TSBVI Coffee Hour: Making Connections: Base-10 Manipulatives & the Cranmer Abacus
12-07-2020
>> Kaycee: Hello. Welcome, everybody. We will wait just a couple of minutes as everybody comes in. We're glad you're with us today. While you're waiting, you can go ahead and set your chat to "all panelists and attendees." It defaults to all panelists so you'll need to change that to "all panelists and attendees." We have Elsa here fromEl Paso, Texas. Welcome. Again, we'll wait just a couple of minutes as everybody comes in, gets ready for today. While you're waiting, you can set your chat from all panelists to all panelists and attendees. Andrea is here from Houston. Welcome, Andrea. Marlisa from Albuquerque, New Mexico. Miami, Victoria, Texas. Denver, Fresno, California.Louisville, Kentucky. Sandra, don't forget to set your chat to all panelists and attendees so everyone can see what you're saying. We're glad you're here today. Rob is here from Western Colorado. All right. We'll go ahead and get started. We're glad that you're here today with us. If you have a question or a comment while our presenteris speaking, please post that in the chat box and make sure, again, that your chat is set to "all panelists and attendees."Your microphones and cameras are automatically muted so you don't need to worry about that. And the handout for today's session will be shared in the chat for immediate viewing. It will also be available for later viewing along with the recording of this and past Coffee Hour sessions shared through a link on our Coffee Hour page, tsbvi.edu/coffeehour.Once you're on the Coffee Hour page you'll scroll down to under the list of sessions where it says visit the new TSBVI outreach Coffee Hour archives. That is a link that will take you to the recordings, handouts, transcript, and chat information. To obtain your CEUs for today you respond to the evaluation that will be e-mailed to you fromour registration website escWorks. You will enter the code and the CEU certificate will generate upon completion of that evaluation. There is no opening code, only a closing code and it will be given at the end of today's presentation. We'll stop the presentation at about 3:55 and give you your code and announcements. Happy to introduce today'spresenter to you, John Rose.
>> John: Hello, everybody. Like Kaycee said, my name is John Rose. I am a teacher in short-term programs at Texas School for the Blind and Visually Impaired. And today I'm going to be talking about Connecting Base-10 Concepts with Abacus Instruction. And I have a slide up right now. There's a picture of an APH work-play tray with some DigiBlocksin it connected by a heart to an abacus with the No. 24,980 set on it. Y'all already knew that, didn't you? If you're following along with the documents that was shared, you should get all the content. There may be a few images, for instance this heart is not on the document but you can get it transferred over. But all the images should havealt text and all the text will also be approximately, hopefully what I'm scripted to say today. If you have any questions, feel free to contact me. Later I'll have my contact information up at the end of the presentation. And also before I begin I have to credit many people in helping me develop my knowledge of abacus instruction,including Debra Sewell, Susan Osterhaus, Rita Livingston and several TVIs in our short-term programs department who have developed some of the instructional strategies that I will discuss today, including Margaret Edwards and Kathi Garza. So briefly -- whoops. There we go. Briefly, I want to talk about short-term programs at TSBVI. We offerweek-long, weekend, summer, distance learning, and individualized instruction classes to students around the State of Texas. Our classes focus on developing and expanding core curriculum skills through classroom instruction, project-based learning, and community partnerships. Obviously, during this time we are -- right now we're all remoteso we're delivering our classes via Zoom and just trying to make the best of it at the moment. Also we're doing a lot of individualized instruction working with students, more than we typically do during the school year. By providing students an opportunity they might not consistently have in their district. For example, access to a TVI formultiple hours, travel and connectively in the city as opposed to rural areas, and experiences with groups of students who are also visually impaired. We hope our classes give students a boost they need to be more successful in their academic and personal lives. One of the classes I teach -- I taught for several years, I can't remember howmany -- is elementary math series class. And this class occurs in the fall and it's intended for students who are learning beginning math, compensatory academic skills. So abacus, Nemeth Code, and tactile graphics. Other series classes are available, so technology skills and that sort of thing. But students who attend this math class typicallyhave some background knowledge. One to one correspondence, some abacus knowledge, et cetera. However, for the most part they're not able to perform addition and subtraction on the abacus correctly, systematically, or efficiently or all of those things. So my goal is for them to at least be able to add and subtract using the accounting methodwith the 4, 5, and 9, 10 exchanges by the time they finish in the fall semester. The three series classes, September, October, November. Hopefully by the end of the class in November they'll have that ability to perform the addition and subtraction. So in this presentation I hope to share with you some of the instructional strategies thathelp us get to that point. Last year we finished the counting method for the Cranmer abacus book. This is a TSBVI