 Now we've talked about counting, right? And throughout that whole process you have to help the student warm, get them to feel comfortable, alleviate any stress that they may have. Okay, once they're comfortable with counting, right? Get them into adding, right? 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 given up to the two numbers to add. When you give them five, four or five numbers to add stacked up together, the number that they're carrying to the top, right, 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. Okay, so for example, get them to add the following number. Nine, nine, nine, plus nine, nine, nine, plus nine, nine, nine. 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 they'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. 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 axiom, 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. 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 a hundred 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 1,000 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 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? Okay. 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 fourth. 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, or 999s 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 students 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 2 times 3, right? If they need to, get them to write it out, right? 2 plus 2 plus 2, that's what 2 times 3 is, which is equal to 6, which is equal to 6. These guys are equal, right? 2 times 5, right? It's 2 plus 2 plus 2 plus 2 plus 2, which is 10, which is 10, 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 2, right? So this is what I end up doing. I go, what's 2 times 1? And get them to fill it out. 2, 2 times 2, 2 times 3, 2 times 4, 2 times 5, right? So in general, with my students, I actually write these down and they fill in this spot, right? 2 times 6, 2 times 7, 2 times 8, 2 times 9, and 2 times 10, okay? Get them to fill out 4, 6, 8, 10, 12, 14, 16, 18, 20. 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 2 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 4, 6, 8, 10, 12, do it that way. After the number 2, in general, I teach them the number 5 and then the number 10. So I do the 5 multiplication same way, right? If you want, we'll do this in red. So I do the same thing, but I do it with 5. Where should we write this? 5 times 1, 5 times 2, 5 times 3, 5 times 4, 5 times 5, 5 times 6, 5 times 7, 5 times 8, 5 times 9, and 5 times 10. Equals, equals, equals, equals, equals, equals equals equals equals equals 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 with the tens, all they gotta 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. 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. 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've 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 and the 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. 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, right? And when teaching multiplication, I usually put a multiplication here so the kid becomes familiar with the symbol, right? When doing this, I either get them to go across one row first or down one column first, right? 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, okay? 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, okay? In general, those are students that I meet just coming into high school, right? When we're straight out, I'm explaining to them, I'm expecting them to learn the multiplication table, right? If they're elementary school, if they're younger, right? Tweens or pre-tweens, right? If they're a kid, spend the time required for them to learn this. It's going to make their lives a lot easier, right? So in general, this is what we end up doing, okay? Once I've gone through this, right? And 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, okay? 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, right? Regarding multiplication, where one of them was the finger method for multiplying nines, right? 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. So it's basically information from the video, right? So the nine multiplication, all you end up doing is holding up your hands, right? And whatever number it is, let's say you're multiplying three times nine, right? 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, okay? If you're going to go seven times nine, you're going to go one, two, three, four, five, six, seven times nine, right? This is the table. So this is 63, right? If you're going to go nine times five, right? Nine times five. You're going to hold up your hand. You're going to go one, two, three, four, five, right? So nine times five is 45, right? My fingers are all red because of the red marker, right? 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, right? 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, right? And if you want to multiply, let's say, seven times eight, which is one of the ones that gives people a hard time, right? Basically, the method is this. You start off each finger, the pinkies are the sixes, six, seven, eight, nine, 10, right? So six, seven, eight, nine, 10. So we're going to multiply seven times eight. We're going to go six, seven, right? That's the seven one. And eight is going to be six, seven, eight. You close these guys off, okay? The ones that are facing away from you, towards the pinkies, counts as tens, including the two ones that are touching, right? 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 50, six, 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 is 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 ten 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 ten is 50. Okay. Once you've done a few rows, and it might take your 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 them 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 very personal teaching someone the multiplication table because 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, 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 3 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 3 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 the 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 have 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 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 add it there, right? So let's just do one right now since we're talking about it, right? So you could go 8, 7, 6, 5 times 36, right? The sixth 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. 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 the student is because this is two digits, for the first digit under it, because there's nothing there, you've 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 feature 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.