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Hi, and welcome to the VEX Classroom. My name is Lauren Harter. In this video, we're going to be talking about the Cartesian Coordinates System and the V5 Workcell. As a former mathematics teacher, I can't tell you how excited I am to be able to show you some of the different ways that you can teach the Cartesian system, reinforce it, or give your students an opportunity to explore it using the Workcell.

One of the key aspects of the V5 Workcell, and mathematics in general, is understanding the Cartesian coordinates system and how things move in 3D space. Whether your students are learning algebra, geometry, advanced physics, or even calculus, understanding coordinates and how they represent different points in space is a valuable skill. This is especially true when working with the Workcell, where programming the arm to move to a designated location in space is essential.

Understanding these points in space is not only crucial for coding the Workcell or manipulating the arm but also in general mathematics and other areas where students will manipulate coordinates, deal with different systems, and solve equations involving the Cartesian system on a larger scale.

Let's start by looking at what the Cartesian coordinates system looks like on the V5 Workcell itself. Here's an image showing the Cartesian system with the X and Y plane, and the Z axis going up in space, overlaid on the Workcell. The X axis moves in the positive direction towards the brain, the Y axis acts parallel to the brain, and the Z axis goes up.

Students may initially find it confusing that the X axis is not horizontal, as they are accustomed to. It's important to remind them that, in this case, the X axis moves towards and away from the brain. This can be a point of confusion at first.

Depending on the version of the Workcell you have, students might also get confused about which axis is which. For example, with the earlier versions featuring a whiteboard and the lab versions with conveyors, there are various ways to reinforce the Cartesian system and help students identify the axes.

One method is using the whiteboard attachment to draw and label the axes. You can write directly on the whiteboard surface, marking the positive X axis. However, the whiteboard doesn't extend all the way to the back. For students who continue to forget which axis is which or confuse positive and negative directions, using tape or another marker on the Workcell can be helpful.

Thank you for watching this video on the Cartesian Coordinates System and the V5 Workcell. I hope you found it informative and useful for your teaching. If you have any questions or need further assistance, please feel free to reach out.

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Add it to the other side as well so you can see. Now, this is something that you can keep on the Workcell as your students are working to give them something to reference until they gain enough experience or they recognize it enough that you don't need it anymore. It's an amazing training wheel situation that you can give your students if they are getting confused.

Now, this is the Y axis that you can see here. Again, the whiteboard doesn't extend all the way to the back, so I can use this. Something else that's really helpful is we have these standoffs at the bottom. You can see them a little bit better in this picture. There are standoffs at the base of the Workcell, and those standoffs are actually what's going to be used to designate the difference between the different axial points. The Y axis actually starts right along that standoff, and the X axis starts right along the standoffs there as well. A great reference point to have there again, if you're wondering where to start these lines or give students something to actually look at, that's one thing that you can definitely do.

Another thing is I can draw on here going in this direction; this is actually in the negative Y axis. Having that tape and being able to write on it is again a really helpful thing that you can use for your students. As far as actually labeling the tape and things like that, we do have examples of what that looks like. You can see this as blue tape here, but you can use any sort of tape. You don't even have to use tape; you can use something else that your students can write on. I've also found that sticky notes have been very helpful in this particular situation. Just some ideas that you can use for your students as they continue to work through the labs and work more with the Cartesian system.

Another reason why this is so important is because not only in this particular application, but being able to give certain points in space an accurate measurement is really important. I can't program this arm to actually go to a certain point to either pick up and move a disc to a particular location if I don't know where the end of the magnet should go. We have these different reference points.

One of my favorite questions that I used to get all the time as a teacher is, why does this matter? How would I ever use this? What is the Cartesian system? Why do I care if I'm graphing points on a worksheet? I got those questions all the time. As a former math teacher, I used to have my students practice working with the Cartesian system by actually plotting points on worksheets, connecting lines, and different elements like that just to get them familiar with the different quadrants and also what's positive and what's negative. In general, the difference between positive and negative and their directions can be rather confusing. Plotting those on worksheets is really helpful to help students reinforce.