curriculum. It's available now. I linked it here in the presentation materials and I'll show you what it looks like here in just a minute. And it includes abacus basic concepts and vocabulary, developing prerequisite skills,reading and setting numbers, exchanges for addition and subtraction, multiplication and division, decimals, and money and fractions. So I feel like it's a good resource and everybody should go get it. So right now I would like to kind of get a sense of where y'all are with the abacus and with teaching it. And so we've got a poll coming uphere, so how comfortable are you with the abacus? Either you have no clue. Maybe you know a little bit about place value but not on the abacus. A little bit about the abacus, its parts, and some vocabulary. Moderate level. You can add and subtract, even with exchanges, and pretty darn good. You can multiply, divide, and work with decimalsand fractions. If that's the case, we're going to turn the presentation over to you. No, just kidding. You don't have to do that today. So I'll give y'all a few minutes to do that. And as I do I'll show this book. Oh. Stop share. There you go. So you should see the book. This is the counting method book and I'll give you just an ideaof what's in here. For each section, for example, it's step by step for how to solve the problems with no exchanges, for example. And then it goes into -- so there's two digit by two digit, three digit by three digit. And there are pictures, images of what the abacus should look like in each event. And then it goes into subtraction as well.I'm sorry. Yeah. There. It goes into the exchanges, and then multiplication. I'm just so excited about this poll.
>> It looks like we're kind of approaching the end of its life, it looks like most people are either a little or moderately understanding the abacus. And then there's a few that don't know much and a few that are really good.
>> John: Oh, wow. Great.
>> I don't know if you can see the results, but most of them are moderate.
>> John: Okay. I can't see the results but that's all right.
>> Maybe now you can. I just shared the Results.
>> John: Good. I'm hoping for those of you who have not -- have no clue or your -- let me get my presentation back here. Or you're just -- you just have a little bit of knowledge about the abacus, I'm hoping that this presentation will kind of give you a little bit of skill set you need to provide instruction to students. For those of you whohave a higher skill level, what I'm hoping is that y'all are able to get some things out of it that maybe you haven't tried before or potentially we can also go, if we have time, go into some more things. All right. So now you should see manipulatives and visual impairment on the screen. I want to talk just a little bit about some researchand the references that I talk about are available in the materials that were provided. The primary takeaway of the research on manipulatives is that it's clear that teachers play a key role in helping students instruct knowledge by helping them connect ideas. However, the use of manipulatives by teachers in classrooms often tapers off afterearly grades. So manipulatives in pre-K, K, first grade and then it tapers off after this. The students with visual impairments may benefit or likely do, in my experience, do benefit from these materials on a consistent basis and for a longer period of time. Students who come to the class are generally second and third graders and they definitelybenefit from using manipulatives. A concrete materials have been recommended for teaching students with visual impairments for more than 40 years. It's been demonstrated that these concrete aids can increase computation accuracy and studies demonstrated that these aids and devices increase the acquisition of mathematics skills. So 40 yearsis a long time and I think that a lot of times what happens in teaching is that we kind of do things -- do the same thing over and over again. Sometimes expecting different results. What I've discovered is that, you know, this 40 years is not because we're stuck in the mud and not adopting new exciting and inventive materials and methods butit's because manipulatives work, especially when they're incorporated with the systematic math curriculum and an expanded core curriculum plan. So these are adaptations that are necessary for accessing all areas of the existing core curriculum and they should be a part of a program that appropriately addresses all of the educational needs ofblind and visually impaired students. Which will include sizable periods of time in order to master the competencies required in the expanded core curriculum. Manipulatives are crucial for learning mathematics concepts and once students have demonstrated basic number sense, one to one correspondence, the skill of counting can be developedby learning three strategy. Those strategies are scanning, organizing, and separating or partitioning. And so that's where we get into the -- there it is. The APH work-play tray. So scanning, organizing, separating, and partitioning. These are all skills that can be practiced using the APH work-play tray and they can be infused into Base-10instruction that prepares students for the abacus. The inserts available for use with the tray divided into two, three, four, or five columns. And sometimes we've used WikiSticks or tape to divide columns further into partitions as needed. I recognize that, you know, especially during this time we have students who are at home, students whoare not necessarily have access to this material, so this type of thing can be made on the fly at home using, like, a baking tray and some type of materials such as WikiSticks or even just like some wooden skewers that maybe cut the sharp ends off and tape them down with some