 So what we're gonna do in this video is set up a 10 by 10 grid, right? And the reason we're gonna set up this 10 by 10 grid is we're gonna learn our multiplication table, the 10 by 10 multiplication table. And since we're gonna have a table, we're also gonna learn sort of a math puzzle game pattern recognition game that we can have fun with, right? That we can use and, you know, sort of chill with and sort of exercise for the mind, right? Playing around with numbers and patterns and movement types, okay? So we need to set up a 10 by 10 grid. Now the method that I'm gonna use to set up this grid is a method that I used for about a decade doing geophysics in the 90s, right? Before I started teaching mathematics, I was a geophysicist, environmental geophysicist specifically, and I worked in the field basically throughout the 90s for a decade or so, and I flew around all over Canada and all over the United States, and, you know, it was an amazing job. You know, it was fantastic. Half the time I was out in the field working with high-tech equipment and, you know, sometimes getting dropped off by helicopters or going out to the wilderness and, you know, being around bears and wildlife. And the other half I was back at the office processing data and writing reports. So best of both worlds, outside and inside, right? Dealing with technology. And what I used to do whenever I went out to the field, one of the things you end up doing in geophysics, in data collecting in the real world is you need to set up a grid because when you collect data, you need to know where that data came from, right? And if you're collecting a lot of data, what happens is you need to have a spatial, you know, coordinates associated with that data so you can place that data in a proper location. That way you can take that data and run software, basically contour it, right? With process it, basically using different techniques that we have, right? A lot of computer power. And what you do is you create maps and take a look at those maps and see if any anomalies stand out, right? Or you get more detail of what's in the ground. And for those of you that don't know, geophysics is basically a field where you use instruments to find out what's going on inside the Earth, right? What's going on under the surface of the Earth. That's what I was involved in anyway, right? Specifically in the environmental field, okay? So that's what we're going to do. What you're about to learn is not just, you know, a trick or some exercise that we're doing to set up a grid to learn our multiplication table. This is something that I used to do and almost every geophysicist does this or has done this and definitely knows how to do this, right? Because it's something that I use for a whole decade, right? Every time I went up to the field I was basically setting up a grid and this is a technique that I used to use, okay? Now, what we need, first of all, is a baseline. So what we're going to do is we're going to set up our grid here, the 10 by 10 grid here, right? And what I need to do is create a horizontal line that's going to be in my baseline and I'm going to have, you know, a 0-0 point, right? And this really connects up to the Cartesian coordinate system that we talked about in, I guess, series one of the language of mathematics, right? It's super important to understand how the Cartesian coordinate system works, right? So we're going to set up a baseline here, right? And I'm going to try to make it horizontal. So what I'm going to do is I'm going to come off the ceiling here the same distance, right? And I need to be able to put 10 numbers, right? I need 10 columns here. So what I'm going to do, I'm going to use my tape measure and I'm going to use, let me show it to you, and I'm going to use 10 centimeters, right? As the width of one column, right? So if I need 10 columns, that means I'm going to go out one meter, right? And I'm going to come down from the ceiling down a certain length. I think I'm just going to put it up here because I do need a little bit of space up top where I can put the numbers 1 to 10 because those are the columns. Those are the titles for the columns and we're going to have rows here going down 1 to 10. So we're going to do our multiplication table, right? So I'm going to measure a distance here and I already sort of framed it, right? So I could, you know, make sure it fits in the picture that you see, right? So I'm going to come down 22 centimeters, okay? And I'm going to go across, that way I know exactly it's going to be horizontal. And I'm going to assume the ceiling is, it is horizontal so it will be level with the floor, okay? Now I need the length of that line to be one meter, right? So I'm going to come from here, go to... So the way I'm going to set up my grid is... I'm not going to draw on it because, you know, I don't want it to be permanently put on there but I'm going to use green tape, right? Painters tape. The seam on it, there's the seam, right? So I'm going to go across horizontally because I put my ticks on there one meter. Actually I'm going to bring my exacto knife as well, that way I make clean cuts, right? So I'm going to go one meter. That's a nice horizontal line that it looks that way, right? So what I need to do now is, I need to come down perpendicular from this, right? Because I want my grid to be perpendicular, like a nice square, right? Ten by ten square. So I need the angle here to be 90 degrees. What I'm going to do is I'm going to use a special triangle. Let me show you how this works, okay? So I've got a piece of board here, okay? And I'm going to show you how this plays out. So in the field, what we end up doing in geophysics is, we find usually, you know, if we're not going against a building or a fence or we don't have some kind of marker set up, we go out to the field and open the field and we decide that we want to collect data in a certain area, right? So what we end up doing, we pick a 0, 0 point, like Cartesian coordinate 0, 0 point, right? And then let's say we wanted to collect data across here, right? So what we end up doing is, we end up creating a line this way, right? So let's say we go out this much, right? Let's assume the distance, the distance here we've traveled, right? That's our 0, 0 point, that's our 0, 0 point, or not 0, 0, 0. But that's our 0, 0, right? 