Tag Archives: Desmos

[DITL] 5/22/17

6:00 am

Woke up at my usual time. It feels like it should be the end of the year, but we have 3 weeks of school left, so I’ve got to figure out how to motivate myself in order to motivate my students to try through to the end. This week is exam week at my last school, so it would already be the end of the year if we had stayed in New Mexico.


7:52 am

Students start coming into class and the morning lesson from admin is to vote on rising 6th and 7th grade students. It does not make a lot of sense for my 8th graders to care about the election, but they care more than I thought the would, so I appreciate their efforts.


8:40 am, 1st & 2nd period, planning

We have a diversity training. I already heard this from my “First year teacher” course, though it is new to most of my colleagues. The best time in the 45 minute session is 3 minutes where they ask us to share something meaningful with our colleagues. I wish we could have more time set aside for just that because we can learn so much more from personal stories.


10:20 am, 3rd period, Merit 8th Grade Math

The students are unfocused. There are always 5 different conversations going on at once and they are unable to stay quiet for more than 2 minutes at a time to listen to my explanation of what we’re doing today. It’s become my roughest period by far. A few students have their phones out and I struggle to ask them to put them away. After five minutes some of the phones return. I know at least one student is having a bad enough day that he might go off if I take his phone again. I decide to ignore him and his phone this time. [1]


In this class we did a “hand squeeze” activity, where students stood in a circle and we timed how long it took them to squeeze each other’s hands all the way around the circle. The goal was to create (in Desmos) a scatterplot with a strong positive linear correlation: the more people in the circle, the longer it should take to go around. Here’s a Desmos graph to go along with some of our data (I couldn’t convince everyone in the class to stand up and be willing to hold hands).


11:10 am, 4th period, Honors 8th Grade Math

This used to be one of the class I had the hardest time getting them to focus, but now they’ve done pretty well for the last several months. Phone calls home to this group really help and I’m staying in daily contact home with at least one of the students.


In this class we’re doing our end of year stats project. This involves finding two things to compare to each other via a scatterplot and creating a few questions for their classmates to answer.


12:00 pm, 5th period, Algebra

My Algebra students took their PARCC test (part 1 of 3) this morning and are taking part 2 in the afternoon. Since this is during their lunch time, they had to have their lunch during 5th period, so they just hung out and ate in my room. One student said “this is the best class of the year!”


12:50 pm, Lunch

Three students came into my room for “tutoring”–however, for these three regulars, they just hang out in my room. We got to have a discussion about various topics, such as religion (since they ask), friends, and family.


1:23 pm, 6th period, Honors 8th Grade Math

Just as before, we’re doing the stats project. I walk around the room, but this class has a harder time figuring out what they’re doing.


2:13 pm, 7th period, 8th Grade Math

This class is not as loud as 3rd period and we get much farther in the “Hand Squeeze” assignment. We just need to discuss the conclusion, but they’re ready to start the next assignment!



The end of the day bell rings and I go through my after school routine. Here’s my current checklist:


The email addresses are students that I contact daily, blurred out for obvious reasons.

I get to go home about 2 hours after the students are done. Tonight I need to grade Friday’s quizzes, figure out lesson plans for tomorrow’s Merit classes, and sign up students for tutoring who didn’t take the quiz on Friday.

Just 13 more days to go!


[1] I ended up making a positive phone call after school. I hope to hold it up to him tomorrow and point out that I could have called about his phone being out, but I want him to succeed. I need to keep trying to build relationships even if we’re in the last 3 weeks of school. This also helps me to feel that I haven’t given up on him: I ignored his lack of effort in class, but didn’t ignore it after school and won’t tolerate more than one day of being angry as an excuse.


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[2016 Blogging Initiative] Week Two: My Favorite = Desmos


Desmos. If you’re a math teacher and you don’t know about it, stop reading this and go to their website now.

It took me a long time to even think of Desmos as one of “my favorites” because it’s so integral and every-day in my math classes that I guess I’ve started taking it for granted. I forget the days when TI button mashing ruled the day.

Here are a few things I appreciate about Desmos.

