2017 – 18 Goal: Empower Teachers


I’m highly goal oriented.  It’s normal for me to be working towards a variety of goals – Personal,Tweet announcing MathTwitter BlogoSphere's blogging initiative professional, short term and long term. When I came across @ExploreMTBoS‘s tweet about their new blogging challenge, I grabbed my computer and started typing.

The one goal I’d like to highlight for this blogging challenge is to empower teachers.  As a TOA/Coach, I hear a lot about change.  Change that the district wants.  Change that principals want.  All of this “change” typically falls on the classroom teacher.  What do the classroom teachers want?  That’s where I’m starting this year.

Last school year, I switched from a Middle Level Math TOA to a K-12 Instructional Technology TOA.  As a district, we are going Google.  All district teachers have been given a professional google account.  Teachers have access to G Suite which includes docs, slides, sheets, forms and classroom (to name a few of the apps).  A major part of my job will be to run trainings and workshops on google apps.

At times, the job requirements feel overwhelming.  I choose to view that overwhelmed feeling as opportunity.  Since there are 4 Instructional Tech TOAs and over 2,000 teachers in the district, we organized a cohort of 149 teachers.  Thirty-seven elementary and middle level teachers are in my sub-cohort. As their cohort leader, my goal is to empower them.

The cohort models allows for flexibility.  Here are some inquires teachers have already shared:

  • Gather data using google forms
  • Start the year using the management system, Google Classroom
  • Learn how to use the chrome extension Screencastify to create listening stations as well as gather student evidence.
  • Use Google sheets to spark conversation
  • Use Desmos more purposefully

I’m looking forward to talking and especially listening to teachers.  Acknowledge their questions, concerns and wishes, then problem solve together to

  • answer their questions
  • address their concerns
  • make their wishes a reality


My next step … READ

Screen Shot 2017-07-31 at 7.09.48 PM

Art of Coaching.  TOAs/coaches in my district go back to work the week before teachers – which means we just wrapped up our first week of the 2017-18 school year.  For me, the week was spent attending a professional development workshop, preparing trainings and leading tech based trainings.

Carolyn, who lead the professional development day, peppered the workshop with a variety of thought provoking activities and protocols.  One activity resulted in this goal. We were presented with a prompt:

The peer coaching structure that I want to build on is  ____  because  ____

We were then asked to choose one of two reading options with the purpose to use the chosen text to answer the prompt.  I chose Aguilar’s blog post describing the framework, Mind the Gap,  Aguilar’s book has been on my must read list for many years and after reading her post, her book will be my next read.

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Desmos Graph: Adding Positive & Negative Fractions w/ Dynamic Labels


A picture of the mixed number 5 thirds

For the past 15 months, I’ve been working on fraction models.  When I brought the models to students, the resulting conversations were great.  Just what I was hoping for.  The downside stemmed from the behind the scenes “coding”.  My original design coupled with the need to import multiple images required lots of conditional statements and therefore caused the program to run slowly.  A picture of the mixed number 5 thirds

Recently, Desmos released their newest feature – Dynamic Labels!!  This feature is a game changer.  I no longer need to import number images.  I also abandoned my need to separate the parts of the mixed number for a more streamlined look influenced by @Klockmath  and  @nathankraft1 ‘s work.  The two changes reduced both the lines of “code” and the number of conditional statements thereby creating a tool with more usability.  You can find the graph here.


Positive and Negative Fraction Model

Now, it’s time to update all my old fraction models.  A task, I happily accept.   I began with a graph that visually represents adding positive and negative fractions.  Positive fractions are blue.  Negative fractions are red.  Use the black sliders to toggle between positive and negatives.

Positive fractions are blue      Negatives fractions are red

One fraction is stationary and the other moveable.  Use the moveable fraction to estimate the answer.


Toggle off and on the common denominator feature.
Toggle off and on the common denominator feature************************************************************************************

For the second picture, I copied the image onto a Google slide and inserted lines to represent the elimination of zeros pairs. Then used the scribble feature to circle the answer of 5/6.

Example 1:  4/3 + (-1/2) = 5/6

Positive 4 thirds added to negative one halfScreen Shot 2017-07-07 at 8.27.41 AM


Example 2:  -4/3 + (-1/2) = -11/6    aka        -1 1/3 + (-1/2) = -1 5/6

negative 4 thirds added to negative one half              Negative 4/3 added to negative 1/2


Closing Thoughts

I love summer. It’s my time to recharge, spend quality time with my family and work on projects too time consuming to complete during the school year.  That said, I’m excited to for the school year to begin.  Honestly, I can’t wait to get this fraction model into the hands of teachers and students.  Let the fraction talk begin!!