0, 0, right? And what we end up doing is, we end up creating a right angle triangle. Let's see if I can draw a right angle triangle approximately. Okay, so we use a special triangle called Pythagorean triple. And the one that I usually ended up using was a 40 meter one, a 30 meter one. And if you do this, go across, this becomes 50. So it's a Pythagorean triple triangle, special triangle, where this is guaranteed to be 90 degrees. So it's a right angle triangle where the legs are 3, 4, and 5, right? And there are other types of triangles like this. There's a 5, 12, 13 one, right? And I think there's an infinite number of these. There must be an infinite number of these. Well, there is definitely an infinite number of these because it can generate multiples of these, right? So it doesn't necessarily have to be 3, 4, 5. It could be 6, 8, 10, right? It could be 30, 40, 50, right? It doesn't necessarily have to be 5, 12, 13. It could be multiples of that, right? And there are other ones as well, but this is the one that I usually ended up using. So what we ended up doing is doing this, we would create a 90-degree angle. And depending on how far we want it to go, all you would do is put stakes here, right? And then you would line yourself with the stakes and continue measuring this way and put stakes down. I'm going to show you how that works, right? So as long as you appreciate how we're going to do this, what we're going to do here, let me show you how this is going to work first. Okay. So what we're going to do, we call it that our 0, 0 point. So I'm going to go 40 centimeters this way, right? And if I go 30 centimeters this way and from the 40 centimeter mark, because I have my horizontal line, right? This is my base line, everything goes off this. So 40 centimeters this way. If I go 50 this way and 30 this way, wherever I end up, that's guaranteed for this to be 90 degrees. And from there, I can just measure down, right? I could do another one with 80 and 60 and 100, right? That gives me one, two, three points. I can connect those up, right? And then that way I can go down a whole meter. And once I get this point, I can go across a meter this way and a meter this way and wherever I end up, that's a right, what do you call it? That's a box. That's a square, right? With everything being right angles. Okay. So let's do that right now and then I'll show you how lining up this stuff works. Okay. So the way we're going to do this is I have some rope here. And this is, I don't know what the name of this rope is, it's a fantastic rope. It comes in super handy. Tying down things in the car, especially. But I ended up using this type of rope for a lot of things, right? And I don't have, you know, in the field, geophysics, we use stakes and hammer, right? We take stakes, wooden stakes, and we paint the top of it fluorescent, you know, orange or red, usually orange, because it stands out, right? So we would take a stake if we were in the field and put it right at zero, zero, and then put stakes along here, lining ourselves up like this, right? And I'll show you how that works on the board after we set up our 90-degree triangle, right? So what I'm going to do is use these gigantic tags that I found, right, as my stakes. So we need to put a stake in at the top here. And I need my rope. And my rope is sort of replacing my tape measure in the field. In the field, we used to take tape measures that were 50 meters long and 100 meters long. And I believe we had 200-meter tape measures, because we used to do huge grids, very large grids. And we actually didn't use nylon tape measures. We used metal tape measures, because, well, we did use nylon as well, nylon as well, but when we wanted things to be very accurate, we used metal, because when you pull cloth or nylon tape measures, what happens is they stretch, and over long distances, your grid ends up being off by a few centimeters. And if you continue that for a while, you're off by a lot. Because, for example, if we take this rope, if I pull it, it stretches, right? Even then, my need to stretch over long distances throws your measurements off. So we used to use metal tape measures where they really didn't stretch very much, right? They're very little, so our distances over long distance were fairly accurate, okay? So I'm going to take this, and I'm going to lay this down here at my 00 point. Now, let me just roll this out. I need this to be a meter. I'm going to cut this a little bit past a meter. I'm not going to pull too hard so it doesn't stretch, but I'm going to pull hard enough so it's not fairly tight. So I'm going to cut it here. Now, what I need to do is I need to mark off the 10 centimeter marks on the rope, on the grid, right? So I'm just going to take my 10 and my line here. I'm just going to go off this way because I put the stake there for now and centimeters on a 100. So we have our 10 centimeter laid out, right? Now, what I'm going to do, I'm going to put the marks on my rope. I'm going to come here. What I need to do is create another one of these strings because I'm going to have one coming down 30 centimeters here and I'm going to have one coming down from going to go across 40 and from the 40 going 50 this way, right? So I need two of these strings. Now I'm