RIMTA Newsletter

Issue 1, Volume 38, September 2016

In This Issue: Co-Editors Lynn Prentiss and Steve Levesque











President's Letter

Dear RIMTA Members,

WELCOME BACK to school! What a summer it has been, and RIMTA has been very busy!

The Affiliate Leaders Conference in July was another productive trip. Members of the RIMTA Board solidified its plans to offer professional development that gives members an opportunity to interact with the strand of Numbers and Operations to Ratio/Proportional Reasoning through to Functions by facilitating vertical alignment conversations with Elementary and Secondary teachers in the fall. In January, our winter workshops will include ways to integrate technology effectively in the classroom and we will offer twice as many options as we did last time! Culminating in the Spring, we welcome Diane Briars, past-president of NCTM, who in her tenure, advocated strongly for the ideas presented in the book, Principles to Action. These ideas speak to the best mathematical practices one could be using in the classroom.

In addition, this year, we will continue to offer two student awards and teacher awards. Look out for these in our January newsletter! We have also chosen to go with Wild Apricot for all of our website and membership needs; we are continuing to make the kinds of shifts that will continue to benefit you, our members, to the fullest; and we are revisiting our By-Laws and Constitution to ensure that they are reflective of our current practices. It will be another big year, and we are excited about moving forward!

As we begin another school year, I've been thinking a lot about the work and effort that goes in to setting up for another group of students, whom we are eager to share our knowledge with. In some ways, I caution you with this scenario...

Have you ever remodeled your kitchen before? Maybe a section of the house? If not, imagine it...

You have lived with this outdated kitchen for as long as you can remember and you decide it is time for a makeover. So, you save your money and you secure a loan. The work begins.

Over the course of the next three months, you have changed the way you feed your family completely. Never has your family survived so long on take out - Chinese, pizza, Italian. You have even resorted to a few nights of Ramen Noodles. You are just about at your limit - where you would rather move out than wait one more day, when the contractor calls you at work. He shares with you that by the time you get home, they will have completed the job to its fullest and all of his men's materials will be removed.

You arrive home from work to see, what just might be, the kitchen of your dreams. You look around and see and smell the newness, the difference - new cabinetry, stainless steel appliances, an island counter top made from butcher block, new recessed lighting, windows that look out into your backyard where the sun sets, beautiful flooring, new ventilation above the stove, multiple ovens… You fall in love!

It’s the first night in your new kitchen and you are able to cook a meal for your family. You pull out your great grandmother’s pot roast recipe - one you have cooked a hundred times prior. It’s always a crowd pleaser! You take out the ingredients, which you always have on hand. You prepare the meal and throw it in the oven.

One hour goes by, the kitchen fills with that tantalizing smell and the buzzer goes off; the meal is ready. You take your dishes out of your new cabinets, slide silverware out of the new drawers, pull the meal out of the gorgeous new stove, call your family to dinner, slice into the pot roast, and place adequate servings on each plate. Your family arrives to the dinner table, sit in front of a plate and smile. You slice into the meat on your plate, you place in onto your palette and you close your eyes….

"FINALLY," you think, "a real meal after all of that remodeling."

Then it hits you. You open your eyes and realize something. The food doesn’t taste any different than it did when it was cooked in the old kitchen!! And why would it, you think to yourself. All of the ingredients were exactly the same.

I personally get so excited about the prospects of a new school year, new students, new minds to inspire, new opportunities and possibilities. We go in and redecorate, set up our rooms, and buy new materials. However, if we do not change or shift our ingredients, I'm not sure we can expect different results - same old pot roast.

I encourage you to try something different, take instructional risks, do what you know how to do already, but make a small shift that increases your likelihood of reaching just one more child. There are always ways to improve our practice. Find those ways by not buying new binders, but by challenging yourself and your students with new ideas!

I look forward to serving you, as RIMTA President, for the next two years. Have an amazing school year!

Lynn Prentiss

RIMTA President


Lynn Prentiss, President, Grants Chair, and Newsletter Co-Editor; lpiq18@gmail.com

Stephen Levesque, President-Elect and Newsletter Co-Editor; leves314@yahoo.com

Cathy Boutin, Past President and ATMNE Rep; cboutin@westwarwickpublicschools.com

Ray Morin, Treasurer and Membership; rmorin1035@cox.net

Lynn Rakatansky, Secretary; lynnrak@msn.com

Eric Simonian, NCTM Representative; esimonian@verizon.net

Patricia Carnevale, RIDE Representative; patricia.carnevale@ride.ri.gov

Susan Pagliaro, RIDE Representative; susan.pagliaro@ride.ri.gov

Meredith Astrologo, At-Large; meredith_astrologo@nksd.net

Donna Christy, At-Large; dchristy@ric.edu

Kees deGroot, At-large; degrootc@mail.uri.edu

Jill Fisher, At-Large; jfisher@westwarwickpublicschools.com

Gina Kilday, Web Communications; gkilday@gmail.com

Sue Osberg, At-large; sosberg1@verizon.net

Christine Payson, At-large; Christine.payson@cumberlandschools.org

Janice Kowalczyk, RIMTA ListServ; jckowalczyk@gmail.com

Please keep the board updated of any ideas or suggestions that you have.

Let a board member know how we can support you in the classroom!


NCTM's President, Matt Larson, June 29, 2016

On June 20, 2016, the Organization for Economic Cooperation and Development (OECD) released a report entitled Equations and Inequalities: Making Mathematics Accessible to All. The report is based on Programme for International Student Assessment (PISA) data from 2012. As is sometimes the case, the headlines in the media are subject to misinterpretation. In this case, the headline was “Is Pure Math Superior to Applied Math?” After reading the article, it is clear this is a question raised in the report, but could leave a reader with the impression that one aspect of mathematics learning is superior to another. An equally valid alternative headline could have been “Conceptual Understanding is Necessary to Effective Problem Solving.”

