Daily Something [WCYDWT]

#WCYDWT

What can you do with this?

Why would a teacher use this?

How would you use this in your class?

What would you add? subtract? replace? other?

How would you use the information from student performance on this?

How could this be used as a pre-assessment? an assessment? an intervention?

Take a few minutes to complete each day. What do you notice?

Hint:
*  **  ***  ****  *****  ******  *******  ********  *********

Answer as many or as few of these questions... or feel free to add your own.

This:

Thanks in advance!
843

Manilla folders [Number Sense]

I must share this short story with you about the number sense I've been witnessing for the past few weeks with many of my students. Be warned: not for the faint of heart.

Today, a few 7th grade boys came in after school today and wanted to help with some things around my room: tidy up desks, organize whiteboards, etc. There was a box of 100 manilla folders that I had just brought back from the office. I needed 80 of the folders and would later return the remaining folders to the office.

Here's my exchange with the student we'll refer to as Albert:

Me: I need 80 folders from that box. Albert, think of a quick way you could get those 80.

***Let's pause. How would you (the reader) quickly get 80 folders from this box?

Albert: I could count in 5's.

Me: Okay. Any quicker than that?

Albert: By 10's.

I get what Albert is trying to do. He doesn't want to count to eighty by ones. To that point, I would say his initial two responses made sense and are practical, in the mind of a 7th grader. I thought maybe I'm asking the question incorrectly, so I try it again.

Me: Right. That would be a good way to organize the folders to keep track of them as you count. Albert, I'd like you to think of a way to quickly get those folders out of the box. 

I can see the look on his face is one of confusion. Not that look like he's trying to figure it out, but that look like he has no idea what I'm asking. So after a minute, I mistakenly ask another question (in hindsight, I wish I would've stopped the conversation and let him do his thing).

Me: How many folders are in the box?

Albert: 100.

Me: How many do I need?

Albert: 80.

Me: Is there a way to get me the 80 without counting all 80?

Albert has no idea. I like this question because now it's specific. His challenge is to get me 80 folders without actually counting all 80. After a minute. He needs some prompting.

Me: If the box has 100 and I need 80, how many will be left?

Albert: 30.

Me: So 80 plus 30 is 100?

Albert: No wait, 20. 

Me: Okay, so I will send 20 back to the office. How can I get 80 folders out of the box without counting all 80?

Albert has no idea. This exact exchange continued for another round. I'd like to say that Albert eventually came to an efficient way on his own, but he didn't. I tossed 100 up on the whiteboard. We subtracted 80 and wrote 20. I thought after Albert saw the 20 on the board, he might realize to count 20 folders from the box, take out the remaining folders and switch them with the 20.

This is quite common. The number sense (or lack thereof) my students have (or don't yet) is quite fascinating. I have a lot of work ahead of me this year. One thing is for sure. I can get better at asking shorter questions. I can get better at looking for these learning opportunities. I can get better at not looking for one answer when asking questions of students. As Max Ray would say, "2 > 4."

Folders,
918

Couch Coins

Today, I had 25 minutes to get as far as possible with Couch Coins and a second grade class at my school. I'd like to debrief on a few things, but here's Act 1.

During the Summer 2012, I found a money/coins concept in a Second Grade Everyday Mathematics book similar to Couch Coins. I was inspired by PES' Coinstar commercial and ran with the concept. The intended question is: "What coins will my wife get?" On my way into work knowing that I would soon be surrounded by seven and eight year olds, I announced to Twitter that I'd be doing this 3 Act lesson with second graders today and wondered how it will go, asking for their thoughts. The response was great. Robert Kaplinsky, Christopher Danielson, and Sadie Estrella all chimed in offering that money can be challenging and to be careful of the "fewest coins" part of the task. In other words, finding the total value of the coins and half the total might just be challenging enough for second graders. Chris Lusto (in true Lusto fashion) provided some comedic relief:

Act One: Which one of these kids do you think has to pee? Act Two: Watch them squirm. Act Three: Reveal. (Act Four: Clean up.)

Why just 25 minutes? I had to bail after 25 minutes to go teach my own students (8th graders) or else I would have had about 50 minutes with these second grade kiddos. So what transpired in those precious 1500 seconds? I asked the students what they wondered and noticed about the Act 1 video. I had them write down at least one thing they wondered and one thing they noticed. I asked them to share, starting with "notice." Keep in mind my time was limited here so I only took a few...

