Saturday, December 29, 2012

Quesadilla - Part 1

My son and I look forward to Saturday mornings because Dad typically makes breakfast. Let me rephrase that, I really look forward to Saturday mornings because I get to make breakfast for the olive-gobbler and myself. It's the highlight of my whole weekend sometimes. I usually go with one of my two staples, pancakes or an egg and cheese quesadilla. Today, we went with the egg and cheese quesadilla. It's easy to make and we enjoy it together. Sometimes we throw in some bacon (the most delicious thing on earth). We also love to dip our quesadilla in Chik-Fil-A sauce.

Since he's only two-and-a-half, he can't man up to an entire quesadilla yet. Likewise, I should probably watch my cholesterol and avoid routinely eating 3 eggs and cheese every Saturday. It's a delicious compromise. That said, as he gets older he eats more and in turn my cholesterol intake is slightly less, I think.

I came up with a 3 Act idea for our quesadilla breakfasts. You'll notice I don't use halves, fourths, and other math related vocabulary on purpose. It gives you a chance to use that vocabulary with your students. Text included below.

"On the weekends, my son and I look forward to making an egg and cheese quesadilla for breakfast. We scramble the eggs, add the cheese, grill up the tortillas, and when the quesadilla is ready, I cut it into sections so we can share. When he was two years old, he’d only eat one of the sections. Now that he’s a little bit older, he’ll eat more than one, but won’t entirely eat two.  So I need to rethink this."

Quesadilla - Part 2
I'm working on another idea related to this whole circle, fraction idea. Stay tuned.

*Fawn, you're temporarily sworn to secrecy while I line things up.


P.S. How many times did I use the word "whole"?

Sunday, December 16, 2012

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 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,

Thursday, December 13, 2012

Bouncy Balls

Today was a good day. Yesterday wasn't and I'll leave it at that (strictly speaking of school). One of those days where I couldn't find a wall fast enough in order to bang my head against it not once, but multiple times. It's a great thing that I get to end my days with my wife and son. My students are having a blast finding Felipe, our classroom Elf on the Shelf, each day. With a waterfall schedule, my last class of the day gets to hide him for the next day. It's a fun little activity for the kids to burn some energy off until the holidays. We did our seasonal estimate today and I started my Algebra classes with this video:

Yes, this video is cruel. Not necessarily perplexing, but enough to hopefully generate some curiosity? So, which ball will bounce higher? Give me a thumbs up if you think the 2012 Super Ball will bounce higher. Give me a thumbs down if you think the 1976 Super Ball will bounce higher. Give me a thumbs middle if you think they will bounce the same. In all three classes, there wasn't a strong majority, but if I had to estimate I think most students voted that 2012 will bounce higher. And... I don't tell them, show them, or even hint to them. I know, cruel. Enter this picture:

This lesson snuck up on me as I was collecting balls. I forgot to get the following balls: ping pong ball, racquetball, tennis ball, and one of those pink spongy balls. Okay, let's get this out of our system; middle schoolers and the word, "balls." So here we go, "balls, balls, balls, balls, balls, balls, balls, balls."

"Now, look at the balls and quietly, to yourself, make a guess. Guess which ball will be the best. In other words, which will bounce the highest? Now, guess which will be the worst? Don't say anything. Write that in the top corner of the handout you are about to receive. Don't share it with anyone." Students were looking at the screen, scoping out the different sizes, shapes, and textures of each ball. I saw some students writing the golf ball as the worst and the lacrosse ball as the best. Some were putting the Super Balls as the best. "Now, share your guesses with your group. Does anyone want more information about these balls besides just a picture." Trust me, it was very difficult not to work "balls" into the conversation as much as possible. Seriously, it can be fun to see them squirm, grin or laugh at times like these. I refrained from making comments like, "Don't worry guys, you'll get your hands on these balls soon enough." or "We're not playing with the balls people. Simply dropping them and seeing how high they bounce." C'mon people, "Make sure you handle the balls with care." You get the point.

