Motion is so common in the world, we probably really don't even give it much thought every day. I mean, things move all the time in the world around us. It's so average as to be easily dismissed. But thankfully, a lot of people who've come before us have thought a lot about things moving. Why they move, how they move, why they don't move, and so forth. As a result of that, we have a very complete understanding of motion in the natural world. I mean, this is really something we're going to spend the bulk of the course on, is objects in motion or objects coming to rest. That's no accident, and after all, the universe itself appears to be constantly in motion. Consider riding in this car. We speed by buildings that appear to be fixed with respect to the ground, but from our perspective, they're moving past us from the forward part of the car to the backward part of the car. We're passing other cars, for instance, this one right here, and we're being passed by other cars over on the left side that you can't see. We change lanes. The car moving from one side of the highway to the other side of the highway, even as it continues its forward motion. We can look at the speedometer, which is a measure of the speed of the car, the distance that it's traveling in each moment in time with respect to the roadway, which is considered fixed on the Earth. Now, one thing to keep in mind about speedometers in the United States is that because this is a country that has not adopted the SI system of units, we don't use the standard units of meter and second, or kilometer and second, to make measurements of speed, that is, changes in distance with respect to time. Instead, we use the unit of miles per hour. Now, of course, one can convert seconds to hours and one can convert meters to miles. It's all a simple algebraic exercise that will exercise a lot in this class, and in fact, being able to convert from one system of units to another is an important skill that all scientists need to have, because after all, numbers come in many shapes and sizes. This is all totally normal to us, though. This kind of motion, or as we begin to slow down here in a traffic jam, this sort of lack of motion. But again, what is speed? I mean, we can think about those units again for a second, meters per second or miles per hour. If I'm driving, for instance, at a speed of 25 meters per second, what that converts into in miles per hour is a convenient speed in the United States. It's about 55 miles per hour, which used to be a typical maximum speed on many roadways. Now, what this means, of course, is if I'm moving at 25 meters per second, it means that after one second, the vehicle that I'm in will have traveled 25 meters, and that seems like a simple, perhaps even a trivial statement. But in fact, it's quite powerful. For instance, I can make predictions about the future based on this information. If this vehicle's speed remains a constant 25 meters per second, then I know that after two seconds, I'll have gone 50 meters. After three seconds, I'll have gone 75 meters and so forth. It seems so simple, but it's extremely powerful predicting the outcomes of the natural world. It's one of the tiny powers that physics is a study of energy matter space and time has and gives to us as human beings. Now, in fact, if I were able to maintain that speed from the front door of my house to the parking lot at SMU, where eventually this car will come to rest, I can tell you a lot of things. For instance, I can tell you confidently the amount of time it would require me to make that journey from front door to parking lot at work. The power of such information, the ability to predict outcomes, that is really the power of physics as a way of understanding the natural world. So, for instance, if I were able to maintain that speed of 25 meters per second or 55 miles per hour constantly throughout the entire commute with no speed ups or slow downs, it would take me about 1,288 seconds to make the journey from front door to parking lot. Now, if you convert that into something a little bit more relatable, that's about 21 minutes. And remarkably, under good traffic conditions, given the highways we have accessible to us, a commute under those ideal conditions takes about 25 minutes door to parking lot at work. That's not bad considering the fact that the highway that we're on now experiences traffic jams and that its typical maximum speed is actually more like 70 miles per hour and not 55, but things kind of average out and you wind up with an answer that's about correct. If I maintain a speed of 55 miles per hour from my door to the parking lot at work, it takes about 21 minutes to commute. I would predict. And in reality, on ideal conditions on these highways, it would take about 25 minutes. Of course, with traffic, it's really more like 40 minutes or so. Now, of course, I've made an assumption here. That is that the vehicle that I'm in is traveling on an exact straight line the entire time from the front door to the parking lot. In physics, we would call that kind of fought game an approximation. It's not really what driving from home to work is like. But it comes close enough for us to make some reasonable predictions about what's going to happen. And, of course, motion is not always on a straight line. It's very complicated. As I've said here, we change lanes. We accelerate. We slow down. We respond to traffic conditions. We exit the highway. We get on the highway again. We get on side streets. We turn left at stop signs. Motion is very complicated. In reality, it takes place in three dimensions. Left to right, going over bumps or into dips in the road, takes us into the vertical dimension up and down. And, of course, ideally we want to continue going forward the whole time. But sometimes you have to go a little bit backward to make progress in a traffic jam. We'll explore these topics of motion, starting with motion in one dimension in this section of the course. Let's move now from a more conceptual attitude toward motion and in specific terms, motion along one direction in space. That is one dimension. It does something a bit more concrete and mathematical. The key ideas that we're going to attempt to absorb in this section of the course are as follows. We're going to try to find a way to describe an object's motion. And that's going to be the case even if the object is large and extended. Now, the trick we're going to use here is that if we have a case where all points on an object, even an object that takes up substantial volume in space, if all of the points on that object are moving together at the same time in the same direction, then we can get away with a bit of an approximation, as we'll see. We're going to learn to locate an object in space along a coordinate axis and describe that location. We're going to learn how to describe the displacement that is the change in spatial location of an object from some reference point. And we're going to define things like the average velocity and the average speed of a moving body. And we're also going to see how that's different from what is known as the instantaneous velocity. That is the speed or velocity of an object at a very specific moment in time, as opposed to over a long period of time. Let us begin by thinking about how to describe complicated objects.  In fact, they're far more common in the world than the oversimplifications that you'll often find in textbooks. But those oversimplifications have a purpose to them, and that is that as long as we can get away with a few key assumptions, and as long as we are clear with ourselves about what those assumptions have been, we can make approximations. That is, reasonable representations of the natural world. And those representations are, in a sense, capturing the very essentials of a given physical situation. So, for instance, consider a light rail train. This is not a simple object. It has many moving parts. For instance, the wheels or the arm on top of the train that makes contact with the electrical transmission lines that power the vehicle. It's got doors that slide open and slide closed. It's got passengers in some cars in some places and not in others. And, of course, it has an engine that's completely distinctive from a passenger car that tapers in the front to make an aerodynamic and so forth. But the good news is that despite the fact that a light rail train is an extremely complicated thing, we can actually describe such a complex object by making a very simple observation. And that is that for a properly working train, even though it is big and it's extended in space, it takes up a large volume, when it moves along a rail, all the atoms that make up the train are bound together and they all move together in the same direction all at once, say, forward along the track or backward along the track, depending on which way the train is going. So, we don't need to describe every single point, every single atom that makes up this train. We only need to pick one representative point and all of the other points on the train are going to do the exact same thing if this point is moving forward, all the other points are moving forward, if this point is moving backward, all the other points are moving backward. So, this will be our approximation. We will imagine taking all of the train and compressing it down to just one tiny representative mathematical point in space and wherever that point moves, the whole train can be thought to be moving. All the atoms, even if they're distributed around that point in the real train, would be moving in the same direction at the same time as this one representative point. And so, instead of drawing an entire train and trying to describe its motion atom by atom by atom, which is an impossible task, let's pick a single point near the center of the train and imagine all of it as being described by just that one point. And there you go. This little green dot is our train. So, it doesn't seem so silly anymore when you look in your physics textbook or in another science textbook and you see a simple dot or a circle or a sphere being used to represent something that's actually, in reality, much more complicated. As long as you are honest and state upfront what your approximations are and the motivation for them, you can go ahead and do things like this because I promise you it will greatly simplify the act of sketching up the problem, which is something you should be doing when you are asked to do this or when you are trying to sketch a problem in order to think about it a little bit more carefully and clearly. Now that we have learned to make an approximation that allows us to say something about where the train is by representing it by a single physical point, we now want to be able to represent the location of the train that point at a given moment in time. And so to do that we need to define a coordinate system. Now, conveniently since trains move along tracks this restricts their motion. They can only move forward along the track or backward along the track. And of course forward and backward are subjective directions, but we can imagine standing next to a train track with the front of our body facing one way along the track and thus facing away from the other direction along the track and to find the direction we are facing in is forward and the other direction is backward. That would allow us to establish a arbitrary but nonetheless useful sense of forwardness and backwardness. So this would represent a single dimension in space forward and backward. So we can say because the train is restricted to moving along the track either forward or backward that it executes a kind of one-dimensional motion. That is its motion can be entirely described as forward or backward along the length of a track system. So we might represent that movement in space that ability to move forward or backward using a single line a coordinate axis which we will label for the purposes of simple references to geometry as an X coordinate axis. A vertical axis would be a Y axis and an axis that goes into and out of the screen would be a Z axis. But since we are not concerned with motion up and down or left and right in this case, we are really going to restrict ourselves just to a X axis a single axis in space. We might imagine that where the train begins its motion we can label as 0.0 The