TRANSCRIPT - Continued Abacus with John Rose (Part 1)

Yes, I I come on. It just turned 30'clock Yeah. So we'll get that one going Take my camera off and get the other one ready to go. Alright! So I'll kind of wait for you to maybe just like count me down 3, 2, one, so I can no one to start the You can go ahead and start. It's it's already 30'clock. So Alright! Thanks. We'll do. I'll get that going right now. Alright! Was everybody able to get the link for the worksheets Oh, we just had Kathy come in, so let's give her a second Oh, it's the last second rush! Thanks. Wait till they get fully, and then I'll link the worksheets again Alright for those of you who just came in. I'm linking the worksheets into the chat. There's Pdf. And word your choice of document, and then I'm gonna make our usual. Announcements, and we'll get started Alright! This is tea time. Welcome back! It's Thursday And we are ready to go. Today is spring. I would series with John Rose. We love having come back for 2 sessions of abacus this spring And before we start the usual business of this is our goal. To build community practice for technology and support each other as we teach technology in the spirit of that goal. We want you to be interactive. So, either by questioning or meeting yourself in question, or coming through chat with questions Be advised at this session is recorded and posted on our website for later viewing in the Tsbi Professional Development Library, as well as on my Google site by registering for this session, you hear by Grant Tsbvi permission to publish contents of this recording which may include your image and audio of you as the registrants Alright. I am going to hand over the share to John so he can have control of it, and I will come back in the end to let you all know what is coming up in the next 2 months for tea time Hello! I'm back alright. So last time we we met was December. Don't remember, but it was we were looking at multiplication. Some division on the abacus. This time you all requested a worksheet, because I was writing the problems down. I guess. And that was then they would disappear on you, and so I thought that was a good idea. Who ever thought of it? That was a great, great idea, and sorry to have this worksheet, now that are late. That's linked in the chat. So we're gonna do a multiplication review. And then division practice, and then we will get into decimals, setting, adding, subtracting, and multiplying decimals. Alright! Seems like a lot, but maybe it is. Maybe it doesn't. I don't know. I didn't time this lesson, so we'll look at Multiplication Review first. So let me put on my Advocacy. So with multiplication, we set the multiple canned the number to be multiplied in the billions section in the correct place value columns. So on our first problem to times 22. The multiple canned is the 2. And that's set in the billions column and the ones place in the billions column. So submit 2. There set the multiplier, the number doing the multiplying in the 1 million section in the correct place. Value call. So that's the next section over. I'll set 22 in the millions. Section. And so I have 2 times 22. The product is set in the units, or hundreds section and 1,000 section. If need be, so when they're working the multiplication problem, I start the we start the process with the smallest number and the multiplier and the smallest number in the multiplication. In this case there's only one number in the multiple canned 2 times 2 is 4. We're finished with this, too, 2 times 20 or 2 times 2 in the tense column is 4 in the tense column or 40. So 2 times 22 is 44, Now I left the multiple can put placed because to show the connection with division. So this, the problem that's set now is the first problem in the division practice. 44, divided by 2 So with division, we're gonna look at the Do divisor dividend! This is me. Thank you. Divisor Right? Okay. So the dividend is 44. The divisor is 2. Yes, this is why my my students like me, because I forget as much about math as as they do. So we say, how many times will the 2 go into the 4 and 40? It goes into the 4 in the tense column 2 times 2 going to the 2 times 2 is 4. It's 2, and the tents cost. So we're finished with that 42 goes into 4 in the ones column. Also 2 times. And so we're 2 times 2 is 4, so we can clear that 4. So we set that 22. This is the same place where we would have set for 2 times 22. So I just wanted to show that connection between multiplication and division So we'll do another one This 1, 480, Divided by 8 So our dividend 480 is in the hundreds, tens and ones column on the right. Our divisor 8 is in the ones column of the billions period. So we're saying, how many times will 8 go into 480? So we begin with this far left digit. How many times will 8 go into 4? Well, there are no groups of 8 and 4, so we move to the next digit of the dividend. The 8. How many times will 8 go into 48? There are 6 groups of 8 and 48, 8 times 6 8, and 48 is in the tens column, so I'm gonna set that 6 in the tens column of the millions place. 