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Diving into Google Sheets: Adding Integers & Pixel Art Multiplication


In August of 2014, I stepped out of the classroom to become a middle level math TOA/coach.  After 21 years of teaching, I craved a different challenge and found that challenge with Desmos.  Once I learned how to make AB’s, I was hooked and began creating Activity Builders for my teachers.

Roughly 2.5 years later, I switched from being a Math Coach/TOA to be an Instructional Technology TOA.  My interest in Desmos was the catalyst. 18 Months of creating and testing activities, providing Desmos based PD and participating in the Desmos Cohort lead me down a new path.  The switch seemed inevitable.

Now, I work with teachers K-12 regardless of the subject.  This new position stretches my established tech skills while continually adding more.  The learning is constant and welcomed.

Level 1: Google Certified Educator badge

My district is going Google.  Our teachers received their Google accounts toward the end of the 2016-17 school year.  When school starts up again, student accounts will be activated.  Upon hearing the district’s plan for the first time, I began studying for and then passed the Google Certified Educator Level 1 exam.  While studying, Google Sheets became a high interest app.

Members of our Instructional Technology and Math TOA Teams attended a math based Alice Keeler training.Book: Teaching Math with Google Apps by Alice Keeler and Diana Herrington Participants received the book, Teaching Math with Google Apps that she co-wrote with Diana Herrington.  Her section on Pixel Art intrigue me. The combination of Google sheets, conditional formatting and math spoke to my creative side.  I had to create my own.



Alice, Me, Jorge, Caleb and Jen H.

Alice, Me, Jorge, Caleb and Jen H.


Google Sheet Math Activities

Although I  work with k-12 teachers of all subject areas, math will always be my first love. Designing and field testing math activities is a passion of mine.  My new position takes me out of my middle level comfort zone and broadens my client base.  For now, I can also collaborate and design activities for elementary and high school teachers.

The goal, for my first google sheets activity, was to create a visual representing the addition of integers.   It’s more of an exploration tool.  The open design allows students and teachers to use the tool however it best fits their needs. Click here to make your own copy.

Picture of the Integer Activity


Imitation is the Sincerest Form of Flattery

– Charles Caleb Colton

My second activity is not original in any sense.  I sat down with Keeler’s book, Teaching Math with Google Apps, read the section on pixel art and used her techniques to create a 4th grade multiplication activity.  The activity contains 3 questions.  1 question per sheet.  Click here to make your own copy.

Multiplication Question #1 on Google Sheets

Multiplication Question 2 on Google Sheets


Closing Thoughts

As I look forward to our district’s venture into Google Apps and my task of helping teachers of all subjects integrate more technology into their lessons, I feel compelled to state that technology alone is not the answer to increase student engagement and learning. Effective lessons overlap content, pedagogy and technology.  How a teacher uses technology to foster discussion, collaboration and reflection within their subject area is the key to creating engaging lessons and increasing student learning.


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Desmos Polygraph: The Periodic Table

A list of elements from the periodic table

Images from the website, The Dynamic Periodic Table.  http://www.ptable.com/


Picture of Heather Wingo


Desmos is not just for math teachers. To support this point, I created a Polygraph activity using elements from the Periodic Table. Eager to field test the Polygraph, I reached out to a few 8th grade science teachers.  Heather Wingo took me up on my offer.


A Desmos Polygraph is run similarly to the games, Guess Who and 20 Questions.  The program randomly pairs up students.  In the pairing,

  • Partner A selects an element
  • Partner B tries to figure out the element by asking yes and no questions.
  • Partner A respond to the questions by pressing the “Yes” button or “No” button.
  • For confusing questions, Partner A may respond with the third option, “I don’t know.

I’ve lead multiple Polygraph activities before but this experience stood out for 2 reasons. First, the type of questions students were not what I had expected.  Second, the conversation with Heather gave me insight to improving the activity.

The Questions

Parts of an element, atomic number, symbol, name, atomic mass and energy levels

Since students studied the periodic table months ago, I provided the pictured reference sheet.

Prior to the start, I set the condition. Students were not able to eliminate an element based on color.

When one student pushed the boundaries and asked, “Is your element blue?”  His partner responded by selecting the, I don’t know, option. This made me laugh.

I then began noticing unanticipated questions, such as

  • Is your element used in making a light bulb?
  • Is your element a metal?
  • Is your element a gas?
  • Is your element in group 1?

Eighth grade science teachers reading this maybe giggling at this point.  Or, saying, “Duh.”  Did I take into account the categories such as solid, liquid and gas, metals, nonmetals etc… , when designing the activity?  Yes and No.

There’s a strategy to creating a balanced Polygraph. My design decisions where based on using the symbol, name, atomic mass, atomic number and energy levels to eliminate elements.  Although I did feel states of matter would be another elimination category, I didn’t strategically incorporate that standard into the design.

