __________ the pentagon and __________ the circle.


Use the shape names to complete the following statements:

The ________ is next to the ________ and above the __________.

The ________ is beside the __________, above the ___________, and below the ___________.

Try Something

The first couple of weeks are always fun, if stressful.  I spend the first 2 weeks introducing my students to the wealth of resources I will implement in the classroom, and today that was Graphing Stories.


My goal is to find a way for my students to create their own videos even though I can’t directly video them or their voices.  They all showed interest in this project, creating something that relates and connects math instead of requiring them to calculate.

This year I introduced the topic a bit different, I am still building my classroom into a safe zone for students to think and share ideas.  I told them the name of the website, and the particular video we were watching, in this case, Christoper Danielson’s How Many Ponies.


I only told my students this: that they would watch a short video clip and create a graph based on it.  I immediately had some students voice their concerns, wanting me to totally structure the assignment and outline every step they needed to perform.  I recognized their concern, most of my students are used to traditional math- performing algorithms in specific orders and steps.  They are the student who won’t attempt any assignment without first checking in with you, wanting you at their side while they work through a problem.  Many of these students are capable mathematicians, needing nothing other than the constant reassurance that they are doing the correct steps.  I try to transition them away from this dependence, to become independent mathematicians so they can become confident in their knowledge and abilities to problem-solve.  I reminded them the nature of what we were doing, that they needed to play with math- try things on their own without worrying about specific structures they needed to follow.  I reassured them after this “practice graph” (one that we were not going to grade- I mean who grades introductory tasks and ideas? How can we expect mastery on a  new concept?) I would give them some more information on the design of the website and what their task was when presented this type of problem.

After watching the video the first (and 2nd slow-motion) time, half of the students sat there and gave me the “tell me what you want” look.  A few even asked “what do I do now?”  My reply was simple, “Make a graph of what you just watched.”  I had Students reply “I still don’t know what to do!” I would ask them to “Try something.”  I reassured my students that I was not grading them on this first graph, I wanted them to play with math, try things when they were not sure, allow themselves to experience math through their experiences.  Most students did attempt some sort of graph.

A few didn’t, and I didn’t want to lose them. So I asked students to finish up what they were doing so I could ask them a question. When they did I asked them, “How many of you feel Math Class is a place where you have to solve problems the way your teacher wants, quickly and with no errors?”  Every student raised their hand.  I followed up with the statement of “I would like to tell you that I am not the teacher that expects you to all solve problems in a particular manner, if you have a question about a problem- expect a question back.  I need to ask you questions about how you think about a problem so we can work together to solve it.” I pointed to my whiteboard that still has the Four 4’s on it.  Just like the Four 4’s puzzle, there are many ways to think about and approach math.  I need to determine what your experiences and method is.”  While I was talking I first saw a bunch of deer in headlights, students who felt like the world was just yanked out from under them. Then things shifted a little as they looked at the work we did this this week.  Those students who hadn’t attempted a graph went to work.

We then talked about things I noticed while students were working: types of graphs, labels, shapes, etc.  I never used a student’s name or placed their work during this time- they are not quite ready for that step yet.  I saw I still need to work on making the room a safe place for them. As we discussed these things generally in class, I watched students as they compared what we talked about to their first attempt.  Of course, I saw many start to erase.  I quickly intervened on this, explaining that their first attempt was just a warm-up, I did not expect them to get it correct the first time they attempted it.  One student told me that they expected everything they did to be corrected, and correct- that’s how Math Class was.  I just replied, “Not in my Math Class.”

I then went over Graphing Stories in general, and asked them what they noticed when they first watched the video.  I asked them what those things meant in their assignment, and connected what they observed to what they needed to do.  We then watched Ponies again, and students were much more confident in making graphs.  Although Christopher’s graph was probably one of the most complex on the site, one I wanted to work with them on.  I was happy with how students progressed on this task, and I let them know that.  Overall Graphing Stories was a great lesson and discussion for students, and our goal this year is to create some of our own!


Diving Back In

Its the second day of classes, and I have done my usual upsetting of student’s beliefs of what Math Class is in School, even one in a Juvenile Center.  (Sorry I have taken a hiatus from the blog over the summer, but it was a much needed break and a lot of recharging)  Before I dive into blogging about things we learned this year, I want to reflect on a couple of the challenges that I continually face here so you understand some more of the challenges teachers in my situation face.

First- because of confidentiality, there are many things that tie my hands as an educator.  Although we can have some limited internet access, students continually find ways around firewalls and security to make contact with friends and family outside- which is a big No-No.  Because of this, I don’t have the luxury of implementing many of the inter-tech goodness that I loved at my old school (losing Desmos in this way is really killing me!).  I can’t video myself teaching, or students discussing things in class- and it’s very touchy for me even snapping pictures to post on this blog or Twitter.  This almost throws me into old-school methods for a new-school teacher, which can be a challenge of its own.  As such, I’ve had to be creative in what I do in order to keep things fresh in the classroom.  I DO have a SMARTBoard, so I can at least give them access to some of those things through my computer and access.

Second- the nature of having students in a Juvenile Center means that they have done some things that are socially not acceptable.  Many times the consequence of that is Separation- the inability to interact with a particular peer, or peers of the opposite sex.  Once again the start of this year, my students were on multiple separations.  I will have to wait a week (or until they earn their privileges back) before I can start instruction on group work. A result of this is that my room has not been set up in a work-station format instead of group-table format.  This is how my room now looks:


(or, it looked this way pre-service as I was cleaning from summer classes/setting up)

As many of you who know me, this is killing my normal teaching routine/style.  I try to keep my students working in groups and talking with each other about math as much as possible, so in an attempt for compromise between Center expectations and my own, I took two perimeter bookshelves from the room and placed them back to back in the center of my room.  That gave the tables room to be placed around the outside of my room and it set up a space I am loving so far.  I also teach LEGO Robotics so I need a workspace to run test tracks.  The two bookcases left a large crack between them, which doesn’t make a nice workspace for assignments or robots (I would be worried about what I would find at the end of the year), so I built a counter-top for it, one made out of white panelboard so I can use dry-erase markers on it.  I could have put in a work order for it, but the project only cost me $65 and a couple hours of work to assemble/finish the wood.


I am really liking this space so far, I have yet to use my whiteboard in class.  I have the students gather around the center island workspace to work out problems and brainstorm.  Students are also really liking the ability to write on the surface, stand and work, as well as having a more casual atmosphere for discussions.  Talks are flowing more naturally, like they would if were were just standing around talking about what they were going to do later that night.

This group is pretty rough so far, there are many new faces and they are not used to my approach to math.  Many have fully bought into the facade of mathematics: if they are smart/stupid, fast/slow, good at math/suck at math.  These first few days have been different for them, a struggle against what they believe math is.  They are having problems with they expect I want (procedures and answers) from them versus what I am asking of them (to just play with Math!).  So far they have experienced WODB, Visual Patterns, Open Middle, Gemini Puzzles and Four 4’s.  Tomorrow I will hit them with the 10 challenge from #BecomingMath, Estimation 180 and Graphing Stories.

This first week is about breaking down those established expectations and getting these Students in a place where they feel comfortable playing with mathematics.


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.