In addition, the OECD report makes a strong case that high-quality mathematics education can be a lever to address social inequalities when school leaders adopt policies such as the elimination of tracking. Unfortunately these findings are not often given the attention they deserve. I encourage members with interest in the report to read beyond the headlines so they don’t jump to the conclusion that applied mathematics is “bad.” There are few dichotomies in mathematics education. Pursuing conceptual understanding, procedural skill, and application with equal intensity—as is recommended by the authors of the Common Core—makes sense, as all three components are critical to student success in mathematics.

To read more, go to nctm.org.

Affiliate Leaders Conference, 2016

We all know: “What happens in Vegas – stays in Vegas.” But that’s not what has happened after the Affiliate Leaders Conference, held at Planet Hollywood Resort in Las Vegas, this past July.

The conference/workshop was attended by RIMTA representatives – President Lynn Prentiss, Past President Cathy Boutin, and NCTM Representative Eric Simonian, who collectively brought back a wealth of knowledge and understanding of how successful organizations are actually “successful”. The overriding theme of the event, based on Simon Sinek’s TED talk from 2009 “Start With Why," was truly inspirational, as it encouraged participants to look at their organization through the eyes of a member who might ask: “Why should I belong?.” More specifically, the “why” actually targets the “purpose” for any business or organization. Not on a superficial level (“To make a profit”), but to address the “soul” of an organization.

In his TED talk (https://www.youtube.com/watch?v=sioZd3AxmnE), Sinek chronicles the seemingly disconnected success stories of Dr. Martin Luther King, the Wright Brothers, Apple, and Southwest Airlines as he explains how these successes were based on accurately understanding what Sinek refers to as the “Golden Circle.” The Golden Circle puts three basic understandings of any activity in a specific hierarchy. The “What”, “How”, and “Why” is typically ranked in that order. What Sinek has found is that those who are successful, have a clear understanding as to “Why” they began their venture. The “Why” becomes the driving force as the venture continues. He believes that people don’t buy “what you do,” but rather they buy “why you do it”.

Although emphasized as indispensable to the success of any organization, it can easily be applied to the goal of success in the classroom. How many times have we all been asked, “why do we need to learn this?” Sometimes, we brush the question off and reply with a typical, traditional response – not really addressing the question nor the need of the student to begin to understand “why.” We, as teachers, must believe that the concepts and skills that we are presenting to students are fundamentally important to them, as students and future leaders, for success – in anything they do. That is certainly a challenge, but one that successful teachers strive to answer.

RIMTA’s schedule of events and Professional Development activities all have a link to teaching and student learning, as we consistently question “why” we teach what we teach – and “how” the “what” is presented to give understanding and success for all students.

Eric Simonian



NCTM's new Innov8 Conference

Have you heard about NCTM's new conference offering - Innov8 2016: "Engaging the Struggling Learner?" This innovative and team-based professional development is centered around acquiring the necessary skills to provide high-quality mathematics education for learners of all abilities.

Innov8 provides opportunities for attendees to:

  • Receive hands-on experience implementing research-based mathematics education practices.
  • Connect with like-minded teachers facing similar problems of practice and collaborate to determine effective solutions to advance student learning.
  • Return to the classroom, school, or district with an action plan and commitment to implement refreshed tools and techniques.

There will be three learning pathways: Building Effective Multi-Tiered Systems of Support (MTSS aka RtI), Supporting the Productive Struggle and Motivating the Struggling Learner. Participants are encouraged to come in teams in order to collaborate and better plan and develop solution strategies for their school and district (participants that do not come in a group will be assigned a group by pathway, grade level or region). Multiple structures are being put in place to support networking and collaboration.

This year's conference will be November 16-18 in St. Louis MO and you can get more information and register at www.nctm.org/innov8. Teams of 5 or more will receive a 15% discount. Because the focus is on a complete conference experience, one-day registration is not available.

Your school or district should consider sending a team to this exciting, new professional development opportunity to help you engage your struggling learners!

Gina Kilday

Web Communications

RIMTA's Professional Development Offerings, 2016-2017

RIMTA Fall Meeting

Wednesday, Oct. 26th, 4-8pm

1 New England Tech Boulevard

East Greenwich, RI

Keynote Address

Let's Make Sure that Students Do Not Think that Ratios are Fractions with Kees de Groot

While we use fraction notation, among other representations, for ratios and we apply equivalence in the same way to fractions and ratios, they are distinctly different mathematical ideas. It is important that students understand this deeply. There is strong vertical power in this understanding. We will explore this by tying together the CCSSM standards across the grades.

Elementary Session


Come along and find out how modeling fractions in multiple ways can take the frustration out of understanding fractions and fraction operations. We will look at modeling with fraction strips, pattern blocks, cuisenaire rods and the number line. You will leave this workshop with hands-on activities that be used directly or easily adapted for your classroom use.

Secondary Session

Welcome to the PROshop! with Donna Christy

Swing into action with PROportional reasoning PROblems for grades 6-12. Score some take-away PROtivities to implement in your classes tomorrow!

RIMTA's Winter Workshops

Thursday, Jan. 26th 2017 at 4-6:30pm

800 Logee Street

Woonsocket, RI

Presentations you can expect!

