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Dr Nicki and Ann Elise's Top Ten Ways to Get Students Problem Solving - Teacher as podcast discussion

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Dr Nicki and Ann Elise's Top Ten Ways to Get Students Problem Solving - Teacher as podcast discussion

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Episode 64: Top Ten Ways to Get Students Problem Solving with Dr. Nicki Newton and Ann Elise Record - The Teacher As

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Dr. Nicki Newton and Ann Elise Record are back! They each have their own lists of the best ways for students to practice problem solving and they collaborate to create one essential top ten list.

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Top Ten Manipulatives - Teacher as podcast interview with Dr. Nicki Newton and Ann Elise!

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Top Ten Manipulatives - Teacher as podcast interview with Dr. Nicki Newton and Ann Elise!

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Episode 44: Top Ten Math Manipulatives — The Teacher As

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In this second edition of Top Ten, Dr. Nicki Newton and Ann Elise Record return with their own lists of top ten math manipulatives and collaborate to create one essential top ten list. Dr. Nicki and Ann Elise are so knowledgeable and share their favorite manipulatives and how they like to use them w

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Dr icki Newton and I joined podcast host Melissa Milner to create a List of 10 favorite math daily routines. Such fun!

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The Teacher As...Top Ten episodes are a new addition to the podcast. Dr. Nicki Newton and Ann Elise Record collaborate to create one top ten list of math routines. The collaboration gets a bit intense when the two disagree as they get closer to the top five picks. These math educators have so much to share in this episode.

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030: The Teacher As...Top Ten Math Routines with Dr. Nicki Newton and Ann Elise Record - The Teacher As...

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The Teacher As...Top Ten episodes are a new addition to the podcast. Dr. Nicki Newton and Ann Elise Record collaborate to create one top ten list of math routines. The collaboration gets a bit intense when the two disagree as they get closer to th...

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Worksheets: 5 tweaks for deeper understanding

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Worksheets: 5 tweaks for deeper understanding

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Moving Forward: NCSM/NCTM Joint Statement

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Moving Forward: NCSM/NCTM Joint Statement

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Moving Forward - NCSM and NCTM Joint Statement - National Council of Teachers of Mathematics

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"We live in uncertain times. Public health is at the forefront of our minds, and our schools have been disrupted in ways we have never seen. Although no one can predict how education might

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Ann Elise: Well, first of all, we need to define fluency. We need to be all on the same page of what fluency means. So in my presentations I ask people, "What words come to mind when you think about being fluent with your math facts?" And, overwhelmingly, people will put words like 'speed.' Speed, fast, automaticity, all words about speed. And then occasionally, I'll get 'accuracy,' right, because kids can give the right answer but then be wrong. Right? So we want to have the accuracy as well as it being, I call it relatively speedy, because it's the least of the four things I want to talk about. But there are two more pieces of fluency, which is crosstalk.

Jon Orr: Today we speak with Ann Elise Record. Ann Elise is a seasoned educator with a career spanning over two decades of elementary classroom experience. These days, she's a K-5 math coach who works with districts on developing strategies to increase students' fact fluency as well as how to use manipulatives in the classroom.

Kyle Pearce: Stick around as we'll discuss effective strategies to help students build their fact fluency, how to help students with the progression from additive thinking to multiplicative thinking, and, how can we help students with concepts that hold them back from their learning?

Jon Orr: Let's do this, Kyle.

Kyle Pearce: Welcome to the Making Math Moments That Matter Podcast, I'm Kyle Pearce from tapintoteenminds.com.

Jon Orr: And I'm Jon Orr, from mrorrisageek.com. We are two math teachers who, together...

Kyle Pearce: With you, the community of Math Moment-Makers worldwide who want to build and deliver math lessons that spark curiosity...

Jon Orr: Fuel sense-making...

Kyle Pearce: And ignite your teacher action. Are you ready, Jon, to dive in to this awesome conversation with a dear, dear math friend?

Jon Orr: Mm-hmm (affirmative), mm-hmm (affirmative), of course, Kyle. We are honored to bring Ann Elise Record onto this show as we've been looking forward to this conversation.

Kyle Pearce: All right, but before we dive in here, Jon, we want to make sure that you folks at home have taken the time to explore some of our most recent full units of problem-based math lessons.

Jon Orr: Right, right. We've been busy adding full units to our Make Math Moments website. And last episode here, we shared some details about our six day unit called the Wooly Worm Race that was created to help educators address teaching fractions, decimals, and percentages conceptually.

Kyle Pearce: Well, we've also tossed in some more context, rich, problem-based math lesson fun with our unit called Snack Time, where students explore the tapintoteenminds.com classic three-act math task called Cheese and Crackers, to use partitive division to partition and distribute slices of cheese to a specified number of crackers.

Jon Orr: That's definitely a classic I've used with my class, and now I'm set up with a whole unit of connected math talks. Sense-making prompts, purposeful practice, and summative assessments, all scraped from my web browser by visiting our test page at makemathmoments.com/tasks.

Kyle Pearce: Yes, it's super exciting, Jon. We hope to see you over at makemathmoments.com/tasks, so that you can run one of these awesome problem-based units in your classroom today.

Jon Orr: All right, enough from us. Let's get on with our great, great, great, great conversation with Ann Elise.
Hey there, Ann Elise, welcome to the Making Math Moments That Matter podcast. As always, we are super excited to chat with someone we've met, someone we know... How are you doing today?

Ann Elise: I'm doing great, doing fabulous.

Jon Orr: Awesome stuff, awesome stuff. Well, we know you quite well, but maybe there's a few Math Moment-Makers out there who aren't as familiar with Ann Elise Record. Can you help us out? Let's learn a little more about yourself. What's your role in education and how did you get to that part in your learning journey?

Ann Elise: Sure. Currently I'm a consultant. So currently I work for myself out of my home and I was traveling around a lot and working in schools and districts, and also presenting around the country for the Bureau of Education and Research. But then once we had the shutdown, I've been working from home. But I had gone to get to, my undergraduate degree was in sociology. So I was not certified or able to teach. And so I got back to school, once our kids were becoming of school age, I went back to school and got my master's in order to teach. And then I taught grade five for 13 years. And then a math coach position opened up in my district, and so I became the math coach K five.
And that was really the start of my journey to truly understand the trajectories of the learning and progressions of kids from the early numeracy on up, and all those connections. But also at that time, I taught some pre-service college classes, the math methods, I helped people, tutored them to help pass the Praxis test, because I've experienced in this role, working with so many different populations of people. And I've seen the anxiety and the stress and the phobias, firsthand, of people.
And I didn't have that growing up. When I grew up, I could answer things quickly and accurately, so I felt good about myself. But to have seen the phobia up close for a variety of people, it was surprising to me how many of the college kids were terrified of math going into teach elementary. And it just became a passion of mine, the more that I learned, why I wanted to share with people. And my husband got a new job two hours south of where we had been living. And then I'm like, "Well, what am I going to do now?" There weren't any math coaching positions. I loved working with the teachers, and the kids, and everyone. And that's when my two close friends and mentors, Dr. Nicki Newton and Christina Tondevold, said, "Well, why don't you go off on your own?" And that's what I did. So my life has been completely different these last few years, doing this new part of my life.

Jon Orr: Yeah. And I think you've brought up a huge point about math anxiety being a huge thing, and I think still is for so many people, and I'm wondering, what suggestions can you give our listeners right now, and teachers, that can help reduce that anxiety? If you've been recognizing it's a problem in your past, in your career, now I'm wondering, I guess, two things. One is, what can we do now to help kids, and even teachers, reduce some of that math anxiety? But then I'm also wondering about, what did Ann Elise look like as a early teacher? Did you recognize that right from the get-go, that we've got this math anxiety, and it's something that you've been using in your career right from the start? Or is that a progression that built up over time? And so those are, I guess, two things to talk about.

Ann Elise: Yes, okay. So first of all, when I think back to when I first began teaching, so I think we all know what we know at the time and we don't know what we don't know. And so, in my master's program to teach, the only class that I had to take that involved math to become certified K eight was math and literature. So it was a literacy-based math class. So I came out certified K eight, really being no more qualified to understand early numeracy than I was to teach an eighth grade math class. I think the assumption was that you'll be given a textbook of whatever district hires you, and you follow the textbook. So that's what I did. I became the grade five teacher, we had a textbook, I was very procedural in my teaching. It's all that I knew when I grew up learning math. It was a very procedural, rote procedure. There was no open tasks. There was no talking about our thinking or having any kind of flexibility of thought.
And so I gave time test to my classroom, all 13 years I was in the classroom. And over the course of that time, I know I did concrete and pictorial things, but it was leading toward the algorithm. I didn't do flexibility with number sense, I was trying to show them why the algorithms worked. I didn't know anything else. So it definitely was not in play the first many years that I was teaching. But as I learned more, and we had a consultant come to our district that showed me how to teach math in a visual way, that was totally new to me. I had no idea that you could teach math visually, like pattern blocks, refractions. It was a mind-blowing thing to me. I had never seen it before.
So it's been, certainly, I call it a journey because I think we're all on journeys. We as educators, as well as the kiddos, right? As we get to find out where we are on that journey, and then you continue and when, Dr. Maya Angelou says, "When you know more, you do better." And that's exactly what I believe and I've been living, that, I know the more that I learn, the more I realize I have to learn. This is a never-ending process. And so, I think we need, I need to send the message to people, I want to let the people know that there is so much more to mathematics and connections and a beautiful journey to it, so far beyond rote memorization and procedures. Because I think that when we think about giving kids worksheets that are just 20 kill and drill things, that's not going to be encouraging a love of math, nor will it build the flexibility of thought that we need to build our number sense and to develop the confidence to try harder problems.
The idea of the growth mindset messages of Jo Boaler from Stanford, the fact that our brains have the way of growing new parts. There is no such thing as a math brain, but think what happens is people have gone on their journey, and I truly believe time tests have begun, well, research is out there that proves it, but, that it's the start of math anxiety. Kids think that because they're not fast at the math, and they're not good at math, and it begins disassociating themselves from the idea that they can be a mathematician. And then it gets harder over the course of the year, as if we're only doing procedures and formulas. That's the only way they've been exposed to thinking and algorithms... Algorithms take lots of steps. And I think, I'm like, a three digit by two digit multiplication problem, that's a lot of calculational work.
But until we explore these things in more flexible ways, it can make it much easier. And I find that my consulting work, the more that I share these ideas, and that they're seeing the math in a different way. Even the parents, I have my districts do math nights, because I want to talk to the parents. It's huge we get the parents involved. And by the end of that 30 minutes, the parents are like, "Oh my gosh, this is a whole new world to me. That's why my child was doing that this morning." Literally they've said to me, "We were arguing with my child this morning about eight plus six. We just told her, 'It's 14.' She's like, 'But no, mom, that's not the way I was supposed to do it.'" And the parents were like, "But now we know why, and we totally get it. We've seen the future impact of that work."
And so, the whole anxiety piece comes from, not the math, but the feeling of insecurity and embarrassment and humiliation people have felt growing up, that they were not a math person, as if it takes some extra kind of brain to be good at math. And it's not true. We all can grow those parts of our brains, and in fun and engaging ways. I want our students to have no bad stories of math growing up. In all my consulting, I would say probably 80% of the people that I meet tell me the most awful, traumatic math journeys of their lives. It's just always negative. They're always about 20% like, "Oh, it was good. It was fun. I loved it." It's like, "Well, you're like me then, because I got my answers correct, I was able to get them done fast, so I thought I was good." But it wasn't until I really began this deep journey that I realized I didn't have any understanding of mathematics, so I didn't see connections to topics within the math. But now the more that I learn, the more I'm like, "Oh my gosh, that connects to that. And throughout the grade levels, even, it's a beautiful thing, to finally see those connections.

Kyle Pearce: Yeah. Well, and we love asking about these things because I worry that when teachers and educators who are at that place in their own journey where they feel like maybe they don't feel comfortable with the content, or they maybe remember their own math anxiety that they had as a student, or they just think plain out that they're doing it wrong and they see someone like yourself, Ann Elise, or Jon and I, and we are so into thinking about how mathematics develops, and thinking about the conceptual connections, all of those pieces. But yet, most of us, most of us didn't have that same experience growing up. And many of us, as you just mentioned, and it's great to hear, that, many of us actually taught it the way we were taught. And it's okay if that's where someone is as they're listening. So I think that is such a huge message for people to see that it takes time.
And I immediately connected when you were describing how you were teaching very procedurally and you were trying to help kids to understand why the procedure works, which I think is part of that trajectory. If you learned procedurally, you tend to teach procedurally, and then hopefully over time you start to see that, "Oh, connections are important." But then what we do, it seems like for me, anyway, I started to still teach the procedures, but then I tried to explain them afterwards. Instead, now we're realizing, "Oh, we really need to start with kids making meaning, and making sense first, and then working towards and allowing those student-generated algorithms to start popping out and helping them to make their connections so that we can essentially get more efficient along the way, but not with the end goal just being an algorithm or a procedure, right?

