TRANSCRIPT-How to Abacus Š Intermediate >>Donna: All right, Good afternoon, everyone. This is Thursday afternoon tech tea time, and I am so excited again to have John Rose here as our co-host. And going over intermediate this session so excited for this session. So let's go over our usual total calls and then we will get started. So as of last week, there is no more beginning code. we will wait to the end, because so make sure you're at the end to get your code. Our goal, as has been from beginning in October. It seems like a long time ago, is to build a community of practice for technology and support each other. When we are teaching technology to our students in the spirit of that goal. This is an interactive session. You can either speak up and ask your questions or put them in the chat. These sessions will be recorded and posted on our website, and by signing up as a participant, you have granted us permission to use the contents of that recording, recording, including your image and audio and so i'm going to hand this share over to John Rose, who's gonna look us in intermediate. because oh, we have a sign. I love it, John. >>John: Thank you again for coming for this session. I yeah. I created a sign using low tech low tech very all about the low tech my phone's not working right now. So i'm i'm just decide i'm thinking maybe I just go back to stone tablets or clay envelopes, or something like that, where I send my messages that way. >>Donna: It's that perfect example of when high tech lets us down we have to have that low tech that's right. >>John: Well welcome everybody. I. Last time we talked about beginning advocates, we talked about prerequisite skills that students require for for for abacus. And we also started, talked about the parts of the advocates. We talked about operations with no exchanges and we also talked about the exchanges as well with addition and subtraction. I'm going to review some of a few of those from first, because I think we wanna get some problems in under our belts. So we're gonna jump right into solving problems using the abacus and the if there are any questions along the way, i'll pause after each problem, and we can go over any questions at that point and honestly if there are any questions in the middle, I can handle that to So let me figure out how I did this. In the first place. Yeah, but and ready to have a kiss Alright. So our first problem we're gonna work on see So the left a little mark there. That's why I brought this other a little cleaner clean x tissue low tech alright, see I tech low tech I don't know. i'm having fun Okay, So our first problem is a problem with no exchanges but we're gonna start with some larger digits and it's 220 plus 214 and what i'm gonna do is i'm gonna work. These problems. on the whiteboard to just show how we work them using place value, and then show them on the abacus to show how they align with how students are doing them on with pencil paper. So we have our one's column or tens column Hundreds call them from right to left, and just gotta sort of do that for anybody who can see it. And I wrote one tens and hundreds over the those columns above the problem 0 plus 4, and the ones column is 4, 2, plus one in the tens column. Or another way to say that for students is 20 plus 10 in the tense column is 3 in the tense column or 30 and then 2, plus 2, and the hundreds column or 200 plus 200, is 4 in the hundreds column or 400 students will talk the both of those are are correct ways of stay up stating that and so let me shift now to using the advocates and i'm just going to push this up it's gonna disappear for a second, and i'm using the large size Kramer advocates. So it's a little bit easier to see and what i'll do is i'll set 2 in the hundreds column a 2 in the tins column, and we have a 0 set in the ones column, and then i'm adding 214 i'm gonna work from right to left once tens to hundreds the same way I worked on the using pencil paper or in this case the whiteboard. So i'm gonna add 4 to the ones column 0 plus 4 is 1, 2, 3, 4, or I will tell students if they can do it just they can just set the 4 And then in the tense column 2 plus one I have 2 sets. I'm gonna add one more, so that I have 3 and then in the hundreds column. I have a 2 sets and then i'm gonna add 2 more students can count on, or they can just they know that they're 2 left to ones left to set, so they can set 2 ones and then get the read. their answer to get 434 and so that's an addition problem with no exchanges, and then a lot of times. What I will do is take that 434 and subtract that 214, so we'll say 434 minus 214, and I know 4 minus 4 in the one's column is 0, 3 minus one. in the tense column, or 30 minus 10 is 2. In the tens column are 20, and then 4, minus 2 in the hundreds. Column, or 400, minus 200 is 200, and and then, with that I should have the same number. I started with 220, and I do yay and So now we'll do that one on the abacus. I