TRANSCRIPT-How to Abacus - Advanced

>>Donna: Let's see, yeah, this is a reminder that we are here as a goal to build community practice for technology. And to support each other when we are teaching technology to our students in the spirit of this goal. This is an interactive session. So please, J. Jill says we're always in more need of John

>>John: Thank you. Jill.

>>Donna: And so in the, in the spirit of that goal that T-time is interactive and you're encouraged to talk and participate, whether that's through chat or through the handy dandy microphone. Just be advised at the session is recorded and posted on our website for later viewing, and that by registering you give us permission to use your image or audio of you during this session. Alright, now that all that is done, I am going to stop sharing and turn over to John. So he can show us some of that advanced abacus

>>John: Hey? Y'all Happy New Year. I'm gonna show you advanced tabs today and and you're all gonna learn it. And there won't be any questions right? Well, I think what we'll what we'll do is go over multiplication and division on the abacus, and and then look at fractions and corrections and decimals. I I have to be honest, I I don't remember how far we got last time, so does anybody remember how far we got last time? It's. This is how I teach most of my classes as students come in, and I say, what do we do? Yesterday. It's a really great tool, for we're I hear. I see Susan talking, but you're muted

>>Susan: We hadn't done any multiplication or division yet.

>>John: Okay, great. Thank you. That is so helpful. I thought that was the case, but I didn't want to jump into it. And then you know, you're like, Hey, we we already did this, which my students say to me a lot of times. Also, I'm like, I know we did. We need to do it some more, but that's not the case for you all. You'll just needs to do it once, and then you've learned it right. That's that's that's how I am. Just kidding. This is the book or work from the counting method for the Kramer advocates. It's available on the Tsvbi website. It's a book that I can claim to have worked on. But really Deborah Sul was the is, the was the person who started this, and because it was a back burner project, it needed somebody to to help move it along, and I work with a lot of TV eyes around the State, and I was working with a lot of the their elementary students Who would come for short term programs. And I was teaching them addition and subtraction and some multiplication. And I was saying, Deborah, we need to publish this book. We need to publish this book. These teachers need this resource. And I was basically sending copies like Wha wha what we used to be called Xeroxes. But I was just like scanning stuff in and sending it to the and anyway. So I I just finished it for her in all my free time. And today we're gonna look at the multiplication section and the print is gonna look kind of small on here. I'm gonna read this stuff, anyway. But what I want to show if you haven't seen it before. Is that the way that we did it was to show each of the steps on the left hand side, along with the picture of the abacus on the right hand side, to demonstrate how each of these problems is worked out. So I did the goal of the tool or of the resource is to give you a script and and an image of you know, with what it's supposed to look like the digital fil also has these images text described, or image descriptions. For the images. As well. So they're hopefully as accessible as possible. Alright. Yeah.

>>Donna: Sorry John, to interrupt. If if you're having trouble viewing John's screen, and if if you turn it to Speaker View, you should be able to see it nice and clearly. So just letting you know those of you that have a little tiny thumbnail hit that speaker view, and you should be able to see him very clearly.