-The coins were moving on the chair like magic.
-There were just coins.
-There were a lot of quarters.

Now, I asked what they wondered. I followed each student question with, "Who else would like to know the answer to that question?"

-Why are the coins moving out of the couch? 10
-How did the coins stack like they did? 7
-How much is half of the coins? 10
-How many coins were moving on the couch? 3

Not one student asked anything about the coins my wife should get. NO PROBLEM! You can see there was a tie between two questions and don't ask why the numbers are so low; the class had 26 kids. I told the students since most of the questions revolved around the animated coins, I would reveal the camera magic at the end while we focus on the other top (main) question: How much is half the coins?

Time for estimating the right answer and guessing a number that's too low and too high. The second graders really enjoyed this part. One student felt 10 cents was too low because they saw quarters. One student was very proud of his $99,999 being too high. Once we got our estimates, I asked the class to read and revisit the main question: "How much is half of the coins?" I typically ask my students to reengage with the task/question before moving to Act 2 so we are reminded of our task.

Here comes Act 2: I asked the students what information would help them answer the main question. Many raised their hands. One student said, "We need to know how many of each coin." This was immediately followed by agreements voiced as "yea" or "that's what I was going to say." I displayed this information and we had less than 10 minutes to work. The second grade teacher broke the kids into groups.

Students were chatting, drawing pictures, using tally marks, adding by grouping, and using other strategies. One student asked, "Can we get out our money bags?" My response, "Shyea!" (translated yes). It was fascinating to see them operate for that short amount of time. I wish I had taken pictures. Sorry everyone! I had to leave.

This morning before the lesson, the teacher and I talked about the expectation of her students and the original task. She knew her kids were capable of finding the total and half. However, she also thought that finding the fewest coins might prove to be a challenge. The second grade teacher and my pals on Twitter were right. I think Act 1 deserves an edit saying, "My wife wants half of the money." This allows the sequel to be, "What coins would my wife get if she also wants the fewest coins?" and this can be used for the early finishers.

This experience reminds me that I need to record one of these 3 Act lessons so you guys can help me get better at doing them. There's still a ways to go, but I'm loving the opportunity to work with other teachers and grade level students. I've learned so much from these other teachers. I have a great respect for elementary teachers. I also love seeing how elementary students remind me that learning can be a blast. They're not going through puberty. They're energetic. They're so much fun! Not fun enough for me to pursue a multiple subject credential and teach primary though. I love my middle schoolers. I received an email from the teacher this afternoon saying:

It was hard, awesome, fun and different, cool, fantastic, interesting, the best, made us smarter, fabulous, I liked it, and magical!  Those were a few of the comments from my class about the math lesson this morning:)  Thanks for spending some time with us this morning!  It was fun for me, too!!

Soon, I will also be posting about my recent experiences in a 4th grade (Back Box2) and 5th grade (iPad percentages) classroom. Thanks for reading!

Cha-ching,
1119

Bottomless Mug

I found this glorious sign a few weeks back at Bruegger's Bagels and ended this post with saying I'll work it into a 3 Act.

As promised, here is the 3 Act lesson.

Act 1: My question: How much money could you actually save?
Other popular questions can be found at 101qs.com. I like getting to that initial question because many of the others will be answered along the way.

Act 2 info would look like this for my area, but the cost of a medium sized cup of Bruegger's coffee might be different in your area (for a limited time, of course). Check their website.

Now you know the cost of the mug, but I find the 3 days, 5 days, and 7 days per week (the rate where you live next door) very intriguing. In solving this one, my natural tendency was to round that cup to $1.90. Be careful, that difference could buy you a bagel or two. Anyway, have fun with this one. My wife and I just celebrated the birth of our daughter on New Year's Eve day. I don't drink coffee, but I do enjoy iced tea and this Bottomless Mug Club is starting to look rather appealing now.

Personally, I like the sequel tasks more than the original task. Sequel tasks include:

• On what day in 2013 would you break even if you get coffee 3 days/week, 5 days/week, everyday?
• When would be the last day to buy the mug and still save at least $1.89?
• What could be the prorated price of the mug if bought in January? February? March?... 

