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?

Four Friday Favorites

Four things made my day today:

First of all, my district switched things up by replacing my smart slate with an iPad. Now when I want to write on the board, I can see what I am writing. Nice. At the same time, writing has become more difficult because I am very particular about what writing should feel like. I NEED to have a precise writing tool, and I NEED to rest my hand on the surface while I am writing. Monday I went home feeling stressed about a lot of things (most are better now). Of all things, not being able to write comfortably was really irritating me. Plus I was first-day-of-first-full-week-of-school exhausted. And grumpy.

My husband loaned me this stylus, and I am a fan. It writes as smoothly as a pen, with all of the precision. I sketched some graphs in class today, and all the points landed right where I wanted them to land. It is expensive, but I am happy with it (so far anyway, it may be too soon to tell). I already owned its less expensive little brother, and that guy doesn't work well at all. They look the same, but the cheaper one skips constantly. I am hoping to continue a long and happy friendship with this new stylus. I gave hubby the other one. He's the best.

Then there is the issue of NEEDING to rest my hand on the iPad. I dug around my house and I found this glove with missing fingertips. It works perfectly. It protects my palm from the screen while keeping my fingers free to use the touch screen. I don't even care that I look like a dork wearing a glove in my classroom in August. Maybe I will buy one in every color and match them to my outfits. It will be the new math teacher vogue.

I really enjoyed this little ice breaker from Dan Meyer. I love that it combines mathematical thinking with a get-to-know-you element. I walked around the room and kids were asking each other how many siblings they had, how many pets they had . . . how often they brush their teeth. The only problem I had was when the number of students in a class was not divisible by four. I learned not to allow a group of three. It makes the task WAY too easy. I ended up making groups of 5 and adding an extra dot in the middle, which provided an interesting additional challenge. Then I started thinking about making a page with multiple configurations of dots. (Or have students place the dots themselves before they get the instructions?) So many options! Maybe next time . . .

Finally, I found these birthday stickers in the dollar spot at Target, and I have been handing them out on birthdays. A senior boy immediately put it on his shirt and today he told me how useful it was because,  "You WANT everyone to know its your birthday, but you don't want to go around telling them it's your birthday". That made me smile.

Happy Friday, everyone!

Highlights of TMC13 (finally)

So many people have done a wonderful job of re-capping the events of TMC13. I am pretty sure I have nothing original to say about the (most amazing) conference I've attended. EVER.

I decided to focus on the aspects of TMC13 that made the biggest impact. This is not even close to a comprehensive list of take-aways:

Rich Problems/Tasks:  It started with Max's presentation on noticing and wondering. The simplicity inspired me. Two powerful questions can bait our students to dig into problem solving. Glenn's session was the perfect follow-up. He showed us how to extend any problem by listing its attributes, changing one thing, and then see where it goes. Then we worked through a couple of tasks with Karim from Mathalicious. I can't wait to use these and others. These sessions all worked together to boost my confidence about implementing these types of problems in my classroom . . . This will be my main goal and focus for this next school year.

Interactive Notebooks:  I will admit to dragging my feet when it comes to INB's, but Megan's session won me over. I learned that I can modify much of what I already have, so my fear of starting from scratch was dispelled. I also learned that INBs are particularly affective in engaging lower-level students and helping them stay organized. I'll be incorporating these into my regular Algebra 2 class this year.

SBG: I might be the only math blogger who hasn't implemented standards based grading. I do not know why, because the philosophy totally aligns with what I believe about education. It was good to talk to people who are using SBG. They don't want to ever go back. It was good to hear that there are a hundred different flavors, not a right way or a wrong way. I figured out where to start. From there, I will make it work for me. I'll be incorporating SBG into my calculus class this year, but I suspect I will be expanding it to the others before long.

The People: Finally, a few words about the social aspect of TMC. Even though I have been blogging for a while, I have had a limited presence on twitter compared to most. I did not know many people going in. Add to that the fact that I am an introvert . . . I had some anxiety at first.

But I was determined, so I carried my introverted self down to the lobby where I folded paper and made plans for the evening. I went to karaoke expecting to stay for an hour, and ended up staying until closing time (and singing!). I had amazing meals with interesting people, and everywhere I went people could not have been nicer.

I decided not to name names because I will surely forget to mention someone. But I truly appreciate the generosity of those who gave me rides, brought me bagels, and included me in their plans . . . Thank you. I am thankful for every conversation, every walk from here to there, every meal, and every thoughtfully prepared session.

This tweet I sent from the airport sums it up pretty well:

Arrived excited and nervous. Leaving with new friends in the 'sphere. :) #TMC13
— Amy Gruen (@sqrt_1) July 28, 2013

I don't want to ever miss this again. And I am really going to TRY to spend more time on twitter for lots of reasons, but especially because all those faces now have really amazing people attached to them.