 Hi everyone, this is Chih-chou. Welcome to my channel and welcome to another mathematics-related video. And what we're going to do today is I'm going to show you how I go about teaching someone, taking up from a position where they're learning how to count all the way to adding and then multiplication. And that's sort of the direction that I take when I'm teaching just basic introductory level mathematics to people. When you're trying to teach them adding, subtracting, multiplying, dividing, I don't go from adding to subtracting. I go from adding to multiplication. And then once we hit multiplication, I kick it back kick it back to subtraction and division. And then we tie up everything together. And then from there, we move on to how to move around an equal sign, right? And these are sort of videos. There's a lot of videos we've created sort of segments of the process of how to add, how to subtract, how to multiply, how to divide, how to move around an equal sign in the language of mathematics, right? And we've also created some videos in ASMR math as well, specifically one video that we put together where we talked about, we talked about I guess it was about 45 minutes to an hour video, just doing examples and talking about what it means to move around an equal sign, which is basically your first meet introduction to algebra. And it's extremely important. So that video is what we're going to work our way towards, right? But right now what we're going to do is sort of I'm going to walk you through how I go about teaching counting to someone that's already knows the rudimentary stuff. They're just having hiccups, right? Because I'm not really into teaching the language. I'm into getting my students past their hurdles, right? So someone who's just learning how to count, right? That's where we're starting this set of videos on or this video on, right? So we're going to start off assuming that someone already knows some counting, okay? We're just going to work towards getting them past the hiccups. And then we're going to work our way towards adding and from there we're going to go into multiplication, right? Specifically looking at how you can generate the 10 by 10 multiplication table and a video for that we put out a while ago, a few years ago on, you know, we talked about why it's so important to learn the multiplication table and put it to memory really, but it's more than just memory. It's basically becoming familiar enough with it to and use it enough to be able to reference it at will, at random, right? So the 10 by 10 multiplication table is extremely important. That's what we're going to work our way towards, right? And if you want to, you know, bypass the counting and the adding and just a rudimentary multiplication, you can take a look at that video and that goes through the multiplication table of the cemetery within the multiplication table and what the best way is to learn it, right? Which is what we're going to talk about right now about an extended version of that, okay? Now aside from that, let's begin with counting, okay? Now the type of students that I get when I'm trying to teach them counting is basically someone that's already learned one, two, three, and they know at least all the way up to 10 or 11 or 12 or so, right? And what we have to appreciate when we're teaching someone counting is counting is just a language, your natural language applied to mathematics, right? So depending on what natural language you're speaking in English, we go one, two, three, four, five all the way up to wherever we want to go, right? In Farsi, it goes, it changes, right? In Armenian, it goes, and it just continues on. In French, you can do it. In Spanish, you can do it, right? So every language has their own words they use for the specific numbers and that's really dependent on where you are, right? I'm more interested in when teaching someone how to count. I'm more interested in, in terms of someone that's teaching mathematics, to focusing on where they have little hiccups, right? And this process is extremely personal, okay? There are kids in, when they're learning how to count, when it comes to English, okay? Because that's the language I teach in, right? So you have to sort of kick yourself into whatever language, natural language that you're, you're using right now, right? But in English, in general, kids have a little bit of a harder time reaching, going from 10 to 20, because the number 11 and 12 are not derivatives of the number 10, right? So number 1 to 10 are basically just memorization processes, right? So we can write, oops, so we can write number 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Now, when you're learning how to count, or you're teaching someone the counting process, what you have to keep in mind that in the English, English language, each one of these numbers has their own unique name, okay? That is not the case in other languages. In other languages, you count to 10 maybe, and number 11 is in general, if you do a direct translation, is 10 plus 1, 10 plus 2. Some of the languages, that's exactly what you end up saying, right? But in English, 11 and 12 have their unique name, okay? So some kids have a hard time getting 11 and 12 into the vocabulary. After that, we got 13, 14, and all the teens, right? So we have 13, 14, 15, 16, 17, 18, and 19. Now, in the English language, this is really easy to do, right? Because these are all just derivatives of teen, 13, 14, 15, 16, 17, 18, and 19, right? So there's a nice pattern there. And a lot of people are just learning this. In general, they don't have a hard time with it. However, there are times where certain students, certain students that I've had, they have hiccups transitioning maybe from 15 to 16, or transitioning from 17, 17 to 18, okay? So if a student is having a hard time jumping from one number to the next number sequentially, let them go all the way through and then kick them back and test that transition, right? Sometimes you have to make the correction right away. Sometimes you have to help them along, right? Whatever you do, whenever you try to teach someone in general, it comes to mathematics, counting, addition, multiplication, doesn't make a difference, don't try to trick them in the learning process, right? Don't give them questions in general where you're trying to amplify their mistakes, amplify their hiccups, right? Make the hurdle bigger, right? What you want to do is eliminate the hurdle that they have. Sometimes it requires you to let them make the mistake until you get to a certain number and then come back and correct it. Sometimes it requires you to stop them when they're trying, when they make the mistake and get them to repeat that. Sometimes you have to start back up here. So if they're having a hard time going from 15 to 16, right? Don't necessarily stop them there. Sometimes let them go all the way to 19 or 20 in general, where I take them to. Sometimes kick them back to 13 and get them to start counting from 13 all the way up, right? So practice that, the location where they're having a hard time counting, right? From 19, what we end up having is a pattern that emerges when you're doing counting, which basically sticks all the way up to infinity if you want to go to, right, forever and ever and ever. And the pattern is basically, from 19 you go to 20, right? And then you have 21, 22, 23, 24, 25, 26, 27, 28, 29, and then you're back to the next tens, right? The 30 and 30 starts off the same way, right? 30 goes 31, 32, 33, 34, 35, 36, 37, 38, 39, and then you're into the 40s, okay? Sometimes this requires a certain amount of time. It takes time for a kid to be able to get their counting down right. The way I end up teaching this, if the student is just getting into counting and they've had some hiccups at the beginning stages, right? I get them to count from 1 to 10, okay? It becomes easy to do because we have 10 fingers, right? So in general, when I'm getting them to count, what I end up doing is I tell them to hold up your fingers and to actually go through it. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, right? We do this a few times. We do it enough until they can do it without their fingers, okay? And then we're going to the 11, 12, okay? Get them to familiarize themselves with 11 and 12, okay? So the next set of counting you're going to do, you're going to go 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. So you're introducing them, letting them know to introduce another hand into their counting process, right? Once they can do 12 without their fingers, you kick them into the teens, right? