TRANSCRIPT
TSBVI Tech Tea Time: Desmos
1/30/25
 
>>Sarah Larkin: I'm Sarah Larkin. I am the statewide math consultant Here in Iowa. So I really focus on supporting our TVIs and math teachers and paraeducators across the state. And Desmos has become more and more popular in our classrooms. So we are seeing more and more teachers and students using it. So we've really enjoyed kind of digging into all of the things that we can do related to Desmos, and I'm happy to share that with you today. Just a little overview of what we're going to be talking about today. Our main focus will be on the Desmos calculators. Mainly the features and the tools of those tools that are within it. Accessibility keystrokes. So when I am demoing it, I will do it with a screen reader. Not that you have to have a screen reader to do some of the things, but we're going to focus on the keystrokes that I would use to access those different pieces. Including that in the demonstrations that I have. And then in the handout, so if you pull down that handout, there are other links as far as lessons and reference sheets that I have included in that. So you might want that handout. For use later. So first of all, what is Desmos? Well, Desmos is actually a free suite of math software tools more and more assessments and curriculums are starting to integrate Desmos within those pieces. And what's nice is the fact that Desmos really does focus on accessibility for everyone. So it is pretty slick as far as our students being able to get what they want out of their calculators and their graphs. And that also includes audio or braille input and output. I will tell you that a lot of our students tend to just use the audio portion. And then when they want to see the graph tactually, then they will actually use a graphics embosser to emboss it themselves. They don't even need someone else to emboss it for them. So we'll talk a little bit about that as well. One of the key things is there are three different calculators that Desmos has done. They have a four function calculator, a scientific one, and a graphing one. And so one of the things that is important is to talk to that math teacher and see. Which calculator are they using? Because that kind of helps you to give your students the same type of calculator. What I've done too is sometimes the students just start at the graphing calculator And just use it as a for function as well. Same thing if they are doing scientific, technically everything that's in the scientific calculator We'll also work in The graphing calculator. So you can't go down levels, but you can go up levels. As far as which one you use. So if you wanted to just start with the scientific or the graphing calculator. Instead of the for function, that's an option. But you can also gear it towards whatever they're using in the classroom. A few different tips and tricks here. For those younger students, if you're going to use it with them, and usually at those younger grades. They're really focusing on learning those math facts and mental math skills. But they could certainly check their answers. Using that for function calculator. But they would need keyboarding skills. And so that's where that numpad is a little easier sometimes for those younger students to use. Because it just has those numbers. And basic addition, subtraction, multiplication, and division on that numpad. So they're not having to worry about all of the other keys that happen to be on the keyboard. I've also included links to a couple of resources. The first one is part of a Perkins project. We have a digital math calculator skills checklist that we've put Along with Tina Hertzberg, Diane Bronner, Susan Osterhaus, and myself. And so that kind of gives a list of skills that a student might learn at different grade levels. And part of that. Are the Desmos skills. Most of the Desmos skills are in that middle school to high school. But you could start with that basic for function at an earlier age. And then the second document that I've linked is just a quick reference step-by-step on the common things that you could do Within the Desmos calculators. And so it's just kind of a nice little cheat sheet that has a lot in a little amount of space. So easier for you to find what you need and the keystrokes that you would need. To navigate some of the different options. And of course, not forwarding. There we go. All right, so getting to the calculator is the first thing we want to do. If you're using it with the younger kids. Depending on whether they're able to find the letters they need, you may have to help them get to the calculator and then they can navigate once you're in But obviously, as soon as the students start leaning the keyboard. They can certainly use it to access the calculators within Desmos. So the way I usually have the students do it is I just have them hit their Windows key They're going to type Chrome to go to the Chrome browser or whatever browser they want to use. Then they're going to type Desmos.com and press enter. And then I like to just have them go to the page and do control F to find either four, F-O-U-R for the for function scientific or graphing. And it goes to that link and then they can just hit enter. And then that page will pop up. And it'll be ready for expressions. So let's go ahead and go through that real quick. So I'm going to just go to my Windows key. I'm going to go ahead and type Chrome. Oops, before I do that, hang on. I'm going to turn my jaws on. You can use JAWS or NVDA. It doesn't matter. So I'm just going to do Windows Jaws. Turn my jaws on. It takes a minute to kind of get it. There we go. Ready Jaws Desmos 1-30. All right. Now I have my screen reader on, so I'm just going to hit that Windows key. Search box edit type HOE Google Pro Enter. I'm going to type in Chrome. Hit enter. Selected blank address and search bar. Now I'm going to my browser. And I'm up in the address bar at that point. So now I could type Desmos.com. D-e-s-f-o-s-p. Enter. Hit enter. Now, I'm actually just at the main Desmos page. Desmos Vertical Bar Beautiful Free Math Dash Poo Desmos. And all three of those calculators are on that page. So we'll start just with the for function calculator. So I'm going to do control F. To find, I'm going to type in for And then I'm going to just hit enter at that point. Virtual find. Jaws FIND Dialog, find F. O-u-r. Enter. Visited link for function. And it took me directly to the four function calculator. So now all I have to do is hit enter. Enter Desmos Vertical Bar Beautiful Free Math Visited link for function Desmos vertical. So now I'm in the address bar and I'm ready to actually type. I've given you what these different keys are that you would use. But we're going to go ahead and talk about those. In the next a few slides. So I'm going to kind of skip through some of the slides here. One thing I want to just mention is there is a wrench icon And in that wrench icon. Desmos vertical bar for There is the option. For reverse contrast large print or braille modes. So there are those options that the students can use as well. I do find that Students that want large print or that reverse contrast, that's very helpful. I don't find that very many of our Braille users use the Braille mode, but that is an option. That you do have available to you if you want to attach a Braille display. So that is an option. I want to minimize our pictures here. So let's go ahead and do some calculations within this calculator. Escape Desmos 4 dash function calculator. So to get out of that settings, I just went ahead and did escape and it took me right back to the equation area. So if I want to do something basic like 34 Plus 768. 