A Jammed Rational-Irrational War, Stacking Cups Week

Some cool stuff happened this week. Well at least I think it was cool.

Monday: 

One of my math fellows was observed by other math teachers from our district. He was starting a new unit with rational and irrational numbers, focusing on 8.NS.1 and 2. I might be wrong, but pretty dry stuff… here’s how we spiced it up a little.

We did a pre-assessment using the Post-It Plus app. Yes, my obsession with Post-It notes has gone to a new level: digital. We created a file within the app, posted it on his Haiku calendar, and had the students download the file into their app on their iPad. 

Students first worked individually to sort the terms from least to greatest for a few minutes. Since his students are grouped in fours, they then narrowed it down to one iPad screen they thought was most accurate. (Quick demo)

*Reflection: we should have had students paired up first, discuss, and narrow it down to two screens for the entire group. Next, the whole group of four students would discuss and narrow the two iPad screens down to one screen for the group.

Once each group settled on a screen they felt most confident with, they took a screenshot and uploaded their group’s screenshot to the Padlet page my fellow created for them.

My fellow used this Padlet page to assess the overall climate of the class (without teaching them a single thing). He used this real-time data to have some really rich conversations and share-out of ideas from students.

Remember to tell students:

• It’s okay if you’re wrong. 
• Make your best guess.
• I just want to see what you already might know.

Flash forward to Friday:

The previous weekend I asked the same fellow what he thought about playing War with rational and irrational terms. Side note: I play a few card games with my young son and one of them is War. My fellow thought the idea was epic. He ran with it. Here how he made it awesome:

• He made these awesome cards.
• Some values had multiple representations
• Printed them out on card stock.
• Made a graphic organizer for students.
• Each group of four was broken down like this:
• 2 people played War while the other 2 people recorded and were the judges.
• The next round, the roles were switched.
• There were 3 rounds.
• Each round was 6-10 minutes
• He stopped class and made a spectacle whenever two students were at war.
• The third and final round was between the winners of the first two rounds.

I asked if I had his permission to share the cards and he said, “Sure.”

Tuesday:

Another fellow asked me to model Stacking Cups in their first period class, which ran less than 45 minutes. My fellow requested I complete the task with students in one period. I explained that I’ve never “finished” the task in one period because there is so much to explore and learn in the task. I respected the request and  tried to cram it into one period. I spent too much time launching the task. 

Act 2 (the best part) felt rushed and we still didn't finish. My fellow and I debriefed and made some adjustments so she could finish it with her next period. She stuck to the adjustments and did a fantastic job facilitating the task. The students were doing awesome and amazing math during Act 2… and what do you know? The class was over. I love that my fellow was going to revisit the task the next day. Could we have spent another day on the task? Yes. It’s a starting point and I’m very proud of my fellow for trying out something new and doing a great job. I’d say the sweet spot would be one-and-a-half days for this task...
*Side note: I encourage you do styrofoam cups earlier in the year, and use Stacking Cups throughout the entire linear systems unit.

Thursday:

Another teacher wanted me to model Stacking Cups as well. When we sat down to plan, she was totally cool with spending one-and-a-half days on the task. Great news!

I launched the task, used a Padlet page to capture what they noticed. I asked the question, "Where will they tie?" and used a Google form to collect their guesses (see my post on using Google forms to collect student thinking). 

We gave each group only 4 white styrofoam cups. Students were making tables, or writing equations, or some were even wanting to graph their equations. Interesting note: some students started their table with zero cups having a height of 9.2 centimeters. The teacher had only taught graphing systems, so students were already thinking ahead to substitution. It was awesome. She did a wonderful job facilitating her first 3-Act task. We didn’t finish the task in one period, but it felt right knowing we had another half-day to wrap up the task. 

Back to Friday:

After work, I started putting the meat in my upcoming session, Math Mistakes and Error Analysis: Diamonds in the Rough. Although I will be showcasing a couple ways I’ve had success with error analysis with students, I love that I’ll be showcasing some awesome work and contributions from:

• my fellows
• Michael Pershan’s mathmistakes.org,
• Fawn’s Visual Patterns with Michael Fenton’s latest mod
• Open Middle by Robert Kaplinsky and Nanette Johnson

Hope to see you in my upcoming session as we explore why error analysis is important to:

• help drive instruction
• curb student misconceptions and
• strengthen formative assessment. 

Hope your week went well too. If not, hope this week is better.

Rational/Irrational,
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A Few Updates

Update 1:
I finally finished Act 3 for my Deodorant lesson. I hope you check it out and can give me some feedback; I think it could be much better with your help. If nothing else, check out how long it took to use 5 sticks of deodorant. Mathematical Modeling should really be at the forefront of this task. It might appear linear, but I would bet a year's supply of deodorant that an adolescent's deodorant use will be far different than mine. I also guarantee students will think of variables ranging from climate to age to geographical location to genetics to more. I think you'll have some excellent conversations with the deodorant task. My favorite part is the sequel: How many sticks of deodorant would one use in a lifetime?