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, okay? And then we do 20, okay? I never teach it all the way to 19 and get them to practice all the way to 19. I get them to 12, teach them the teens all the way to 20. So the next time that we're counting or the next step in the teaching process, right? I mean, it may be during the same session and maybe in a follow-up session or two sessions later, right? Depending on how fast the student is progressing, right? I get them to count to 20. And I do this often, right? Because if they can count to 20, they can count to whatever number they want as soon as they learn the hundreds and the thousands and stuff like this. And we'll talk about that, okay? So I get them to go 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, okay? Without their fingers. Once they're comfortable with that, I teach them all the way from 20 to 100, okay? So what we end up doing is we do 20 and then 21, 22, 23, 24, 25, 26, 27, 28, 29, and then you teach them the number 30. From there, and I usually try to do this in one session, maximum two sessions, okay? Preferably, I try to teach them from 20 all the way to 100 in one session, okay? When you're practicing a little bit of time all the way, counting all the way to 20, and then when they're really familiar with it, you lay it on hard, right? So you go from 20 to 29 and then you teach them 30, okay? That's a new word, right? And then you say, hey, the process continues, 31, 32, 33, 34, 35, 36, 31, 32, 33, 34, 35, 36, 37, 38, 39, and then you go to 40, okay? Once they're, you can see the lights shining in most students, once you start teaching them this, right? Because they realize as soon as they know this and they already know that, then they know how to count all the way to 100, right? So you keep on doing this until you get to 100. Now, once they go through 100 once, okay, you've gone through the whole process, I get them to count from one to 100 every time I meet them until they're 100% comfortable counting from the number one to 100, okay? Where most of my students that I've encountered have hiccups are, as I stated, in the teens, okay? Because from one to 12 is just straight up remembering new words, okay? From 13 to 19 is a pattern and they have to bring two words together, right? The number they already know plus 10, okay? So students in general have a hard time in the teens, okay? Once they learn the 10s, right? 2021, where they're connecting again two words together, learning a new word, 20 and then connecting it up with one, right? So 21, 22, 23, and then you teach them another one, 31, 32, 33, and so on and so forth. Where students end up having hiccups when it comes to learning how to count are transitioning from 29 to 30, 39 to 40, 49 to 50. So what I end up doing when I'm teaching them how to count, I focus in on where they're having a problem. And in general, that's where the problem is. If the problem lays somewhere else, please focus on that as well. And the way you can focus again is what we talked about earlier, where you can let them either count all the way to a specific number you want to and then go back and correct them. You can correct them right away and just ask them to repeat the hiccup, the problem spot or get them to start off at a sort of a node, right? So if they're having a hard time with between 24 and 25, you can get them to count 24 to 25 multiple times, right? Or you can kick them back to a node where you've already moved on from the teens and you're hitting at about the 20, right? At an important point where the language changes, right? And then you go, okay, start from 20, you go 21, 20, 21, 22, 23, 24, 25. And if they have a problem, you say, okay, say that again, 24, 25, or let them count all the way here and do it again, right? When they're counting all the way to 100, the hiccups usually occur from the nines to the tens, right? 29 to 30, 39 to 40, 49 to 50. So I tend to focus on those. So keep your eye out. Keep your, listen for the where the student might be having a problem, right? And once they get to 100, okay, then they know how to count to 200. They know how to count to 300, right? It's just repetition of this, 101, 102, 103, 120, 200, 135, right? So if they know 35, the 100 is just another word, right? So they're tagging on another word in front of words they already know, right? And most students catch up pretty fast with this. Where they end up having a hiccup is the transition from 199 to 200, 299 to 300, 399 to 400, right? And again, I focus on those things. I don't get students to count from 1 to 1,000. That's a waste of time. It burns out the students. It's, it emphasizes too much repetition, right? Because if they can construct the number, the word, you don't have to get them counting all the way up to the word, you can start giving it to them at random, right? So from 100, right, you're really teaching the pattern, right? From 1 to 100, you're teaching them how to count and become familiar with it so they can do it rapidly, right? From 100 to 1,000, you're teaching the pattern. You're teaching them to add on the extra word in the front to make the word whatever it is that they want to say it is, right? So once they know how to count to 100, what I end up doing is I teach them the 100 counts, right? And then I go back, I start giving random numbers for them to say. Sometimes I introduce the random numbers when they reach 100, right? So when they count from 1 to 100 and it doesn't take it, it's very rapid, right? Start throwing down some numbers in front of them randomly. See if they can say it. If they can't say it, you know you still need to continue doing the count. You know you're finished teaching them or getting them to count from 1 to 100, right? Every time you meet them, when they can read off 90% of the random numbers that you show them, right? So that's one way you can test to see if a kid, if a student is ready to move on to the next level. And once they reach that state where they can randomly pick off any numbers, I start giving them random numbers in the hundreds, right? 259, right? 345, 899, right? So I start dropping down random numbers. If they're having a hard time saying what those numbers are, go back and explain to them how the 100 counts go, okay? Now once you know how to count into the hundreds, the only thing left for you to do, if you want to teach them extremely large numbers, is introduce the new names, the thousands, the tens of thousands, right? The hundred thousand, the millions, the billions, right? But you're basically going with the three digit markers, right? So let me show you how that works. Nice sympathy. So once a student knows how to count to 100 and they're familiar with the hundreds, right? Then what I end up doing is I introduce them, the thousands, right off the bat, and then I show them the pattern, which is the same pattern for the hundreds as it is for the thousands, right? So basically, if they know how to count to three digits, okay, I introduce them the thousands, which is the fourth digit. And I explain to them that counting or mathematics in general, and this is something that's extremely important to do, is constantly to remind the students that mathematics is extremely visual. So for them to use the pen and paper, use the symbols that we have in the language of mathematics and whatever natural language we have, to make the reading process easier, right? To let their minds subconsciously appreciate what's happening with the language of mathematics, right? So when we get into the thousands, almost right away, I introduce the comma, right? And I let them know to do a little separation so they're visually, automatically their subconscious realizes that they're in four digits, right? And once they get into the thousands, you can guess how this goes. You get them to randomly read some thousand numbers. So I don't necessarily get them to go thousand and one, thousand and two, even though I do sometimes. But in general, usually when a kid, when a student has learned where we've reached the level where they're into the thousands, then they understand that concept very well, right? So what I end up doing is I usually just kick it into five digits and six digits right away within minutes, really, right? So these numbers here, these are the thousands, okay? This is your hundred, that's your tens, and those are your single digits, right? In general, I don't really need to explain that, right? Once we reach this level of the thousands, right? If the students receptive to this, right away in the same session, I teach them the millions and the billions, okay? Because these are just two new words or three new words they're adding to their vocabulary. And in general, students that I've dealt with, they understand, they know the words a million or a thousand or a billion. They've heard it through their social networks, right? They've heard it in school, they've heard it in media, right? So the new word is not necessarily new to them. What I end up teaching them is, and what they really need to learn is, is how to put it all together to read off numbers, right? So after this, we got obviously the millions, right? You have your billions passed it. I don't have enough room right now to put it in, but basically it's the same concept. You put three little dashes there, show them that. And what I end up usually doing is just placing random numbers on the sheet that we're working on, let the pen and paper do the work for you as well. And that's not just for students, that's also for teachers, that's also for people, for parents, right? Or if you're helping a sibling learn mathematics, right? Or helping a friend learn mathematics, right? You teach them the millions, you teach them the billions, and then having this up, you start dropping numbers on the sheet, right? Start putting random numbers on the board. 