Browser Based & Free

The fact that students can access these from any computer with internet, or install the app and have them without internet access is incredible.

I have a class set of iPads, but increasingly students are asking to use their own phones. I point out to them that their eyes are going to go bad, but many of them have become proficient at using the tiny screens.

Sharing Graphs

I am increasingly using the “share this graph” feature. A student will create an awesome graph and instead of just presenting with the projector, all the students in the class are interacting with their own version of the graph on their device. Or I’ll create a graph (usually a table that I don’t want to waste class time having students type in the data points) and share it quickly with the whole class. It’s great!


Nothing beats building intuition with function transformations like having students move the sliders to manipulate the values. Before Desmos, I used Geogebra, but I spent a lot of class time showing students how to make sliders–it was not nearly as streamlined and intuitive as in Desmos.

Activities & Activity Builder

I was a huge fan of Function Carnival, Penny Circle, and Central Park when they first came out. I even had my students do these, even though we weren’t exactly on those topics when each activity came out (it was review, okay?). Now Desmos has Polygraph[1] and, the latest that I’ve yet to try with my class, Marbleslides, each excellent activities.

But I think the best thing that Desmos has done in this area is the Activity Builder. I haven’t had enough time to dig in and create activities, but the possibilities are endless. And no need to reinvent the wheel–activities that other teachers have created are available for you to see, too! Holy smokes!

To access all these cool things, go to teacher.desmos.com. I haven’t even started talking about the awesome teacher-view for when all your students are working on these activities.

And So Much More

It would take me way too long to mention all the incredible things that Desmos can do and is doing[2]. And they’re constantly improving things. They respond quickly to feedback, both in communication and by doing the thing you asked for within Desmos.


Thank you, Desmos!


[1] There’s a huge bank of polygraphs since people can make their own!

[2] To list a few: recognizing function notation, derivatives, inserting images,intuitive click-on-the-point to find the intersection or x & y-intercept, domain & range restrictions, lists, click & drag points, regressions for any equation, implicit function, colors!, labeling axes, easy animation, and converting equations to tables. I’m sure I forgot ~90% of the features that I like.


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Function Transformations

I tried something new this year when teaching function transformations: I had students come up with the “rules” in groups with little help from me.

Day 1

Students created a DesMan (person using Desmos) and built up an intuition for how functions move[1]. We spent a block day (1.5 hours) doing this. Students were free to share what they discovered with one another and that helped tremendously. Here are some of their creations:

And here’s one that has moving parts:


Day 2

No students finished the DesMan on the first day, but I told them that they could get credit for “Modeling with Math” if they finish it.

We split into random groups of three and I had them move to their vertical whiteboards with these instructions:

  • Split your whiteboard into 4 parts.
  • On each part you should explain to a Freshman (these are Juniors and Seniors in Precalculus) how to transform a function in these four ways: Translate up (they suggested the word “translate”, I was going to use “shift”), translate down, translate right and translate left.
  • Please include a graph, use function notation, and an explanation using the ideas “input” and “output”.
  • You should use Desmos to confirm your explanations with some examples.

Here are some of the whiteboards they created.

IMG_20151002_150615906 IMG_20151002_150229253 IMG_20151002_150601495

As groups finished[2], I approached them and made sure everyone in the group understood each idea, especially the input/output language.  I asked them to do the same thing on a second whiteboard, but this time with stretching vertically, shrinking vertically, stretching horizontally, and shrinking horizontally. Here are some of those whiteboards:

IMG_20151002_154405792 IMG_20151002_152324286 IMG_20151002_151618290

Even though their whiteboards are great, that wasn’t the best part of the activity. The best part was the discussions that I overheard. Every student was involved because every student (a) had some experience with all of this through their work on the DesMan and (b) felt comfortable asking “why?”. I felt as though we had reached a classroom culture of safe inquiry and curiosity, where “why does that work?” questions are empowering rather than embarrassing.

It also helped tremendously having Desmos as an outlet

Some groups finished this part before the end of class, so I had them examine vertical and horizontal reflections. Here’s their work:


Or maybe I drew those pictures in red, I forget.