units of direction, the units of distance along this axis are kilometers. And so the train can be said for instance to begin its life at 0 kilometers. Now, if the train moves in what we have defined as the forward direction that is in the direction you are facing along the tracks, then we can say that it's moving along the positive X direction. And so for instance along this direction numbers increase in magnitude from 0 to 1 to 2 kilometers to 3 kilometers etc. Of course all numbers in between these tick marks are possible but for now just let us concern ourselves with the numbers that are labeled here on this coordinate axis. If the train were instead to reverse its direction and go backward from 0.0 then we would note that it is going in the direction in which negative numbers decrease in size. Negative 2 is smaller than negative 1 negative 3 is smaller than negative 2 etc. So this is the negative X direction and this allows us to denote whether or not the displacement that is the change in location and space of the train is in the positive direction, forward or in the negative direction, backward. So now we can mathematically represent our notions of forward and backward. So here for instance is the train at time 0 seconds so we will label this T with a subscript 1. We might imagine that 60 seconds later at a second time T with a subscript 2 that the train has now moved 2 kilometers in the forward direction. So here now is the train dot and we can define the displacement of the train over that 60 second time period using some mathematical notation. Displacement in general will be denoted with the Greek letter delta preceding the coordinate that is changing. So in this case the train is moving along an X coordinate axis its X coordinate in kilometers in space is changing with time and we would denote that displacement as a capital Greek delta preceding X or delta X. So in shorthand verbal nomenclature in physics this displacement would be referred to as delta X. This is defined as the location of the train at the later time T2 minus the location of the train at the earlier time T1. And we would denote that as X2 and X1. So we simply take the difference of these two numbers and if we read those off of our coordinate axis the later displacement is 2 kilometers the earlier location is 0 kilometers and so the full displacement over the 60 seconds is a 2 kilometer positive displacement in the forward direction. Let's imagine taking our train back to its original location X equals 0 kilometers at time T1 equals 0 seconds and this time when we run the clock forward 60 seconds we observe that the train displaces not in the forward direction but in the backward direction. So now it's it's a spatial location after 60 seconds is not positive 2 kilometers in front of where it started but negative 2 kilometers behind where it started. This is perfectly fine trains go in reverse all the time. So this time we observe that the displacement defined identically as before delta X is the later distance minus the earlier distance X2 minus X1 this time we have the later distance is negative 2 kilometers the earlier distance is 0 kilometers and negative 2 minus 0 kilometers. This is now a negative displacement. Delta X is a quantity that is less than 0. So it is important to note at this point that when we speak of displacement we are speaking of something that is a directional quantity that is the sign positive or negative in front of the resulting number carries information about what has just happened. If the sign is positive the train has moved in the forward direction along the X axis that is it has moved in the direction of increasingly larger spatial locations in kilometers. If instead the sign of the displacement is negative it tells us that the train has been moving backward it is displaced backward from the origin 0 kilometers the negative sign tells us that we are moving into increasingly smaller negative numbers. So negative 1, negative 2, negative 3, negative 4 kilometers, etc. The sign carries tremendous information you must never lose the sign positive or negative in front of the displacement when you are asked about the displacement. Now let us consider questions about how the spatial displacement and the time information taken together can give us new information about what the train is doing. If we want to understand how place changes with time then we want to define the quantity known as velocity. So imagine again the train at time 0 that is the first time T1, 0 seconds and then 60 seconds later the train is now at 2 kilometers along the X direction in the forward direction this is the same situation we had a couple of slides ago we can define a quantity known as the average velocity and you will see why it is called average velocity in a moment it will become crystal clear. The average velocity of the train is merely defined as the displacement which remember is a signed quantity that carries information about direction positive or negative it is the displacement divided by the displacement. So if we want to run through the math of this V for velocity with a subscript AVG for average so V average or average velocity is defined as the ratio of the displacement in space and the displacement in time delta X over delta T and just like displacements in space displacements in time are the later time minus the earlier time so this ratio just winds up being X2 minus X1 all of that divided by T2 minus T1 and if we plug in numbers we find of course here that the displacement is 2 kilometers the time displacement with 60 seconds and if we take the ratio of those and put them in a calculator and calculate it out we find that this comes out to be positive 0.033 kilometers per second about 33 meters per second so this is very close to typical highway speeds this is not an unreasonable speed for a train to be executing when it's in a straight away section of track and able to increase its velocity in order to move passengers from point A to point B more quickly now the reason that this is known as the average velocity is because between 0 seconds and 60 seconds for all we know the speed of the train might actually vary maybe the train speeds up on a little straight away but then as it approaches a slight bend in the track although it's still moving forward along the track it slows its speed so as not to fly off the track and cause a derailment which of course is very bad but what we all care about is just how long we can get from point A to point B and what the distance was between point A and point B if all we care about are those two pieces of information then we can immediately compute the average velocity that the train was moving at which takes account of the fact that maybe it spent more time moving more slowly and less time moving more quickly and that ratio gives us some information about the typical speed that the train was moving at as it's moving from point A to point B so really all we're doing is just using the beginning point and the end point information to bracket the motion of the train and get some quantity that gives us an average amount of information about the kinematics that is the way that the movement occurs the actual details of the motion occurs in that time period now we can again do this exercise with displacement and time but this time consider at time zero the train located at zero kilometers and at time two sixty seconds later the train located at negative two kilometers what this time has been the average velocity well again we run through the calculation the average velocity is defined as the displacement in space divided by the displacement and time that gives us negative two kilometers of displacement over sixty seconds displacement and time and this time we wind up not a positive number but with a negative number negative point o three three kilometers per second or again about thirty three meters per second this time however it's in the backward direction so again this sign in front of the displacement carries information that's crucial to understanding the motion it makes a big difference if the train you care about is moving in the wrong direction while you're waiting for it it's important when somebody tells you how fast a train is going that it also is moving in the direction you care about that is toward you to pick you up and take you to your final destination it's moving away from you at that speed it doesn't help you very much now speed is a related concept to velocity speed is the magnitude of the velocity it is a quantity that is always positive regardless of whether or not the velocity is positive so in order to get the speed or the average speed in this case all you have to do is ignore the positive or negative sign in front of the velocity and just quote the number after the sign so in this example and in the previous one the speeds have been exactly the same the speed was always point o three three kilometers per second whereas in the first example the velocity was positive point o three three kilometers per second and in this example the velocity was negative point o three three kilometers per second on average now let's do one last exercise where we do a graphical representation of changes in space with changes in time so we're still talking about motion only along one dimension that is along one coordinate axis but we can represent all of the information of the motion the displacements along the spatial dimension as well as the displacements in time using a two dimensional graph with the vertical axis representing where in space for instance the train is located and the horizontal axis representing where in time those spatial measurements are being made so it is true that we're now looking at a two-dimensional graph representation only of motion in one dimension one spatial dimension so this is something to keep in mind when you're reading these graphs always read the axes always read the units on each of them note I've switched to meters on distance and I'm still keeping seconds on time don't just look at the graph and go aha it's two dimensions therefore this must be two-dimensional motion read the graph and when you're making a graph about what you need to represent and how you're going to represent it so let us now draw two points on this graph point one is down here at the origin in both time and space zero and zero zero seconds zero meters point two which is at four seconds represents a distance along the x-axis of three meters so I've now drawn two points on this space time graph so I can ask a question what is the average velocity represented by this drawing? think about that for a moment what would you say in response to that question given a first space time point here and a second one later in time four seconds later giving a distance of three meters what would you say is the average velocity represented by this drawing? pause the video here think about this for a moment make some notes on a piece of paper and when you're ready for the answer, resume the video here's the answer in order to get the average velocity all you have to do is take the displacement in space divided by the displacement in time well the displacement of space can be read off of the vertical axis the final displacement point is three meters from the origin and the original one is zero meters from the origin in time the later time is four seconds and the earlier time is zero seconds so this is just three meters of displacement divided by four seconds of time and if you take that ratio three meters over four seconds you should have found that the average velocity is point seven five meters per second and the fact that it's a positive number is important in the positive direction but nonetheless that sign that positive sign is implied here if you're feeling really paranoid you can always write the positive sign at no extra cost so if you got this three meters divided by four seconds by reading off this graph three meters minus zero meters four seconds minus zero seconds and take the ratio of those two differences and you got point seven five meters per second you're doing well if you didn't think about this again in the context of the definition of average velocity and to try again the insight that you should take away from this is that graphically when you represent this kind of motion using a space time graph like