packaging tape. Anything that will provide that distinct separationin the tray. And you can separate it into, you know, two or three columns. Honestly, I only use the two and three columns in the tray, unless we kind of -- the four columns, five columns is kind of novel and the students maybe see it a few times just to kind of get a sense of a place value. I'll get more into that in just a minute. But Iwanted to -- I'm trying to incorporate a few things that are, you know, ways that we can -- like things around the house or ways that we can [Indiscernible] having to acquire materials for students if it's not available immediately. So the next tool that we use are Base-10 blocks. For Base-10 blocks we use DigiBlocks in short-term programsbecause of their unique nesting features. I don't have a thousand block but each thousand block unpacks to reveal ten hundreds blocks. I do have several hundreds blocks and so I'm going to show y'all what these look like. This is a hundreds block and you can kind of see just by how its size by my hands here. And this is four of them. I didn'tbring the thousand block home because, like, it's super heavy and I didn't -- and plus with the web cam it's kind of hard to show. I just don't have very much room. So, anyway, so these are the hundreds blocks. You can see this is four of them and ten of them fit in the thousand block. They stand up and they fit in the thousands block. Andso you can get a sense of how big a thousand block would be. And they nest inside there. And so students can open up the thousand block and discover that there are ten hundreds in the thousand block. And then they can open up the hundred block and discover that there are ten tens in a hundred block. And so this becomes kind of a funthing to do, just a whole, you know, lesson of discovery on what is in the boxes. And so there are ten tens in the hundreds. And then they can open a ten and find that there are ten ones in the tens -- in the ten block. So you have your ones. And they're so much fun to take apart but then, you know, students also have to put them backtogether. And so if you're able to see this you can watch as I place this inside one side of the block. And you can see that for a student who is younger, second grade, maybe. Third grade. This takes a lot of manual dexterity and it's really good practice for their little fingers to practice putting those in there. And I'll show you a lotof times what happens is they kind of fall down like that and you can get them in there. And so I like to slow down with the students and just practice putting these in and back together. And eventually they get a lot better at it. After some, you know, some time of practice. But just letting them do it and not helping them too much, unlessyou're really on a super deadline. I like to give them time to work on those and explore how to take them apart and then to put them back together. And even the tens going into the hundreds block it's not -- it also takes some coordination. It's a good little O&M practice while you're also working on math. So that's a DigiBlock. And I'llgo ahead and reshare. And those are available from DigiBlock. DigiBlock.com. It might be DigiBlocks.com. That link might be wrong, but easy to Google. And then there are also Base-10 blocks available from ETA hand2mind. They have the cubic system with the shorts, longs, flats, and blocks. APH offers some of those in its FOCUS in mathematicskit. That's available. And I always recommend checking at schools. Sometimes there are, you know, random storerooms. Maybe ask around with some of the math teachers. There's a chance that there are manipulatives available that aren't being used, especially in classrooms beyond K-2. As I mentioned before sometimes that gets tapered offin those later grades. So this is what the cubic system looks like. Hopefully. And the rest of the pictures that I share will be of the DigiBlocks, just because that's what we have and use in our department, so that was easier for me. But in the Base-10 system, using the cubic system there's one short is a one, and that's just one littlecube. And then a long is 10 cubes. And that makes up a line of the shorts. And then a flat is 100. This slide did not come across very well, I see. And then the big block is 100 flats so it's 1,000. It's a very large cube of 100 of the flats. So you can kind of get -- the thing that's great about the cubic system is that you get a bitbetter sense of the multiplicative concept of how it builds upon itself and how the Base-10 builds upon itself. So I like that about that system as well. So as far as recommendations go, I really think the best thing to use is what you have. And even if it's, you know, beans and jars of beans, you can use that as well. Just as long as it'stangible and as long as the student understands what the meaning is. So if it's a bean, one bean is a one. And if it's a, you know, ten beans in a little envelope, then that is a ten. That's the main thing is understanding what each of those things signifies. So I mentioned this as being multiplicative but what I mean is this cubic systemscan be used for volume instruction later. So sized accordingly so everything is the same size. So Base-10 is also known as the decimal numeral system. It's the standard system for denoting integers and non-integers. As I mentioned before, there are ten ones in a ten. Ten tens in 100 and ten hundreds in a thousand and so on. I can'tsay it enough because it's something that will apply as soon as we transition to the abacus. And then when we switch over to decimals, there are ten tenths in a one. Ten hundredths in a tenth. Ten thousandths in a hundred and so on. From here we can begin to discuss place value. And this is something where the work-play tray comes