A Tour of our Room – A Work in Progress

Welcome to our room.   It is a work in progress and filled with imperfections.   We are learning together and building it as we go.

We are working on being kind and brave.

We believe that making mistakes is part of learning.   We believe that everyone is good at something and no one is good at everything.   We believe that we can all be successful if we work at it together.


We believe in making sense of problems.

We believe that seeing is believing, so we have pictures of people who look like us doing amazing work in STEM.  We also believe that experiences change lives so we code all manner of things (video games, apps, robots, 3D printers)

We believe math should be collaborative and fun, so we have a lot of card sorts and games.    We also have a poster of Lure of the Labyrinth that was signed by the artists and developers of the game because we love Lure of the Labyrinth.


We believe learning happens over time, so we keep portfolios.


We believe life should have a little silliness.   We put elephants on our heads when we take a test and get a shower of wisdom by pouring the elephants on our heads on birthdays.


Our room is a work in progress, just like we are.




Be Brave – A Work in Progress

This afternoon, as I scanned the room, I was pretty sure that a good 2/3 of the students were confused by something.   I asked them if they understood what we had just been discussing.   I was met with a chorus of “yes”.   I looked at them and said something to the effect that I wasn’t really confident of that.   I stood in the echo chamber of “all is well” until suddenly one girl spoke up.   She said, “I don’t really understand.”    I looked at her and said, “I’m so glad that you were brave enough to ask for help.”   Then, I told her to go get a piece of candy from the candy jar.    After she sat back down, we returned to the problem and talked about it a different way.   Then, I heard a chorus of “Oh! I get it.”

We are still working on our quest to be brave.   Today, I hope we took another step forward.

Random (and not so random) Acts

Last week, as I was walking down an aisle in the grocery store, I had a sudden flashback to my childhood.   A little girl was hopping down the aisle, making sure to only land on the white tiles.   I smiled as I remembered doing the exact same thing, selecting a color at random and then looking for the pattern in the tiles to navigate my way.   Seeking patterns and building structure has always been the way that my brain works.

Given my penchant for structure, it’s no big shock that my daily classroom routine follows a regular pattern and has a definite structure.   (I do all kinds of different things within that structure, but I stick pretty closely to the overall structure.)     I close each lesson with a summary and then take the last five to ten minutes of class to revisit material that we have already covered.   It is a chance to force delayed recall and to try to find new ways to address something when the first time didn’t work well enough for some kids.   This is where I differentiate instruction most days.

My Favorite Thing – Random Acts

Every once in a while, I step out of my box.    Yesterday, after our exit card,  I gave students a different kind of task.   They had to select a random act of kindness.     They must do the random act of kindness sometime in the next week.   I had my student aides create the set of tasks.   My only direction to my aides as they created the tasks was that the tasks had to be free and they had to be something that kids could actually do with relative ease by themselves.    These are some of the tasks they created.

  • Hold a door open for someone.
  • Help someone who needs help with a problem (math).
  • Smile at someone.
  • Give someone a compliment.
  • Do an extra chore for your parents (without being asked and without drawing attention to it).
  • Help a teacher clean up the room (and doing it for someone who gives you a reward doesn’t count)
  • Save pop tabs for the Ronald McDonald House (our Builder’s Club collects them)
  • Make someone laugh.
  • Share paper or a pencil with someone who forgot theirs.
  • Save Box Tops for Education (our SPSO collects them)
  • Compliment your parent’s cooking

The ground rules are that the act must be done without seeking reward/attention and that it should be a small thing to make someone else’s day a little bit brighter.

This was a follow-up to two other closing activities.   First, I had students share one brave thing on a post-it.   About a week later, I had them share one kind thing.    These small acts of bravery and kindness that they have done or witnessed at school fill a space on our classroom wall.

I have a plan in mind for my next step on the “brave” front.   I don’t know how well it will work, but I am trying really hard to bring “Be Kind and Be Brave” to life.

Not So Random Acts – Only if you want a “math”y answer

After each quiz or test, I track each student’s mastery of the different skills/concepts in a spreadsheet.   I use this information to form intentional groupings for different activities.  Sometimes, the groupings match skill levels.   Sometimes, the groupings pair someone with mastery with someone who is still working on putting a concept together.    The only thing that is consistent is that the groups are constantly changing and that everyone is an expert at something and no one is an expert at everything.