Day 3

We did a short game of “guess the type of function transformation from the graph”. It helps having 2 screens: one that I only I can see, which I use to edit Desmos and the other that the class sees, when the function is hidden.[3]


In three short days, I feel confident that students will be able to use these transformations the rest of the year[4]. It’s important to note that I’m not introducing this to students the first time (it is Precalculus and they should have seen this at least once in Alg II), though they often act as though they haven’t seen it before.


[1] I didn’t use this Desmos page, but it’s another way to do this: https://teacher.desmos.com/desman. I just had them graph a parabola, restrict the domain {-3<x<3}, then move it and they were off!

[2] This is where the vertical whiteboards was tremendous: I could catch groups right as they got to finishing their work.

[3] I only have this setup in one of my classrooms. In the other I have to use the “freeze” button on the projector to work out the next graph.

[4] And they will use them them since I like 3-act lessons where students have to figure out what the function is. It’s important that they practice this throughout the year.  Maybe one day I’ll show them how to approximate data using the tilde (~) in Desmos.

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3 Acts: Volume of a Box

I’ve done this activity before, but I can’t seem to remember whether I’ve blogged on it. Here’s the gist of it (with pictures!).

  1. Ask students if they can make a box out of 8.5 x 11 paper. Give them paper, scissors and stapler (or tape).Paper Box
  2. Once they’ve made the boxes, ask the students (or let them ask) “What’s the biggest possible box with an 8.5 x 11 paper?”
  3. Let them make guesses first (way too high, way too low, just right).Guesses
  4. Point out that we should get a bunch of trials and have students, as a class, decide which boxes to make (students select which box they’ll make which is different from other students. Have students make one box each to contribute to the table.Stack of Boxes
  5. Plot these on Desmos. Then put the boxes on the board so we see what each of the points represents.Boxes on the board
  6. Talk with students about equation for volume. Have some students provide the equation.Table and Equation for Boxes
  7. Plot the equation and click on Desmos for the maximum (this is Precalculus, not Calculus). Acknowledge who was the closest and have students write down what they learned.Boxes on the board with equation


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Video of a Lesson: Robert Kaplinsky’s In-n-Out Burgers

First off, thanks to Dan Meyer for alerting me to the idea of 3 Acts problems. This particular problem was created Robert Kaplinsky. You can find all of the lesson materials at this page, free of charge.

I had seen Dan Meyer present the 3 Acts lessons to teachers, and that helped shape my understanding of these problems tremendously. However, I hadn’t see one “in action”, with a bunch of real students, who may or may not already be “done” with math.


We start with some bare-bones math problem for the warm-up. Unlike last year, where “participation points” were given for working on the warm-up, there’s no obvious incentive for them to work on the warm-up, other than “so Mr. Newman doesn’t get on your case”.

Watching myself, one thing I’m glad I did was ask “if you messed up, how did you mess up?” I’m really pushing this year trying to make mistakes not only acceptable, but a great source of learning.

We open with a prayer (I try to open each class that way–this is a Christian school), and jump right into the warm-up.

The rest of the power-point is right here because you can’t really see it in the video.

Act 1

This goes pretty smoothly–most students know what In-n-Out Burger is, and the images that Robert Kaplinsky found are definitely riveting and shocking, if not simply gross enough to draw student attention. In my other period, the first question (How much does it cost?) jumps out before I even ask for questions. In the past I would have discouraged the somewhat-off-topic questions, but I find they often keep the interest of the students and makes the task genuine.

One of my favorite exchanges is:

S1: “We’re getting an In-n-Out Burger”

S2: “That’s a lie.”

It doesn’t contribute to the mathematical side of things, but it draws all the students in a little more. Time well spent (maybe 15 seconds talking about whether an In-n-out burger is coming to town?) in my opinion.