Coding by Sharon Ficarro (Elementary)

Can I Teach Coding to Elementary Students? Have fun trying out an “unplugged” activity from one of Code.org’s elementary school curriculum. Learn about, self-guided and self-paced tutorials that use “unplugged” activities that require no computers at all. Learn how to make computer science available to all students.

NCTM's Electronic Resources by Gina Kilday (K-12)

There are so many resources out there. Have you seen NCTM's? Come see all they have to offer!

Scratch by Janice Kowalczek (Gr.s 3-8)

With Scratch, you can program your own interactive stories, games and animations and then share your creations with others. Scratch helps young people learn to think creatively, reason systematically and work collaboratively!

Desmos Activity Builder by Steve Levesque (Secondary)

At this workshop, participants will review the basics of Desmos’ powerful Activity Builder and then create their own activities that may be used immediately. Participants should arrive with some familiarity with Desmos and an idea of a topic about which they would like to create an activity.

Blended Learning Implementation by Hiliary Lundgren (K-12)

The presentation will model station rotation and participants will learn from teachers and administrators about the “moves” that we are making to personalize learning for every student at West Broadway Middle School. This K-12 focused session will allow for ideas to be adopted or adapted to bring back to your own school!

"3-Act Series" Videos by Nancy McGonagle (K-12)

Three Act Math format was originally developed by Dan Meyer. Storytelling gives us a framework for certain mathematical tasks that is both prescriptive enough to be useful and flexible enough to usable. Many stories divide into three acts, each of which maps neatly onto these mathematical tasks.

"Show Me" App by Christine Payson (Secondary)

Turn your iPad into your personal interactive whiteboard. Showme allows you to record voice-over whiteboard tutorials and share them online. It's an amazingly simple app that anyone can use!

PARCC Tools & Resources by Susan Pagliaro (K-12)

This 90 minute session will provide participants with a greater awareness of the resources provided by the Partnership for Assessment of Readiness for College and Careers to assist teachers in preparing their students for the PARCC assessment. Released items, technology tutorials and practice tests are some of the resources that will be highlighted.

Google Classroom, GAFE (Intro & Adv. Sessions) by Dean Palmer and Paula Mcmillan (K-12)

There will be two sessions offered, one for the beginner and another for the more advanced. Explore all that Google Apps for Educators has to offer you and your students!

Intro. to Blended Learning by Deidra Rossi (K-12, Secondary)

Blended Learning is where we are going in education, but what does that mean? What does it look like and sound like in practice, you ask? Come found out! Participants will leave with a better understanding of what Blended Learning is and strategies to begin creating a more Blended environment for your students!

Twitter for Educators by Jonathan Santos-Silva (K-12)

Everyone's using it, but are they making the most of it? Come learn how Twitter can be a personalized experience for professional development.

RIMTA Spring Meeting

Thursday, May 11th 2017 at 4-8pm

2081 Post Road

Warwick, RI

Aligning to our annual theme of the Numbers & Operations Strand (fractions --> ratio and proportional reasoning --> functions), Diane Briars will facilitate converstaion with teachers around building procedural fluency from conceptual understanding, posing purposeful questions and supporting productive struggle. These concepts and ways of engaging in mathematics effectively are among some of the best practices highlighted in Principles to Action.

Diane J. Briars, PhD, a mathematics education consultant, is past-president of the National Council of Teachers of Mathematics. She was mathematics director of Pittsburgh Public Schools for 20 years. Under her leadership, Pittsburgh schools made significant progress in increasing student achievement through standards-based curricula, instruction, and assessment. She is past-president of the National Council of Supervisors of Mathematics and co-director of the Algebra Intensification Project. Dr. Briars began her career as a secondary mathematics teacher. Dr. Briars has been a member of many committees, including the National Commission on Mathematics and Science Teaching for the 21st Century. She has served in leadership roles for various national organizations, including the National Council of Teachers of Mathematics, the College Board, and the National Science Foundation.

She earned a PhD in mathematics education, an MS, and a BS in mathematics from Northwestern University.

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Elementary Math Leaders Group (EMLG)

EMLG Update

RIMTA's Elementary Math Leaders Group continues to grow. We are a group of elementary math coaches, teachers and administrators representing over 20 districts who collaborate digitally and face-to-face. We meet several times a year, but resources are also shared digitally for those who cannot make the meetings. We always welcome new members, so please spread the word to the appropriate people in your district! Contact Gina Kilday at gkilday@gmail.com or Meredith Astrologo at meredith_astrologo@nksd.net to join and to get more information.

This year we have already scheduled our first meetings and topics, although locations are still being finalized.

· Tuesday, October 4 - We will share ideas for How to Use PARCC and other Data 9-11:30 and then 12-3:00 we will have two breakouts. Those breakouts will be How are you preparing for PARCC in K-2 Using the Model Content Frameworks and Other Resources and Revisiting Visual Models Across the CCSSM professional development materials that were developed previously by the group.

· Friday, December 2 - We are planning to reflect briefly on Data Use to follow-up from the first meeting of the year, and then focus on RtI in the morning. Then in the afternoon, we will be breaking into groups to share ideas to support specific resources. Many districts are using things like i-Ready, Eureka and Advantage/Intervention. We are open to other materials suggestions, also.

· Thursday, Feb 16 – topic to be determined

· Friday, May 26 - topic to be determined

The power of this group is the collaboration opportunities within its membership, so we hope to see you there!

Gina Kilday

Math Coach

Metcalf Elementary, W. Greenwich

Math Interventionist - Google Forms

I was up for the challenge when my principal and I sat down to discuss promoting a “math day,” in conjunction with the popular, and established, reading week in schools. I ran with it and it soon became the highlight of my first year of teaching math - Launching Pi Day.