My Conversation with Heather 

During the debrief, Heather addressed her curriculum in conjunction with the activity. Her points:

  1. Students need to know the states of matter (solid, liquid and gas)Students referencing a periodic table while playing the Desmos Polygraph: Periodic Table
  2. Students need to know which elements are metals, non-metals
  3. Students need to know which groups on the period table contain alkali metals, transition metals, halogens and noble gases
  4. Students need to know how to read, understand and identify parts of a periodic table

The activity I presented addressed point 4. She wanted to scaffold questions to include a discussion of points 1 – 3.  Our solution was to create a second Polygraph focusing on the states of matter, and the various types of metals and non-metals.

Closing Thoughts

This was my first time field testing an activity in Heather’s classroom.  As in every field testing situation, I walked away with more information that I walked in with.  I enjoyed listening to Heather share her content knowledge,  expectations of students and ideas for improving, or in this case creating a complementary activity.




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Desmos Marbleslides: 10 Frame Addition


Many many months ago, I saw an intriguing tweet. Kristin, @mathminds, had made a Desmos AB focused on 10 Frames and was inquiring about the possibility of an interactive one. Challenge excepted.  I viewed her inquiry as a chance to broaden my skills while providing a service.

After a few interactions with Kristin, I gathered enough information to begin, however without a way to count the number of dots within the frame, I couldn’t finish.  Thanks go out to Luke Walsh, @lukeselfwalker, who gave me the counting method needed to complete the activity. Here’s the AB:  Exploration: 10 Frame Addition.

I like giving students time to explore, observe and discuss what they notice AND I like having specific tasks for students to complete. Exploration: 10 Frame Addition, addresses the exploration.  My field trip to kindergarten provided the experience needed to build the challenge based activity, Marbleslides: 10 Frame Addition


Jenn working on the Prowise computer

Working on the Prowise touchscreen


Field Testing

Picture of Camille and Jenn VadnaisBeing a middle level teacher for over 20 years, I’m solid with grades 6 – 8.  Primary grades, especially k- 2, are a mystery.  It was time to head to kindergarten and conduct some research.

I partnered with Jen (elementary math TOA ) and Camille (kindergarten teacher).  We split the class in half.  Jen and I worked with one group and Camille the other.  Then after 25 minutes, we switched.  Students scanned QR codes on their tablets to reach the website, student.desmos.com, easily



Expected Outcomes

  • The zoom feature caused a learning curve.
  • Once students learned how to navigate the zoom feature, they enjoyed moving the dots and creating number sentences.
  • They were eager to share their number sentences.
  • They were able to find more than one number sentence for a specific number.
    • 4 + 4 = 8
    • 2 + 6 + 8
  • Camille wanted an activity that would provide immediate feedback for students

Unexpected OutcomesTwo 10-frames displaying the number sentence, 6 + 1 = 7

  • One excited student, showed me his example.  When asked to read his number sentence,  he said, “3 + 3 + 1 = 7”. His response caused a flood of observations and questions.
    • He was only focused on the dots, not the symbols.  Who else is doing this?
    • Where there other students who focused only on the numbers & not the dots?
    • Which students are connecting the dots and the numbers?
    • What questions can I ask to help students connect dots and numbers?
    • He’s not subitizing the number 6.  Who else is not subitizing larger numbers?
  • When a second student showed me his tablet and joyfully said, “2 + 2 + 1 + 1 = 7”, I knew I needed to formulate follow up questions.
  • Two 10 frames showing the equation, 5 + 2 = 7


Follow up Questions

Although asking questions is a favorite strategy of mine, I felt unprepared when responding to kindergarten students.  This experience caused me to reflect on my interactions with students and develop a line of questioning that would benefit both students and teachers.   Here are a few possible follow up questions.

If a students says, “6 + 1 = 7”

  • Will you show me your 6 dots?Two 10-frames displaying the number sentence, 6 + 1 = 7
  • How do you know that group of dots is 6?
  • Will you point to the symbol 6?
  • Where is your 1?
  • Explain how to make 7?

If a students says, “3 + 3 + 1 = 7”

  • Will you show my your groups of 3?
  • Will you count all of those dots for me?
  • What do your 2 groups of 3 make?
  • Will you point to the symbol 6?
  • Where is your 1?
  • Explain how you know the dots make 7?



Closing Thoughts

I’ve come to rely on field testing my activities – especially when I hit designer’s block. By highlighting areas of need, my kindergarten experience gave me the direction I was looking for.  I had to address the zooming action and create an age appropriate challenge based activity that incorporated immediate feedback.  My observations and conversations with students guided my future design plans.