It was 10 minutes before class when I realized I hadn’t printed out the sheet that I wanted. Here’s what I had seen before and wanted (from Robert Kaplinsky:

Here was what I created, which gets at most of the same ideas:

Block Day Lesson.pdf or Block Day Lesson.docx (scribd isn’t working at the moment)

Block Day Lesson, page1Block Day Lesson, page2


I want the answers to the math questions to be earnest, so I try to treat all the questions more or less equally. That’s why I go ahead and answer the questions that I can, and we later tackle the questions that they can get. My goal is to answer everyone’s question in the end–or at least leave them with a good idea of the answers (or the tools to answer all the questions).

Act 2, part 1

I’m not sure where Act 1 ends and Act 2 begins, but I decided to cut the video where I said “Go” to the students. I was less than thrilled with students’ creative thinking, so I had a divergent thinking interlude.

Divergent Thinking interlude

My goal of this task was getting them to be more creative[1]. Part of that is helping them realize that they are more capable of being creative than they think they are.

Act 2, part 2

Now the students are more oriented to the task, and come up with a little better information. I give them the necessary information (the menu) and they take off.

Act 2, part 3

Here the students are working in groups at different rates. I do an okay job giving the group that was done first the longest/most difficult task. I really wanted one of each of the following from different groups: (1) a graph, (2) an equation, (3) a table, or a solution in another way. Some groups “thought it out” and used words, which was great.

Act 3

We (I) talked about what the graph means, what the axes mean, and what the equation “y=mx+b” means in this situation. After that, I showed them the “answer” (the receipt) and they thought it was cool. I mean, I got several of them to clap–that’s always fun when that happens in math class.

Unfortunately we ran out of time and I didn’t really get to explore “How many calories is that?” in this class, although one group in my other class (which I didn’t film) did. They found the information online by themselves (identical to the numbers that Robert Kaplinsky provides!), answered it, and even answered the question of “How much does that weigh?” They put their answer in terms of Chromebooks so we could compare to what was right in front of us.

The last part of class (which I cut from the film) just involved me teaching the students how to log into ActiveGrade. Mostly just classroom-administrative stuff that’s not nearly as interesting to watch.

Things to Improve On

Others talk about having students make approximations or estimates to increase “buy-in”. I didn’t do that because I forgot about that aspect of it, however, I think there was sufficient “buy-in” (this is pretty close to the start of the year). That’s definitely something I’ll need to do in the future, though, because it also increases their estimation abilities and allows us to discuss afterwards “Does this answer make sense?”

One thing I struggle with is finding a balance between giving students the distance they need to be creative and think on their own, yet being close enough to make sure they’re focused on the task at hand. Ideally the 3Acts is a great hook and I don’t need to be hovering over students to get them to work. But this hasn’t been my experience.

For the first half of class, the student in the front had his head down, and I had to go over and talk to him to make sure he was participating.

Watching myself teach, I talk way too much. And I answer my own questions way too much. I’ll walk away from a class thinking “that was a good class”, probably because I understood everything that happened. I need to do more formative assessment to make sure that they understand everything that’s happening.

I also haven’t made my Popsicle sticks in this class yet, so I also had the problem of the same 2-3 students answering all of my questions. Oh, and my wait time is awful. Every now and then I consciously think “just wait”, but not often when I’m excited about something. And these 3-act lessons always make me excited.

I didn’t end the lesson with a “summary activity” to make sure the students learned something. I even have a box at the bottom of my sheet “what did you learn?”, yet I didn’t take the time to fill it out. Now another day of school and a weekend will have passed, and I’m left asking myself whether it would be worth it to return just to answer that question.

One other thing I think I do is that I teach as if I’m in a rush. Yes, it feels like we have a lot to go through, and we do, but if I could slow down, I wouldn’t lose so many students, and I could take time to do things like acknowledge when a student is brave and submits his or her own mistake for review by the class.

Other Notes

I used Doceri to write on the iPad and have it show up on the projector.

I introduced Desmos to students, and they got a small glimpse of how awesome I think it is as a tool. I don’t they understand just how truly awesome it is yet, but that’ll come.