I had heard of middle and high schools celebrating Pi Day before, but I wanted to research how I could make this happen with the younger students, whose concept of Pi may be the blueberry kind with a dollop of whip cream! It was important to me to make this day interactive and fun. Being as this was the the first time the community would come together to celebrate a school-wide math day, we had to get off on the right foot so that we kept students yearning for more. My challenge was to think of something I could do with every single classroom and connect it in a way that it felt school-wide. And then it occurred to me... Technology was the only way to logistically, physically, and effectively make this happen.

Since it was called Pi Day, I knew I had to incorporate pie to keep the students' interest and curiosity. I used google forms in every classroom to find out Northern’s favorite pie among students and staff. Also, using Google Chrome Casting, I easily tapped into each classroom within seconds from my chromebook, project a graph on a whiteboard, and move from classroom to classroom with nothing but a chromebook and the lesson floating in the internet air.

Through the use of Google Forms, I created a survey that generated a pie chart of the results. Each student voted for their favorite pie. I stood in the back, input their data into my Google Form and students saw the sectors of the pie drastically change with each vote instantly before their eyes. We had deep meaningful conversations about the impact of voting, how the pie changes, how data is represented, and much more!

Pi is accessible at any age - Just ask the students at Northern!

Colleen Buffery

Math Interventionist

Northern Elementary School, Lincoln


A Response from the Comissioner's Office

In light of RIDE’s most updated Strategic Plan,

where does the commissioner’s office feel mathematics education fits in?

Improving student achievement in mathematics is at the heart of all we do as educators, and we remain committed to the idea that our students need to develop skills in numeracy in order to be globally competent graduates ready to succeed in the 21st -century economic landscape. Mathematics remains a central part of our assessment and accountability systems, with all high-school students to be tested in algebra and all graduates required to take four years of mathematics. Proficiency in mathematics at all grade levels has been a priority of Governor Raimondo’s administration, as you can see in Governor Raimondo’s support for STEM education, for bringing computer science to all Rhode Island schools, and for building “skills that matter for jobs that pay,” particularly in growing fields such as technology and health care. To prepare students for success beyond high school, whether that be in post-secondary education or in a challenging career, we have to ensure that our graduates have the skills they will need, with mathematics at the forefront.

As we continue to support student achievement in mathematics, it will be increasingly important to bring parents into the picture. Recent media coverage has raised the question: Why do teachers like Common Core mathematics, while parents don’t? Many parents find it hard to understand why we ask students to explain their reasoning when they solve math problems and why we ask students to show several different pathways to the same solution. We need to bring these parents into the conversation and make them comfortable with our math standards and instructional practices – perhaps through “math nights” at school, direct communication to parents, take-home or online resources, or other communications strategies. We’re open to ideas that can help you, the members of RIMTA, bring the Common Core home to Rhode Island families.

Ken Wagner, Ph.D.

Commissioner of Elementary and Secondary Education

Rhode Island Department of Education

PARCC Updates

PARCC Assessment for 2016-2017 School Year

In response to Governor Raimondo’s championing of the PSAT/NMSQT and the SAT, as well as requirements set forth by the Every Student Succeeds Act (ESSA) and President Obama’s comments on testing, RIDE has made adjustments to its testing policy for PARCC during the upcoming 2016 – 2017 school year:

 All students in grades 3 – 8 will continue to take the assessment for mathematics and

English Language Arts (ELA)/Literacy.

 All grade 9 students will take the English Language Arts (ELA)/Literacy assessment.

 Students in grade 9 to 11 will be required to take one PARCC assessment during their

high school career. For most this will be the Algebra I test. However, if students take

Algebra I in middle school, they will be required to take either the Geometry or Algebra

II test while in high school.

 All sophomores have the option of taking the PSAT at no charge if taken during the

school day on October 19, 2016.

 All juniors have the option of taking the SAT at no charge if taken during the school day.

On another front, all schools will be expected to administer the PARCC computer-based

assessments in this coming school year. PARCC paper-based assessments will be allowed only for students with documented accommodations that require assessments to be administered via paper and pencil or if a waiver is granted to a school that has not yet been able to fully implement its plan to transition to a full computer-based administration.

Susan Pagliaro

Mathematics Specialist

Rhode Island Department of Education

PARCC Data Analysis Workshops

Those interested in attending can register through eRIDE.

Sept. 21st, CCRI- Warwick

Sept. 23rd, Middletown Admin. Building

Sept. 27th, NRIC

Sept. 29th, North Kingstown Admin. Building

Presidential Awardees for Mathematics and Science, 2014 & 2015

The White House has announced that the Rhode Island winners of the national Presidential Awards for Excellence in Mathematics and Science Teaching (PAEMST) are:

2014 Mathematics: Barbara Pellegrino, from the Harold F Scott Elementary School, Warwick

2014 Science: Debra Turchetti-Ramm, from the Sarah Dyer Barnes Elementary School, Johnston

2015 Mathematics: Kristen Jahnz, from Cumberland High School

2015 Science: Anthony Borgueta, from Barrington Middle School

These awards recognize these four teachers as outstanding educators who exemplify the highest standards of mathematics and science teaching. They serve as models for their colleagues, inspiration to their communities, and leaders in the improvement of mathematics and science education.

The Presidential Award for Excellence in Mathematics and Science Teaching (PAEMST) is the highest recognition that a kindergarten through 12th-grade mathematics or science teacher may receive for outstanding teaching in the United States. Enacted by Congress in 1983, this program authorizes the President to bestow up to 108 awards each year. The National Science Foundation administers PAEMST on behalf of the White House Office of Science and Technology Policy. Awards are given to mathematics and science teachers from each of the 50 states and 4 U.S. jurisdictions. The teachers are recognized for their contributions to teaching and learning and their ability to help students make progress in mathematics and science.

