Category Archives: Visual math

Ten Percent Increase – Pt.2

During the last blog post, I described the circumstances at the beginning of the year (September 2017).  Teachers were fired up about comments made by our superintendent.   As a matter of fact, there were teachers who attended and spoke at a board meeting.  Let’s just say the board wasn’t thrilled by our superintendent’s words.  

And this brings us back to my school.  My principal called me into her office one afternoon and we had a long chat.  She wanted to make the after school intervention strictly about math. (We already do 4-5 hours of reading intervention each week within the school day).  She wanted to overhaul what was happening.  She wanted the after school program to have direction/purpose.  (I don’t know what the program was like in years prior).  She asked me what I could do for the school.  Um…..where/when do I begin?!?!  Off the top of my head, I bounced some ideas to her.  She liked what she had heard.  I got to work on the preparations.

She was looking for consistency across all grade levels.  She was looking for routines beyond the textbook.  My K-5 colleagues had been dealing with Envision Math for years, so they needed something fresh.  Biggest obstacle of all, we needed to make math engaging and worth a child’s time to come after school for 3 extra hours a week.

Here are questions that I grappled with before I started planning.  How do I hook students into an engaging hour of math afterschool for 3 hours a week?    How can they become active leaners rather than it becoming a study hall/homework help?  Most importantly, how do I convince my colleagues that my program is worth their time and energy?  How do I get everyone on the same page?

And for the next 6 weeks, I was teaching 6th grade and designing a full math intervention (from the ground up).

  • First I built a schedule and it looked like this…..

Screenshot 2018-09-13 07.28.35

Take notice that this was a schedule built on everything I learned in the past 4 years in conferences and via Twitter.  My principal was giving me the chance to train our teachers on all that I had learned (well….maybe not ALL…but certainly a lot).    

Here’s the breakdown of each component.

Number Talks – consisted of a bunch of pictures from my files and other websites.   Each teacher was given a a file of over 200 pictures that included “Which One Doesn’t Belong”, dot images, and powerpoint of any number talk images.  Some pictures were found on while others were pictures I have collected over the years.  All teachers had to do was find a picture they liked, show the image, and have a conversation.

Fluency Games – rather than practicing our fast facts with worksheets, students would engage in games/activities in which they practiced their facts.  I gathered all kinds of games from Pinterest or TPT (Only the free ones that looked worth while).  

Front Row/Freckle – this is a free website for students to get more experience with problem solving.  It’s engaging (unlike some others I’ve seen).  Students gain coins as they  conquer different topics.  They love it!  

Numberless Word Problems  Brian Bushart introduced math educators to numberless word problems.  Taking the numbers out of a word problem and then “layering” information helps students focus on the context of a problem versus becoming “number pluckers.”   

Performance Tasks  –  In the Envision text my teachers were using, the performance tasks were really weak.  Performance tasks can be effective for students to apply what the skills they have learned.  With a discerning eye, I gathered performance tasks for 7 grade levels (kinder – 6th) for them to practice with the students.  

I wish I had a picture of all the binders of information that was given to the teachers.  7 grade levels worth of all these magnificent routines.  Each binder was at least 1 1/2 inches thick.  Each teacher had number talk pictures downloaded onto their desktops ready to go.  They were thrilled.  Maybe I went overboard with providing  them with each and every single piece of this puzzle, but I didn’t want any excuse as to them NOT doing the program.  The only thing they had to do was figure out which performance tasks or game to use.  No research needed.  And NO EXCUSES.

It was a labor of love to put the program together.  However I would be remiss if I said it was all me.   It wasn’t all me.  I can put together an A+ program, but it achieving a 10% increase was a team effort.  There was buy in from every teacher at my school (including the Transitional Kinder team!)  There was support and leadership from our principal.  It was a school wide effort to help the students.  

  • We were the only school in our entire district to pull a double digit increase in mathematics.
  • 6th grade nearly doubled their scores!  
  • Every grade level increased!

I need to get packing for Palm Springs (CMC – South).  Excited to do not one, but 2 sessions on Clothesline.  Stop by and say hello.  

Until next time,


New Routines for 6th grade

In my district, there are several 6th grade teams at three separate elementary schools. They are an anomaly in that they are invited to secondary professional developments & textbook trainings with other middle school teachers, but yet they are their own special group.  It’s not easy to have secondary expectations, all the while being at a site with kindergarteners passing by your window.  With all these new expectations, new standards, and a new curriculum guide, I saw the need for help.  Me –being a middle school teacher turned math coach–jumped right in.