4, 4, 4+, plus 6. 6. Eight, eight. 34 plus 68 equals 102. Notice a couple of different things. When I typed 34 plus 68, I just used the keyboard to do that. When I paused after typing that eight. It automatically told me the answer. So I didn't even have to tab over to that answer. It just went ahead and read it to me. Now, when I go to hit enter. Enter expression 2 colon edit blank type and text. It told me I was on expression two and it told me it was blank. So now I can do another set of expressions or I can do something with the answer. For that first problem. So let's say i had 34 people and another 68 came in the door for some big theater group. And so now I have 102 people. Now, let's say their tickets are $12 a piece. So to figure out that total money I put in, I can take that 102 And then times, now the time sign is the one that's not as obvious It is the asterisk, which is shift eight. 0, 2, 2. If I had that numpad. If I had that numpad, I could simply just hit that time sign. I wouldn't have to do the shift date. Star Times. 102. And I believe we were doing $12 a piece. And then I can hit enter. 1, 2, 2. Enter expression 3 colon edit blank type and text. Now I went down before I listened to what the answer is. But I can just do a shift tab The expression 2 colon 102 times 12 equals 1224 edit blank type and text. So I can always go back to those previous problems and those previous answers. By tabbing or shift tabbing through those different equations. Another thing that's handy for the for function is I can do decimals, which is just your period. I can do parentheses by doing shift nine or shift 0. And there's even square root. And so if I go down against that third expression. Enter expression 3 colon edit blank type and text. For the square root, even in that basic calculator I can do SQRT. S, Q, R, T. Start root and root radical cannot be empty. And it said that I was in that radical, but it said it was empty. And that's because I haven't told it what I'm doing the square root of. So I could now type a value I want to take the square root of, let's say 25. 2, 5, 5. Start Route 25 and root equals 5 And I like that it always reads the problem to me. That way I know if I type something incorrectly and need to edit that. So that's really handy as well. Another thing I wanted to mention is I can use that answer key as many times as I want to. So if I go to that next line By hitting enter. Enter expression for colon edit blank type and text. M's equals 5. I can just do ANS again. And instead of having to type that 102 or the five or the last answer or even remember what that last answer was. Just typing ANS is going to use that last answer. And then I could do maybe minus three. Dash-3, 3. And minus 3 equals 2. And then hit. So it took the answer to the last problem, subtracted three, and told me my answer was two. So that ANS is a really nice feature. Of being able to use previous answers. So we went through some of the keystrokes for the for function. So let's go ahead and go to that Desmos page Again, and I'm going to go ahead this time and just go to the scientific calculator. So we're going to go back a page. Desmos Vertical Bar Beautiful Free Math. Virtual Find Desmos Vertical Bar Beautiful Free Math. I'm going to do control F. But this time I am going to actually type scientific. S-c-i-e-s-e. Enter. Visited Link Scientific. Now it's taken me to the scientific calculator. And when I hit enter Enter main region scientific link. Blank type and text. It takes me right to that field where I'm putting in a problem. So I like that it takes me right to where I want to be. Now, there are buttons that I could use a mouse for any of these buttons. Remember, I can do the the high contrast. I can do the large print Or I can just go ahead and type in those problems. I don't even have to see any of the buttons that are down there. I can just use keystrokes for everything. So for instance. I can go, let's say I wanted to do a fraction because they start getting into fractions before long. Especially in those later elementary grades. All I have to do for a fraction is do a slash between the numerator and denominator. So I could do like one slash two. 1. Slash 2. 2. 1 half equals 0.5. And so it gave me that answer. Now I'm going to go ahead and arrow to the right to get out of the denominator of my fraction. After start fraction 1 over 2 and fraction. And it said it was after the fraction. And then I can go ahead and do, let's say I wanted to divide, let's go ahead and do actually subtraction this time. 1 f minus you need something on both sides of the apostrophe dash apostrophe symbol. And I'm going to go ahead and subtract one. Fifth. 1.055. 1 f minus 1 fifth equals 0.3. Now that gave me a a decimal answer. And I can toggle that between decimals and fractions. All controller. And we'll go through that in a little bit. So I can do fractions within that scientific calculator. I could also go down and do Percent. Enter expression 2 colon edit blank type. Or exponents. There is a key that I need to know to do exponents, and that is a little, it's called a careat key. It's above the six key. So I would have to do shift six. Now the numpad isn't going to help me for for exponents. So I would have to use shift 6 for exponents. So then I can do four Shift six. 4. Carrot superscript baseline for superscript baseline superscripts cannot be empty. And then put what my exponent is. So let's say I just want to square it. Two, two, four squared equals 16. And it told me that answer. Again, I can do enter You can take that answer. Enter expression 3 colon edit blank type and text. A. Ed. S. M's equals 16 And do anything with it. So let's say I wanted to then cube that last answer. I could do shifts. Care is superscript base 3. 3. Adds cubed equals 4096 And so the third power. And it gives me that answer. So it's really straightforward there. I could do square roots the same way as I did in the for function. It's still SQRT. I can also do cube roots or nth roots, any sort of roots that I want. By just typing in CBRT for cube root And, and… route or other routes. Enter expression for colon edit blank type and text. I can even type pi if I'm doing something like circumference. I could do two times, which is shift day. And I just typed pod. Two. Star Times. 2 Type P. I, quote, I quote 2 times pi equals And then I could do times. So shift eight again and do my radius of 25. Star times 2 times pi times u2. 5, 5, 2 times pi times 25 equals 157.0796327. And I have figured the circumference for a circle with a radius of 25.