this the average velocity is just the slope of the line connecting the first point to the second point if you want to check the math on that pause the video here write down the equation for a line y equals mx plus b and keep in mind that y in this case is distance and x is time so really we have x equals mt plus b b is the y intercept of that line which in this case is zero it intercepts the y axis at zero and m of course is the slope of the line so given that information from a high school geometry class that y equals mx plus b gives you the information about a line and from m you can get the slope so solve for m verify in fact that graphically the average velocity is just the slope of the line connecting point one and point two now what if I leave this graph here I have point one and point two point one point two nothing has changed what if I now show you how the speed of the object actually changed from time to time during this whole four second interval so what if I now show you this aha it wasn't that the object whatever it was kept a constant speed the entire time in the first second it went from zero but in the last three seconds it went from two meters to three meters and if you think about that for a moment the speeds are obviously changing from the first second to the last three seconds so given this information the blue line followed by the red line now representing the way the distance changes with speed during the whole four second trip what now is the average velocity of this object take some notes write some things down think about this and see what answer you can come up with if you said that the average velocity is still point seven five meters per second you are absolutely correct what why how can that be in the first second you go two meters but in the last three seconds you only go an additional meter so how can it be that the answer is still point seven five meters per second it's a much more complicated motion than we thought was going on originally but in reality nothing has changed because after four seconds we have still displaced only three meters from the origin and it's still true that three meters divided by four seconds is point seven five meters per second the average velocity of the object over the whole period of time now of course if I asked you what's the average velocity between zero and one second you're going to get a different answer and if I asked you what's the average velocity between one second and four seconds you're going to also get a different answer but from zero to four seconds the answer is still the same point seven five meters per second and so the insight you should take away from this is that this graph really begins to illustrate the difference between the concept of instantaneous velocity which we'll dig into more in a minute that is the velocity at a given moment in time an average velocity which may be over a long period of time when fluctuations in the velocity might kind of cancel each other out to give you the same number that you were going to get anyway over the four seconds it is true that in the first second the speed is much greater the slope of the blue line is quite steep compared to the black line and it's also true that in the next three seconds which is represented in the blue line the slope is much less steep than the black line or the blue line so it's moving more slowly so it moves quickly at first then much more slowly later and that just averages out to the same answer we got in the first exercise point seven five meters per second the beauty of physics now let's take a look at a much more complex motion using this space time graph so again you're going to get one more crack at this concept of average velocity ready? here we go now this very fancy curve represents the way the distance changes with time during the four second trip I mean look at this, it's magnificent it seems to be relatively straight but then it bends very gently until it finally sort of straightens out again and we arrive at the last space time point two so what this time average velocity that the object has during this trip again pause the video take some notes, write some things down and when you're ready for the answer go ahead and unpause the video well here's the answer if you said nice try but the average velocity is still point seven five meters per second you are right what? why? look at this curve, it's ridiculous this isn't too straight line stitched together look how much this thing bends like a gentle elbow and then heads into point two it doesn't matter again nothing substantially has changed we start out at zero zero we end at three meters at four seconds the average velocity is just the displacement divided by the time required to make the displacement nothing has changed it's still three meters over four seconds it really doesn't matter that the speed was doing all these fancy things in between that space was changing in some very non-linear way with time the average velocity remains the same so the insight we can take away from this is that really this graph better illustrates the difference between instantaneous and average velocity in this representation of this motion we have a very complex curve that relates displacement time and at each moment the velocity is clearly varying I mean not so much here maybe not so much here but definitely in this region there is a gentle change in the way the displacement occurs with time but it doesn't matter because the ultimate end point in space is still three meters at our end point in time of four seconds and so the average velocity remains exactly the same regardless of all this fancy behavior in between now looking at this curve for a moment however we really can begin to dig into the concept of instantaneous velocity and do so mathematically I mean for instance it's very clear that at this tiny moment in time if I could slice through this curve that the slope of this part of the curve is much steeper than over here where the if I slice in a very tiny moment in time here the slope of the curve is more close to level it's a much flatter slope than the one over on the left side of the curve it's very hard obviously to exactly describe this in terms of a bunch of little straight lines adding up to make this curve but nonetheless mathematics allows us essentially to do that it allows us to ask questions like if I were to look in a very thin little slice of time and define the average velocity in just that little slice that might get me closer to understanding what the exact velocity at that exact moment in time is and in fact that's the basis of calculus it's taking problems where you have say a continuous change in space with respect to time and it's breaking the problem up into tiny little slices let's say in time in this case and looking at what the displacement is doing in those tiny little slices as we make the slices thinner and thinner and that allows us to get a mathematical definition of velocity at an exact instant in time or instantaneous velocity rather than the velocity averaged over some long period of time in this case four seconds and the mathematical notation for this is that the instantaneous velocity or simply just the velocity v is defined as indeed the average velocity delta x over delta t but in the limit that we make very tiny slices in delta t smaller and smaller and smaller and smaller sending the size of the slice down to zero dimension in time giving us access to the smallest unit of space and this can be represented this whole cumbersome thing this limit as delta t goes to zero of delta x over delta t this thing can be represented by the much more compact notation of calculus dx over dt where d is a symbol that's sort of like the greek delta except that the greek delta represents large chunks and the little d represents infinitesimal little chunks the tiniest thin slices of distance you can imagine that's what dx stands for it is representative of the linguistic concept of a thin slice and so we're looking at thin slices in space over thin slices in time and that allows us to define mathematically velocity at a given instant in time we'll come back to this concept a bit more but this is the foundation of calculus in mechanics and the study of motion so if we want to understand this a bit graphically we could imagine again first computing the average velocity over the whole spatial time of four seconds so I could enclose the curve in a box whose corners are at the locations on the function where four seconds is located and zero seconds are located and then just draw a box like this this is my time slice it's not very impressive because it encloses all time in this problem but I could imagine keeping the box centered on two seconds and slicing more thinly and so instead of looking at a delta t of four seconds I could look at a delta t of two seconds from one second to three seconds centered on two and again the box now not only shrinks horizontally in time but because we're enclosing a very specific segment of this function where there's less overall curvature there's still some curvature but less compared to including all of this we now have enclosed a thinner slice in time of the function we're beginning to just zone in now on what we mean by velocity at a given instant in time and I could take another slice that is in fact just 0.5 seconds in width but still centered at two seconds this is allowing us to conceptually understand what it would mean to ask the question what is the velocity of this object at t equals two seconds in order to answer that question we have to take a very thin slice of the displacement in a window of time around two seconds and calculate the average velocity in thinner in thinner in thinner slices around two seconds that will mathematically allow us to answer the question what is the velocity of this object at two seconds at means two with no uncertainty on it but this definition allows us to conceptually slice very thinly in time around two so thinly that it in fact doesn't even matter that this slice has any width and you can imagine now going down to a tenth of a second a hundredth of a second a billionth of a second a hundred trillionth of a second until we find a slice so thin that we get a very straight little segment enclosed in this little green box and that little segment would allow us to compute an average velocity that so short in time it represents an instant of time in the universe that's conceptually what's going on in all of this and so what we learn is we narrow the time window and just keep recomputing the average velocity in our heads or imagine trying to measure it on this graph by using thinner in thinner time slices we are sampling a thinner in thinner slice of this displacement curve until in the limit that we sample an infinitesimally thin time slice we're ultimately measuring the average velocity over an infinitesimally small moment in the motion that's what instantaneous velocity means it is impossible to measure at instant in time even with the best measuring instruments that humans have ever developed you'll never do better than a certain tiny uncertainty in time so it's better to adopt the concept that you think about motion in space and time in thin slices and those thin slices allow you to define mathematically an instantaneous quantity like velocity or as we'll see in a moment this language applies equally to the concept of acceleration changes in velocity with time not just space but also velocity itself can change in time and that is the concept of acceleration that we will get to next let's look at some real one-dimensional motion that is movement of an object along only one dimension I have here a small cart with some very low friction wheels and I've marked it with a green ball so that it's easier to see in the video and all I'm going to do is give it a push and let it go and once I stop making contact with this it will essentially have no forces acting on it any longer while my hand is in contact with the cart I am accelerating it I am changing its state of motion from no motion to moving but once I release my hand from the cart in principle there are no more forces acting on it now of course in reality that's not that simple and we'll look more at that later but let's take this approximation and run with it for now and see what we can learn the cart