For more information, please go to the White House web page, at https://goo.gl/tDrLoL


Making the Most Out of RTI at Your School

Let's be honest... The question we really all want answered is: What do we do to make sure every student is learning the most that they can at any given grade level? Isn't that it?

I am a Math Specialist at Chariho Middle School, a rural school serving just under 950 students in grades 5-8. My job description lists 25 Essential Duties and Responsibilities with the last one being ‘other’. Not on the list, but my goal each day is to help students understand and enjoy mathematics. As a Math Specialist in my building, I have a unique opportunity to work with a variety of students and teachers at different grade levels. Every student has unique needs, however when you take a step back, you can see patterns of similar need across grade levels.

Last year, over the course of many RTI meetings, a common need was emerging at our school. This is the story of how we used the problem solving process, which started in RTI, to improve learning at our middle school.


After attending many RTI meetings, a pattern began to emerge - one that we heard over and over as we discussed students who were struggling. Students were giving up on challenging problems, they were writing answers that didn’t make sense, and they didn’t know what to do when they got stuck. Soon most of our interventions for problem solving were for using Polya’s 4-Step Problem Solving Process. Through discussions with teachers, we discovered that many students, even the ones not seen for RTI, were having similar struggles. As we were implementing the Common Core, we were increasing the level of rigor for the problems we were assigning and in turn, we needed to support all students. RTI discussions made us realize that the students at our school needed more direct instruction for using problem solving strategies.


All the students in our school needed strategies they could utilize when they were solving challenging problems. We decided to use Polya’s process school-wide, based upon the discussions being had at RtI meetings. Those discussions gave us the springboard we needed to guide our discussions in our monthly after-school content meetings, when all of the math teachers meet together.

During this time, we continued to brainstorm what good problem solvers would do at each step, and then we came up with a mnemonic students could use if they were stuck. We came up with many great ideas and voted on a winner. MONEY was established.


We created a reference bookmark for all students. When students would say, “I don’t get it,” the teachers were able to refer them to the MONEY strategies and ask, “Did you organize your information? What do you need to interpret in this problem?,” etc... Students who received RTI support for problem solving would get additional support during RTI, but they wouldn’t be learning anything new. The classroom instruction and small group interventions were supporting each other.


Our school-wide tier 1 intervention for problem solving started at the end of March. Right away, we could see the students in RTI embracing this idea. They were so excited to report that their teachers were using the MONEY strategy in their math class. They were seeing that what they were expected to do in class and what they were expected to do in RTI, was the same. The more exposure they had to problem solving strategies, the more they were able to internalize the process.

We will continue to evaluate our process and make necessary changes as needed. As we start the new school year with the same structure in place, we are expecting students to feel more comfortable using this process right away. Our RTI teams will continue to work to provide interventions that support individual students, while looking for patterns of need that will help our whole school.

What does your school need? How can you make it happen?

Kristina Sparfven
Math Specialist
Math Content Leader, Chariho Middle School

Elementary Level Resource

Which One Doesn’t Belong?

Standard for Mathematical Practice:

#3 Construct Viable Arguments and Critique the Reasoning of Others

Students are presented with four math concepts. As students consider the four possible options they decide which one doesn’t belong, then justify and defend their answer.

8 2

5 10

(in a table form)

(Example from Putting the Practices Into Action: Implementing the Common Core Standards for Mathematical Practice K-8 by Susan O’Connell and John SanGiovanni-Eliminate It activity)

Some possible student responses:

● I think 5 doesn’t belong because 5 is an odd number and all the other numbers are even and if I pair chips together, there will be one leftover when I show 5.

● I think 10 doesn’t belong because it as a number in the tens place and the other number only has a number in the ones place.

● I think 5 doesn’t belong because 2, 8 and 10 can be used to show the relationship between addition and subtraction. For example: 2+8=10, 8+2=10, 10-2=8, 10-8=2.

● I think 8 doesn’t belong because 2, 5 and 10 can be used to show the relationship between multiplication and division. For example: 2x5=10, 5x2=10, 10

● I think 5 doesn’t belong because all the other numbers are the sums of a whole number doubled. For example: 1+1=2, 4+4=8, 5+5=10.

Hmmm...not only can there be more than one correct answer, but there can be more than one correct answer using the same numbers!

Which One Doesn’t Belong (also called Eliminate It from Susan O’Connell and John San Giovanni) allows students to consider a variety of mathematical options, then construct a viable argument while justifying their answer and reasoning about the process they used. Students also consider the reasonableness of others.

In addition to Math Practice #6, other Math Practices are also evident including:

● #1-Make Sense of Problems and Persevere in Solving Them

● #6-Attend to Precision

Which One Doesn’t Belong allows students to consider possible solutions with multiple entry points and access for learners at different levels, including grade levels. Mathematical concepts can include numbers, equations, words, shapes and more. The possibilities are endless!

Possible Resources:

Video of Eliminate It routine from Howard County Public School System:


Website-Which One Doesn’t Belong created by Mary Bourassa

(Examples with no answers provided, just many possibilities):


Biloxi Public Schools - Examples grades 3-5 (far right column)


Stenhouse Blog:


Meredith Astrologo

Math Specialist

North Kingstown

Middle Level Resource

Covering the Patio

The apartment complex wants to purchase outdoor carpet to cover a portion of the patio outside of the community center. The patio is shaped like a parallelogram with no right angles that has a width of 20 meters and a height that is 5 meters shorter than its width.

