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  • 1 Jun 2020 2:48 PM | Wendy Weber (Administrator)

    Reflections from  Deb Little, the 2018 PAEMST elementary math awardee

    It sure is a strange sounding acronym. And this acronym is necessary, it stands for a mouthful of words! PAEMST, pronounced pam-st, stands for Presidential Award for Excellence in Mathematics and Science Teaching. Read on to learn more about PAEMST, my journey as the 2018 PAEMST elementary mathematics awardee, and why you should consider nominating yourself or someone else for this award. 

    What is PAEMST? 

    The PAEMST is the highest recognition that a kindergarten through 12th grade science, technology, engineering, mathematics, and/or computer science teacher may receive for outstanding teaching in the United States. I had never heard of it before I got nominated for it. Teachers do not go into teaching to get awards. When we read about someone getting an award we think something like, “Oh! Good for them! They must be a really gifted educator.” And then we continue about our work with children trying to do our best. 

    How did I become nominated for the PAEMST?

    In November of 2017, Sandra (Sandy) Ubben had written and asked me if it would be okay to nominate me. Sandy is currently an Illustrative Mathematics Certified Facilitator. When I worked with her, she was a math consultant for Central Rivers AEA. To say that I was flattered to be nominated by my mentor and someone whom I consider a math educational genius is an understatement. I said, “Yes,” and didn’t think anything more about it. Then the emails from the PAEMST organization started to flood my inbox. 

    What happened next?

    As I read over the emails from the PAEMST organization, I became a bit overwhelmed. I quickly realized that applying for this award would not be as simple as filling out a one-page application form and attaching my resume. It includes a written narrative and video recording of one’s class in action. The narrative would be a reflection of my lesson and a description of  my contributions to education focusing on Five Dimensions of Outstanding Teaching:

    • Mastery of the content being taught in the lesson.
    • Use of instructional strategies that support student learning.
    • Effective use of assessment to support student learning.
    • Reflective practice and lifelong learning to improve teaching and student learning.
    • Leadership in education outside of the classroom.

    I also learned that the PAEMST program is organized and run by the National Science Foundation (NSF) on behalf of the White House Office of Science and Technology Policy (OSTP). If chosen as an awardee, I would receive a certificate signed by the President of the United States, a trip to Washington D.C. to attend a series of recognition events and professional development opportunities, and a $10,000 award from the National Science Foundation. To be honest, I was not sure if I was worthy of such an award and decided at that point not to apply. 

    Why didn’t I think I was worthy?

    Let’s face it. The words “excellence” and “highest honor” are a bit daunting. As a teacher, I’ve strived for excellence in my practice, but there are many lessons that I’ve reflected on that I would not describe as “excellent.”  My journey as a teacher is constantly evolving. I could be described as Christina Tondevold says, “a recovering traditionalist.” In my practice of 27 years, I’ve moved from an “I do, we do, you do” approach to one that’s inverted. Now, my students grapple with a problem first and reason to find solutions in their own way. Next, class time is spent with students sharing their reasoning and sense making, asking questions of their classmates’ solutions, comparing what’s similar and different and most efficient. Conjectures are made and recorded and reflected upon in subsequent lessons.  It is a flip of what went on for many years in my mathematics classroom. In January of 2015, I had taken a course offered by my AEA that gave me my first taste of the meaning of cognitively guided instruction. During the 2015 -2016 school year, Sandy Ubben worked closely with me to help me get better at facilitating this flipped version. At her request, I opened my classroom so that other educators could see these sense making learning sessions. I really felt like I was at an infant stage with facilitating this kind of mathematical learning.  

    What changed my mind about applying?

    Right before my school’s winter break in December, I had a discussion with UNI professor, Amy Lockhart at a school event. I had taught both of Amy’s sons when they were in fourth grade. She encouraged me to apply for the PAEMST if for no other reason than to “honor the person who had nominated me.” I decided to apply and give the application process my best effort. I wanted to honor my nominator, Sandy Ubben.

    What happened next?

    I’m not going to lie. The application takes a considerable amount of time to complete. From January to the May 1 deadline, I spent many hours choosing a lesson video and then reflecting, writing, and revising my written narrative. I consulted with former PAEMST Awardee Annette Louk for advice on my application. I attended the online question and answer informational sessions held by the PAEMST organization. I spent hours reading research from math education leaders from sources like the National Council of Teachers of Mathematics (NCTM). Through this whole process, I learned so much about myself as a teacher because I was constantly asking myself why I do what I do in my mathematics work with students. It inspired  me to dig deeper into my understanding of the practices that I had implemented in my classroom.  By the time I submitted my application, I had grown as an educator.