will be in free motion along the x-axis which I have defined as the horizontal direction in this video let's watch the motion and see what we can observe let's rewind and look at that motion one more time but a bit more slowly using special software on the iPad it's possible to analyze the motion in this video and get information about space and time and how they relate for the movement of the object but also how space and time together can be converted into velocity information this graph shows exactly this kind of analysis the cart was tracked by the software in the video and as you can see there is a roughly straight linear relationship between the position of the cart shown on the vertical axis in the top diagram and time on the horizontal axis in the top diagram each dot represents a sampling data point that's captured by the software and you can see that they line up very well on a straight line that makes an angle with respect to the horizontal this looks like constant velocity and indeed that is confirmed by the computer software in the lower diagram the lower diagram is generated by the analysis software using the same kinds of techniques average velocity and instantaneous velocity that we've developed previously in this lecture the velocity of the cart is calculated and shown on the vertical axis and time again is shown on the horizontal axis and as we can see apart from a few glitchy places in the time sequence of the data points where maybe there was some small force acting on the cart perhaps my hand at the beginning or a bump in the table something like that this velocity versus time is extremely flat it looks as if the cart has indeed executed one dimensional motion very faithfully with a constant velocity or at least a nearly constant velocity so close to constant that we can't really tell the difference so in this lecture I hope that you have learned how to recognize how to measure the spatial position of an object and how that position changes with time how to convert that information into information about the motion specifically the velocity the average velocity the instantaneous velocity and also come to some understanding of the difference between speed and velocity


Hello everybody hooded cober commander 788 here and it's time for another patrons choice poll I've been trying to do these more frequently because I kind of neglected them for a while voting will be on Patreon if you'd like to find out how to vote just check out my patreon Support at any level gets you the right to vote. This is your chance to decide what will be reviewed on this channel So just go to patreon and select the one you want the one with the most votes will be reviewed option one is the 1985 Cobra ferret. I think this is a fairly popular vehicle and I'm looking forward to reviewing it But maybe this will be the next thing to be reviewed if you would like to see a review of this classic vehicle from 1985 the golden age of vintage GI Joe just go to patreon and select option one option two is the 1987 Cobra Pogo ballistic battle ball. This one is sort of a classic, too I admit this one's weird But maybe you want to see a review of the Cobra Pogo and I will give it a fair shot If you would like to see this one reviewed just go to patreon and select option two option three is the 1988 GI Joe swamp masher. That's right. This perennial loser is an option again I have posted this in so many of these patrons choice polls and it always loses Well, maybe this is the swamp masher is time to shine I'm giving it another chance, and I'm not gonna review this thing until it actually wins one of these polls So maybe you want to see the long-awaited review of the swamp masher If you do go to patreon and select option three Those are your options You do need to be a supporter on patreon in order to vote But support at any level gets you the right to vote The voting will start as soon as you see this video on Monday, June 29th It will end on Friday, July 3rd, and the winning review will be published on July 19th If there is a tie, I will break the tie. I'm looking forward to seeing what you choose voting starts now


Hi, welcome Linda here from ITTT back this week with another live session. I hope you're doing well. Thank you so much for joining me today. I'm happy to see you. If you can see me and if you can hear me clearly, if everything's working, please just leave a high in the comments section and maybe also let me know where you are right now. Where are you watching from today? What time is it there? How are you doing? Let me know in the comments. We are live on Facebook and on YouTube at the same time. And we also always turn our live sessions into podcast episodes. So if you're listening to this as a podcast, thank you so much for the download and thank you so much for listening. We really appreciate that. Don't forget to like and subscribe. So you're always up to date whenever we go live. Last week we had a podcast listener who joined us live for the first time last week at this on Facebook or on YouTube.  So you never know. And yeah, we always also share a lot of really useful and interesting content on our social media, on Facebook and on YouTube, on Instagram, wherever, whatever your favorite social media platform is, we are on there and we share interesting information, whether you are already teaching. So we have like teaching materials on there or if you're just getting started, we obviously also share Teflon T-Soul course information on there. So everything for you on our socials. Oh, Crystaline is here. Hi, Crystaline. How are you doing? Good to see you. I love this purple hair on you. It looks so amazing. I love it. Someone's asking, are you Flemish? No, I'm not Flemish actually. I'm not. Interesting. I've never had that one before. Thank you, though. That's cool. All right, so this is what we're going to talk about today. Young learners and top tips for teaching English to young learners, because teaching children is a very big thing. Teaching children, young learners is a big field of EFL. If you want to teach English abroad or also online, you're very likely to encounter children along your teaching journey. So now that's all right. That's fine. Crystaline says, I'm doing great so far. And thank you so much. Awesome. I really love it. I want to try that hair. It looks great. All right, nice. Yeah, so that's basically the agenda today. And as you know, as always, feel free to leave your comments. And I'm going to get back to them. And yeah, we also have a 30% off opportunity. As always, 30% off your TEFL or TESOL course. We only share this during our live sessions. And it's also here in the upper right-hand corner. If you want to scan this QR code, you can do so. But if you can't scan it, we also have a link. So I'm going to share that with you now in the comment section. And this link will get you 30% off any TEFL or TESOL course from ITTT. So it looks like this, Facebook Live minus Linda at the end. And it will lead you straight to the application page. And you fill out your application. And it also says congratulations. You qualify for 30% off or something like that. So yeah, you know that you will get 30% off of that. Yeah, I'm also going to share this again at the end because we have people coming in and out. And I don't want anybody to miss that. So yeah, what is next? Next up, just a quick introduction about myself, who I am, because I know we have a lot of new viewers here today. So this is me. My name is Linda. And I do many different things. I always like to introduce myself this way. I just do many different things. One of my main things that I do is I'm a travel writer, content creator, and also language teacher. If you're interested in that sort of thing, so travel content, especially Asia, you can go to Linda Goes East on Instagram, at Linda Goes East. East because I'm very interested in Asia. And I've been living in Asia since pretty much 2012. I started out in China. And now I live in Korea. But I've already been in Korea for like, it's my eighth year this year. 2023 is my eighth year. Before that, I was in China. And I also run my own website, lindegoseast.com. And there I share travel information for people who want to travel around Asia, also solo travel around Asia and places, and also teaching English abroad, all of these things. And I'm originally from Germany slash the US. My mom is German. My dad's American. And I'm based in South Korea. Been here, yeah, like I said, this is my eighth year. So very exciting. I really like living here. It's a lot of opportunities, especially for teachers or people who can speak multiple languages. It's very useful. You can always find a lot of opportunities. And kind of I started out with ITTT. I took my TEFL course with ITTT, ITTT. I always have to count the Ts, ITTT back in 2014. And I just Googled, you know, TEFL course and ITTT was one of the ones that came up and the reviews were great. And I just decided to take their course. And then I also started working for ITTT, ITTT, ITTT. ITTT later on. So ITTT stands for International TEFL and TESOL Training. And we are a leading TEFL and TESOL course provider for people who want to teach English professionally, abroad or online or in other countries, then you're in the right place here. So yeah, and what else? Yeah, our website is teflcourse.net. I also want to mention that. So yeah, I think that's enough about me. If you have any questions, let me know. As always in the comments, feel free to comment. I love answering you guys's questions at any time. Also B, A, Q and A, part of the end where you can ask even more questions, but that's about it. And please guys, still let me know. Where are you right now? Where are you watching from? Let me know. I'm always super curious. Where are you watching from today? Let me know. Let me know please. Where are you watching from? Where are you at? I want to know who I'm talking to. So I'm in South Korea. I'm kind of, I'm not in Seoul. I'm like an hour and a half south of Seoul, the capital in a city called Cheongju. It's kind of in the center. And yeah, that's where I am. And it snowed yesterday and last night. So it's actually really pretty outside.  It's blue skies. Oh, it seems to be very windy. The clouds are moving very fast, but it's also snowy outside. It's very nice. All right, we have somebody here from Belgium. Unfortunately, I cannot read Russian. I'm so sorry. I really want to say your name, Belgium. Oh, is that why you thought I'm Flemish? And I guess I was born and raised in Germany, so maybe also that's why. Interesting. Oh, my sister is from Seoul. She's never been there though. Oh, cool. Maybe you can visit one time. Oh, Yana. All right, thank you, Yana. Maybe you can come and visit with her. That'd be so fun. Cool. OK. And we have Taco in France. And Lynn in Minnesota. Nice. Oh, how's the weather in Minnesota? Is it also really cold? I bet. Nice. Yana. Yeah, Yana. You and your sister, you should come and visit Seoul. That would be fun. OK, fun. OK, so good group here, France, Belgium, Minnesota, Korea, really good. Cold and snowing. Yeah, that's what I thought. Kind of like in Korea. I'm sure you have more snow than Korea though. We have a question here from Fiona. Just let me get to that. And then we jump right into our topic today. So Fiona says, do you know where I can get training so I can tutor online? I only did it face to face until the COVID. Now everything has changed. Do you do videos? I'm in Scotland. Everdeen from Edinburgh. Oh, nice. I really always wanted to visit Scotland. I'm super into it, so I really want to visit. Hopefully soon. But yes. So our courses are also good for teaching English online. We actually have a special TEFL course. And if you go to teflcourse.net, let me just share the link with you. We have a special course that is specifically for teaching English online, which is the 170-hour course. And I'm going to share the link with you so you can check it out. And I'm going to include the discounted 30% off link at the end of that link.  