25, 375, right? Start off with the low numbers that we know, right? And then put that number on. Don't put the commas on, right? Let the student do the work, okay? Let the student realize that they have to put a comma here. And if they're not putting the comma there, they're having a hard time reading it, then tell them to put the comma there. If they're able to read it right off the bat without the help of the comma, without breaking it down, then don't emphasize this yet, okay? Only start emphasizing these breakers when you get to really large numbers, okay? Don't break the kid's pattern of thought. If they're having a hard time, introduce this, right? If they're not having a hard time, kick it up to higher numbers. Do that. See if they can read that. 375,679, right? 12,070, right? If they can't read that, tell them to look above and see where the comma is and to break it up, okay? And in general, they know how to do. Some students I've had, the comma when they're placing it, they make the mistake of going this way. This one's symmetrical, it works, right? But if you give them a number, let's say again, with five digits, right? Let's say we had, let's say we had 75,764, right? And your students having a hard time saying this, reading it? Tell them to put the comma. What I've noticed is some students start off putting the comma here. They think the three-way, the separation can occur from here, which it doesn't, which is something that you're going to have to end up correcting, right? So if they put the comma here, just tell them no. You're always going to count from this side, right? From your right side going this way, okay? That's one place that hiccups appear as well. But if they can't read it, put your commas in, right? Once they know how to read the tens, the hundreds, the thousands, the hundreds of thousands, kick them into the millions, kick them into the billions, right? And once you take them to this level, do not add the comma when you're asking the question. Get them to do it themselves, okay? So put that number down, see if they can read it, okay? Rare where I've had a student who's able to read this, or even an adult who's able to read this without putting the markers on, right? Let's put the markers on. Not there. I almost put the marker in the wrong place, right? Watch your students. It happens. Now this becomes easy to read. 76,777,074, right? Now, once they know how to read these numbers, and don't give them extremely hard numbers to read yet, right? What you need to do is start not necessarily trying to trick them, but start giving them numbers where they're similar, where they have to sort of pause and think about it for a second, right? So for example, you can give them these numbers here. 720, 702, 712, right? So you constantly need to push your student to challenge themselves, right? To put all this information into muscle memory, into their minds and make it automatic, right? And sometimes students, learning mathematics, this is something that a lot of students repeat like a mantra, right? Which is basically a social construct where they say, oh, math is hard. This is so hard. Math is hard. This is so hard. And my reply to them is, in general, this is one of the things that I use to motivate my students to learn, to make them appreciate that this stuff is not hard, right? This stuff is just new, right? And if I work with the student for a long time, and we've progressed rapidly or not, right? As long as we've progressed from where we were, I remind them that when they say math is hard or this is hard, I remind them that they used to say the same thing about a previous concept that we're working on that they find really easy, right? And sometimes I give them a question from that specific concept and get them to do it. And they say, oh, that's too easy or that's really easy. Or I mentioned that was really easy for them. And once they agree, you say, well, there was a time where they thought that was extremely difficult, right? But in general, if you're new to working with a student and they're showing signs of stress where they're having a hard time with a certain concept and they're struggling with it, right? One of the stories that or one thing that I mentioned to them to get them past this hurdle is that if they remember learning how to walk and there isn't a single student that I've had that remembers the time where they were learning how to walk. And I tell them that, listen, you don't have to think about that when you're walking, you have to put your left foot in front of your right foot and then so on and so forth, right, left, right, left, right, left, right, left. They just walk. And sometimes they end up falling and all they got to do is get up and keep on walking, right? That process is the same as learning this information, okay? It's new to them. They struggle. If they're still not sold on this concept that even walking was hard for them when they were first learning it, ask them if they've ever seen a kid, an infant, a toddler trying to learn how to walk, right? Some students that I've had, they have siblings, they've seen that happen. Some students don't, right? Or haven't had it. But no matter the reply, I go, listen, next time, look at your sibling, look at a kid, look at that toddler when they're first learning how to walk. They usually pull themselves up on some kind of table, some kind of ledge. And the first thing they end up doing is they end up standing and they're very wobbly, right? And if you've ever seen a toddler trying to learn how to walk, when they stand up, they're ridiculously happy, they're wobbly, they get so happy, they lose their concentration and fall down, right? And then they go crawl over to wherever they had the ledge, they stand up and they do it again and again and again and again. And then slowly they start to figure out that walking means moving your legs. And what they end up doing is they bounce, bounce, bounce, bounce, until they can put one leg in front of another leg, right? So they wobble, wobble, wobble and then go boop. And once they do that, like a child does, right? They get extremely happy, they lose their concentration and they fall down, right? They do that a few times. They get up, put one leg in front of the other leg or one leg in front and they wobble, wobble, fall down. And then slowly they figure out that, hey, I can't keep on putting my right leg forward because the first thing they do is they try to move the same leg again because they moved. So they do the right leg again, boop, they fall down, right? It takes them a few tries or a few days or a few weeks until they figure out that, oh wow, I can't go right leg and a right leg again. I got to go right leg and then left leg. And the progression from then figuring that out to learning how to walk is ridiculously fast, right? And I end up telling them the story, my students, when they're trying to learn this information or any other information, and this is a lot of my students that I worked for for a long time, they've heard this story that I tell them and it triggers something in them where they realize that what they're working on is not hard, okay? So this is the concept, this is how I go about teaching counting, okay? And it's very basic for me, like it doesn't take long. I don't want to say if it's basic but in general this process doesn't take long working with the new students if they're, they already know the numbers from one to ten and we're just adding on a little bit of information, right? And sometimes I, again I get them to use their fingers, sometimes I get them to use tick marks on a piece of paper, right? Maybe group them in fives, group them in tens, group them in fives is easy, put four tick marks, right? One, two, three, four, you put a line over it and that gives you a five, right? Sometimes I use that, in general I don't have to go down to this state, but sometimes you do, sometimes you do. And again this is extremely personal teaching someone how to, teaching someone anyway in general is extremely personal, but teaching someone the language of mathematics becomes very intimate in general because there's a lot of, when students that I've encountered, they hit an obstacle, sometimes it's a little difficult getting past this obstacle, especially for mathematics. With physics I haven't encountered that too much because physics it just uses the language of mathematics to teach them physical concepts, right? The mathematics applied to the physical world, right? In general it's with mathematics, I haven't figured out why that is. I don't know if it's because of a society or because of the new language they're trying to learn because I've never tried teaching anyone a different language, so I don't know if this sort of struggle exists when people are trying to learn a natural language. I know for me it was a little frustrating learning English for the first time, but learning mathematics can really throw some people off, right? And that makes it extremely intimate, extremely personal, so you have to have patience when doing this type of thing, especially when you're teaching them counting, because that's their first exposure to mathematics and what you want to do is eliminate the stress for someone when they're trying to learn math, so help them along, don't give them any trick questions until you get to the end where you're trying to test their ability to recognize the minor differences between the numbers, and that's the process I use to teach someone how to count. I hope you find this useful. What we're going to do now is we're going to go into the process I go through to teaching someone how to add. Let me take this guy down and we'll talk about that. Our student knows how to count into that at least all the way from 1 to 100. Hopefully into the hundreds, thousands, hundreds of thousands or millions, depending on how fast they've progressed, but once the student knows how to count from 1 to 100, I start introducing them to addition, and in general we do the single digits, so I write down basically 2 plus 3. And if the student's having a hard time doing this, I get them to do it using their fingers. I say, okay, hold up 2 on this one, hold up 3 on this one, how many do you have? And they go 1, 2, 3, 4, 5. And I do this a few times if they're in that state. Once they're past the finger state, once they, if you're doing 4 plus 3, what is that? 4 plus 3. 