I found that actually giving them an extra layer and giving them that real-time analysis, that ability to be able to see what those very abstract concepts are, is beneficial. The X and Y axis in the Cartesian system is a very abstract thing. It is on different graph papers and things, but in terms of actually putting that into a real-world situation or giving that a context can be very confusing and also difficult, not just for students but also for educators and anybody that's trying to reinforce this concept with students. I found that actually using the Workcell to enforce that concept has been extremely helpful and beneficial. It gives students that answer to, when would I see this? How would I use this? Why is this important?

So giving that manufacturing context and more specifically with the Workcell allows them to see, "oh, I can see that the X and Y are these boundaries that I necessarily can't see but I can label them." And I can see how the tool tip of the Workcell actually moves in those different quadrants, and then I can relate it to the code when I'm telling it to go to a specific XYZ location.

So that's just one other element to this is again, bringing that to life, bringing that abstract mathematical concept to life is an amazing way for the Workcell to be able to do that. So again, dealing with the labeling, that's just one technique that I have used that I have found very helpful for students.

Another thing that they get confused with is the quadrants. So understanding which quadrant is which, and not only can you do this with labeling either with tape or with the whiteboard marker itself, but something else that you can also do is I take sticky notes, and if you want to just give students something to reference as they are moving the arm around, you can leave a sticky note either here or up there as well. And you can actually label these, if this is quadrant one, quadrant two, quadrant three, quadrant, et cetera. You can also write it right on the whiteboard.

So again, just depends on what's helpful to you and your students, but I found that dealing with the sticky notes and tape is very helpful as I progress up, because when I get into the later builds and actually take the whiteboard off, I could still leave parts of the tape on or parts of the sticky notes on that I can still have on here as reference even when I add the conveyors and other elements such as sensors.

Now, getting into not just the quadrants in this way, but also thinking about how I can take it one step further. We do have the display position example project in VEXcode. And when I go forth and do that, it gives me the X, Y, and Z location of the current point. So with the jig in it's, approximately 402, or X is four, Y is zero, and Z is two, approximately, when I have the electromagnet attached there at the tool.

And one other thing to note is that when you're discussing this with your students is, where exactly is the reference point? Where is the zero zero location? Where is the point that I'm actually measuring from? Now, this is something that you may need to reinforce with your students, especially if they are getting confused on how to measure this because, if I'm dealing with a piece of graph paper, for example, I know where the zero zero location is, it's where the X and the Y axis meet, that's the zero zero location.

Now, it may be a little bit more difficult for students to know where that is, especially on the Workcell. So we have these pictures, they're also in lab three of the Workcell stem labs that you can use as reference, but again, talking about how to use them as reference the zero zero location is actually in the center of the turntable, and this image does a really nice job of showing that.

And furthermore, where the distance from the zero zero location is to the center of that tool tip is the measurement that's actually being recorded. So, if I think about what that actually is saying, so what I'm getting the reading of 402, what that means is from the zero zero location down here in the base of the Workcell, that's the zero zero point, which means that it is four inches in the X position, which is here, zero inches in the Y position, which is going this way, and two inches in the Z position or two inches off the ground.

So again, this is the reference point that's actually being measured because your students need that deeper understanding of, what is 402? Where is it starting, where is it stopping? And also understanding that these are actually being measured in inches.

So, if I took a ruler and actually measure that, which is part of the activity in the third STEM lab of the Workcell, where I actually go through and check out those manual movements, that's something that they made the connection for. But again, one thing that I've found is that students get confused on where it's stopping and where it's starting, because it's hard for them to bridge that gap between looking at just a regular piece of graph paper with the X and Y, and being able to make the connection between that and this. Bridging that gap for them and being able to relate to where it is starting and where it is stopping is crucial. You can even use graph paper to draw the Workcell on there. We have a printout in the lab three Workcell lab that allows you to do that, but again, strengthening that understanding is key.

One thing that you can see is we do have the XYZ that actually shows as you move the arm around, you can see that certain things get negative and other movements as I move through. To further reinforce the concept of the quadrants, which again, students can get rather confused on at times because understanding what's positive and what's negative can be confusing, one thing that I have found very helpful with the quadrants is I actually wrote a program. It's simple enough that your students can also write it. This particular program that I wrote, actually grab it there, is called Quadrants. What I did was when I moved this, not only does it display the coordinate, but it also tells you what quadrant it's in. This is something that you can either have your students create themselves, or this is something that you can create and then have your students use instead.