going to take this guy down. I'm going to put this where 40 centimeters is one. So 10, 20, 30, 40. And I'm going to go approximately in the center of the tape and I'm going to go another tack, right? I'm going to tie my rope to it, my measuring tape, I guess. So let's put this down here. Cut this again. Approximately a little bit more than a meter. So I'm going to cut it here. We're going to take our Sharpie and mark this up again, right? So I'm going to take this and this one is going to be hard to do here. What we're going to do here, if you see the stakes here, right? We have basically one at here and one at here. So I'm going to go down 30 centimeters this way vertically and that 150 and where that ends up, that should be a 90 degrees, right? It should dislodge. It was going to be perpendicular to this line. Now what I'm going to do to make sure this is accurate as possible, I'm also going to go to 80, right? And I'm going to go down 60 and I do the same thing and that way my three points should be in a straight line. If they're not, I know there's a problem, right? But hopefully they will be, right? So if they're in a straight line and then that way all I've got to do is just go down and put little ticks every 10 centimeters, right? Because I've got a perpendicular line. So I'm going to mark it up with a pencil. Let's see. So we're going to go 30. So 10, 20, 30 is here and 50. 10, 20, 30, 40, 50. But that mark should be here. It looks like a 90 degrees. I'm not sure. We'll have to test it out, right? So we're going to go down to 80 here right now. 10, 20, 30, 40, 50, 60, 70, 80. Let's go in the middle. We go in the middle. So we've got 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. So I'm going to go to 100 and I'm going to go to 60. So 10, 20, 30, 40, 50, 60 and 100. And this line here is going through the stick. So I'm pretty sure these two lines are going to be perpendicular, right? So let's go. It's right there, right there. And what we're going to do, we're going to come down to 1 meter. And I have one 1 meter marked here. So 1 meter is going to be right there. Let's see if this works, right? So we're going to take our stake out because we don't need it anymore. We're going to bring our green tape back and pull this off. And we're going to go all the way to here. It looks like a fairly square grid that looks like a 90 degree angle, right? So now all I need to do is take the stake, right? Put it down here. Go out 1 meter this way. Take this other stake up here, put it at the 1 meter mark, come down here, right? Hopefully they'll meet here and that'll be my square grid, right? So let's do this and hopefully it all works out. I'm going to grab my pencil and make sure I can put the mark in. Now this guy is going to go straight there, plaster walls. This guy is going to come here. These guys are going to meet here. Now I'm not going to pull too tight because I don't want the tape to be stretching very much, right? Now I'm going to put little ticks here that way. Markers along the way, extremely anyway. So let's see if this ends up working. So I'm going to bring this guy out first. Let's take this guy down. The middle of this comes straight down to this and not that. Now what we're going to do is take this guy down, right? And we're going to go from here and that's my square, right? Now all I have to do is put my vertical lines, my columns and put my rows in, right? So all I need to do is really take my tape measure, right? And put it at the holes and mark off the distances. And what I'm doing is going right in the middle of the width of this thing, right? Approximately anyway. Again, if this thing was on the field, on the ground, it becomes easier than doing it on a wall. You become more accurate because you can lay the tape down and line yourself up. We need one more across down here, right? So now we're officially done with these guys with the big tags until I show you how we do the line-up stuff, right? So all I have to do now is bring my green tape and go across, right? So let's do this. I'll put the verticals in first. What I'm going to do is I'm going to make these a little bit longer up top, right? Because we do want the column markers sort of to lay out the headers, right? One, two, three all the way across. For geophysics, just so you have an idea of what we used to do, we used to set up our 00 grid here and then start collecting data going this way. And it's basically a Cartesian coordinate system. And then we'd go across and collect data going this way and then collect data coming back and then collect data. So we would just cover a whole area with an instrument collecting data such as electromagnetic or magnetic methods. And what we would do is take that data into different types of programs and grid them. We would basically extrapolate data between the points. If we wanted to, if the data wasn't sampled extensively or if we sampled extensively, if we had a lot of data points then we didn't have to do any extrapolation. We would grid it, we would contour it. We put a color bar on there and we just look for anomalies, right? Or patterns if we're looking for patterns. So those are all our vertical lines. Looks fairly accurate, right? Nice square. Now we've got to put in the horizontal lines, right? So I'm just going to come this way. And I'm going to extend it a little on this side. That's the beauty with green tape. So easy to work with. It's not permanent tape but it's really easy to work with doing this type of stuff. Looks good. Let's actually... It sags a little in the middle, eh? Horizontal lines. One thing I did promise to show you was how we actually... Because when we did geophysics is... When you do geophysics is you basically put stakes here and you're not going just a meter. You're not going just 50 