So which is this one? Go ahead and check it out. But I also took this course. Actually, I also got the online certification because similar to you, I was teaching in person and then COVID hit. And I never saw myself teaching English online. I was never really interested in that. But because of COVID in 2020, I started teaching English online as well. And now I'm still doing it. I really, really love it. It's so much fun. You get to meet so many people from other countries. The platform that I teach on is mostly Japanese people. So I have a lot of Japanese students, some Korean students, Chinese students. So mostly Asian because the platform that I'm on is mostly for people in Asia. But that's what I like. So I'm not mad about that. But that's kind of the beauty of online teaching. You get to meet so many different people, which is so, so cool. So yeah, this is the link. Sorry, Fiona, for you. Check it out. This is the course for teaching English online. All right, good. Then let me get rid of the spanner here. We don't need that anymore right now. And then I am, yeah, jumping in. Let's jump in. Top tips for teaching English to young learners. I've taught children of very different ages. I think the youngest student I ever had was two years old, which is crazy. So yeah, and then, well, the oldest were adults. But like young learners, I'm going to talk a little bit about the age range we're going to talk about as well. So just quickly, today's objective. So what I want you to kind of take away from this today, just to get a better understanding of how to create fun, effective, and especially age-appropriate English language learning experiences for young students. So this is basically today's objective, what I want you to take away from today. So that's what we're going to talk about. How to create fun lessons, what you should incorporate, how to make it age-appropriate for learners, and all of these things, kind of what sort of activities you can do, yeah, basically all of that fun stuff. And what we're going to talk about first, so we get a better idea. We need to understand young learners. So who are young learners, and what are kind of their issues. And then we can take that and look at the activities and the hands-on things that we can do. So understanding young learners, and I'm going to make myself smaller so you can read this. I hope it's still not too small. I think it's OK. But let's have a look at the developmental characteristics of young learners. And young learners, well, here it's a 6 to 12. I would actually say literally 0 to 12, probably, are young learners. So sometimes the age ranges, depending on the book or whoever talks about this topic, it varies. Some experts have different opinions about what young learners are. Some people put it as high as 18 years old, or even, yeah, I think 18 is probably the highest somebody would put it. But here it's just, like I said, 6 to 12. I would even go lower than that. Like I said, my youngest student was two years old. And definitely the information that I'm covering today also would apply to that. So I would say 0 to 12, probably, would be the age range that we're going to talk about today in terms of young learners. And here in yellow, listed the things that make up the mind or the characteristics of a young learner that you, as their teacher, should be aware of. So as we all know, children have very short attention spans. So that's very important to know. And that's, I think, one of the most important things and one of the biggest differences compared to teaching adults or older children that their attention spans are short. So you really need to take that into consideration. And that's why you really should mix up the activities as much as possible so that they don't get bored and that they can stay focused and motivated. And that's also something we're going to talk about. All right, Daniella. Let me take this question real quick. Daniella asks, what would you recommend between the young learners course versus the business English one? So I took both of them. And I also took the online course. It depends on where you want to go. What kind of students do you want to teach? And also maybe the country that you want to go to or whether or not you want to teach English online. Like I said, young learners is actually a very big field of English language teaching. And especially if, say, you want to go abroad and teach English in Asia. Asia, most of your students are probably going to be children. Most of the positions for English teachers in Asia are going to be children. So then the young learners course would make a lot of sense. However, if you're like, no, I only want to teach English to adults. I'm not interested in teaching English to children. And obviously maybe the business English course would be better for you if you want to go in that direction. So it really depends on you and what you want to do. All of them are extremely useful. That's why I took actually both of them. But the one that I took first was the young learners course because I was already teaching children at the time. And I knew that I was staying in Asia. In Asia, you teach children more. So I took that first. But then I also ended up taking the business English one. And I also taught business English after that. So both of them are extremely useful. It just depends on you, what you want to do, and also the destination where you want to go to. All right, great question. Let's get back to that. So like we said, the first thing was the short attention spans. We all know this, children have short attention spans. So that's the number one thing to think about. And then also that they have difficulty with abstract concepts. That's why it's important to bring in actual props and flashcards and little things they can see physically in front of them, basically. And yeah, they learn through play and hands-on activities because of that. They also, this works so incredibly well. They get highly motivated by rewards and praise, of course. So rewards and praise is extremely important for young learners, more so than any adult learners. Of course, you should also praise adult students. But with young learners, you really have to continuously praise them and say, good job, good job, great. And we're going to talk about that more also later on with reward systems. Young learners, they also enjoy learning from music a lot. And this is also something we probably all know, that music rhymes and any kind of song works extremely well. And this is really a big thing you should incorporate into your lessons as well. Any kind of music or song to help with new vocabulary. I mean, just think about head, shoulders, knees, and toes. And those songs, they just work incredibly well to learn vocabulary and are fun. They also have limited vocabulary, of course, and difficulty expressing themselves. So we're also going to talk about this, how to deal with that. But basically using easy language, you can't talk to a young student the same way as you would talk to an adult student. Obviously, you have to use simpler words, easier words, a lot of visuals, these kinds of things. So also the next point here, they are very visual learners and they respond well to pictures and videos. We all know this too. And they're also not capable of deep reasoning and critical thinking. This is where some classroom management techniques will come into play. So I think these are the most important things that you should know and recognize that are the characteristics of young learners. And I know that many of us know most of these things already, but it's just good to kind of internalize these things again and really think about what that means for us as teachers, for our teaching, what kind of effect this will have on our lesson planning and on our classroom management strategies. That's very important. Just kind of think about this again. Yeah, think about you when you were younger or any other younger siblings or cousins that you had and how they are. And then you can also take that experience into your classroom. So anybody wants to add something to this list or any other comment or experience, please let me know to here. Hi, Amitava. Amitava says, hello, Linda. How are you now? I'm doing great. How about you? Thanks for joining us. All right. Good. So then once we kind of understand what young learners are and how they are, their characteristics, we can then have a look at also why it's important to create each appropriate lesson plans for them. So each appropriate lesson plans are tailored to their developmental levels. So all of these things that we just talked about, you need to think about these things and then create appropriate lesson plans for these. So you want to make your lesson plan as engaging as possible so the more engaging, the more effective it will be. You need to take into account also your students' interests and abilities. Interests very important. This works really well with current Disney movies, whatever is in right now. You can incorporate these characters or stuff about them into your lessons. That's what I do. Or whatever, like Baby Shark was a thing a few years ago. Like whatever, there's always a hot thing right now that they love, right? Or some kind of character, movie character, cartoon, I don't know, some kind of thing. You can use that, their interests. And it's already more exciting to them. Obviously provide appropriate challenges as well. So don't make it too easy, but also don't make it too hard. So have challenges, but also a support system for them. And then foster positive and inclusive, foster a positive and inclusive learning environment. That's also very important that everybody's welcome here. And it's just a very positive experience for these children that's very important, a lot of, especially in English, foreign EFL in English as a foreign language teaching. Many of these kids, they only use English in your classroom. And it might be strange to them to use a different language. And they might not feel as confident. So having a positive and inclusive learning environment is really, really key here. And from there, you can really help the students develop a love for learning through all of these games that we're going to play and talk about. And also build your students' self-esteem and confidence here and just make the learning process more efficient when you keep these things into consideration. All right. Yana has a question here asking, do you have videos where you are teaching? Oh, I actually don't. I don't think. No, I don't have videos of myself teaching. But we have other examples of other people teaching on our YouTube channel. You can check that out. Cool. Then, oh, Fiona. Fiona has a question. Let me take that real quick. So Fiona says, hi, thanks for the link. I'm already a qualified TESOL tutor already, not full TESOL. Although I did it years ago, do you have shorter courses with ideas, tips, how to tutor online? I think a lot of people would like ideas like this. Yeah, so if you are already TESOL or TESOL certified, you can do a specialized, just a top-up course. And this is a really short one, 60 hours. Let me also send you that link. And you can see the information there. So this is for people who are already certified and have the minimum 120-hour course. Let's see. Let me paste that link here for you. Here. Looks like this. So these are the specialized ones. And here, as you can see, there are three here. We have teaching business English, teaching young learners, and teaching English online. So you can take these individually. They're very short, 60 hours only. And like I said, the requirement is you already need to have a Teflora TESOL qualification to take these. If you don't, you would go through the 170-hour course, which is the 120-hour course plus the specialization. OK, good. Great question. All right, let's make this bigger again. And now, once you understand all of these things, let's look at how exactly we create engaging lesson plans. How does this all work? What does this look like? Some tips and tricks here. What you should do for young learners. Let's have a look. Oh, I really hope this is not too small. But basically, these are a lot of really great tips. And I'm going to show you some pictures also and where you can find some resources and ideas. So obviously, for young learners, using games and activities are great. And also, that involves multiple senses are really, really great. So with children, you can really activate all of their senses. And that really increases the learning process even further. So that's really fun. And then also using real-life examples to connect the topic to the students' experiences, because this is that they cannot really imagine or process abstract information. So you want to have as much real-life examples as possible. I mean, the textbook example here would be the fruits and vegetables that you bring in or the props, the plastic fruits or wood fruits, the props. When learning about fruits and vegetables or you bring in the real thing, whatever, it's reasonable. But this is the classic example, bringing in those things. Yeah, you could also do things like show and tell here. So they bring in things. Just having the real thing in front of them is very important. It really enhances the learning environment. Of course, you cannot do this with everything. So I'm not saying you always have to include all of these things.  