have 434 sets that's what I ended up with after the addition problem. and so I will start with that. And then subtract 214 some subtracting a 4 in the ones column. I know there are 4 set in the ones column, so I can either count them one at a time. 1, 2, 3, 4, or the student, knowing they're for there can just subtract the 4. I give the students I work with autonomy to or to do that as long as they until they make an error and at the point they make an error. Then I ask them to to count count by ones to See where they made an error then i'm subtracting one in the tens column. So I have 3, set, i'm subtracting one and then over in the hundreds column I have 4 set subtracting 2, 1, 2. So I get 220, and that is the correct answer. That's what the number that I started with so I give students an opportunity to practice both addition and subtraction. And I will often have students work on a Perkins Braille writer to Braille. These write these out as they're doing them on the abacus, any questions about the no problems with no exchanges. >>Donna: We'll move on to working on some with exchanges. That was a wonderful review. >>John: Thank you so much. We have no questions at this point in the in the chat, and i'm just so excited to get on to those extremes. Little bit little bit of an advocate Chunky myself, great Alright, no nerves. Here we go. We can do it. so I want to talk a little bit about the 4, 5, and exchange. So i'm writing out on my board 4 5 exchange and i'm just gonna spill it's exch for the sake of time. And did I say Ex. I just wrote x xch for the sake of time and i'm gonna use a large numbers again. 3 digit numbers again, and if we need to we can always go go back. 2 smaller digits. I have 324, plus 453. Now this is the one where this is where we have a difference between what we do in prints and what we do on the abacus So in prints the we had 4, plus 3 to get 7. We had 5 plus 2, to get i'm sorry 2 plus 5 to get 7, and then we get 3 plus 4 to get 7. We get that 7 7 so all seven's lucky number lucky winner. That's right all right on the abacus however, this is where we have to make an exchange, because we don't have 10 beads in each row. Something that we talked about last time we have those these 5 beads up here. So we have 324 sets on the abacus in the hundreds tens and ones columns. And we're gonna start in the ones column we have that 4 set. We're adding 3 to add one more we have to make that 4, 5 exchange. Let me actually get a little bit closer Here. Alright. So yeah, to add on my camera doesn't fall to add one more. We have to make that 4, 5 exchange. So we set the 5 clear. The 4, and count one and we're adding 3 2, 3. So I had to show that one more time I had for adding 3. Set the 5 clear, the 4 to get 1, 2 3 then I have a 2 in the tense column. I'm adding 5 to that. Now we can account that on by saying, 1, 2, 4, or 5 exchange to get 3, 4, 5, and we have 7. Now another thing that if students feel comfortable doing if they're if they're adding 5, and there is not a 5 set, they can always just set a 5. Some students I found her just not comfortable with that they want to count on That's fine. Some students really want to, you know, save that time, you know, feels more advanced. Some students could care less. They just wanna count on, and they like it. So yeah, I give them that freedom. alright. so then we have 3 in the hundreds column, and we're adding 4 hundreds. So 1, 4, or 5 exchange makes 2, 3, and 4. So we get 777 now same routine. i'm gonna subtract the 7 7 7 from that. >>Donna: I'm going to subtract the 4 53 John I'm sorry. >>John: Bother if you slide down Yep. Thank you. Sorry. I forget. I forgot that I had I change my setup a little bit, but forgot that I had moved my camera down alright. So in the ones column I have 7 minus 3 i'll get 4. The tense column, 7 minus 5 to get 2 and in the hundreds column, 7 minus 4 to get 3, and so I should end up with 324 that number that we began with. So let's see that on the abacus so we have 777 sets from our last problem. And we're gonna subtract 453 we'll start in the one's column and subtract 3 one just counting down 1, 2 and then this is the 4 5 exchange for subtraction. So in this case I clear the 5 and set the 4 to get 3 Move into the tense column. I have a 7 set i'm subtracting 5 I can count it off. 1, 2, and then the 4, 5, exchange for subtraction, 3, 4, 5. So i'm left with 2 or as same as in addition if i'm subtracting 5, and I have a 5 set. I can just clear that 5, and then in the hundreds column we're, subtracting 4, and so I can subtract 1, 2, 4, 5 exchange for subtraction. So I clear the 5 set the 4 that makes 3 and then one more makes 4 left with 324. That's that number that we started with and so this is an activity that I like to do with students where we go back and forth between addition and subtraction. practice practicing the exchanges both ways and it gives them that opportunity once they're you know once they're