Desmos’ marbleslide lab technology addressed all my design needs.  Marbleslides uses a fixed screen which fixed the zoom issue.   If the launched purple marble passes through the stars, then that trial is successful.  Therefore the marbleslide technology allowed me to create challenges that could be immediately checked by launching the purple marbles.

Teacher tip:  Camille requires her kinders to record their number sentences on a separate sheet of paper to draws their attention to corresponding symbols.

Desmos Activity Builder 1:  Kindergarten: Making 10 with Ten Frames

Desmos Activity Builder 2:  Exploration: 10 Frame Addition

Desmos Activity Builder 3: Marbleslides: 10 Frame Addition



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Flashcards for Faridabad

My Inspiration

A classroom of students in India.

My students are absolutely amazing!!!

My niece Kyra, who graduated from college in December, made plans to travel before settling down with a job.  She posted her traveling adventures on social media.  My heart skipped a beat when I saw the picture to the right. There had to be a way to connect her school with a classroom in my district.



Kyra had signed up to be a short term volunteer teacher at Kishitiz Public School in in Faridabad, India.  She was employed to teach 4 & 5 year olds how to speak English. Classrooms are baron of items found in an American classroom and she was using her own money to purchase paper and pencils.  Plans A and B were thrown out the window. Plan C – Flashcards.

Classroom in India filled with benches and backpacks.


The Project

I partnered with Kim, a 6th grade math and science teacher, and then introduced the Flashcard Project using My Maps, to her Exploratory Class.

Map of the world highlighting New York and India.

Map of the world highlighting Southern California and India.


The Project Details

The Prep

  1.  Using Google Docs, I created a blank template and an example
  2. I copied the blank template 20 times and stored them in a folder that I shared with Kim.
  3. For each of the 20 templates, I created a shareable link and toggled the settings to Edit.
  4. Used Google URL Shortener to convert the very long original link:  https://docs.google.com/document/d/1j8c-xga_D0UD1Ncp54IXDwyXIMlSUQElhJycNxdNw68/edit?usp=sharing  to  https://goo.gl/QJ7nXE
  5. Each template was assigned to a pair of students.
Spreadsheet: Names, title of document, link

Student names                    Flashcard template number               Shareable link    


The Day Of:

  1. Introduced the project
  2. Made sure the students were sitting next to their partner.
  3. Passed out the shareable goo.gl/ URL to each pair.
  4. Assigned the left hand column to Partner A and the right hand column to Partner B
  5. We all created one example flashcard together.
  6. Passed out themes:  breakfast food, lunch/dinner foods, shapes, weather, school supplies, transportation, vegetables, sports, plants/grass/trees, clothing etc….
  7. Students erased the example and created 6 flashcards that matched their theme.

The Benefits of Google Apps.

Hands down, GAFEs best feature is the sharing button.  With a few clicks, a document, slide presentation, sheet or drawing can be shared to colleagues or students.

The choices of edit, comment or viewThere are 3 permission settings: edit, comment or view.

  • Edit:  The person who you shared the document with can make changes to the document.  This is the highest permission setting.
  • Comment:  The person who you shared the document  with can add comments that appear on the side of the document.  He/she can not make changes to the document.
  • View:  The person who you shared the document with can only read it.  This is the lowest permission setting.

Our students were given full editing rights. Once they opened their template, they could add and erase content.  Pictured below:  These 2 students used separate computers to collaborate simultaneously on one template.

Computer screen showing flashcards.


In Faridabad, India

Screen Shot 2017-04-02 at 8.58.08 AM.png

For the video of teachers and students working with the flashcards, click here


The Follow Up

I want to see the kids using the flashcards”   – 6th grade student

When I scheduled the follow up visit, I had two activities planned.  First, Kyra’s video. Second, a survey using Google Forms.  As students where logging on to their computers, I observed one student turn to a classmate and say, “I want to see the kids using the flashcards”.   During the movie, students reacted positively especially when they noticed the flashcards they made being used.  The Google Form provided students with the opportunity to voice their reactions to the project.  Listed below are a few of the responses.

  • After the video I felt happy that the kids loved the flashcards. I saw how thankful they were. I am very happy that they loved the flashcards.
  • It makes me happy to see that because of all the kids smiling faces. It makes me feel good about myself that I did something good for kids, who cant afford all the things that we have.
  • I felt like I did something good, important, and happy. I felt these ways because, they looked so happy, and excited to learn English. Also, I got excited when I saw Lauren and I’s flashcard. The aftermath, I wish I could learn their language one day.
  • I felt like I help a lot of kids learn English words.
  • It was fun to make the flashcards
  • I was very happy to be making flash cards for kids in India. I had lots of fun making them. I love making people happy and I hope to be doing things like this more often.
  • I felt so happy seeing them so happy. I felt so proud
  • I helped out people that don’t have as much as me and it felt good to help a lending hand.
  • I love seeing the look on these kids faces as they learn
  • When i heard we were making flashcards for kids in India. I was excited because, I know transferring to a different language is hard. Therefore, I got intrigued in this making of flashcards.
  • I felt like I made a difference. Those kids at least learned 20 new words that they haven’t known before.
  • I enjoyed making these flashcards because I knew it was going to go to a great cause and i love helping other people. So thats why I enjoyed making these flashcards
  • I felt happy and a little emotional because of how thankful and excited the children were about learning.