Part 1:

Draw the entire patio and find the area of the entire patio. Write an equation and explain how you found your answer.

Part 2:

The apartment complex wants to cover the entire patio except for a triangular region that is ¼ of the width of the entire patio and the same height as the patio. Label the dimensions and find the area of the patio that will not be covered. Write an equation and explain how you found your answer.

Part 3:

The apartment complex has between $350 and $400 to spend on the patio covering. What is the price range that they can afford to spend per square meter to buy the patio covering?

For access to the entire lesson, including alignment to standards and the rubric, please visit the link below:


Jill Fisher

Deering Middle School, West Warwick

High Level Resource

One of These Things Is Not Like the Other...

CCSS Standards for Mathematical Practice: 2, 3, 7

CCSS Content Standards: HS.A-SSE.1a, HS.F-IF.7a, HS.F-BF.3

Looking for a new warm-up to get class discussion flowing? Try a little activity called “Which One Is Different?” In this activity, display four equations, expressions, or graphs to the class and simply ask, “Which One Is Different? Why?” After giving students a few minutes to ponder their own answers, and possibly pair with another student (Think, Pair, Share!), ask students for their responses.

An example of this activity with four quadratic functions is shown below in figure 1. Student responses may vary, and that’s the idea! For instance:

#1 is different because its graph is concave down.

#2 is different because its graph does not have an x-intercept.

#3 is different because it is in standard form OR because the graph is concave up with

two x-intercepts.

#4 is different because its vertex would be on the x-axis.

While this example is applicable for Algebra I or Algebra II, the concept is easily adaptable to nearly any topic of study, and the prompt can be created quickly.

Teachers can revisit main ideas, reinforce proper vocabulary, and address misconceptions while allowing students to investigate and be a bit creative. Students may even delve more deeply and find differences that you did not anticipate!

One other thing to note: adding a little color can make the activity more visually appealing to students. Compare figure 1 to figure 2 below.

If you want to share any “Which One Is Different?” activities that you create, please contact me at Leves314@yahoo.com. I’d love to see them! Good luck and have fun creating!

-Credit to Sara Van Der Werf and her webinar “The Pursuit of 100% Engagement: 7

Practical Ideas for Getting Us Closer”.

Steve Levesque


East Greenwich

Problems to Challenge Our Students


As a new feature of the RIMTA newsletter, we will feature challenge examples for your

students. Some of these examples were culled from sources such as Rhode Island Mathematics League contests and qualifying tests from the American Mathematical Society’s Who Wants to Be a Mathematician? competition. Hopefully, these problems will challenge your students and inspire them to engage in such competitions in the future.

But we don’t want to end here. Please share your results with us. Send samples of your

students’ work (creative approaches are especially welcome!) to Leves314@yahoo.com and we may display them in our next newsletter.


1. The roots of the quadratic equation (x^2 + 85x + C = 0) are prime numbers. Determine the value of C.

2. Find all possible ordered pairs (A, B) of digits for which the integer 7A8B is divisible by 45.

3. Triangle ABC has AC = BC. Point D lies on Segment BC such that AB = AD = CD. What is the measure, in degrees, of Angle ACD?

Answers to High School Questions

1. 166 2. (3, 0) and (7, 5) 3. 36 degrees


1. How many three digit positive integers exist such that the product of the hundreds digit and the tens digit equals the units digit?

2. If two cards are selected at once from a standard deck of cards, what is the probability that the two cards are of the same suit?

3. What is the largest four-digit prime number less than 2010?

Answers to Middle School Questions

1. 32 2. 12/51 or 4/17 3. 2003


1. You bought an Iron Man figure for $5, sell it for $6, buy it back for $7, and then sell it again for $8. What is your overall profit? (It is understood that you may have to explain the concept of profit to students.)

2. Barry has some chickens and goats. The animals have a total of 12 heads and 30 legs. How many chickens and how many goats did Barry have?


1. $2 2. 9 chickens and 3 goats


RIMTA Teacher Grant - Reflection on the Stock Market Game

At Ponaganset Middle School this year, the entire school took part in the Stock Market Game on Fridays during the enrichment period. Each student was part of a group and participated in two different sessions of the Stock Market Game. The students learned valuable information about financial literacy and the stock market. As a school, students reflected after the first session of the Stock Market Game and completed a culminating project (poster, pamphlet, Google Slides Presentation, Prezi, interviews, etc.). Before students began learning about the Stock Market and after the culminating event, students took a survey to see what they knew and to see what they learned.

Most teachers took part in the Invest Now piece and had Mr. Michael Laliberte from Baystate Financial come in to discuss financial literacy with the students. The students truly enjoyed listening to him and the teachers learned from him also.

Below are some of the teacher responses regarding the implementation of the Stock Market Game:

Ms. Valente (sixth grade, purple team) said that every Friday she would have a focus topic about what the students were to look for or what to research. She said this worked out well because in some cases, students needed to be redirected because this is such an extensive topic. Her students got very good at diversification and at looking at the news and predicting how that affects their stocks. All in all, they learned a lot and really enjoyed the experience.