5, 7. As long as they can do it all in all the single digits without their fingers, we can move on into the double digits. And the double digits is usually where it's harder to do with the fingers. That's why I introduce, I get them to do ticks on paper. So once they hit this stage, what I give them is 8 plus 9. Numbers that when added up, kick them into the double digits, right? If they can do it with their fingers, right? If I, you know, tell them, okay, use your fingers. So they go 1, 2, 3, 4, 5, 6, 7, 8, right? Or they start off with 8. That's in general what I do. But if they're at a state where they're still using their fingers, they go 8 and they've got to add 9. They've got to go 1, 2, they have to keep in mind that's 10, 3, 4, 5, 6, 7, 8. So they have a 10 plus, oh, 9, right? Plus 9. So that's 17. They keep that in mind. Kids usually have a harder time with that. Or I get them to start off with 8. So I say, okay, you're at 8 already, add 9, right? So they go, I'm at 8. So I go 9, 10, 11, 12, 13, 14, 15, 16, 17, right? That's their 9 being added. So that's two ways you can do it. The third way I do it is I get them to do ticks on a piece of paper, right? So if we go 7 plus 8, right? They can start off at 7. And then they go 8, 9, 10, 11, 12, 13, 14, 15. That's 8 numbers. Those are the ticks that we talked about in counting that you can get them to group 5s, right? So this becomes 15. Or some students that I've seen, they do the whole thing, right? They go 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 3, 4, 5, 6, 7, right? And then 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, right? And when they do this, most of my students don't stick doing this for too long, right? Because they realize that it's too hard visually to see what's happening and really emphasize the visual when you're teaching counting as well to your students. Right now we've got 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, right? If your student does this, show them how it's easier to do if they do 1, 2, 3, 4, 5, 6, 7, that's their 7, right? And then 1, 2, 3, 4, 5, oops, 5, 6, 7, 8, and then get them to count that way, right? So what you're doing is, I should do that more clearly, right? So let's do it more clearly, 1, 2, 3, 4, 5, 6, 7, 8, right? So we have 5 and 5, that's 10, 2 and 3, that's 15, so the answer is 15, okay? It's again very personal, very tricky, depending on the students. I'm even making mistakes using ticks, right? So your student is going to make mistakes doing using these tick marks. Just tell them to cross it out, do it again if they're having a hard time with it, okay? So when you're teaching adding, what personally, when I'm teaching adding and it might work with you as well if you're teaching your student, right? Start off with single digits. Don't get them to go past the single digits yet, so you're doing the small single digits. When you get into the bigger single digits, right, get them to use their fingers, get them to start off with the first number and add the next number, or get them to use tick marks, okay? Once they're comfortable with this, start adding the teens in there, right? Start off with the teen, right? 13 and then add 6, okay? In general, the easiest way to do this is, is the method where you say, okay, you're already at 13, add 6, right? So they go, okay, 13, 14, 15, 16, 17, 18, 19, and they write down 19. It's rare for my students that I've worked with, for them to use tick marks when they're doing double digits, starting with double digits and continuing on, right? In general, that's the way they end up counting, okay? Once you've hit this stage, show them two double digits added together, 13 plus 17, okay? Now make sure you have enough time in your lesson or in your day and your student is functional enough to be able to do this, right? Because you need time to explain what the process is here, okay? And actually, I don't usually do carry-overs yet, right? So I'm doing the low teens first, okay? And I'll explain to you why I don't do that yet, right? So when a student is trying to do this, doing it with the fingers is harder. It takes them a while. They will try. They might do it with tick marks, but it's rare, right? Once they struggle with it for a bit, and some students will be able to get the answer quickly, some won't. If they get the answer quickly, give them harder ones, go into the 20s, go into the 30s, go into the 40s, right? If they're having a hard time with it, basically show them the addition, the stacking method, right? So I basically show them, you know, I tell them instead of writing it like this, visually, it's easier to write them on top of each other. So we basically go 13 plus 12, and you draw a line, right? So that's what I end up showing them. And then I tell them, all they need to do is add these two guys together, put the number there, and add those two guys together, put the number there. And that's the reason I don't start off with anything that you need to, when they're added, they give you a 10 or more where you have to carry it over, right? So in general, when you reach this state, they already know how to do these, right? So this becomes easy, this becomes five, and then one plus one is two, right? And we have videos out, I put some videos out for language of mathematics for this on how to add numbers together, larger numbers in general, I didn't kick it down to this level, right? I usually start off with bigger numbers, okay? But we've got a whole bunch of videos in the language of mathematics showing this, or at least one video showing this, right? So once they figure this out, and they should, fairly rapidly, I give them numbers that you have to carry stuff over, right? 27 plus 34, right? And in general, whenever I'm doing this, at the beginning, I write them stacked like this for them to practice. Later on, what I do is I put them in a line like this, and get them to stack it because some students need to have a hard time appreciating right off the bat that you're flushing things to the right, okay? Once you get them to do this, then seven plus four, get them to write the answer, right? So seven plus four is 11, and students usually in general pause a little bit in this process, they go 11, they really don't know what to do until you show them how to do it. Don't let them struggle with it, show them right off the bat, you go okay, seven plus four is 11, so you put your one here, but you can't put the other one here because that's in the tens, so what you do, you put it up top, right? One plus two is three, plus three is six, okay? So the answer is 61. Students will appreciate this, give them a whole bunch of practice, work with them, show them more examples, right? 