8 times 6 is 48. Clear, my 48. You're also saying 8 times 60 is 480. But we're looking specifically at that tens column. So 8 times 6 is 48 clear that 48 we have no more left, so we're finished with our problem and can clear the 8. Check our work. Typically as we go along. And we just did that when we said, with this 1, 8 times 6 is 48. And so when we multiple did that multiplication, we went ahead and cleared that from the dividends Any questions in my this is review for the most parts, little bit more division than what we did last time. Okay, so. You see how I was gonna do this? I think we'll start with the If no, we start with the multiplication Where. Where is it? There. It is. Okay. So this next, this multiple application problem, the third one on the worksheet is 430 times 25 So for that one. I'm going to pause and let's work on this And I will start in a minute, and I'll just work through it One step at a time, but I'll let you go ahead and start Looking at this 5 and 25, and multiplying times, the 0 and 435 times 0 is 0. So I said nothing in my product, and stick with the 5 and move over to the 3 in 33 times 5 is 15. That's in the tens column. The 3 is in the tens column. So I started my tense column. I set the 5 and 50 and the one so 15. There. It's the same as saying 5 times 30, which is 150, which is what I have set now in my in my product place So we're finished with the 3 Now left with the 5 in the ones column and the 4 in the hundreds column 5 times 4 is 20 So I go over to my hundreds column and my product place, and there's a 0 in the ones column and a 2, and the tense column in 20 Same as saying 5 times 400, which is 2,000. So I've set a 2 in the thousands place and is and well, Zeros all the way back. So my partial products are the amount that I have currently with. Oh, no, I'm sorry I was not finished with that 3 that was incorrect. We are not finished with that 3, we still have this 2 to multiply. Pardon me, so we've finished with the 4 400. So our partial product, we're finished with the 5 that's where we're finished with. Our partial product is is 2,150. Now we move on to the 22, and the tens place 20 times 0 0. So I have nothing to set there 20 times, 30 or 2 times 3 is 6, add 2 zeros to the end, 6. 0. 0. That's 600 or 2 times 3 or 20 times 3 is 60, in the tense column. Go to my tense column So my 6, Or 620 times 30, Now I am finished with that 3 because I've multiplied it by the 2. I'm left with 400 times 22 times 4, and the Hundreds column. Sorry 20 times 4 and hundreds. Column is 80 in the hundreds. Column. So I'm going to add 8 to my thousands. Place 1, 2, 3, 4, 5, exchange 4, 5, 6, 7, set a one, and clear the 9 for the 9. 10. Exchange Finished with the 2 and the 4, the answer, 10,750, quite a large multiplication problem with a lot of steps Wanting to connect that with The division. So we have 10,750, divided by 430, This problem, obviously much more challenging because you have a 3 digit divisor, 430 will 430 go into one? No. 10, no. Well, 430 go into 107. Those are the first 3 digits in my dividend. Still no. Well, 430 go into 1,075. Yes, so at this point, this is where student will start considering the estimation skills that they've they've used. And up to this point. So how many times will 430 go into 1,075? Well, 400 plus 400 is 800, 800, plus 400 is 1,200. So it can't be 3 times it has to be 2 times. So that's in the tens column. The 5 is in the tens column. So we come over to our millions, place and the tens column and set it to Now we get to do our multiplication 0 times 2 is, I'm sorry. 0 times 2030 times 20 is 600. So we subtract 600 from the quotient 1, 2, 3, 4, 5, 6, And 20 times 402 times 4 is 8, with 1, 2, 3, zeros. That's 8,000. So we subtract 8,000 from 10,150. So we clear the 10 set. The 9 is 12345678000 Okay. So we're left with 2,150 Alright! Now we go back to our divisor, and we say, Well, 430 go into 2, No. 21, no. 215, no. 2,150. How many times will 430 go into 2,150? Again, this is, gonna use that skill of estimation 5 times would be 5 times 4 is 20, so 2 that would be 2,000 3 times 5 is 15, so third, 30 times 5 is 150, so that should be the right answer so I'll set a 5 in my quotient place. The ones place my quotient place, do my multiplication again. 