>>John: Cool. Thank you. So at the beginning of the section it it gives the steps for for how we're going to for How we're going to do this. One of the things about multiplication is that as we talked about is we've talked about in previous sessions. The separation bar has period markers and place value indicators. So the period markers are the up and down kind of hashes or line raised line, and the place value markers are raised. Dots, and the important, the the primarily, primarily, or the, I guess, most important thing to know about this, when you shift into multiplication is that these periods are used for their place values. So in each period you have ones, tens, hundreds, one's tens hundreds in the thousands period once tens hundreds, and the millions period and one's tens hundreds in the billions period. And that's the abacus, the basic concepts that are required for understanding how to set problems for multiplication. So what we can do is set the multiplican the first number to be multiplied by in the billions section in the correct place value column. So in this case I'm gonna set a 22 in the billions section. So 2 in the ones column, and the 2 in the tens column, and then I'll set the multiplier. That's the number doing the multiplying and the millions section. So I'm just gonna move from my 1 billion section over to my 1 million section and set the 2 in that section. And so the product. Your answer is going to be set over on the right in the correct place. Value column. What this allows the student to do is use the same place. Value method for multiplication that students use in on using paper and pencil. So, for example, in this case, the students, you start the problem with the smallest number in the multiplier in the multiple cans. And you say 2 times 2 is 4. That's in the ones column. So I set my 4. I'm finished with this 2 and 22, so I can clear it. So I'm left with 2 and the tens column, or 20 and 2 times 2 in the tense column is 4 in the tense column or 40, so I can finish with the 2 in the tense column. I'm finished with my multiplier so I'm left with my answer. 44, and that's the that's the basic method. And so what I'll do is I'll demonstrate another problem with with a one digit multiplier and then give you all a practice problem, and then I'll go into 2 digital multiplier, which is just a little more complicated So the next problem I'll show is, let me do this one Let me do. Yeah, let me do this. 1, 243. So I set that in the billions. Section 2, 4, 2, and the hundreds 4, and the tens 3, and the ones the 1 billion section times 5. I set that in the 1 million section. So I have 243 times 5. And now I have a 5 times 3, and the ones section is 15 and so, and go over to the ones section. And I can set the 5 in the ones place, and I'm one in the tens place of 15. The key is to remember what place for you you're starting in for the 2 digit products. So I'm finished with the 3, and now I have a 5 times 4 in the tens column, or 5 times 40. So since that's in the tens column. I'm going to come over here to the tens column. I know 5 times 4 is 20. So that's a 0 Anna 2. So 0 and the 10 are in the what if it's 5 times 4? It's 0 in the tenth column and a 2 in the I'm sorry 0 in the ones column, the 2 in the tense column, but we have to remember that this is 40. So we're saying 5 times 40. And so students are use a lot of students use a the tool of saying 5 times 4 with a 0 on the end. So 5 times 4 is 20 with a 0 on the end. So you can use the 5 times 40, which would be 200, or you can say 5 times 4 in the tens column. So 20, starting from the tense column, so that would be a 2 in the hundreds, place and a 0 in the tens column. Intense place. I've found both of those strategies for describing that process to work equally well with different students it just kind of depends on the student and how they are understanding how the they're kind of numeric understanding or understanding of numerous scene. So I've finished with this, for in the tens column, and I'm re my! I'm left with a 5 times 2 in the hundreds. Call, and 2 times 5 is 10. I start at the Hundreds Column and set a 0 and a one the other way to think about that as a similar to what I mentioned before is 5 times 200, and that's 2 times 5, which is 10 with a zeros or 1,000, which is the same as what I've set here 1,000 something finished with my multiplier and my multiple cans, and I'm left with my answer. 1,215, and that is correct. Initial strategies for multiplication for students include well one of the prerequisites really is knowing multiplication facts. But that's not always the case for students. So for students who's struggle with multiplication facts, I will encourage them to have a multiplication chart alongside them so that they can ensure that they're getting the correct answer to the to one digit by one digit Facts. Okay, any questions before I give you all a problem to solve on your own Do we have any prizes, Donna

