Wow where do I start?

Ok so I didn’t come up with this idea out of nowhere.  I was reading this awesome book–> Number Sense Routines by Jessice Shumway and I had this awesome class of students who were lacking in number sense.  They were also a class of students who were very used to being unsuccessful in math and most of them did not enjoy interacting with mathematics.  After reading through chapter 4 (Counting Routines) I thought my high schoolers would be much more receptive to sitting in a circle and counting than using visual routines (Chapter 3). So I decided to try it.  If you are going to dive in and try this I HIGHLY recommend reading chapter 1 and Chapter 4 (if you can read the whole thing, please do).  Chapter 1 discusses what number sense is and talks about subitizing, unitizing and lots of specific skills that most math teachers never thought of.  My definition of number sense was almost verbatim described in Chapter 1 of this book!  In a nutshell, its a great book for any math teacher even though the book states K-3 grades.

Moving on to WHY? I came up with this idea.  You can read about it here (THE BLAME GAME) and read through my #TMC13 presentation here.  In a nutshell, I am unable to live with myself if I allow students to graduate high school (pass my class) without having  mental math strategies.  It is equivalent to allowing a student to graduate from high school without being able to read.  I refuse to be part of this movement anymore.

So I start this idea with my high school class of 12 students who’s only relationship with mathematics was very negative.  To be completely honest, these students’ relationship with school was very negative and they were kind of ready to give up on school all together.

Counting circles in general seem on the surface like a routine that is just done 10 mins a day however it is much more than that.  They help start a culture change in your classroom.  They give students the opportunity to own math, to be successful in math, to “create” and share their strategies, to make mistakes and learn from them.  They are asked to verbally describe their mathematical thinking not just write it like we have always asked kids to do.  You will find that students are NOT used to these kinds of activities in math.  Learning a new way to feel and be in math class (at least if you are doing these in gr 4-12) is not a FUN process for students.  They are scared!  School has trained them, for s0 long, to conform to learning as a  feeling of success and ease at all times.  For anyone that has actually LEARNED anything this is very far from the truth.  The learning process is messy, ugly, scary, tiresome, filled with failure, extremely hard and you normally pick up scrapes and bruises along the way.  So when you start counting circles in your classroom it is extremely important to start slow.  Start with something students will be successful with: Gr 3-5 start with counting by tens starting on either a decade or non-decade number, Gr 6-8 start with counting by tens on a non-decade number, Gr 9-12 start with counting by tens on a non-decade number. (These recommendations all depend on where your students are, do not start with these if you know they will be unsuccessful)

When I started this with my class I started with counting up by 1s.  Yup I know what you might be thinking…”Why 1s? That is too EASY?” YOU. ARE. EXACTLY RIGHT!  My students were so hesitant to do math that I had to start with 1s.   I had to build their trust with me and the trust within themselves.  Everyone can count by ones so I knew that my students would have NO excuse not to be able to participate.  I also wanted to change their mindset about mathematics and the relationship they have had with mathematics (extremely negative).  So I needed a hook.  I need to show them that they CAN DO math, that they aren’t unsuccessful ALL THE TIME.  This is where you start the culture change in your classroom!  You are giving them the opportunity to change the mindset have had about themselves for years!

So you’ve decided what you are going to count by and what you are going to start at….Now what?!  YOU COUNT IN A CIRCLE!   I normally ask for volunteers (“who’s wants to start for us today?”) and we start there and I decide to go counterclockwise or clockwise.  Depending on the number of students my classroom (I have done it in as big of a classroom as 30 5th graders) I normally go one time around the whole circle and sometimes more.  It really depends.  When I am starting the routine and want them to get used to the routine I make sure that the focus of the counting circle is not on the math but more on feeling successful (hence the choice of starting easy) and the way the routine functions.  So students count around the circle and I’m paying attention to what they are saying, how much time it is taking them to answer, any fingers being used to count or any other type of non-verbal clues students are showing  me as to how hard the adding is for them or strategies they are using to find their answer.  In addition to this pay attention piece, I am writing their answers on the number line as we go around the circle.