56 plus 79, okay? Once you show a few different examples for them to do, and you get them to do it, make sure you stay below 100, and then you could click it up to numbers that add up to be above 100. And again, this process here, I'm going through it fairly rapidly, right? This process here might take a day, might take a week, might take a couple of weeks, okay? Depending on how fast the student is absorbing the information and how many lessons you've had, and how many practice problems they've done, okay? But once they're comfortable sticking within the two-digit range, being able to kick the numbers up, then you can kick them into numbers that add up to more than 100, right? Nine plus six is 15, and you bring the one up, right? Five plus one, or one plus five is six, six plus seven is 13, and you can put 13 down here. From here, what I end up doing is given of gigantic numbers, okay? I don't go up slow from here, right? So from here, let's take this down, let's do some numbers, and I'm going to give you some of the patterns that I show you how to do, right? And one of the things, before we move on, one of the things I also do, when we're doing this, your student has to read every number that you're adding and the result, right? So get them to say 13 plus 12 is equal to 25, 56 plus 79 is equal to 135. That helps them not forget how to count numbers, not forget how to read numbers, right? And gets it into their muscle memory, mental memory, okay? Now, once my students in general learn how to add two-digit numbers together, I start giving them numbers in the hundreds, and then right away kick them into numbers that are into the tens of thousands or hundreds of thousands, right? As long as they know how to count those numbers, right? So for example, I would give them something like this. And what I end up doing is when we reach this state, I don't stack it for them. I get them to restack this, put it in the proper position so they can add it, right? So they take this and they go, oh, two, five, seven, plus six, seven, four, right? And the process again, it's quite easy. Seven plus four is 11. You put the one in the bottom and the one up top. Five plus one is six, plus seven is 13. You put the three here, you put the one up top. One plus two is three, plus six is nine, right? And the student has to read this number as well. And then I give them numbers that don't have the same number of digits enough, right? Seven, four, seven, five, plus six, four. Let's go for five. Okay. Now, one thing I've noticed when students are learning how to add, okay, when you need to stack these things, they end up stacking them here. They go, they write it like this. I'm going to write it incorrectly first, right? They go, seven, four, seven, five, six, four, five, right? Sometimes they do it that way. Sometimes they're all over the place. In general, they're all over the place. They would go something like this, seven, four, seven, five, and then six, four, five, right? So visually, it's hard for them to line things up, right? It is extremely important to correct them when they're doing this. Make sure they're flushing everything to the right side, right? So six, four, five. The whole purpose here for us is to take stress away from the student learning this and doing this, because this can be a little bit repetitive for the student, right? Because you have to get them to do a few of these before they're very comfortable with it, so really important to help them in that process by getting them to line things up properly, right? And in general, when they're, initially, they write both numbers, but students usually catch on pretty fast that all they have to do is just take that number and put it below this guy. If they haven't, save them time. Tell them that, hey, you could take this number and put it here, right? And put the addition here. You don't have to rewrite it, right? And then you add this, five plus five is 10. You put the zero, you put the one, eight, 12, one, 10, 11, one, and you get an eight, right? And get them to read this number. If they're having a hard time reading it, tell them to put the comma in there, right? Once you give them a few of these things where they're adding double digit numbers, three digit numbers, two, three digit numbers, two, four digit numbers, a four digit number and a three digit number, give them numbers that are larger and vary in the number of digits that they have, right? For example, seven, five, six, four, three, two, plus five, six, four, three, plus five, zero, zero, one, right? Get them to do numbers like this. Get them to read it, right, when you write it down. Before they begin, you say, okay, read this number. In general, they need to put a comma, 756,432. Get them to move their fingers across if they need to. Put your comma, 75643 and 5001. In general, students don't have a hard time with four digits. Get them to add these by stacking them. Usually, my students write this number here because they're not comfortable at the beginning to realize that this is five digits, so they can just go to the five digits here and stack them, right? So this is usually what they end up doing. Three, four, six, comma, five, seven, okay, and one, zero, zero, five. Two plus three is five, plus one is six. Three plus four is seven, plus zero is seven, and a lot of students actually say that, right? Seven, let them say it, okay. Six plus four plus six is ten, you put the zero, you put the one up top, get them to say it, put the one up top, put the two up top, if there is a two, right? Three, five, six, whatever it is. One plus six is seven, five plus five is ten, so that's 17. Once you start doing this, the students will do this. One plus six is seven, seven plus five is 12, 12 plus five is 15. That's what they'll do. They'll go in order, let them do that. Slowly teach them the grouping, right? That they can go five plus five is 10, six plus one, one plus six is seven, 10 plus seven is 17, right? Move the one up, one plus five is six, six plus seven is 13, put the one up, one plus seven is eight. Get them to read this number. If they need to, and the odds are they will, they need to put the comma in, 837,076, okay? Now, once you've reached the state where you're giving them random numbers, and it doesn't have to be just two numbers or three numbers, give them four or five numbers to stack, right? They don't necessarily need to be this big, but give it to them anyway, right? Because that way when they do one problem, you've tested them the equivalent of five of the smaller problems, right? So they're getting a lot more practice in without even in general realizing it, okay? So give them like two or three large numbers, three numbers, four numbers or five numbers, get them to line it up properly, get them to read every single number and the result and put the commas in the appropriate places. Once they're able to do that, give them numbers that force them to quickly distinguish between one number and the other number. We showed this set of three numbers in the counting section, right? We went, get them to add 720 plus, what was it, 702 plus 712, right? Get them to add those numbers. Once you reach this level and they're reading it properly, they're adding it properly and they're reading the result properly put in the commas in the right places, we're going into multiplication, okay? Once you reach this level, we can start teaching them planting seeds for them to learn multiplication. So let me show you how that works. We've talked about counting. Throughout that whole process, you have to help the student more, get them to feel comfortable, alleviate any stress that they may have. Once they're comfortable with counting, get them into adding single digits at first, double digits, triple digits, digits that are into the hundreds of thousands or millions, get them to add multiple numbers together, get them to stack it properly, put the commas in the right place, get them to read every single number, get them to make sure to carry forward not just ones when you're giving them two numbers to add, when you give them four or five numbers to add stacked up together, the number that they're carrying to the top is general or it could be more than a one, more than a two, could be a three or four, right? Get them comfortable with that. Once they're comfortable with adding, start showing them how to add numbers that repeat. So for example, get them to add the following number, 999 plus 999 plus 999. Get them to add that number. Okay. You're planting seeds right now. Once they do that, emphasize to them, hey, look, that was the same number added three times, right? Get them to add single digits, okay, but repeated numbers, right? Repeated digit. So get them to add three plus, three plus, three plus, three plus, three plus, three. What is that equal to? Right? Do a couple of these. Get them to do it manually. And it's going to take them a little bit of time to do in general, right? Because they don't know multiplication. So you're going to go three plus three is six, six plus three is nine, nine plus three is 12, 12 plus three is 15, 15 plus three is 18. So you have six numbers, six threes added together gives you 18, right? And you write down 18. Now you're ready to introduce them to the concept of multiplication. Okay. Once you show them a handful of these. And this is the process of, we've talked about this. We've got an ASMR video out there. I believe anyway, talking about what multiplication is and what not. I believe anyway, if we don't, this is it. This is the process I use to teach multiplication or this is the process that really I found that gets kids to appreciate what multiplication is because you're getting them, you're helping them to do things faster, right? So this is basically what I end up telling my students. Now in mathematics, one of the things that mathematicians do is try to simplify things, right? And I usually tell my students that mathematicians are the laziest people on this planet because what they're trying to do is try to take shortcuts, make things faster and faster. They're so lazy that they want to take the whole world and be able to quantify it into one equation, right? Now is that mathematicians that try to do this or physicists that try to do this? I tell my students as mathematicians, right? They try to look at systems and figure out what the easiest, simplest way there is to understand the system, right? And that's in general physicists that are doing