>>Donna: This week. Unfortunately, we have no prizes

>>John: Okay, if you get this correct, you get to come. Say Hi to me. The next time you come visit Tsp. Vi. Alright, it's a 135 times 3 135 times 3, and I'll go ahead and set that just so that you get a reminder about how it sets on the advocacy Also going to work. It's using my whiteboard Just to kind of show one of the things I like to show This light does not help with my whiteboard Do we have an answer? Oh, we do, Angela! I just saw it, Susan. Good. Nice. Okay, all right. Everybody got it. If that's correct, or 405, 405 For 405. Alright any questions or concerns So let me what I wanna do is go through this real quickly. So when a student multiplies pencil paper, using the and a standard algorithm, and what I learned in school was, you know, you look at your multiplier and you just multiply it by each one of these digits in the in the multiple cans so you have 3 times 5 is 15 so I write the 5 and I carry the one up here above the 3, and then I say 3 times 3 is 9, plus one is 10. So I'm gonna write the 0 and then carry the one again. And then I say one times 3 is 3, plus one is 4. So here 400 and and 5 for my for my answer, and then you start getting into the constructivist math, where you know you're looking at breaking it into parts right? So you have 5 times the 3, which is 15 plus 30 times 3, which is 90 plus 100 times 3, which is 300, and this latter method is the is basically what's happening on the on the abacus. So you have your number set here, and then you have your 5 times the 3, which is the 15, and then you have your I'll go ahead and clear that 5 cause that's what we're supposed to do, and then you have the 30 times the 3, which is 90, so I'm gonna add 90 to this so I'm gonna come over to my tens column and say, 5, 6, 7, 8. I have to do a 9, 10 exchange. Set the one in clear. The 9, and that's 10. So I'm I'm finished with the 30, so I can clear that a lot of times at this point I'll say to students, what's your partial products? What is your an impartial product means whoops Oh! Whew! My screen went off a partial product just means, what do I have so far? What's my product so far? And my products right now as 105. So now I am left with 100 times 3, which is 300, so I can add 300 to my product. 100-20-0300and I can clear my multiplier multiply, and then I'm left with 405 And any questions So it's basically the same as this where I I have the 15 added to an added the 90, and then added the 300 to get my answer Alright, cool, math.

>>Donna: Brittany. Was that a typo on your answer? In the chat. I wanted to make sure, because we wanna know if if there's a an error and have John show that and make sure you've gotten it

>>John: I didn't want to give pretty a hard time, because, as my

>>Donna: I'm not giving Brittany, or I'm being very supportive.

>>John: Okay, that's I had it. Thank you. Thank you. Thank you.

>>Donna: Yay, okay, that's what we wanted to. That's what we wanted to know.

>>John: Donna. I was out worried to call Brittany out because she has my email address. And I just I just I just got finished working with her and one of her students. So.

>>Donna: No, we are absolutely on the 100% supportive side. And wanna just make sure we know where we make our mistakes.

>>John: Okay. Alright. Good deal, and I will be. I will say that that's seeing Brittany type, that in there is one of the reasons why I went ahead and worked it out as thoroughly as I did, because I I also wanna see everybody succeed here. So again, and if you do have any questions about any of this stuff, feel free to email me about abacus questions, I'm I'm happy. I might not immediately reply, but I do, will reply

>>Susan: What did you call the math strategy, where you broke that down into the 3 separate equations and added them together

>>John: Well, okay. So Hi, I I called. I called this constructivist.

>>Donna: Construction, constructs

>>John: I don't know if constructivists would agree with that. Constructiveism is a a method of math. Let me pull out my little, no cheat, cheat, sheet here. It's something that is that some some math programs use. That is it it it involves like breaking things. Down like a lot of the like, you know. They they, those those those jokes about new math and like how things are like broken into. PC, and you know, using like area models for addition and supportion. And those types of things. A lot of that is used in constructivist models. Math models, I think, is also part of part of it. I I have an article. If you're interested. But basically, that it, it's it's it's. It's also full, like a full philosophical model of learning, being like being active, that knowledge is constructed that it's a social activity. That there's context involved. They they personalize activities for students. So it's more than just the math part of it. So I don't. I call it that because it I don't. I don't know because I didn't know a better way. A better word to use for it. To be honest with you.

>>Donna: It's a good word and hard to to to say, but you know I it makes more sense to what is going on in the classroom now, when you see it as an outsider who hasn't had that type of instruction of what it looks like in the classroom.

>>John: I did not get this, or if I did, I don't remember this type of thing from when I was in school. So this is, I can post this in the chat about

>>Susan: So a couple of people in the chat suggested expanded form

>>John: Yes. Okay, so right? So yeah, so that's expanded form, correct. Okay, yeah, that's right. That's a that's a good. I see reading here? Yeah. So I didn't have the chat up. So I appreciate that. Now I do. Yeah. And honestly, if you're not a big fan, I don't necessarily blame you. I expanded form. That's the word. I should have used. It's more appropriate, I think, for this, mathematically speaking. So, yeah, good good question and good answer. Thank you. Alright!