This is an important visual piece to counting circles that makes it attainable to all.  Also it allows me as a teacher to hear any mistakes students might be making with place value or verbal descriptions of numbers.   It also gives students who don’t have a lot of mental math strategies to use the number line to look for patterns to help them with another aspect of the counting circle:  Stop and guess (I will get to this shortly)

As students are counting I am writing the numbers they said on the number line and I am also pay attention and making note of any common errors I see.  As a teacher you already know some hard transitions for students to make while counting.  For example:

  • Counting up (or down) by 10s on a non-decade number common error happens when counting to the next place value unit and also the teen numbers (i.e. 97, 107, 117,..)
  • Counting up or down by tenths common error happens when counting to the next place value unit (9 tenths and one more tenth makes the next whole number not 11 tenths)

The basic errors that happen can all be pretty much pinpointed to place value unit changes.  As you do more and more counting circles you will see common errors and will be able to anticipate errors so you have an idea of what you want to ask in the stop and guess part.

While we are talking about errors another part of the counting circle is that I (THE TEACHER) DOES NOT correct ANYONE!  If a students says an answer I write it up and I DO NOT EVEN HESITATE!!  I keep counting, I keep on moving along.  I wait to see if any students will speak up or if there are lots of whispers happening after a couple other people have said their numbers.  If a students says something I make sure that the way they say it to other students is using what a colleague of mine calls “synergizing” language.  For example: “Can you please check your answer?” “I want you to check your answer”  The key to this is that students are NOT being talked to negatively.  You do not want to hear “that is WRONG!”  This ties back into the culture change in your classroom you want students to feel safe and comfortable to make mistakes and learn from them instead of them being reprimanded and feeling stupid for making those mistakes.

After you count around the circle, see some common errors, now is the time to stop at someone.  This is where my paying attention part allows me to decide where I should stop.  I normally stop on a number that students made errors on or in the past I have seen students make errors on or if I want to see IF they are going to make a common error.  When I stop at that student I write his/her name under the number and then I choose how many people down the circle they have to guess.  For example: “What number is Ashley going to say?”  <–Ashley might be 6 people down the circle from the person I stop at or 7 people or whatever you decide based on what you see students struggling with previous)  In the example below, we stopped at Kauhi and I asked them “When you figure out what number Megan is going to say, put your thumb up.”

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Now we be patient and wait.  We give kids as much time as possible.  I have done this in a class of 30 fifth graders and I will wait and expect them to also wait patiently while everyone is able to come up with an answer.  If someone doesn’t put their thumb up we continue to wait until they are ready or at least pretend they are ready.

Now comes the fun part!  NUMBER TALKS!

I have students share ALL their answers.  EVEN the ridiculous ones!  I can’t stress enough how important this is…ALL ANSWERS!!  Take them all!  The wording I use “What answers do we have?”  “Are these all the answers?  The number you were thinking about in your head is on the board?”

After I take all answers from any students I ask for volunteers to share HOW they got their answer.  This piece I am not going to describe because it is basically a number talk and you can find lost of info on the internet about number talks but I have also added my video of jotting down one of my students strategies.  I normally try to take around 3 DIFFERENT strategies and I make sure to put the students answer, their name and to write ONLY WHAT THEY TELL ME VERBALLY!  NO ADDING TEACHER THINKING IN!!  VERY IMPORTANT HERE!!  We are asking kids to be verbally specific about math and I want them to learn that their words are not specific enough or maybe they are but I write exactly what they say.  I often here “you know what I meant” and I tell them “I am only writing what I hear you say”  This forces my students to think about the way to verbalize their mathematical thinking (addressing SMP 2, 3, 6).  After they have shared sometimes I have to verify the answer so I will start where we stopped and continue to the person we were guessing and confirm what is the correct answer.  This normally only has to be done in the first half of the year because after they get accustomed to the routine they are critically thinking about answers and are able to catch their own mistakes more often and don’t need the validity piece.  After the number talk is over the counting circle is over.

Once this routine gets used regularly and gets built into your classroom it should take no longer than 10 mins.  I normally only do one circle a day, everyday for 8-10 mins.  That is basically it.  I have added one more video for an example and I still working on more videos to show the various ways counting circles change based on classroom and students.  There is no one set way to really do it.  I am kind of outlined a good start here but there have been lots of days that I ask different questions:  “What mistake do you see in today’s counting circle?”  “Who is going to say (certain number?” etc.  I am in the process of starting a website that will have a post a day for a counting circle progression.  I am hoping to get that started by next school year.  Sorry for the delay and thank you for being patient.  For now I have compiled a album of pictures that I have taken for some important reason of my counting circles throughout the 3 years I have been doing them.  Feel free to ask me on twitter (@wahedahbug) or via email (hhs.mathplc@gmail.com) if you would like a description about the picture or if you want to chat more about counting circles.