    After submitting my application, I learned that the applications are reviewed first at the state level.  The Iowa State Selection Committee spends countless hours to choose 2 to 3 applicants to move on to the national level. The NSF convenes a national-level selection committee composed of scientists, mathematicians, education researchers, school and district administrators, and classroom teachers. Recommendations are sent to the White House Office of Science and Technology Policy (OSTP) for final selection.

    In August of 2018, I found out that I was a state finalist along with Natalie Franke and Chris Mathews. In October, the three of us were formally recognized at the Iowa Council of Teachers of Mathematics Conference for being state finalists. In March of 2019, we were honored by Governor Kim Reynolds at a reception and luncheon in Des Moines. When I learned of the exceptional math leadership of my fellow finalists, I thought that there would be no way I would be chosen for the national award. I felt so honored to be standing alongside educators of their caliber.

    When did you find out you had been selected as the national PAEMST awardee?

    I had an inkling in late June of 2019. I was contacted by the PAEMST organization that they needed the FBI to do a background check. They were clear that this did not mean that I was the finalist and that saying anything about it to anyone could disqualify my application.

    Then on September 27, 2019, I received an email from the PAEMST organization that I had been selected as the 2018 PAEMST Awardee and was given the steps to make flight and hotel arrangements for the recognition ceremonies and professional development events to be held from October 14 - 18.  I was stunned, humbled, and so honored! 

    Why do I encourage others to apply for the PAEMST?

    It is an  excellent opportunity to reflect on the work you're doing in your classroom, to network, build relationships, learn with outstanding educators and other professionals across the country, and to be recognized for the skill and leadership with which you approach mathematics and/or technology, and science learning. You also will receive feedback from both the state selection committee and the national committee about your work. Rarely do we receive feedback from STEM leaders outside of our own districts.  In addition, there is the $10,000 reward money. Unlikemost monetary awards that are earmarked for school-related use, this money can be used at your discretion. I am using it to help cover the costs to attend mathematical conferences and to take additional mathematics courses.  

    So how do you nominate yourself or someone else?

    If you're interested in applying or nominating someone, you can find more information by visiting the PAEMST site.  Every other year the award is open to either a K-6 or 7-12 teacher. The current 2020 nomination cycle is for K-6. Because of COVID-19, the application dates were adjusted. Part of the K-6 cycle application was due on May 1, and then those applicants have until October 26, 2020 to submit final applications.  That would mean that the next cycle for applications will be for 7-12 STEM teachers.

    What should I do while I wait for the next nomination cycle?

    In the meantime, keep growing as a professional in the area of mathematics. If you haven’t already, sign up and become an active member of Iowa Council of Teachers of Mathematics (ICTM).  The membership is very affordable and offers excellent resources. Become a member of NCTM so that you have cutting-edge research articles at your fingertips. Attend ICTM and NCTM conferences to learn in person from leading educators. Consider presenting at the next ICTM conference or writing a journal article for ICTM or NCTM. Invite other educators into your classroom. Learn and grow by honing your practice by working with a district math coach, a math consultant from your AEA, or a mathematics education professor from a local college. Get on Twitter (I call it my nightly P.D.) and connect with math educators across our state, nation, and world. I believe that we grow the most when we share our classroom practice and reflections with others. 

    Deb Little is a fourth grade teacher at Denver Community School District.  She can be reached at and on Twitter: @Mrs_Little_17. 

  • 6 Jan 2020 2:51 PM | Wendy Weber (Administrator)

    With all the fanfare leading up to ISASP, taking ISASP in April and May, and then waiting for the ISASP results, the process was draining on myself and the students. We didn’t do anything different to prepare for the assessment, but there were a lot of small events that brought on some unneeded anxiety. For example, I could tell my students were feeling the heat, as many teachers, including myself had mentioned a new and more expansive assessment throughout the school year to the students. When we took the test, students even had to deal with the Pearson person coming in and observing them testing. I have visitors from other districts come into my room regularly to check out what we are doing, so the students are used to it, but I can imagine as a student, that there is nothing like having a random stranger sit in during one of the more nerve wracking days of the year watching you like a hawk. I’ve got no problem with anyone having tattoos, but this guy had 100 of them, and my students commented that the tats were a little distracting! Students have plenty to worry about in their lives, and it was unfortunate that anything associated with ISASP stressed any of them out. The stress for myself and my students certainly wasn’t worth it, especially with the relative letdown that came when we took the test and realized that it really wasn’t a lot different than the old Iowa Assessments, and finally getting the results that didn’t help me to inform my teaching at all. All I learned is that my students did “well.”