>>Donna: Yeah, I think Kathy's right there. That regrouping is tough for some of our kiddos, and so having the alternate way to show is nice

>>John: Yeah. What's the what's the alternate way that I showed?

>>Donna: The expanded form versus the the way we learned it, which you know.

>>John: Oh, oh, right right right! As opposed to the sorry I'm just a little out of swords as opposed to using the that that algorithm the the standard algorithm.

>>Donna: Column after column.

>>John: Yeah, I agree, breaking it down, I think, is really helpful. Also, though I will say I've worked with some students this year who for whom the expanded form was challenging because of the amount of braille they had to write in in doing it. So it was like. And and a lot of times in math classes. They make you write it out, and words, too, which just adds to the amounts. And some some students are more averse to writing. Braille and others I've learned so somebody I would love for somebody to do a presentation on strategies for that, and maybe you've had one, and I missed it So the next one we're gonna look at is I'm gonna get back into my comfort zone of just the abacus and and is 62 times 17. Now this is 2 digits by 2 digits, so it makes it a little bit more complicated. We have, but we still look at it in basically the same way we're gonna start with the 7 in the ones column in the multiplier. Multiply that times the 2 in the one column of the multiple cans. And so you have 7 times 2, which is 14 so you're in the ones column. So we're gonna go over here and set 14 And here's the thing about 2 to 2 digit by 2 digit. I'm not finished with the 2. I still have to multiply that times. The one in the ten's column of the Multiplier, so I don't clear that yet. I'm left with a 6 or 60 times 7, 6 times 7 is 42, so I can. Either. I can go to the tense column, and I can set a 42, or I can say, 6 times 7 is 42, but it's there's that 0 on the end. So it's 420, because it's 60 times 7. So I come over here, and I set 420. So now I am finished now with the 7 in the multiplier, so I can clear that 7. Currently my partial product is 434. Now I have 10 in the as a multiplier, and so I have 10 times 2, and the multiple can 10 times 2 is 20. So I come over here. Say, okay, 20. So I add 20 to the 2 to the tenth column. 1, 4, 5, exchange, mix 2, and now I am finished with that, too, so I can clear that, too. I have 10 times 6 or 60 to 10 times 6 in the tens column, or 10 times 60. One times 6 is 6 of 2 zeros, and I'm dealing with. So that's 600 or 10 times 60. Yeah, one times 6, with 2 zeros or 10 times 6 in the tens. Call, then come over to the tens column, set up 60. Well, can't quite finish that. So I have. I can set a 5 in hundreds column but in order to set one more I need to set a one in the thousands and clear the 9 in the hundreds. So I think I'm finished. I think I just set 600. So, I'm gonna clear the one, the 2, 1, 10, and the multiplier and clear the multiple cans. And I think I should have 1,054, is my answer. That's correct. Okay, I'm gonna do one more, 2 digit multiplier With an eye on time. So I have 91 times 86 whoops. So everybody see what I did wrong there. Does anybody want to correct my mistake? I set this 86 in the wrong place. Value for the wrong period and the wrong place value, so it should go in the millions. Place, and the tens, and the once So have a start with the ones in the multiplier, and the ones in the multiple cans. 6 times one is 6. Set that one time 6 to 6, and then 6 times 90 6 times 9 is what 54. I need. My multiplication chart Yes, 54. So, but it's 90. So that's 540, or go to the tins instead of 54 So now finished with the 6. I have a 8 or 88 in the ten's column, or 80 left in the multiplier 80 times. One is 80. That's helpful, because it's easy. So I need to set an 80 over here. I can set a 5 in the tense column. So that's 50. Set. One more. I said. A 100 and clear the 90. So that's 60, 70, 80, add 2 more So now I am finished with my one move on to my 9 or 99, and that since calling or 90, so I have 8 times or 80 times 98 times 9 is 72, and then I have these 2 zeros. So it's 7,000, 207,200, so I can set a 2 in the hundreds. Place, 5, 6, 7 in the thousands. Place, finish with my multiplier and multiple cans. So 7,826! I got it. Oh, okay, good. I was worried. So that's the 2 digit by 2 digit multiplication questions. Or do you feel like this is on a scale of one to 5 with 5 being really hard and one being really easy, where would you? Where would you put this 2 digit by 2 digit multiplication