I am briefly going to just list some of the math “things” that counting circles address without really going into them:

  • Problem solving
  • Standards for Mathematical Practice: 2, 3, 5, 6, 7, 8
  • Perseverance
  • Linear equations
  • Patterns
  • Mental math strategies
  • Multiple strategies for 4 basic operations in all different number rings (whole numbers, integers, rationals, etc.)
  • Adding polynomials
  • Metacognition
  • Formative Instruction
  • Self confidence (in relation to mathematics)
  • Igniting math interest
  • Skill practice
  • Classroom Routines
  • So much more that I will be updating continually

Here is a good overall video of how counting circles works in my classroom.  Please note that this video is with a class that needs a lot of support with counting circles so I don’t normally help as much but because I need to adjust to what my students need I have to give more support for this class of students.


By Teachers, For Teachers! #TMC13


Twitter Math Camp, a place that you show up and everyone knows your name. A place where people know you before meeting you in real life because you interact with them on a daily basis via twitter. It’s a professional development conference that is designed BY teachers FOR teachers! GUERRILLA STYLE!

I have gone to some PD in my years of being a teacher and I have to say that nothing gets better than a session that a teacher is sharing something they have used, within this past year, IN THEIR CLASSROOM. It is hard to “unsell” me on this concept, that I should at least TRY their ideas they are sharing with me. Why you ask? Because this teacher is not a company selling their product or marketing their new teaching strategies or whatever else shenanigans you have experienced at other PDs sessions. Instead this professional development consists of  teachers sharing ideas that have worked for them.  They aren’t getting paid by TMC (as far as i know) to present on ways to make their class more engaging, how to orchestrate a math discussion or what determines stickiness of a lesson.  This is one main reason why I was determined to attend TMC this year (not to mention meeting amazing like minded people).

I can’t say enough about my state of mind  at TMC.  It was very similar to ____.  Being surrounded by people who have shared ideas with me to help me become a better teacher.  Being surrounded by people who one of their main reasons for being a teacher is to make a difference in children’s lives.  Being surrounded by people who when they say they are student centered truly mean giving up a piece of them to create a classroom focused on student success.  Being surrounded by people who take the utmost pride and honor in being a teacher for the future of our up and coming communities.  Being surrounded by the only math department I could ever have, being the only high school teacher at my school.  Being surrounded by people who love mathematics and nerd out on it even more than I do!  How do you describe this experience in a word or phrase?

I got to fly from LA to PHL sitting right next to the biggest ROCKSTAR EVER, Fawn Nguyen (@fawnpnguyen).  Get greeted and hugged in the middle of baggage claim by the most generous, Nathan Kraft (@nathankraft1). Ride backseat with Julie Ruelbach (@jruelbach) as I RT her tweets.  Get tackled by my sister Hedge (@approx_normal) as my friend, Nik (@nik_d_maths), from the UK is somehow in front of me in real life!!  Getting twirled by Justin Aion (@justinaion) and being welcomed by the amazing Philadelphia street arguments (yes someone punched a glass door and shattered it).

Thursday starts the real reason I came to TMC#13, TO LEARN!  But I can’t forget my long awaited hug from Karim Kai Ani (@karimkai).  And WHAT!!!!!  Ms. Ginny Stuck (@gstuck)!!  HOLEY MOLEY I have been waiting for this day forever!  We start our trek to our Algebra 1 session.  Michael Pershan (@mpershan) pushed us to produce a usable product out of this session.  Oh boy did we accomplish that.  After two days in the Algebra 1 session we came up with a pretty sweet progression for teaching linear equations.  My team members were amazing to work with Sara (@msrubinteach), Matt Owen (@_MattOwen_), Caitlin (@caitbbrowne), Peter O’Byrne (@pwobyrne).  Our progression can be seen here and we are still working on updating it.

In the afternoon the MAGNIFICENT Anne (@sophiegermain) told me to “SHUT UP AND LISTEN!” and Mr. Max Ray (@maxmathforum) helped me notice and wonder much more than what was around me.  Both of these presentations gave me some great strategies to add to my “teacher toolbelt”.  Next up was, Mr. Christopher Danielson (@trianglemancsd) who showed me more ways to use the 5 practices for orchestrating math discussions and how to use tootsie rolls in an amazing fractions lesson.   And to finish off my first day at #TMC13, Mr. John Berray dazzled me with ways to make math more memorable in your classroom.