intoplay. And so what we do with the work-play tray is we set it up with the single divider or with the double divider. So we have two columns or three columns. And we label the columns. Ones on the right, tens on the left. And this can be a label with a Braille print label. You can use a sticky Braille on the -- so that it remains a littlebit more permanent so the student sees it. One of the great things about using these cards is that -- pardon the noise. Okay. So if you can see my tray here, I have the three columns divided. I'll explain -- there's a WikiSticks. I have Braille print cards labeling the columns at the top. On the right I have ones. In the middle I havetens and on the left I have hundreds. And I have them attached with Velcro so you can take them off and have the students, you know, replace them to say the ones is on the right, the tens is in the middle, the hundreds is on the left. Or you can, you know, mix them up and say rearrange them so that they put the ones on the left, the tensin the middle, and the hundreds on the right, right? No. It's the ones on the left, the tens in the middle, the hundreds on the right. Tens in the middle, hundreds on the left. It can be fun to do that and you can even have the student try to fool you, once they're a little bit understanding a little bit better. Can we switch back here?Sometimes I get away from myself as far as these presentations are concerned. Oh, yeah. Students can use their hands. Let me just show this. Students can use their hands also. So one thing when we remove the cards, we can have the students -- you can say, okay, put one hand in the ones column. Pick up one hand in the hundreds column. Ortwo hands. Some of them can fit both hands right in here. That's cute. The great thing about this work-play tray system is place value using these dividers is very similar to the place value rods on the abacus. So each column represents place value, just like each rod on the abacus represents a place value.And share. Okay. So here's a picture of the abacus. Let's not get too overwhelmed. The primary differences that a student's going to notice when transitioning between the work-play tray and the abacus are the abacus has many more place value columns. The beads are stuck in the columns and they can't be added or removed. And the countingbar is integral to using and understanding the abacus. So let me grab an abacus and talk about this just a little bit. So the counting bar is the bar that's between the ones beads and the five beads. So it's in the middle, kind of in the middle between the top beads and the bottom beads, if you will. And it's integral because it helpsstudents identify where the place value is on the abacus. So some ways that we can help with the transition between the tray and the abacus are to work with students to thoroughly explore the abacus and ensure that the student can identify all the parts of the abacus before they even start setting and reading numbers. Just going through, whereare the ones beads? Where are the five beads? Where is the accounting or separation bar? Identifying place value. So that exploration is also great tactile discrimination practice as well as exploring the Base-10 blocks. And we can also focus on just the right-hand side of the abacus. So I have this picture cut off here but one thing thatwe've done with abacus in the past is just put a piece of cardboard over the left side totally, just to kind of like -- and rubber band it -- just to kind of eliminate that whole side so we're just focusing on the ones, the tens, hundreds, and maybe the thousands place values. Some students may benefit from using a beginner's abacusbut honestly I typically try to jump right into the Cranmer abacus because of the five bead. That in and of itself is a big transition to make anyway. I like the beginning abacus for accounting and we definitely use it for some students, so I'm not not recommending the abacus, but definitely try the Cranmer first. And there are instructionalmodifications and strategies that might assist some students. So we use -- in the picture that I have on the screen, I have a work-play tray with ones, tens, hundreds, and thousands columns and they're divided. The top part of the tray is divided using art tape and WikiSticks. And so that top part represents the five bead. And the WikiSticksrepresents the counting bar. And there's also a little Wikistick in between the hundreds and the thousands. It's right on the divider so that represents the mathematical comma, the period marker on the abacus. And also further down the line it represents the decimal point, but we don't need to get into that right now. So and I'm going todemonstrate this here soon so don't worry too much about this. When students count, have them make similar movements as they would on the abacus. So, for example, once they have five counted, move them up above to the upper portion. Above the WikiSticks counting board. And, note, some students may not need these modifications at all so itshouldn't necessarily be seen as a starting point but if a student is struggling with the five-bead concept or remembering place value, these types of things may help. Okay. We'll talk about reading numbers. Let me go ahead and go off my board just a little bit.Because I want to have a little more fun here. All right. So I have my work-play tray. I have some DigiBlocks. And so when working with the Base-10 blocks on the trays, I like to use the same vocabulary as when I'm going to be working in abacus. So this will help students transition with the concepts. So setting numbers is adding amountsto place value section. So I can say set 4 in the ones column. So I take four --
>> Kaycee: Hey, John. It's Kaycee. Do you want to stop sharing so that can be big on our screens?