Final Thoughts

In May of 2015, I wrote a post titled,  A Genius Hour Brainstorming Session – A Wake Up Call.  Here’s the opening paragraph:

Last month, my son participated in Claremont McKenna’s 3rd Model UN Conference. The College‘s President,  Hiram E. Chodosh, addressed the delegates during closing ceremonies. In his speech, he described 3 values that he believes all students need for success:  Creativity, Empathy and Courage.

I often find myself coming back to these 3 words.

I appreciate Kyra’s

  • courage to travel thousands of miles away to learn about her own culture
  • empathetic nature to volunteer her time teaching underprivileged students in India
  • creativity and determination to find a way to connect her students with mine.

I appreciate Kim’s

  • courage to run this project with me.
  • sense of creativity and empathetic nature for generating more ways to help the students of Faridabad.

I appreciate Kim’s students’

  • bringing a sense creativity to the project by determining themes and choosing words for those themes.
  • excitement, desire to help others and general understanding of the challenges when learning a second language.
  • courage to share their feelings
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Desmos Polygraph: Geometry Basics

16 smaller picturesToday, I had the pleasure of introducing Desmos Polygraph: Geometric Basics to a group of 4th grade students.  It was my first time teaching in an elementary classroom and I enjoyed every minute.


To avoid answering the same question 100 times, I either show this slide or write these steps on the board.

Depending on the class, the code may or may not be omitted.  If it’s the first or second time using Desmos with that particular class, I’ll insert my initial digital citizenship “talk” before sharing the Class Code. Digital citizenship is an on-going discussion and is always weaved into computer based lessons.

Let students play through the practice activity.  Once finished, regroup the class and ask them to share out what they experienced.  Here are some of the comments:

  • Student:  I asked questions
    • Me:  What kind of questions?
    • Student:  Yes and Nocapture
  • Student:  We saw kids.
    • Me:  What did you see afterwards?
    • Student:  Math symbols
  • Student:  I answered questions.
    • Me: How?
    • Student:  I picked yes or no.
  • Me:  What happened after your question was answered?
    • Students:  We had to x out pictures.
    • Me:  Yes, you have to select pictures to eliminate.

Me:  How many have played the game, “Guess Who.” (Hands waved in the air).  This activity is just like Guess Who.

I proceed to clarify the directions, then let students play.


Having never been exposed to the awesomeness of Desmos, Tricia (teacher) hunkered down at a computer and played along side of her students.  Her decision also addressed the issue of having an odd number of students.  Often, when there are an odd number of students, I’ll ask two kiddos to pair up and work on one computer.  Jen (elementary math coach) and I circulated the room addressing student needs.


As mentioned, this was my debut as an elementary teacher.  Here are some observations:

  • By asking questions, students practiced spelling and sentence structure.
  • Students openly helped each other.
  • Conversations flowed throughout the room.
  • Students were animated.
  • Understanding vocabulary terms became cool
  • Refinement of questions occurred naturally.
  • After 45 minutes of playing, students were still going strong.

At one point, Jen listed all the vocabulary words she was hearing. Since I noticed most students were not using acute and obtuse.  I challenged the students to intentionally use the words, acute, obtuse and right angles.  They rose to the challenge!

img_2247 img_2248





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Desmos: Gr 6 Inequalities

I recently co-taught Andrew Stadel’s 6th grade Desmos Activity Builder on Iequalities with Monica, Joe and Allison. This post is a summary of what happened in the different classes.

Capture3  capture Capture3

The AB was facilitated using the Desmos Classroom Conversation Toolset.  In general, I either activate Teacher Pacing or Pause Class immediately after creating the class code.  If the first slide has key information that I don’t want students to interact with just yet, I’ll use Pause Activity otherwise I’ll use Teacher Pacing.  For this activity, I used Teacher Pacing.


Classroom Conversation Toolset

Day 1

Slide 1:  Students read the directions.  I then gave them a 10 second countdown before activating Pause Class. I warned them ahead of time to avoid over dramatic reactions.  Using Graph Overlay, I revealed the collective responses. My last step prior to the class discussion was to turn off  the Show Original feature.  By doing this, all the points on the number line correctly represent the given instructions.