After all the fun learning I did on Thursday I couldn’t wait to hangout with some of my tweeps at the karaoke (NOT care-e-oki) bar!  But first my long awaited room sharing with THE MAGNIFICENT…..Kate Nowak (@k8nowak).  OH EM GEEE you guys!  She is one of the most amazing women I have ever met.  Can I be like her when I grow up?  I have no other words to describe how awesome it was to share a room with this woman and thank you for allowing me to do so Ms. K8 😉

Dinner preceded the karaoke bar and I got to sit, eat and chat with Mr. Francesco Noschese (@fnoschese).  Meeting him and chatting with him is something I can CROSS OFF my #bucketlist.  It was so amazing to actually meet him in person!  I can’t wait til we open our own school together (I am kind of not joking here Francesco).

Karaoke night was amazing!  Besides the fact that we were all breathing each others breaths the whole time!  It was so extremely hot down there!!  However, the night was fun and I got to do something I have been waiting forever to do…..DANCE WITH MY SISTER, HEDGE!!  I will not go into detail about the type of dancing that happened but let’s just say I….PLEAD THE FIFTH! 🙂

Friday morning was filled with finishing our Algebra 1 product.  What was kind of cool was I got to chat a little with Steve Leinwand (@Steve_Leinwand).  Need I say more??? #speechless.  The afternoon was filled with lesson sharing from my favorite math team Mathalicious (aka The `Lish, @mathalicious).  They were using their fancy new @Desmos stuff and I was totally jealous!  I also figured out why Chris Lusto (@lustomatical) tweeted a while back about disappearing after planning this TOP SECRET lesson.

My next session was run by none other than Elizabeth Statmore (@cheesemonkeySF) where she showed us how to make lessons “sticky” (icky).  I learned some GREAT strategies that I would use in my classroom.  My favorite was when Marsha (@MarshaFoshee) and I sat back to back and had to take turns describing step by step how to calculate the slope of a line.  It was a great strategy that I am TOTALLY going to use in my classroom!

Next up was my own presentation which went well.  I just need to make the time to get the resources fixed up and posted on the wiki.  I know I am a slacker.  I am hoping to get it up by the end of the month at the latest (no promises).

Friday night’s activities consisted of a DUELING piano bar, which was a first for me!  I had never heard of  (let alone been to) a piano bar.  It was super cool!  Many requests were made, the SWEENSTER (@sweenwsweens) got roasted and Nathan Kraft (@nathankraft1) did quite the Beyonce cover (Single Ladies).

Saturday morning had me sitting in the high school “Peel It Back” session with The `Lish (@mathalicious) team members Chris Lusto (@lustomatical) and Kate Nowak (@k8nowak).  I learned quite a bit of strategies and questions to add to my already extensive and time consuming lesson planning techniques.  There were great discussions had and many of them ended with more questions than answers (as it should be).

Saturday afternoon was where all of us math teachers and oober-nerds were ooohed and aaaahhhed by the captivating and extremely genius Eli Luberoff (@eluberoff).  He showed us the new happenings of the @desmos team and also showed us some up and coming features that are shortly to be revealed.  I just want to point out that this @desmos team is basically amazing and as Michelle (@park_star) said:


My last session was not picked by me.  I was basically following people and ended up in DOCTOR Raj Shah’s (@drrajshah) Using games to promote mathematical thinking session.  OH BOY!! Was I glad to have followed my friends because they did not lead me astray…This was an awesome session with some great games!  There were 3 games, that I saw, that forced us to use logic and reasoning to play.  I am guaranteeing that I will be using these games in my classroom.

We got lost trying to get out of the building and broke Chris Lusto (@lustomatical) PROOF –>


Got out when we ran into Max (@maxmathforum) and learned a fun fact about him – he trains service dogs!

We made it to the main lobby thing where THEE most AMAZING stats teacher was collecting data (@approx_normal).  DOCTOR Raj Shah (drrajshah) and I teamed up to calculate our horsepower.  I was worried about falling down and making an ass of myself so I ran up without skipping stairs.  Turns out this is the best strategy to get the slowest horsepower! #LAME

I ended up at New Deck Tavern with @rdkpickle (sexy woman), @sweenwsweens (hilarious jokester), @calcdave (Calculus Davidson), @sarcasymptote (cool city cat), @jruelbach (dancing queen), @lustomatical (tattoo junkie & soft teddybear) and @k8nowak (superwoman) where they collaborated on #TMC13 theme song.  This is where we met one of the MOST AMAZING servers EVER!!!!  MACKENZIE!!!  Chris basically said it “Its hard to find good sass these days!”  Mackenzie could not even be topped!

