 Hello, my name is Heidi Rathmeyer and this Wednesday webinar is on Desmos. It's a graphing calculator tool for math teachers. I think it's great for upper elementary clear through 12th grade. So let's get started. First of all, it is a free resource. It has a web-based version and I haven't had any trouble with Chromebook laptop. It also has an iPad app, and I've also used it with several different web browsers, and I haven't had any problem. As a teacher, I would recommend that you start with the web-based version so that you can create an account on there, and the web-based version has some other resources that are great for a teacher. In terms of the student, the web-based or the iPad app, either of them are really, I don't see much of a difference in the functionality when I'm on either, so either would be appropriate for the students. And if you happen to have a Google school where you have an account, the students can create an account as well. So it's just www.desmos.com. Okay, so again, it is a very user-friendly graphing calculator. There are some other features too that we'll talk about that are very useful for the teacher. I think it's great for exploring several different math concepts. For our upper elementary, graphing points, just looking at a coordinate system. That's a great way for them to explore that. You can create tables of data and then show obviously the graph that's associated with that table. Inequalities, and it will do the shading for you. Functions, all sorts of functions that are actually pre-built in that you can use. It has both Cartesian and a polar coordinate system, and it also does regressions. And I will show you most of those when we go into the program. Okay, some other features. As I mentioned, if you happen to be a Google school, your students can create an account. That gives them some other features that they can use such as sharing graphs with you, the teacher. There are lots of preset examples that can be used and can be a starting point for students to visualize and explore what may be different variables and different constants will do to a graph. And there are also classroom activities that are pre-built into the web-based version. I think those are great for substitute teacher days because there is some accountability built in so you can see what your students did. And I will show you those also. Okay, so we're going to go ahead and go to the website. So I will share my screen with you here. Okay. So if you go to www.desmos.com, this is what you should come to. The launch calculator will take you directly into the calculator. I will take you into the classroom activities, which is the same as the teacher.desmos.com here in a moment. They give you, if you want to do some more exploring, these are some examples that they will show you also, but I will show you them myself. So let's go ahead and launch the calculator. Now if you opened up the app on the iPad, this is what you would see. So it takes you directly into the graphing calculator. All right, so let's just take a little walkthrough here. Obviously on the right-hand side is your graphing area. Over on the left-hand side is where you can put in tables and functions and some settings. Down on the bottom right is where the keypad is. So you can type with either your keyboard or using this built-in keypad. It also has a lot of built-in functions either with trig or stats or some miscellaneous. Okay, I am not signed in. So I'm going to go ahead and sign in with my account or you could create an account up there. Okay, so now it knows who I am now. So I have my account and notice I have some other features up here that I mentioned before if you have an account and that same would be true for your students. Okay, so we're going to start by adding a new item and I am going to make a table first and I'm basically starting. If I was upper elementary, how could we possibly use this? Okay, so I'm just going to start typing in some points and it is so simple. Okay, and then over on the right you should see that our points pop up. So again, I think this is a great way for students to explore and look at you know, based on negatives and positives or a zero, what axes are we on, what quadrant are we in, a great way for them to explore. Another feature here if you select this, you can turn the dots off and on. If you press and hold, you can change the style, whether you want to line the lines and the dots or just the scatter plot and you can change the color. Okay, so that's a table. Pretty simple. If I want to delete that table, I will just close that. Okay, now I'm going to do an equation. So I'm just using my keyboard. I'm going to type y equals 2x minus 3 and you'll note it. It gives the line. Also another feature which I think is great is it gives you intersection points. You can just hover over it with your mouse and it'll give you those values. So it's a great way for the students to verify maybe some of their work after they've done some work on their paper. They can come in here and very quickly verify it. Okay, but let's say I want to do something a little more general and I want to just explore slope intercept. Okay, now notice it's asking if I want to make the values m and b sliders. So I'm going to say yes to all of them. And again, this is a great way for students to explore and see what happens when I change my coefficient to the x. So you can have some discussions about, you know, what effect does that have? If you push this play button over here, it will just do it itself. And then I can do similar process with my y-intercept value. And then you can have a discussion in class there, too. So I think this is a great way to introduce a lot of these equations and then they have some conceptual understandings as to what those values mean. Right now, let's try an inequality. So we'll do y and I'm going to pull up my keypad over here. Let's do greater than or equal to negative 