TRANSCRIPT - Abacus Continued with John Rose

Okay. Good afternoon. Everybody. Welcome to techy time. This session is going to be on the advicates, and tech tat time is kind of like a chat with teachers and par professionals, and it happens every Thursday and around 3 3 p. M central time. So today's topic is going to be the advocates, and I'm your facilitator. My name is Cecilia Robinson, and welcome everybody. Today we have spring advocate series with John Ros and welcome, John, and thank you for teaching this class before we start our goal is to make sure we build a community of practice for technology so that we can learn from each other and support one another thank you. Time is an interactive session, and you're encouraged to ask questions and participate. This session will be recorded and posted on our website for later viewing. So by registering for this session, you will grant Tsbvi outreach. Permission to publish the content of the recording, which may include image and the audio of you. The registrant, and I hope this is okay with everybody. Today's techy time is again the topic of the advocates, and we are going to have questions and discussions. And so on, and I hope you will feel free to ask questions and talk. So maybe that I am going to stop sharing, and I am going to pass the screen to John. Hello! Hello again! Everybody! Welcome to what I think is my fifth or sixth advocacy session. And today we're gonna be talking about decimals. And hopefully, if we get into, we get that far, we'll talk about fractions. Before we get into division of desimals. I wanna talk about just to do a little review of what we did, what we talked about last time so I'm gonna switch over to my abacus here. Everybody should have received a worksheets. It's I've printed mine out because it's just easier for me, and it has the problems that we're going to be working on today. The first thing I wanna do is just a quick review of decimals with decimals. The period marker is the decimal point on the advocates, and so, if I'm adding a decimal such as whoops 22.2 2. I would start by to something else. I would start by setting it up with 2 2 decimal point 2 2 22.2 2. And I'm just gonna add $11 and 11 cents to this $22 and 22 cents. So that's one penny one dime, $1 and 1 $10 to get $33 and 33 cents, and so I'm gonna subtract that 11. 11, let's say. I'm buying a bunch of bananas that cost $11 and 11 cents. And so when I subtract those, I just subtract the ones from the hundredth place, the ten's place, the units place the ones place the ones place and the ten's place. So just a quick review of addition and subtraction, using the desk. We also talked last time about multiplelication with decimals I'm gonna clear the advocates with multiplication. What we talked about was that. We set the problem up in the same way that we would a standard multiplication problem. And we keep in minds how many desk places there are in the problem. So in the problem, we're gonna look at, it's 0 point 4 4 times 7. And so what we do is we set that up as though we would a problem with whole numbers 44 times 7, and then we do our multiplication 4 times 7 is 28. And then we're finished with that 4, and the ones play then we moved to the 4 in the ten's place, 4 times 7 in the ten's place, or 40 times 7. Is 28 in the tens place, or 280. Let me add this, I'll add the 8, first, 123-45-6782 exchanges in there, and then I'll add the 2. In the hundreds place. Now I'm finished with that 4 finish with the 7, and I have 308 set here. But what I had to keep in mind was that there were 2 decimal places in the problem. 0 point 4 4 and so my desktop is going to be a 2 over from the rights so it's gonna be between the 3 and the 0 in that. In that product 3.0 eights. Now, if I wanna demonstrate that I can do some just by shifting things over and using the period marker as the desktop point, so I can just move the 3 over the 0. I don't need to do anything and then I can move the 8 over to the right. I'm sorry to the left, so that I can show 3.0 8. And so those are the types of problems that we worked on last time. And I promise this time we would do some division of decimals any questions before I get started. With division of decimals. There are 4 scenarios that may arise. The first scenario is a whole number division resulting in a decimal. The second is a decimal in the dividend, and a whole number in the divisor. The third is a decimal in the divisor, and a whole number is the dividends, and finally, does decimals in both the dividends and the divisor. So don't worry about all of that. I'll go