Mrs. Noll (sixth grade yellow team) said that the Stock Market game encouraged sixth grade students to learn more about financial literacy as they engaged with investments, stocks, shares, trading, etc. Students worked in groups on their Chromebooks and practiced cooperative learning and technology skills. After the first game session, she had students write a reflection piece on what they had learned. Some of the students’ comments were: ¨It was a fun way to learn some adult skills,¨ ¨I would invest my own money in the stock market because you can make a lot of money,¨ ¨It was a great and fun opportunity,¨ and ¨stocks go up and down like a roller coaster.¨

Ms. Tancrede (seventh grade orange team) said introducing the stock market game to our students helped to expose the students to an aspect of the real world that many adults are not familiar with. It opened a line of communication between students and their parents/other adults in their lives regarding school and specifically, financial literacy. Students learned how to research and interpret information displayed on stock websites like Yahoo Finance, as well as understanding the information available in their own portfolios. One aspect she did not like so much was the accessibility to every piece of information only because the students, then, are required, and in-turn not inspired to, calculate the information themselves. It alleviates them of a responsibility that was a big part of playing the game before being online. Some of her students’ responses after playing the Stock Market, ¨I started paying attention to the Money Matters report on the news,¨ I learned a lot and might invest when I am older,¨ and ¨It is better to spend your money on stocks rather than let it sit in a bank account.¨

Ms. Barrows (seventh grade green team) said students worked together to research companies and determine which companies to invest in. Students calculated total cost of stocks, profits and losses, including fees. She felt it difficult to implement because she was not familiar with the stock market. The students enjoyed working on the final project together.

Ms. Grant (eighth grade blue team) completed the Stock Market Game with twenty students last year during enrichment. This year during Friday enrichments, she would have the entire team in the pod and would do mini-lessons about different topics, such as, bonds, diversification, being a public company, and having discussions about what companies to buy. In her teacher group, one teacher wanted to buy Chipotle, then the E. Coli broke out and the team had a great discussion about the risk and who would have expected that. Overall, the students learned a great deal from the Stock Market Game this year. She thinks competing for one session would have been better because it would have held the students attention. Students on her team completed culminating event projects.

Ms. Shaw (eighth grade red team) said her students enjoyed the Stock Market Game. During the first sessions her students had many questions and were hesitant to spend very much money and began to realize that the news had an impact on the performance of their stocks. They started discussions every day about how their stocks were doing. At the end of the second session, students were asked to write a brief summary regarding what advice they might give their future selves. Many of their summaries included advice that they should invest early and take an interest in their financial health.

Monique Grant

Ponagansett Middle School



Hosted by Doherty's Ale House in Warwick, RI

Facilitated by Steve Levesque

RIMTA will host its second Trivia Night on Monday, November 7, at Doherty’s Ale House in Warwick. No cost to play and no pre-registration is required; just show up, have fun, and test your knowledge of math, education, and pop culture!

The game starts at 7:00, but please stop by early to mingle and catch up with old friends. If you speak to people who attended the first Trivia Night on March 24, they will probably agree that it was a blast.

Hope to see you there!!


Developing Informed Citizens through Mathematics

The New Hampshire Teachers of Mathematics is proud to host the 2016 Fall Conference for the Association of Teachers of Mathematics in New England.

We welcome you to join us to Vote with Math! Developing Informed Citizens through Mathematics! on October 20-21, 2016.

We have an exciting line-up of Keynote Speakers and are working to put together a quality program. We will schedule sessions and workshops by speakers from all around New England and beyond!

For more information, visit https://sites.google.com/a/nhmathteachers.org/atmne2016/

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NCTM Annual Meeting and Exposition, 2017

April 5–8, 2017 • San Antonio

Save the date and plan to join more than 9,000 of your mathematics education peers at the premier math education event of the year.

Why attend?

Hear what makes the NCTM annual meeting a must-attend event year-after-year from fellow attendees and your colleagues in the classroom, then make your plans to join us in San Antonio!

For more information, visit http://www.nctm.org/Conferences-and-Professional-Development/Annual-Meeting-and-Exposition/

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NCTM Regional Conference, 2016

Great Math at Your Doorstep

Philadelphia, Pennsylvania | October 31 - November 2

Plan now to attend the NCTM Regional Conference at the Philadelphia Convention Center this fall! Sharpen your skills, gain new techniques, and achieve your professional goals when you make your plans for this focused professional development opportunity.

Six focus strands allow you to hone in on the topics most important to you while keynote speakers and networking opportunities let you engage and expand your expertise.

Featured Speakers include:

Francis (Skip) Fennell - Past President of NCTM

C3 - Coaches & Collaborative Communities: Professional Learning that Matters!

Dan Meyer: Math is Power not Punishment

For more information, visit http://www.nctm.org/philadelphia/


Math League

Rhode Island Mathematics League

c/o Raymond Morin

19 Bouvier Ave

Manville, RI 02838-1104

401-766-7512 email RIML@COX.NET

This past school year, the Rhode Island Mathematics League celebrated its 50th year of competition. 737 students representing 36 schools participated in the league’s contests It is our hope that you and your students will join us in the 2016-2017 school year!

Important dates for 2016-2017 are:

Wed 14 Sep 2016 Advisors' Meeting 3:45 pm @ Bishop Hendricken HS

A representative from each school MUST be present as division assignments

and host schools are determined at this meeting. $25.00 discount is applicable, if registration fees are received by this date.

Wed 19 Oct 2016 ALL registration fees are due by this date

Wed 26 Oct 2016 Meet I Wed 25 Jan 2017 Meet III

Wed 7 Dec 2016 Meet II Wed 1 Mar 2017 Meet IV

Wed 12 Apr 2017 State Playoffs

Each school may enter up to six teams of five students composed as follows: at most two seniors, if there are two seniors, then not more than two juniors and at least one student grade 10 or below. Underclassmen may replace upperclassmen. Each of the five team members participates in three of the five rounds with three members in each round. A sixth and final round is the team round. Incomplete teams are allowed.