at that stage where they can. Perform the exchanges with a little bit more rhythm. >>Donna: So let's move on to the ninth in exchange any questions about the 4 5 before I move on none so far in the chat >>John: Have to take the my this is tea time so i'll just have to take my tea back out right now. So just let me know and then you'll know i'm on the same page. Alright. So next problem is We have 600 whoops, 642, plus 100 costs very well 6,842, plus 162 Now this is a excuse. me this is one where we're gonna see Some similar, some more similarity between print and the abacus And so in this case in the one's column we have 2 plus 2. There's no exchanges there but that's but in the tins column. We have 4 plus 6 and 4, plus 6 is is 10 and so i'm gonna write a 0, and then I have to kerry the one over to the hundreds column is that yes, And when when I do that I do that in print for the same reason that I do it on the Ab. Because I can't write 10 in the 100 I mean in the tense call. I can only write a 0 through 9, so i'm taking that one from the tense column, adding it to the hundreds call, and I have 6, one plus 6, plus one, which is 8, 6 plus 2 some left with 804, and and I can transition to the abacus and we'll look at the 910 exchange. So i'm gonna set 6, in the hundreds column, 4 in the tense column and a 2 in the ones column of 642, and then i'm adding the 2 to the ones column to get 4, and i'm adding 6 to the tens column. So i'm gonna i'm gonna count this on. just so I can just show the process of the 19 exchange. So i'm gonna do a 4, or 5 exchange first i'm gonna set the 5 and clear the 4, and that's what keep counting 2, 3, 4, 5, and then i'm I have 9 sets so I can't add any more into that column so I have to make a 9, 10 exchange where I set call one and clear the 9. So I set a one in the hundreds column, and I cleared the 9 in the 2 S. Column, because, like we talked about in the last session, the 9 Cent Exchange can occur across any column in the any place. Value column, and you know and ones in tens it's 9 and 10, and tens and hundreds. It's 10 and 100 or 9 90 and 100 and hundreds and thousands. It's 901,000 so but it's the same exchange. And then, so we've added 6 to 4 to get 0 in the tins column. And now we have a we've already added that one so that's when i'm pulling back the print version of this, so that one that we added in the in the 9 10 exchange that's the one that we carried in the in the print version so that's already been added. So we have 7, so we just need to add one more to get 8 0 in the tense column. 804 Any questions about that before I go into subtraction >>Donna: Great. do you want me to go faster? most of the time I was thinking maybe after this next one time, if we can give them a a problem to solve on their own through their advocates and we're gonna we're gonna take their >>John: word for it since they don't have their cameras on it. they're working it on their advocates some kind of neat little prize for anybody wants to share they are more than welcome i'm looking at you, Jill cribs i'm just teasing jill alright. So we're gonna do 804 minus the 162. >>Donna: And Joe says she knew you were gonna say that yes that's one of my favorite past times is putting Jill on the spot. >>John: Alright. So we have 804 minus 162. We're subtracting 2 from the ones column to get 2. And now we have this 0 over here in the tens column, so we have to subtract 6 from that. But we cannot, we cannot. So in prints we have to. We usually cross through that 8 and change it to a 7, and then we write a one next to the 0. So that we know we have 10 and we're subtracting 6 from 10 to get 4, and we've changed that 8 to a 7, and so we're subtracting one from that 7 to get 6. So we're left with that same 642 whoops, 642 that we started with So on the abacus that we're doing that 9 10 exchange. We're gonna do that 9 10 exchange in reverse So cleared my abacus, but we would have had that 804 sets from the previous addition. Problem, and we're subtracting 2 from the 4 to get to. And now we have 0 in the tens column, and we need to subtract 6. So for that on the abacus you, instead of in the 9 Cent Exchange, we set one in the to the left and cleared the 9. In this case for subtraction, we're clearing a one in the hundreds column, and setting a 9 in the tense column. So adding, because, like that's subtracting goes like that so You're either setting a tin and clearing the 9 for adding and clearing that 10 and setting the 9 for subtracting and that is, that was one so i've subtracted one from this tense column. And now i'm going to subtract 5 more, 2, 3 for 5, 6. I'm gonna do that one more time so I had a 0 i'm going to clear the tin set the 9. That's 1, 2, 3, 4 5 and 6 so i'm left with 4 in the tens column, and then i'm subtracting a one from the hundreds, column and I get 642 almost read that incorrectly 642. >>Donna: Okay, challenge time right before we get to that challenge. There was a shit, all