3 5, times 30. It's 150 and 5 times 400 is 2,000. So I'll clear the 2,000 in the questions, and some left with 25 as my quotient, which we know to be true, because we just did that multiplication. So in that problem, you could probably see a number of mental hurdles that students have to make during the process of of doing those long division problems. So I I'm not sure that there are, aside from practice, I'm not sure that there are any tricks or secrets. Long division is challenging for all students, because it it does require a certain degree of grit and determination. So I just you know, I just wanted to put that out there that that I don't have any magic for for the hurdles that students, you know, encounter along the way. So sometimes students will, for example, say that we had. We had 2,150, and we were trying to get that 5 in 25. So sometimes students might go too small, so they might go, but with a 4 in that place, and then do the multiple multiplication. And so you have a 3 times 4 is 1230 times 4 is 120. So you would clear the subtract. 120. So 1, 2, subtracted, 20, subtract one from the hundreds place that's 120, and then 4 times 4 is 4 times 400 is 1,600. So, I'll subtract 102, 3, 4, 5, 601,000. So I'm left with 430. Okay? So that is actually, you know, sometimes the student will wanna kinda go over to this next place as they're thinking about this. But what? What? I try to remind them is that there's still there's still dealing with the ones place we can't go anywhere past this period. Marker. That's the ones place. Are there any? Is there anything left? Yeah, they're 430 left, and we have 430 in our in our divisor. So 430 will go into this divisor one more time. So we can add one to the quotient If a student goes over, say, what was it? 2,000? 150. Right? So if the student goes over and says 6 when they're estimating it, it's through doing the the math, they'll start to find that that they were incorrect. So again, 6 times 30 is 180, so they'll start subtracting. I'm going to start subtracting 81, 2, 3, 4, 5. 6, 7, 8 left, with 2,070, and then 6 times 4 is 200. 240. I'm sorry. I'm sorry. 2,400. So I have 2,070 over here. So there are now, I know that that's too much. I can't subtract 2,400, so I must have put. I must have put too much on for my for my quotient, so those are just a couple of things that I've noticed with students is either estimating high or estimating low. And then knowing what to do in those situations. So that was a complicated one. I think this next one is more fun. Maybe so I'll give it to you all the practice this one is whoops. 24,980, divided by 6 So I'll leave that up for just a second and give you some time to start working, and then I'll start in in a minute, one step at a time. So initially, we're looking at 6 and 6 will not go into 2, but it will go into 24 One of the things that I work on with students is developing a script to have when working through these division problems. I think that hmm, math teachers typically use that with with all students by saying, Okay, you have to 24. How many times will 6 go into 24? 6 times for is 24. In this case we have a little bit of a conundrum, because our 4 is in the thousands. Place. So we were setting our number in the millions. Our quotient in the millions place. So our divisor is here in the billions. Place, so we can't set here. So what do we do? We can use this place here, and the millions, the one millions place and start working toward our toward our dividend. So 4 in the one millions place, and that will be our thousands in the quotient. So 6 times 4 is 24. So we clear the 24 from the quotient, and we're left with 980. 6 goes into 9 once, so that's in the hundreds place. So to one. Now our hundreds place is here in the thousands period, 6 times one is 6, so we clear 6 from the hundreds. Place, so we're left with 386 goes into 38 6 times. That's in the tens place set a 6 in the tens. Place over thousands. Period, 6 times 6 is 36. I'm gonna clear the 30 and 6 from the 8 I'm left with 26 goes into 20. How many times, 3 times, so I'll set a 3 in the ones. Place, 6 times 3 is 18, so I'll subtract 1, 2, 3, 4, 5, 6, 7, 8, and a one from the tense place. Some left with 2. So my answer is 4,163 remainder 2. This kind of gets into some fun situations where you can, you can actually continue this problem. How good? Question! Well, the 2 in the remainder, when we get into fractions, goes over the 6. So? The answer to this question or to this problem in fractions is 4,163 and 2, 6, or one third. How, however. I'm