this, right? But it applies to mathematicians. So what I end up usually telling my students is that multiplication is just an extension of addition because mathematics is really built on five axioms, five rules, right? And everything else is layered on top. And this is one of the core, core teachings of mathematics where multiplication is really just an extension of addition. So to explain to them how this works, I usually use the number two because most kids are pretty familiar with number two, right? So I go, okay, what's two plus two? And they say four. And then I go, what's two plus two plus two? They say eight. What's two plus two plus two plus two, right? And they say, did I say eight on that one? That's a six. This is an eight, right? Two plus two plus two plus two plus two, right? Ten. And I go, well, what's two added together 100 times? Right? So we've got two plus two plus two plus two plus two dot dot dot plus two plus two 100 times, right? Sometimes the students have to think about it. Sometimes they give the answer right away, right? And they go 200. Now it's really important to make them understand the student appreciate that it's going to take a lot of effort to write down two 100 times. If they don't appreciate it, tell them to add two together 1000 times, right? Just imagine how much space it would take, right? So mathematicians, what they ended up doing is they made life simple for us. What they did was add a new symbol, which basically states, if you're adding the same number of multiple times, then all you need to do is take the plus sign, right? Rotate it 45 degrees. It changes to multiplication. And once that happens, all it means is, if you have this number two here, and you do this, and if you want to add it 100 times, you're going to go two times 100, which is 200. So the multiplication symbol is really a representation of you taking a number and adding it together this many times, right? So for this one, it would be two times two. This one would be two times one, two, three. This one would be two times four, two times one, two, three, four. That's how many times you're adding it together, right? So if we're going to write down the multiplication version of this, this would be two times two, two, oops, two times three. Two times four, two times five, two times 100, right? Once they know how to do this, once they appreciate what this is, in general, I start off with simple numbers, right? You're starting off with single digit numbers. You're going to go five times four. Just throw down some simple concepts, and we're not doing this right now to teach them the multiplication table. Right now, at the beginning stages, the process is to teach them what the multiplication means, represents. We're not trying to get them to memorize the multiplication table yet. We're going to do that as soon as they appreciate what this concept is, right? So two times four, if they don't know it right away, get them to add four fives together, right? And that's sort of the process, initially, when I'm trying to teach someone mathematics, trying to teach my students mathematics, is get them to do it through addition, right? And they have to do that initially when they're doing this, right? So you go five plus five plus five plus five, 20, right? Five times four is 20. Once they hit this level, where they're able to do very simple versions of this, that's when we start talking about the multiplication table. So let me set up the 10 by 10 grid here. And again, we have a video out there showing the 10 by 10 grid, how to do multiplication, right? But we're going to go through it right now. I'm going to show you the exact process I use to teach my students the multiplication table, because once they've reached this stage, right? I drop a little bit of hint on how to multiply 99 by three, it would be the same as adding 399s together, 399s together, right? But I sort of drop a little hint for them, for them to appreciate that what we're about to learn is going to be applied here, okay? So let me set up the grid here, take this guy down, and then we're going to go through the process of doing the multiplication table, okay? How I go about anyway, teaching the multiplication table to students. So now that the student sort of appreciates what multiplication is, which is just basically an extension of addition, right? Really important to emphasize this. Multiplication is an extension of addition. And if they don't really appreciate it yet, they will by the time you're done teaching the multiplication table, right? So in general, you would give them simple single-digit numbers at random to multiply, right? You'd go two times three, right? If they need to, get them to write it out, right? Two plus two plus two, that's what two times three is, which is equal to six, which is equal to six. These guys are equal, right? Two times five, right? It's two plus two plus two plus two plus two, which is ten, which is ten, right? Once you're at this stage, right? What you can do is teach them the multiplication table, but one piece at a time. Don't lay out the multiplication table yet. I usually start off with the number two, right? So this is what I end up doing. I go, what's two times one? And get them to fill it out. Two. Two times two. Two times three. Two times four. Two times five, right? So in general, with my students, I actually write these down and they fill in this spot, right? Two times six. Two times seven. Two times eight. Two times nine. And two times ten. Get them to fill out. Four. Six. Eight. Ten. Twelve. Fourteen. Sixteen. Eighteen. Twenty. The reason we're doing this is because this directly links up to them with the addition, right? Because all they have to do is just add two to the previous one. And they'll figure this out really fast. Like really, they'll figure it out super fast. So they'll go four, six, eight, ten, twelve, do it that way. After the number two, in general, I teach them the number five and then the number ten. So I do the five multiplication same way, right? If you want, we'll do this in red. So I do the same thing, but I do it with five. Where should we write this? Five times one. Five times two. Five times three. Five times four. Five times five. Five times six. Five times seven. Five times eight. Five times nine. And five times ten. Equals, equals, equals, equals, equals, equals, equals, equals and equals. Get them to fill it out. Do it with the tens as well. Because the tens, it takes, it's weird because initially most kids don't really appreciate when they're multiplying what the tens, all they got to do is add a zero at the end of whatever number they get. But once they figure it out, their speed of Gonzales with it, okay? So get them to the tens as well. Sometimes when I'm teaching this at the end, I like throwing in five times 11 or two times 11, right? So I add it here at the bottom. Five times 11. And most students pick that up as 55, easy, right? Or five times 12. And they go 60, okay? Once we reach the state, we're ready to create the multiplication table. So let's create the multiplication table right now, okay? I'm just going to lay down the table here. And then we're going to go through it. I'm going to show you how I get them to fill out the table. And it's not just a one-time process. The multiplication table is, it takes a little bit of time for students to learn, right? A lot of students that I have worked with when they enter high school in grade eight, they don't know the multiplication table. That's how bad our current education, math education system is in Canada, United States, okay? So what I get them to do is to learn the multiplication table. And they have to be able to generate it fairly rapidly. They have to know it well, okay? So let's create the table here. And let's write down the numbers here. So we got one, two, three, four, five. Let's put number one here. One, two, three, four, five. We got there. One, two, three, four, one, two, three, four. Yeah. So I'm going to put that there. One, two, three, four, five. Yeah. One, two, three, four, five, six, seven, eight, nine, 10. And then we're going to put one here. So what we're going to do, one, two, three, four, five, six, seven, eight, oops, nine, and 10. Then let me put a grid on here. Let's do it with the red. Look at my, this guy. So let's do this here. Actually, let's do it like this first. So we've got our multiplication table up. Now, when teaching multiplication, you're basically going to be getting the student to transfer this information into a table so they see it visually how it plays out. And when teaching multiplication, I usually put a multiplication here so the kid becomes familiar with the symbol. When doing this, I either get them to go across one row first or down one column first. So if we're doing the two multiplication table, I get them to do this and I explain to them that this is basically the way they can read it as two times one is two. Should we do this in blue? Let's do it in blue. Now, keep in mind, if you have a multiplication table like this to grid up, make copies of it, the blank version, right? Because you're going to use a lot of these. It takes a while for most people to learn the multiplication