What happens when the overlay looks like this…


Me:  There’s something on the number line that makes me go hmm.. I’d like you to talk with your elbow partner and find the part of the Overlay that concerns me.

I circulated, listened and mentally selected a few students to call on when I called back the class. Once the students revealed my concern that a student graphed the 8, I say …

Me: I don’t want names because it doesn’t matter who graphed this point.  I would like the person who did slide the black dot to the 8 to regraph the point.  I’ll unpause the activity and give the class 5 sections to make changes.

Once the pause button is turned off, many students took this opportunity to change their answer including the student who made the error. I counted down from 5 and then pressed Pause Class. Now that the number line represents correct solutions, the class discussion begins.

Me:  Talk with your face partner about what you see.

Most students mention

  • There are a lot of dots
  • I see all of our answers
  • A lot of kids picked number ___
  • No one picked ____

Me:  Why are there so many dots (solutions) on the number line? Talk to your partner.

Students: (summary)  

  • We were told to pick a number greater than 8
  • There are a lot of numbers greater than 8
  • There are a lot of students in the room picking numbers

My Pitfall:  At first, I didn’t incorporate the vocabulary word, solution, enough before moving onto slide 2.  This over site became evident when students were working on slide 10.  I adjusted my plan for future classes.


Slide 2: Using Teacher Pace, I advanced students to slide 2.  To foster mathematical discussion, I apply the following format.

  • I gave students 20 seconds to read through the slide.
  • Students are instructed to discuss the slide prompt with either and elbow or face partner.
    • I like to press, Pause Class, at this point.  If I don’t, some students jump right into typing their response thereby ignoring their partner and skipping the discussion.  To develop mathematical understanding, students need daily opportunities to interact with math both orally and auditory.
  • The co-teacher and I circulated, listened to conversations, asked questions etc…
  • The Pause Class feature was turned off and students were given time to write and submit their response.
  • We circulated and read responses.  I also scanned the teacher dashboard for responses.
    • I like to circulate and read over students’ shoulders to provide editing support. Some students need help transferring their mathematical reasoning to written form. I’ll often ask a student who’s stuck to explain their thought.  If it makes sense, I’ll ask the student to type what they shared with me.  If their thought is jumbled, I’ll ask clarifying questions to flesh out a clear response.
  • A few students are selected to start and add to the discussion.




Slide 3:  I used the Think-Pair-Share format again.

  • Silently read for 20 seconds.  Everyone is silent, even the teachers.  Some students are easily distracted, so I don’t talk or answer questions.
  • Pick a piece of information to share and share it with your partner
  • We circulated, listened and selected students to start the conversation and others to keep it going.  I’ll often prep students ahead of time.  I’ll ask them if they’re willing to share with the class what they told me.  If they are nervous, I suggest they practice by repeating their comment to their partner.


Slides 4 – 6:  These 3 slides are a repeat of slides 1 – 3 using the less than and less than or equal to symbols.

Slide 7:  I used the Think-Pair-Write-Share  format on this slide.  Writing about math isn’t an easy task which is why I asked students to process with a peer prior to typing.capture

Day 2

Prior engagements conflicted with the co-teaching of Day 2, therefore I was only able to run Day 2 with Allison’s students.  We started off the day with some A/B partner work.

I wrote an equality sign on the board and asked the A’s to say it to their B partner.  If I hear any discrepancy (half the students saying greater than and half saying less than), we practice one more time as a whole group before moving on.  This process is repeated for all 4 inequality symbols.

To practice vocabulary, I ask students to show me (using their fingers) a solution to x < 5. I scan and jot down what I see.  I’ll ask why I didn’t see the solution of 5 before moving on. This process is repeated for the next inequality:  x is greater than or equal to 1.

Slides 8 & 9:  In my 20+ years of teaching, I was my first time teaching 6th graders about inequalities. I quickly realized that a clear distinction between the purpose of Day 1 and Day 2 needed to be made. During Day 1, students graphed a single point to collectively show a range of responses.  For Day 2, they were learning how to graph ALL possible solutions.


When first responding to slide 2, almost all students moved the circle to a number greater than 10 – like they did the day before.  I took the time to discuss the concept of a boundary number, ask for solutions and mark a few with red arrows. Capture.PNG

Next, we discussed which inequality symbol to select.  The distinction came full circle when students mentioned that all 4 suggested solutions were found in the green shaded region.


Slides 10 & 12:  By incorporating the word, solution, from the beginning, students zipped through this slide.



Slides 11, 13  & 14:  For these slides, students practiced graphing 3 more inequality statements.  I picked 1 student per group to be the Table Leader/Captain.

Me:  Groups, each group member is to graph the given inequality.  Captains, when your group agrees on a graph, please raise your hand.