Ann Elise: Absolutely, 100%. And in fact, the more learning that I'm doing, I've been trying to work on my own knowledge of middle school mathematics, in terms of the conceptual understanding. I can get right answers, I help people pass the Praxis test. That's not the issue of getting right answers. It's, I want to get the connections that I missed first time around. And so I've been doing a lot of work on that. And the more of the work that I'm doing, I am doing mental math or ratio tables and things of using chunks of numbers that are nothing to do with the algorithm. And I'm getting easy answers really quickly, I'm breaking apart numbers in ways I never had done before, and it's just a matter over time. I do a lot of Pam Harris' Math Strat Chat every week, and inaudible Academy. I took a class with Pam Harris on proportional reasoning, that is just like, I'm learning these ways of thinking about it. When I learned it the first time, I had no idea of those connections, I was just following procedures. And it's just a beautiful extension to what I already know as a foundation of understanding K five, and to extend that to that middle school level.

Kyle Pearce: I love that. And it's actually ironic that, nowadays you'll see, both in your messaging and so many others who come on our show and obviously Jon and I, who, we do not believe, like math fluency is not speed. Yet, when we actually start to help kids become more flexible in their thinking, and start to play with different strategies, and really just give them the freedom to think and use critical thinking in order to reason and solve through problems along a trajectory, along a progression, what I end up seeing is actually kids end up becoming more quick with their math facts than kids who are memorizing the procedure. It's actually mind-blowing when you're saying ,"No, no, we're..." It's not about speed, but then the end goal ends up oftentimes becoming speed anyway, which isn't the holy grail, it's just like a symptom of having flexibility and fluency with number. And I'm hearing that in your voice, I hear that in your message.
So before we dive deeper into fact fluency, because we have a lot of questions for you, we know your connections with Christina Tondevold, as well as Nicki Newton. We know you're big into that, and we'll be diving into those questions, but before we let it get out of hand here and we dive too deep, we've got to hear about a math moment from your past. So you've described a few things about how you began teaching, how you taught for a while, also, a bit about your experience learning in the classroom as a student, but is there a moment that pops out in your mind? It could be defining, maybe it's something that, like a celebratory moment, or it could be one that maybe you remember, and it's one of those memories that you sort of wish you didn't remember. What's a math moment that pops out in your mind that you're willing to share with our audience?

Ann Elise: First of all, I'm just so happy to be able to share you my math moment, because I've been listening to your podcast forever. And I walk my dog listening to it. Whenever you ask your guests, I'm like, "Oh, I would tell this story if I was ever inaudible them." When I became math coach, K five, before I began that part of my job, I took a one-week class with Dr. Mahesh Sharma, on, really, it was K eight type content. And it was the first time I saw the connection between grade levels of things I could do at a lower grade level that affected what came up. It was my eye-opening to that kind of procedure. Well, we did the area model of multiplication, and he loves Cuisenaire rods, they're my favorite math manipulative. I think they're the key to helping our kids move past the counting phase of reasoning and into strategic, additive thinking, multiplicative reasoning.
inaudible we had these Cuisenaire rods and we built area models of basic facts. So in the third grade content, right? Well, over the course of that week, we kept using the area model to do double digit by double digit, or to do decimals by decimals, or mixed numbers by, like the same area model, I was able to use with harder content. Well then he said, "We get to division, and we're using the area model to do division," which I had never, ever thought of before. And we were doing it concurrently with the Cuisenaire rods. And he put on the board 'X squared plus five X plus four.' That's the exact problem that he gave. And he wanted us to divide it by X plus one. Now, I remember my brain saying, "I'm out." I took calculus in high school and again in college, it wasn't like, I really thought I did well with math. But, it had been decades since I had done that before.
So I'm like, "Okay, well I'm out. I'm not even going to attempt this." But then he said, "Try doing the same thinking we've been doing with the division for the area model. Can you make a rectangle that is X plus one by something?" And within 20 seconds, I built the area model, I knew the answer was X plus four, and I could explain to you why. And that was my moment that I went, "Oh my gosh, a model that I can show the thinking with the kids in third grade, can follow them through their entire math journey, and the math journey will make sense." It's not just getting a right answer. And I was sold on the whole idea of, "Wow, this is just a learning progression." And the more that I see that, the more that I know, it's all about that journey.
My husband has been working from home since the shutdown in March, and he says, and after doing a lot of trainings online, he's like, "Hon, you say the word 'journey' all of the time." I'm like, "I know, but it is true." We're all on a journey, right?

Jon Orr: Yeah, yeah, for sure. And I'm glad you brought up the area model because we love using it, we love talking about it, and we think it's...

Kyle Pearce: Didn't we just talk about it last night, Jon?

Jon Orr: Yeah. I was just going to bring that up, Kyle. Kyle and I talked about it last night, but I just had a recent discussion with a friend who couldn't see this new math, and why did their son or daughter have to learn this diagram or this way of multiplying? And when I can show her how to multiply, and get done in 30 seconds, and he referenced that Facebook post that we've all seen crosstalk...

Ann Elise: Oh my gosh, I know...

Jon Orr: Somebody being done in 30 seconds, and then twiddling their thumbs for the rest of the time and...

Ann Elise: Yup, exactly.

Jon Orr: Versus somebody who's drawing the area model. And we had this long conversation about that, and that was exactly what I referenced, Ann Elise, is that this model can carry forward, whereas this algorithm works in this one instance, and... We use it in high school and, listeners of this show know I'm a high school math teacher, and I just helped model my students this morning. And yesterday with completing the square, using the area model, and completing the square for a grade 10 student can be tough. And some teachers think it's one of those procedures you just got to show kids. "They just got to memorize this procedure." And it's hard to explain why it works unless you use a square to model it. And the area model works perfectly. And I love how it carries forward from there. And I really like how you referenced, both Kyle and you referenced that, by using these models, kids can get that fluency.

Kyle Pearce: I was sold on the area model from high school and then downwards. Whereas you went from an area model from lower elementary upwards, because I was sold downwards, because after using the area model to help kids complete the square in high school, they're completing the square in their heads. They didn't have to draw anything, they didn't have to write anything, because they could actually imagine the square and what the dimensions of the square would be. And so that they could write the vertex form of a parabola or quadratic expression, so it is a great tool, and I know that we'll talk about many other things.

Jon Orr: And I'm being a high school teacher and still trying to learn more about elementary math. I know Kyle's been on a journey for that for the last few years, but I don't get a lot of experience into the elementary math unless I do that on my own, or I talk to fantastic teachers like yourself. So I'm really hoping for this episode and the remainder of this episode to be a master class in fluency, and a master class that I can learn from, and all our teachers can learn from. So if we just think about diving into early mathematics in particular, and if we could help educators and parents learn effective strategies to help their children and students with fact fluency, let's think about some practical suggestions, some tips that we can help our teachers with on fact fluency at an early age.

Ann Elise: Well, first of all, we need to define fluency. We need to be all on the same page of what fluency means. So in my presentations I ask people, "What words come to mind when you think about being fluent with your math facts?" And, overwhelmingly, people will put words like 'speed.' Speed, fast, automaticity, all words about speed. And then occasionally, I'll get 'accuracy,' right, because kids can give the right answer but then be wrong. Right? So we want to have the accuracy as well as it being, I call it relatively speedy, because it's the least of the four things I want to talk about. But there are two more pieces of fluency, which is flexibility and efficiency. Those are the four pillars of math fact fluency. And I want to honor the fact, also, that there may be some of our students that are not ever going to fast, but they are using gray strategies and number sense.
I have to mention to you right off the bat, that, a lot of my consulting work has been focusing around what's called a math running record. It was a protocol designed by Dr. Nicki Newton. She did 10 years of research on math affluency, and created this interview protocol for us to talk to our kids about their thinking. I believe it is the key to transform schools and districts and the mathematical journey for our kids, because it's looking for that flexibility of thought. And if we explore flexibility with our different operations with the kiddos, it'll set a foundation for thinking that will then apply to the actual grade level content we're trying to teach. Without having to go to algorithms, they'll become much more efficient problem-solvers, and with their fluency, with the calculations, because they're using strategies and number relationships, which will build their number sense.
It's the start of everything. I've found it's been my key to educate people on early numeracy, because myself, having gotten, honestly, a master's degree, certified K eight, I had no idea the world of early numeracy, until I took a course from Dr. Sharma, that whole beginning of that journey. But then I also took the Number Sense 101 course with Christina Tondevold. And that was like, "Oh my gosh, what is this world?" And then Dr. Nicki as well, and it filled in more information. And then I just continued to learn about the early numeracy. So I want us to think, first of all, about that, there are developmental journeys our kids go through. Typically what our kids do for math inaudible journey is they begin counting on their fingers, right? Fingers are very important for the brain, very important for kids to do that.
But there's also something called finger agnosia, which is the discrimination of the fingers, but not finger counting. So the idea that the kids are going to start by counting, they usually count all, our youngest kiddos. If you ask them three plus two, in a context, I like putting all the fluency work in context, but you ask them three plus two, they put out three fingers and two fingers, and they would count them all, starting at one. Then kids developed to count on. So they may have all five fingers up, but they know this hand has three, and it's four or five. That progresses to head counting on. So the three isn't even out anymore, they might finger count four or five, or then, in their head, go, "four or five."
Then we have a whole section of derived facts. And that's typically the phase people skip. They tend to go, "Okay, you're counting on." So kids are counting on their fingers when they do their teen sums, because how else do you count on eight without keeping track on your fingers? And then we tell them, "Memorize them. I want you to play games with all the math facts, I want you to memorize these." As the kids are waiting for numbers to pop in their brain, when you ask them the questions, so that they don't know what it is. If they don't know what the answer is, that nothing pops in their head, what do they do? They count on their fingers, which is their comfort level, to find out what the sum is. And then when you think about a double digit addition problem, where we have raised to put the algorithm in front of the kids so soon in their journey, they're usually grade one, I find, a lot. Well, within the algorithm, it's just single digit basic facts. And in each of those basic facts, they're counting on their fingers. So they're in a counting phase of reasoning, within the context of addition problem.
I love this work of Pam Harris on the development of mathematical reasoning. That image of her graphic that she has, to go from the counting phase into additive thinking, and then by grade three, the multiplicative reasoning, before the proportional, and then the functional, the whole K-12 journey. So when I try to think about the math the kids are doing, what phase of reasoning is it? And the algorithms, adding and subtracting, are usually, kids are counting, they're counting on their fingers. So how can we get that? Well, we can work on the flexibility of thought. The idea that I could ask kids what's eight plus five, and that the kids could break apart that five and give two to the eight to make a 10, and then I can rename eight plus five as 10 plus three. That's a lot easier for my brain.
So the heart of that addition of breaking apart numbers and putting them back together in flexible ways will be the key, because I can then forward that to 48 plus five, or 98 plus five, or 98 plus 25. I can take two from it to make a 100, so 100 plus 23. It progresses all the way through their journey, including to fractions. Adding four fifths and three-fifths... Rather than adding numerators, keep denominators the same, uh oh, it feels weird, this large number on top, right? Break apart the three fifths and give one fifth to the four fifths and rename it as a whole plus two-fifths. It just will affect everything down their journey, starting with the basic facts.
So the Math Running Record allows us, when we're interviewing our kids, to be aware of that learning journey. Because there are codes for that. This is all based on Carpenter and Moser's research, inaudible research of the developmental trajectories, that the kiddos, we ask them sets of facts as a benchmark inaudible question for each of the set of facts. So you find which set of facts are causing a super slowdown, inaccuracies, or inefficient strategies, like just counting on. And then within that zone, where are they on that trajectory of the having no strategy to even try it, the counting all, the counting on, the head counting, the derived strategies, and the automaticity. Because we can't take kids from counting all to automaticity in one step, that's not how kids learn and develop. So it's a protocol that allows us to learn about the expertise needed for early numeracy. It's a brilliant protocol, and it's been a lot of my consulting work, because Dr. Nicki is just brilliant and she's so prolific, and she just talks about all different areas of mathematics. But I've latched on to this Math Running Record of the fluency piece, because I really feel it's my gateway to get people to understand, teachers and the parents, to understand the foundations of the operations, and to build the fluency through flexibility. And it alters everything, because it applies to every other content that you're doing.

