My Take On Desman

One of my favorite course projects is the Graphic Art Project. Students will design an image on graph paper, write all the equations for it, and type them into Desmos. To intro this assignment, I have students complete my own version of the amazing Desmos Des-man activity.

Instead of having students create their own Des-man, I ask them all to recreate this picture:

The main reason I start by having all students create the same face is because this is a review activity for us. At this point in the year, students have learned to write equations for linear, absolute value, and quadratic equations. They have also studied domain and range restrictions. I want them to practice these skills, and not just guess/play with the sliders/numbers to see how the equations transform. Each student is given this sheet to show any work they did to find the equations:


The Teacher Desmos interface allows me to see very quickly who gets it and who needs help (see above). Some students will play around and choose their own colors, or add additional inequalities. When they are all done, we move on to Part 2, and I let them create their own designs. This year we are trying something special for the final product and it is still in the works… so, to be continued!

Stations Labs

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To review for major assessments, I like to set up stations labs around my classroom. They usually take about 40-60 minutes for most students to complete, though some students end up finishing some stations for homework. I make one master answer key and keep it on me during the activity. The students check in with me after completing each station so I can give them immediate feedback. If they work is completely correct, I either sign my initials or stamp their sheet, and they move onto a different station. It can be a little chaotic but I like knowing where each students stands as the period progresses. I make the students move around the room (although many would like to stay in one seat) so they are active and get a chance to work with different students. Hope your students enjoy them too!

S-L-O-P-E Stations Lab:

W-R-I-T-I-N-G Equations Stations Lab (previously written about here):

S-Y-S-T-E-M-S of Equations Stations Lab:

F-U-N-C-T-I-O-N-S Stations Lab:

A-B-S-O-L-U-T-E Value Functions Stations Lab:

Q-U-A-D-R-A-T-I-C Functions Stations Lab:

(Some formatting errors have occurred due to uploading to Scribd, hopefully they can be fixed when the documents are downloaded!)

Favorited Tweets #2

Last year I described some the tweets I had favorited here. After another lull in blogging, I thought this might be an easy way to jump back in. Here are some recent tweets that I favorited, forgot about it, and now want to document.

1) Math Coherence Activity from Achieve the Core: This activity would be great for teachers on a PD day. Teachers must place the standards in the correct progression order without looking.

2) Row Games: Kate describes them very well in her blog post, and when Rachel was looking for one on properties of Exponents, Lisa directed her to this folder with a plethora of them!

3) This awesome graph/activity from the Shell Centre written about by Megan and tweeted about by Cliff.

4) CueThink: This tweet below from Caryn Trautz and this blog post from Andrew Stadel were my first introductions to CueThink.

Norma Gordon from CueThink has since presented at the Global Math Department and you can find the webinar here. It’s an app that will change the way our students communicate, problem solve, and receive feedback. Check. It. Out.

Big Dreams Small Steps

Last week I had the privilege of visiting High Tech High in San Diego as part of a 12 member team from my district. It was Exhilarating. Eye-opening. Invigorating. Rewarding. Productive. Positive. And because of that, I’m scared to go back to school tomorrow.

This string art is a representation of each member of this [High Tech High] team as well as you, the community. We are all capable of creating great changes.

This string art is a representation of each member of this [High Tech High] team as well as you, the community. We are all capable of creating great changes.

How do you accurately share these emotions with colleagues who didn’t make the trip? How do you turn all of these emotions into change? It was overwhelming to experience, and there were definitely moments of questioning: How are we going to do this at our school?

Our students are not electing to be here. Our teachers didn’t sign up for project-based learning. We don’t currently have technology for all. The list could go on and on, but these are complaints instead of solutions, and I’m not ready to hear them. They shouldn’t matter. They don’t matter.

I’m not naive. I know that we have to be realistic about our circumstances. But realism shouldn’t correlate with negativism. I love my district. We do many great things here. And we will continue to do great things. But we have to be willing to make changes along the way and admit that we always can and should be striving to get better every day.

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Sitting around the fire pit after touring HTH Chula Vista, we debriefed by sharing small, immediate changes that we know we can make. You have to start somewhere. My first change: making our projects have a more meaningful impact on our community. As our student tour guide stated, “Why would you even do a project if it doesn’t mean anything?” It was a theme heard constantly during our visit and one that will have a strong, positive impact on doing projects for our students.

“You need to have the courage to mess up,” shared one HTHCV Biology Teacher. Although a part of me is fearful for the work that lies ahead, I know that we can do it, and I know that we have to do it… Together.