Way back when this task first started, I opened up a little estimation competition in the comments at 101qs. Don't listen to a word Nathan Kraft says. The person with the closest guess would win an Estimation 180 prize. With so many close estimates, the following gentlemen will be the first to receive the new Estimation 180 stickers, hot off the press!

Congratulations to:
1st place: Chris Robinson (May 14, 2014)
2nd place: Robert Kaplinsky (May 5, 2014)
2nd place: Michael Fenton (May 15, 2014)
3rd place: James Cleveland (May 3, 2014)

Update 2:
Estimation 180 will be getting a facelift and other updates over the summer. Here are a few things to look out for:

• New logo
• New fields for entering student estimates
• Clean spreadsheets containing "other estimates"
• Updated Lessons
• Search by Categories
• Sentence frames for student reasoning

I'm most excited about the last update; sentence frames. I occasionally browse over student responses and notice many students entered "I guessed." I think it would be extremely helpful for teachers to provide their students with sentence frames in order to better articulate their reasoning. I will be focusing on this tool in upcoming presentations and workshops.

The new logo was done by my niece. I love her simple design, the two 180 degree arrows, the metric reference, and her idea to transform me into a stick man. That reminds me, I still owe her a pizza!

I hope to get a few t-shirts made too. You can sport them at your next PLC, department meeting, casual Friday, or math conference. Any takers?

Update 3:
I've accepted a Teacher On Special Assignment (TOSA) position with my district for next year. It's a bittersweet feeling at this point. On one hand, I'm very excited because I'll be working at various secondary sites throughout my district, collaborating with other math teachers, helping design lessons and implementing various technology. My official title will be a Digital Learning Coach. I hope to seek advice from people like John Stevens, who have been doing this for some time now. As I pack up my room, I already miss my own classroom and students. However, I look forward to learning a great deal from the teachers I will be fortunate to work with and the students I'll be able to interact with at each site.

Updates,
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Guest Blog Posts at Estimation 180

Today, at Estimation 180, I posted some guest blog posts I collected from the beginning part of this year. I'm grateful, honored, and inspired by the stories they (or their students) shared. I hope you have time to check them out and share your story too.

Read their stories here. 

CCSS Workshop 2013

I did my first workshop this past week (5-30-2013), discussing the transition to Common Core State Standards, with a focus on the 8 Standards for Mathematical Practice. I'm working with K-5 elementary teachers, a couple of middle school math teachers, some support teachers, and a couple of administrators in the room. I'll admit, I'm not as eloquent a speaker as Steve Leinwand, but there might be a few times where I actually make sense. I'm throwing this video out there for some feedback. I don't expect you to watch the whole thing so I've provided some chapter markers you might be interested in. At the end of the notes for each chapter, I reflect by creating a wish-list of moves I would've done differently. They come across as rhetorical questions, but feel free to chime in. However, here are a few angles I'd appreciate you considering:
What did I forget to talk about?
Where could I have been more explicitly clear?
Where coud I have used a better strategy? ...and so on.

Opener: 0:00-10:10
I use an estimation task (Day 127) to kick things off, providing teachers with the handout Michael Fenton created for estimation180.com and my students. The handout has been through many revisions and I think we have a final version that's a winner.

I use the whiteboard to write the "Too Low", "Too High", and "My Estimate" of a few teachers, asking for reasoning along the way. We watch the answer and discuss.
8:15 is a precious moment where a teacher asks, "Wait a minute! What was it (the song length answer) really?" I love how a teacher is demanding more information. I wish I spent more time expressing the importance of her question. I feel rushed because of all the workshop content I have prepared. I wish I had allowed the other teachers to address her question more. I do with my students, why didn't I do this here?

Active Notebook Part 1: 10:15-12:55
Teachers glue their Estimation 180 handout to the inside cover of their workshop Blue Book and the Table of Contents to the first sheet while listening to Can't Buy Me Love.

Preview of Workshop: 12:55-20:50
I attempt at working on the following question throughout the workshop,

What's our role as we reshape the classroom with the Common Core State Standards?

I share with teachers what today will not be and what today will be. On a parallel universe I share with teachers what I perceive the CCSS to not be and what I perceive the CCSS to be. Then I share a few personal items from this past school year. Seeing that I'm doing a workshop with multiple grade level and content teachers, I'm expressing the focus of the day to be the 8 Mathematical Practices and what we do in the classroom. How do we help facilitate the learning?

Estimation Task #2: 20:50-26:45
We use Day 129 where teachers see that the song length is also the track length. Listen to their reasoning. I love this! Hearing this reasoning from teachers and students is one of the many joys I get from doing these daily estimation tasks. However, I wish I did a better job (23:50) of getting the teachers to justify their reasoning and "argue" a little more than I did. I wish I created a little more tension. Check out (25:00) the excitement of the teachers as they watch the answer.