gonna go off book here, but not really. If we just move our problem a little bit, I'm gonna move the Divisor, the one I can't remember today over to the trillions column. We could do it for this one, because it Trillion's column has just one place. Other problems make it more challenging. And I'm gonna move my quotient over one whole, one whole place. Also 2 is 4,163, 4,163, and then I'm gonna move my remainder over to the ones place in the thousands. So I'm left with some more room, and I can keep going. So 6 will go into 2. No, it won't. 6 will go into 23 times now my 0 is no longer in the ones place. It's now in the tenths place, so I can set my 3 here 6 times 3 is 18. Well, it's gonna into. So I'm gonna do it again. 1, 2, 3, 4, 5, 6, 7, 8, and one from the tens. Some left with 2. Again. We'll 6 going to 2. Now we know that we'll 6 going to 20. Yes, we know that 3 times. What's gonna happen when I do my subtraction, my 2 is just gonna move again. 6 goes into 23 times do my subtraction. I can't. I can go farther, but I don't need to. So the answer now is, 4,163.3 3 3, and so this is kind of a fun way to get into decimals is by showing how division turns into decimals. Students can even look on it and look at it on a calculator talking calculator, and then, you know, show, you know, do do both use the talking calculator and the abacus getting the same answer. And show how the abacus can can continue that decimal progression. You know, with another advocacy you can go on forever and ever. So this is setting decimals. You use your period marker, as your decimal place to indicate where the decimal is in the value. So the first one will practice setting is 26.9 6 5, and for this I mean, you can use your decimal. Can be any one of the period markers. But typically we'll, you know, start with the one on the right. And so that's gonna be our first period marker. I'm sorry. Our first period marker, will be our decimal points. Everything to the right of the decimal are fractional values or decimal values. So we have T. One hundredth stth to the right of the period. Marker, decimal point, and then our ones place has shifted to the thousands period ones, tens, hundreds, thousands, etc. So 27 whoops Points, 9 6, 5 looks like that. You have a 5 in the thousands. Poem, place 6 in the tenth place, 9 in the tenth place. Wait. Did I already say that hundreds place thousands, place hundreds, place 9 in the tenth place? And 7 in the ones place and a 2 in the ten's place. This is just another opportunity to practice. Place value with students, especially if they are learning decimals at the time, because they can practice you. You know you know the whole. All the games about dice, rolling, or just handing them an advocacy with with desktop set, and then telling you which digit is in a certain place value. This is just another opportunity for those skills that we talked about in beginning advocacy. So our next one is a big one, and it is 64,972.3 0 9 1 8 a number that most students will never set except when they're practicing decimals. So where is our decimal point going to be They have to be at the second period. Marker That's right. The second period marker. So our sixty-fourths is going to be, or we can work from left to right, from right to left, from the decimal point. Sometimes with setting decimals. Students do have some challenges with shifting, of shifting of digits. And so typically, the main thing I notice is just reminding them to check where their decimal point is set. This is an exaggerated example, so they you can go from the decimal and say, Okay, it's point 3 0. 9, 1 8. So I'll start there and set 3 0 9, 1 8. So my decimal part is finished, so I know where that starts, and then from here I can set 64,972. Sometimes when students try to set a larger desk from the left and then go right. That's when they get that shifting, incorrect, and they'll be like a little to the right or left of the decimal point. Any questions about setting decimals. Now. No, all right. Silence is golden. So now adding and subtracting the great thing about decimals, and adding and subtracting is, you don't have to learn any new skills as far as adding subtracting or multiplication, and division for that matter It's just remembering that the decimal point is there and where to set it I made an error on this page. I just noticed it. The second problem should be subtraction. It's addition. It says it addition, but it should be subtracted. Oh, I made a note of it, so I'll remind you all when we get to it. But it's the $25 and 83 cents should be more $22 and 96 cents. So included money