Timotha, I haven't tried the Polygraph Parabola activity (below) which sounds worthwhile, but I want to share the way that a friend used Desmos this year.
He had his students solve a number of 'two equation, two unknown' problems algebraically. The students' homework assignment was to check each problem graphically using Desmos (or a graphing calculator). They had to correct the ones with mistakes algebraically. He said he liked this for two reasons. First, the students had to find their own mistakes. Second, for the problems with no solutions or an infinite number of solutions, he liked the graphical feedback that Desmos provided. "Mr. Jones, I thought I made a mistake when I only saw one line, and then I realized that since there were an infinite number of answers, they were actually two versions of the same line. Richard > Still *another* Desmos strength are classroom > activities designed by teachers and constructed by > Desmos. > > For a good example, check out the Polygraph Parabolas > activity. > > https://teacher.desmos.com/ > 
Timotha, part II:
Given that I don't teach Calculus, I wondered if any folks posted uses of Desmos in teaching calculus. I came upon this with links to interactive worksheets and more: The poster was (still is?) a visiting professor at Smith College. http://thalestriangles.blogspot.com/2013/12/someofmyfavoritedesmosprojects.html Richard 
In reply to this post by Richard Strausz
And here is 'Timotha #3':
The link below takes a teacher and students to some 'Math My Graph' worksheet replacements. I think this would be helpful in prealgebra and algebra I. http://www.mathycathy.com/blog/2015/01/tradingworksheetsfordesmos/ Richard 
In reply to this post by Richard Strausz
On 5/6/15, 1:31 PM, "Richard Strausz" <[hidden email]> wrote:
This is an example of really bad teaching. In fact, it isn’t even teaching anymore. Another example of his pedagogy…
http://thalestriangles.blogspot.com/2014/08/lowthresholdexercisesforanalysis.html
This is taking students who are not prepared for the material and rather than preparing them for the material, dumbing the material down.
This is why we have such issues with Desmos. Even champions of it, like yourself, end up in fraudville in no time flat. I think you should should create some standards regarding proper use of technology versus improper use of technology. You keep veering
so fast off into teaching fraud. Or at least, point out to us that this is a teacher in a situation with no expectations at all. It is really annoying that you don’t seem to care what the expectations are, just as long as it has Desmos in it.
Bob Hansen

That crappy teacher led to an even crappier teacher…
https://symmetricblog.wordpress.com
I like what he wrote on his profile…
"My name is Bret Benesh, and I am a mathematics professor who is trying to figure out how to teach well.”
At least he is an honest crappy teacher. Doesn’t he know he is teaching misplaced students who show up at his school? That is why they hired him. That is why a teacher that is trying to figure out teaching even has a job teaching.
Thanks Richard. Now I am going to spend hours going down this rabbit hole of the blind leading the blind. We seem to have two worlds here, one authentic, one very much not, and Desmos keeps showing up in the latter. Why?
Bob Hansen
On 5/6/15, 3:17 PM, "Robert Hansen" <[hidden email]> wrote:

In reply to this post by Richard Strausz
> ...Now I am going to spend hours going
> down this rabbit hole of the blind leading the blind. It's a good thing you have the time for this and the preceding 9183 posts. Richard 
In reply to this post by Robert Hansen
I've been keeping track and Richard is staying with his 25% but it's
almost all used up through December. Of 2017.
Wayne At 12:41 PM 5/6/2015, Robert Hansen wrote: That crappy teacher led to an even crappier teacher 
In reply to this post by Richard Strausz
On 5/6/15, 4:18 PM, "Richard Strausz" <[hidden email]> wrote:
It's a good thing you have the time for this and the preceding 9183 posts. No, I don’t have the time for this! Please check the sources before you post links to Desmos usage.:)
Thank You
Bob Hansen