I'm a slow learner. You've probably heard me say this before. This might be one of the best parts of my day. When introducing projects this year, I've made the mistake of displaying the handout on the screen first, having students read parts out loud, and throw in some pointers before they get their supplies. You can predict what happens next. Students get their supplies and start exploring the project in the wrong way or ask me questions to parts I already reviewed. What's the typical response? "Read the handout again." or "I already went over that. Ask a classmate." And you know with each student that you see not following directions or that comes up to you and asks what to do next simply gets more irritating with every time. For example, when we stole from Fawn Nguyen's Barbie Bungee, I'd see students simply letting Barbie hang freely from the top of their meter stick and measure that distance with every rubber band they added. They weren't dropping Barbie and measuring the lowest point she extended to. So it dawned on me, once again because I'm slow. "Everybody, you are to read the entire handout with your group first. When you've done that, come up to me and explain what you are doing. If you accurately tell me in your own words the objective and directions of the project, you may grab a ball and start collecting data. If you can't, I send you back to read it again." Money! It worked like a charm. Students knew what they were doing. They knew the correct steps. They knew what increments and how many drops per ball. It was great. I still have to do the Barbie Bungee project with my Algebra Honors class and will see how well they do with reading the directions.

Here's what students did today. Students were to use one ball at a time to drop the ball from 10 cm to 1 meter using 10 cm increments and at least three drops from each increment. Once they completed that, they were to exchange their ball for another ball and do this for a total of three balls. Hint: no one was allowed to use the 1976 Super Ball until they collected data for two balls first. Plus, I don't let the 1976 Super Ball out of my site. I've had that since I was a kid and do you know what those guys go for on eBay? They kept track of the rebound heights and were to make observations. Were there any constant changes? If not, was there a close average change? Our goal is to predict the rebound height of a drop from 3 meters and from our balcony of 5.7 meters.

At least I didn't play this video to intro the lesson.


Monday, December 10, 2012

We don't need no stinkin' homework!

What are our students saying when they don't do practice exercises outside of school? This isn't a revolutionary thought. I'm just a slow learner. Last week I finally had enough of seeing too many empty desks when they're supposed to get out their Home Jams (homework) after our daily warm-up. I assign about 3-4 questions nightly Monday through Thursday. They're not worth any points because of the Standards Based Grading model I've adopted this year. I use Dropbox to sync all my home jams so students have access at home and I don't need to make photocopies or rely on students using a workbook or textbook. I don't collect them. I don't keep track of complete or incomplete home jams. Furthermore, chances are pretty good I will spend the first 5-8 minutes of class having students review the previous night's home jams as a group on their giant whiteboards. My school is in an affluent area and every family has internet access so why do I still see a strong majority of empty desks? I'm not the only one who is absorbing this pain and bafflement. Chris Robinson, Hedge, and Fawn Nguyen (my trusty cohorts) jumped in on this conversation/quest.

Let's find some scapegoats: laziness, apathy, age, adolescence, immaturity, puberty, hormones, SBG, points (or lack thereof), Gangnam style, etc.
Are these really worth my blame and energy? Should I be looking to point fingers, because I'll run out of fingers if that's the attitude I take. There seems to be a more productive use of my time and energy. I like Chris' idea of designing meaningful tasks for students outside of class, but right now I battle the clock with trying to design meaningful tasks for students inside of class. Therefore, should I be associating my home jams with incentives? Let's ask our kids what they think first before we rack our brains out. Here are the two questions we asked our kids today:
1. Briefly explain what reasons cause you to regularly complete or regularly NOT complete the homework assignments.
2.What incentives would motivate you to complete more homework assignments?
The results.