New Deck

Our group migrated to the Farmer’s Cabinet where we got to see an amazing old timing band and Karim (@karimkai) showed off his knife drumming skills 🙂

old band

My night ended with a trip to the convenient store with @samjshah (queen bee), @jruelbach (dancing queen), @compactspaces (David Price), @k8nowak (superwoman), @j_lanier (chuckles) and getting some amazing FROYO that put all of us in a food coma!

OH NO!!! wait…..how could I FORGET!!  MY GOOD NIGHT HUG!!! Given to me by one of the sweetest persons I met.  Greg Hitt (@sarcasymptote).  This guy plays ukulele to his students to be less helpful in his class.  He is also the one person who I said HI to every second I saw him and I had to also ask him what his last name was because I just kept referring to him by his twitter handle (yup that is how famous is air bud jokes are!)  Thanks Greg!  YOU are awesome!  And he gives great hugs people!  go out and get yours from him!

I left Sunday morning with Calculus Davidson (@calcdave) graciously taking me to the airport so Miss country bumpkin didn’t have to be so scared to ride the bus, taxi or train.  I am not going to lie I am ALWAYS scared to ride public transportation even on my small little island.

There are so many people I have missed and I know it!  Please don’t be offended!  I am very good at remembering your FACE but not the name verbally (visual learner).

I want to close with something that has stuck in my brain since being a part of this MTBoS.  There are so many amazing teachers out there in this world and there is no way that we can do it all by ourselves but when we get together and share these ideas with each other and push each other to be better teachers there is no stopping the difference we can make in a child’s life.  As the saying goes here in Hawaii:

`A`ohe hana nui ke alu `ia

No task is too big when done together by all!

Thank you all for pushing me to be better than I ever thought I could be!


*Kate Nowak (@k8nowak) falling out of the elevator because we were laughing hysterically at being in the “cool elevator” HAHAHA!!


*Being taught about how avenues and streets work and the distance involved in the unit of “blocks” by the coolest city cat Greg Hitt (@sarcasymptote)

*Christopher Danielson (@trianglemandcsd) recommending that I present about counting circles at other math conferences.

*Anytime I was able to interact with the FAMOUS Francesco Noschese (@fnoschese).

*Dragging my two friends Mitzi Hasegawa (@mmhasegawa) and Judy Keeney (@JudithKeeney) to #TMC13 and them TOTALLY enjoying themselves.

*Riding the plane with this amazing woman named Fawn Nguyen (@fawnpnguyen)!

Camera 360

*Meeting Chris Lusto’s (@lustomatical) parents.

*Waiting for our trivia and watching the mishappenings of Philly with these characters!

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*Meeting Optimus Prime (@rawrdimus).

*Sitting adjacent to the superhero loving woman, @mgolding!

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*Witnessing this amazing bromance evolve! @eluberoff @karimkai

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*Getting an amazing hug in the lobby by the tallest woman in the world, Ashli (@mythagon)!

*Getting drooled on by this handsome English Bulldog.

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*Dinners with Team`Lish (@mathalicious) and the most genius and cute Eli (@eluberoff).

*My first taste of a cheesesteak and chicken and waffles with my laughing buddy Matt Lane (@mmmaaatttttt)

*Chatting it up with Steve Leinwand (@steve_leinwand) and him saying he will NEVER drive to my town again.  (yup that is how bad the road is people, consider yourself warned/lucky but also please come visit sometime)

*Smelling sweaty armpits with Nathan (@nathankraft1), you had to have been there to understand 🙂



*Making sexy eyes with Rachel Kernodle (@rdkpickle) every time I saw her.

*Being extremely jealous of EVERY SINGLE outfit Anne (@sophiegermain) wore at #TMC13.  (Plotting to steal her wardrobe as I type this)

*Meeting Chris Robinson (@absvalteaching) and realizing how skinny and tall he is!  Which is basically not equivalent to his amount of amazing-ness!

*Hearing Elizabeth’s (@cheesemonkeySF) radio voice.

*Seeing in real life how absolutely ADORABLE Michelle (@park_star) is!  Girl you are too cute!

*Being yelled at by the Queen Bee (@samjshah)

*Walking around a REAL city and living in the eastern time zone for 4 days.

*Spending 4 amazing days with a group of people who truly know me and share the immense passion for teaching with me.

By Teachers, For Teachers! #TMC13