Our latest venture at one site has been to start math talks.  I introduced them to Which One Doesn’t Belong, Estimation 180 and Would You Rather. They were excited by these routines because they are engaging for the students.  It’s not their usual math.  It’s different.  The teachers are now sparking conversations with the pictures and questions.  It’s been incredible for them.  I recently took their principal on a math walk into the three 6th grade classrooms so she could observe their new routines.  The principal was supremely happy.


One popular thought that came up during our work last year and this year was a simple question….how do you review previous units?  How do we keep information that we did at the beginning of the year fresh?  For instance, 6th grade began the year introducing rates and ratios.  Part of their “Would you rather” routine reviews rates.  For instance…would you rather buy a Starbucks Venti for $3.59 or a Starbucks Grande for $2.99.  Essentially we are asking which is a better buy. We are starting a math argument.

So how do you bring fractions, decimals, percents, and ratios to life?  How do you make that lively and different from what they see in their textbooks?   Well…let’s first look at this pic….

Donuts from a gift bag at Target

What do you see? What do you notice?  What math questions could we ask?

What fraction of the donuts have green icing?  What’s the ratio between sprinkled donuts to stripped donuts?  What percentage of donuts have chocolate icing? What fraction of the donuts have purple icing?  Can you turn that into a decimal?  

A simple routine comprised of many pictures of donuts, cupcakes, legos, or any variety of objects.  I’ve seen many math educators use pictures like this to start a visual routine/number talk.  Pictures are an amazing way to wake the students up and look at things differently.  I might bring this routine to my kindergarten teachers as a sorting activity.  

So many donuts… many possibilities.

Until next time,


Clothesline Fractions

Fractions is one of the “F” words in math.  (The other is functions, but I’m not working with that grade level).   Whenever these two words are said, teachers usually groan with frustration (that other F word). Understood because both can be hard to understand for students.  Part of my job is to turn that frustration into FUN!

Third grade has been working on their fractions for the past 4 weeks. This week I went in to work with them.

First I started off my visit with a number talk using a picture that has been floating around Facebook.  This picture had the potential to initiate lots of discussion and it surely didn’t disappoint.

5 watermelons

I let the students just stare at it awhile. Rather than taking observations and questions right away, I like my students to just have quiet time to internalize what they’re seeing. Next, they shared with their elbow partners their thoughts and questions. Then, I let them share their thoughts with me.  Watermelons provoke lots of discussion (who knew?).  Lastly, I asked them what possible question I could ask of them.  One of the teachers rose her hand and said, “how many watermelons are there?”  Being picky about words and vocabulary, I politely added to her question.  I asked the students “how many WHOLE watermelons are there?”

Here are some of the highlights of the three classes’ discussions….

  • I see eight pieces of watermelon.
  • They are in a square.
  • It looks like an optical illusion. It’s kind of like the 4 outside melons are the frame and the half melons are the picture.
  • Some of them look like Pac-Man
  • How are they standing up like that?
  • Finally, the quietest girl explained how she saw 5 watermelons.

Onto the class activity.  The third grade knows I come with something different, innovative, and unique.  I like to surprise them.  I didn’t invent this idea.  As a matter of fact, my inspiration was from a workshop I had attended given by Andrew Stadel.  He introduced me to Clothesline Math.   I wanted to use this idea of an interactive number line with fractions.   I envisioned a single clothesline with students approximating where to place certain fractions between 0 and 1.  However, one question lingered.  How can I maximize the engagement with the whole class in this activity?  Print out 30 fraction cards?  With my active imagination, I saw kids running for the number line, tripping over each other, and ending up in one gigantic entangled web of limbs, fraction cards, and rope.  Yeah…that wasn’t happening.

After a trial run in my office, one of my colleagues suggested that I put up two clothes lines.   LIGHT BULB!!!  That was it!  Split the class up.  13-15 kids working on a number line was a much better option than 30 kids per one number line.

So happily, I strung up two number lines in the classrooms (one in the front and one in the back).  I printed out about 20 fraction cards on colored cardstock.  I not only used unit fractions, but also chose equivalent fractions, and pictorial fractions.

The students were stoked and excited.  I promised them that they weren’t being timed (don’t like to pressure students with that element) but emphasized that they needed to work as a team.  Off they went.

One of the teams decided to analyze and read all the cards first.  Good strategy.  Other teams just started grabbing cards and ran for the line.  One of the teachers approached me and asked if the kids could use their fraction bars.  My compromise was to let them work for 10-15 minutes first before using their fractions bars.  They ended up only using their fraction bars to check their work after their number lines were completed.  Very resourceful.

Here’s something I found intriguing.  One of the kids clipped together these two cards as equivalent fractions (see below).  He saw the picture as 1/5.  I intended for the answer to be 4/5, but could a student validate this as equivalent fractions?  I asked one team this question and none of the kids wanted to take ownership of it.  I think they were embarrassed to admit to it in fear that they would be wrong.