Reasons for NOT doing home jams:
I forget: 17
Online hassle: 12
Not worth points: 10
I don't need the practice: 1
I have other homework: 9

Reasons for doing home jams:
Master/practice skills: 18
I don't understand: 3
Prepare for assessments: 10
My parent makes me: 3

I didn't enjoy homework as a student and still don't (BTSA). I don't think students should be doing hours of homework. When my children get older, I hope they don't have hours of homework because I believe it would rob them from family time or time simply being a kid.

As for incentives, students suggested the following:
Make them worth points [that's not happening].
Make them fun [curious what that means].
Give candy [yup, all I need to do is encourage tooth decay, obesity, or diabetes].
Extra Credit [really? Again, that's not happening].
Put them on paper [I'm listening].
Bring in food [that co$ts money, y'know].
Play music [yes, I considered that and I like].
Redeem points for class prizes [who's paying for the prizes?].
Work it into Math B-ball [I considered that too and I like].

So now what? Enter my thought process and your input here. I'm open to the incentive idea. Could there be something for the group (since my students sit in groups) who completes their home jams all week? Their group DJ's music. They get comfy chairs to sit in during class. They get extra points when we play Math B-ball. They wash my car. Oh wait, that last one seems out of place. I'm going to sleep on this.

My parting thoughts go like this. It eats at me that learning just isn't more intrinsic, valued, and supported at home as much as I'd like it to be. Could that be another job for some caped homework crusader we all dream about? Incentives are cool, but is that just trickery? Am I tricking kids into practicing math? Once again, I think I'm asking more questions than necessarily providing answers. I'm not going to rack my brain out here. I'm not looking for a permanent and magical solution. It would be great to see students participate more and value their learning by practicing math. Is this asking too much of my 8th graders?


Saturday, December 8, 2012

Zero Olives

My two-and-a-half year old son loves black olives just as much as I do. Tonight at dinner, my wife placed two olives on our son's napkin. Surprisingly, the olives remained untouched for a few minutes. He made some descriptive comments like, "The rice is delicious. The egg is delicious. The milk is delicious." You can tell what vocabulary we use around him, right? Quite the eclectic dinner, I know. Unbeknownst to me as I was taking a bite, he grabbed an olive with his hand so he could put it on his finger to eat and says, "There's one olive left, Dad!" Here's how the rest of this played out:
Me: "Yes, after you eat the one on your finger."
(we've had this conversation before)
He quickly shoves the finger-olive into his mouth.
Not wasting anytime, the olive-gobbler grabs the lonesome olive on the napkin and exclaims, "Now there's zero olives!"


This made my heart skip a beat. We haven't talked about zero for a couple weeks now. In previous olive consumptions, I've questioned my son how many are left after he devours his portion. He would sit there quietly and perplexed or would usually reply with a little, "hmph?" After giving him some time to think and reply, I would jump in and offer him a description simply labeled "zero." It kills me that a couple of his toys have the numbers one through nine, but no zero. For example, check out his toy phone. Where's the zero people??!! Seriously?

I'm a huge fan of using zero in math as much as humanly possible. To see it missing from toys means it could be missing from my son's vocabulary unless I work it in. He has placemats with letters, shapes, and numbers. Guess what number is missing. Zero plays a key role in number sense and math. My students know one of our class mantras is, "We love zero!" Zero is a wonderful number.

Our dinner conversation didn't end there. Let's see if this olive-gobbler has some depth. I held up two fingers and asked, "How many fingers do you see?"
Olive-gobbler: Two
(I take down one finger)
Me: How many fingers do you see?
Olive-gobbler: One
(I take down the last finger)
Me: How many fingers do you see?
Olive-gobbler just sits there......... "hmph"
He holds up his hand with all fingers extended and says, "Five!" (Wise-guy!)

I start over by holding up two fingers and repeat my questioning. Same exact response from the olive-gobbler. So it didn't work with the fingers. Later on during our dinner I put one of my olives on his napkin. He grabbed it.
Olive-gobbler: Zero olives left!
Me: You're right.
I put our workout on zero to rest for the night. We're getting there.