Becoming a Better Teacher

Originally posted on MPS Mission to High Tech High:

Watching other teachers teach is one of the best, if not THE best, form of professional development. Visiting countless classrooms at both High Tech High campuses reminded me of many great instructional practices that I need to use more in my classroom, and gave me many new strategies to begin to implement.

1) Several teachers had playing cards taped to the corners of the student’s tables. During class, the teacher pulls a random card from the deck and that student answers the question or shares an opinion. The goal is to increase student participation and include everyone. It works better than pulling Popsicle sticks because playing cards give a teacher more options. In addition to pulling one card for a particular question, the teacher can say, “Turn and talk with your neighbor about _________, red cards speak first.” During group work, “Can all diamonds please grab the materials for your…

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Global Math Department TweetUp Boston




When: Saturday, December 13, 2014 at 4 pm

: Cornwall’s Pub, 654 Beacon Street, Boston MA

What: Connect or reconnect with math tweeps, share practices/experiences/tips, play pool/board games, MATH!

RSVP here!

Questions? Post them here in the comments! Or contact @heather_kohn or @crstn85 on Twitter

Check out the Global Math Department – we sponsor weekly virtual professional development (hosted at Big Marker) and have a weekly newsletter with blog reviews.

Ambiguous Sports Graph

“Oh shit, I think I just changed my mind.” -Student

Sports Graph

Today in class we talked about the above graph. For 45 minutes. One graph. And almost every single one of my students was engaged the entire time. Here’s what happened…

During the summer I attended an institute at Boston University on facilitating productive math conversations. We learned how to set up norms for math talk and how to use talk moves (student and teacher ones) to help us facilitate the conversation. Luckily, I attended this institute with a fantastic colleague, and we have been able to share strategies as we start to implement more math talk in our classrooms. My colleague has used the original graph for years, but now it’s more clear what we want the students to talk about and how we want them to do it.

Student goals for this lesson:
• Describe the behavior of the function using precise mathematical vocabulary
• Make a choice about the sport that can best be modeled by the given graph
• Defend their own choice and respectfully critique the choice of others if they do not agree
• Reconsider their choice if they have not taken into account the time that elapses in each section of the graph

Teacher goals for this lesson:
• Use the talk moves
• Stay neutral – don’t pick a sport to keep the kids wondering
• Say very little

I started the lesson by projecting the ambiguous graph on the front board:

Sports Graph

I asked students to “Turn and talk” with their partner about the behavior of the graph. Essentially, what is happening here? I asked volunteers to share with the class. Some pairs made up their own stories. We heard about objects, cars, runners, and animals. They were accelerating, then something happened to cause the speed to change quickly. Then “object” returned to a constant speed and stopped abruptly. There was a great debate over the vertical line at the end of the graph, with many students sharing that an object cannot have more than one speed at one moment in time. Misconceptions became clear as some students referred to the distance of the object from the starting point. Some thought the object stopped and turned around. Students jumped in to clarify. We didn’t move on until everyone understood the difference between a distance/time graph vs. speed/time graph.

Then, I threw this slide at them:

Sports Graph with Sports

Without talking, students were told to choose the sport they believe is best modeled by the graph. Convince me, I said. Students wrote their responses on this interview grid, then swapped ideas by interviewing two other students (See this post for more on the interview grid strategy).

By this point, students could barely keep their ideas inside anymore. Sharing with only two classmates was not good enough; they wanted, needed, to discuss their ideas with the whole class. I asked for one volunteer to start off. It was really hard to choose. And then they talked. I didn’t say much, just kept the conversation going by calling on students and using some of the talk moves. My above mentioned colleague observed one my lessons and wrote down some of the phrases I used to keep it going:

-Say more about ________
-Can someone rephrase what ________ said?
-Can someone add-on to what ________ said?
-Does anyone agree or disagree? Why?
-Are you changing your mind? Why?

I barely talked about the actual characteristics/behavior of the graph, because I didn’t have to. If a student said something incorrect, another student shared his thoughts to help clarify. Some students came up to the board to draw additional graphs to support their thinking. The students led the conversation and I just went with it. The goals above were always on my mind, and eventually we met them in each class.

So what did the students say? I didn’t write anything down because I wanted to give my full attention to the conversation. Here is a snapshot of their interview grids:

The student work is a great representation of the different ideas discussed during our conversation. Many students stuck with their original sport, but many were influenced by the thoughts of their peers and changed their minds. Students wanted to know what is the right sport, but, there isn’t only one right answer I told them. Many students came to this conclusion on their own as well. If we had more time, I would’ve asked students if they could think of another sport that could be modeled by this graph.

We will follow up this activity with the Desmos Function Carnival. I think students are really going to like this unit.

Update: The “Which Sport?” graph was originally published in the The Language of Functions and Graphs by Malcolm Swan.