>>Kathy: After I watched you put your fingers where the Zeros are. It. It really made it clear to me. Then, when you went over, then to answer and put your fingers for the 2 Zeros then said, like, set to 72.

>>John: Okay.

>>Kathy: So that made it like it's so much easier now. Thank you.

>>John: Oh, okay, good. Yeah, you're welcome. So Oh, okay? Good question, Brittany. I typically do have students count through the exchanges. So I'm not doing it now, because we are in advanced this is the quote, unquote advance section. And so I'm I'm I'm moving a little bit more quickly. Alright, so so typically, I I think what I think, Brittany, what you mean is, you know, why am I just setting the 5? And then, you know, moving more quickly through the exchanges, and that is, that's the reason why I'm doing that. Because I. But typically if I were working with the students I would want them to be I would want to know that they're comfortable doing that before I let them do that. If students express that, they're like they don't. Wanna they don't wanna count one at a time to go through the exchanges, and that they they know how to do it. I say, Okay, that's fine. Go for it. Give it a shot. But if if they make an error, then I'll say, Okay, that's my deal with them. You can do it. But if you make an error, you have to go back and count them. Count through, you know, one at a time, and I think that that's you know it's a it's a good practice, because you know it gives students a little bit of motivation to to challenge themselves to see if they can do it. But then also reinforce the skills of of counting and and practicing the exchanges when they, when they kind of. So that's a good question. And, Penny, I I I totally understand how you feel that it looks easy when I do it, but on your own it's it's more difficult. I I was I I've been in that. I've been in your shoes, so I totally empathize, and I think it's something that takes time. Laura asks about the name of the book. This is called counting method for the Kramer Abbeus, and I think, Donna, if can we put a link to that again in the okay cool?

>>Donna: I can, and I will.

>>John: Thanks. Yeah. It was like, Deborah started it and as soon as I started using it I was using that nonstop in my classes, and I just was like we have to keep. We have to do this. Okay? So I'm gonna let's I'll give you all a 2 digit by 2 digit. Problem, and then I'll let you start working it, and then I'll start working it After a minute or so. So, if any, if any of you all get kind of stuck, then you can. You can kind of watch what I'm doing us

>>Donna: And these real. These are recorded and posted on on my website. So if you want to go back and look at a problem we've done today again, you're welcome to go and pull it from the site and watch it over again. Or if you need recommendations to other videos, we can definitely help you out there

>>John: Nice Okay. So we'll do 23 times 34, 23 times 34, and I'll give you a minute to work on it, and then I will Let's start it. Thank you, Donna. I needed that to So I've worked the first step, and that's the 4 and the multiplier times. The 3 and the multiple cans, which is 12 And so the next step will be to multiply the 4 times the 20. And that's 80 So. I'm gonna go. I'm gonna set that directly. 5, 6, 7, 8, So I have the partial product. 92. And I'm finished with the 4 In the multiplier The 30 times 3