table. Really important. This is one of the main places where I tell my students, if they don't know the multiplication table, by heart, they have to go back and learn the multiplication table. In general, those are students that I meet just coming into high school when we're straight out. I'm explaining to them, I'm expecting them to learn the multiplication table. If they're elementary school, if they're younger, tweens or pre-tweens, if they're a kid, spend the time required for them to learn this. It's going to make their lives a lot easier. So in general, this is what we end up doing. Once I've gone through this, I usually do this for the twos, the threes, the fives, the tens, the fours, the lower numbers, and the six and seven in eight and nine kids have a harder time with. Now, to teach them that, once we reach that state, let me remind you of this one too. We put out a couple of videos regarding multiplication, where one of them was the finger method for multiplying nines. So you can take a look at that video and see how that works. The nine multiplication is easy. You basically do this. Let me show it to you. It's basically information from the video. So the nine multiplication, all you end up doing is holding up your hands. And whatever number it is, let's say you're multiplying three times nine. So you go one, two, three, you pull this down, and whatever result you got, which is two, this counts as the tens, so 27. If you're going to go seven times nine, you're going to go one, two, three, four, five, six, seven times nine. This is the table. So this is 63. If you're going to go nine times five, nine times five, you're going to hold up your hand. You're going to go one, two, three, four, five. So nine times five is 45. My fingers are all red because of the red marker. So 45. That's what nine times five is. You can take a look at that video if you want more examples of how to do that. The other numbers that students have a hard time multiplying are six, seven, eight, nine. And there's another finger multiplying technique that a student might show me how to do. And we put out a video for that as well. And if you want to multiply, let's say, seven times eight, which is one of the ones that gives people a hard time. Basically, the method is this. You start off, each finger, the pinkies are the sixes, six, seven, eight, nine, 10. So six, seven, eight, nine, 10. So we're going to multiply seven times eight. We're going to go six, seven. That's the seven one. And eight is going to be six, seven, eight. You close these guys off. The ones that are facing away from you towards the pinkies counts as tens, including the two ones that are touching. So this is 10, 20, 30, 40, 50. Right? That's your five fingers. Those are the tens. That's 50. And two, the rest of the fingers, two times three make it six. So seven times eight is 56. Okay? Let's do another one because it's a little tricky, but you can definitely take a look at that video if you want to know how this works. Right? Let's go six times seven. So here's the six, the pinky. Seven is this guy. Six times seven. You got 10, 20, 30. Right? And then you got four times three. Right? These are gone. Four times three is 12. 30 plus 12 is 42. Okay? So six times seven is 42. If they need a sort of a trick to remember how to do this, they won't need it for long. Okay? They won't need it for long. Okay? So those are two finger tricks for multiplying the nines with any of the number from one to 10 or multiplying the six to the ten with the six to the ten. So it generates that finger multiplication technique, generates this batch over here. Okay? The nine finger multiplication technique generates this column and this column. And these ones usually students find fairly easy. Okay? Now, again, we've put out a video regarding the multiplication table. We've generated this already. We did this a few years ago, right? When we set up the grid and we did the 10 by 10 math puzzle game on it as well. Right? So it's really important to take a look at that video as well because there's a certain amount of symmetry within the multiplication table and the symmetry goes along here. Right? This is the perfect squares where it's like three times three, four times four. Right? And whenever you're doing the multiplication table, initially you're going to generate it with the student in the rows or in the columns. Right? Once they know how to do that, you're going to show them once you get the whole grid up and we will go through this. Once you get the whole grid up, just point out that this is the line of symmetry and everything above this line, this diagonal repeats over here. And you're going to have to do this multiple times for that concept for the kids, for the students to really appreciate what that concept means. Okay? So in general, with all the numbers, right, from one all the way to 10, I go through this at least once with them, with some of the numbers multiple times. And then what we end up doing, we'll go to the grid. I get the students to fill out either rows or columns. Let's start off with the two row. Right? So what we do is we go, what's two times one? Two. What's two times two? Four. What's two times three? Six. What's two times four? Eight. What's two times five? Ten. What's two times six? Twelve. What's two times seven? Fourteen. What's two times eight? Sixteen. What's two times nine? Eighteen. What's two times ten? Twenty. Okay. Initially, you're not going to go that fast with them. You might go that fast with them if they're comfortable with this and you just want to show them how you end up filling this out, which isn't a bad idea. But don't expect your students to be this fast with them. Right? So we end up doing a couple of rows in general. Usually I teach them in one direction first. Right? Once they're comfortable with that, I teach them the columns. Right? Five times one is five. Five times two is ten. Because multiplication, it really doesn't matter if you go this number times that number, that number times that number. And these are things that I fill in plant seeds for future lessons. Right? Which isn't really necessarily in this initial phase of teaching someone how to count, add, and multiply. Right? Five times three is 15. Five times four is 20. Five times five is 25. Five times six is 30. Five times seven is 35. Five times eight is 40. Five times nine is 45. Five times 10 is 50. Okay? Once you've done a few rows, and it might take you a whole grid for them to really appreciate how you multiply the rows together, it might take them more than doing one grid or two grids or three grids. It takes a while to learn the multiplication table. That's why a lot of kids, a lot of students have a hard time with it. When they come into high school, I've met a number of students that don't know how to multiply. Right? One of the reasons is because of centralized education system gives them the calculator and says use the calculator, which is horrendous. Right? They need to be able to do this manually. Right? Once they know how to do, how to rows work, how to columns work. Right? And once they filled in a few tables, and it's going to take them filling in a few tables for them to really appreciate this. Right? Get them to do the easy columns and rows first. Right? The 10 column is easy for a lot of students. Right? 30, 40, 50, 60, 70, 80, 90, 100. Right? You can get them to do mirror. Right? The sister row to the column. Right? 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100. Right? You can also get them to do the diagonal where there's a line of symmetry with everything above showing below. Right? You can go one times one is one, two times two is four, three times three is nine, four times four is 16, five times five is 25, six times six is 36, seven times seven is 49, eight times eight is 64, nine times nine is 81. Right? Once you've done it once with all the rows, at least, once you've done it one with all the columns, at least, you can show them the diagonal, start there. And then around the diagonal, you can give them numbers at random and then give the mirror number for them. Right? You could go four times seven is 28. Right? And bring another highlighter out. Right? And highlight that box and tell them, okay, what's this one? Or give them a grid with 12 things highlighted at random as a test and get them to do that or as an exercise and get them to do that. Right? Four times seven is 28. Right? And then what you can ask him is, you can go, hey, what's seven times four? Right? Seven times four. It's the same thing as four times seven. And if you take this line as being the line of symmetry, your two squares that way, your two squares this way. So that's 28. It takes a while for students to figure this out, that there's a mirror factor here. Right? Five times two, we already got five times two here. So two times five is 10. Five times two is 10. Here's the line of symmetry and your two squares away. Right? What did we have here? Two times nine is 18. So nine times two is 18. Okay? And that's the way you can start showing some of the symmetry in this. Okay? There are other patterns, but that's a pretty good pattern. That's really the most important pattern in this. Aside