4/5 or 1/5?

As a closing activity, we did a “would you rather” question.  Would they rather eat 2/3 box of cookies or 4/5 box of cookies?  They could write out their reasoning on the paper.  They were allowed to use whatever strategy they could to validate their reasoning.   I didn’t get to see how these turned out as my time ran out with each class, but my hope is that it was worthwhile.

After the excitement of the day, my mind is reeling with other concepts that could be used on the number line.  The third grade teachers also want to use the clothesline concept for other topics.  This especially excited me because it means I’m empowering my teachers to try new things in their classroom.



Share your thinking!!!

I love it when my teachers take an idea and run with it.  Not only did a teacher run with it, but added even more to a suggestion.   And that’s what I saw today.

One 4th grade teacher that I’ve been coaching (Mrs. P) had asked me to work with her on number talks.  She had wanted me to demonstrate a few on division and fractions before she tried one herself.  And that’s exactly what happened.  A few weeks back, I did one on division (one that I’d seen on the Teaching Channel) and I did another one on fractions.   I whole heartedly admit that they didn’t go as well as I had wanted, but we live and learn.

This week, we continued our work on number talks especially with fractions.  We went back to the basics.  We watched a video online (Dr. Jo Boaler) and went over the purpose of the talks.  Instead of over-complicating matters, we agreed to simplify the process.   Let’s use number talks to gauge where the students were in regards to their background knowledge of fractions.  Perfect.

We started off with a visual from Which One Doesn’t Belong.IMG_6186

I sat back and listened intently to what the students were saying.  One student says “It’s not about which ones don’t belong, it’s about which ones DO belong.”  Mrs. P asked him, “How so?”  Some of the students noticed that the top two fractions were equal.  Some students noticed that the bottom two were improper fractions.  They also noticed that the bottom two weren’t equal but similar (being improper fractions).  The students loved to agree and disagree with each other as long as they voiced their reasoning.

Mrs. P and I debriefed really quickly at the end of that session.  She had the biggest smile on her face as did I.  It was a success.

But then the awesomeness kept going!

She asked the students to create a thinking map with another WODB on fractions.IMG_6188

She turned the whole idea of numbers talk with WODB into a full class activity.  Each student had to first pick a fraction (that they thought didn’t belong) and then write down their reasoning.  The students were interviewing each other.  There was tallying going on.  There was “writing in math” happening!

This was incredible!

Some examples –


The check marks represent how many agreed with that statement.
The students even interviewed me.


Here’s why I think it worked –

  • With number talks, you may not hear from every student.  By doing this, the teacher got to see/read about their knowledge of fractions and get every students’ participation.
  • Teachers have difficulty figuring out how to incorporate writing into math.  This was one example of how to overcome that.
  • Students are using math vocabulary to explain their reasoning.
  • In this class, the students don’t always collaborate well.  This gave them time to work together.

Mrs. P and I have been on this math journey together.  She’s the type of teacher who wants to push her practice and just do better with “mathy” stuff (her words).   I appreciate that we can have real conversations without worry of judgement or pressure.   It’s exciting on my end to see her grow as a teacher.  She’s one of the reasons I love being a coach.





Number Talk Images

Can I just say that I can’t get enough of visual math routines?  Or do you call it a number talk image?

Some call it a visual number talk.   It’s a picture that’s shown with a known quantity.  Students may start by making observations and ask questions that are lingering in their heads (AKA Notice/Wonder–thanks Annie Fetter!)  Once their questions are answered, they may try guessing a number that’s too low.  Next they’ll try to guess a number that’s too high.  The last number they’ll write down is an actual estimation.

Why should we do this?

  • Develops students’ understanding of quantity
  • Give numbers meaning
  • Help students see the relationships of numbers to one another
  • Support an understanding of how numbers operate

The conceptualization of quantity is foundational to number sense. As students’ abilities to visualize amounts improve, their number sense improves. Their strategies and mental math become efficient and quick.

Once I was introduced to this routine, I was ADDICTED!  It became a mission of mine to find my own pictures.  My goal was to develop a collection of everyday items (thanks Target!) that any other ordinary human would pass up.  Well, this April Fool has you covered.  Every now and then, I stumble across something and take pics like a crazy person.  And yes, I will sit there and count.

So here is something I came across during the after-Christmas sales. How many storage boxes are there?IMG_5834

Just in time for Valentine’s.  How many hearts are on the front side of this bag?



If you are interested in more of these, I suggestion Andrew Stadel’s Estimation 180.  And if you are interested in more images ,Pierre Tranche’s Number Talk Images is really cool.


Oh…and not to leave you hanging.  There are 60 storage boxes and 388 hearts.