The teacher and I circulated the room and supported collaborative groups.  Here are some statements we said:

  •  (To a Captain)  I see that your hand is raised, but not everyone is finished. Please check in with your group.
  • I see both red and green shading.  That’s interesting.
  • I see 3 different graphs.  Will you all compare your graphs and discuss.
  • I still see 2 different graphs at your table.  Please discuss.

When a group is ready to be checked, we start questioning.  I tend to direct my questions to a specific student within the group.   This is to avoid multiple people talking over each other as well as allowing for quieter students to have a voice. Some questions are:

  • Explain why the 10 is shaded in?
  • What made the group decide to shade to the right?
  • Is 10.1 a solution? Why or why not?


Slide 15: I love this slide.  Teachers, please spend a chunk of time on this slide exploring, uncovering and clarifying misconceptions.


Here’s how it flowed for me…

  • Me: Repeat after me:  5
  • Students: 5
  • Me:  Is less than or equal to
  • Students:  is less than or equal to
  • Me: x
  • Students: x
  • Me:  Now show me, using your fingers, a solution to the inequality 5 is less than or equal to x

I was planning on jotting down some of their solutions.  When I looked around the room I saw students displaying a variety of answers ranging from 1 to 10. Uh Oh!  This was critical moment.  I could either acknowledge only the correct solutions or I could set the stage for conversation by acknowledging both correct and incorrect.  I chose the latter.


The minute I jotted down 3 and then 3.5, I could sense students questioning my move. YES! I could hear students mumbling comments and see others wildly raising their hands. After soliciting a few more solutions, I stood back from the board and said:

Me:  If someone disagrees with a given solution, please state which one you’re questioning and explain why.

Student 1:  I disagree with 3 because 5 is not less than or equal to 3.

I’d then draw a line through the 3.  This process repeated until all solutions were deemed acceptable by the students.

The Activity Builder is displayed onto a whiteboard, which allows to me to highlighted the correct solutions.  See the recreated picture below.  Once I mark up the number line, I ask students to determine which inequality would shade the section covering the correct solutions.


Even with the above visual displaying, I saw the following:


Typically there was a mix of right and wrong answer at each group, therefore I used my go to statements:

Me:  I see different answers.  Please discuss.  I’ll be back to check in.

At this point, the students do all the work. Group members help each other out.  They explain & discuss. Upon my return, I check for understanding.  After I’ve checked in with many groups, we discuss whole class.


The confusion surrounding this problem was eventually clarified.  The best part:  The students clarified the confusion on their own.  When I stepped back and listened, I heard (paraphrasing):

  • You have to shade the bigger numbers because x is bigger than 5.
  • 5 is less than or equal to x is the same as x is greater than or equal to 5
  • If 5 is smaller than x, then x is bigger than 5


The Exit Ticket:  

I walked up to each group and said:

  • Me:  5 is less than or equal to x is the same as:

then I pointed to them, and they responded with:

  • Group: x is greater than or equal to 5.



Closing Thoughts

Students enjoyed the flow of choral response, picking a solution, silent reading, A/B partner share, writing a response, reading the other responses, discussing the difference between less than and less than or equal to, circling the boundary number and determining which side to shade.

I spent 2 days working through Andrew’s Inequality Activity Builder and we reached slide 15.  Inequalities are abstract for 6th graders.  Students needed a lot of processing time. Time to articulate the new vocabulary and notation.  Time to discuss the meaning of an inequality and its solution.  Time to graph inequalities.  And finally time to clarify misconceptions surrounding  x < 4 and 4 > x.


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Teacher Moves – Soft Skills

 A long term substitute, who’s currently in a credentialing program, recently made this observation.
“In my program, I’m shown all these activities and my professors assume students want to participate.  They (professors) don’t tell us what to do when students don’t want to engage.”

One of the more challenging responsibilities a teacher has is creating a classroom culture where students want to participate and feel safe participating.  To attain this climate, teachers can commit to teaching their students soft skills. Some soft skills
are (but not limited to) screen-shot-2017-01-13-at-8-36-40-pmhelping students:

  • Communicate effectively
  • Manage time
  • Make decisions
  • Self-motivate
  • Work as a team member/group dynamics
  • Problem solve
Teaching soft skills is a daily commitment.  Some teacher moves required are overt and others subtle.  Consistency is key.