Also with young learners, it's very important to encourage group work and collaboration. So that is something that works really, really well. With young learners, they like to do things in a group and that further enhances the learning process as well. Of course, then sometimes you have some classroom management issues, people fighting or children. Also, some of them are very competitive. But that then further increases also the learning. They really want to learn and they want to be the best. But it just can also be a really nice experience to have them work in groups. Also nowadays, what we see a lot is using technology to enhance learning. So we have these big interactive whiteboards. And this is something that we used at the English-speaking kindergarten that I used to work at. We had this big whiteboard and the school had their own interactive lesson materials so you could pull up all these videos, interactive things. Sometimes you can even touch things. So that's always really fun. We see a lot more of these things available now in classrooms. And if you're teaching English online, you have so many unlimited opportunities here with using technology. Zoom has so many amazing features or even the thing that I like to use is MyRow. It's basically a whiteboard, an online whiteboard. I'm just going to put it in the comments. MyRow, what it's called. I use this for online teaching as my whiteboard and it also has a lot of features. You can include videos and songs. And it's very interactive. It's really, really nice. So with this kind of stuff, the world is really your oyster. You can do what you want. It is so exciting for children. Or even what my students really loved. If you Google ESL Games or something for the classroom, you have cool little games that you can play in the classroom. And you can make teams, for example, that also really works well. And the students always really enjoy that. Then we have using visual aids. Of course, we talked about this already. Images, videos, or even diagrams work really, really well with children. And then also, you want to incorporate movement and physical activity. I think sometimes that kind of we forget about that. Because it kind of can get out of hand when you have children moving around. They can go a little bit riled up and crazy. So sometimes you need to read the rooms sometimes when you know your students. And today might not be the best day to do this activity. Then you know. But yeah, just incorporating any kind of movement is great. A lot of clapping activities you could do, especially with phonics and things. Spelling, when they clap for every syllable of the word. That's very common. Or clapping is super easy. They don't have to really get up. But it's still movement. And then, of course, things like mime are popular. Or when you learn any kind of verbs, they can come. And you can all do a swim. You can do the movements together, run, jump. So these kinds of things.  And then also, of course, we talked about this already. And we mentioned that a little bit of music and songs to teach new vocabulary. Literally, there's so many English songs out there for children. Pretty much for every kind of new vocabulary, you can just type that into YouTube. You can put it up little songs that they can follow. Usually they have a dance attached to it too. So you can kind of have a two in one here. And that works really well to kind of introduce new words, because they just sing along, follow along. And then that works really, really well as well. Then we have, of course, storytelling and role playing, fairy tales, any kind of story, books. The school that I worked at, we had a big library. And we would have reading lessons there as well. You could get books from the library for pretty much any level. You can show the book. And you can maybe read a page together. That works also really well. And of course, role playing. Maybe for a little bit older children, role playing is great. They can come up with their own stories.  So these kinds of things are role playing things like buying something at a store. These are very common role play activities that works really, really well. Anything like that. And then also using hands-on materials like manipulatives. So manipulatives are things like letter blocks, magnetic letters, dominoes, puzzles, dice, flashcards, even Play-Doh or clay. Anything that they really can touch and that they can do something with. So these are really, really great things to do. Okay, Fiona says, thank you. It's 2 a.m. here, so hope to watch this again soon. Oh, thanks so much. Thank you, Fiona. Have a good night. All right, good. And depending on a lot of teachers, if you are teaching alone or whatever your situation is, a lot of schools will provide you with these kind of materials.  I also have a jar of magnetic letter blocks here. That's just something nice to have, you know, around the house, I guess as an English teacher, you can use these. So that's really, really fun. Good, okay. I hope maybe this gave you a good idea and some ideas for creating hands on activities. I also have some pictures here and I really love to use Pinterest for these kinds of things. So literally you can type in whatever it is you're looking for. So like EFL or, you know, EFL, I don't know, color activity or something and something will come out. So there's so many really cool things and you can get a lot of inspiration from Pinterest. So these are a couple of cool things that I found. We talked about using five senses, which is the first one which you have, touch here, smell, sight, taste, really, really good. And then also again about the five senses, something with Mr. Potato Head here, which is cool, you have to kind of build his face. I thought that was kind of neat. And then we talked about dough, clay or play dough. So we have that here too, the number three. And again, you can do this with letters. They have to form like little letters or with animals or anything like that. That works really, really well. Up there with the alphabet, there are some hands on activities. I think they put on little marbles on all the words that start with a B, looks like it. And then also phonics, ideas. I mean, really, Pinterest will be your best friend. I think for teaching English to young learners, definitely sign up if you haven't yet and just you can type in anything in the search. And I mean, just getting this, I think took me five minutes. So imagine if you spent an hour on there, you will have so many things to work with in your classroom. Okay, then let's have a look at how to make learning fun for young learners. So here we have two kind of ideas. These are games and activities to support learning when you first learn something and then games and activities to practice the language, what you've already learned and then practice that. So for supporting learning, we have using songs and chants to introduce new vocabulary in grammar. So we already talked a little bit about that, but you can find a lot of songs free on YouTube to use for new vocabulary. A lot of teachers also make up their own songs if you are good at that, you can do that. Of course, also crafts and art activities to practice vocabulary and grammar in a creative way are really good to introduce new words. I think also one great way is to introduce something new with the video, perhaps, or flashcards. I'm really like, it's up to you and your imagination what you wanna do here. Then we have the games and activities to practice language. So here you can use popular things are games like charades and Hangman and bingo, very, very popular for vocabulary words to use to practice. And then again, we already talked about this, but incorporating movement and physical activity wherever you can, incorporating technology like videos and interactive whiteboards or apps are great for practicing the language and then also using storytelling and acting to practice language and encourage creativity is great. Using puzzles and matching games are always really fun ideas for children to reinforce vocabulary and grammar concepts. Those are really, really great. And flashcards and memory games to practice the vocabulary, but you can also practice grammar things and sentence formation. You can have cards of different words and they have to put it in the correct order, for example, things like that. And again, we have incorporating real-life scenarios and examples to make learning more readable and meaningful. So yeah, these are the things that we can do to make learning fun. And then let's talk a little bit about the classroom management side of things, what you should be aware of when teaching young learners.  Very important here, based on what we talked about in the beginning and their characteristics. So first it's important to establish clear rules and expectations. And this is where things like rules posters come into play. And I put one up here. Again, I found this also on Pinterest. You can type in pre-K or EFL rules poster. And things will come out. So I thought this was really cute. This looks like something for really low level beginner, even with the pictures on it and just two words, very easy to remember. And this is something you should refer back to, maybe even multiple times throughout the day. When there's something, someone's not listening. It always also point pointing, so you're just listening ears or something. And then the whole class repeats. So make it fun, but also kind of make it clear, hey, these are the rules. And this is also something you can do together on your first day as the class really established these rules early on so the students know and make it easy. Again, age appropriate adapted to their level. This is a really basic one with pictures and just two words. So I think this works really, really well. And then once they are getting better the next year you can kind of change it up and make it a little bit harder with whole sentences and things like that. That's one thing, the class rules. And then also one important thing are the reward system. So children work extremely well with positive reinforcement and praise. We talked about that, but they really love something kind of hands on that they can see how well they are doing. They really love that. And I like to use a reward system like a sticker board. So this is something like this here. And at my old school, we had every student had their own like actual physical sticker book at the front of the class. It was like under the white board. So they would always kind of see their own sticker board. And whenever they did something good they gave a good answer or they were sitting nicely, listening nicely, whatever helping someone, they would get a sticker. And then at the end of the day all of their collected stickers they can come up and put it on their sticker board. And then once that sticker board is full there would be some kind of reward, right? Up to you to decide what the reward is. So at our school that was kind of like just a school how they did it when the sticker board was full they would get I think some kind of vouchers. And then once a month they had a market day at the school and they use these vouchers to buy little pencils and little erasers and little notebooks and stuff like that or little toys. But now that I teach online or private students I also adapted the system for one of my students online we have online a virtual sticker board. And once that is full we play a big game for the whole next lesson. So that's kind of the reward. And that student really loves that as well. It works extremely