Have a sequel to add? Toss it in the comments.

Happy 2013,
1050

Small, medium, or large

My wife, son and I went on a walk this morning. Destination: Bruegger's Bagels. There's a park between our house and the bagels. We frequently use this park since it has a play structure, monkey bars, slides, and swings (one of our favorites). Our two-and-a-half year old son (the olive-gobbler) loves to request that Dad (me) use the swing adjacent the swing he's on. Still a kid at heart, I frequently will jump off the swing in midair and my son has come to expect it. Of course, he requests, "Dad'll do a big big jump!" There were other kids around and I didn't want to be a horrible example and/or jump off and hurt one of them. As I explained this to him, he responds, "Dad'll do a medium jump."

I jump off the swing without hurting anyone, myself included. I turn to my wife and say, "I'm going to test something out when we get bagels." We walk over to the bagel establishment, place our order, and I grab a couple of straws. Enter this picture:

I took the straw wrapper and ripped it into three different sizes and ask him to identify the large one. He puts his finger on the piece on the right. I then ask him, "Which one is the medium one?" He places his finger on the piece in the middle. Lastly, I ask, "Which one is the small one?" and he places his finger on the left. Let's be clear here. I am not claiming my son is a genius or that my next magic trick is that he knows his multiplication facts. I was simply assessing if he really understood the difference between small, medium, and large. He does. I don't have another two-and-a-half year old kid to compare him to so I'm not sure if this is fair. What I do know is that he's making a one-to-one association and comparing sizes. I find this fascinating. As a family, we've been using the Your Baby Can Read series and have found it wonderful. I highly recommend it. The following is in one of his books.

Find the biggest comb.

This series has many wonderful ways of communicating language with children. My wife, an elementary teacher, would probably do a better job writing this post as she would be able to explain it all better than me. Knowing that he has a pretty good understanding comparing, let's see if he can order them if I mix them up a little.

Me: Okay, let's order them from least to greatest.
He looks at me blankly as he chews on his bagel. I didn't expect him to understand what I had just said. That's okay. I'm still going to use this language. I follow it up with this.
Me: Let's put them in order starting with the smallest.
Son: Hmph.
Me: Where is the small piece?
He points to the small piece.
Me: Okay, let's put that first (as I place it on is left). Where is the medium?
He points to the medium size piece.
Me: Let's put that next to the small piece.
Son: Hmph.
Me: Here, let's move it next to the small piece. What piece is left?
Son: The large! (saying it like he's just won the lottery).
Again, I'm not claiming my son is the next Einstein. I need to keep him honest and humble at the same time so here's how I proceed.  I take the largest straw wrapper and rip off a tiny piece so that it's smaller than what we previously agreed was the "small one". I temporarily hide the piece previously known as the "large one".
Me: Now which piece is the small?
He points to the new tiny piece.
Me: and the medium?
Son: This one (pointing to the piece formally known as 'small')
Me: and the large?
Son: This one (pointing to the piece formally known as 'medium')
I hope you're following me. If not, here's a picture to compare to the first one.

Previous small, medium, & large

New small, medium, & large

Let's see what this kid is made of. I reveal the piece I ripped the tiny piece from, formally known as "large one."
Me: What size is this?
Son: Hmph.
Me: This is the small, medium, and large (as I point at the new small, medium, and large) so what size is this piece (pointing at the piece formally known as "large")?
Son: Hmph.
I give him a few seconds to contemplate, mull it over, and possibly share his own name. Nope, nothing. He's perplexed. He's staring at it. He wants to call it something. He wants to have a name for it and compare it to the other three, but is looking for some direction here. I can see he's just about to take another bite of his bagel and be done with his dad's straw wrapper experiment. I jump in and say, "It's EXTRA large!" If this conversation was happening six months from now, I'd ask if the newly named piece would be "extra large" or stay known as "large." Likewise, would the tiny piece now known as "small" be correct or be known as the "extra small" piece? You decide.

Do you have these conversations with your students? If I was having it with my students, I'd hold out longer and force them to come up with a way to classify all four pieces using their own language. The teacher in me does not take a vacation nor do I take time off during the weekends. I love these conversations and I am now seeing them naturally occurring with my son. I cherish these opportunities and love seeing how his brain is working.