>>Donna: And Sarah, we had a question come in. How do you do subscripts without going into the function menu and using the log or other function?

>>Sarah: So notice… Yes. So in the calculator, you're not going to have to use subscripts, but you do use subscripts in the graphing calculator. And all you have to do is type the subscript number right after it. So when we get into the calculator, we'll do a subscript And so X sub one would just be x1 And that number following the letter will automatically be a subscript. Yep. So you don't have to use really any command there, but put the number, the numeric subscript after that letter. Because within the calculators, you really, the only time you use subscripts is when you're doing equations and a lot of times you have an x sub one column of a table and a Y sub one column of a table. And that's when you're going to use those subscripts. Good question.

>>Donna: Great question, Lucy. Remember, get those questions into the chat and to the Q&A, and we will get them answered.

>>Sarah: Context menu to navigate. Sorry. All right, I'm going to turn off JAWS for a second so we can talk through just a few of these. I'm going to go. Unloading jaws leave and her. Desmos vertical bars. Let's go ahead and go. We went through some of these slides, so I'm actually going to move ahead now to We talked about the different settings and the keystrokes. So I have a poll for you. So you can, let's go through these questions. Oops, it looks like I left out an E on my word square. But how did we type in for the square root? Did we type square? Did we type root or did we type SQRT?

>>Donna: Drop your answer in the chat.

>>Sarah: And let me know what answers we're getting.

>>Donna: Got some coming in. We've got some A and some C. Majority saying C.

>>Sarah: Good. It is C. We typed SQRT. For square root. Let's go to a second question. How do you use the previous answer in a new calculation? Did we type out the word answer? The word last or ANS.

>>Donna: Looks like we've got ANS and C coming through.

>>Sarah: A and S and C, yes. So A and S is what we typed, which is choice C. Nice work. All right, our next problem, how did we type a fraction? Did we write the word fraction? Did we write FRAC or did we do numerator slash denominator for that one?

>>Donna: Looks like we're a little split between B and C on this one.

>>Sarah: Okay, it is C. We have numerator slash denominator. So if I wanted 1 third. I would just do one slash three. And the fourth question, how did we do an exponent? Did we type the word exponent? Did we type EXP or did we use the carrot? Which is shift six.