well. Yeah, and then also for the classroom management things like I said, using gestures and visual aids. So you wanna have things like these, these classrooms hung up in your classrooms they can see it. And then again point, looking eyes, listening ears, quiet mouth, gestures. A lot of gestures, right? And just using, this is great for classroom management again using diverse teaching methods, lots of different activities. And this had to do with the short attention spans that we talked about in the beginning. Young learners have very short attention spans so you really need to mix it up. And this can be very daunting for new teachers because you don't know a lot of activities yet or it can be quite challenging when you know you're doing something and then the whole, the young students they just, it's a mess and they don't pay attention and like, you know, it kind of gets out of controls. It can be very overwhelming but the more often you do it, the better it will be. And you should always have a few extra activities on hand that you can do in case one of the activities that you wanted to do doesn't work. Always have something extra up your sleeve basically. And also use interactive group work. This works really well for classroom management. They kind of keep each other in check a lot of times. Of course, if you have two students, you know, who can't work together very well, they create trouble together then separate them, put them into different groups. But I think these, how many five techniques for classroom management for young learners are really, really important and you should definitely keep that in mind. And again, Pinterest for researching reward systems. There are many different reward systems out there and different classroom rules, posters and stuff you can find on there as well for different levels. So I highly recommend checking that out. Good. I think nothing more to add to this one. This one was great. Again, if you have any questions throughout the live sessions, don't hesitate to leave your comments.  I do it a certain way because the school that I worked for did it that way and then I put my spin on it and now I do it like this. Obviously this is not the only way to do things. So if you have any other ideas that would be great, I love to learn something new and just share something different perspectives, different ideas with other people. Thank you. Parkush says, very useful tips. A very good morning from Pakistan. Hi. Very good morning from Korea. Thank you so much for being here Parkush. Okay. And then, so this is already the quick review of what we talked about and the main things that you should keep in mind from today's lesson. So emphasize on visual aids, interactive activities and games. Games, games, games will be your best friend to mix it up and get that variety in there. Again, also incorporating real life examples is very important and also personal experiences. That's also very important. Every time I kind of talked about myself with my students, they were all yours. They were like, oh, what did Ms. Linda do? What is her experience? They're always curious to learn about you as well. Again, age-appropriate and interesting materials, make sure they are age-appropriate and level-appropriate. They're not too difficult, but they're also not too easy and still a challenge. Providing immediate feedback and recognition, that's what we talked about right now. Giving out praise and then the stickers, if you wanna do a sticker board, whatever reward system you're using, do that. Then just encourage them the whole time. Encourage active participation, you can also do that.   Is Anna like, you can encourage other students to also participate. Does only Anna know the answer here?  Who has the answer to this one? I think I'm gonna give two stickers for this answer and then you're gonna have a lot of hands up. So just little things like that. Again, also using diverse teaching methods, don't just stick to one. Use a variety to keep it fun and interesting. Provide opportunities also for natural language practice. Try to have a natural conversation with your students or using songs and let them sing in a natural way. Incorporate music, songs and rhymes, really good. Group work, again, is really good. And the technology in the classroom. You can use a lot of different things nowadays. A lot of opportunities for technology in the classroom. Like I said, especially also online, the virtual classroom has so many opportunities. It's really, really interesting. So these are the main takeaways from today's live session. I hope that that was something interesting and that you'll learn something new. And please, if you have any additional comments or feedback, please, please add that. Here are some more examples and ideas of actual things you can do. But it's something we already talked about a little bit, but just you can have a read through those things. And also let me know what you think, what some good ideas would be. Yeah. So, and now it is time for the Q and A. Let me know. Of course, this was a quicker teaser. If you are more interested in teaching English to young learners, of course, we have this course. And many of the things that I talked about today are in this course as well. Of course, the course goes into a lot more depth than today's session. So today's session was a brief overview of young learners and what that all means and a few little techniques here and there and just understanding. We are 48 minutes in already. So thank you so much for being here. And yeah, I'm not leaving yet. So we still have time to answer questions. And Taku says, thank you, really interesting. Thank you. I appreciate it. I hope there was something interesting in there. I know a lot of people already know this information, but keep in mind we are all at different stages in our teaching journey. So there are a lot of people who are here who are listening to this for the first time. And have no idea about it. There are some people who've already taught children and this is all not new information maybe for a lot of people. Just keep that in mind. We're all at different stages in our teaching English journey. Yes, Yana has a few questions before she leaves. Of course, I'm still here and the Q&A session is just kicking off now. So now is your time to ask the questions. So first of all, are these courses only for native speakers? No, no. So they are for native speakers and fluent English speakers. So from what I can tell you're fluent in Korean, I almost said fluent in English. So definitely you can take these courses. You don't have to be a native English speaker to do these courses. And there are also many online platforms or countries where you can teach English and you don't have to be a native English speaker. Then the next question is, did you encounter people, teachers that just lived for many years in an English speaking country, but while English not being their mother tongue? Yeah, I know several people, yes. I would say I'm probably no more foreign because I live in Korea. I've lived in Korea for so long. So I know many people living in Korea who come here as English teachers or in China, people who moved to China to become English teachers and many of them were native English speakers. Many of them were non-native English speakers from other countries. So it's very, very mixed, mixed people. And that's why I really enjoy this career path because you can really meet people from all over the world. It's really, really interesting. Yeah, Yana says their slight accent doesn't bother the future employer. Well, that's why they have interviews, right?  They have interviews before and maybe some employers would be bothered depending on how strong your accent is. It depends on the employer. So some schools are very particular about that. They even go that far as to say, we only hire American accent teachers or we only hire British English accent teachers. Some schools are like that. I would say they're fewer, not that many schools are like this particular. The school that I worked at, we had people from everywhere. We had people from the US, from the UK, Ireland, from Australia, South Africa. So all different kinds of accents. And I also think that this is something that's changing in the Tethil world, whereas an accent is not seen as something bad because everybody has an accent, right? Even Americans have different accents in America or in the UK. There are many different accents in the UK. So nobody speaks exactly the same. And yeah, Yana says I've always wondered, I'm not worried about my accent, no worries, everybody always asks if I'm from the US, got my English from friends to come. Oh yeah. Oh, a lot of people actually say that. Learned English by watching friends, that's interesting. Yeah. So it depends on the employer. That's the answer I would say. It depends on the employer.  And then if they don't like you for any reason, they would not hire you. It's just as simple as that. If you are a non-native English teacher, we always recommend the more qualifications you have the better. So for non-native English teachers, you wanna have an English proficiency certificate, if possible, like a Cambridge certificate or TOEFL and IELTS, any of these things that will really give you a boost as well. Or if you went to school, if you went to university, in an English speaking country, those kinds of things, they will also give you a boost. I hope that answers your question. All right, thank you so much. Let's see, who has another question? Who has another question? Yana says, I gave the TEFL course tip to my Irish friend. He's now eight years in China teaching English. Oh, great, cool. Thanks a million for the answers. You're welcome. Daniel, hi Daniel, how are you doing? I'm doing fine. Would you encourage young learners to use AI tools for learning English? I've just learned about this chat GPT app today. I mean, why not? I think AI can be good, right? So why not? If that helps you, everybody learns differently. So what might work for you, doesn't work for me. What works for me might not work for you. So things like that. But if you can learn, let me know how you use it to learn English. That'd be interesting. Can it create, it can probably create quizzes. You could also use it as a teacher to create material. I think that would be great. Create, like, you can create all kinds of things, I think, with that. That will help you with your teaching preparation, I think. All right, Parkush has a question. Is it important to choose American or British accent for young learners during their English learning journey or should they continue with their natural accent? I would say also American or British English. These are also not the only two English accents that there are in the world, right? I would say let them discover their own accent. That's why at my school, we had, like I said, teachers from all different countries. So we had many different accents and kind of the students. In the beginning, the students didn't really notice that there was a difference, but as they got older, they were like, oh, this teacher says it like this and that teacher says it's like that. Why is that? And then we explained to them, well, because this teacher is from Ireland. I am from America, so we say things differently. But then they would just pick, you know, whichever pronunciation they prefer and they would go with that. So I think let them decide on their own, which, what kind of pronunciation they prefer. They will figure it out and they will just naturally slip into their own and what they prefer. That's a good question though, thank you. In Poland, they'd kill for an English teacher with an American accent. They don't like British accent there. Oh, they don't. Oh, okay, interesting. Okay, yeah, with the accents. I think that is just kind of overrated. You know, do not worry too much about your accent, American accent, British accent. I don't think that matters much.  