Kyle Pearce: I love how you reference, even, how, we jump the gun on the memorization of those derived facts, right? They're not really memorizing derived facts or memorizing facts, when we skip all of these parts, and composing and decomposing number is so important. And I'm hearing that in what you're saying here, and this idea of equivalence pops out. And as you're working with young kids and, my son, who's an SK and my daughter who's in grade two, I get to have fun with these things, by playing with numbers and using strategies and seeing the strategies that they're using. And it really is pretty magical when you see them thinking.
And I just had this, I guess, a bit of a sad moment there, reflecting, as you had mentioned, like a student who's sitting there trying to bring up a fact that they've tried to memorize, but now it's like they're recalling facts they haven't derived themselves, so they don't have a connection. They also don't have a path to help them get out of a jam. And we talk about that a lot on this podcast and it continues to cause more and more problems down the road, because if students don't have a understanding of how they got to where they are, which I think many of us are like, as adults, many of us are like that, right? Those adults, like Jon, you had mentioned that friend who was thinking of the algorithm like, "I can multiply two digit by two digit numbers, no problem." But could they do it any other way? Or if they forgot one step of that algorithm, well, how are they going to get themself out of that jam?
And this is happening to so many young children, because I think for so long, we've made them take that leap, and the students who had the memory, the ability to memorize a little more easily or fluently than some other students, they were rewarded in the schooling system, but not necessarily rewarded with any sort of extra reasoning skills in mathematics. They just got the big gold star, and that was about it. Jon always references his puffy stickers that he used to get as a child. So I love that you're referencing this trajectory. And when this episode comes out, it'll be a few weeks after we had Doug Clements on, and his work.

Ann Elise: Oh, my goodness.

Kyle Pearce: Yeah, how fantastic.

Ann Elise: Clements and Sarama, they're just like the king and queen of early numeracy.

Kyle Pearce: Exactly. She was stuck out of town and we wanted to have both on the show.

Ann Elise: Oh, my goodness.

Kyle Pearce: I'm telling you right now, hearing you and your passion about this trajectory, it's so, so critical. And again, I know Nicki Newton thinks so highly, as well, of Doug Clements and Julie Sarama, and...

Ann Elise: Absolutely.

Kyle Pearce: It really all does come back full circle. So whether you're sitting at home right now, and you're thinking to yourself, "Maybe this episode isn't for me, I'm a middle school teacher, or I'm a high school teacher..." I hope that people are seeing the connections, and you brought up Pam Harris and the development of mathematical reasoning that, way down the road in high school, some of our students that are struggling the most, their struggles began way down here in this area where we didn't help them make those connections and really start to use reasoning to get themself through number fluency. And that's really hindered them.
And it makes me think, "What do we do?" Do you have any thoughts, if someone's sitting there thinking, and maybe I have a vision of a specific student in their class, and they're like, "Oh, this student is really struggling." What might be a get started tip for someone who, maybe this is a new idea for them, what are you going to say to them? Where might they begin? Might it be PD of some type, or might it be just a website to get them going? What are your thoughts on that?

Ann Elise: Well, I typically go right back to the Math Running Record, honestly, because it's going to help you understand where each child is on their journeys. You can develop instructional response derived for the kid, and then to get a sense of where all of your kiddos are. Because typically what I find, I'm training districts to implement this and then to do the next steps of how we explore fluency with our kids, in concrete, pictorial, and abstract ways. That's what our book is about. Dr. Nicki, Dr. Alison Mello, and I collaborated on a book about fluency doesn't just happen with addition and subtraction. So the idea that, now I know where I need to begin working with each kid, what can I do then to explore these concretely pictorial and abstract, and develop this fluency program for my kiddos?
So the Math Running Record, I have a Math Running Record Facebook group that I began close to three years ago now, because Dr. Nicki, she's doing so much all the time. I said, "Yo, do you mind if I make a group, of a support group for those of us that are really going in depth of implementing these?" She's like, "Oh, go right ahead." So there are videos in there of she and I talking for an hour about Running Records, and I have a whole Padlet of resources for the group that has all kinds of information, great resources on fluency as well. So it's a wealth of knowledge in one place that you can learn all about this. And I'm always right there. A lot of my time is online, providing advice to people within Facebook, because it's a great platform to be able to share things like that. And so a lot of my life is being in there, and providing advice, and guiding people along.
inaudible beginning a book study starting next Monday, but I know this will not be out in time for that, but all the information in the book study is going to be within the Facebook group. So no matter when anyone joins the group, it'll be there for you. So you can see the posting, and the questions, and the comments, and all. Because until we understand that trajectory of learning, and, then you can't really be looking for that, right? We've got to know, "Oh, that child is counting on. They're counting all." Now, what I want to make sure I'm clear about a derived strategy. So, for example, one really important fact for me is when I get to the progression, the beginning of the progression, say to add zero, and add one to numbers, and then counting on within five, and then within 10... But then I'm going to get you teen numbers, you have the doubles, and then doubles plus one.
So when I ask kids five plus six, most kids tell me that they know it's an 11, because five and five is 10, and one more is an 11. So it's a derived fact. The using a fact that they know to figure out one that they don't know. But the very next question in part two gives them more problems in that zone. The very next question is six plus seven. And that's where I can tell the kids who have begun using strategies, and breaking apart numbers in flexible ways, versus the counting on, because the kids will count on six from the seven. So the very same student that tells me five and five is 10, one more makes an 11, so they know five plus six makes an 11, will count on their fingers, six, higher than the seven. So I can tell that there's no strategy thought there.
So for that kiddo, I'd want them to go on to explore what doubles plus one is. And I would show them like a rekenrek. So a rekenrek is a tool that, one version of the tool, you can have two rows of 10, and the beads are color-coded in each five. So I can slide six beads over and seven down in the bottom row, so kids can see that amount of the 13. And I'll ask them, "What do you see? How do you know?" And some kids will count all the beads. So I know they're in a counting all phase, some count on the six from the sevens, they're in counting on, but other kids will say, "Well, I'm seeing five and five red, and that's 10. And then I see one white and two white, that's three. So I see ten plus three, which is a 13." But other kids say, "Well, I see six and six is 12, and one more makes 13." Other kids say, "I see seven and seven is 14, I take away one is 13." And still other kids say, "Take three from the six and make a 10 with the seven. So it's 10 plus three."
So I'm aware of all these different look fors to then develop my own instructional response with them. Because the kiddo that tells me that six plus seven is 13, because they could break apart that six to be a 10 and a three? They go to the end, they do all their math facts, and do whatever strategies they want with any of the addition math facts. But the kiddos that are counting on their fingers at that point? They go to just having visuals, to see the quantities, and describe what flexible ways can we get to that total, and make it easier for our brain. So that's where I find it's a great place to begin the journey.

Kyle Pearce: Right? And, forgive me, I'm not an elementary school teacher, haven't had experience working, other than with my own kids, talking about numeracy at that level... I'm wondering, if I'm a teacher who wants to have that interaction, that lesson with my students, and, what do I do beforehand? How do I prepare for that? We often talk about, that preparation is so important. Another quote that we've used from Tom Schimmer is that you want to plan with precision, so that you can proceed with great flexibility. In that preparation, we can't underestimate that. So I'm wondering, what does a teacher do to help prepare so that when they get in a conversation like that, they know to look for those strategies, and they know, "If I have that strategy, I'm going to push them this way." What would you suggest the teacher can do to help get ready for something like that?

Ann Elise: Well, I think it's a matter of us building our own knowledge about that. Dr. Nicki has a class, an online class, on her site. I've also, on my Padlet, have created videos for each of the strategies, and how we can explore them with math tools. And there's no cost to any of this. The protocols to interview the kids are free, there's no cost to the Running Records. But really it's a matter of us learning what we're looking for, right? And so how do we do that? Well, her Math Running Record book describes all the four operations, and the thought behind each of the operations, and the strategies.
And then our book we've written so far, the addition/subtraction, we are currently working on a multiplication and division book to go along with it. But that's a matter of learning about it, the matter of just building our own... Christina Tondevold, building our math minds, so we can then build the math minds of the kids, right? Because if you don't know what you're looking for... I ask people all the time, when kids are counting. You put eight objects in front of a student and ask them to count - what are you looking for? And very basically I always hear about one-to-one correspondence, and saying the numbers in the correct order, and that's pretty much it.
Well, Clements and Sarama has 20 levels of counting, right? So their site, learningtrajectories.org, I send all my participants to that site, because it is the most wealth of information about, from birth to grade three, of early numeracy and mathematics. But until you know there are 20 things you could be looking for with counting, you're going to look for one-to-one correspondence and if they say it in the right order, right? So it's a journey.

Kyle Pearce: I know. And I love that response because I think that's where the content knowledge piece is so important. And I think in mathematics, I mean, in education in general, oftentimes teachers, we have this drive to find new pedagogical moves. And while they are important, and they are a huge part of how you're going to organize and run your lessons, the content knowledge is key because if you don't have that, then it doesn't matter how hard you try to prepare, you're underprepared, because that look for is not there. Being able to notice and name, and then being able to, essentially, once you've noticed and named what a student has done, to know what comes next. And Jon and I are constantly talking about that with our igniting the next moves piece of the framework, which is this idea of really understanding that trajectory of math learning that students travel down. And that's something that we continue to try to do, and, clearly, you are also an advocate for that, continuing to try to grow your own math mind as well.
And we're just thrilled that we've got some great ideas and some great links to share. We're going to definitely get that Facebook group up there in the resource page. We'll throw in learningtrajectories.org, which is a great resource. And we'll also grab some of those Running Records links, as well as to the book, so... I'm wondering, before we wrap up though, is there anywhere that the Math Moment-Makers can learn more about you specifically in your work, some of which that you've already mentioned here, but where can they find more about you and get connected?

Ann Elise: Sure. I have a webpage, anneliserecord.com. You can check that out, and check out all the different offerings and things I have for you there. And honestly, I have found that connection in the Facebook community because I was living in Northern New Hampshire for over 20 years, and I found this amazing collection of people online. So they're just brilliant and generous and kind. And so, I began in Twitter a little bit, and then in Facebook, creating communities of people willing to learn. So I run a Facebook group of my own called Elementary Math with Ann Elise, and that's any math topic, K five is on the table, anything you want to talk about to give advice and all.
And then I facilitate the Math Running Records one. We have over 13,000 people in there right now. And so that group is focused on fluency. So that's the fluency piece. So the Elementary Math with Ann Elise is that, anything, like fractions or any other topic on mathematics, but the Math Running Records is that fluency one. So joining in those groups or following me on Facebook... I have a growth mindset tree as my picture, because that's my math profile on Facebook. So I only share math things there. So if you follow me there on Facebook, you could continue learning about me.
And I also have a newsletter that I do because I know and respect the fact that people may not want to be on Facebook or social media, so they can subscribe to my newsletter, and I send it out but once every week or two, with all the links and the great things that I come along.

Kyle Pearce: Awesome stuff, thanks for sharing that. We'll make sure that all of that is in the show notes page for this particular episode. Ann Elise, we want to thank you for taking time out of your day to share your expertise with us and our listeners. And we hope you enjoy the rest of your day. And we really appreciate talking to you and hopefully we can catch you at a face-to-face conference sometime in the future.

Ann Elise: Let's hope, absolutely. Thank you so much for having me, I really appreciate it.

Kyle Pearce: Thanks so much, we'll talk to you soon.

Ann Elise: Okay, take care.

Kyle Pearce: It was awesome to finally welcome Ann Elise onto the show to chat with us about her amazing efforts in conceptualizing mathematics.

Jon Orr: Hopefully this conversation has inspired you to dive into your next math class using a problem-based approach.

Kyle Pearce: Right? So be sure to check out the Wooly Worm Race, the Snack Time unit, or any of the other problem-based units that are available for you to dive into right now over at makemathmoments.com/tasks.

Jon Orr: Absolutely, Kyle. Get on over to makemathmoments.com/tasks to run one of these awesome problem-based units in your class today.

Kyle Pearce: In order to ensure you don't miss out on new episodes, make sure that you smash that subscribe button on Apple Podcasts or on your favorite podcast platform. And, did you know that these episodes are also on our YouTube channel? And you know what, Jon? We've been doing a lot of these YouTube lives lately, so be sure...

Jon Orr: Yeah, we're getting ready...

Kyle Pearce: To subscribe over on YouTube, because we got some pretty cool little tricks up our sleeve that we're hoping to do each and every week.

Jon Orr: Yeah, we've got some new stuff coming. Also, if you're liking what you're hearing, please share the podcast with a colleague, help us reach our wider audience by leaving a review on Apple Podcasts, and tweet us over at Make Math Moments on Twitter, or Instagram, or on Facebook.

Kyle Pearce: Show notes and links to resources, including full transcripts that can be downloaded or read right from the web for this episode, and all the other episodes can be found over at makemathmoments.com/episode113. Again, that's makemathmoments.com/episode113. Well, my friends, until next time, I'm Kyle Pearce.

Jon Orr: And I'm Jon Orr.

Kyle Pearce: High fives for us...and a big high five for you.

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Episode #113: Fluency Doesn't Just Happen - An Interview with Ann Elise Record - Make Math Moments

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Today we speak with Ann Elise Record. Ann Elise is a seasoned educator with a career spanning over two decades of elementary classroom experience. These days she's a K-5 math coach who works with districts on developing strategies to increase students' fact fluency as well as how to use manipulatives in the classroom.