>>Donna: Looks like a pretty unanimous C on that one.

>>Sarah: Nice. They're all C. They are. Nice work. All right, on the next slide, I have two different They are to some. The first is a paths to technology post Because Valentine's Day is coming around the corner. I thought it would be nice to have just they have a post about doing word problems using the Desmos scientific calculator related to Valentine's Day. And then the second one is actually a TSBVI session. Were the people from Desmos actually came in. And did a webinar as well. The first half hour is on the scientific calculator and the second half hour is on the graphing calculator. So just a couple of nice links there. That you might find helpful. All right, so now we're going to actually get into the graphing calculator. The link to the graphing calculator is desmos.com. Calculator. It doesn't have the word graphing in there. But just like our other ones, we can just go to Desmos.com Control F to find that graphing calculator and type the word graphing. It'll find the link and we can hit enter. Just a note, everything in the for function calculator is in the scientific. And everything in the scientific calculator is also in the graphing calculator. The advantage to using the graphing calculator is then you can start doing tables and graphs. You can't do that on the previous calculators. So if I want to graph functions or inequalities. On a coordinate plane, that's with your x and y axis. That graphing calculator is going to be your best choice. I can also do things like statistics and random number generators. As well. And there's lots of miscellaneous functions within that. So what I've done is given you the link to all of the shortcuts. Available within the graphic calculator. So you can go back to that. In fact, we'll go one of the later slides There is actually a link to both the Word file for the shortcuts and BRF files that you could emboss for your student. So I often give the students the BRF file If they have a note taker, I send it to their note taker and then they can Just look at it that way too. She could always emboss it and give it to them in hard copy braille. As well. There are a few more keystrokes within the graphing calculator. So it does take a little longer to learn the graphic calculator just because of those additional keystrokes. If I ever get off of the expression and I want to get back on. Control Alt-E will get me back to that expression area. If I want to add a new expression, I might just hit enter. To go to a new one, or I can do control alt X. To add an expression. If I want to delete out what I already have. I use Control-Shift D. And the table, to add a table. Technically, you could learn the shortcut control alt t But I usually just type the word table. Rather than memorizing another keystroke. If I type the word table, a table is going to appear and I could put in the values that go within the table. So another handy keystroke is when I need to go over to the graph. If I'm in the expression and then I want to go to the graph, I do Alt T. You'll hear when I show my screen reader here again. That it actually tells me after I do an expression to hit Alt T to go to the graph. So it's nice that the student doesn't necessarily, even if they don't memorize it. It's going to give them the cue of doing Alt-T to go over to the graph. Then if I'm on the graph and I want to go over to the table, I can do or over to the expression list or the table. I can do Alt T again. It's just a toggle. Back and forth between those two areas. Another nice command is going between decimals and fractions. If I do Alt Shift. A. Then that will actually change it. If I'm at a decimal, Alt Shift A will make it a fraction. If I'm in a fraction, then Alt Shift-A will change it to a decimal. So it just toggles those answer values. If at any time I'm not sure what a keystroke is. Control forward slash will give me a list of those keystrokes. So that is another nice thing. All right, let's go ahead and go back to the calculator. So I'm going to go ahead and just do my Windows kick or let's turn on JAWS. Or NVDA, you can use either one. Or even if you're on a Mac, you can use voiceover. Please wait.JAWS PowerPoint slideshow dash Desmos escape. Ready Desmos 1-3s. And then I'm going to go to Windows. Go to my Chrome browser again. Search Talk E. Enter Google Chrome app press right to switch preview address. Desmos. Dot com. O. Enter. Desmos Vertical Bar Desmos. Now, I'm going to do control F. To find it. Virtual find. Jaws FIND Dial G-R-A-P. H. Enter. Put in graphing. Or graph. Visited link open graphing calculator. Enter Desmos vertical bar beautiful free math visited League Open Graphic Calculator. And I'll hit enter on that. And again, it takes me right to the expression list. So right to where I want to be to input something. Alert, close message. Let's go ahead for a minute and do that fraction piece again. So I'm going to do one half, one slash two. So out of my fraction. 2. 2. One apple starts Friday. That is probably one of the things the students forget to do is to write arrow out of that fraction. Otherwise, they start entering that plus sign down in the denominator. So let's do plus this time. We did a minus last time. So I am going to have to do shift. Plus, plus. 1f. 1, 3. I don't have a numpad. Now I'm going to do, let's add one third. One slash. 