In reply to this post by Richard Strausz
> On 5/6/15, 4:18 PM, "Richard Strausz"
> <[hidden email]<mailto:Richard.S > [hidden email]>> wrote: > > It's a good thing you have the time for this and the > preceding 9183 posts. > > No, I don’t have the time for this! Please check the > sources before you post links to Desmos usage.:) > > Thank You > Bob Hansen Bob, think about what the Ph.D mathematician said about wanting to teach better. Is there anyone (other than you) who shouldn't want to improve? Einstein once said: “Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.” In the world of Hansen I guess that meant he was dumb... Richard 
In reply to this post by Richard Strausz
Richard Strausz wrote:
http://mathforum.org/kb/message.jspa?messageID=9765744 >> Given that I don't teach Calculus, I wondered if any folks posted uses >> of Desmos in teaching calculus. I came upon this with links to interactive >> worksheets and more: >> >> The poster was (still is?) a visiting professor at Smith College. >> http://thalestriangles.blogspot.com/2013/12/someofmyfavoritedesmosprojects.html Robert Hansen wrote (in part): http://mathforum.org/kb/message.jspa?messageID=9765800 > This is an example of really bad teaching. In fact, it isn't even > teaching anymore. Another example of his pedagogy? > > http://thalestriangles.blogspot.com/2014/08/lowthresholdexercisesforanalysis.html > > This is taking students who are not prepared for the material and rather > than preparing them for the material, dumbing the material down. At the risk of tipping too far towards the side I always felt I was marginally on the opposite of, I thought these desmos uses were fine, at least assuming a large amount of student time wasn't spent with gathering/recording data and other activities that contribute very little to mathematical competence, and it doesn't appear so to me. It does look like the instructor spent a lot of time with these kinds of activities, however, but that's nothing new. Math teachers from at least as far back as the mid 1800s have spent lots of time on planning lessons and creating "neat problems" for their classes (or for various entrance, exit, and scholarship exams). I happened to notice this example . . . ** In discussing differential equations, we took a day to look at the logistic ** model of population growth. I asked on Twitter if anyone had a suggestion ** for realworld data to base a project on. Lia Santilli came up with a great ** idea I would never have considered: the number of Starbucks locations open ** t years after the company started. I had the students create a table using ** the data available here, then try to match the data as nearly as possible ** with a logistic curve. and it occurred to me that with all the publicity and press about school students and testing, the following might also be something to look into for an example of logistic model: https://www.google.com/search?q=logistic+item+response&tbm=isch Dave L. Renfro 
On 5/6/15, 5:25 PM, "Dave L. Renfro" <[hidden email]> wrote:
Yeah, I am sure they don’t spend a lot of time on Desmos, that is why we are discussing all the mathematics they do. Not!
This is a true avoider…
=================
For teachers planning to use Desmos with their students, I would make the following suggestions:
1. Draw them in with something interactive and manipulable. Teach them early to recognize that different shapes can be given by the same formula simply by changing a few parameters, and to explore the effects that the parameters
have.
2. Get them to create their own graphs. In the past, we had to do all the work to create the worksheets and the models, but now students can be enabled to build their own; when they do, they will benefit from creating, not
just responding.
3. Give them questions that require thoughtful use of the technology they have; simply having access is not a panacea. For example, realworld problems often have models that call for very different scales on the vertical
and horizontal axes. Students can be tempted just to use the zoom buttons, causing them to miss important details. Make sure they know they have to think about the graphs they’re creating, not just rely on the computer to show them everything, because it won’t.
=================
This is an example of second generation avoidance, brought up by first generation avoidance.
First Gen…
Me: Your students can’t do arithmetic with fractions.
Teacher: We teach understanding, not rote procedures.
Me: Let me rephrase. Your students can’t do arithmetic with fractions and thus can’t possibly understand them.
Second Gen…
Me: Your students can’t do arithmetic with fractions.
Teacher: What do you mean?
Bob Hansen

In reply to this post by Dave L. Renfro
On 5/6/15, 5:25 PM, "Dave L. Renfro" <[hidden email]> wrote:
And have them “guess” where they lie.:)
Bob Hansen