I cherish this post because it involves my son, olives, zero, and number sense. This is my first time blogging about my number sense experiences with my son, inspired by Christopher Danielson and the many number sense conversations he has with his children. Thanks man!

Olive-gobbler's dad,

Tuesday, December 4, 2012

Instructional tool: student cell phones

Tomorrow, I'll embark on the crusade of letting my students use their cell phones in class as an instructional tool. I will both email and send home the following letter/policy with students for parent approval. Understandably, my school has many hoops regarding things of the sort. Currently, cell phones are not allowed to be used during school hours anywhere on campus. Students may only use their phones before and after school. This is a K-8 school. I teach 8th grade. Over 95% of my students own phones and it kills me to see them carry around these expensive devices all day and not be allowed to use them as an instructional tool. You can see from the letter that the primary use of the phone will be for capturing student work. Tomorrow, I'll be laying down the law.

In case you missed it, here's the letter/policy again. Hopefully, what I call Phase 1, will be one of many phases for cell phone use in my class. Phase 1 has two objectives.

Objective 1: Capture student whiteboard work
My students do a crazy amount of work each day on their giant whiteboards. How lame is it that we have to erase it and never see it again. Even a black hole will never have the opportunity to consume it. It's gone. I've learned not to waste time having students transfer their work to their notebooks. BIG waste of time. We could use that time for learning, discussions, group work, etc. That said, I need students to capture what they're doing, because some of it is absolutely amazing. Even mistakes can be useful. For example, check out the student work done on these 3 Act lessons:

and Dan Meyer's Taco cart.
Seriously, I was lucky enough to capture it. So there you have it, I intend to support my students in capturing their work while at the same time assist them in using their devices responsibly. It's definitely going to be a change of thought for students to think of their phone as an instructional tool. That's why I'm easing into it with this simple task. We frequently do "gallery walks" in my class where students circulate the room and check out other student work. This will present another opportunity for students to capture whiteboard work. I'm thinking of some class 'lingo' and/or routines that will set everyone up for success. Make your math look good, now say, "CHEESE!" If you have any routines or tips to share, please let me know. When I assess this after a week or two, I'll let you all know what has been working and what has failed.

Objective 2: Send students and parents notifications
There is a great FREE service that my good buddy @mrkubasek sent me in this article. I will be using to send both students and parents notifications about class activities: Home Jams (my homework), quizzes, due dates, links, etc. I can send them notifications from a phone, computer, or tablet and they won't see my phone number. Likewise, I don't see their information. Furthermore, they can't send me anything back... mwoohahaha. I mean, how fantastic is that? They can email me if they have a question. I love the idea, because I won't be strapped to my phone answering questions related to the notification I just sent out. More importantly, my forgetful 8th graders will receive the ever-so-loving nudge or reminder about something vital to their success in math.

It doesn't stop here. Realistically, I can't pull off numerous uses for their cell phones a third of the way into the school year. Therefore, I will chip away at this. First and foremost, I plan to nurture responsible and mature digital citizens in my classroom. I hope that this works and I don't ruin it for other teachers at my school to test out. Speaking of which, I have to email them and keep them in the loop here. I hope I can work out any bugs and prevent any huge mishaps. I've seen and heard some of our student population abuse technology and that saddens me. Literally, less than a mile down the road are a couple of schools where students lack technology and/or personal devices. I'm fortunate to be in a place where this is possible and hope to learn with my students. Here are a few things to leave you with.

Bryan Meyer is on to something because I eventually want to have students create some type of digital folder, file, journal, blog, etc. I'd love for them to keep track of their work and either post it or submit it to me.

Dan Bowdin is doing some really amazing and inspring things in his class. Bounce around his website  for about ten minutes and you'll run into some fresh and inspiring ideas. I'd love to pursue the use of QR codes in class one day.


Sunday, November 25, 2012

When does a rock stop being a rock?