through each of those types of problems. The key is that when we set up these problems and when we solve them, each one of these scenarios requires a slight variation. But there are some primary guidelines. We wanna make sure we maintain the place value. We wanna ensure the divisor is the whole number. We want to add zeros to the remainders to continue to dividing. And we wanna set a quotient decimal values in the that section. Let me just kind of review a couple of these points. So! I saw a question that about the. Worksheets. This is the word sheet for this week. I think it should have been sent out with the. Reminder. This is Celia, and I want to say that the worksheet was sent up when you registered for this session, and the link that I put in there was what Donna Clement share with me. So it there is a chance that it may not be the same worksheets. Oh, yeah, this is the worksheet from last time. Let me let me pull up the worksheet. Thank you. John. From from this time, and then get a link to it. So give me just a second for that, and Q. Queue music, cute elevator music. Let's see. Okay. Okay technology technology. Anyone with the link. Okay, here it comes. Alright! Try that link that I just put in the chat and. Then let me know if it's the correct. If it looks good. If you're able to access it and. Should be marked ninth, 2023. The 3 little problems I just did. And then the points about the division of decimals. This is Celia, I think, is the correct one. Now. Thank you. Yup. Yup, okay, you're welcome my pleasure. So where we are in this is talking about these, the slight variations that are involved in the guidelines that we can like to stick by with this division of decimals, because division of decimals is a little it is probably well, I would say one of the more complex abacus skills and there's some finesse involved in it. So really have to have a good base of knowledge already, and a good understanding of the parts of the advocacy. So maintain in place values, important and ensuring. The divisor is a whole number is important, and this is something that we do in in prince as well. So if we have a problem such as Oh, let me just use one that I'm gonna use here so that it's not too far from so if we have a problem like 36 divided by 2.2 4 in Prince, we move this decimal over to the right? And we do the same thing in the divisor, which is. This number? And we do the same thing in the dividends. So we add some zeros to the ends, and we move that over to the ends. So we get once the decimal points are moved, we get 2, 24. I'm sorry. 3,600, divided by 224, and that's the that's the problem that we work we'll end up doing the same thing on the advocates. And that's just another example of ensuring that the that there's a whole number. I'm sorry the divisor is a whole number. Another thing that we ensure is that when we work, these problems say, I'm just gonna work this one out real quick. I know 224 goes into 361 time. So I get. 6, 4, 1, 46. I bring the 0 down. So I get 16, 6, 24. 1344, so I still have the remainder. Can this still be seen? Yes, barely so. I still have this remainder, which is 6. 1, 1, 6, and in order to keep going I need to add another 0 to the dividends to keep. Bring this 0 down to keep going to keep deviding 2 24 into 1160, and then I'll keep going. We'll see this one on the advocacy later. It's so. That's the third point, adding zeros to the remainders to continue dividing and then setting quotient decimal values in the 1,000 section. We'll see this as we go along. But just to kind of give a. Adjust of it when we've divided in the past, we've set our dividend here on the right. I'm just gonna say, like 110 divided by 10, and I'll set my divisor over on the far on on the left, in the billions section, using correct place value in the billions section, and then we'll set my product in either the 1,000 section or the millions section. It really didn't matter, because I was dealing with whole numbers now, when I'm dealing with decimals, I'm gonna make sure that my decimal values are in my quotient are gonna go in this thousandthousandth place. So my whole number, in my quotient is going to go in the millions, place the deimal value or the decimal for the quotient will be this period. Marker that divides the 1 million section and the 1,000 section and so that's that point of setting the quotient decimal values in the thousands section. And we'll see that more as I do some demonstrations. But I wanted to kinda go into those points in a little bit more depth, so that it was a little bit more clear. Hopefully. Okay. So the first example we have is a 3 divided by 4. And this is an example of a whole number. Division resulting in a decimal. And really, you know, for most students, not a huge challenge, because this is an example of of fractions 3 over 4 typically students have a pretty good understanding that 3 over 4 is so point 7 4 or 75%. 