    Current 8th Grade (As 7th Graders With Me)
    Proficient 66%
    Advanced 22%
    Not Yet Proficient 12% 
    State Average 60/10/30

    Current 9th Grade (As 8th Graders With Me)
    Proficient 42%
    Advanced 49%
    Not Yet Proficient 9% 
    State Average 61/11/28

    Before you say that I have the best students already (I do love my students), both of these classes had been right at or below the state average as far back as the 6th grade. My students are improving because of what we do in class on a regular basis, and my high expectations for their learning. In this post, I will outline what I believe we do in class that makes us successful on ISASP and otherwise, and my strong recommendation for an appropriate amount of time to take the ISASP assessment, as I think this is one of the biggest misconceptions about ISASP that needs to be explained, especially to those who don’t have a mathematics education background.

    I had a lot of curious people come up to me at a recent State Mathematics Leadership Team meeting and asked how my students did on the test. I let them know how well we did, and I got a lot of questions that made it sound like I had some sort of secret formula for success. Here was my “secret formula.” Avoid test prep. Avoid trying to dumb down material to work on “basics.” Avoid cramming before the test. None of these things work. Everything in this category promotes surface level learning. Students also sense when they are doing something that isn’t as rigorous as it probably should be, and worse, students know if you are giving them different material because they haven’t been successful with whatever everyone else is working on. If you think that is building confidence, it does the opposite and makes students feel worse about themselves. Special education students are no different, and I feel our special education population was successful on ISASP because I have similar expectations with them as I would any other student. 

    Here are some of my “secrets” I do that I would contribute to our success on this test. I am not into telling anyone how to do things in their own classrooms. Teachers are unique and should be allowed to let their uniqueness shine through. This may look different to you in your classroom than it does for me, but if you would like to talk about how this looks in my classroom, I would be happy to discuss. 

    Assess EVERYTHING, giving feedback to help make revisions

    Anything my students do is assessed by me personally. I leave personal feedback on every assignment no matter how small or how large. I use class time to give verbal feedback as well. I want my students to have a good understanding of where they are, and I want to have a solid understanding myself of what my students know. A lot of the more informal ways of assessing don’t give me the information I need as a teacher to make informed decisions about my students’ mathematical understanding. Things like thumbs up/down, fist to five, completion points, and going over the homework as a whole class doesn't give me enough information about what a student really knows. Sure, assessing everything is time consuming, but it is worth it. Have you ever gotten to a final assessment and were surprised that your students did poorly? You may have been using one of those methods above. You should always know how your students will do on an assessment prior to the assessment because you have been giving feedback and assessing along the way. By the way, this has nothing to do with grades, just feedback. 


    After I assess an assignment/assessment/task, it is always given back to a student to revise. The expectation is that revisions are made. I even work in time during class to allow for these revisions. It doesn’t make any sense to let a student move on who has only mastered 80% of an assignment. I can go over the answers with the class and pretend that the students thought through their mistakes in the 2 seconds I would give them, but I would be kidding myself. I allow for ample time for students to revise, and I will reassess after the revisions for full credit. Almost all of my students get 100% in my class because of this, and I absolutely think this is fine. I am only concerned that the content is understood and mastered. This is one reason we do so well on the ISASP assessment, or the NWEA MAP. We tie up any misconceptions right away. 

    Tasks to promote productive struggle

    Some people shy away from 3-Act type tasks because they may take up large chunks of time, and most of the ISASP questions are more general multiple choice, which wouldn’t fit the format of a 3-Act task. I will give you an opposite viewpoint. My students excel on long and grueling tests because they have multiple chances throughout the year to develop productive struggle. They are willing to stick with something and not give up. They know how to make adjustments and persevere through tough situations. Part of fostering productive struggle is through the teacher’s questioning techniques, which obviously isn’t happening during ISASP, but another part is students utilizing strategies that they have learned to help themselves move forward when stuck. How many students have you had who have started out on fire on one of these large tests working hard and reading each question, only to revert and finish the last 30 questions in four minutes? Working on tasks that require some productive struggle can help students stick with the test for the long haul, because they are used to doing this daily in class. 