3x plus 4. Okay, does the shading for you? You can see that it made my line solid. I can change that, however. And I just hit a backspace once and it deleted the equal sign and now it is dashed. So it even does that for you. Let's say I want to look at a system. So now I can type in another one. And let's do less than or equal to 2x plus 1. Okay, so now you can look at systems of equations or inequalities. So again, another great way for the students to maybe do their work on paper and then come in here and verify their work. And I believe, yeah, you will still give you intersections. So you can look at these intersections also, whether you're doing an inequality or equations or linear equations. So let's just look at one of those. So again, y equals 2x plus 2. And how about y equals x? I want to do an x squared. So I'll come over to my keypad and use the squared. Okay, so now again, I can come in and look at my intersections. And I think I can zoom out and find this one up here too. All right, let's look at some settings that we have. Over here, if you go to your little wrench on your graph settings. If you happen to be projecting to your class, maybe on a smart board, you can go to projector mode. Let me type in a line so you can see what effect that has. Notice that it's made it a little thicker and bigger so it's easier to see for the students. So we'll turn projector mode back off. We have some grids, as I mentioned, we have polar coordinates. The grid, you can even turn the grid off if you wanted. I like the grid on. So I'll leave it on. You can change how your axes look and whether or not you have your angles and radians or degrees. And this would just be zooming in and out. Okay, and this home will just take you back to what the default is for your axes. Okay, the share. A great way for your students to send it to you so they could send it to an email. They could type in your email address here and it would send you a link of their graph so that you can check their work. So let's look at now some preset examples. Now, if I come over here to the top left, it has the current graph that I'm working on and notice I haven't saved it. I could if I wanted to. These are the graphs that I have done. And that I have saved. And then these are all the preset examples that they already have in here. This one is very similar to the one I just showed you. So it's already built in. Now maybe let's look at a parabola one. So we'll go ahead and open this one up. And very similar to what we had before. They can take these coefficients, these values and see what effect it has on the graph. Great way for them to visualize and explore what each of those values means and does to the graph. You can see it gets up to trig. We can even do conic sections, some examples on polar coordinates. We get into statistics and some calculus. So there is a great deal of resources that you can use here for all different levels. Now I will say that I have had some upper level math teachers express that though Desmos is creatively simple and the students love it. They do still need to have knowledge of how to do very similar work on their graphing calculator so that they can use those on the ACT. And I get that, but if you don't want students to get caught up in the syntax of the calculator usage or you really want them to, and you want them to explore the concepts more so than getting caught up in typing everything incorrectly on your calculator, Desmos is a great way to do that. Okay, let's take a look at a regression example. And we are going to open an example that I already did. I'm going to close this part because I'm going to show you what I did. All right, I have a table of data and also it's pretty slick. You can copy and paste a table of data either from Excel or Google spreadsheet right in here. So I'm going to do a linear regression on this. Now in order to do this, I need to express in my equation these particular variables. So I have to use y1 and we use this symbol instead of an equal sign and I'm going to do a linear regression. So it's going to be m and then again x1, I have to reference my table of data plus b. And there it is, does it for you right away. You have your correlation coefficients. You have your m and your b values. And it's that simple and you can certainly do other regressions too. It doesn't have to be linear. Okay, so pretty slick. Again, a very quick way for students to visualize as well as verify their work. All right, so now I'm going to go to classroom activity. So I'm going to go back to the homepage. Classroom activities we can either get to from up here or the teacher.desmos.com, they go to the same place. And notice I'm still logged in and you don't have to have, there's not really a teacher account. If you have an account, anyone could get to this. And these are the activities that Desmos has created for classrooms. Probably my two favorite are the parabolas and the lines. And we will do the parabolas one. I'll show you that and I'll explain a little bit about each of the others. So I'm going to select the parabolas one. Okay, here I can make a new session, which I will do in a minute. And over here on the right hand side, as I mentioned before, there's some accountability. You can take a look at your past sessions. Okay, what it does, it will give the students a code that they type in. They do not need an account to do this. And it can be done on an iPad or a laptop or just a desktop. And let's just all go ahead and go into an old one just so you can see the type of information it'll give you. It'll tell us who was playing the game, what questions they asked, and how they answered specific questions that were in the program. Okay, so there is some accountability there. Okay, so we're going to create a new session. So if you were the teacher, you would just put this up on your smart board. And this class code is what the students would need to do. Now the