1 app plus 1 third equals 0.83333333333333333. All right. I got all those threes that are repeating. Now let's say I want to switch that to a fraction. That's where I can do Alt Shift. And A. Alt Shift to show us fraction 1f plus 1 third equals 5 sixths. And now I have it as a fraction. If I did Alt Shift again with an a Now I'm back to my vessel. Expression 1 colon edit Alt Shift, show us. So that's just toggling it between a fraction and a decimal, which is a really nice feature. I'm going to hit enter this time. And let's look at that table. Enter expression 2 colon. Remember, there is a keystroke for the table, but if I don't remember it. I can just type table. C, A, B, L. Grid with three columns and three rows. Edit Blank column 1 row 2, type and text So it tells me that I'm in column one, row two, so I can go ahead and type in coordinates now. So I might type in And then to go to the y coordinate, I just hit tab. Two. Type in text. 5. And then five, let's say. So now the 0.25 is actually graphed. On my coordinate plane. Now, if I hit tab again it tells me I'm in column one, row three, so I'm typing X. Edit Blag Column 1 Row 3, type and text. So I could do maybe a negative this time. Which is just like minus three for the negative three Hit tab. 3, 3. Edit Land Column 2, type and text. Zero. Let's just type a zero in there. So now I have the point negative three, zero on my graph. And I could put any number of points. If I keep tabbing, I'm just going to be able to continue to put as many points as I want to put in here. I could also copy. From an Excel spreadsheet into this table as well. Now, sometimes I like to find the equation of the line that goes through those points. No matter how many points I have. It can give me the line of best fit. And that is a common eighth to ninth grade skill. So if I hit enter It's going down, hit enter one more time. Enter edit blank type and text. Enter expression 3 colon edit blank type and text. Now I'm in a new expression. Now, this is where that subscript comes in. Because my x's in the table are really x sub And the whys are the Y sub. So x sub 1 and y sub 1 in this case. To get the line that goes through those points. I can type Y1. Why? 1. Subscript 1 baseline quote y quote subscript 1. Baseline equals a list of numbers, two items. So that Y1, I did not type anything to make it a subscript. The fact that I typed one after the Y made it a subscript. Then I'm going to use tilde. The tilde is above the tab key on your keyboard usually. So I'm going to do shift tilde. It's kind of a little wavy line. 1. Base. And then lines are normally in the form mx plus b. So I'm going to do mx plus b, but instead of just x, I'm going to put that subscript of 1 on there again. So I would do m. That's one. Plus, plus B. Quote, quote, y quote subscript 1. Plus B. Now on the screen, I have the line that goes exactly through those points that I entered on the table. If I had more points and they weren't all on a straight, the same straight line, it would estimate the most approximate line. Through the points. Now, at this point, I can find out the slope, which is m. And the y-intercept, which is b. And I just have to tab to find what those are. The slope is? Well, I don't want to delete it. Hit tab again. Expression list region, delete expression 3 button to activate press enter. Regression parameters region quote m quote equals 1 edit blank type and text. So it said, quote, m equals one quote. So I know m is one. So my slope is 1. Now, if I tab again Quote equals 3 added blank type and text. B equals three. So my y-intercept is three And so this equation is really y equals 1x So those two values that m and b, are something that the math teacher might ask for. And it's really slick to just memorize that equation that I need to enter. And then go ahead and tab to find that slope and that y intercept. So kind of a nice feature there. Now, let's say I'm not wanting to do tables. I'm wanting to do equations and I'm given the equation of a graph I can go ahead and do control shift D to delete out everything I put in. Control shift, control shift control shift D, expression 1 colon edit, blank. That takes out the expressions that I had in there. Now I can just type y equals Let's do x squared. Y equals, equals. Superscript base 2, 2. So I did shift six for that carrot. Now I have to get out of the exponent to add something on there, so I'm going to right arrow or hit my minus sign. Why? Baseline minus quote 5, 5. Graph to audio trace result plus t. Wow. Notice when I waited, it told me to go to the graph, press Alt plus T. So that y equals x squared minus 5, I'm going to do. Alt T. All T. Audio Tracer. Use arrow keys to navigate to hear the graph. Press H to disable audio trace. Press Alt plus T expression 1 intercept and extra moment x colon 0. White colon negative 5. Graph paper x-axis visible from negative 10 to 10. Y-axis visible from negative 5.88565 to 5.88565. Grid lines are visible when audio traceable curve graphic. So it's giving me an idea of the types of things I can do to find out what's on the graph. So if I want to hear it. Which is the most common thing the students start with. I can just type H for here. Just what here starts with. So let's type h So that tells me that the graph went down and then came back up. Eight. There was also some static in there that static. In the middle of it was actually where the graph was below the x-axis, below that x-axis. So I can hear the graph, but I could also just arrow between the different points. X colit 0.2 y colon negative four. Go a little bit further. So I'm going left right now on the graph. Too far. Come back. X colon negative 1, y colon negative 4. X colon negative 1.2. Y colon negative 3.56. X colon negative 1.4. It's repeating those points as I was going. Y colon negative 3.04 X colon negative 1.6. Y colon negative 2.44. I go one more to the right. 0 at x colon negative 2.23607. White colit zero. So it tells me those points. As I'm moving that. Now, let's say I want to find, oh, yes.