Lastly, a wonderful 3 Act opportunity made an appearance at the end of our bagel extravaganza today. I'll be posting it on Dan Meyer's 101qs.com so let me know the first question that comes to mind right here. It might be winter, but math is not in hibernation. It's still out there in the wild. Be ready to capture it any chance you get.

Small, medium, or large,
849

Hey points, meet my new friend SBG

Dear Points,

We've been in school together for such a long time. Remember those book reports in elementary school where I just read enough to complete the book report so I got a good enough grade? or that time in high school where I colored a few extra maps and did some word searches in my geography class to earn points and raise my grade? or how about that senior English class in high school where I racked up massive extra credit points for turning assignments in early? or that one time at band camp? O wait, I wasn't in band. We had some good times, didn't we? Or so I thought.

When we went to college, we hung out way less and I wasn't ready for that. I missed you because my classes and instructors actually wanted me to demonstrate understanding of course content. They didn't really have a relationship with you. Now I know why. I had those math, science, and engineering courses that simply assessed my understanding through tests and labs. You abandoned me many times throughout college. After college, I fell into teaching and you showed your face again because I was confused and thought we could be friends again.

After teaching for 8 years now, our relationship has taken a toll on me. Last year, we definitely butted heads mid-year with a student and their parent who demanded I give them a point-based assignment to raise your grade from an F to a D-. What did they learn? Nothing. What did I learn? YOU SUCK! Our relationship while being a teacher has always been constrained. I'll admit, I was never 100% committed and vested in our relationship. Each year I was trying new ways to convince myself and my students that we needed you on campus or in my class by revising homework procedures, quizzes, tests, etc. I couldn't wait for last school year to end and be free from you during the summer. I ran into someone new over the summer: Standards Based Grading. He goes by SBG.

SBG introduced me to friends (teachers) who keep learning exciting and relavent for their students: Sam Shah, Shawn Cornally, Frank Noschese, Dan Meyer, etc. They have open relationships with SBG and share how their students are benefiting from it. In the short months of summer 2012, I've already learned more with SBG than my entire academic career with you. Points, you suck! Even better, I got to spend my summer getting well acquainted with SBG and discussing with Fawn Nguyen and Nathan Kraft about how flexible SBG is. All three of us had our reservations about committing to SBG, but we have now seen how SBG is the BFF to both students and teachers. SBG doesn't put any clamps on student learning nor hold a carrot in front of them. SBG has a circle of friends that welcomed me. They have unconditional love for my students and their learning. It feels naturally right. Recently, Chris Robinson even devoted an entire website to SBG.

This isn't the first goodbye letter you've received. I read the letter my pal Timon Piccini sent you and I was thoroughly excited to write you one as well. There's been others and I hope you receive more... maybe more letters than Santa receives at Christmas time. Be lucky it's just a letter and I'm not filing a restraining order. I wish I could. However, I know that we will have to coexist at my school. I'm not moving to another school, but if I ever do I know SBG will come with me and can only hope there are SBG friends there too. Since we have to coexist at the same school, I will respect those you hang out with, even if they're in my department. You still have their friendship based on fear of changing. Leaving you intimidates them. Points, you suck! My department wants to see how long and fruitful my relationship with SBG is this year. They're ready and willing to spend next summer getting better acquainted with SBG. I think your days are numbered. However, my greatest joy is that you will no longer bully my students this year. On the flip side, I hope you don't bully kids in other classes too much or let teachers abuse the joy of learning. I wouldn't want them to be the victims of your rebound.

I bid you farewell, points. Feel free to keep anything I've lent you. Keep my worksheets, handouts, CDs, that one t-shirt you borrowed, and even my book report from third grade. I need a fresh start and SBG has given me that. If we see each other on campus, in the hall, or in another teacher's classroom, I won't turn my nose up at you or talk down to you. We can still coexist at school, just know that you're not welcome in my classroom. If I see you bullying any of my students, expect me to stand up for them. SBG has my back, know that!