meters. Sometimes you're going for a couple of kilometers when you're doing work like this or even longer, right? So you don't have tape measures that go that long. You wouldn't want tape measures that go that long, right? They'd be huge, heavy to carry, right? So what you end up doing is you put stakes down. Let's bring out our thing again. Let's bring out our two stakes that we're working with, right? These guys. So let's assume our tape measure was only 40 meters long, right? But we wanted to go all the way across, right? So what we would do is we would put a stake at the zero-zero point. We would put a stake at... This would be, I guess, 40 zero if you're doing a Cartesian coordinate system, right? And what you would do is make sure that these things were vertical, right? They weren't tilting one way or another. And we would have painted the top of these guys so they stood out. And then what we would do is we would attach our tape measure here and go out and what we would do is line up the stake, another stake. Let's grab another stake. Let's grab a white one, okay? So we would take our tape measure, right? Along here would go out as far as we want to go or as far as the tape measure takes us. And what we would do is we would line this guy up with these guys, right? I'm not sure if this is being lined up or not, if you can see it. So you usually close one eye, right? And you would line it up. Let's do it this way. Probably better. So I'm taking a tape. I would have attached the tape measure to this, right? To the second one. I would walk out, walk out, walk out, walk out, walk out. And I would say, okay, I need, you know, as far as my tape measure goes. And this stake is not fully straight, so I'm going to straighten it out a perfect. So I would come out, right? From here. I would come out, come out, come out, come out, come out, come out, come out, come out, come out. And I would try to line this guy up with these guys. And that gives me a fairly accurate line. If you want, you can see it. If you're offline, the three points don't line up, right? If you're here, you're all exaggerated. Obviously you're not in line with those two points, the two stakes, right? So you would have to come back, come back, come back, come back. And that looks like it's almost in line. That looks like it's in line. And I would put the stake down, right? Looks fairly accurate. And then if you want to go further, you know, you grab another stake and line up, line up, line up, line up. And you would go further and further and further, right? And if you look at this thing, you know, is it a straight line? Looks fairly straight, right? Not bad. Now, for me laying out grids like this, I've gone to sites in the 90s, you know, for mapping water contamination around brine ponds or mapping, you know, trying to map leach, contaminating leached out of landfills, going to water, water table around landfills or whatever it might be. I would set up grids like this, going. Like maybe my 0-0 point would be somewhere here, and I would go, the biggest one I did in this, using this method, was about two kilometers in one direction and then go up another kilometer and then come back down and I had to go around brine pits, right? So I had to set up a really fairly accurate grid 90 degrees, right? So two kilometers, one kilometer, doing a couple of zigzags around and having to come back to my 0-0 point. And when you get to the end, you realize how accurate you are. And when I got to the 0-0 point, just using tape measure and stakes and line a site, setting up the initial grid using two people and the rest of it, one person, right? I would get to the last point and I was maybe three meters off. And this wasn't for mapping, you know, trying to find drums, metal in the ground, because for that stuff you have to be more accurate. This was mapping out large areas where you're looking for contaminants leaching into the ground. So going two kilometers and one kilometer and coming back and only being three meters off is extremely accurate, right? So this isn't just a system that we use to set up grids as an exercise. This is a system that's used to set up grids all over the world, not just for geophysics but other systems as well, other disciplines as well. Okay, very powerful, very powerful. So what we're going to do in the next video is learn our multiplication table, right? We're going to put numbers here, one all the way to 10 and one all the way to 10 this way, right? And then we're going to go down rows and up columns and find out what this number times a certain number is here. And the way it's going to work is we're going to do the bottom part of this first because the bottom of the part of this flips over to the top part because there's an axis of symmetry diagonally here and you'll see how that works. And the reason it works is because basically two times three is the same as three times two. It doesn't make a difference which order you multiply numbers in, right? So we're going to do our learn our multiplication table in the next video and the video following that since we have a grid set up what we're going to do is we're going to learn a math puzzle game the students showed me a few years ago that I really like and I got sort of addicted to for a few months I was playing it a lot. So I'm going to show you how that game works and it's a fun little game, it calms you down, it's very chill and it really doesn't require calculations, mathematics too much but it does hit on one aspect of mathematics which is pattern recognition so the game is really a pattern recognition game. And that's it, I hope you enjoyed it. I hope you find this useful at some point in your life. And remember, multiplication table, learn it. Super, super, super important. I'll see you guys in the next video. Bye for now.