In reply to this post by Dave L. Renfro
Well, I guess we have about the full range of reactions, assuming we're all talking about the same problems. I think these calculus problems are fine (don't seem dumbed down to me), but I don't see why anyone would want Desmos for them. Maybe I just don't understand Desmos well enough? (The Smith teacher links to these:) Timotha On Wed, May 6, 2015 at 5:25 PM, Dave L. Renfro <[hidden email]> wrote: Richard Strausz wrote: 
On 5/6/15, 9:17 PM, "Jake W" <[hidden email]> wrote:
Well, I guess we have about the full range of reactions, assuming we're all talking about the same problems. I think these calculus problems are fine (don't seem dumbed down to me), but I don't see why anyone would want Desmos for them. Maybe I just don't understand Desmos well enough? (The Smith teacher links to these:) If you can’t model the volume of box without having it spelled out for you in Desmos, why are you taking calculus?
Bob Hansen

On 5/6/15, 10:42 PM, "Robert Hansen" <[hidden email]> wrote:
These examples, with Desmos being used as it is being used, are basically PaintbytheNumbers. I can’t believe that 40 years ago, colleges were doing this with advanced subjects like calculus, which makes you wonder how it devolved to this. Don’t these
liberal arts students have something better to spend their $65k a year on? Something they can actually do?
I shouldn’t be that hard on them, they (Smith College) don’t even have a math major[1], so it was just silly to use this as a “good” example of Desmos use. Show us examples where the students are expected to actually become good at math.
[1]  http://www.math.smith.edu/major.php
Bob Hansen