right, comment and a question. Carol says that When she learned Abacus it started with the column to the left instead of starting with the ones she knows. It works that way. does it work? Does it always work this way as well? >>John: Yes, that's a good that's a great question That's a great question. I have a lot of thoughts about this. We could do a whole abacus theory section. I would want to invite some other people to help but I So I also learned from left to right. and >>Donna: I I don't remember why it was taught that way yeah it now. >>John: It could have to do with how how problems were worked in multiplication and and division, which, in the way I learned it, are different than how I teach it. Now in the using place value. I for a couple of reasons, the the first one being that if a students in a math class, the math teacher is going to be instructing students operations from right to left. And so I wanted I will. My preference is for students to be learning things as closely as possible to how their peers are learning them. So if we can do that on the Abacus great. Now there are some caveats, so it everything works right to left and left to right. If there's a student who's working problems from left to right i'm not gonna stop them from doing that. I typically will. What I explained to them is that it does work both ways. And, in fact, if you go, if you work problems from left to right, you are going to have fewer more complex exchanges. Such such as 49, 50, or 99, 100 exchanges. You actually reduce the i'm gonna make up a term exchange weight. You you reduce the complexity of the exchanges by working that that way. I don't know that that's the reason why I I think I remember. I seem to remember it being because it helps students understand the processes that you have to learn to work multiplication and division problems. And that's it was those problems that led me to do to teach multiplication and division a little bit differently. Well, I mean I think it's a lot differently but you know depends on how math you are. So that's that's what I think so far is that does that help that answer the question? >>Donna: A great question, Carol, and as soon as we get selected sips of Rt. >>John: And Carol says, Thank you. might be a one up for debate on some sides, So we're going to throw out this problem next, and the person that gets their answer correctly on the and shares it will when something nice from t time. themes. Okay. So how are we gonna have them? Show it, John, are we gonna have them in the hold of grabbages? >>Donna: So, bonus that you have to actually turn on your camera this tea time. >>John: Yeah, how hard should I make it? I Okay, here we go. This is gonna happen. all right, Everybody ready. We have 587. This is intermediate. So, plus 384 >>Donna: Cool I didn't i'm sorry this is why I don't switch my camera back. >>John: I I there we go! >>Donna: I 500 584 sorry about that y'all Once you have your answer, hold it up in your camera Alright, it looks like Jill. got it up. there just a fraction of a second before Adriana did. But let's check them and see if they're right. >>John: They say that it is. Let me check my reading here. 971 Is that what? Yes, yes, that is correct. you know what's funny is I wrote the problem down wrong. So when they showed their answer I was like now that's wrong. But then I realized I wrote the problem down incorrectly. >>Donna: So they actually got the correct answer. My address in the chat is, if you would privately send me your >>John: Your mailing address. Then you will receive your price, and just let me work this out, and France first. So 7 plus 4 is 11. carry the 1 8 plus 8 is 16 plus one is 7. Carry the 1, 5 and 3 is 8 plus one is 970. One. and so what I want to show is we just talked about the left to rights. So you know. I I I do I share with students one there once they're at a certain level. I say you wanna work it left to right try it you know let's let's see. So we'll just do that so 5 plus 3 is 8 I'm Sorry I just added the 3 I just put this, added the 3 on, and then we have 8 plus 8. So in this case we had one 9, 10 exchange. Add the 10. Clear the 9 to get 2, 3 4, 5, 6, 4, 5 exchange makes 7, and one more makes 8. So I've added 8 i've added 3 i've added 8. And now i'm gonna add 4 in the ones column. 1 2. This is another exchange, 9, 10 exchange set of 10. Clear the 9, 3 and 4 makes one. so I get the same answer. 