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Mathematics K-8 Remote Learning Activities

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There is nothing elementary about teaching elementary math!

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Graham Fletcher blog and video

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Question: If you memorizeyour basic math facts have you learned them?

The term from memory is used twice in the K-5 math standards, and they continue to be the most misunderstood words I encounter each day. The term "from memory" does not suggest that students mindlessly their basic facts the way we were taught.

Here's my first stab at an Ignite Talk explaining the difference between from memory and memorization that I recently shared with some teachers and administrators.

Here's the link to the Prezi

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From Memory and Memorization: There IS a Difference

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Question: If you memorize your basic math facts have you learned them? The term from memory is used twice in the K-5 math standards, and they continue to be the most misunderstood words I encounter...

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Achieve the Core Grade Level Focus Areas

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Achieve the Core Grade Level Focus Areas

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Achievethecore.org :: Instructional Content Nav - Mathematics: Focus by Grade Level

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The Common Core and other college- and career-ready (CCR) standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, CCR standards require us to significantly narrow and deepen the way time and energy are spent in the math classroom. We focus deeply on the major work of each grade so that students can gain strong foundations: solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. The following documents illustrate these concepts using the Common Core State Standards, but Focus, Coherence, and Rigor are integral to all college- and career-ready standards.

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Build Math Mind's Podcast - Interview with Ann Elise is Episode 4

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Build Math Mind's Podcast - Interview with Ann Elise is Episode 4

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If you don't know whether or not you are a Recovering Traditionalist, here's how I define us. We are math educators who used to teach math the traditional way.

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Sesame Street: Janelle Monae - Power of Yet

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Download PDF Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts By Jo Boaler, Professor of Mathematics Education, co-founder youcubed With the help of Cathy Williams, […]

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Parent version Subtraction Haitian Creole

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Parent version Subtraction Haitian Creole

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Parent version Multiplication Haitian Creole

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Parent version Multiplication Haitian Creole

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The Progression of Fractions (Meaning, Equivalence, & Comparison)

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Don't need to be fast at math to be good at math

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Don't need to be fast at math to be good at math

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.
Watch the video to learn how sharing works.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.

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IT'S THE NUMBER THAT A STUDENT WORKS WITH UNTIL HE KNOWS IT "UPSIDE DOWN AND BACKWARDS" WITHOUT HESITATION. THAT IS WHY WE CALL IT A "JUST RIGHT NUMBER."

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Elementary Math materials for distance learning Include a revised scope and sequence adjusted for distance learning, content priority documents, and slide decks for every unit in our curriculum. Many educators are continuing to use these resources, even while teaching in person.

​ Secondary lessons contain proprietary content that is licensed by SFUSD and therefore can not be shared outside of SFUSD.

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Elementary Math materials for distance learning Include a revised scope and sequence adjusted for distance learning, content priority documents, and slide decks for every unit in our curriculum. Many educators are continuing to use these resources, even while teaching in person.

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Cross Number Puzzles Puzzles credited to: @MrsUnsworthWTT @BakerinBombay @Howell2ndGrade @MurrayH83 @BerkeleyEverett @SproutzS

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Dr. Nicki Newton (drnicki7) - Profile | Pinterest

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Dr. Nicki Newton | Dr. Nicki Newton is a an international elementary school math consultant. Check out her blog www.guidedmath.wordpress.com! Book her today:(347) 688-4927

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I was interviewed by Melissa Milner on her podcast. We talked everything elementary math!

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How to reach Ann Elise Record:

Website and newsletter signup: https://www.anneliserecord.com

Facebook: https://www.facebook.com/annelise.record.94

Twitter: @AnnEliseRecord

Instagram: ann.e.record

Email: aer@anneliserecord.com

Transcript:

(transcribed by kayla.r.fainer@gmail.com)

Melissa Milner 00:09

Hi, this is Melissa Milner. Welcome to The Teacher As... podcast. The goal of this weekly podcast is to help you explore your passions and learn from others in education and beyond to better your teaching. The Teacher As... will highlight uncommon parallels to teaching, as well as share practical ideas for the classroom.

In this episode, I interview Ann Elise Record. She is a New Hampshire certified K-8 educator, as well as a New Hampshire elementary math specialist. She's been an educator for 20 years in the roles of classroom teacher, K-5 math coach, adjunct faculty member for Plymouth State University, Bureau of Education and Research presenter, and currently an independent elementary math consultant providing training for both in person and virtually. She's a contributing author, too. Together with Dr. Alison Mello and Dr. Nicki Newton's book, Fluency Doesn't Just Happen with Addition and Subtraction.

Ann Elise works with school districts and presents at educational conferences. Her passion is working with educators to help them implement best practices within the three basic pillars of classroom math instruction that encourage growth mindset messages, math fact fluency, word problem structures, and understanding progressions of the standards. I hope you enjoy my interview with Ann Elise Record.

Welcome to The Teacher As..., Ann Elise. What would you like The Teacher As... listeners to know about you?

Ann Elise Record 01:37

Well, I am passionate about elementary mathematics and helping to create students that have a foundation of mathematical understanding that will follow them their whole journey and that they understand that everyone can learn math. It's not just certain math brains. That's a myth, and everyone can learn and grow.

Melissa Milner 01:55

Absolutely. You have done a lot of work with Dr. Nicki Newton with Running Records. I was part of the book club for Choral Collections & Counting Collections. You talk about the three pillars of math instruction. There's so much to talk about. Where do you want to start?

Ann Elise Record 02:15

Well, honestly, I think the start is Math Running Records, because I find that to be the key to help transform the math journey for not only the students, but the teachers as well. Because my undergraduate degree is in sociology. And so in order to teach, I needed to get my Master's degree. And I had taken some mathematics courses in college.

So when they look over my transcripts, they wanted to have the mathematics covered. I had one class in my grad program, and it was Math in Literature. So I love using picture books to explore math and all. But I really was not taught about the intricacies of building number sense and early numeracy. And so I came out certified K-8 to teach. But I really wasn't feeling any more qualified to teach kindergarten than I would have an eighth grade science class or something. I think the expectation was you would be getting a textbook and following whatever the lessons are in the textbook, and so indeed, I did.

I taught grade 5 for 13 years, and we had a textbook for most of those years. But all I knew was how I taught, which was rote procedure, and memorization, and valuing getting the right answer. And over the course of my career now of understanding mathematics and having kids talk about their thinking and build flexibility of thought and that the algorithm may not be the destination, all that work is embedded within the Math Running Record. Because it's getting us to be able to interview kids about their thinking and knowing for the research--

So Dr. Nicki spent 10 years researching math fact fluency, and then created this protocol of how we can interview students. She created a progression of strategies for each of the four operations. So we can find out where the students are, what set of facts are causing them a super slow down or inaccuracies or inefficient strategies, and then find out where they are on the trajectory of Baroody's research of counting all and counting on and then counting it all in their heads, and then derive strategies until finally developing a mastery with understanding. So it becomes a blueprint and a layout for the instructional response for the kids.

But in the process, when I'm training districts on how to do this, I'm really teaching them about early numeracy. And so everything else benefits. And then if we apply those same strategies to larger numbers, and eventually decimals and fractions, I mean, it unlocks the math journey for so many more of our students that typically had been excluded, because they weren't able to memorize or they weren't able to follow the 10 step procedures of long division. And so it just transforms the idea of mathematics. And I find a lot that teachers that really did not like teaching math, it becomes a favorite part of their day. And they had been literacy describedpeople. But they're like, this is so amazing.

Melissa Milner 04:53

It is.

Ann Elise Record 04:53

I know!

Melissa Milner 04:54

It's so diagnostic. It is time consuming, but it is so worth it. And it actually saves you time in the end. Because you realize how your kids think and what strategies they do use. And you know, I started doing them this year. I found I was underestimating what these kids could do.

Ann Elise Record 05:14

And the opposite, too.

Melissa Milner 05:16

Yeah. And these were kids that were historically struggling math students. And they were doing the most sophisticated mental math and taking these steps. And I'm like, oh, I get it now. I can play on those strategies that work for them and make them more efficient. And you know, it was amazing. It was amazing.

Ann Elise Record 05:39

I think it works the other way too, though. There are a lot of teachers that tell me that the kids they thought that would ace the Running Record did not.

Melissa Milner 05:47

Nope.

Ann Elise Record 05:47

Because they've gone down the memorization path, and they've got no strategy sense and no number sense at all. They're just-- they've memorized the answers. And they won't even try harder ones, which is why after I give the multiplication running record, that tends to be something that kids have traditionally memorized. I don't find many that have done it successfully.

But there are many kids who have successfully memorized the math facts. So I asked them when it's all done, when I'm assured that most of the higher facts are accurate and relatively speedy, I asked them 4 times 17. And that separates out the kids who have some kind of number sense from kids that don't.

The kids who are going down a path of memorizing, they literally will tell me, I haven't learned that one yet. They think it is a discrete thing. The kids who are going down a path of exploring their fluency, they've developed automaticity. They've developed their mastery of the facts. When I asked them 4 times 17, they're like, well, I don't know it offhand. But I could double double!

Melissa Milner 06:41

4 times 10. 4 times 7. Right, yeah.

Ann Elise Record 06:46

Exactly. They have some strategy of number sense to attack it, and they understand that they might make a mistake, but that's okay. And it just unlocks that math journey, and it can be much more accessible for many more of our students.

Melissa Milner 06:59

It's so exciting. And I mean, I was like you. I graduated in '91.

Ann Elise Record 07:04

Oh, I was '90.

Melissa Milner 07:06

Yeah. And it was absolutely like, here's the textbook, and here you go. And just the Build Math Minds site, being a member on that has changed my whole world. And I have to give my district credit. The other thing that pushed me into really looking into Build Math Minds and basic number sense, and Van de Walle, and all of it was that my district decided not only are we doing reading workshop and writing workshop, but we're going to be doing math workshop.

And I'm like, okay. I've got to think a different way to make math workshop work, you know? I can't be sitting in that book all day long in a math workshop. So that's what pushed me into it. And then I mean, Dr. Nicki, you know, we made the beaded number lines, and it's so fun, and it's so creative. I had no idea math was creative.

Ann Elise Record 08:00

Yes, exactly. The two of them have changed my life honestly. I had gone to a Bureau of Education and Research conference. It was a two day conference back when the core standards had just come out. So there were literacy sessions and math, you could choose which ones you wanted to go to. And one of the first ones I went to was Dr. Nicki. And she was showing me things I had never seen before with math, open number lines - it was the first time I'd ever seen an open number line - and double number lines. I'm like, what world is this?

And I stayed with her the entire two days. And then when I became a math coach in my district, we had some money to be able to hire her to come to our district for a week and do some PD with all the teachers. And she doesn't like to drive, and so I became a taxi driver. Because in Berlin, New Hampshire, in the north, there are no taxis. At least there weren't at that point. And so we became fast, close friends, and we put the entire week together. And she's one of my treasured friends, and so that began our collaboration together.

And then during that same year was when Christina Tondevold did her first number sense one on one course. And I knew becoming a coach K-5 that I had to learn about the early numeracy. I did not know how kids learned about early numbers. And so I took that course, and that changed my trajectory, as well. And so then that continued my journey with Christina and working with Build Math Minds, and then creating content for her site. I still do that to this day.

Melissa Milner 09:17

Yeah, it's fantastic.

Ann Elise Record 09:18

So those two have been my mentors, they have changed my life.

Melissa Milner 09:22

I was about to teach fluency for multiplication. So I went on, and I looked at the number sense, there's the four pieces, the subitizing, the--

Ann Elise Record 09:34

Is it the verbal counting, the object counting, the decomposition, subitizing. Yes.

Melissa Milner 09:39

As part of my instruction for multiplication, I was really checking and making sure that the kids could do those things. And then I was getting ready for fractions. And she was like, same thing for fractions. I'm like, oh yeah, benchmarks. Okay.

Ann Elise Record 09:57

It all fits together. That's the beauty of it.

Melissa Milner 10:01

Amazing.

Ann Elise Record 10:02

It really is. The biggest one for me, when I'm doing parent nights with districts, I do like to have a parent night in the districts that I work with. Because we have to get the parents on board, they have to understand why we're doing what we're doing. And so I share with them some foundational understanding of fluency. But then I show some future impact. And I say 4/5 plus 3/5.

And a lot of the people have trauma with fractions, because that tends to be a gateway where some people have very negative experiences. Multiple I meet have negative experiences with math, but fractions tended to be one place where they're like, oh, I can't do it fractions. They have anxiety about it.