Tiered Grouping

I use tiered groupings early in the year as students work on number operations.   Students  play Jenga to practice decimal division.   I have three versions of the game with three levels of difficulty (dividing a decimal by a whole number for students who don’t know the standard division algorithm and need some 1:1 or small group instruction, dividing a decimal by a decimal for students who are learning how to manage the decimal point, dividing a decimal by a decimal with a zero in the quotient for everyone else).  Students are assigned to a version of the game using a color coding system.   As students progress, versions of the game are retired.

Skill Grouping  

I use skill groupings for number operations  in addition to tiered grouping.    Students are assigned to play a game to practice a targeted skill.   Students play Don’t Get Zapped to practice decimal multiplication, rational number addition and subtraction, and rational number multiplication and division,   They use Fraction Fortune Tellers to practice mixed number addition and subtraction.   They use Fraction Flip It (a game with cards) to practice mixed number multiplication and division.   I set these games up as stations and I circulate, working with students as they play different games.  The games don’t have a high DOK, but they aren’t intended to do so.   They are fun ways to squeeze a little bit of practice into a routine on a regular basis.   I try to make my lessons higher DOK, so I don’t worry too much if the last few minutes are just fun.

Mixed-ability Grouping

I use mixed ability groupings most often.

Oftentimes,  I pair a student who has mastered a concept with a student who has not (none of them know this – I am just intentional in forming the grouping).

  • I do this with task cards where students practice making double number lines and tape diagrams.      (For some reason, some of my students really struggle with these models.    A lot of these kids seem to view math as algorithmic.   Pairing them with a kid who is more of a “sense-maker” seems to help them make sense of the model.   The combination of the kid talk and the “this is not going away – you have to learn it” seems to help bridge the gap better than anything else I have found.)
  • I  do this with “find the error in the graph”
  • I do this with card sort activities for all kinds of concepts
  • I do this with manipulatives that build 3-D shapes.   Students create the net, find the surface area, and/or find the volume.
  • I do this with exit cards using green/red marking.   I send a kid with a green mark to work with a red mark.   (I can’t have a 1:1 conversation with every student who needs help in a couple of minute span, but someone can. )

I do this with the whole class with Quiz/Quiz/Trade card sets or Give One/Get One card sets.   Right now, I am collecting spice mixture recipes from my students (trying to reflect their cultural experiences in some of our problems) to create a set of cards to practice modeling mixed number division.   (Too many of my students didn’t do well enough with this skill on our last test, so we are going to keep working on it.)

What Does Division Really Mean

Fraction division is a messy business.   Now that we have Common Core State Standards, students must be able to model fraction division in addition to performing the task algorithmically.   This is no simple task for many of them, because it forces them to grapple with the question of what it means to divide.   In order to do it successfully, they must really understand that division represents one of two things.   It can be dividing something into a specified group size to find the number of groups. (I have twenty four cookies and I want to make packages of 2 cookies, how many packages can I make?)  It can also be dividing something into a specified number of groups to find the group size.  (I have twenty four cookies and I want to serve 12 kids, how many cookies can they each have?)  They have to be able to read a problem and figure out which of those two types of problems it is and then form groups accordingly.     Making sense of these ideas and constructing a real understanding of fraction division is hard, even for a lot of adults.

As we were wrapping up our work with these ideas this week, I wanted to do a quick formative assessment to see where everyone was on these ideas.   I took two of the ACE  questions (this is the set of problems from which we draw homework assignments)  from the Connected Math textbook that I use.   Instead of using them as part of a homework assignment, I turned them into a Vote With Your Feet activity.

Vote With Your Feet is a Marzano high engagement strategy that incorporates movement into a lesson. In the activity, students are presented with a multiple choice item.   They move to different locations in the room based on their chosen response to the question (e.g., north wall for A, east wall for B, south wall for C, west wall for D).  The activity gives students a chance to get up and still stay focused on the task at hand.   It also is a really quick formative assessment, taking only a minute or two to see what each student thinks and where their misconceptions are (if the question is well-designed).

Here are the two questions that I posed.


I had students vote on each of the two items without commenting on their choices.    Afterwards, we debriefed both questions by discussing what problems each model might represent.   Kids talked to partners and in table groups.   The class talked about it together.    As we talked, I asked students to give me two division problems for each model.   What is the problem if you are dividing by a specific group size?   What is the problem if you are dividing by a certain number of groups.

These are two of my favorite problems for a formative assessment on fraction division.   This year, I used them as a Vote With Your Feet activity.   Next year, I might take the four options and make them Quiz/Quiz/Trade cards.   I might take them and just use the model and present it as a “here is the answer, what is the question” formative assessment.   In the meantime, I will probably go ahead and make Quiz/Quiz/Trade cards with problems like this to use as a quick review of fraction division from time to time later in the year.