3 fourths, but learning how that works, as far as division is concerned, is is interesting, and also something that the students do in print. So we'll take a look at that. What we'll do is set the 4 in the. So we have 3. Sorry, not the 4, 3 divided by 4, and so what you'll notice is that I've set the 3 to the left of this decimal. The first decimal point. So I have 3.0 0 0. Divide it by 4, and so I make sure that I have these decimal places open so that I can use them in the division process. Because, for does not go into 3, but 4 does go into 30, and how many times 7 times? But what place value am I in? I'm in the tenth place. And so, for my quotient, I wanna use that tenth place in the thousands thousands period. This is just to the right of the decimal in my quotient to set my 7. And I can say 4 times 7 equals 28, and I'll subtract 28. S012-34-5678, and then 20. And so I'm left with 2. 4 will not go into 2, 4 will go into 20. How many times? 5 times, and I'm in the hundredth place now, and so I wanna set my quotients. I wanna set in the hundredth place, and that's a 5, before we go into 25 times. 4 times 5 equals 20. I can clear the 20 from the dividends and clear my divisor, and so I have points 7, 5 for my quotients. The desktop being between the millions placed and the thousands place. I've set my decimal value in the thousands period. Any questions, so far. Okay. I don't see anybody writing anything in chat, so everybody is ready to to keep going. If you have a question, please write it in chat. Okay, thank you. Jill corrected me. I think from something earlier. Thank you, Jeff. I was going really fast. Okay. So the next example is an example of Desimal in the dividend. Whole number in the divisor. In this case we have. We set the problem up. It's 49.3 6, divided by 4. So 4 9.3 6, divided by 4. And do my division. We'll 4 go into 4. Yes, how many times? One time, and I'm in my tens place, and so I'm gonna to the left of my decimal point in the quotients I find the ones, and then the tens place set my one there 4 times. One is 4. I can clear that 4. I have 9. Will 4 going to 9? Yes, how many times once so I'm going to set a one in the ones place 4 times one is 4. Oh, wait! 4, 4 will go into 9, 2 times. Was waiting for Jill to correct me. 4 times. 2 is 8. So clear. The 812-34-5678. And now I have 14 won't go into one, for we'll go into 13 before we go into 13, 3 times 3 times 4 is 12, and I'm now in the tenth place. So I'm gonna go to my tenth place to set the 3. 4 times 3 is 12. I'm gonna just go ahead and clear 12 from the 13 I'm left with 16. Thank goodness, because 4 goes into 16, 4 times I'm in the hundreds. Place, so I can set the 4 there. 4 times 4 is 16. And I'm finished. My answer is 12.3 4 12.3 4 1, 2, 3, 4. Whoever came up with that one was brilliant. It wasn't me. Okay, so that's an example of decimal in the dividend. Whole number in the divisor still haven't really had to do any fancy fancy footwork. Okay. So now we have 36, divided by 2.2 4. And so in a similar way, as students do this in prints, we're gonna do the same thing in on the advocates. So instead of, you know, setting up 36, divided by 2.2 4, we're gonna set up 224 to it. I'm sorry. 3,600 divided by 224. So we'll begin with the first 3 digits here, because 224 won't go into 3 or 6 or 36. So 224 will go into 361 time I'm in the ten's place. And so I'm gonna find my tens place here. And set my one there. And now 224 times one is 224, and I'm gonna subtract that from my 360. So subtract. 4, 1, 2, 3, 4, subtract. 2 oops, 1, 2, and then I'll subtract 2 from hundreds. Okay. Alright. So I'm left with 1, 3, 6, 0. Okay, 1, 3, 6, 0. How many times will 224 go into 1, 3, 6, 0. I think there are 6 groups. So I'm going to and that's in the ones column so I'm gonna set 6. There and then do my multiplication. Or it's. 2 24 times 6 is, I need a calculator. 1,344. So I'm gonna subtract that from 1,360. Okay, s013-44-1234. Right, 40. Subtract 41, 2, 3, 4, subtract 300, and then subtract one. Okay. So now I have a remainder. Everybody keeping up. So because I have a remainder of 16, I want to keep going to get my desk value. And so in order to keep going, I'm gonna need to move this over. So 224 I mean, you know. Another thing. I can do is just put another advocacy over here, I guess if I wanted to. But I have room to do this. So I'm just gonna move the 16 over didn't make it 1,600. I'm just basically adding zeroes to the end of the problem. 