problems, because I found them to be the most motivating with students. It's also probably the first, you know, decimal values that they that they see and consider for the most part. So I even desimals that are listed as decimals in. You know, my some of my practice problems. I'll turn them into money problems for for students and make up word problems based on that. Students having so much money. Yeah, and then doing something with it, or getting more stuff like that, just seems to motivate them a little bit more to to work the problems. So for this one I have a $16 and 49 cents. So I'm gonna my decimal point will be the first period marker. So I'm actually gonna set my 49 cents. And then my $16, and I'm adding $31 and 72 cents. So I'm gonna start on the far right at the 9. Add 2 to my hundreds. Place Hundredths place. So for this is actually a 49 50 exchange. We don't see these very often. So we set the 5 and the tents column and clear the 49 for one, and then add one more to the 10 hundredth place that makes 2 neat. I'm glad we get to see one of those I you just don't see them. That often and then we're adding 7 to the tenth place, 1, 2, 3, 4, set a one. And now next column over clear. The 9 makes 5 right. I got lost. I had a 5 sets Yes, that was 5 Thank you. Oh, my gosh, thank you so much. Who is that? Angie. Thank you. So thank you so well. I was a Vi. Hey, g Al rod! I was the math teacher before I became a Vi. And then I became math teacher. So thank you very much. That's that's that's why that's why you know it. And I'm in bizarrely knowing it all right. I forgot what I did completely. Had 5, 1, 2, 3, 4, 5, 6, 7. Right did I do that? Yes, pretty sure. I'll check myself, adding one to the ones, and then adding 3 to the tens. So you have 47, 21. Is that right? I make mistakes all the time. So my students end up checking my work as often as I checked theirs. No, it should be 48, 21 Would he? 8? That's what I have. What did I say? Yeah. 7, well, I read it wrong. That's another thing that students do often read it wrong. And so you just what I would have said to me in that case, is checking your answer. Go back and read it one more time. Make sure you look at your 5 bead. Make sure you've counted all your beads, John, so that's the teacher teaching the teacher this time. Alright! Our next one is 2583, and this time we're subtracting $22 and 96 cents. So in this case my principal gave me $25 an 83 cents for my monthly wages, and I went out for breakfast in Austin, and spent $22 in 96 cents. See how motivating that is for students so subtracting 6 from the hundreds, 1, 2, 3, clear the one, and the calling over that's the 9 that makes 4, 5, 6. And now I'm subtracting 9 from the tenth place. 1, 2, 3, 4, 5, 6, 7, 59. Exchange dates 9, that's and then subtracting 2 from the ones and 2 from the tens. I'm left with $2 and 87 cents to pay my bills Good, one right. Okay, any questions about addition and subtraction with decimals? It's the same as it's addition, subtraction with without decimals. The only difference being that you're adding, these place values So multiplication of decimals. You can maybe guess. Not much different. Then multiplication without decimals, we're multiplying decimals. We treat each decimal as a whole number. When the multiplication is complete, we count the number of decimal places in the multiplier multiplication, and then indicate that many decimal places in the product so we can set the product using the first unit marker on the right as the decimal Points, unless the product requires more than 3 decimal places. So typically we'll use this first period marker for the decimal place, and unless it requires more than 3, in which case we move over. So our first problem is point 5 times point 9. So we just set set it up like a regular multiplication problem. 5 times 9 is 45. Often when students are at this point in their mathematics careers, they can say, Okay, there was one decimal place in my point in my 5.5 one decimal place in my point 9. That's 2 decimal places. So it's point 4 5 when they first start out. I do ask them To to demonstrate that, using the abacus. But typically at this point they're able to get that without demonstrating it. So like other things. I will. I'm okay with that as long as they're not making errors, and when, if they start making errors, then I start asking them to demonstrate it, they're understanding. So our practice problem is point 6 2 times 4 So we set it up just like a regular multiplication problem. 