>> John: Thank you so much. I had a note to do that. I lost that note.
>> Kaycee: That's better. Thank you.
>> John: Thank you. Sorry, y'all. Okay. I've set four ones in the ones column. And then I will also use -- I'll say, okay, let's set two in the tens column. So I've set two in the tens column. And so when we -- other vocabulary we use is clear. So we clear numbers also. So I'm going to say clear two from the ones column. And so I can taketwo away from the ones column. And then we also use the term count. Counting numerically each time a block is moved, each time a block is set or cleared from a place value section. On the abacus, counting occurs when the beads are moved toward or away from the counting bar. So I'm going to hold my abacus over here and make sure I can seemyself. There we go. Okay. Sorry. Technical details here. Counting. So I can count on the abacus by pushing beads toward the separation bar. One, two, three, four. And then I do the same thing when I count beads into a tray for a set. One, two, three, four. Okay. So in this case the teacher has set two tens. I'm going to be the teacherand the student for y'all. The teacher has set two tens in the tens column and four ones in the ones column. And now the student counts the tens column and the ones column. And there are a variety of ways that you can do this. I tray not to be too particular with students because some students do things differently and I don't want to discouragethat. But, you know, if we want to do it like we would do it on the abacus, you know, we would pull all the -- everything down to the bottom and then I can count up toward what would be the separation bar and say one, two, three, four, in the ones column. 10, 20 in the tens column. 24. And some students prefer to go the otherway. 10, 20, 1, 2, 3, 4. And sometimes that is just fine too. In fact, I love it when students can do both. Any time they can count one way or the other way, they're doing well. So they can -- students can read numbers that are set on the tray and then we can transition to the abacus. And so I have that number set on the abacus. The teacherhas set the same number on the abacus and the student can read it in the same way. Typically, by counting away from the separation bar. I like to talk to students about using both hands on the abacus. It's kind of hard for me right now because I have to lean over under this camera, so just FYI if I don't practice what I preach it's becauseit's sore on my back. So I'm holding both fingers on the abacus so I can feel where the ones column is and where the tens column is. And I can count 10, 20, 1, 2, 3, 4. 24. On the abacus. And so the student should also be able to answer place value questions. And that can be either on the tray or on the abacus. So in what place value columnis the 4? That's in the ones column. In what value is in the tens column? There are 1, 2 tens or 20 in the tens column. What value is in the hundreds column? We can look at the hundreds column on my abacus and see that there's nothing set in the hundreds column. I can look on my tray and see that there's nothing set in the hundreds column.And that value is zero. Zero. So students may need more practice with manipulatives on the tray before they're comfortable switching back and forth between the tray and the abacus seamlessly. And I'm just checking to see if I'm missing anything right now. Okay. So, great. So I want to talk just a little bit about reading numbers on theabacus. And to do that I'm going to set a different number. So I have the number 104 set on the abacus. I have a 1 in the hundreds column, zero in the tens column and a 4 in the ones column. So it's important for students to remember when they move from right to left to see, is there anything set in the ones column? Yes. Is there anythingset in the tens column? No. So my number is 4. So that is sometimes challenging for students to recognize that to be careful of the zero and know to check the columns to the left to make sure that there's nothing else set. In this case there is. There's a 100 set so the number is 104. So some -- we'll talk about some organizational strategies.I'm going to kind of go a little bit more quickly. If I can. Whoops. Oh, my gosh. Sorry, y'all. Technology. Technology happens to me. So that's okay. What I'm going to do is just talk about this in a fun way. So a lot of times the students will find that things are kind of all over the place so we like to encourage students to use organizationalstrategies. And so what that