971, so it does work left to right, right, to left. Either way that's what that's what's that's why we're getting into intermediate advocates. Alright. So let's look at 49 50 exchange 481. I'm not i'm losing my system I gotta stick to the system 481 plus 423 one plus 3 is 4. I'm just adding this up 8 plus 2 is 10. So right a 0 carry the 1 4 plus 4 is 8 plus one is 9 under 4. Alright, no 40, 49, 50 exchange in print, but so on. The Abacus. What happened? What happened? So already? had it set 481. So we're adding 3 to the ones column 2 3 i'm, adding 2 to the tense column. One. Now I have to add another one to the tense column I can't have 9 set. I have forced in the hundreds column so I can't add another one in the hundreds column. So in this case I have 49, set I have to set a 5 in the hundreds column, and clear the 4, and the 9, and that made 2. And then I'm adding 4 to the hundreds column 1, 2, 3, 4. So I get 904 49, 50 exchanges are relatively rare. They don't come up as often as 4 or 5 exchanges, 9, 10 exchanges and 10,000 exchanges 49, 50 exchanges are basically a combination of a 4 and the 9 10 exchange and I found them to be maybe more complicated for students. Then other exchanges but so once they once they get it. they're able to to process them pretty quickly. So i've got 904 here i'm gonna shift back to my prints and subtract the 423904 minus 4, 2, 3, some subtracting 3 from 4, to get one So I borrow. I have a 0 in the tense column, so I borrow a one from the hundreds column. So the 9 becomes an 8, and I set a one alright, using my advocates terminology. I write a one to make this 10 in the tens column, 10 minus 2 is 8, and then 8 minus 4 is 4. So I get the same. The 4 81 that we began with so i'm gonna try that on the abacus So I have 904 set i'm subtracting 423 subtracting 3, and the ones column 1, 2, 3 from the 4 left, with one have a 0 in the tense column. I need to subtract a 2, some subtracting a one. From the Hundreds column, and setting 9 in the tense column, so that subtracts one. And now 2, and as you see we don't have a 49, 50 exchange in reverse for subtraction. This point, then, i'll subtract 4 from the hundreds column 1 2 3, 4, and i'm left with 481, so we only had the 49, 50 exchange moving right to left for addition. >>Donna: And Carol has another great question. Yeah. We might just have to get her to. and her address to the to my email as well as participation is king. With the 49 50 Exchange? she asks. Do you show the students with blocks or something first, so that they understand why they are making this kind of good exchange? >>John: Yes, yeah last, at the previous session, I talked about using digit blocks to to demonstrate the exchanges and as well as the Ap. Workplay trays, and then we excuse me, we use either wiki sticks or art tape up at the top of the workplay trays to To represent this separation Bar and so that we we kind of have to kind of collect the blocks and create a 5 bead, using 5 blocks. And actually I I don't I think that resource may be shared. Donna in the previous from the previous session on the if you'll have the the resources that I shared from last time. >>Donna: The was it a How are I do have your handouts from the last time, and I I linked the Did you block some chat I'm: also gonna link the website where last time session? >>John: Is with all of its resources. Excellent. Yeah. And And that really helps the students a lot. The connection with the manipulatives. yeah thank you it's a great question. So I was in a try to see if I can find a subtraction problem with the 49, 50 exchange because they do exist. So I have here I have 544 minus and i'm subtracting 254, and I wanna show a couple of things here, so i'm subtracting 254 so i'm subtracting a 4 from the ones column and then i'm subtracting 5 from the tense column. So i'm gonna count this off 1 2 3 4 i'm left with 0 in the tense column, and I have a 5 set in the hundreds column, so I have to clear the 5 and set a 4 and a 9 so i've cleared the 5 in the hundreds column and i've set a 4 in the hundreds column, and a 9 in the tense column, so that I had 50 or 500 minus 1 10. So that's sorry is I lost track of where it was sorry. >>Donna: This is a perfect example of the kids, too. I know what happens all the time. all right. Where was it? >>John: I had 540 for subtracting a 5, so I just have 1, 2, 3, 4 accounted off the 4, and then I clear the 5, and set the 4, and the 9 for the 49, 50. Exchange in this. these only come up if you have a 5 set and end up with this 0 in this column, and need to subtract one more. So again, I encourage students to just especially when they're first starting to practice counting up by ones, and down then subtracting down by ones Just so they they get the opportunity to practice those exchanges. So if even if I started at 500 and counted down like my next set, would be 507, 7, 6, 5, 4, like I the timing I get to before I get to another 49 50 exchange would be like 450. you know so they just don't occur that often. And then another point to make is that if we go I think if we say, okay, I'm gonna go from left to right. With which Carol mentioned that we talked about earlier. you can subtract the 2 from the hundreds column, so I can say 5 minus 2. So i'm gonna do a 4 5 exchange 1 2. and then it's it's done I can do everything else without having to deal with that 4 or 5 exchange So that's what I meant earlier when I said, that you reduce the the weight of exchanges. I guess the cognitive load a little bit of exchanges working from left to right. It's just gonna be different than what the students are getting in their classroom who may be working right to left. So that's, you know explain to your students based on you know your assessment of their their needs. So then i'm gonna keep going i'm subtracting 5 from the tense column. 