Now, this is just giving me the X and Y, but again, you can add the Z if you want to go up and down. This not only shows you, okay, quadrant one where both X and Y are positive. I can see that actually, I can actually go and refer to the chart there and see, oh yeah, they're both positive. I can see that as I move it. Let's go back to quadrant two. Oh, I can see X is negative and Y is positive. Okay, that makes sense now. If I had this label, I could see when it crosses that line, I can see that that is now going in, the X is going in the negative direction. Okay, that makes a little bit more sense. Going back over here getting into quadrant four, I can see that the Y is negative. I can see as soon as it crossed that line, that that connection is now made.

So again, making that learning visible for your students instead of just having that X and Y on a piece of graph paper and missing that interactivity, to be able to see that when points cross certain lines into those different quadrants, what is actually happening as things are moving. That's a huge advantage the Workcell gives compared to just using X and Y on a regular piece of graph paper and graphing points. This enables the points to be interactive. It allows them to move. It allows them to see the relationship between positive and negative axes and how they actually work together in order to be able to have a particular location if I want to pick up and place a certain object. Not only does it give that, the flexibility of being able to see points move in real time and in 3D space, but it also shows how that application is actually used in industry.

The other thing, like I mentioned before, is the Right-Hand rule. If students are getting confused on what axis is what, as I mentioned before, because again, they may not remember that the X is actually in this direction instead of horizontal. If you're standing behind the Workcell and you make this movement where the pointer finger is actually going in the X direction like this, you could always remind your students that that is the way that the X, Y, and Z or the Right-Hand rule is used.

Thank you for your attention and dedication to enhancing student learning through practical applications. Your efforts in making complex concepts accessible and engaging are truly appreciated.

So, anytime you get into larger manufacturing industrial robotics, this is the Right-Hand rule that's used to remember the axes. You have to be standing behind the Workcell, not behind the brain, but behind the Workcell. The pointer finger is the X, my middle finger is acting as the Y on the horizontal there, and Z is going straight up and down.

Just a couple more things to note about the Cartesian system and the Workcell. I can't stress enough how amazing of a product this is to be able to bring this to life. Being a mathematics teacher in the classroom, some of those really hard abstract concepts are very difficult to teach on pencil and paper. We do have 3D software out there, 2D software, and a bunch of things to bring this stuff to life, but being able to allow your students to go through and actually explore that is just a fantastic way.

You can have them create different projects that they can display if they need certain things, such as not only the quadrants but also the coordinates. That's doable. There are many other things that you can do as well. The only other thing that I'd like to mention as far as the X and Y is actually the Z axis. Students have a hard time understanding not only for X and Y, but also where is the distinction between where we cross the positive and then go into the negative or hitting that zero location where the two are split.

The zero location that we have here in the Workcell is actually the base of the Workcell. Everything above the base and up is positive Z, and everything below this base is negative Z. You can actually see that using the display position project, that if I go all the way down towards the center, I'm gonna start to approach zero. I can't actually break through that and go all the way down, but giving that a barrier and also giving that visual representation almost as if the Z does have that breaking plane, because both X, Y, and Z are all planes that are intersecting. Being able to use the Workcell to illustrate that and give students a real-time physical example of such an abstract concept is, again, really fantastic.

If your students are struggling to understand what Z means or what Z is referring to, I would refer to that plate, and again, remind them that it is a plane that is broken both of the positive and then I can go down into the negative version, but I can use the plate as reference there.

Just wrapping up some of the different tips and tricks that I have and how you can actually expand on the Cartesian system using the Workcell, there are many different activities that you can do that you could have done using a worksheet or you could have done graphing. One of my favorites is actually solving an equation. You can solve an equation using the Workcell. If I'm trying to find out, using linear equations, things of that nature, and I'm trying to solve systems of equations or anything like that, I can actually use what I know about the points and go back to the whiteboard if I want to, and actually draw to solve different equations and make that a little bit more visible as well.

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I hope that all of this information has been helpful. I can't wait to see how you and your students are using the Workcell to further explore the Cartesian coordinates system in your classroom or your environment.