15:42:55
That's 90 Can't set 90 So I have to set a one in hundreds. Column. Clear the 9 And that's 1, 2, 3, 4, 5, or 5. Exchange. Make 6, 7, 8, 9, So I'm finished with that 3. And then the multiple cans. And I have a partial products of 182 So now I'm left with this 30 times 20 So it's 2 times 3 is 6 with the 2 zeros, 6 0 0 620 times 30 is 600. So I go over here to my Hundreds column, and I can set the 6. I can just set the 6 directly, or I can count count on 1, 2, 3, 4, 5, 6, And the answer is, 782 And how'd you do I see one thumb up. That's good. I see 2 thumbs up I see. 30, my gosh! All the thumbs, sweet, alright good to see! So there are more problems we can do. But I wanna get I wanna demonstrate a little bit of division to you all while I have you here, and we have a few more minutes. So you know one of the things that I talked about with addition and subtraction was using similar, like using the same problems and just going back and forth doing the addition problem. And then subtracting the same thing to just to get the practice of of addition and subtraction together. And you can do the same thing with multipleocation and division that you know. That's once the student gets to that point. So The reason for that. And I want to use one of the earlier problems that we that we did So you'll remember 22 times 2. And then our answer was, 44, right Well, that one doesn't work as well. But it's okay. So. Reason for that is more complex than I thought. I thought I could just go dive right into it, but but I but I can't, so, not as great as I thought I was. Let me just show you the the the basics, and then we'll get into the more complicated stuff with division. It. It's you're basically saying, like, you have your products So we have say we have So this is our multiplication problem, our multiplication problem would be 3 times 3 equals right? And then we'd be looking for the 9. Our division problem is what what goes here 3 times blank or question mark equals 9. So with division on the abacus, you're basically setting it. It's. It's your business, you know the products already. So you put your 9 there, and it's divided by 3 which you set in the in the billions section, and then you have a a a lot of space. I mean we in in the, in the book, we say, to set the the the quotients so right now you have 9 divided by 3 over here on the left, so in the book we say, to set the question in the ones in the 1 million. Section. Well, that's where you would say, put your multiplier 3 times 3 is not 9. Divided by 3 is 3. So you're basically just filling in it with division. You're filling in that blank on the abacus, and it corresponds with your With your sort of standard algorithm you're looking for this number that you know, we have this 3 divided 9, divided by 3, with the division bar, we're basically looking for this number right here for this times. This. Equals that looks kind of silly to me, but I I think that that on the abbe is this is what makes sense, because these are the numbers we're looking at 3 times 3 is equals 9. But this is, it's the middle number we don't know at at this point

>>Donna: Which honestly helps with algebraic thinking.

>>John: Exactly. Exactly. I I absolutely agree. And one of the reasons why I prefer this. This Method and strategy is because it it sets up the the problem in a way that to me is is intuitive. And so you, you say, okay, well, what about problems with with remainders? So that would be a problem sort of like like this one where you have 9, divided by 2. So I have a 9 set in the ones column on the far right, and I have a 2 set in the ones calm, and the billions place, and so what I'm gonna ask myself is my say, well, how many times does to go into 90, well, 2 goes into 8 4 times so but it goes into 15 times. So it's 4 goes into 9, 4 times so I'm gonna say, 2 times 4 equals 8 and I'm gonna subtract that a 8 from the 912-34-5678I'm left with one and so my answer is for with a remainder of one for Remainder, one No, I I didn't really do the the 3, the 9 divided by 3, because I just assume that that was that that made sense. But what a student would say is, okay. Up 9 over here, divided by 3. 3 goes up to 9, 3 times so I'm gonna set a 3 and then one millions place. I'm gonna say 3 times 3 is 9. I can clear my 9. Nothing left. That's my answer. It's 3. That's my quotient So with those problems. Those are mental math problems. But it just shows you the how it's done. So what I'm gonna look at now is 480, divided by 8. So 480 set on the far right in the once period or hundreds period and then I have an 8 set in the billions period. So I say, okay, as a student, I say, I have 8. Well, 8. Go into 4. No. Well, okay. So I go over to the right. I say? Well, 8. Go into 48. Well, yes, it will. How many times what that's saying, what times 8 equals? 48? The answer 6, 6 times 8, is 48. What place? Value is that aid in that 8 is in the tens column. So I'm gonna set my 6 in the tens column of the millions place And then I say 8 times 6 is 48. But there's 0 here right over here on the right. So what I'm really saying is, 8 times 60 is 480, and that's my 480 that I'm looking at over here. If I say 8 times 6 is 48 in the tense column, I can just come over here to the tens column and say, Okay, there's 8 and clear my 8 and my 4 clear my 40 eights don't have anything left so I'm finished 480 divided by 8 equals 60. My quotient set in my in my millions column. If I wanna check my word, I can do that. I can have my Dividends over here cleared, and I can say, Well, 0 times 8 is 0. Okay, 6 in the tens. Column times 8 is 48, 486 times 8 is 40. Yeah, 8 times 6 is 48, 8 times 60 is 4,080. And so I really just wanted to before we resign for the day. Demonstrate how the 2 are are linked in on the advocacy and multiplication your You have 3 times 3, for example, and you're looking for this number, and then division. You have this number and this number, and you're looking for this number. And that's precisely how it looks on the abacus Well, not precisely. But you, I think you understand what I mean. So I know there's not a lot of time for questions about division, and I didn't really get that deep into it. So I'd be happy to come back and talk more about division and fractions and decimals.