In reply to this post by Richard Strausz
Timotha, I made a total of 3 Desmos suggestions; I should have stuck with one at a time. The nature of posts here is that something can get lost quickly. I began the posts on 5/6 with one about using Desmos in an Algebra class.
http://mathforum.org/kb/message.jspa?messageID=9765447 Here is what it said  Timotha, I haven't tried the Polygraph Parabola activity (below) which sounds worthwhile, but I want to share the way that a friend used Desmos this year. He had his students solve a number of 'two equation, two unknown' problems algebraically. The students' homework assignment was to check each problem graphically using Desmos (or a graphing calculator). They had to correct the ones with mistakes algebraically. He said he liked this for two reasons. First, the students had to find their own mistakes. Second, for the problems with no solutions or an infinite number of solutions, he liked the graphical feedback that Desmos provided. "Mr. Jones, I thought I made a mistake when I only saw one line, and then I realized that since there were an infinite number of answers, they were actually two versions of the same line. Richard > Still *another* Desmos strength are classroom > activities designed by teachers and constructed by > Desmos. > > For a good example, check out the Polygraph Parabolas > activity. > > https://teacher.desmos.com/ Richard ========================= > Well, I guess we have about the full range of > reactions, assuming we're all > talking about the same problems. I think these > calculus problems are fine > (don't seem dumbed down to me), but I don't see why > anyone would want > Desmos for them. Maybe I just don't understand > Desmos well enough? (The > Smith teacher links to these:) > > https://docs.google.com/document/d/1q5jet6GMEWOPU6ykwC > zP9lsu9qaeN_GGQOS7FgyfQvk/edit > > Timotha 
Yes, thanks. I hope to find the time to reply to that one and also the Mathy Cathy one soon. Very busy here right now. Timotha On Thu, May 7, 2015 at 3:41 AM, Richard Strausz <[hidden email]> wrote: Timotha, I made a total of 3 Desmos suggestions; I should have stuck with one at a time. The nature of posts here is that something can get lost quickly. I began the posts on 5/6 with one about using Desmos in an Algebra class. 
In reply to this post by Richard Strausz
> Yes, thanks. I hope to find the time to reply to
> that one and also the > Mathy Cathy one soon. Very busy here right now. > > Timotha That's fine; I understand. Richard > On Thu, May 7, 2015 at 3:41 AM, Richard Strausz < > [hidden email]> wrote: > > > Timotha, I made a total of 3 Desmos suggestions; I > should have stuck with > > one at a time. The nature of posts here is that > something can get lost > > quickly. I began the posts on 5/6 with one about > using Desmos in an Algebra > > class. > > > > > http://mathforum.org/kb/message.jspa?messageID=9765447 > > > > Here is what it said  > > > > Timotha, I haven't tried the Polygraph Parabola > activity (below) which > > sounds worthwhile, but I want to share the way that > a friend used Desmos > > this year. > > > > He had his students solve a number of 'two > equation, two unknown' problems > > algebraically. The students' homework assignment > was to check each problem > > graphically using Desmos (or a graphing > calculator). They had to correct > > the ones with mistakes algebraically. He said he > liked this for two > > reasons. First, the students had to find their own > mistakes. Second, for > > the problems with no solutions or an infinite > number of solutions, he liked > > the graphical feedback that Desmos provided. "Mr. > Jones, I thought I made a > > mistake when I only saw one line, and then I > realized that since there were > > an infinite number of answers, they were actually > two versions of the same > > line. > > > > Richard > > > > > Still *another* Desmos strength are classroom > > > activities designed by teachers and constructed > by > > > Desmos. > > > > > > For a good example, check out the Polygraph > Parabolas > > > activity. > > > > > > https://teacher.desmos.com/ > > > > Richard > > ========================= > > > Well, I guess we have about the full range of > > > reactions, assuming we're all > > > talking about the same problems. I think these > > > calculus problems are fine > > > (don't seem dumbed down to me), but I don't see > why > > > anyone would want > > > Desmos for them. Maybe I just don't understand > > > Desmos well enough? (The > > > Smith teacher links to these:) > > > > > > > https://docs.google.com/document/d/1q5jet6GMEWOPU6ykwC > > > zP9lsu9qaeN_GGQOS7FgyfQvk/edit > > > > > > Timotha 
Richard, I notice that some of these examples seem to be trying to turn math into a game. While I am pleased when students enjoy the puzzles that are an inherent part of mathematical practice, I don't try to turn math into a game. I only have a very small amount of time, and the amount of ground I'd love to cover is pretty much unlimited so my top priority is always trying to maximize the amount of learning per hour. I have not found a math game that is a particularly efficient way of learning so I don't choose to use them. (I feed them snacks; I invite them to come early and stay late to socialize or play board games; I try to be cheerful and kind, but I don't play games during the math lessons.)
As I think I mentioned, my students are volunteers who come to do math of their own free will over the summer; perhaps I would feel differently about trying to turn math into a game if I had a classroom with different students. I doubt it, though, because I think the best way to help students feel better about math (and/or their ability to succeed in math) is to do the most effective job possible *teaching* them math. The more they fall behind, the more they hate math and the stupider they feel, even if the falling behind is through no fault of their own. If their math class is taught inefficiently, they fall behind. Although they might enjoy it in the moment, I don't think it serves them well in the long run. I guess that is a super inefficient way of saying I think the games are inefficient. I don't understand what the student is supposed to do with the MathyCathy stuff, for example: I think this is written for people who already understand how to use Desmos, but also I wonder if the verbiage is defective or is it just me? (e.g., "Use a vertexform equation to plot a parabola through the three points.") My favorite of the three you kindly posted was the Riemann sum gizmo that I can't find right now, from the calculus guy's website. But still, I like this one quite a bit better: It's a shame it isn't bigger, but it does a nice job of demonstrating families of Riemann sums. I will have more positive comments about your popcorn room when I have time to write more. Thank you for trying to help me. Timotha On Mon, May 11, 2015 at 6:37 PM, Richard Strausz <[hidden email]> wrote: > Yes, thanks. I hope to find the time to reply to 
On Tue, 12 May 2015 03:51:32 0600, Jake W <[hidden email]> wrote:
While I am pleased when students enjoy the puzzles that are an inherent part of mathematical practice, I don't try to turn math into a game. It's gilding the lily to do so. Mathematics is already a game! And reflecting on the time and energy that kids will put into gamessports in particular, but video games as wellmay be a personal investment that will repay a teacher. Lou Talman Department of Mathematical & Computer Sciences Metropolitan State University of Denver <http://rowdy.msudenver.edu/%7Etalmanl> 
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