from the rows in the column, of course. Right? And once the students appreciate this, they go from here to here and from there to there and from there to there, give them the doubles. Right? Then start giving them numbers of random. Five times eight, 40. Three times two, six. Eight times three, 24. Three times eight, 24. Right? Mix it up. Give them the mirror numbers. Remind them how it works. Okay? And the name of the game is, when you're teaching the 10 by 10 multiplication table, is get them to do it. Correct their mistakes. If they need to start off, if they need to know what three times seven is, they need to start off with three times one. Let them. Right? Even though these ones might be filled out, once they start doing it, just point to them. Emphasize to them that, hey, if you want it to three times seven, you just have to go back to three times five, which was 15. And you got two more threes. You got to add on to that. So that's 21, which is a six. Right? I hope that's clear. It's, it's very personal teaching someone the multiplication table because you can, you can see how their minds clicking, how they do pattern recognition. Right? And from there, basically you can start doing combinations of things. Right? And the combinations of stuff we can talk about in future videos. But basically right now, this is sort of where I want to stop because the multiplication table is one of the first places that people have a hiccup. Okay? That takes people out of the math game. Right? Because once you know this, then you can do all types of multiplication. Right? You could do here. Let's do one here where you'll see where you can take it from the multiplication table. Right? If you want to, for example, multiply, let's take this guy down. I'm going to take this guy down and might as well take it one level further. Right? Let's take it one level further. So previously, what we did, we said one of the things that I like giving students is three 999s added together. Right? So you're going to go 999 plus 999 plus 999. Right? Now, if the students learning this in addition, which they are with me, and I love giving this, right? They just line up the 999s, 999, 999, 999, and they add them. Right? So 9 plus 9 is 18. Plus 9 is 27. So you put the 7 here, you move the 2 up top. Right? That's three 9s added together again. That's 27. Some students don't see that right away. Right? They go 2 plus 9 is 11. 11 plus 9 is 20. 20 plus 9 is 29. So they go 9 and they put the 2 up there. And then they sometimes recognize, hey, these are the same numbers as here. So that's 29 and they go 29. So what I do when I've, we filled out the multiplication table and they're comfortable with it. They know how it works. I go back to this, right? Give them three 999s added together. And get them to do this and tell them by learning the multiplication table, they could then make their lives a lot easier here because they can do multiplication in a stacked format. Right? This is 999 added together three times and it really brings it home to them that, hey, multiplication really means adding that number together that many times. So that's three 999s added together, which means instead of doing addition, you could go 999 times 3. Right? So you can go 999 times 3. And remember, you have to flush everything to the right side. Right? And then all you do, right, explain to the student that this process is the same as the addition process. Right? But instead of going 9 plus 9 plus 9, you're going to go 9 times 3. Well, what's 9 times 3 or 3 times 9? 9 times 3. Oh, we haven't done it yet, have we? No, not yet. 3 times 9 is 27. And 9 times 3 is 27. Right? It's the same number. So 3 times 9 is 27. And they should know by now that they write the 7 in the bottom and the 2 goes up top. So 3 times 9 is 27 and the 2 goes up top. This is one place where you have to explain that you do the same thing here, but then you're just adding the above numbers. Right? So 3 times 9 again is 27. Plus 2 is 29. So you put your 9 here and you put your 2 up top. 3 times 9 is 27. Add 2. You got 29. You got 29. And do this right beside each other. Okay. Really, do it right beside each other because that way you can explain to them that this took a lot less work than this. You had to write less. It's faster. Right? From there, you can start doing more. You can add, you can give them large numbers, multiple numbers to add together, small multiple numbers to add together. And then you can skip the whole adding process because they should understand it by now and just go straight into multiplying numbers together. And after the multiplication table, I usually just go to this level. One digit multiplied by multiple digits. Two digits multiplied by multiple digits. There's a little bit more to it. We have to add the zeros. Right? And that is fairly easy to teach once a student has reached this level. And we got video out there from the language of mathematics that we did back in 2007, I guess, where we go through it again with chalk and on the walls graffiti styles talking about how you multiply, you know, multi-digit numbers together where you have to compensate for zero you added there. Right? So let's let's just do one right now since we're talking about it. Right? So you could go eight, seven, six, five times 36. Right? The six number is easy. You just do it exactly the way you did here. Six times five is 30. You're going to go zero. You're going to put your three up. Six times six is 36. Plus three is 39. You're going to put your three up. Six times seven. We did this. Right? Oh, we didn't do it. Did we do it? Six times seven. We didn't do it. It's 42. Right? So let's put 42 here. And seven times six is 42. And again, you can see the mirror line here. That's the mirror line. That's over there, right there. Right? So seven times six is 42. Plus three is 45. Five, four, six times eight. We did this one. Oh, we didn't do it. Did we do it? Six times eight. Oh, we didn't do six times eight. It's 48. Right? Eight times six is 48. Right. Six times eight is 48. Plus four is 52. Right? And then we're going to deal with the three. Now, all you have to teach this tune is because this is two digits for the first digit under it. Because there's nothing there, you got to add the zero. Right? Now, you can go into detail saying that this is the tens here and the hundreds if there was another one and stuff like this. But you don't need to write away. You can just say, hey, this is the second number in. So you're actually going to start here. Okay. So three times five is 15. You put your five here. You put your one up top. This guy's gone. You can cross it out or just remember that you're not adding these numbers. Some students like crossing it out. Okay. Three times six is 18. Plus one is 19. You put your one up here. Three times seven is 21. Plus one is 22. Two. You put your two there. Three times eight is 24. Plus two is 26. And really emphasize that everything has to line up properly. Okay. Extremely important. If it's not lining up properly, it's not going to work. Okay. It's really important to show the structure of the language of mathematics to students and make sure they're starting off on the right foot. Okay. And then once you get to this level, you're just adding these guys up. So zero plus zero, zero. Nine plus five is four. Five plus nine is four. Oops. I forgot to carry the one. Nine plus five is 14. You carry the one up here. Right. One plus five is six. Plus nine is 15. You put the one up here. One plus two is three. Plus two is five. Five plus six is 11. You put the one up here. And that becomes a three. And this number, 8,000. And again, get them to read the numbers. Right. 8,765 times 36 is 315,540. Okay. That's a big number. That's a big number. I hope that's clear. I hope that's okay. This is sort of the process that I use to teach my students, take them from a point where they're just learning how to add, adding to, sorry, take my students from a place where they're just learning how to count, from counting to adding to learning multiplication, emphasizing the multiplication table, and from the multiplication table, showing them what it means to multiply numbers together, large or small. Okay. Once they know how to do this, you can layer on top of this. And for me, from here, I go into subtraction, negative numbers, and division. And that's something we'll talk about in a future video. And I hope you found this useful. I hope it helps you teach your loved ones, your students, anyone that you're working with that needs to learn the multiplication table, to teach them more rapidly and sort of help you navigate your way through some of the places where they might be having hiccups. And always remember, this is extremely important, always remember, teaching someone mathematics, teaching someone anything is very personal. Some students will have problems, have to overcome obstacles in certain places where other students can easily navigate through. Okay. Take the time required to make them feel comfortable, relieve stress from them, don't punish them for making mistakes, just get them to correct their mistakes. Okay. That's it for now, gang. I'll see you guys in the next video. Bye for now.