>>Donna: Absolutely.

>>John: Later, this semester. If you all have me, I'm happy to get into that, and the more d in more detail

>>Donna: Absolutely. In fact, we're gonna talk about that right now. We have some open and open sessions coming up soon.

>>John: Alright, cool, well, I'm happy to do it, and I wanna I wanna say that I appreciate you. So let me share my screen.

>>John: All's patience with me as far as my my mathematics. Knowledge is, concerns, I'm a relatively new math. Teacher per se. I've been a Tvi teaching math for a long time, but I've really only, and but I was like a I was a you know, English and social studies, liberal arts person before I was a TV, I so math is new to me. Also, you know, except for teaching the the abacus and those skills. So when we start getting into those questions about terminology and things like that, I I just wanna let you all know that I'm I'm still learning some of that stuff. So I learned from y'all as well, so I appreciate I appreciate you all's advice and stuff like that. Thank you.

>>Donna: Kathy says you did a wonderful job, and I totally agree, and Penny says your math knowledge has always been great. Hey? Great job from her, and we're all in the same boat together.

>>John: Okay, thank you. I I appreciate it. I was a fishing for compliments, but I appreciate I appreciate them. So we appreciate your time. And let's We could all use some compliments now and again. Alright! So if you go to my site, I did link it in the chat. This recording, and any handouts will be linked. What I wanted to share with you My share doesn't want to be cooperative today. Let's go here. Is that if you're on my site and you see that some t times have disappeared. Well, it was getting client of Chunky. So up here at the top we have an at live binder link that is in progress Can everybody now see a live binder And in that live binder you will find the link to all of the tea. Times passed and their handouts. So you were able to find those any of the device help sheets that we've posted, or that I've created as well as any software help Now last thing before we go Is that coming up we have jaws, basics, so keep those littles in mind. These are going to be beginning jaws, lessons, little one style. February we have Star and the Braille display. Step by step, setup February ninth, is to be determined. February sixteenth Aph. Is new and upcoming. They had to reschedule from last month. So they're gonna come and fill us in on new and upcoming things from Aph the 26. There will be no t-time join us at the deaf, blind symposium, so we'll be there instead of here. Early March is to be determined. We're still trying to figure out when everyone has spring breaks and things like that. March sixteenth. I will be on spring Break, so we will not have one there, and march 20. Third, join us at T. Aer in Denton. So March is looking a little thin. Is John still here. I'll have to send him those those dates. We may see if we can get John back to do the decimals and other items. Alright. So, please, we need suggestions. Click on this form Or we would put it in the chat to give us your suggestions on what upcoming t-times you'd like to have our closing code 0 1, 1, 9, 2, 3, That is 0 1, 1, 9, 2, 3, Alright! Everyone have a great day. There was no opening code, Robin, just closing codes down. They were getting confusing. In the chat. I've put the suggestion link. So, if you have any ideas of what you want to see into end future T. Times. Please, please, please, please. I check it regularly. Put your suggestions in there. Everyone have a wonderful rest of your week and weekend. And we'll see you next week