>>Donna: This is Donna Sarah. I'm sorry to interrupt. I love that we can now do this bit by bit. And so if someone if one of our students is learning what that graph sounds like, we could slow it down from the Full here and take it piece by piece. And so I love that. Exactly. And it's only going to go as fast as I hit those arrows. So I can just hit the arrow one more time And it will give me more points. X colon negative 2.2. Why? So the student can do it at their pace then, which is really nice. I can also find key points. Those places where the graph hits the x-axis, the y-axis, if there's another graph, I can get the intersection of that. Let's go ahead and get another graph on here. Just so we can get some intersection points. So I'm going to go back to my equations. And I do that the same way I got to the graph part, Alt T. Alti audio trace-off expression list region expression 1 colon quote. Notice it told me I was in the expressions list. And then I'm going to hit enter to put a new equation in. Enter expression 2 colon edit blank type and text. Let's do a trig function. I wouldn't have to, but I'm just going to put one in so we can get a couple of intersection points. Why? Equals equals s. I. N, N. Y equals, we'll do sine. X. Alti, graph paper x-axis visible from negative 10 to 10. Y-axis visit. So now visually I have on the screen two different graphs in two different colors. But I can go ahead and go back over to the graph. By doing that same Alt T title. Now, I'm going to hit H to hear the graph. And this is my new graph. It's not just the one that went down and came back up. This is now my sine x graph because That is the equation that I was on at the time. So we're going to type H to hear it. H. Did you hear those two pops? Those pops that don't sound like the rest of the graph are signaling the places where those two graphs crossed. So that is really nice to be able to find out about where those actually cross or how many times it crosses, how many intersection points do I have? Now, if I want to find those exact points. I like to always go to the beginning of the graph first. So I can do home or function home depending on your computer. Home. X colon mega. That takes me to the beginning of my graph. That's on the screen. And then I'm going to tab through the important points. So we'll do our first tab. 0 at x colon negative 3 pi y colon 0. So it told me that there was a zero, that a zero is a place where it crosses the x-axis. Tab again. Extramomodex colon negative starts fraction 5 pi over 2, and fraction y colon negative 1. So now I know at negative 5 pi over 2 comma negative 1 is my extra bum. Those are like high or low points. So in this case, it's a low point. I'm going to tab again. 0 at x colon negative 2 pi y colon 0. That was a zero again, so I crossed the x-axis. Extramomodex colon negative start fraction 3 pi over 2, end fraction. And it's an extra mum again. So I know it's a higher low point, but since the tone went up. I know I'm going to a high point. I'm going to hit tab a few more times. That's a zero. Tab again. Ah. 0 at x colon negative pi y colon 0 Intersection with expression 1 at x colon negative 2.02521. So now it's telling me it's telling me it's an intersection. Y colon negative 0. It's a place where those two lines crossed. So it always tells me when I tab what kind of point I'm at. Whether it be a zero or an intercept, which is a y-intercept or an intersection. So it always tells me those. All right, let's go ahead and go ahead and turn off our jaws here. Unloading Jaws quencher. Desmos vertical bar graph. And go back to the presentation. So I have a quick… Poll for you again. So let's see what you have. A, B, or C again. For the table, did I type table? Did I type tab? Or did I type control alt T? I'd put that in the chat. What kind of answers are we getting?

>>Donna: I'm wondering if we might have stumped them. I am not seeing any responses yet.

>>Sarah: So not any responses. Okay, well, it is just typing table. Now control alt t will work as well. Either control alt t or table will work, but I usually just type table. All right. How do you add an expression? That one for time's sake, I'll just tell you, you can think about your answer, but it is. Control Alt-X. All right. The next one is to delete an expression. They're all Ds there. The one we need is B, which is control shift d And the last one, this we did more often. How do you toggle between the equation and the graph? And that should be Alt T. All right. So in the next one, I will just give you a lot of those common keystrokes. We used H to hear the graph. P gives me how many points of interest there are, how many intersection points, zeros or y intercepts. But it's not going to tell me what they are. It's just going to tell me how many of them there are. At home or function home gets me to the beginning of the graph. Tab through those points of interest. If I don't hear the point, I can type X to just hear the x coordinate. Or just why to hear the y coordinate. And then O gives me where it is on the origin. Alt-s is kind of a global summary of the graph. And if I wanted to go between those two graphs. I could actually use alt page up or alt up arrow and same thing with the next graph, do all page down or alt down arrow. To get to those. About 15 minutes. So there is a quick poll here again, but I'll just run through these to hear the graph. I'll bet you can guess whether it's F, G, or H. To hear it. Hopefully you got the, ah, yes.