    Requiring justification for EVERYTHING

    For anything my students do, they turn in accompanying work that gives me an idea of their level of understanding. For me, the point of assigning something is to see what they know, and if my students turn in pages of answers, I really don’t learn anything from that. I am looking for things like charts, tables, numbers with context, paragraphs, pictures, etc. I can diagnose misunderstandings much easier when students justify everything, and students feel better with their levels of understanding because they can explain it as well. 

    We are a 1:1 school, and while we use a lot of computer programs, we also probably use more paper than any school in Iowa. We use common programs like IXL, Buzzmath, and Desmos, and while answer are often typed onto a screen, I always check the justification to go with these question and answer screens. If you don’t require justification, 1:1 mathematics can quickly turn into a button mashing event. And you wouldn’t believe how easily students can hit buttons on computer programs and eventually get something correct….

    This helps with ISASP as my students are used to showing this level of understanding for everything, including a standardized test. My students each averaged 5 pieces of scratch paper each during ISASP. Having students justify answers slows down the thought process causing students to think deeper about whether an answer is correct instead of just picking what first pops into their heads. 

    Longer time limits for assignments

    Anyway you can build this into your classroom would be ideal. I have students that understand the mathematics at much different rates, and I have learned that it is silly to go with the one section of a book, and then move onto the next section the next day format. Some students will figure things out in a day, some will take three. When I bring this up, people always say that maybe the universal instruction needs to improve, and I wholeheartedly disagree with that opinion. When more time isn’t built in, oftentimes students move on without understanding. This happens multiple times over a student’s career putting them further behind each time until they are years behind. This takes the teacher being flexible and having multiple activities going on at once, but since I have changed to being more of a facilitator/questioner anyway, this works well. My students do well on ISASP because we have actually taken the time to make sure everyone understands each standard at a high level without moving on and leaving gaps in learning.

    On the surface, ISASP appears to be untimed and very supportive of my students' everyday experience in class where they have time to think through and process problems and tasks. However, once I figured out how many questions were on the assessment, I knew I had to lobby for more time. The untimed moniker of ISASP was frustrating because it really wasn’t untimed. We had to finish the mathematics test in a day. While our district is very supportive of our needs as educators, it was probably hard for an administrator to understand that a middle school test could take an average of three hours to complete. Believe me, it sounds crazy just typing it. Couple that with administrators from our district hearing other districts say it took an average of 40 minutes for their students to take the mathematics portion on ISASP, and I could see how people could be skeptical about my three-hour time frame. 

    Here is my thought process. In my classroom, my students are used to analyzing a problem, thinking about their next steps to solve the problem, solving the problem, and providing justification for each problem showing their understanding. To do this for a standard mathematics problem, it may take 2 to 4 minutes. That doesn’t sound at all far fetched to me since I live it everyday in my classroom. My students have a deep understanding of mathematics because that is what I encourage. That is what the expectation is. Rewind back to ISASP. 52 questions. Each question different than the next. 2 to 4 minutes per question mimicking what we would do in class. About 500 sheets of scratch paper later. There is my  average estimate of three hours to complete the test. If we averaged 40 minutes for the test, that would be less than a minute per question. I can only imagine the effort and thought going into each question would be low in that circumstance. 40 minutes seems like the more far-fetched option to me. Needless to say my middle school students were extremely successful. I am so proud of their efforts. The level of buy-in from my students was incredible. 

    Reading this post you may think I love standardized assessments and think about them often. I actually despise them if we are being honest. They take a long time to finish, and the results that I get don’t help me make better decisions in my classroom. Unless I can have the test questions after the test is over, and I can keep the scratch paper to match up with each question so I can examine my students’ thinking, the results don’t help me. 

    After participating with my role within ISASP the first year, I know I won’t be as stressed out the next time around. I plan on keeping things simple. I will continue to do the things that have worked in my classroom, that consequently translate to a deeper level of mathematical understanding, which will yield better results on these types of assessments. If I were to make a recommendation for ISASP, cut the number of questions in half. I think the state could still get the measurements they are looking for with far fewer questions, especially since the results received don’t help teachers make meaningful decisions anyway. Until the next iteration of ISASP, I will be saving my money to make an even bigger Cheez-It pyramid so the students’ will have plenty of testing fuel, for our ultra-fancy scratch paper pencils, and for the massive roll of paper it will take to cover all the walls in my room! I certainly will not be living for the next test, but rather the genuine excitement my students feel on a daily basis when a level of understanding is achieved!