1, 2, 3, 4, and this is a 9, 10 exchange for subtraction, 5, and then subtracting for from the ones column. And so I give 290 is that the same that the right answer. That's the right answer in my book so I think I got it. My brain is is kind of overloaded right now with the abacus. Okay. So any questions now about the 49, 50 exchange, or have I thoroughly confused You >>Donna: So far nothing has come up about the exchange now we're gonna get into the 10,000 exchange the big one. >>John: I also. Okay, 3, 46. all right we'll do this one rule, and then we'll i'll show you a couple of other little things. So we've 971 plus 433 So I'm adding 3 to one in the ones column to get 4 i'm. Adding 3 to 7 in the tens column to get 10 and I'm adding, have to carry that one. So I have 9 plus 4 is 13, plus one is 14. So I have 1,404 so let's do that on the abacus, and see where our exchange happens. 971 plus 433. So I had 3 in the one's column to get 4 have a 7 in the tense column, so I'm adding 3 to that 1, 2, and you see I have a 9 and the tense column and 9 in the hundreds column. So I, to get to add one more. I have to set a one in the thousands column. Click through the 900, and clear the 9 tens to get to add the third 10 that I needed to add. So now i'm adding 4 to the hundreds call 1, 2, 3, 4, that one was easy. So I am left with 1,404 One of the things about that if you like. Think about that problem there were. There was no exchange in the ones column. There was that big exchange which was basically 2, 9, 10 exchanges. We had 7 sets we're adding 3 1 2, and so I can't do a 9 10 exchange, so I have to just come to this next column set a one and clear both nine's to make 3 at that point you know that's your big exchange that you're problems practically done. You're just adding 4 to the hundreds column and to get 1,400 force. So a lot of problems are like that where there might be one. Exchange in the problem. That is a little bit more complex. But the rest of the problem is pretty well you know not or the other place value columns or are typically not as challenging. So let's. do this i'm kinda scared to do it in reverse, cause i'm not gonna get a the exchange again. So i'm gonna have to show you a different problem this is the thing with these larger exchanges and what I mentioned earlier is that you don't necessarily see it. >>Donna: Oh, we have a good question before we move on to that next problem. >>John: Let's do it, and I i kind of have the same question, because I think kiddos get a little bit confused here whether or not to go back to that dens or move on to the 100 and carol asked is it confusing for the student if they had a 4 in that tens column instead of the 3. If they had a 4 in So we set that Okay. And so if we do the 3 and then instead of a 3 in the tens, we have a 4, Yeah. Okay, so that's a great question and yes, yes, it is so we'll add we're adding 4. right? So we have the 2. We still have to do the same. Exchange. We have to set the one in thousands column and clear the 9 and the 9. Now you're right Sometimes students will want to come to this column to see the extra one. What I remind them we talked last time. about you know making sure we're in the correct place value column, and so typically, what i'll have students do, is it There's no typical But what I in this case what I would have a student do is when they're adding I would say, I would maybe ask, Okay, what what place value are we adding the 4 tens column? Okay, let's add the 4 to the tens column and so they start adding 1, 2, or I might they might count 1020, and then they need to make the exchange. So let's we got to go all the way over here to the thousands column to set the 1,000 clear the 9 and the hundreds clear. The 9 and the tens and we've set 30 so now we need to set one more 10 to set 40. So really using that explicit language to can continually remind them which place value column. They're in that's a great question and a great point I think that when i'm talking to adults about it, I you know wanna just demonstrate. but the whole teaching aspect of it is a really great point as well because once you're working with the students you typically will know how explicit we need to be in those instructions because they will make an error like that, and you'll start to sort of reflect on how how you need to adjust >>Donna: instruction, or maybe just be explicit from the beginning, and and and step back when it's when they are more independence. I completely agree, and it's appears to children as Well, she thinks it makes a big difference when we >>John: use that explicit 