>>Donna: Looks like we're getting… pressing pressing answer C or H seems to be a unanimous.

>>Sarah: Yes. Nice. So it's really a lot of these are pretty intuitive to find a point of interest. So this is the thing that I pressed over and over to go through those key points. What was the key that I pressed for that?

>>Donna: We're looking at answer C coming across.

>>Sarah: Yay. Good job. It is the tab key. What do you suppose I type for the x coordinate? C, P, or X.

>>Donna: Looking like answers C and X.

>>Sarah: And… for the y coordinate. C, P, or Y. Do you see how intuitive it is? It just, it's like it gives it away to me.

>>Donna: I think we've caught on to some of your pattern here, Sarah.

>>Sarah: So that's always really nice. So the next slide we already did. We went to the line of best fit and I've just given you the exact steps for doing that. Typing table. Entering the coordinates and pressing tab between the coordinates. And then once I have those in, I'm going to do control alt x for that new expression. And then type y1 equals mx1 plus b. That gives me two subscripts. And then I can tab to that slope and y-intercept. So you've got all the steps right there for you. All right, sharing a graph. This is really a nice feature. Because the students can actually, let's say they have an email or they have Word document that they're entering in their answers. They can actually get a link to what they have just done. They do that by going control alt s And then it takes them to a link area where they can copy the link and paste it into an email or a document. So I'm going to show you that real quick. So if I was Back on my page. In my expression and now I want to save this graph that i just did I can do that control alt s it takes me to share graph. And now it has already highlighted the link for me. So I could do control C on that link. Or I can tab and it takes me to the copy button. And hit enter to copy it. Now, you'll notice my screen reader was not on. That means even if you have a low vision student. They can use those same keystrokes Whether that screen reader is on or not. All of the keystrokes I've talked about will work for even your low vision users. So you don't have to have that screen reader on to do any of that. Great. The next slide here. Is embossing a tactile graph. And what I like about this is we have a lot of students that have the page blasters or the Romeo 60s or a Tiger embosser. If you have a graphics embosser, you can actually emboss this graph and it's accessible for the student to do so by themselves. So they don't have to send it to someone, have someone else emboss it. They can just connect up to the embosser and do it themselves. And so I've given you the steps for doing this. But it's that same control alt s Then go into the export image button And then they're going to select the file format they want and the type of embosser they want. So let's look at that real quick on that screen. So if I was back in that expressions list. I can do that same Control Alt S. But instead of copying the link. If I want a tactile of it. I can tab to export image. And then hit enter. And now I'm in the file format so I can just arrow down to either a PNG file, an SVG file, or if I'm a Braille user, I can choose Nemeth or UEB. So let's say I choose Nemeth. I'm going to go ahead and hit enter. Now I'm going to tab to the size and I have to look at what kind of embosser I have and which kind of paper size I have. So I can arrow between those. Any tiger embosser will work for the vp max And so I could pick my narrow paper eight and a half by 11. Or arrow down and pick my wider paper. Of 11 and a half by 11. The ETC Romeo juliet Oh, by the way, the VP Max also works for the Pix blaster so Because that is like a tiger embossers. So any of your regular tigers or the pix blaster The ETC Romeo juliet works for your Romeo 60, Juliet 120, Or the page blaster. So then I can select my paper size for that. Hit enter. And then I could tap down to my download png And the student can literally then, it'll download that PNG and they can go into Firebird can actually open up that PNG file from their downloads folder. And hit file emboss. So I've given you all of the steps in the slides that you need. To be able to emboss that graph.

>>Donna: And what exactly is Firebird, Sarah?

