Homecoming Balloons

Me: Okay, the balloons are in my closet. Now, there are 50 pink and 50 silver but only 25 of the black. Remember that when you are planning out your rows.

 . . . later . . .

Decorating girl:  We decided to put the rest of the balloons on the floor.

Me:  Oh, I thought you were going to do three rows on the ceiling.

Decorating girl: Yeah, but there weren't enough black balloons to continue our pattern.

 . . . sigh . . .

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.

Zombies, Logs, Noticing, Wondering, Precalculus, and #TMC13

I attended the precalculus morning sessions at twitter math camp. Among other things, we made a list of topics that can typically be problematic when teaching precalculus. Then we each signed up to work on one of these topics and produce something useful.

I ended up working on logarithms with Summer (@mathdiva77) and her adorable southern drawl. I am not sure that she would appreciate the adorable adjective, but it's my blog.

We agreed that we both felt pretty comfortable with the procedural part of teaching logs, but we were missing some pizazz. We were missing a hook.

Our fearless leaders, Sam and David, had suggested that we start by trying to focus on our topic's big idea. We decided that logs, being the inverse of exponents, allow us to find an unknown exponent. Check.

So . . . How could we get our students wondering about exponents? We started talking about Max's session on noticing and wondering (one of my favorites!) and then Summer started talking about zombies because they're all the rage right now and we started getting super excited.

Zombies! We needed pictures of zombies! More importantly, we needed pictures of zombies multiplying exponentially. It took some effort to find some classroom appropriate, mild-looking zombies in groups of one, two, four, and eight. We pasted them onto a page in that order.

Then we typed the words "What do you notice?" and "What do you wonder?" at the top of the page and we were done. We basked in the glory of our creation. We envisioned our students noticing the number of zombies and wondering when there would be 1000 zombies, or when zombies would outnumber people. They would be putty in our hands. They would be begging us to tell them about this thing called a logarithm.

Next Sam said that it was time to share what we'd created. At this point I started to have doubts because, hey, did we seriously just paste four pictures into a word document and call that a project? The group offered some helpful suggestions, like attaching the pics to a timeline. We might let our students wonder about that, too, but we would ultimately have to provide that information in order for the questions to be answerable.

The more I think about it, being simple is kind of the beauty of it. Maybe it isn't that hard to bait students to ask the questions we want them to ask. Maybe the chasm between being teacher-centered and student-centered is much smaller than we think. Maybe all you have to do is start with a carefully selected picture, and then get out of the way.

We'll let you know how it goes. Stay tuned.

Unintentional Math Encounters of the Non-Mathy

If you are a math teacher, this has probably happened to you . . . Someone you know has come across a problem involving math and they ask you for the solution because, hey, a math teacher must know how to figure it out.

First, a little background story:

I grew up on a farm in Kansas. (So that's what me and Superman have in common.)

Over the years, my Dad's specialty has been modifying the equipment he uses to make it more efficient, user-friendly, and/or comfortable for the farmer. Several manufacturers have visited our family farm and utilized his ideas in their designs. I am proud of him, if you can tell.

On the fourth of July, after grilled hamburgers and before the small town fireworks show, my 73-year-old Dad pulled out a yellow notepad and sketched this:

He has been working on a piece of planting equipment, and he needed to know the length of x in order to form interior angles of 11 degrees and 6 degrees. It is a pretty simple right triangle trig calculation, but he didn't remember how to do it. I figured it out for him and we discussed the feasibility of my answer (x was smaller than he expected).

Since then I have been holding onto this sketch. It has me thinking about other times that I have been asked these types of questions . . . A former student building a garage with his Dad, another farmer calculating a complex feed ratio for her cow herd, and others.

It seems like these should be some of the best problems to put in front of our students because they are from non-mathematicians, unintentionally encountering math as a part of daily life. This, for lack of a better phrase, is "real life math".

I'll put this sketch in a folder and start collecting other questions as non-mathy people corner me for answers. But I am afraid my collection is not going to grow very quickly. And even if it did, the scenarios from the rural community in which I live are limited. I am always looking for ways to expand my students' perspectives.

I'd love to have help here. What math have your non-mathy friends asked you to solve?

Summer Work

I had a great summer work day with my colleagues this week. We worked on a plan of attack for the changes coming our way, and there are a lot of them. When I recently complained that "change everything" was on my summer list, I was only kind of kidding.

1. Incorporate MTSS. Our district has decided to implement multi-tiered systems of support in the area of math. This means that our most struggling students will have extra time to work on deficient pre-requisite skills. We have a plan for identifying these students and scheduling an extra period in the day for intervention.

2. New Courses. In addition to adding extra support at the lower levels, we also felt the need to do a better job challenging our advanced students. So, as a fairly small school (lower 300's for 9-12) that has traditionally offered only one track for math, we have decided to expand our course offerings to include a regular and an advanced course at each level. (There will be a regular Algebra 1 and an Advanced Algebra 1, etc.) We think this will be great for students . . . but it means that each of us will have at least one additional prep in order to incorporate all of these new classes.

3. New Textbooks. This year was the adoption of new math textbooks district-wide. I actually stopped using a textbook several years ago, so this isn't a huge deal for me. My colleagues are planning to follow their new textbooks, so they are stressed at the thought of starting from scratch. I am needing to make a lot of changes myself, due to #4 . . .

4. New Standards.  Common Core.

5. New Technology. We are fortunate to have some very current technology available in our district, but as new purchases roll in and old ones are removed and/or re-distributed, we are finding that our comfortable way of utilizing these devices is in need of a revamp. We spent a chunk of time figuring out the best way to meet each person's technology needs utilizing a laptop, iPad, apple TV, projector, and smart slate.

6.  New Teacher! In related news, we hired an additional math teacher to help make all this happen. We got to meet and hang out with him all day. He did not run screaming from the meeting, so that's a good thing. We have a challenging year ahead, but I am feeling a lot more confident that it will be a good one!