But then I talked to them about the same thing. I talked to them about basic fact fluency to break apart numbers to make a 10. And I'm like, well, what if you broke apart that 3/5 into 1/5 and 1/5, and just rename it as 1 and 2/5? I mean, it's so much more accessible than just add numerators, keep denominators the same. And it feels weird, because there's a large number on top, that whole thing just goes away, and we have conceptual understanding. And the parents are like, if I had learned it this way when I was younger, I wouldn't feel the way that I do now.

Melissa Milner 11:05

It's so true. It's so true.

Ann Elise Record 11:07

It's so true!

Melissa Milner 11:08

Yeah, it's really-- I'm like, I'm a mathematician. That is a shocker, because I really struggled in math. And I worked and worked and worked to just get by. And if it had been taught this way, I would have gotten it. I would have been zooming along, and maybe I would have decided to become a veterinarian instead. The math and science scared me.

Ann Elise Record 11:33

But I think that's also true of a lot of our students. A lot of our kiddos get put in interventions, because they can't follow the procedures. Because what we're expecting of them is to get a right answer and to follow algorithms. And they're not able to follow that with all those different steps when it has no meaning attached. Whereas if we taught it in these conceptual ways, we wouldn't have as many kids needing an intervention.

Melissa Milner 11:52

Yes. You mentioned the consulting. What do you usually ask to come and do in schools? Or what is your goal when you walk into a school or a district to make their math curriculum and teaching and pedagogy better?

Ann Elise Record 12:07

Well, first of all, I focus on the eight math practices. So these are gonna be in place for kindergarten classrooms all the way to high school. Things like having kids problem solving and persevering at that, modeling with mathematics, using math tools, talking about their thinking, the underlying structure, not only our number system, but also of word problems structures, as well.

So I imagine they're like three pillars to our math instruction. We want to give instructional time, too. There's the fluency piece, which needs to be given some instructional time and attention. There's the word problem and structures of those, so it's not just solving word problems and certainly not keywords. Those lead the kids astray.

That develops kids that are number pluckers, as Graham Fletcher calls them, where they pluck the numbers out and do a random operation of trying to find one word that tells them what operation to use to get the right answer. But if we explore the structures of thetypes based on the research of Thomas Carpenter and his colleagues in Cognitively Guided Instruction, then we can show what's happening with the situation and then give the flexibility to the kids to numerically solve it however they want.

But if we give a typical problem that people think of as being division, which really, there are three different types. And if one of the factors is unknown, then it could use division to solve it. But I could use addition, subtraction, multiplication or division to solve it. I don't have to use the division operation for it. So we need to get away from talking about problem types as being defined by the operation that we want kids to use to solve it, and instead talk about the structure of a situation.

Melissa Milner 13:34

Yeah, take that poster down, take it down.

Ann Elise Record 13:38

Yeah, oh my gosh, take down those posters. So when I go into a school, I'm certainly looking on the walls. Because Dr. Nicki says that the walls reflect what's important to you. And generally, what I see is 75% of the walls are covered in literacy posters. There usually is a calendar corner or a hundreds chart that I'll see.

But beyond that, I'm not seeing much else for mathematics in many places. And so I'm looking for that. And I'm looking for those keyword posters to have a conversation about why we don't want to have those on the wall. So typically, I've been brought in-- this is my second school year being a consultant. And I've also been presenting for the Bureau of Education and Research, which is a full circle for me to be a presenter at the same conference I met Dr. Nicki at.

Melissa Milner 14:20

Wow.

Ann Elise Record 14:21

Fabulous for me to have that. But so I work with districts. Very often the Math Running Records is the one that gets me in the door, because the fluency piece is just so important. And that is, I believe, the gateway to help fix everything else. But then once you've gone beyond exploring the strategies with the basic facts and how they apply to larger ones, then I tend to go into the problem solving.

And so the idea that there are 15 different problem types and involve adding and subtracting, and there are 9 that involve multiplication, division, single step, teachers are like, what? So if we don't know that stuff ourselves, then certainly we're not facilitating that learning with our students. So that tends to go into the next time, next phases, and then we go into daily routines, things we can do every day that can kind of get that fun and engaging way to get the mathematics out in front of the kids and having them talk about their thinking and building the flexibility and respecting each other's viewpoints. So there's not just one way to get an answer.

So all that kind of work tends to be what I've been doing so far in my consulting work. And then whatever districts want, I'll do. I've done workshops on fractions and place value, those kind of things. But generally, it's the Math Running Records, because it's really teaching everyone about early numeracy and then the problem types. Because I find those two pillars-- because we have the fluency, the problem solving, and then we have the regular content standards. How do I teach kids about subtracting two digit numbers in grade two? And that takes a lot of sophisticated thought.

It's not the algorithm. The algorithm should be in grade four. There's a reason why it's in grade four. There are other ways you can do it. But very often, when I ask people, I usually do 52 minus 38. And I ask them to think about how many strategies they can think of to figure out the answer. And I usually get two, three or four. But there are a lot more than that. But we just haven't exposed our brain to it yet.

So it's just a matter of exposing our brain and practicing it and just building those new neural pathways that allow us to think more flexibly about it. But I could apply that same thinking to mixed numbers and subtraction. So I no longer do that regrouping algorithm when you give me two mixed numbers. I have many other ways to think about it that are much more efficient for my brain.

Melissa Milner 16:31

Do you have any suggestions about doing this work that you've just talked all about, Running Records, and that deep word problem, delving into those different word problems and so on? Do you have any suggestions about how to do that with a remote model or a hybrid model when we're not in person with the kids all the time?

Ann Elise Record 16:57

Well, I've been doing a lot of virtual Math Running Records, actually. Because since the shutdown in March, all the districts I was planning on working in couldn't have me because the schools were closed. So my consulting and being on the road all the time came to a screeching halt. And so I had special time on my hands.

And I thought, you know, I should ask for volunteers to have kids talk to me about their thinking. And so I did a lot of virtual running records. And it actually worked out really awesome, because I could easily record it. I did it in Zoom. I would have my phone signed in as another device, and I just pointed it down. I put it on some Harry Potter books, because they're really thick, and put my phone facing down onto the desk and showed the benchmark expressions for the kids for the part one.

And then I talked about their thinking, and I could easily just record it and have it to go back to look at later. And then I could figure out from the interview where I want them to begin working on their fluency. And then I could suggest games and activities to the parents to help work on that with the kids. Because I want to engage parents in this learning. And I think basic facts and playing games is a really great entry level to it. They can feel comfortable with that.

And so it can help us fix that problem by encouraging the parents and encouraging positive interactions between the kids and the parents and not having it be this fearful, anxiety prone-- The parents don't understand what we're trying to do right now with math, and so they freak out, and they call their friend. Did you do tonight's homework. Or they go on Facebook, and they bash it. They need to understand that there's a larger thing at work here beyond what they see, what they don't understand. It's scary to them, you know?

So if we can have them play games with their kids and encourage flexibility of thought, yeah, it's a win win. And so certainly with the fluency piece, I like interviewing the kids. And a lot of teachers were meeting with their kids one on one anyway to kind of build a relationship. So while you have them with you, you take 10 minutes and ask them about their math thinking. And then that can help guide your decision on what you want them to do moving forward.

Melissa Milner 17:14

Yeah, that sounds doable. But my other question, I think it's still going on, your Cuisenaire course?

Ann Elise Record 18:54

Oh, yes.

Melissa Milner 18:55

Do you have remote ideas for manipulatives?

Ann Elise Record 19:01

Yeah, in fact, with my course, you get a four month subscription for a classroom to Brainingcamp. And Brainingcamp is a web page that has virtual manipulatives that are fabulous. And in fact, research has shown that virtual manipulatives have shown to improve engagement with mathematics, as well.

So doing it virtually, I mean, I totally believe that doing hands on things and getting concrete objects in the hands of the kids is really important. But virtual is not a bad second place right now when we're dealing with a pandemic and don't want to have to wash off any hands on things with germs and whatnot, right? So having it virtually is not a bad second choice.

Melissa Milner 19:38

Even if you're in, even if you're in school.

Ann Elise Record 19:40

Yes, exactly. And Brainingcamp actually is affiliated with Hand2Mind, which is the company that has the trademark on Cuisenaire Rods.

Melissa Milner 19:47

Oh, yeah.

Ann Elise Record 19:48

And so they've offered to give a four month subscription for a classroom to their app. And they have a Cuisenaire Rod app that is amazing. It's the best that I've seen. So yeah, that is a part of the course. I mean, in the course, I do go through the three pillars. I go through fluency, problem solving, as well as the content standards for each grade level. I have a K-2 version out now, and then also, I just released my 3-5 version.

Melissa Milner 20:11

And is it too late to get into the K-2 if people are listening and interested?

Ann Elise Record 20:16

I don't have plans to close it. I want it to be available for people when they want to learn about it. So no, I don't have any plans to close it. It is asynchronous. So there are videos and some resources within it that people can do it at their own pace.

Melissa Milner 20:29

Gotcha.

Ann Elise Record 20:30

So yeah, you've got the K-2 version and the 3-5, and then I go through each grade level of the content standards and how Cuisenaire Rods, they're my favorite manipulative. Because I think they have the key to help us move our kids from the counting phase of reasoning into strategies into additive thinking, and then from additive thinking into multiplicative reasoning. So it helps us move them all on the journey. Pam Harris has a wonderful graphic, that she developed on the development of mathematical reasoning.

And so we think of our kids entering kindergarten, they're in the counting phase of reasoning. When they go into addition, and particularly when we use the algorithm too soon, kids are doing the algorithm, which of course, is just single digit facts. And if they haven't developed the fluency yet with the math facts, they end up counting on within the basic facts of let's say a two or three digit addition problem. So they're doing a counting phase of reasoning in the context of a multi-digit addition.

So instead, I want to help move them into additive thinking, which has place value attached to it, as well. And then, very often, kids - beginning in multiplication - will start skip counting. And then they continue doing the skip counting for the basic facts. So in multiplication, we want multiplicative reasoning. They're doing a multi-digit multiplication problem, which is, again, just basic facts. They're ending up skip counting on the basic facts.

And so these are the things we're aware of in the Math Running Record to see where they are on that phase of that journey. And then we're able to explore those things with games, activities and daily routines to help move our kids forward on that journey. And the Cuisenaire Rods, the numbers exist as a group. So when I use Base Ten blocks, which I did in my fifth grade classroom to do subtraction for my kiddos who still couldn't do the algorithm up, I wanted them to understand why the algorithm worked.

So we traded in a 10 rod for 10 cubes, and we already had 8 cubes sitting there. And you can't subitize 18 cubes. The kids, then, would take away the ones that were being removed. And then they would count the ones that were left. And I realized, all they're doing is counting. They're not doing any strategies. So that, to me, the Cuisenaire Rods are the key to help moving that forward. And so that's why I just love them so much.

Melissa Milner 22:29

That sounds pretty amazing. And you said you're doing a grade 3-5, as well?

Ann Elise Record 22:33

It's already open. I opened it a few days ago.

Melissa Milner 22:36

Oh, great.

Ann Elise Record 22:37

And you can get a bundle, as well. You can get both classes for even less money.

Melissa Milner 22:41

You'll give us that information at the end.

Ann Elise Record 22:43

Yes, absolutely.

Melissa Milner 22:44

All right. So what are you zooming in on right now with your work?

[ZOOMING IN SOUNDBITE]

Ann Elise Record 22:51

So certainly, being in person and doing trainings is not feasible right now. But it's been actually kind of nice. I've been doing virtual trainings from my house. So I've had lots of sessions with Nebraska. I had Texas last week. I did New Jersey this morning. So I'm able to still meet with people in this virtual space. I do it through Zoom. It allows me to have breakout groups, and people can still be having those small group conversations.

There are also some ways virtually to get people active, like doing a Google Drive, like a sheet, a Google Sheets file. So people can access that file and collaboratively work together. So I'm still finding some ways to be able to do the trainings. But I'm able to have dinner at night with my husband and be home with our puppy.

Melissa Milner 23:30

That's amazing.

Ann Elise Record 23:32

And so I also still work. I do make content for Christina Tondevold's Build Math Minds for pay, professional development site. And facilitating the Facebook groups takes me a lot of time. I do the Build Math Minds for Christina. That's got over 56,000 members. And then my Math Running Records one, all working on fluency with Dr. Nicki's work, that's got over 13,000 people. I think for me, creating these online courses that teachers can access at a reasonable price for teachers and to be that support to people online is really the heart of what I'm doing right now.

Melissa Milner 24:08

That's great.

Ann Elise Record 24:09

I'll get back out in person as soon as there's a vaccine for it, but I'm not in any hurry to get out there because this is scary stuff. And Dr. Nicki had COVID.

Melissa Milner 24:19

I know.

Ann Elise Record 24:20

And she was in a coma for two months, but she is getting stronger every day, which we talked yesterday. She's looking great. But you know, it's a long journey to recover. So, you know, this is no joke. So I'm not in any hurry to get out there traveling or flying around the country like I was doing.