means is if the blocks are scattered in the tray, to feel top to bottom, left to right. Pull all the blocks down to one corner and then collect them in one location and then count them one at a time. One, two, three, four until they're all collected, either at this separation bar or at the top of the tray, dependingon whether or not you have that. So this is good for orientation practice as well as far as, you know, the complete strategy of the tray. So setting and reading numbers is really great practice for your students and it can be a challenge for students to set numbers following certain rules, setting numbers that have a 3 in the tens column,for example. So they have a 3 to set and then they get to choose what they set in the ones column. Setting and reading a number that has a zero in the ones column, for example. Setting and reading a number that has a 9 in one of the place value columns. So this is really good strategy for a place value, especially as in regards to standardizedtesting. And it can also be incorporated into Braille Nemeth Code instruction. So once a student's comfortable with reading and setting numbers on the tray and abacus, we move in to performing operations. And the first operation we perform is addition with no exchanges. So in this case the problem is 13 plus 21. I have a 10 set in the tenscolumn and a 3 set in the ones column. So that's 13. And I'm going to add 21. So that's a 1 in the ones column and two tens to the tens column. And from there I can count. So I'll just bring everything down to the bottom and count 10, 20, 30, 1, 2, 3, 4. So that's adding with no exchanges on the tray. Then when we transition to theabacus, we started with 13 on the tray. That's a 1 in the tens column and a 3 in the ones column. And then we add 1 to the ones column and a 2 to the tens column. Then we can count from the separation bar. Also we have 1, 2, 3, 4 in the ones column. 10, 20, 30 in the tens column. That's 10, 20, 30, 31, 32, 33, 34. We got the correct answeron both the tray and the abacus. So I want to note that students can add from right to left or from left to right. Ideally they'll be able to do both. I promote that with my students to be able to do it both ways. Students in elementary math classes, they're going to be adding from right to left. They're going to add the ones first and thetens next. On the tray and abacus it's possible to do it both ways. So I try not to discourage too much in my math classes. And now we go into -- I go straight into subtraction using inverse problems. So in this case I have the number already set, 34. And I'm going to subtract 21. So I have 34 already set. I'll subtract 21. So I'm subtracting1 from the ones column and two tens from the tens column. And I can count now. 10, 11, 12, 13. 34 minus 21 is 13. Let's just check that on the abacus. So I'm subtracting 21. I have my 34 already set from the previous problem. So I can subtract one from the ones column, two from the tens column and count one in the tens column. 10, 11,12, 13. So you can see how using the tray and the abacus to transition is relatively seamless, especially with the exchanges. One question I get a lot is when to introduce the abacus for addition and subtraction. I like to begin working with them side by side. If I feel like the student's prepared for that. If not, we'll do a few additionand subtraction problems on the tray and when I feel like they're, you know, they have some mastery with this I'll start to introduce the abacus and show them some similarity. They have already seen it for counting so it's not brand new. And setting numbers and reading numbers. A lot of times they're ready, you know, to try it on the abacus.If the student seems to be confused or not performing as proficiently on the abacus, we can check for understanding. Does the student understand parts of the abacus? Do they understand place value? Do they understand addition and subtraction on the tray? And then we can try very simple problems. So zero plus 1, 0 plus 2, 0 plus 3. Thereare a whole set of problems you can work with in each place value column for addition and subtraction with no exchanges.
>> Kaycee: John, sorry to interrupt, this is Kaycee. I just want to give you a five-minute warning.
>> John: And I lost my presentation right now so I'm going to try -- I'm trying to get it back and talk at the same time. I'm just doing my best. So I got it. But y'all can still see the tray, right?
>> Kaycee: Yes. We see the tray.
>> John: That's the important part, I think.