2, 24 can't go into 16, can't go into one. 60 goes into 1,607 times. I know that because of magic, and I have it written down right here. And I have 200, and 24 times 7 is 1,568. So let's see, we need to subtract 81234567860. When tens, and then 150015000, and I forgot to set my 7. Something happened. Something happened. I'm in an error. Okay? Is, is everybody awake? That's my first question. One. Yes. Okay. Good one. Yes, all right. Excellent. Thank you, Natalie. Alright. We don't do it because it's easy. We do it because it's hard. I agree, Allison. It is not easy to follow. Yeah, hang on just a second. When you were in the tens place, the one should have gone in the ten's place instead of in the hundreds, shouldn't it? I'm not sure I'm not sure which part you're referring to, cause I got lost myself. Well, let's go back to where we got lost, and see if this helps might not. This is a big example. So we had a 16. Was our remainder right? And in order to continue dividing, we need to add zeros to the remainder. And so we we wanna shift this right to the to the left. And because there's not a like a more space on the what we're not sort of seeing is that. This where this decimal point is. So let me just sort of go back to my and go back to my print copy so we can kinda get a better look at this. So! We had. Yes. Dawn. You need to go back up and fix at the very top. 5 minus 2 is 3. So you should have 1360 right there instead of yeah. That's where I messed up here. Right? Okay. Thank you. And then this is 16. That was my remainder. Right? Thank you. Alright. So this is where we are in the advocates, too. I'll get my finger blue. I don't care. Alright! This is where we are on the advocates. Also, we've done the long division all the way through. We have this remainder? 16. Okay? So we need to add some zeros to make sure that we can still do this problem. We can bring this first 0 down. Make it 0 right? But 2 24 won't go into 160, so we need another 0. 2, 24 will go into 160 times right? So on the advocates, because we don't have this next place value area. There's we can shift it over. We can say we can either use our understanding of the math, or we can. We could shift it here. Well, we can't shift it like. What do we have? We have 1,600. We basically, we don't have enough space on the havoc is to shift everything over. And I think that when. So I guess if we had another we could set this accordingly right, because really what we're looking at is another decimal place here. Is that right? So we could shift it to here. Now the problem with this is that when we do that we need this space right? So, we're gonna have to do kind of a quick shift. Let me get another advocacy and kind of show you what I'm talking about. So glad I get to do this with you all, because when I practice it seems so easy, and then I try to show it to you. It's like, what was that thinking? Alright? And also I just love to get up in front of people and fail that's one of my favorite things to do. So, just. This is this is Cecilia, I think, Emily put a comment in there that it is too abstract for my student. Yes. It is abstract. And, John, may I add a comment that when you firstre first teaching it, it's not a bad idea to have to have to there, just to make sure that they can follow through with it? But what John is showing you is possible with one advocates. But if you feel that to epic, I may help, then try it. Yeah, I think that using a second abacus is really helpful. For long division, because it it allows you to keep the dividends set on a on one abacus. And you can keep going and going and going. So to kind of give you an idea of what that would look like. So let's just say. We have. 3,600, and I have set the decimal points is the place between the once section and 1,000 section. So 3,600 set, and this is my dividends. So what I'm gonna do is I'm just gonna use this larger space to that. We have all this room for my portions, so I can still still start setting my question over here. But I have all this space over here to work with for my for my work, and so then I can just do the same thing I did before, which is to set, and I agree with Cecilia this is seems like it will be easier. Sorry late computer stop working. And so we had. What did we have here? 2, 24 into 3 C. I'm in the tents column of 3,600. So I'm good. Use this tens column here and set a one, and then I'm subtracting 224. To get. I think we had 1, 3, 6. 