If your grammar is good, if you can speak fluently, if you can have like proper conversations, that's important. I don't think having this or that accent is important. That's not what matters. Mmm, last question. What was your biggest obstacle to starting teaching in class? Oh, let me think about that for a second. I think really, so I first taught in China, also children, and then I came to Korea to also teach children. I worked on an English teaching kindergarten. I think like really, for me personally, and this is just me personally, everybody's experience will be different. I think classroom management is very important, especially for young learners. So adult students, you don't necessarily have to worry about classroom management because they, adult students, they really wanna be there, and they usually pay for your class. They wanna be there, they wanna learn, so they behave with young learners. It's usually the parents, you know, taking them to that school. It's oftentimes something that they don't particularly wanna do, right? So sometimes they act out or they just are not motivated. So that can be a challenge. So just knowing like these little techniques that you can do, you know, to get them motivated, to get them interested. I think sometimes that can be challenging, but it's also about, I think that that's something that happens over time. Every class is different, every student is different. So the more you teach them, the more you get to know them and they get to know you, then you'll find out what kind of person they are, what do they enjoy, and that will help you in your lesson planning and that will make your lessons better after a couple of times once you know them. So the first few times when you don't really know them yet, the classes aren't going to be perfect probably, but that's just normal, that's just normal. You have to get to know them, they have to get to know you. That's why it's so important to establish these class rules right at the beginning so that they know basically who's boss. These are the rules, you have to follow them. If you don't follow them, you know, something's gonna happen. If you follow them, you get rewards. And so I respect you, so please also respect me. So have you a mutual respect? I think that's kind of what I always aim for. So that's kind of difficult. And what method do you apply for the pronunciation? Well, you can do pronunciation drills, you know, usually depending on the country that you work in, that you teach in, you will kind of figure out, oh, like the Korean speakers, Chinese speakers, oh, they have like this problem with this pronunciation, R pronunciation, F pronunciation.  Oh, how, you know, how do you, how do we say that correctly? Always also repeat, right? Say the word, have them repeat it. I think that works really well. And a lot of times with young learners, I tend to be like not too strict with these kinds of things. For a lot of them, these are, you know, English, they don't use this at home. They only use the, they only use English in your classroom for a lot of them. So they don't have any other way of learning and it's very new to them. A lot of sounds in the English language don't exist in other languages. So it might be just hard to replicate for them, but usually kids are very smart and kids pick up new languages very fast. So that too. But yeah, I would say vocabulary drills and just correcting them, not over-correcting them, but just when it's really bad, correct them. That's what I personally do. Linda, have you ever used a British accent when speaking? So my dad is American and I've spent a lot of time in the U.S. So my accent is an American accent. Of course, I think we all kind of tried to do a British accent before we, you know, we try. I'm actually fascinated by accents. I'm very fascinated when, especially in movies, right, when actors from different countries play roles and they have to change their accents. It's very fascinating to me. So I used to watch, there's this lady. It's a very old video now, I think on YouTube, but this lady called Amy Walker and she has a video out of all the different like English accents and she does them flawlessly. It's amazing. You can search on YouTube, Amy Walker, English accents or something. If it's still there, it's a very old video. I've watched that long time ago, but that was very fascinating to me. So I always, I always admire that I cannot really do a British accent. So I'm not gonna do it.  Then Yana says, do you encourage knowing the local language of the place you're teaching and use it in class? Mix it up a little or would you say to no go? So there's two sides. So if you, for me, I moved abroad to China. I moved abroad to Korea. So for you personally, when you live in a foreign country, it's always a huge plus to know a little bit of the language, of course. So if you know, hey, I'm moving to Korea, take some lessons before you arrive is great, right? So that you can know, yes, please, no, thank you. This, please, whatever, you can communicate a little bit. That's always great for you. It makes your life abroad a lot easier. In class, I would say no, I would not use, I personally do not use other words unless absolutely necessary if there's like something they really do not understand. And I know the other word, I can just say it.  So at our, at the school that I worked at, we had an English-only policy. So in this school, everyone was only allowed to speak English, total immersion. So some schools are like that, some schools they don't have a problem with you also using their language. For me personally, I just don't think it's a good idea because like I said, especially young learners, once they know that you understand their language, they get lazy and they don't make an effort to speak English, so I would avoid it if you can. Daniel says, the Scottish one, the Scottish accent is really hard to get and imitate. Yeah, it's so fun though. I love Outlander, the show, and which takes place in Scotland, most many time or like parts of the show. The people are from Scotland and it's really fun to listen to their language or their accent. Yeah, that's cool. Okay, one more question. I have time for one more question and then I think I'm gonna head out. But thank you so much for asking all the questions. It's really, really interesting and really fun to answer. Thank you, Yana and everybody, Daniel. I appreciate that, Parkaj, Fiona, everybody who had really great questions. Daniela, Lynn, thank you so much. So one more question guys and then I'm gonna say goodbye, but I will be back next week. And next week we're gonna have a full Q&A session for the whole hour because next week is the first Friday of a new month and every first Friday of a new month we do Q&A for the whole time and a general Tefalteasal information, anything that you're curious about. All right, Yana says minimum class course online to be a perfect teacher in my opinion. Ooh, well, it depends. Is it your first time teaching English online or teaching in general? You know, this will really differ and vary from person to person. So I started teaching English online, like I said in 2020, before that I was already teaching in person. And of course, a lot of the techniques that you use for teaching in person, you can also use online, but you also have to learn a lot of new things, especially the whole different way of how a lesson like works in a virtual classroom. There are no worksheets, you don't have a board, you can't write anything on a board. So you have to use all of these virtual tools and there's so many features and stuff. So I think that takes time getting to know the platform and everything you can do. Because once you understand the tools that you can use that are available to you, then you can know what I can do in my classroom, what kind of activities I can do, what stuff I can plan. So I think it takes time to understand your online platform. And then from there, there are just a lot of things, also the technology. So it took me a lot longer to get ready for an online class. I would sit on my desk like 15 minutes before the class starts, probably, or even maybe my first class, I was there 30 minutes before. I was getting everything ready, going through the lesson material again, and then it came down to 15 minutes. And now it's like, oh, I have to teach in five minutes. I'm going to sit down now. So the prep time, I mean, depends. Yeah. All right. Thank you for your questions. It was nice meeting you. Hopefully I'll see you again next week. We'll have a more Q&A that time. You can ask me all your questions again. Or new questions, of course. More questions. Have a nice day there. You did a great job here. Oh, thank you. You also did a great job in asking questions. Thank you. Amitava says, Linda, I have an important question to ask you. I want to know whether there are any basic income inequality or discrimination between native and non-native speakers for teachers who receive offers to teach abroad. That's a great question. I'm not sure I'm the best person to answer this. Of course, I do not have a actual comparison. I can tell you that there is definitely some difference in pay and salary between people who are TEFL certified and not TEFL certified. This is something that I personally experienced. I had a TEFL certificate when I applied for my school and my colleague who started work at the same time didn't and I actually made more money. That is true.  Now, with your question, the difference between native and non-native English speakers, I actually have a really good video for you. This is from, I think, two years ago. Me and my then colleague Lisa, if you remember her, we did a video together. The difference is between a native English teacher and a non-native English teacher. We went through that and I believe sometimes, I'm not quite sure anymore of her answer, but she said it depends, of course, on the school, on the location, but in some cases, yes, non-native English teachers made less money. But in some cases, they made the same money or even made more because they had more qualifications. So it really depends. But go and check out this live session that I did with her because we talked about these differences and it was super interesting because she obviously is a non-native English teacher and she's taught in China and online. And I'm the same, but I'm a native English teacher. So that was very interesting. And it was one of the first videos we did. It was a long time ago. So search for that in the playlist. It's very, very far, like in the back. Let me see if I can find it. But it's with us together. This is a really good live session. So it will answer a lot of your questions, I think Amitava, and I really hope I can find it quickly. Yeah, I think I'm almost there. Oh, here, I found it. So this was December 4th, 2020, native English teacher versus non-native English teacher. Let me share that with you in the comments and you can have a look. Very interesting. And I think, like I said, it will answer a lot of your questions. And Amitava says, thanks a lot for all your kind suggestions and support at all the times to come. Here's wishing you a happy weekend. Thank you. So Amitava, copy and paste this YouTube video link and then have a look at me and Lisa. We discuss native English teacher versus non-native English teachers. You know, what are the differences from our own experiences and pay and salary definitely was one of the things. And Lisa talks about that there. So I hope that will help you. Okay. All right. Then this will be it. We are in one hour and 12 minutes. So thank you so much for all of your questions. I really appreciate you guys always being here and asking so many questions and tuning in every week. I really, really appreciate it. And please tune in again next week when we have even more time for Q&A and information about Tefl TESOL. I would really love to see you there. So any questions that you have, please save them for next time and ask me then. And yeah, thank you so much for today. And I hope you have a great weekend. Don't forget to like and subscribe. And if you're interested in Tefl and TESOL training, use this 30% off link. And let me just share the whole link with you one more time in the comments. This will get you 30% off any Tefl or TESOL course from ITTT. So this is a great start, especially now it's a new year. So if your goal for 2023 is to get Tefl or TESOL certified and to start teaching English as a foreign language, this code I think could be your first step. Don't pay full price, save money with this code. And then I hope to see you all again next week. Thank you so much. And I see you all next week again, I hope. All right, I'm out. Thank you guys. Bye.