Melissa Milner 24:36

Absolutely. It's not worth it. Can you tell us about the book that you worked on with Dr. Nicki?

Ann Elise Record 24:42

Sure. Dr. Nicki and also Dr. Alison Mello and I collaborated together on a book called Fluency Doesn't Just Happen with Addition and Subtraction. So it's all about this fluency work and exploring strategies and number relationships with kids. But what we're bringing to the conversation is also about using concrete pictorial and abstract ways to explore the strategies.

So in the book, there's guides about creating fluency plans and including parents on the journey and the foundation of the flexibility of thought. But also, for each of the strategies, you get ideas for videos you could show the students, and picture books you could use, and all kinds of ideas for your workstations that are concrete, pictorial and abstract, word problems you can use, and even a quiz to help measure at the end of working on a strategy whether a student's ready to move on to the next strategy.

So we have not yet begun to write the next one on multiplication and division. But that's certainly our goal, to get that one done, as well. But yeah, it's a wonderful, wonderful book. It's really the next steps to the Math Running Records. The Math Running Records by Dr. Nicki Newton, that book is about how we talk to the kids about their thinking with all four operations and then the codes involved with that, because the research informed that went behind that. And then this book is the next steps.

Now that I have the Math Running Record done and I know what strategy I want each student to be working on and what level they are with that progression of counting all, counting on, doing that also within their head, and then derive strategies to mastery, how can I help them move forward? These are getting all kinds of ideas at your fingertips that you can do with the kids.

Melissa Milner 26:13

That makes me so happy. Because it is! It's like, great, I have all this great information about each of my students. And I think I know what to do next. So that's really, really helpful. And I know everything you guys do is based in research and work with real students.

Ann Elise Record 26:30

Absolutely. And if anyone's interested in that, I do run the Facebook group called Math Running Records. And with that, I've created what's called a Padlet, which is a web page. So it's not affiliated to Facebook or social media. So if you're not doing social media, totally fine. It's a web page that has lots of resources on there for you. And there are also some videos of me giving running records that you can see. And Dr. Nicki has her own site called mathrunningrecords.com. And that's where you can get the downloadable sheets.

It's all free. There's no cost to them. And so you can check out her site, and there's some videos of her giving them, as well as the downloadable recording sheets. And then on my Padlet, I have lots more information for you. It's a rabbit hole of time, but you can get access to that, as well. So there's lots of resources for no cost out there.

Melissa Milner 27:16

Very cool. Are you on Facebook and Twitter and stuff like that, too?

Ann Elise Record 27:21

I sure am.

Melissa Milner 27:21

Do you want to share that? You can share that with us, yeah.

Ann Elise Record 27:24

Sure. So on Facebook, you can befriend me at Ann Elise Record. But look for the logo that is a growth mindset tree. If you see a picture of me and my adorable Marty McFly puppy, then that's my personal one, and you'll see pictures of my kids and my three year old niece and the dog. But if the growth mindset message tree, that's all my math postings. I only post in Facebook on that profile math things. And so I have that.

And then within the groups, the Math Running Records Facebook group, as well as the Build Math Minds Facebook group. And I have my own one called Elementary Math with Ann Elise. And that's for any topic of elementary mathematics, fractions, anything else you want to talk about. And then on Twitter, I'm just @AnnEliseRecord, just my name. And in Instagram, I'm ann.e.record.

So I'm active in all three areas, mostly Facebook. I find Facebook is my home. That's where I live. Because I'm able to share something so easily within the Facebook, videos, and links to webpages, and then the Padlet that has links to everything.

So the Padlet has everything that I offer. I have the free version for the Math Running Records. But I also have a version for my consulting work, because of course, that's my livelihood. So I will not give that link away, but I will give the free one away.

Melissa Milner 28:42

No, that's awesome. Have you ever thought of doing a Twitter chat?

Ann Elise Record 28:47

I had actually led several within the Elementary Math Chat. So it's a #elemmathchat. So I've led several of those. I've got one that was coming up at the end of September. I'm not sure whether it will correlate to the date that this releases. So I do participate in those. I haven't yet led my own special hashtag one, no. I have not done that.

Melissa Milner 29:11

I think you should.

Ann Elise Record 29:13

An interesting idea. I've never thought of that.

Melissa Milner 29:17

Yeah, it's time consuming. But I think a lot of people would love to, once a week, be able to interact with you and ask questions or however you want to structure the chat. I think it would be great.

Ann Elise Record 29:30

Well, what I've been doing, actually, I have held some Zoom calls with my Elementary Math with Ann Elise group.

Melissa Milner 29:38

Oh, cool.

Ann Elise Record 29:39

So if you're a member of that Facebook group, then I share a Zoom link, and then we get together and just chat.

Melissa Milner 29:44

That's great!

Ann Elise Record 29:45

Oh, yeah. I find Twitter to be a little constraining with the characters.

Melissa Milner 29:50

Yes, I agree. All right. So my last question is very-- I don't know how to say it. A lot of people have found it to be difficult. What is your favorite movie, and why?

Ann Elise Record 30:01

One movie that I will watch over and over and over again is While You Were Sleeping.

Melissa Milner 30:06

Oh, I love that movie!

Ann Elise Record 30:07

Have you seen that one with Sandra Bullock? I just love that whole storyline of the family taking her in and falling in love with the other brother. And yeah, that's the one that if it's on television, I will just sit and watch it. I just love it.

Melissa Milner 30:21

That's definitely a guilty pleasure movie.

Ann Elise Record 30:25

Yep.

Melissa Milner 30:26

Bill Pullman is great in that.

Ann Elise Record 30:29

Oh, he's so good.

Melissa Milner 30:30

He's so lovable.

Ann Elise Record 30:31

I know it. And then the end when he puts the ring in the-- Oh my gosh, I just-- And then the whole family is right there, too. It's like, oh!

Melissa Milner 30:40

That is such a funny movie. And she's so lovable. She's such a great actress.

Ann Elise Record 30:43

Oh, she totally is. Yeah.

Melissa Milner 30:45

Thank you, Ann Elise. This was absolutely wonderful to talk to you. And I appreciate you taking the time out to do it.

Ann Elise Record 30:51

Oh, thanks so much for having me. It's been a treat.

Melissa Milner 30:56

If you enjoyed this episode, and have not done so already, please hit the subscribe button for The Teacher As... podcast so you can get future episodes. I would love for you to leave a review and a rating, as well, if you have time. For my blog, transcripts of this episode and links to any resources mentioned, visit my website at www.theteacheras.com. You can reach me on Twitter and Instagram @melissabmilner. And I hope you check out The Teacher As... Facebook page for episode updates.

I am sending a special thanks to Linda and Lester Fleishman, my mom and dad, for being so supportive. They are the voices you hear in the Zooming In soundbite. And my dad composed and performed the background music you are listening to right now. My intro music was "Upbeat Party" by Scott Holmes.

So what are you zooming in on? I would love to hear from you. My hope is that we all share what we are doing in the classroom in order to teach, remind, affirm and inspire each other. Thanks for listening. And that's a wrap!

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The Teacher As Mathematician with Ann Elise Record - The Teacher As

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How to reach Ann Elise Record: Website and newsletter signup: https://www.anneliserecord.com Facebook: https://www.facebook.com/annelise.record.94 Twitter: @AnnEliseRecord Instagram: ann.e.record Email: aer@anneliserecord.com Transcript: (transcribed by kayla.r.fainer@gmail.com) Melissa Milner 00:09 Hi, this is Melissa Milner. Welcome to The Teacher As... podcast. The goal of this weekly podcast is to help you explore your passions and learn from others in education and beyond to better your teaching.

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Inside Mathematics is a professional resource for K-12 teachers, coaches, and administrators.

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Choose your own maths adventure with our interactive tools that allow you to build a custom playlist of inspirational activities!

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Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them

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Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them

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Baroody 2006

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Kling and Bay-Williams

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Assessing Basic Facts Fluency - National Council of Teachers of Mathematics

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Have you had it with timed tests, which present a number of concerns and limitations? Try a variety of alternative assessments from this sampling that allows teachers to accurately and appropriately measure children's fact fluency.

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Henry and Brown 2008

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First-Grade Basic Facts: An Investigation into Teaching and Learning of an Accelerated, High-Demand Memorization Standard on JSTOR

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Valerie J. Henry, Richard S. Brown, First-Grade Basic Facts: An Investigation into Teaching and Learning of an Accelerated, High-Demand Memorization Standard, Journal for Research in Mathematics Education, Vol. 39, No. 2 (Mar., 2008), pp. 153-183

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by Berkeley Everett

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I was interviewed by Dr D. on this podcast on fluency and Math Running Records.

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Get to know Spotify for Podcasters, the free, all-in-one podcast platform for every creator.

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The 3-Read Protocol

The Three Read Protocol is one way to do a close read of a complex math word problem or task. This strategy includes reading a math scenario three times with a different goal each time. The first read is to understand the context. The second read is to understand the mathematics. The third read is to elicit inquiry questions based on the scenario.

Why would I use this strategy?

The Three Read Protocol is designed to engage students in sense-making of language-rich math problems or tasks. It deepens student understanding by surfacing linguistic as well as mathematical clues. It focuses attention on the importance of understanding problems rather than rapidly trying to solve them. It allows for the use of authentic, instead of overly simplified, text. This strategy also allows for natural differentiation within a class of diverse learners.

When do I use this strategy?

This strategy can be used for math tasks that include complex language structures or language that lends itself to a variety of interpretations. While this is a particularly useful strategy for English Language Learners, all students can benefit from the deeper understanding of word problem structures and open-ended questioning.

How do I use this strategy?

The Three Read Protocol uses the " problem stem " of a word problem. This is essentially the word problem without the question at the end. The purpose of presenting the problem stem alone is to have students focus on the contextual and mathematical information before dealing with any question that is involved. This gives students the freedom to create their own questions for a given scenario, which is an excellent skill to develop both in math and in reading in general. It is important that the teacher choose the problem carefully and anticipate potential linguistic and mathematical roadblocks the students may encounter.

1. First Read: Teacher reads the problem stem orally.

The teacher may have visuals to accompany the oral read of the problem stem. Students listen to the story with the goal of turning to a partner and sharing what they remember of it. Memorizing it is not necessary. Students may act out the problem if that helps them grasp the context.

Key Question: What is this situation about?

After the Turn-and-Talk, the teacher asks students to volunteer information they remember from the story. Teachers and students ask clarifying questions about the vocabulary as needed.

2. Second Read: Class does choral read or partner read of the problem stem.

The teacher projects the problem stem so the whole class can see it. The teacher leads the class either in a choral read of the problem or has partners read the problem orally to each other. Choral read is preferable because it allows all students to participate without excessive pressure, but a partner read can work fine if that is a better fit to the classroom culture or age of students. The teacher explains that math stories usually have information about quantities (numbers) and the units that are being counted.

Key Question: What are the quantities in the situation?

An example is 25 cats, where "25" is the quantity and "cat" is the unit. Sometimes the quantities are implied. For example, "some cats" implies a quantity but we do not know what it is. There can also be implied units. An example is "I have one at home." The implied unit in this case depends on the context of the story. Bottom line : The discussion of quantities and units can be important for focusing student attention, but how deeply the teacher delves into the explicit and implicit information depends on the math and language objectives.

3. Third Read: Partner or choral read the problem stem orally one more time.

The teacher asks students to do one more read of the "story" and asks them to think, " What is missing to make this a good math problem? " Students volunteer their answers to that question. Responses will likely vary because many students assume there is a question without actually reading one. Without correcting student responses, the teacher probes until the class decides that a question is missing. The teacher asks, " Is there only one question that we can ask of this story? " Students responses may vary, but there are usually many different questions that can be asked of almost any scenario.

Key Question: What mathematical questions can we ask about the situation?

The teacher asks partners to determine at least two questions that can be asked using the problem stem. Students share their questions. The teacher writes a couple of the questions and clarifies language as appropriate. After each question, the teacher asks the class, " Can this question be answered with the information from this story? " and the class discusses why or why not.

4. Students work in collaborative groups on the problem.

Students work in groups to solve a question based on the problem stem. The teacher may assign a specific question for all groups to answer, or groups may choose a question from the list asked by the class. If groups are asked to choose their own questions, it is important that the teacher circulate and clarify expectations for the work. This can be an opportunity to differentiate the math work because the range of possible questions to a problem stem is broad.

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Download the description of the 3-Read Protocol from our Math Teaching Toolkit

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Education Unboxed

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EducationUnboxed.com - Free Help for Homeschool

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The goal of Education Unboxed is to rethink the way we do education, challenge assumptions, and provide information to help people teach more effectively. We offer math tutoring help through lessons, activities and games in the free math videos listed by category below! Be sure to check out the Math Resources page to get the simple supplies you'll need to use with the videos!