I know that this is a ridiculously long post, and I don’t expect many people (anyone?) to read it all the way through, though I hope that the video of the lesson was at least helpful. That is one thing that I would like to see more of on the MTBoS: video of teachers in real-time. I understand that many teachers (mostly public school, but some private as well) have tons of red tape to walk through to put videos online of them teaching since it usually involves students’ faces. Teacher blogs are a great window into a teacher’s classrooms, but I want to see how other teachers handle behavior problems, or keep students excited about a lesson when it starts to turn sour. This is like getting to observe other teachers in the MTBoS, which would be an awesome experience!

Another note: while this reflection/sharing was good, it took way too long–especially the video editing on my 6-year-old computer!

[1] I know that divergent thinking and creative thinking aren’t identical, but for the purposes of this activity, I used the two phrases interchangeably. Sorry.


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Entire Lesson Videotaped: Intro to Parametrics

On a whim, I decided to videotape an entire 45 minute lesson in one of my classes. The only thing I had on hand was an iPad (2nd Gen), so the video quality is low, but I’m also kinda banking on that so I don’t have to blur out students’ faces.

Other information possibly of importance:

  1. There are 15 students in this Precalculus class.
  2. This class is the last period of the day. [1]
  3. Yes, that is my principal who strolls in at [29:43], and yes he picks up a student’s guitar and starts playing in the last 10 minutes of class.   (Oh, and it was his birthday.) Don’t you wish you had a principal as cool as mine?

Outline of the Video

[0:00] to [3:46] Waiting for class to start. (I should have edited it out, but this is why the video starts at [3:46].

[3:46] to [5:40] Waiting for student let out of choir to get to my room (they’re late most of the time because our choir teachers let them out late).  Because I have all these students for Chemistry, we discuss a little Chemistry while waiting for everyone else to get here.

[5:40] to [8:36] I show students how they can find all the standards from the class on my website.  We also discuss Inverses of functions and they convince me to give the quiz on Tuesday instead of Monday of next week.

[8:36] to [12:30] 1st Act: I develop a reason for Parametric Equations and we do a really rough experiment of a student walking into the room.

[12:30] to [31:47] 2nd Act: Through questions I build an intuition for Parametric Equations through graphs and the measurement of our “experiment”.

[31:47] to [40:04] 3rd Act: We answer the questions I provided for them at the start of the lesson (although I didn’t vocalize them, and I didn’t have a “hook” for them like your typical good 3 Acts lesson. We look at two ways to use technology to graph this equation and I give them two of these types problems for homework (see the sheet below). I use the TI Calculator because they’ll need to know how to use that for most standardized tests. I use Desmos because it is awesome and easy to use (and way cooler than the TI Calculators).

[40:04] to [50:03] I promised them from the day that I would do the Fibonacci Magic trick.  If you haven’t seen it, here’s a video of it being done, long with an explanation of how to do it (however, I don’t like his explanation of how to multiply a 3-digit number by 11).  If you prefer to read, here’s an good explanation of how to do it.

Supplemental Materials

Since the board is hard to see in the video, here are two pictures of what I put on there.  For the most part, the black is what I had up before class started and green is what I added during class.

Picture of Classroom

Four Representations of a Parametric Equation

Here’s the worksheet I gave for homework.  Notice how I set up the board so all 4 parts match the worksheet.

Please leave feedback on my lesson and on my teaching style: both constructive and destructive comments are welcome, so please let me know what you think!


[1] The students recognize their tiredness at this point and frequently complain when I ask them to do a particularly mentally challenging problem or task.  I suppose I am fortunate that they recognize this, though I wish they had a bit more motivation and didn’t use it quite so often as an excuse.  Fortunately these are all good kids who try despite their tiredness, though they have vocalized to me that they wish this class was taught earlier in the day.

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SBG Progress: Creativity at Work

Here’s an awesome graph that a student of mine created when I gave them the open-ended “Show me that you know how to manipulate functions and you know several different types of functions.” Thanks to SBG, I can now give this student an excellent grade, even though she may be the only one to turn in this assignment.

A cute function cat!


I hope to do more of this in the future: reward thoughtful creativity.


Edit: I showed the students this picture today in class, explained how it had the potential to impact their grade, and the other faces started to flow in! Here’s my website with other student work on this assignment.

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