When does a pebble stop being a pebble and become a stone?
When does a stone stop being a stone and become a rock?
When does a rock stop being a rock and become a boulder?

I ask my wife these three questions too frequently. She's had enough of my philosophizing. So maybe you can help me out here? Are the answers too subjective? Is there an objective, definitive, agreed upon set of answers to these questions? Are the answers determined by weight? size? volume? mass? density? ootsies? (a la Christopher Danielson)

I'm thinking bigger picture here: How do we bring this type of thinking or wondering to our students more often? When dealing with measurement, how do we get our kids to know the correct (or most logical) way to measure quantifiable items without telling them? Would asking these types of questions help encourage our students to be better problem solvers or be better at applying the right terminology?

So many questions... here's more:
Living in the USA, our customary units system of measurements seems counterproductive with inches, feet, yards, fathoms, miles, ounces, cups, pints, quarts, gallons, barrels, etc. Terminology can be difficult enough for students and to throw all these different measurements at kids (nay, humans) can only seem daunting. When should we use feet to measure something instead of inches or yards? I envy the metric system and, well, let's leave it at that. These measurement questions become even more relevant as I dive into estimation with my students and as I update each week.

I haven't posted in a while and feel like I need to ease back into my blogosophy (blogging philosophy?). I'm not sure I just eased back into it. What do you think here?


Sunday, October 28, 2012

CMC - South: What could be?

November 2 and CMC South are only a few days away! I'm excited for a few reasons:
  1. World of Nathan Kraft is flying in (if Hurricane Sandy isn't too absurd this week) from PA to attend. I'll pick him up and we'll carpool to Palm Springs for the conference.
  2. Fantastic Fawn is literally missing her favorite football 'game of the year' to attend and cause some trouble with Nathan and me.
  3. Mullet King Matt Vaudrey is both attending and presenting.
  4. Recent doctorate and newly appointed Mathalicious brain Matt Lane is making the trip.
  5. The infamous Dan Meyer is presenting (need I say more?).
  6. ... and there will be a Tweetup on Friday with all these fab people, hopefully with John Berray too.
There are some appealing conference speakers this year. I wish there were more on Standards Based Grading. I think the two presentations I'm most looking forward to (besides Dan's) are Standards Based Grading to Evaluate Mathematical Practices by Lisa Miller and Take Your Places by Brad Fulton. I've seen Brad present before. He has got some great ideas and is hilarious with a capitol H. Sorry Mullet Vaudrey, I truly wish I could be at two places at once. Video record yours and post it, will ya?

I'll admit, there are parts of me that would get a kick out of the following:
  1. Nathan checks his tuba at the airport, pays the outrageous fee, and carries it around CMC testing out the echos. Heck, we are in the desert, but there is a small mountainside nearby and we could test the echo off of that sucker. 
  2. Tuba Echo from Nathan Kraft on Vimeo.
  3. Matt Vaudrey needs to sport a mullet the entire CMC (if he hasn't grown one out by now) and have his camera ready to take pictures of some locals with mullets. I'll bet Matt a beer that by the end of Friday, we spot at least 3 mullet-y locals worthy of your ratio lesson for this year.
  4. Fawn, better bring me that box full of avocados she owes me from File Cabinet. I'm tempted to pack my OG Nintendo and Tetris so we can have a little Tetris showdown. That way, she can't cheat on her Xbox (Okay, she might still kick my butt). At least I'll stand a better chance, right? If she doesn't bring me the avocados, maybe she'll bring me all her Brad Fulton books so I can steal, I mean copy them.
  5. As for Dan Meyer, I'm looking forward to meeting him and actually looking up at someone for a change. I'm speaking of height here people. I look up to everyone mentioned in this post! However, wouldn't it be fun if our Twitter group heckled him during his entire presentation?
Stay tuned for a full report from CMC and some fun contributions to

CMC to be,

Thursday, October 25, 2012

Transversals, Tape, and Stickies

Today in Geometry, we're discussing two lines, a transversal and the angle relationships formed. We did a few minutes of word wall pics and direct instruction of Corresponding angles, Alternate Interior angles, Alternate Exterior angles, and Same-side (or Consecutive) Interior angles. Then students were presented with the following setup on my walls. I used three strips of masking tape to create the lines intersected by a transversal and numbered stickies. I was able to set up 3 stations since I have a small group of 8th grade Geometry students this year.