1020, 30, instead of just counting 1, 2, 3, yes, absolutely great question. Great great points. So do you want me to keep keep working the problem? >>Donna: We can finish that one off. We have 7Ā min, just all right. Well, I have the 2 points I wanna make before. >>John: Before we wrap up, and that is what I wanted to shift to is to discussing multiplication concepts just a little bit. But then I also want to talk about how you know we've been working with these 3 digit numbers. but sometimes, and this is a little bit more of it. This is a little bit of an intermediate concept. Students really like to be impressive with their place value. So once a student has mastered no exchanges or 4 or 5 exchanges, we can take numbers and put them in a very large place. Value columns, so students may have mastered place value into the millions. So you could set 2 to 22,333,222, and then If they've mastered the 4 or 5 exchange, they can add to that 33,000,003 222 1,000 333, so that they would add one to 3, 4, 5 exchange i'm sorry, and I could say 1020, 30 million 1, 2, 3,000,001 200,000 one 1020,000 and i'm going from left to right just 1 point that that i'm, just i'm just add just for demonstration. And because I reverted to my habit and that to 1, 2,000, and then i'm adding 3 look, i'll go from right to left. 1, 2, 3, and the ones column 1020, 30, and then 100. 200. 300. So then they can read that big number 55,555,555. And students really love impressing everyone. some students really love impressing everyone with their knowledge of place value, and how they can do all of those big numbers on the abacus. So that's one one strategy 1 point the other one has to do with multiplication concepts, and there are some when you're just starting to work with students on multiplication concepts. You can use the advocacy as a as a as a tool for multiplication concepts. So we can say that We have 3, 3 people, and they each have 4 cups of tea, and so I have one person with 4 cups of tea, 2 person, 3 persons, with 4 cups of tea So we're basically we're starting to ask the student to forget about place value in this case. We're just using these as holders, each rod is a holder, and it's just holding a value for you, and then they can just count back down 1, 2, 3, 4, keep counting 5, 6, 7, 8, 9, 1011, 12, so they can use the beads as counters to count that we had 3 people who had 4 cups of tea. So all in total. they had 12 cups of tea just by using those as counters, you know, maybe a little bit abstract for some students, not maybe maybe better for a lot of students to use manipulatives instead. But this works, as a you know, as a tool if you don't have anything else, and that's those are the 2 things I wanted to mention, as far as intermediate is concerned. Next time we really get into multiplication and division >>Donna: That was the little bit more thing that put a a stick in the you know a sticking load, whatever it is, just made it that little bit harder. >>John: And so we so appreciate you coming and and teaching us about the advocates Today it's my pleasure if anybody has any questions feel free to reach out more than happy to talk about it, and let's see what we have to finish up >>Donna: and know everybody really wants that that code, and I will get you to there as soon as I can get my screen back here. All right. So great discussion today I would love to have everyone for it was participating in that, and I linked the site into our chat. If you haven't already visited please, come and visit our our tech resources, all the tech t times are posted as well as different resources that are requested, and written throughout the school, year, so definitely come and visit our site and check out what resources we have. Alright, the other thing before we get to the code is contribute to tea time by picking a topic. We do Have our topics through February, this real quick. Before I give you your your code. Our last one for December is going to be a call combination. We're going to be pearson math xl which if you haven't heard of math excel that is they're gonna come to tell us how it's accessible for their textbooks. And we're also going to be talking about apps and typing programs in January. We have a ph coming to visit. So our new technology person from Aph and I might have those dates backwards. are you? On the twelfth of the ninth? I will check on those in january we have advanced advocates with John, and then on the 20 sixth we have teaching jaws. So that's going to be your basic jaws and then in February, February second we have star in the Braille display. I'm working with some of the help documentation to make sure that your kiddos are able to now, navigate and access. So really, really excited about using some of their resources and work with that program. Oh, right. So your code to end today is 12. Oh, 8 22, 1, 2, 0, 8, 2, 2. That's our code for today, and I have gotten the addresses of our people that won.