>>Sarah: So let's… Okay, good question. So Tiger software already has that graphics piece with it. But if you're using the Romeo Juliet embossers or the page blaster it requires the use of Firebird software, which is free. So if you went, for instance, onto the the enabling Technologies website, it would have the Firebird software there as a download, free download. Or on the APH's website go under the page blaster, it'll have a download for Firebird And all it is, is it's software that produces graphics. So you can take any sort of PNG picture file And then open it in Firebird and send it to a graphic that that graphics embosser and it'll emboss that picture So the Firebird software gives you the graphic capability on those Romeo, Juliet, and Page Blaster. Devices, those embossers. Good question. And it's free, so you don't have to pay extra for that software. And it's a quick download too. To install it. So it just gives you that ability to be able to do those graphics. If you're doing the Tiger software, then you don't need the Firebird software. You only need the Firebird for the Romeo, Juliet, and Page Blaster. We're doing for a time okay So the next slide I have is really just a set of links. Sometimes it's nice to be able to get some lessons to help you work with a student on how to use the Desmos software. So what I've done is just included a bunch of links to different posts on Pads to Literacy. That actually have some lessons. On how to do what I've shown you today. But it's a full lesson with the students. So there's a getting started lesson. A couple on sonification or sonified graphs. And then there's some on creating data tables and line graphs. Jennifer Bliss did an outstanding job With part one of that. Where she showed how to actually have a set of dots, set of points. And connecting those with lines. And how to do that within Desmos. And then Diane Bronner added parts two, three, and four to add on to that for some Thanksgiving activities. And the last one is creating a scatter plot graph with JAWS. So those are just some fun lessons. If you want ideas of things you can do with your students.

>>Donna: And Sarah's Shannon says. Fabulous in all good caps. We love those fabulous in all caps. She says that'll be so helpful for just learning Desmos even. Before we're getting ready to teach our kiddos. Is my part of that comment.

>>Sarah: Exactly. Great.

>>Donna: And it's always good to have lesson plans.

>>Sarah: You know, time is always critical, isn't it? It's hard sometimes to find the time to do everything you want to do. When it's already laid out for you, it really helps. There are ways to bake histograms, dot plots, and box plots. And so I've given you The code for that, you would use tables again And then create those different plots. I will say that for those three types of plots, I find audio often isn't enough. So I do recommend embossing those particular types of graphs to an embosser if you can. It just is easier to read those types of graphs in hard copy braille. And then I've given you some pictures of kind of what that looks like within the Desmos environment and those have been described in alt text. If you don't have vision to see the pictures. The first picture is the code that says box plot. Open parenthesis. X1, close parenthesis. So that creates a box plot For my set of data that's in the data tables. This particular data table has three, six, seven ones four twos and a three. In that particular table. And then the other code is for a histogram, which is just the word histogram. Open parenthesis That's one comma one, close parenthesis. And that gives me a histogram that says there are those seven ones four twos and the single three. But I do really like those embossed over just doing the audio. The other stuff I showed you with the audio, you don't necessarily need those hard copy Braille pages, but I do find that these box plots and histograms are better with with the Braille.

>>Donna: And Laura and Katima both say thank you. That is good information.

>>Sarah: You bet. The next slide that I have is using Braille. Most of our students don't even bother taking the time to hook up a Braille display when they're using Desmos They do do most of what they want to do just using audio. Because it's just so straightforward. That most of the time they don't need that braille display attached to it. But I have included the links on how to do that And it's right on the Desmos site in their accessibility area. The next slide we have here is the translation between print and braille. This is a demo site. And this particular site actually A lot of people don't even know it exists. But it is just a very basic screen that has a field for Braille and a field for formatted math. So you can type in Braille using SDF and JKL for six key input if you select the six key input. Block. So if I were to select that six key input I couldn't braille. Type an X. Whoops. Thought I put my six out. My keys weren't, my fingers weren't on the right keys. Let's try that again. So there's my x, then I can do my superscript. And my two in Nemeth, and it is showing me x squared in print. So I can type in Braille and have it show up in print. Or if I am visual, I can show I can just do the letter X. And do my shift six for my exponent and my squared And it's producing the braille. So it goes You can either do braille and have it show up in print or you can do print and have it show up in braille. They don't advertise this on their website. So I just went ahead and gave you the link in case you ever feel like using it. It's just kind of a nice feature and it does UEB as well. So that's what that next slide talks about. The digital classroom activities. This, I do have a little bit of a caution for you. The activities Some of them are accessible with screen readers and some are not. So they're tagged if they are screen reader friendly. So you can in the search field, type in screen reader. And it will give you the activities that work with a screen reader. So some of them are more accessible than others. This is an open platform that any teacher can upload any of their classroom activities So if they didn't purposely make it screen reader accessible, it's not going to be. So that's why you can't count on all of those classroom activities being accessible. You can look for that tag of screen reader for the ones that are. A little newer. They have come out now with a geometry drawing tool that is accessible. It is a little bit more of a learning curve. But it allows them to actually create different shapes, different types of graphs they can lay out different points. And draw lines between different points, do constructions It's a little newer. They're still adding to this they're still doing more creations.