    The Iowa School Performance Profiles were recently released to the public, and our students got some outstanding news. The mathematics growth category is measured by matching students across the state by percentile on the old Iowa Assessment and comparing what they got on ISASP. For instance, all students in the state scoring at the 74th percentile on the old Iowa Assessments were compared using ISASP. We were very successful in those comparisons. We received the highest mathematics growth score in the state for both 7th grade (current 8th graders) and 8th grade (current freshman).


    My students were extremely excited and proud to hear the news. There are a lot of middle schools in the state, and it is an honor to be considered the best of the best.

  • 14 May 2019 12:00 AM | Wendy Weber (Administrator)

    Hello ICTM members! My name is Angie Shindelar and I serve on the ICTM Board as the Vice-President for Elementary. I previously taught elementary and middle school math at Nodaway Valley CSD. I am currently a Math Consultant for Green Hills AEA.  

    My recent articles have discussed effective instruction for addition and subtraction basic facts. You can find the articles on the ICTM website in the three previous newsletters if you are interested and missed them. In this article I continue with the basic fact theme but turn the focus to thinking about the learning progression prior to basic fact instruction. Understanding this progression and being intentional about building a foundation for basic fact instruction can ensure our students’ success in achieving fluency for addition and subtraction basic facts in a timely way. These critical understandings are important for K-2 teachers but also for teachers working with older students that are struggling to make sense of basic fact strategies fluency. 

    Prior to instruction in basic facts students should develop understanding of parts and wholes. There are three critical components to this work: 

     1) subitizing

    2) knowing plus 1 and minus 1

    3) composing and decomposing numbers

    Below is a description of each component and a list of Iowa Core Math Standards that encompass the learning for each component.

    The first critical component of developing understanding of parts and wholes is subitizing. Subitizing can be described as instantly seeing how many without the need to count. The human brain can instantly tell “how many” of up to 5 objects without having to count. Beyond 5, our brains have to break a quantity into smaller chunks. Subitizing experiences provide students opportunities to think about quantities in different arrangements and using different models. A typical subitizing experience is when a teacher quickly flashes a quantity for students to see and ask students, “How many do you see?” The teacher asks several students to tell how many they saw and how they knew how many there were. Students will describe everything from attempts to count the items individually, relating to arrangements they are familiar with, and describing smaller parts within the whole.

    The quantity might be represented with a dot arrangement, a five/ten frame, or a rekenrek (number rack). Below are examples of different arrangements of a quantity. To build understanding of parts and wholes, students should experience visualizing quantities in various arrangements and with the different models.

    When subitizing is a regular routine, students first become familiar with arrangements up to 5. Once the arrangements move beyond 5 the goal shifts to looking for the parts within the whole. Students learn to resist the temptation to count and instead focus on the arrangement looking for the smaller parts. For example, when shown the quantity of 6 in the arrangement below, students may agree there is 6 but describe how they knew differently. Some may see 3 and 3, while others noticed 4 and 2. By working on subitizing as a regular routine, students learn to look for parts they recognize in quantities typically up to 10.  

    One of the best resources for subitizing is Number Talks by Sherry Parrish. There is an entire section on subitizing with many examples of arrangements and models for quantities up to 10. This book really helped me understand the importance of providing different arrangements for each number and varying the model.

     While subitizing is not specifically referred to in the Iowa Core Math Standards, it lives within the Counting and Cardinality standards. You can find references to subitizing when you read further about the standards and unpack the specific learning within them. This standard relates most closely to the subitizing work: 

     Understand the relationship between numbers and quantities; connect counting to cardinality. (K.CC.4.)

     The second critical component of developing understanding of parts and wholes is plus 1 and minus 1. This can be tricky, because we often think of it as facts like 5 + 1 or 4 -1. However, prior to working on basic facts in this format, it is critical to build understanding of what plus 1 and minus 1 actually mean. Students in early grades spend a considerable amount of time counting and thinking about what number comes next, what is one more than, what number comes before, and what is one less than. They develop this understanding by connecting it to the count sequence and are typically successful and confident. However, when given problems like 5 + 1 or 4 - 1, too often we see students not make the connection of what is one more than, what number comes before, and what is one less than to addition and subtraction. It is often baffling to teachers as they see students counting fingers to solve.