students would need to go to student.desmos.com. And what I did on the iPad is I just made an icon for this particular site right on their home screen so it made it very easy to get to. Okay, so they will need to type in that code. And I will show you what that looks like. So I'm going to go over to, here's, if you went to student.desmos.com, here's what it would look like. So if I was a student, I would type in this code that you gave me. And what it does is the program will pair up students when they enter to play a game with each other and it just does it randomly as they come in. So the student on my laptop that you're going to see here is going to be Anna. And you can't see this, but I also have my iPad here with me and I'm going to sign in as another student. And the student on my iPad is going to be William. Now they give you a practice round that the students, for the first time, they can try this. In this case, Anna, who's on my laptop that you're seeing, could pick one of these. So if I happen to pick this one, then William would have to ask questions to try to figure out which one I had picked. For example, William could ask, is it a boy? And if I say no, then he could eliminate all the boys. And then is it an issue wearing a solid colored shirt? So that's the process. I'm going to go ahead and skip that and we're going to go straight to... using the parabolas. Okay, so Anna has the opportunity to select a parabola. So she's going to pick this one. Okay, now it tells William on my iPad, ask a question. So I'm going to ask my first question, does it open up? Okay, so Anna sees that. Does it open up? And mine does not. So Anna would say no. Okay, now over on my iPad, William sees no. So I'm going to eliminate all of the ones that open up. And you should see that on the screen that you can see. And then I can eliminate those. Now, if the student happens to eliminate the one that Anna picked, then the program will say, oh, you picked the wrong one or you eliminated the correct answer you too need to get together and talk. Okay, so William has to ask another question. So I will ask, is the vertex on the origin? And is the vertex on the origin? Anna would say no. So you can see that they have to use quite a bit of vocabulary. So now I can eliminate the ones... Oops, looks like there's only one that's on the vertex. Okay, so I'm going to go ahead and ask a question so I know that we can get the answer and move on. So is the vertex zero one? And Anna will say yes. So now William can eliminate all the others. And it tells us we got it right. Okay, now each student then would also get another question. So at the end of the game, you have these two left. What question could you ask to distinguish between these two? And again, I could say is the vertex on the origin. So as the teacher, you will see these questions that they asked each other. You will see these other questions that they do at the end. And now it's just waiting for another partner. And they would continue that process. And you notice now that I can see what the students did, what they asked. What's the question that Anna came up with for this one? So again, there's a great way to have some accountability. Or this is a great tool for sub-days. Or maybe half your class is missing. I know that happens a lot, especially in the spring when track season kicks in. Okay, so there are some other activities that you can use also. If your students maybe for your junior high are working on lines and linear equations, you can do a very similar process with the lines. The tile pile is another game that can be used to look at ratios. The students primarily work independently on the rest of these. The first two are the ones where they partner up and work with someone else. The water line, this is a great for modeling equations. I remember, I don't know if it was in a calculus class or an upper level algebra class where we had to determine the function for how quickly a different shaped containers would fill up. And if you're doing any sort of problem like that, this would be a great activity to start with for them to get a conceptual understanding of it and model it. Central Park, this is another one for algebra and algebraic expressions. I really liked this one. I thought this one was pretty neat. I would say for junior high kids a great way or first year algebra kids, if you're probably eighth or ninth grade would be my recommendation on that one. Okay, I think I covered most of the activities that are available through Desmos as well as the calculator. Again, I think it's a wonderful tool to visualize for some conceptual understanding. Again, if you don't want students to get too caught up in the syntax maybe of using their calculators. And most importantly, it is free. All right, so let me go back to my presentation. All right, I've created a Google folder with some middle school worksheets. These are some that I used at NATM this fall. I gave you two links there. I know sometimes these shortners are blocked in your school. So if you can't get to the Bitly or the tiny URL, just send me an email. Please let me know and I will be happy to send you that direct link in this Google folder. It is a user's guide that I found for Desmos, which is very simple and does a great job of explaining some of the features. Though I think you'll find, especially for the students that they go take off with it and they don't really need a whole lot of training on it, which is one of the things I really love about it. I know when I would first be working with calculators that it would take half a period or almost a whole period just to work on getting their calculator set up right. So if you want to introduce something and don't want to take a whole lot of time for that, Desmos is a great tool for you. If you have any questions, please contact me and let me know. Or again, if you need this direct link, please email me. Thanks for watching.