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Welcome to Education Unboxed! - EducationUnboxed.com - Free Help for Homeschool

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Free Math Videos The goal of Education Unboxed is to rethink the way we do education, challenge assumptions, and provide information to help people teach more effectively. We offer math tutoring help through lessons, activities and games in the free ... Continue reading →

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Tile packets

complete list of tiling tasks tiling tasks by grade levels

counting, addition, subtraction time, money, application, word problems place value, rounding multiplication, division vocabulary, concepts, estimation, situation fractions, decimals, percents measurement, geometry mixed operations, exponents, progressions,
intergers, order of operations logic, functions, relationships algebraic thinking double tiling

Tangram tasks

Quiet Tiles & Dominoes

Marcy recommends

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Tile packets complete list of tiling tasks tiling tasks by grade levels counting, addition, subtraction time, money, application, word problems place value, rounding multiplication, division vocabulary, concepts, estimation, situation fractions, decimals, percents measurement, geometry mixed operations, exponents, progressions, intergers, order of operations logic, functions, relationships algebraic thinking double tiling Tangram tasks Quiet Tiles & Dominoes Marcy recommends

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Achieve the Core Guidance for new School Year 2020-21

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Achieve the Core Guidance for new School Year 2020-21

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Human-Centered Learning

Create positive, affirming learning spaces that center student identities and experiences.

Teaching For Equity: A Guide to Integrating Academics, Well-Being & Anti-Racism in Student Experiences | Create supportive learning environments using this teacher-designed framework from Leading Educators. The framework includes five strands that facilitate structured reflection of classroom practice, school and community relationships, and your own identity as an educator. Working through the framework will help you translate beliefs into action.

EdResearch for Recovery Project School Climate Evidence Briefs | Identify research-based strategies to improve school climate and foster safe, inclusive learning environments. This project from Brown University asked researchers from across the country to develop evidence briefs that point to research-based recommendations for supporting students. The school climate briefs cover topics such as trauma-responsive educational practices, community engagement, and how to rebuild a positive school climate after disruptions to in-person learning.

Disrupting Inequity: Having Brave Conversations About Bias | Invite colleagues to join in a brave, honest discussion about bias in schools and its effect on students. The toolkit from UnboundEd contains individual PowerPoint presentations and materials containing detailed notes, resources, and activities designed to facilitate challenging discussions in a supportive professional learning space. Topics include microaggressions, historical implications of race, and actionable steps you can take to identify bias and improve school culture.

| Encourage students to be changemakers by creating a classroom environment where critical conversations about racial injustice, social inequality, and discrimination are addressed openly and often. This detailed guidance from Learning for Justice will help you develop the skills to facilitate honest communication around difficult topics through the implementation of classroom-ready strategies.Let's Talk: Facilitating Critical Conversations With Students

Social, Emotional, and Academic Learning

Addressing students' social and emotional needs and development is a critical component of human-centered learning environments.

Academic Acceleration

| These documents name instructional content priorities in mathematics (K-8, high school) and ELA/literacy (K-12). They support planning focused on keeping all students working on grade-level content. These were developed for the 2020-21 academic year in response to the disruption of the global pandemic, and they remain helpful for those setting academic priorities for the 2021-22 school year. Plan instruction that builds on the foundation of CCR-aligned standards to prioritize content.
Companion guidance is also available for families.
Learning acceleration is different than remediation - and more effective. Acceleration requires focusing on grade-level work, ensuring students access to that work, and offering support and connections to prior-grade learning, as necessary. Learn more in Accelerate, Don't Remediate, a report by TNTP and Zearn.

2020-21 Priority Instructional Content in English Language Arts/Literacy and Mathematics

Reading and Fractions

Customize content decisions in these critical areas based on research and the specific needs of students.

Reading science emphasizes two critical pieces in systematic early reading instruction: securing foundational skillsand building knowledge and vocabulary These "Early Reading Accelerators" are essential content that all readers need access to in order to become proficient. While each student and their experiences are unique, we can accelerate the development of reading proficiency for all students by implementing these practices strategically through classroom instruction and materials. To learn more and examine the research base for literacy accelerators and the intersections of equitable personalization for students in ALL grades, explore Reading as Liberation. Invite students and their communities to understand how we learn to read and be partners in that learning with How We Read: A Graphic Guide to Literacy.
A robust body of research tells us that flexibility and accuracy with fractions are among the most critical elements for student success in later mathematics. The resources and support in this fractions collection are designed to develop educator understanding of fractions as well as facilitate the teaching and learning of fractions with students. For support on approaching unfinished learning in math on other topics visit Instruction Partners' Supporting Unfinished Learning in Math.

Integrated Scaffolds and Support

Support access to grade-level work for all students.

rning by creating learningAchieve the Core Learning Supports Collection | Address unfinished le a Prepare to meet all students where they are with these proven strategies and practices. environments that focus on scaffolding and just-in-time instruction, rather than remediation. Every student is capable of grade-level work that keeps them on track for success after high school. Nearly all students contend with some degree of unfinished learning each year.

The Rethinking Intervention series from Instruction Partners features videos, PLC guides, and blog posts to help you rethink the concept of intervention to focus on student-teacher relationships and access to grade-level content.

Perspectives on Scaffolding Student Work | Discover teacher-tested scaffolding strategies in this collection of blog posts.

English Learner Success Forum Resource | Deepen and accelerate English learners' content area learning by implementing the strategies included in this collection of teacher-facing guidance. The activities and scaffolds in this collection from the English Learner Success Forum can be built into existing lessons and units to help English learners engage fully with the curriculum.

| Expand access to grade-level content with these guidance documents from the New York State Department of Education offering grade-specific scaffolding guidance for instruction in grades 3-8. Examples are drawn from the open-source curriculum EngageNY, but can be applied to any set of materials.Supporting all Students: Resource Guides for Scaffolding Instruction of English Langauge Arts and Mathematics

Culturally Relevant and Responsive Pedagogy

Meet student needs by honoring all aspects of their identities and by helping them to make connections to the world around them.

Whether you are practicing culturally relevant pedagogy (Dr. Gloria Ladson-Billings) or culturally
responsive pedagogy (Zaretta Hammond), teaching requires thoughtful planning and a commitment from educators to get to know each and every one of their students each year. This work not only helps all students excel academically, but also helps expand perspectives, reaffirm identities, and prepare students to create a better world, using the skills and knowledge they gain in the classroom to demand and design change.

For a quick introduction to culturally relevant pedagogy, read this three-part blog series. Educators preparing to design culturally responsive learning environments can find tools, guidance, research, case studies, and more in NYU Metro Center's Culturally Responsive Education Hub. Make sure to download Transforming Our Public Schools: A Guide to Culturally Responsive-Sustaining Education and the Culturally Responsive Curriculum Scorecard Toolkit, to jumpstart your work.

Looking to take the first step toward translating these concepts into action in your classroom? Begin by learning about the students you serve and their unique identities. Creating lessons and learning environments that are culturally relevant and/or culturally responsive will look different from classroom to classroom--because the students are different!

Understanding Student Progress

Rethink how to understand student progress and integrate ongoing practices to understand where unfinished learning exists and support students with grade-level content.
Humanizing Assessment Blog Series | Gain practical, research-based advice on expanding the ways educators can gain insight on student progress that go beyond traditional assessment. These student-centered monitoring methods will transform the way you think about assessment.

| Reenvision how you collect and use data on student progress. This collection by Instruction Partners includes a short video, professional learning materials and resources, and an overview blog post.Rethinking Intervention Blog Series

What the Data Can't Tell Us | Learn about the limitations of summative data collected at the end of the 2020-21 school year. This blog post outlines cautions and concerns about using summative assessment data and presents alternatives for monitoring student progress.

Are there additional tools and resources that should be a part of this collection? Share them here.

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Priorities for Equitable Instruction: 2021 & Beyond

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Create positive, affirming learning spaces that center student identities and experiences. Teaching For Equity: A Guide to Integrating Academics, Well-Being & Anti-Racism in Student Experiences | Create supportive learning environments using this teacher-designed framework from Leading Educators. The framework includes five strands that facilitate structured reflection of classroom practice, school and community relationships, and your own identity as an educator.

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by Steve Wyborney

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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20 Days of Number Sense & Rich Math Talk - for all grades from K-12. That is the goal of this series. Entirely new, exclusive content fills this post in a ready-to-use format that will allow you to deeply explore 4 rich math routines.

By downloading each day, you can have a clear pathway to presenting rich number sense and math discourse opportunities to your students.

Additionally, each day contains multiple levels, so that a 2nd grade teacher, a 5th grade teacher, and a high school teacher can all be using the same file - and can all have access to other grade levels. The opportunities to differentiate across levels abound in this series as well as the opportunities to see into other grade levels from K-12.

Update: If you would like to read about Kathy Iwanicki's journey into 20 Days of Number Sense & Rich Math Talk, you can find her blog post here. Thank you for sharing your story, Kathy!

After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.
Quick Access to Days 1-5 Simply click on the blue link to download the file. Quick Access to Days 6-10 Simply click on the blue link to download the file. Quick Access to Days 11-15 Simply click on the blue link to download the file. Quick Access to Days 16-20 Simply click on the blue link to download the file. Quick Access to the solutions for the Advanced Cube Conversations
Quick Access to the Cube Conversations Book The Cube Conversations Printable PDF Description of 20 Days of Number Sense & Rich Math Talk (K-12) Days 1-5
The Answers to the Advanced Cube Conversations Tasks (Days 16-20)
I've opened the series with a brand new set of Estimation Clipboards. The Estimation Clipboard strategy is a very invitational way to draw students into rich number sense discussions as it layers in more and more context and continues to provide students with estimation opportunities. The Estimation Clipboard strategy is also where a very important math instructional reality becomes abundantly clear: Writing is a powerful springboard into math discourse. As students WRITE their estimates (particularly for images 3 & 4) the math talk in your classroom will become very rich. You'll find the power in the pattern of (1) students estimating (2) writing their estimate (3) explaining what their estimate is, and why they chose it. Then right before each reveal, your classroom will become very quite in anticipation of the reveal. Don't be surprised if there is a lot cheering as the answers are revealed.
Days 6-10
Days 1-5 have set the stage with The Estimation Clipboard. Not only have the 20 Days of Number Sense and Rich Math Talk begun, but both students and teachers have detected the power of invitations, estimation, writing, sharing their ideas aloud, and experiencing the joy and wonder of math.

Day 1 - The Estimation Clipboard

Day 2 - The Estimation Clipboard

Day 3 - The Estimation Clipboard

Day 4 - The Estimation Clipboard

Day 5 - The Estimation Clipboard

After the highly invitational nature of the Estimation Clipboard, opportunities to richly explore numbers continue in the Splat! images which are all brand new - and are all designed to work in both PowerPoint and Google Slides (just like everything else in this series - so feel free to use either one).

Ranging from Splats through 10 through Fraction Splats! and now including 10 of the most challenging Splats! that I have ever publicly released, your students will have very rich opportunities to lean into number sense and richly discuss their mathematical thinking while also hearing from other students. They will be able to see and explore multiple strategies for decomposing numbers, adding, subtracting, multiplying, dividing, and connecting many concepts together.

Since every day includes materials across a wide range of grade levels, there is also a really good opportunity to take a look at content from other grade levels and offer even more challenges to your students.

Let's take a closer look at each of the Splat! levels include in 20 Days of Number Sense and Rich Math Talk.

Splat! Level A includes numbers through 10 and is ideal for grades K-1. In these sequences the dots appear so that students can count them. Then, when you click, the total number appears in the corner. On the next click, the SPLAT appears and covers some of the dots. The immediate question is, "How many dots are under the Splat?" You will be amazed at how many different ways students see this, solve this, and even how they mentally move the dots around to decompose and make sense of the numbers. If you look at the images below, you'll see that some of the Splats separate the visible numbers and create a Part-Part-Part-Whole scenario. Splat Level A appears in all 5 days.

Splat! Level B includes numbers through 10 and is ideal for grades 1-2. It also provides the first example of a grade level (kindergarten) that may recognize the opportunity to venture to higher levels. Just like in Level A, the first click introduces the dots, the next click brings in the Splat and the question, and then the Number Sense and Rich Math Talk begins. When I use numbers through 20 in the classroom, I sometimes quickly move through the counting step by saying, "Here are some dots. There are 19 of them. This is the Splat!" I find that counting so many dots can slow down the opportunities that the Splat introduces. Of course, counting is critical, and so is finding many different ways to count, so at other times I spend more time on a variety of grouping and counting methods. The reality is that there are so many opportunities in these slides that you have many opportunities to focus on a wide range of concepts.