Students worked in groups and were instructed to start with the two parallel lines and the transversal. It's a lower entry point as opposed to the three lines intersecting to form the triangle (which my textbook chooses to introduce this concept. Silly publishers). Groups are given the following handout and need to place the stickies in the correct places, based on the given clues. Work together, GO!
Handout and solutions here.
If you have limited space, create 1-2 stations and have groups rotate as other students are completing a task at their desk. Put a timer on the board and tell the students to get as far as possible within the allotted time. When the timer finishes, I'd take a picture of their work, reset the stickies, and let another group tackle it, resetting the timer.
Here are possible solutions. Let me know if you find any errors.

It went well. There was a lot of tension in the groups. Some kept moving stickies around because they disagreed. They disagreed because of the overall connection, not because of getting the relationship wrong. It was so fun to hear them get so excited about this activity. We ran out of time and the quote of the day came from a girl, "That's upsetting me." She wanted to finish. She wanted to know the answers. She wanted to figure out the puzzle. Many other students had similar feelings. I love it!

What I learned: Don't make the groups too large. Go with about 2-3 students (4 max) per group. Use really good stickies. The orange ones you see in the pictures were old and had lost their stickiness. If groups are struggling too much, encourage them to find a set of angles that has the least amount of possibilities.


Friday, October 19, 2012

Parent Conferences 2012

Today I had Parent Conferences from 7:45am to 3:30pm with a 45 minute lunch in there somewhere. We hold them in the gym as the middle school teachers sit at tables placed around the perimeter of the gym. Parents roam around the gym looking for teachers to talk with. I suppose I should back up a few days before I dive into today's happenings.

Wednesday, I did two things. First, I sent all my parents an email saying how excited I am to meet them on Friday during conferences and that I request they bring their child so they can help lead the conference. Secondly, I gave students a Review Quiz to assess their mastery, growth and retention of the concepts from the first few weeks. Many students demonstrated mastery, substantial growth, and are retaining algebraic concepts. They came into class Thursday to receive the results of the Review Quiz and were expected to fill out the following form. This form [editable version here] would help students lead the conference with their parents.

This form had multiple benefits such as guiding the student and giving them talking points. It was so cool to hear kids tell parents the concepts they were mastering such as "Distributive Property" or concepts they needed to improve like "Number Systems." It gets better. I had kids explain to their parents how Reassessments worked and how many they've set up with me. Again, there were some fantastic moments of kids proudly explaining the process. Of course, there were kids who haven't even set up one reassessment who should have by this point and it really drove the point home that their learning and 'grade' is ultimately in their hands. I wanted students to remind their parents that I only assign 2-4 home exercises each night and although they're not worth points, I wanted students to use their own words to illustrate why it's important to still attempt and complete them. Behavior was an additional suggestion by Chris Robinson and kids were actually very honest, if not modest at times. Lastly, let's move forward and have students come up with some specific, yet attainable goals and ones other than "Get good grades" [BORING!!!!]. Check some of these student created goals:
  1. Don't be afraid to ask questions.
  2. Do all Home Jams completely.
  3. Keep myself organized throughout the year.
  4. Avoid doing PS on Sunday night.
  5. Ask at least one question per day.
  6. Learn with a smile.
  7. Avoid making careless mistakes.
Avoid making careless mistakes! I found myself telling parents that 'careless mistakes' are a natural feature built into a middle school student. My job is to help them get better at strengthening their skill of double-checking their work by being their own "math lifeguard." Yes, having goals, working toward mastery, and learning concepts will lead to "good grades." It was amazing how little I actually informed parents of their child's current percentage and grade in my class. It was amazing. Compared to previous years, there was a huge, apparent, and welcome shift in the context of Parent Conferences. Thanks SBG! Numerous times I told parents that students are being less "grade enthusiasts" because they are owning their learning and working on mastering concepts one at a time. See ya later points!