     As students are learning about these important understandings, it is critical to make explicit the connections to the language of addition and subtraction and representing with equations.

    Explicitly discussing and modeling that one more than and what number comes next is written as +1 is critical to students making connections. They have to see visual models, hear the language relationship to addition and subtraction, and have opportunities to use mathematical symbols by writing equations to represent the plus 1 and minus 1 concepts.

     Word problems also help students make connections to addition and subtraction. Posing addition and subtraction word problems as a regular part of students’ learning provides opportunities to use the language of one more or one less and make connections to addition and subtraction. Including connections to equations is key to this work. Here are examples of intentionally connecting the concept of plus 1 and minus 1 in word problems:

    Sam has 6 toy cars. His brother gave him 1 more. How many toy cars does Sam have now?

    Mei has 7 cookies. Rob has 1 less cookie than Mei. How many cookies does Rob have?

    Students work on finding ways to represent the problem and solve. While sharing ways to represent, the teacher brings forward the discussion of what 1 more or 1 less means and how to record mathematically with an equation. 

    While plus 1 and minus 1 is not specifically referred to in the Iowa Core Math Standards, it lives within both the Counting and Cardinality and the Operations and Algebraic standards. You can find references when you read further about the standards and unpack the specific learning within them. The standards that encompass plus 1 and minus 1 are listed here:

    • Count forward beginning from a given number within the known sequence instead of having to begin at 1. (K.CC.2.)

    • Understand the relationship between numbers and quantities; connect counting to cardinality. (K.CC.4.)

    • Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (K.OA.1.)

    • Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. (K.OA.2.)

    • Fluently add and subtract within 5. (K.OA.5.)

     The third critical component of developing understanding of parts and wholes is composing and decomposing numbers. Understanding that any number can be composed and decomposed in different ways is essential to later fact fluency work. For example, think about all the ways to make 6. Through exploring ways to make 6, for example, students build understanding of the quantity 6 as well as patterns and properties. Discussions of the combinations can highlight patterns like when we have 3 and 3, we can take away 1 from one group of 3 and give it to the other group of 3. So now have 2 and 4. If we again take away 1 from the group of 2 and give it to the group of 4, we now have 1 and 5, etc. Or we might highlight that 4 and 2 is a way to make 6, and we also see that 2 and 4 are shown. Exploring this brings forward discussion of the commutative property for addition.

    Providing regular opportunities for students to engage with composing and decomposing numbers is essential. Discussion of students’ findings and connections to patterns and properties will deepen understanding of parts and wholes. Resources that highlight activities for parts and wholes understanding are Student-Centered Mathematics by John Van de Walle and Developing Number Concepts, Book 2 by Kathy Richardson. Here are a few activities I have assembled in this document based upon activities I have used from these resources.

     In addition, the Put Together Take Apart problem type that requires finding both addends is a perfect opportunity for students to work on composing and decomposing. Below are examples:

    • There are 6 animals in the zoo. Some are tigers and some are bears. How many are tigers? How many are bears?

    • There are 7 chairs. Some are red and some are blue. How many are red? How many are blue?

     Composing and decomposing numbers is specifically referred to in the Iowa Core Math Standards in the Operations and Algebraic standards. You can find more specific references when you read further about the standards and unpack the specific learning within them. The standards that encompass composing and decomposing numbers are listed here:

    • Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. (K.OA.1.)

    • Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. (K.OA.2.)

    • Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). (K.OA.3.)

    • For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. (K.OA.4.)

    • Fluently add and subtract within 5. (K.OA.5.)

    Note:  There are first grade standards that also could be included, however I chose not to include them because the intent is to describe essential learning prior to working on basic fact strategies.

    These three critical components for developing understanding of parts and wholes set students up for success as they begin formal work in fact strategies. Students that are learning fact strategies with ease and steadily working toward achieving fluency have a solid understanding of parts and wholes. Contrastly, when students are struggling with learning fact strategies and are not progressing as expected toward achieving fluency, you can almost guarantee the gap in their learning centers around unfinished learning around parts and wholes.

     I am always interested in your thoughts and feedback for any of the topics I discuss in the ICTM newsletter. You can reach me at

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