A MAXIMUM of 30 students may participate in any one meet and a MAXIMUM of 40 students may participate from any one school during the year.

Awards are presented to the highest scorer from each participating school. The top one third of the participating teams in the state after the four regular meets are invited to the state playoffs.

The registration fee for 2016-2017 is $150.00 per school (A $25 discount is applicable if payment is received by 14 September 2016.)

League officers for 2016-2017 are:

President: Dominic Dougherty III

Vice-President: Mary Misiaszek

Sec/Treas: Raymond Morin

If your school is interested in participating, please reach out to Ray Morin NO LATER THAN 9 SEP 2016. Registration fees are due NO LATER THAN 19 Oct 2016.

Interested schools may request that a sample contest be emailed to them. A CD containing all fifty years of contests is available at a cost of $10.00.

If you have any questions, please email me at the address found above.

Raymond Morin

Math League

Rhode Island Mathematics League

Participating Schools 2015-2016

Barrington HS

Beacon Charter School for the Arts

Bishop Hendricken HS

Burrillville HS

Chariho Regional HS

Classical HS

Cranston HS West

Cumberland HS

East Bay Met

East Greenwich HS

Exeter-W.Greenwich HS

LaSalle Academy

Lincoln HS

Middletown HS

Mount Hope HS

Mount Pleasant HS

Mt St Charles Academy

Narragansett HS


New Cubed Conference

The first New Cubed (New^3) Conference, sponsored by ATMNE, AMTNYS, and AMTNJ (hence the title from math teacher organizations of New England, New York, and New Jersey), was held at Iona College in New Rochelle, NY from July 26 through 29. A committee of Executive Board Members from the three organizations worked over two years to put together a three-day conference that would be reasonably priced and held at a time when most schools had finished for the year. This would enable educators to attend without missing time with their students and needing to be released from school.

In addition to the usual workshops, sessions and highlighted speakers from the three organizations, this conference had some extra special features:

1. Grade band sessions (PreK-K, 1-2, 3-4, 5-6, 7-8, high school subjects) which enabled presentations to be very grade level specific,
2. About a dozen presenters who gave sessions on each of the three days on related topics which allowed for in-depth exploration of topics in mathematics and/or teaching,
3. A STEM Camp for the children of participants, and
4. An opportunity to build an educational community, sharing ideas and questions with peers, by living and working together on the college campus.

Many participants and presenters said that they liked the series of presentations by the same presenter over the three days, and the grade bands rather than grade spans of elementary, middle, and high school. The children and their parents enjoyed the activities, such as Unit Origami and Scratch, at the STEM Camp.

Overall, this conference was a great success! Thanks to Jim Matthews of Siena College for being the spark that launched New Cubed!

Lynn Rakatansky

RIMTA Secretary

When you join RIMTA, you automatically become a member of the Association of Teachers of Mathematics in New England (ATMNE). ATMNE members receive two annual newsletters, the New England Mathematics Journal (NEMJ), invitations to regional conferences and more! All ATMNE publications have gone GREEN so make sure you keep your email up to date.


RIDE and RI Educators Bid a Fond Farewell to Patty Carnevale

After eight years at the RI Department of Education as a mathematics specialist and twenty plus years as a mathematics educator for the communities of Central Falls and Warwick, Patty Carnevale has decided to retire. Most know Patty as a passionate advocate for mathematics education – believing that all students can succeed and all should have equal access to higher level mathematics. As a teacher she was responsive to her students’ needs with a loving and caring heart, but she always expected the best of them, just as she did of herself.

Patty’s quest for excellence and attention to detail proved to be valuable assets when she undertook assessment work at RIDE. Her RIDE accomplishments are too numerous to list, but some are worth noting. She worked tirelessly on fine tuning the NECAP assessment, coaxing others to laser-like precision when designing items. She rallied behind the Common Core State Standards using her broad understanding of mathematics to help educators throughout the state see their value and understand their conceptual foundation. Drawing on these experiences, she guided educators through the transition from NECAP to PARCC and counseled districts on scrutinizing and improving their local assessments.

Patty loves people as well as mathematics and this is very apparent in her interactions with students, parents, classroom teachers, administrators, higher education professionals, and her colleagues at RIDE.

She is always willing to talk about “the math” (she adores the unit fraction), expressing her opinions with conviction. People may not always agree with Patty, but they always know where she stands. Her candid nature, quirky sense of humor, deep content knowledge, and her aspiration to excellence make her a respected professional in mathematics education. The community of mathematics students and educators has been well served by her efforts.

We wish Patty many happy days of retirement in which to follow her other passions in life – her family and friends, the theater, cooking, and the beach. We hope she continues to serve on our Board.

Susan Pagliaro

Mathematics Specialist

Rhode Island Department of Education

A Tribute to Margaret "Peg" Kenney

Anyone who had the opportunity to be privy to her practices through workshops or coursework, is very well aware of her many contributions to the educational community. All those involved in mathematics education have suffered a heart wrenching loss in the passing of Peg Kenney. For decades Peg has mentored, monitored and directed mathematics education locally, regionally and nationally. Unequivocally she was a superstar in her chosen career of mathematics education. Countless educators were nourished by her wisdom, understanding, expertise and leadership. How lucky we have been for well over 5 decades to have had Peg’s inspirational leadership, dedication and devotion to mathematics education. We will miss Peg, but there is not a doubt in anyone's mind who knows her that she is continuing to be counted as a major influence in math thought.

Lillie Alpert at BC, the SOE math educator, forwarded this link:

http://www.bc.edu/bc-web/bcnews/campus- community/faculty/in-memoriam- margaret-kenney.html