Desmos Test Question

I am kind of excited about this (bonus) test question I used today . . .

My advanced algebra 2 students just finished studying a few of the basic parent functions and their transformations. Today, they took a test.

First there was a standard paper/pencil part of the test. Nothing unusual here.

Next, they picked up one of these cards containing the description of a parent function and a transformation.

The cards were color-coded according to difficulty level. Students were free to choose. Every card is different, so you won't be working on the same graph as your neighbor. Students were to pick up an iPad and use Desmos.com to create the function described.

Green Cards: Create a graph using a given parent function and animate one given transformation.  
Purple cards: Animate two given transformations.

When finished, students bring me the iPad. I check that the graph matches the description, stamp the card, and clear out the graphs for the next person.

I was really pleased with the results. Almost everyone was successful in creating their graph. I don't feel like this needs to be a bonus question next time. It might even become a regular part of test-taking in my classroom.

Now I am thinking about the possibilities. My head is already spinning with ways I can use this question format for other topics:

Quadratics/Polynomials: Create a function with given vertex or given zeroes. Can you keep the vertex in place while animating the zeroes? Can you keep one zero in place and animate the other(s)? Create a function with given end behavior.
Systems: Create a system with one solution, no solution, or infinite solutions. Create a system with a given solution.
Rational function: Create a function with given vertical and/or horizontal asymptotes. Animate one or both asymptotes.

P.S. If you are wondering what we did in class BEFORE this assessment, here is a quick summary:

1.  We spent several days sketching parent functions and transformations the old fashioned way, using paper and pencil. Students completed tables and plotted points, sketched graphs, looked for patterns, and generalized their discoveries.
2. Once students had mastered the basic functions and their transformations, I spent one class period introducing Desmos.com. I reserved our math department's shared iPad cart. I showed students how to enter equations, create sliders, and click play to ANIMATE (<3). They were as enamored as I was when I saw this a month ago at TMC13! Then I just let them play.
3. Finally, I started giving them a few challenges. Try to make an x^2 that moves vertically while stretching. Can you keep it from turning upside down? Can you restrict its movement to the second quadrant? Can you make it move horizontally along the line y = 2?

Best TMC Ever!

I think twitter math camps are like children or students . . . you're not supposed to have a favorite. But if I HAD to pick a favorite, it would be TMC16. The reason is largely because there was so much usefulness in the sessions I attended. I came home excited for the upcoming new year and ready to implement what I've learned. 

Here are a few things I hope you will hear more about this year . . . 

1. Debate and Discussion in math class! My HOPE for this year . . . my #1TMCthing . . . is to put structure to the discussions that happen in my math class. I've had my students seated in groups of four for years. Years! And yet I've never felt like the conversations they are having have reached the productive level that I desire. Chris and Mattie did a great job of showing us how to structure discussion so that it focuses on answers AND reasons. There is always a "because". If you would like more detail, I recommend you read this post by Sam (specifically "Talk in the Math Classroom" near the end). He did a beautiful job summarizing our morning sessions.

2. Make it Stick! Unlike every other session, this one stressed me out. It exposed some weaknesses in the way that I teach that I really want to address. The problem is that the correction involves more of a fundamental shift than just a little tweak here or there. And I'm really ready for a year when "change everything" is not on my to-do list. So I decided to commit to making two baby steps: First of all, I'm reading the book and participating in the chat on twitter. This one is already underway. Yay me! Secondly, I'm going to begin spiraling practice of content through warm-ups. It's a start. 

That's it. That's my 10%. Well, that and a few other takeaways . . . 

*Getting Triggy: Kristen shared a great collection of trig activities. I heart trig, and I'm excited to add her goodies to my toolbox . . . and to make some of my old favorites BETTER.

*Box Method: My math department has just decided to begin using the box for all things polynomial, so I was excited to see how Anna presents these to her students. I love how the box pulls together multiplication, factoring, and division in a way that will hopefully lead to better conceptual understanding.

*New Desmos Stuff: Sadly, I did not get to attend the Desmos pre-conference. But card sorts and marble slides oh my! I'm as excited as everyone else to bring the latest in Des-awesome to my classroom.

*Warm-ups: I've decided to go the spiraled-practice route for my warm-ups this year, but thank you to Jessica and Lisa for a really nice list of resources for great problems that can really be used for more than the beginning of class. When it's time for trig, I want to try a counting circle and clothesline for counting/ordering in radians!

*The Fun Math Game with The Lame Name

*Regrets: This is almost verbatim from last year's TMC post . . . I was lucky enough to travel to TMC with my entire math department (all four of us) for the third year in a row. I love sharing this experience with them, and coming home with some shared vision for our school. I get how rare it is to have that kind of collaboration at home. But once again I really missed out on connecting with the other attendees. 

*Lunch: Following the Make it Stick session, I asked a few others if they would like to have lunch and continue our conversation. It was a GREAT time talking with some people who I really admire, and I learned so much it was like a whole other session. It took some stepping out of my comfort zone to make this happen, but I'm so glad I did. If I'm lucky enough to attend TMC again next year, more of this is on my list of goals FOR SURE. I don't want to come home from another TMC regretting that I didn't seize the opportunity to speak in person with those I admire and learn from throughout the year.