What I Should Have Said

This week, I was presented with a powerful teachable moment and I dropped the ball.   A student said something and I was so stunned that I just stood there.   I needed words that I didn’t have.

I had commented to the student that I was surprised another teacher had commented that she wanted him to speak up more in class.  I was surprised because he didn’t show any reluctance in my class.   He was always ready to jump in with his thoughts.    He looked down at the floor for a minute and then this is what he said.  “In that class, I don’t want to make a mistake in front of everyone.   The questions have an answer and you are either right or you are wrong.   In your class,  there’s not just one answer and it’s OK to make a mistake.    We learn from our mistakes.  It feels safe.”     I looked at him and after a long pause, I said “I’m glad you feel safe in here.”

I’m glad that he feels safe in my class, but I feel like I let him down.   I didn’t have any wisdom.  I still don’t.   I want to tell him to be brave, to be fearless.    I can’t, though.  I’ve seen too many scars from the things kids say to each other.

Maybe I should have told him to believe in himself.    Maybe I should have told him that I believe in him.  Maybe I should have told him a thousand things.    I just don’t know what the right truth was for that moment.     I should have said more, but I still don’t know what it should have been.


One Brave Thing

Be kind and be brave.   These have been my parting words to my students each period of each day for 3 1/2 weeks.   I want these words to have power, to be words that echo in the hearts and minds of my students as they face all the big and small decisions that fill their days. I want these words to become the actions that populate their lives.   Saying the words matters, but it isn’t enough.

The question of “what next” has been hovering at the edges of my mind for weeks now.     Today, my students and I took a first step in our journey.   I had a few extra minutes in class today (which never happens), so I decided to use them in a new way.   I asked my students to each take a post it note and to write down one brave thing that they had done or that they had seen one of their 6th grade cohort do in the last week.   They then put their post-it notes anonymously on the “One Brave Thing” table.

This is what they created.


It is only a beginning, but it is a beginning filled with being brave enough to reach out to someone else who needs a friend, being brave enough to stand up for someone else, being brave enough to ask questions when they don’t know something, being brave enough to ask for help, being brave enough to persevere.   It is a beginning that fills me with hope.

Anecdotal Records – Three Ways

Anecdotal Records Take One – What Can You You Do

When we are about to start working with a mathematical process fraught with pitfalls and errors, I make an anecdotal record form unique to that process.   The form consists of a bunch of boxes (one for each student) filled with key components of the process.

img_1819 This  is one that I use when I teach students how to make a line graph.   I put a student’s initials in each box.   Each day, I walk around and watch my students work with this form on a clipboard, making note of what they can do correctly with a check and what errors they are making by circling an item in the box.   At the end of the period, I have a snapshot of exactly where each student’s mastery is. The next day, I know exactly what conversations I need to have with each student.   Sometimes, I use the same form multiple days and track progress by using a different color ink on different days.   Sometimes, I just use a new sheet on different days.


This is another one that I use for proportional relationships

I love using these kinds of anecdotal records because I know exactly what each student knows and exactly where I need to target instruction for each one of them.   The record keeping is easy to do during class and easy to access when I want to check progress.

While I primarily use this to target instruction, it is also very useful when I need to track progress for an IEP or SAT intervention.


Anecdotal Records Take Two – Knowing What Do You Do When You Get Stuck

While knowing what students know is important, knowing what they do when things get tough is equally important.   I found this form in  Mathematics Assessment – A Practical Handbook .


I like this form because it gives me a snapshot of where the student is getting stuck and what he or she does when that happens.

Anecdotal Records Take Three – Knowing Whatever Else 

I keep a folder like this for each class period.   Each index card corresponds to a different student.   (No, these are not all the students in the class.   There are more on the other side of the folder).  I put the student name on the bottom of the index card, and then use the lines to record relevant observations.  I date the line and then write whatever I observed.   I use these to document whatever I need to remember about a particular student.   It can serve as a record regarding a particular intervention.   It can serve as a record of behaviors.   Mostly, it serves as a means for me to detect and recognize patterns.   By using this, I am able to recognize things like a particular student being more of a sequential thinker or being more of a conceptual thinker.   Recognizing the patterns in the way a student thinks helps me do a better job of meeting his or her needs.


I keep the forms in “Anecdotal Records Take Three” in each folder.   The set of them are in a file holder on a table beside my desk so that I have easy access to them as needed during class.