1360 right, and then 224 into 13 sixties was 6. And that's 1344, 2, 24 times 6 is 1344. And then when I subtract that and I'm left with. 16. I think that's where we were. So! I'm left with 16, but I still have this room over here. I can use 2, 24 it won't go into 16 it won't go into 1, 60. So what that means is that this tenth place is gonna be a 0. It goes into 160 times, and so. Hi! Good! Move over one more space. So I have 1,600, and then my hundredth place, it goes into 1,607 times. I know that's true, and to 24 times 7 is 1,600. So! 7 16.0 7. You get your answer that way. So instead of having to shift and try to figure out which you know what your place value is, you can use the second advocacy as a way to to make it a lot easier. Thank you, Cecilia. Good idea! Yeah, students may get a kick out of using more than one. I agree? Yeah, I've tried to like, share that shifting method in the past, because sometimes people don't have more than one advocates. But it's worth it for stuff like that. Okay, well, that's a lot of our time. Sorry about that. Our next problem, 12.2 5, divided by 3.5. This is an example of desktop and the dividend decimal in the dividend decimal in the divisor. And let's just continue to use to abacus or abicuses. We have 12. I'll just set that there 12 points, 2 5. Divide it by. 3.5. Now for problems with the decimal in the dividend and in the divisor, we need to ensure that this divisor is a whole number. And right now it's not so. We want to shift this decimal to the right to make it 35. And we'll do this same thing in the dividends. We'll shift everything over to the left to make it 122.5. So now we have 102 2.5 to 35. So in this case we begin with the first 3 digits from the left in the dividends, 122. There, let me say how many times will 35 go into 122, or how many groups of 35 are in 122? There are 3. I'm in the one place in 122 and so I'll set my 3 in the ones. Place of my questions. 35 times 3 is 105. 2, 3, 4, 5, and so I think I'm left with. Did I see? 105? I didn't, did I? I did. Yes, I did. Phew! Which said 35 times 3 is 105. So should be left with 1, 7, 5. I am, if you okay, and then I say, how many times will 35 go into 175. There are 5 groups of 35, and 1, 75, so I'll set my 5. I'm in my tenth column here, set my 5 there, 35 times 5 is 175, so I can clear my dividends and my divisor, and my answer is 3.5. That one worked few. Yes. John, this is Celia. There is a comment that it seems like you just have to know the answer in order to use the advocates, and Allison says I haven't used it with my students. Have you all seems way too difficult for most blind and visually impaired students. And then Taylor has a comment, and she says, I think you really have to understand spatial concepts of math, and how numbers relate to each other, and so on. Yeah, absolutely knowing the math. Facts are critical. I'm going through these really quickly. So when we talk about how many groups of certain things are in other things, that's sort of one of the like, how many groups of 35 are in a 122. So, you know, that's something that for a lot of students, you're gonna be thinking about. Well, how many groups of 30 are in 100, and so you're practicing your skills of estimation. And sometimes students miscalculate. So one of the things that I've showed with division last time was how students can miscalculate with division. But then know that well, if they they would have had one more group then it would have worked, and so they'll add one more now also. Yeah, and you can also use a calculator as well. The challenge comes down to the fact that students are still required to do this in print. And so when we're asking students to do certain things in print, then we also need to have analogues for them to do it in either braille or on a device technology device so it's a good question. And I mean I don't I don't have any quality answer to that question, because students do use high tech devices to to access answers the challenge with accessing answers. Is, it does not conceptually, it doesn't provide the math concepts. Yeah, absolutely. This is Cecilia John. May I add a comment to, I think it's it's true that they are other ways to get answers, and and students definitely can use the calculators or ask Syria Google for the answer. But the fact remains what John just said, that they need to show solid understanding of how they get an answer on like the division and the multiplication, and so on. And when they have that solid background it makes it a little easier like, even when they're guessing