Attending to Soft Skills

I was assisting an 8th grade teacher implement cooperative groups.  For cooperative groups to be successful, commitment to soft skills is necessary. The posed question was:   What can we do to help kids get along?
Background: I had spent 2 days with this teacher. Day 1 focused on introducing the concept of cooperative groups.  Day 2 started off with a team building activity, followed by a content activity.  On the second day, we were both busy circulating the room working with groups.  Although we touched base regularly, we were too focused on students to observe the other in action.  In response to the question, What can we do to help kids get along?, I compiled a list of concrete examples from the second day.  All names have been changed.
Angela’s group:  They were the first group to finish listing their 5 commonalities.  I mentioned this and applauded their cooperative behavior.  Discussed how productive they were when they were cooperating instead of antagonizing each other. They took pride in their accomplishment.  Soft skill:  Working together as a group
Bill (and Carlos’ group).  The girl who sits across from him always answers in a condescending tone.  Bill mentioned this when I told him to ask his group for help instead of asking me.  At that point, I spoke with the group about Bill’s (and as it turns out Carlos’) hesitation with asking for help.  The girl apologized on her own.  I thanked her for apologizing.  I hope she has more patience with her group in the future.  Soft skills: Working together as a group & communication skills
Diana kept asking me for help.  I sat with her group and discussed how they have to work together.  I said, “Diana has a great question” I looked at Diana and said,”Will you repeat it to the group?” Diana repeated the question.  I then stepped in and said to the team, “I’d like you to help your group member. I’ll be back to check in.”  When I checked in, Diana was progressing.  I thanked the entire group.  Soft skills:  Working together as a group & communication skills

Everett/Frankie/Gabe:  I tactfully called Everett out on his behavior. He made the decision to participate appropriately.  I praised him and his group every time I saw them be productive. Soft skills:  Working together as a group & making decisions


Henry/Isaac/Jared:  Isaac can be fragile at times.  If he gets irritated, then he wants to be left alone. Henry wants to ask if he’s ok, which irritates Isaac more.  Henry doesn’t back off. Isaac gets angrier.  We talked about giving Isaac space and what that means.  We discussed that it would be best not to talk to Isaac until he feels better, therefore he should work with Jared for now.  I thanked Henry for being flexible and working with Jared.   Soft skills:  Working together as a group & communication skills

Keith:  Sat with Keith’s group multiple times.  Always highlighted positive behavior and addressed distracting behavior. If we are consistently highlighting positive behavior and calmly addressing negative behavior, I believe Keith will turn his behavior around.  Soft skills:  Making decisions & working together as a group


Laura:  I noticed that a group member graphed the line for her, so I asked Laura to describe how it was graphed. She couldn’t. I gave the group instructions to help her and told them I’d be returning to assess their progress.  I had to return three times because the group was off task.  Laura was able to explain how the line was graphed the third time I returned. I thanked the group for completing their assignment.  Soft skills:  Working together as a group & making decisions.


These examples describe covert ways of teaching soft skills (in my opinion).  Although I was direct when speaking to students, only the targeted students received the message. Each message was personalized to address the presented concern.
Facilitating academic skills and nurturing soft skills simultaneously is not easy at first. One must consciously work to make the practice a habit.  Like most practices, some days are easier than others.
When tired or irritable, I’ve learned to identify and acknowledge positive student actions. My go to sentence starter is, “Thank you for …”
  • Thank you for getting out your materials
  • Thank you for helping your group member
  • Thank you for being patient
  • Thank you for being productive
  • Thank you for being flexible
  • Thank you for sharing your thinking.
When it comes to giving thanks, NO action is too small. This gesture turns my mood around, works wonders with students and reminds me that attention to soft skills maintains the cohesive nature of my classroom.
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A No Fail New Year’s Resolution

My To Do list often looks like this:

  • Laundry
  • Clean closets
  • Finish garden project
  • Fix clogged sink
  • Breathe

At the end of the day, if I didn’t tend to the laundry, closets, garden or sink, I can still cross off, breathe and feel good about it. For 2017, I wanted a to make a no fail resolution. One that is guaranteed to be successful – Like adding, breathe, to a To Do list.

After some thought, I decided my  2017 New Year’s Resolution is to make mistakes. The more I let this decision sink in, the more I likto-doed it.  Here’s my updated To Do list:

  • Laundry
  • Clean closets
  • Finish garden project
  • Fix clogged sink
  • Breathe
  • Make a mistake

At the end of each day, I can cross off 2 items. I’ll be twice as productive!


On a serious note:  

I’m not afraid of mistakes.  Mistakes have aided in my personal and professional growth and I’m grateful for them. For years, I’ve been activity promoting Carol Dweck’s & Jo Boaler’s work with growth mindset.  First at home with my children, then in the classroom and recently as a middle level math TOA/coach.

Although I joke about being twice as productive, there’s some truth to the statement. If I acknowledge the learning connected to the mistake, then each error in judgement, each incorrect move, each trial was not in vain.  They’re experiences to be valued for they’ll help me make better decisions in the future.

As 2016 draws to a close and the new year begins, I wish everyone a happy 2017 filled with joy, love and mistakes!


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