>> Kaycee: I have your handout pulled out so if you want me to share your screen, I can.
>> John: Okay. I think I got it. Okay. Here we go. So as per usual I don't have enough time to present -- to show y'all everything that I'd like to. But then, you know, once we've done addition and subtraction with no exchanges -- can you see the presentation now? Yes?
>> Kaycee: Yes.
>> John: We move into the 4/5 exchange for addition and for subtraction. The 4/5 exchange on the abacus, all that means is you have four ones set in the ones column or in any column, to be honest. And you add one to that column. So you bring a five bead down and clear the four beads. And a 4/5 exchange for subtraction means you clearthe five bead and set the four one beads. To give you a brief idea of how that works on the tray, you have four sets and add one and then you have five. When we first start out we like to have those set -- we set those five at the top so the student kind of gets an idea of what the five bead's going to be like once they make that transition.Sometimes it may help to tape some blocks together. She loves doing this. She just liked it because it gives a good representation of the five bead. You can actually feel how there are five blocks taped together as one solid piece. And so makes that transition just a little bit more seamless. And so for subtraction, you have five sets atthe top of the tray in the ones column and you subtract one and move the four down to the lower portion of the tray. I want to remind you, you can do this without that separating bar. We just use that for students to make the transition to the abacus a little bit better. And then the 9/10 exchange just simply means that you have nine set inthe ones column. You add one so you can't have any more ones set in the ones column so you have to set one 10 and clear the 9. This works in any column across the abacus. And so this is what it looks like on the tray. Now, when it comes to making these exchanges, like the 9/10 exchange, I like to have students try to figure out what comesnext. You know, reminding them they can't have any more ones in the ones column and then maybe giving them a suggestion by putting an open block in the tens column. Just to see if that may clue them in to what they do next. And hopefully they figure out that they need to put the ones -- fill up that tens block and set that ten in the tens column.9 plus 1 equals 10. Same for subtraction. I've had lots of students talk about like opening up -- they love -- any time they get to open the blocks, it's just magical. So that makes the 9/10 exchange for subtraction fun any time they do that. I'm just going to move forward. I have practice problems in here. I have other strategies for countingpractice, multiplication process and I have a little bit more detail on complex mathematics and how using place value is really a good strategy once we get into multiplication, division, decimals, and fractions. And I would be happy to talk to anybody about how using place value methods to teach these concepts on the abacus. I learned initiallyusing abacus made easy and then I read a little bit more of this stuff that Debra Sewell had done. And I finished working with that book and really got into the multiplication and division. There's more details about that, my references. If you have any questions, feel free to let me know. Sorry I went over. Thank y'all so much. I appreciateit.
>> Kaycee: Thank you so much, John. To remind you we have different times for Thursday sessions and Monday sessions. Mondays are at 3:00 p.m. central standard time and Thursdays are at noon. Check tsbvi.edu/coffeehour forupdates and registration information for upcoming sessions. We do have on the 10th will be our next part of the WREIC series title screening and assessment for birth to three, looking at virtual screening and assessment. It will start an hour early because it runs for two hours, so that will be 11:00 central. On December 14 we have usingthe intervener team model for students who are emerging communicators. On the 17th we have our last session with Deanna Peterson and she will wrap up our Coffee Hour series for this semester. We will be back in January with more sessions. Check our Coffee Hour website at tsbvi.edu/coffeehour. And we will have the registration informationfor upcoming sessions up soon for January. Also the handoutsand past Coffee Hour sessions are available through a link on our Coffee Hour page which, again, is tsbvi.edu/coffeehour. Once you're on the Coffee Hour page, you'll scroll down to under the list of sessions where it says visit the new TSBVI outreach Coffee Hour archives. That is a link and it will take you to the recordings, handouts, transcripts,and chat information. On the evaluation you receive from escWorks this evening, there are two boxes numbered 10 and 11. They say additional comments you would like to share with the presenter and then the event planning committee. Please let us know in those boxes if the times and days offered for Coffee Hour are working for your scheduleor if you have other suggestions. We're actually meeting this week to make decisions for spring so make sure you let us know what you think. And also we would love to hear your topics for future Coffee Hours. Thank you so much for coming. A huge thank you to John for sharing all this awesome information. Thank you all so much.