The images in Splat! Level C are some of the most wide-ranging images I have ever worked with. It offers opportunities across so many grade levels. I've labeled it as primarily matching grades 2-5, but I've seen it used very effectively in many grade levels. Level C is where multiplication and division begin to play a much stronger role. While students in younger grades may access the image above (the one that shows 14) by adding, subtracting, grouping, counting on, repeatedly adding 3 to 5, or repeatedly subtracting 5 from 14, I've seen other strategies across grade levels. For example, fourth grade students sometimes view it as 14 ÷ 3 with a remainder of 5. Likewise, high school students have viewed is as 3x + 5 = 14. Imagine the power of the conversation among the students across those grade levels!

A very interesting option opens up in Splat! Level D. In the images above you are seeing the first of the reveal clicks. In the moment before this - when all of the Splats are opaque, and none of the dots beneath the can be seen - students approach a new question, which is "What could the total be?" In the first image above, before it is revealed that each Splat is covering 3 dots, students find themselves working with the concepts that the total must be 3 more than a multiple of 3, so the total must be a multiple of 3. However, in the second picture above (again before the first Splat is revealed like you see in the picture) students can see that the total is unknown, that there are 4 visible dots, and that there are 7 splats. By rule, each splat is covering the same number. So students can work with the concepts such as that total must be 4 more than a multiple of 7. As the identify possible totals, they can see that it could be 4, 11, 18, 25, ... Then when you choose to reveal the value of a Splat by clicking, you'll see a single Splat turn transparent (which is what you see in the images above) and the students can determine what the total number of dots is. You may expect the students to use multiplication to do so, and many will, but they will also surprise you with a wide number of strategies that you may never have expected. They are showcasing both Number Sense & Rich Math Talk!

Level E is a favorite of many teachers. In this level, all of the whole dots and all of the fractional parts of a dot can be seen. Then when you click, the Splat appears, and covers some of the whole dots and fractional parts. The immediate question becomes, "What is the value beneath the Splat?" I am amazed at how students approach these questions.

Level F is similar to the previous level with one exception. While, Level E allow the students to see all of the images before the Splat appeared, Level F simply presents the total, the Splat, and the visible parts of the total all at the same time. Students once again bring very impressive insights into the conversation. It's Number Sense and Rich Math Talk and the way that students contribute to one another's insights is eye-opening.

Level G allows the students to see the all of the whole numbers and all of the fractions on the screen and gives the students the opportunity to determine the total. When you click the total will appear. Then, with the next click, multiple Splats will appear on the screen. By rule, each of the Splats is covering the same number (the same value), although those numbers may be represented in different ways. The students task is to determine the value of the Splats (not the specific pieces) under each Splat.

Level H is similar Level G, accept in Level H the Splats all appear at the very beginning, so the first image the students see are just line the ones that are showing above. The question is, "What is the value of each Splat?" Within Level, H (on days 9 & 10), I have included 10 of the most challenging Splat questions I have ever publicly released.

Day 6 - Exclusive Splat Sequences Days 11-15

Day 7 - Exclusive Splat Sequences Day 11 - Exclusive Esti-Mysteries Days 16-20

Day 12 - Exclusive Esti-Mysteries

Day 13 - Exclusive Esti-Mysteries

Day 14 - Exclusive Esti-Mysteries

Day 15 - Exclusive Esti-Mysteries

Day 8 - Exclusive Splat Sequences

Day 16 - Exclusive Cube Conversations

Day 17 - Exclusive Cube Conversations

Day 18 - Exclusive Cube Conversations

Day 19 - Exclusive Cube Conversations

Day 20 - Exclusive Cube Conversations

Day 9 - Exclusive Splat Sequences

Day 10 - Exclusive Splat Sequences
Remember that I've written slides for ALL levels on EVERY day. Download the day you are on, find the level you want to work with, and let your students exercise their Number Sense and engage in Rich Math Talk.

Also, consider challenging your students by trying out 2-3 slides from another level.

Exclusive Esti-Mysteries

15 brand new Esti-Mysteries fill these 5 days, and each day includes 3 different levels, ranging from kindergarten to advanced math concepts. As a bonus, the first 3 Esti-Mysteries include appearing charts on the screen. Additionally, 2 of the Esti-Mysteries include multiple perspectives and hidden clues that can be found in the 2nd image.

Esti-Mysteries strongly call upon number sense and promote rich math talk while also giving students rich opportunities to COMBINE estimation with a range of math concepts in the context of rich math talk. Students will be discussing their estimates - much like in the first 5 days when the work with the Estimation Clipboard - but will also be looking carefully at math concepts and seeing how those concepts are interrelated.

Exclusive Cube Conversations

The highly visual cube conversations strategy is used in the final 5 days to promote number sense and rich math talk. In addition to brand new Cube Conversations Images, the downloadable set of matching pages will give students clear opportunities to annotate and describe their insights to one another.

As with all other days in this series, there is a very good opportunity to see into other grade level bands, and this can be use to differentiate content, challenge students, and promote even deeper number sense and rich math talk.

At the end of each day there is also a challenging task, which is placed in the highest grade band. The printable PDF includes 2 different versions of each task. One version includes 4 copies so that students will have an opportunity to try out 4 different entry points into the task, while the other page simply offers a larger, easier-to-use version of the image.

The beginning level of Cube Conversations provides very good opportunities to visualize and decompose small numbers in a wide variety of ways. The middle image shown above is animated to showcase 3 different ways that students may see how to decompose the shape. Likely, they will find many more than the 3 examples, but the animated examples typically provide a nice momentum and a clear invitation to seek out many different ways to decompose the number. Then another image appears (like the third one shown above) with 4 additional copies below it so that ideas can be shared with the entire class. As with all levels, every image is also available on the downloadable PDF so that each student can decompose the images on their own and then share their ideas with one another.

Deepening Cube Conversations (grades 2-5) introduce some layers of complexity that allow students to work with additional concepts, such as visualizing sets in multiple ways, visualizing shapes that overlap (so the overlapping cubes may need to be subtracted), and shapes that appear to have holes in them.

The 2nd image above shows layers that will appear when you click (although on the slide you download the images will all be in a single location on the slide). If you look at the middle image closely, you will see how the image has been decomposed into 9 + 3 groups of 3, then 2 groups of 5 and a group of 3 and 5 groups of 1. Still focusing on the blue and yellow shape in the middle image above, you can see why students describe it many ways. For example, a student might say, "I see 3 groups of 5 in the blue and yellow image." If you look carefully, you'll also see 3 groups of 5.

Then moving the the last image in the center picture above (the image which is red, yellow, and blue in the bottom right corner) you can see how a student might say, "I see three groups of five plus three more - but I see it in a different way." Remember, that is just the example page and it is followed by the wide open opportunity presented on the next slide. When you look at the third picture above you can see how a student might describe two groups of 9, two groups of 8, or even 2 groups of 7 while other students describe groups of 2, 3, or 5. You may also hear that a student sees a 25 minus two groups of 4 and 2 groups of 1. The possibilities go on and on as your provide students with rich opportunities to explore Number Sense and to explore and describe their insights together.

The routine continues - but at a deeper level - in Textured Cube Conversations. Remember, every level is available on every day in this blog post, and all content in 20 Days of Number Sense and Rich Math Talk is exclusive to this post.

The first image will present a structure, several examples of how the structure can be visually decomposed, and will finally reveal the number of unit cubes. Then a new image will appear with 4 opportunities on the bottom of the screen for students to show their thinking to each other.

All of the Cube Conversations images are available in PDF format so that you can provide each student with their own copy to annotate - and then to share their ideas with one another.

Advanced Cube Conversations will feel very much like a rich task. Two of the Advanced Cube Conversations are illustrated in the pictures above.

The thinking that comes from these tasks is tremendous!

On the downloadable PDF you will find a page with a large image of the structure an an additional page that provides 4 smaller versions of that picture so that students will have multiple opportunities to try out a variety of entry points.

In each case the question is, "This structure is composed of how many unit cubes?"

I hope you enjoy 20 Days of Number Sense & Rich Math Talk. If you do, please leave a comment. You can even share who is using it. Perhaps we'll see some classrooms from around the world leaving comments like, "We are using #20DaysNS in Hunters, Washington!"

As always, you can find me on Twitter @stevewyborney

I'll be keeping an eye on #20DaysNS on Twitter.

I wish you well as you work with your students and give them opportunities to develop their numbers sense and engage in rich math talk.

All my best,

Steve

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20 Days of Number Sense & Rich Math Talk (K-12) - Steve Wyborney's Blog: I'm on a Learning Mission.

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20 Days of Number Sense & Rich Math Talk - for all grades from K-12. That is the goal of this series. Entirely new, exclusive content fills this post in a

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5 Weeks of Daily Routines by Berkeley Everett

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5 Weeks of Daily Routines by Berkeley Everett

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Here are 5 weeks of number sense routines (5-10 minute math talks) tailored to each grade K-5. Every slide deck includes a "how to" and a week each of:

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Teacher use of Esti mystery  Mar 27, 2020 3 36 PM

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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Steve Wyborney's Blog: I'm on a Learning Mission

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Steve Wyborney is on a learning mission to spread math joy to classrooms everywhere! On this blog you'll find math resources for teachers and for kids of all ages.

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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For my educator friends who have access to Google Slides, but do not have access to PowerPoint, this post is for you. Since Google Slides does not have the animation that makes the Splats become transparent, the Splat! reveal does not work in Slides. Now - with these materials - it will. I've rewritten the first 20 Splat! lessons and the first 20 Fraction Splat! lessons with a different method so they will now include the reveal when using Google Slides.

The content of the lessons is the same as the original lessons.

Visit these links to see the original videos about how to use the and the Fraction Splat! slides.

Quick Note: The file sharing power of Google Drive is impressive and highly useful. However, for the purposes of sharing these resources, I need to use a method that I can personally maintain, update and support - and I've learned that the best way to provide resources from my blog is through the download links and the sign-up forms.

I hope you enjoy these Splats! formatted to work in Google Slides!

Splat Through 10
How many dots are under the Splat?
SPLAT 1.1 - numbers through 10 (Google Slides compatible version)
SPLAT 2.1 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.2 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.3 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.4 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.5 - with numbers 12-20 (Google Slides compatible version) SPLAT 1.2 - numbers through 10 (Google Slides compatible version)SPLAT 3.1 - multiple splats (Google Slides compatible version) SPLAT 3.2 - multiple splats (Google Slides compatible version) SPLAT 3.3 - multiple splats (Google Slides compatible version) SPLAT 3.4 - multiple splats (Google Slides compatible version) SPLAT 3.5 - multiple splats (Google Slides compatible version)
SPLAT 4.1 - instant multiple splats (Google Slides compatible version) SPLAT 4.2 - instant multiple splats (Google Slides compatible version) SPLAT 4.3 - instant multiple splats (Google Slides compatible version) SPLAT 4.4 - instant multiple splats (Google Slides compatible version) SPLAT 4.5 - instant multiple splats (Google Slides compatible version) Note: These lessons use a single splat along with a mixture of unit fractions and whole numbers. In Level 11, you control the Splat! SPLAT 11.1 - fraction splats (Google Slides compatible version) SPLAT 11.2 - fraction splats (Google Slides compatible version) SPLAT 11.3 - fraction splats (Google Slides compatible version) SPLAT 11.4 - fraction splats (Google Slides compatible version) SPLAT 11.5 - fraction splats (Google Slides compatible version) SPLAT 1.3 - numbers through 10 (Google Slides compatible version)Note: These lessons use a single Splat! which appears at the same moment as the whole numbers and fractions. Each question instantly presents missing information. SPLAT 12.1 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.2 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.3 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.4 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.5 - Instant Fraction Splats (Google Slides compatible version) Multiple Splats! with Fractions Note: These lessons include multiple Splats! and you control the timing of the Splats! The entire screen can be seen, the total can be determined, and then Splat! Remember: Each Splat! that is the same color must be covering the same number. SPLAT 13.1 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.2 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.3 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.4 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.5 - Multiple Fraction Splats (Google Slides compatible version)
Note: These lessons use multiple Splats! which appear at the same moment as the whole numbers and fractions. Each question instantly presents missing information. Remember: Each Splat! that is the same color must be covering the same number. SPLAT 14.1 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.2 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.3 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.4 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.5 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 1.4 - numbers through 10 (Google Slides compatible version)
SPLAT 1.5 - numbers through 10 (Google Slides compatible version)

Splat Through 20
How many dots are under the Splat?

Multiple Splats
Note: Splats that are the same color must cover the same number.

Instant Multiple Splat
Note: An additional feature of this level is the opportunity to ask, "What could the total be?"

Instant Fraction Splat!

Multiple Instant Splats! with Fractions

After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

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Splat! for Google Slides - 40 Lessons - Steve Wyborney's Blog: I'm on a Learning Mission.

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For my educator friends who have access to Google Slides, but do not have access to PowerPoint, this post is for you. Since Google Slides does not have the

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.

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with special thanks to Christopher Danielson and his Which One Doesn’t Belong - A Shapes Book.