62 times 4, 2 times 4 is 8 6 times 4 is 24 There are 2 decimal places, and the problem point 6 2 And so we're gonna show this products over 2 or it's 2.4 8 Typically, it is the case that you can shift the the product over one or 2 places, just depending on how many decimal places there are in the products Okay, got a few more minutes. Are there any questions or anything that's anybody like to see demonstrated again? I don't want to get into division of decimals this time, because there are several different scenarios involved. It is one of the more complicated advocacy. S. Tasks. I could show fract. I could show some fractions, or we could do that next time. We have about 10 min. If anybody has any questions at all, or wants something to be gone over again. So let me just I'll just share the fractions. Basics, and then we can get into the get into the fun stuff next time. Fractions are well for addition and subtraction of fractions. Well, let me just start with this fraction. The Fraction Bar is similar to the to the decimal points. Right. So your period markers act as fraction bars in the in, the, in the fraction addition and subtraction are set differently. Then multiplication and division, but for the most part you you for addition and subtraction. Your denominator section is your your ones. Period or units period, hundreds period, also known as your Thousands period is your numerator. Section, your whole number section is the millions period, and you're determining your least common denominator is done over on the far left of the abacus. So we can set freshions, such as 3 and 4 fifths Okay. 8 and 1 8, 21, ninth And then addition and subtraction with the common denominator becomes simply adding and subtracting. In this numerator section. So if I were to say something like 21 ninth, minus 10 ninths, I would just subtract one from the tens column, and I'm left with 11 ninth So as are all the fractions done as improper fractions? Or they add fixed numbers. No. So with with improper fractions. When, let's say, we have I'm just making this up with 31 nights. Okay. The question then, is, how do you represent that as a mixed number one of the kind of critical prerequisite skills for fractions is understanding that a fraction is just a representation of division. So this is another way of saying 31, divided by 9 Or 31 one nights. So we have 9 will go into 31 3 times, so I can set my 3 here in my whole number. Place 3 times 9 is 27. I can subtract 27 from my numerator. 123-45-6720and I'm left with 3 and 4 ninths. And so that's converting an improper fraction into a mixed number Thank you. That makes more sense. Now. Yay, I'm so glad. So it actually, you know, having that division background really helps with with doing that, because you're doing division. But you're doing it in a different, in a different way. Right, you're doing it in a in a in a manner that is unique to fractions, and different than you would when setting up a division problem. What you know across the the advocacy. Good question. So I'm not gonna go more into fractions. There's it's because I don't wanna get too deep. Awesome. Thank you so much, John. But we'll do that next time. Yeah, really happy to to share advocates with people. I'm really glad you all are here, and I'm I'm happy to get this little break in my schedule to to do this, to use this fun. Little ancient technology, tool Well, we definitely appreciate you coming and joining us for tea time, and I agree. Everybody said, Thank you. And it's awesome, and chat. Alright, guys, let's wrap up tea time for today. We have oops in the wrong place. There we go. We have our resource site, where everything will be posted as of tomorrow, so you will have the worksheets and any handouts, and the recording posted on the site. As of tomorrow coming up the rest of this month we have a Ph is coming. I just confirmed with her again today. So she is coming next week to go over what's new. And happening with Aph and to fill us in on what they have cause. Everybody loves that catalog, don't we? And loves the website? I can't stand the website, but I'm hoping she can fill us in on things that we may miss on the the website by having it be a little strange February 20 sixth is the deaf plan. Symposium. Come and see us. I'll be there March second is teaching voice over where to start. March. Ninth. John's gonna come back to see us for more fractions, and March sixteenth is spring break, so we will not have a t-time and march twenty-third. We will be in Denton at t ae R. Come and see us there in den If you have any ideas for upcoming topics, the link to the form is in the chat. Drop us a link. Let us know I do check that. And do you take into consideration any suggestions for TV?