on the advocates during the calculating of the answer. Sometimes if they make a mistake, that's okay. But learn from the mistake. What did they? What didn't work and let them talk about it to you? That, I think, is the most effective way for some of the students to learn. And in my experience. And, John, please stop me. I'm just offering my comments. No! If you want me to, I can sometimes just keep back the students. Show me what you mean. Show me what you are, not understanding, what is confusing, and let them tell you, and listen to them, and then think about maybe another way to accommodate how they learn it, but what John shows you is pretty much the same method that. All of us use to help them get to the answer, but I do think all your comments are very valid that sometimes is really abstract as really difficult for some of the students to understand. But keep working with them on it. They will get it with more practice. It will come easier. Yeah, I absolutely agree. And I agree with the the common about it being being abstract, being challenging. I mean, this is our our, abacus sessions have gone from. This is the most difficult one, and you know, as you've seen me struggle with it today, you can see that it's not something that just rolls off the rolls off the tongue. And similar to long division for for students and in print, as well. That's not always a an easy concept for any student to understand. Comprehend it always comes down to like, why am I doing this? You know, and the. Yeah, a lot of students who I've worked with using advocates. Some have reached this level, but a lot have not. A lot. We get to sixth grade or seventh grade and start using the calculator before they get to this point. John, do you wanna answer the question that Debbie put on in chat about whether Siri and Google are allowed on the Star math and end of the course test. Right. I don't believe so. No, and in fact, I don't think that calculators are allowed up through, up until. You'll probably know this better than I do. Eighth grade, maybe seventh grade, and I think they might get to use scientific calculators. They're definitely in high school. Yeah, absolutely. I know I had a fourth grader last year that because he used a calculator to do in class to do it. That was one of his accommodations. We also were able to add that to his star accommodations, just a basic for function capture. Or 4 or 5 function talking calculator. Yeah. So it's I know that it's there. And it's your third grade. Okay? Yeah, I think so. And Allison had a comment about she does not have any totally blind students. Currently with using the advocates and so on. So, yeah, in the United States, the advocates is usually used with our students who are blind, but the advocates is really not a blindness type device. I happen to be from Hong Kong, and my father was a schoolteacher. When, when we were little, he would always use the advocates to do all his calculations. So the appetice is a device that is used in Asian countries whether you're blind or not, it's just a device before everybody has a calculator. It's still one of the most used devices outside of the United States. So if you look at it that way is kind of like a univers universal device. But here in the United States we have to use the advocates for students who are blind. But anyway, John, I am looking at the clock and the's already 5. I mean 6 min to 40'clock. So do you want to tell them what's upcoming for the next one or. Okay. I don't think I have another one, but if I do, please come, we'll talk more about the the first computer. The advocates. Thank you, Sistercilia. Thank you, John, and thank you, everybody. Before you go. Let me tell you about 80 resources at that site is a good go site, so make sure you visit us and find out more about what's going on with lessons and resources. And then Tsb. Vi. Outreach techy times. Have a couple of sessions upcoming. Know that the week of March sixteenth and the 20 third we won't have a session, and I hope to see some of you at the Texas. Ae, our conference in Denton, and then on the thirtieth there will be a session on document accessibility, and then we'll skip one week and April and on the thirteenth is accessible stamp with great Chris carrel and then teaching vo I have no idea what vo stands for, and then document, accessibility. Again at assessment, for tbis will be in May. Document, accessibility with math, and then we will finish up with technology for students, with multiple employments and visual impairments as well. So the tech team will welcome your topics for discussion.