I introduce the language of creating a task that has a low-entry point and could see that many teachers had no idea what I was referring to. Not their fault. However, I like their reaction when I translate "lower-entry point" to being easier. I wish I explained "low-entry point" better. I wish I had explained it as creating a task where most, if not all students have an equal opportunity to engage with the task, regardless of their mathematical proficiency. I wish I expressed the importance of providing students with a task where math vocabulary and thinking come as a natural result of solving the task.

Math Tools & Two Uses: 26:45-33:55
I ask teachers to glue a picture of a math tool to the front of their Blue Book and write down at least two uses for each tool. They have two minutes to complete this task. After We Will Rock You, I ask the teachers for their uses instead of telling them. This serves two purposes. Yes, I have a list of uses that I anticipate them to come up with, but I want to hear from them first, selfishly providing me with additional uses that I didn't anticipate. Secondly, I'm using this activity to illustrate how students need to provide the answers in the classroom. I wish I could have given this more time in the workshop where the teachers actually used the tools in the manners they suggested. I also should have had the teachers write down all the uses we came up with.

Introduction of 8 Mathematical Practices 33:55-1:04:00
Again, I'm feeling rushed for time! Yes, I said it, "Let me talk about these 8 Math Practices real quick." Real quick? How silly of me. These practices are not something to gloss over. Don't worry, we spend ample time doing a Jigsaw activity so teachers are out finding information about them. I provided the teachers with the handouts found at Jordan School District's site. The practices are presented in a manner representative of the grade level you might teach. Thanks Fawn for this link.  I could have explained and facilitated this a lot better, but the redeeming value is hearing teachers that were appreciative of this specific activity because they were "forced" to explore the practices instead of just receiving a handout with the information embedded. If I were you, I'd skip the section (39:30-52:00) unless you want to hear some of the teachers talking in their groups as they rotate around the room to their four different stations. I'm proud of the rotation table I provided and how teachers travel together according to their "math tool." DON'T miss the "perfect high-five" at 38:10. I love that a teacher commented that "perfect" is subjective. I say this all the time to my students.
At 52:30 I give teachers time to regroup and complete the practices by receiving information from the other teachers in their group. I recap (1:00:00) and then show teachers how to create a pocket (1:01:00) inside their Blue Book so they can store a Quick Reference "teacher" version (I referred to as "adult") of the 8 Mathematical Practices.
I wish I gave more time for reflection. I wish I reviewed each practice with the whole group by having them share out loud something they learned. During the Jigsaw activity, I was told that my time with the teachers was cut short by about ten minutes so I had to hurry things along. Arghh!

Find My Mistake: 1:04:20-1:13:00
I made an executive decision to skip the model lesson I had prepared for the worksop. I'm glad I didn't skip the Find My Mistake segment of the workshop. I'm very adamant about teachers finding the mistake quietly here. I encourage them to share with each other before we review with the whole group. I give props to Michael Pershan for mathmistakes.org. You can hear kids in the hallway, alerting me that our workshop is coming to an end very soon. We listen to each other make corrections or talk about the misconception and why us teachers are good at knowing the content we teach. We're constantly telling students what their mistakes are and telling them how to fix it. Let's switch that role. Make the students find, correct, and tell each other what the mistakes are, especially items that use algorithms. Remember, most of the teachers here are elementary teachers. I also point out that I haven't been jumping for joy every time a teacher gets an answer correct. Instead, I try my best to throw it back on the class for what they think, allowing them to critique the reasoning of others. I love how estimation and number sense is addressed with teachers on how to help encourage students to avoid these mistakes.
I hit a nerve (1:10:45) when I was asked, "What about simplifying?"
I could very well be wrong here, but my current understanding is we (as teachers) are to allow for multiple representations of the correct answer, unless explicitly instructed otherwise. In other words, ten-eighths is just as acceptable as five-fourths.
I wish I reviewed with the teachers the importance of doing an activity like this quietly and individually first, before group discussion. I wish I expressed how much I love group work and collaboration, but need to remember both teachers and students need that quiet time FIRST. The worst is being in a group where one person dominates the conversation and you don't have time to think or worse, problem-solve. I wish I had covered this with the teachers.

Summary: 1:14:15-1:19:00
I provide teachers with a fill-in-the-blank handout to glue to the inside of the back cover. Again, watch their reaction when we get to "low-entry" point. I hope I drive it home when referencing the "Cent-ed Whiffle Ball" task I recently did in Geometry. I remind myself and the teachers to listen to the students. I'm constantly working on allowing students to finish their thoughts. Don't cut students off or finish their sentences for them. I ask teachers to create a couple of goals. I provide the teachers with a list of resources found here. I like how they (at least some of them) want another in-service/workshop.
I wish I emphasized the importance of knowing the 8 Mathematical Practices better and to use the summer to better prepare for next year. I wish I had more time to pump up these points in the summary. I wish I had more time!

Unleash yourself in the comments if you will.

Thanks!
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