Sincerely,
Andrew Stadel

Estimation 180

Estimation initiative:

[*UPDATE: www.estimation180.com has gone live]

Last year I willingly started adding an estimation question to my daily warm-up, inspired by Steve Leinwand, Dan Meyer, and a monthly ASB gag we did a few school years back. Everyday, I greet my students at the door and hand them a 3x5 index card for their warm-up. They get the first 2-3 minutes of class to complete the warm-up exercise and estimation question. The first question reviews the previous day's skill. As for the estimation question, last year I was putting questions that were comparable to fun facts and students had no context clues for making logical estimates. It got silly. Here are some examples:

• How many miles is the California coastline?
• How long does an elephant stay pregnant?
• How many In-n-Out Burger restaurants are there?
• How many miles from the Earth to the Sun?
• etc.

Stepping back over the summer and really fine-tuning the goal of estimation (improving number sense), I began using estimation questions that were more relative and provided better context clues. Every chance I get, I use a picture or something inside my classroom that will allow students to make logical estimates. Here's today's (Day 10):

I've had to cover up the bottom half of the screen now because students come in and immediately want to go for the estimation question. They want to come up to the screen and do weird measurements, or ask me factual questions, and they flat out forget about the first question. I don't blame them. It's fun. Once we go over the first question (favorite yes/no), I usually have students give me estimates that are too low or too high and then we "go right at it." "Who thinks they got this?"

Once I get about 8-10 estimates, I reveal the answer and it's so cool to see how the students react. "Ohhhh, I was sooo close." Or "I was way off!" Either way, I ask the student or students who were close to explain their logic. It's fascinating how kids think.

For today's, I snapped a picture of a measuring cup full of almonds (my new favorite snack). Tomorrow, they'll estimate how many are in the jar from CostCo. Estimation should build. The whole first week we talked about height, based off my height. 

Day 1: What is Mr. Stadel's height? They don't need a picture for that.

Day 2: What is Mrs. Stadel's height? They needed a picture for that. 

Day 3: What is my son's height? Another picture.

Day 4: What's the height of a lamppost Mr. Stadel is standing near? etc.

The first four days used my height as a frame of reference. Check out Estimation 180 (Google doc will be replaced with estimation180.com )and you'll see what I mean. My estimation initiative is to begin documenting my 180 days of estimation, simply titled Estimation 180. Seriously, do I need one more thing on my plate right now? No. However, I do this every day and would love to share this stuff and receive feedback. Estimation is important to me. I've already seen student improvement with number sense in just 10 days of school.  

I'm starting small here, but would love to expand this idea: stay tuned. In the meantime, check out the spreadsheet catalog (tab at the top).

[UPDATE: estimation180.com is live. Forget the spreadsheet!]

Number sense,

1056

Future students

Recently, I've been developing and staging 3 Act lessons for elementary students (my future students). However, who's to say the tasks can't be applied at the middle school level, or even higher.  I've been looking through the Everyday Math series our elementary school uses and have found it refreshing to see what concepts students are introduced to or expected to master at each grade level. Ironically, I came across a second grade "Exploratory" lesson that Dan Meyer recently nailed with Popcorn Picker. Second grade if you missed that.

Popcorn Picker — Act One from Dan Meyer on Vimeo.

It was fun to share the textbook scans with Dan.  Christopher Danielson jumped in with some thoughts about elementary curriculum. He works with future teachers and is a very insightful fellow! Check out his Tootsie Roll and the Ootsie.

As a middle school math teacher, this elementary stuff is all new to me, but I'm open to the challenge. Especially since I'll be helping coach a handful of teachers next year with 3 Act lessons. I'm using the summer to investigate some ideas and build up a small catalog of lessons. My working goals are to:

1. Work on turning the abstract to concrete.
2. Look for overlapping concepts throughout K-8 grades.
3. Further investigate the importance & relevance of estimation.   

My first attempt is Paper Cuts - Act 1 (subconsciously inspired by Popcorn Picker and Everyday Math). Again, my intended student would be from elementary school. Would your students benefit from this task?

Paper Cuts - Act 1 from Mr.Stadel on Vimeo.

Lastly, it's great to know there are teachers helping students with life skills and not workbook skills. Sadie Estrella shares an experience she had this year by embracing those teaching moments we frequently have with our students. Should we eliminate 're-teach' from our vocabulary and change it to re-explore? Your thoughts on all this?

Future,
255