Some parents came in with agendas, skeptical of this "different way of teaching". Oh, you mean the teaching where I present students with a question, task, or problem and let them grapple with it for a few minutes, fleshing out ideas with their group members on their giant whiteboards as I circulate the classroom listening? The teaching where I only jump in if they are a hundred miles off base? The teaching where I look for students to discover solutions on their own and then share their work with the class using a document camera? The teaching where students are learning from each other and not following a contrived algorithm or procedure blindly without direction, interest, or appropriately struggling with it first? The teaching where I encourage students to take ownership of their learning? Right. Well, after a few weeks of ironing out some kinks from being too 'hands-off' at times with instruction, I've found my groove and I've found that happy medium between being hands-off and knowing when to intervene and instruct students. Not all students are ready or welcome the idea of a teacher being hands-off. Some, especially these middle schoolers, still need that procedural learning from the get-go. I respect that and am sensitive to that. Therefore, my happy-medium place is that where I allow students to grapple with concepts at first and with each other, but students will always leave my class that day knowing an efficient way to navigate to a solution, even if it's procedural.

Ending on a positive note, I had two conferences that truly brought warmth to my heart! Two girls in separate classes struggled in my class the first few weeks of the year. By no means are they strong students. They try and work hard, but not as hard as many of my other students. At first they wanted good grades, but that's changed to wanting to succeed and learn. They figured this out on their own. Their 'grades' were in the dumpsters the first few weeks. I gave the Review Quiz this week and holy smokes, they kicked math butt! Giving them back their assessment yesterday, sharing this news with their guardian at conferences today, and seeing their current 'grade' was an experience that confirmed that SBG is here to stay.  I'm proud of you two girls! We don't need no stinkin' points-based-grading.

Conferenced out,

Wednesday, October 10, 2012

Global Math & 3 Act tonight

Stop in tonight at #globalmath for a discussion about Dan Meyer's 3 Act lesson format. I am fortunate and honored to discuss the use and implementation alongside Dan Meyer and Chris Robinson. Hopefully, my pal Nathan Kraft will join the fun too.

Wednesday October 10, 2012
6pm PST

Be sure to register, ask a few questions, and check it out. Thanks to Megan Hayes-Golding for organizing this.

Sunday, September 30, 2012

Estimation180 site

Its official: I've launched

The Google doc was a temporary holding place for my daily estimation challenges. I'm proud to announce that I will be updating my daily estimation challenges through this site. The site is way more interactive than a Google doc spreadsheet... and quite possibly, more fun too. You can make estimates, share your reasoning, see how others estimate, and more.

The goals of the site:
  1. Document my daily estimation challenges.
  2. Create opportunities for teachers & students to build number sense together.
  3. Share!
What you can do:
  1. Click on a picture.
  2. Read the question.
  3. Look for context clues.
  4. Make an estimate.
  5. Tell us how confident you are.
  6. Share your reasoning (what context clues did you use?).
  7. See the answer.
  8. See the estimates of others.
The most important part is step #6. It's so valuable to a classroom when students share their logic or use of context clues when formulating an estimate. After you make an estimate, feel free to give us a brief description.

I've posted the first 15 days and will continue to update the site. Go do some estimating, build some number sense with your students and throw me some feedback if you find any glitches or ways to improve it. I want to sincerely thank Fawn Nguyen, Nathan Kraft, Chris Robinson, Michael Pershan, Dan Meyer, and Steve Leinwand for any help, inspiration, and/or feedback you've given me regarding You all are amazing!

Happy estimating!

Friday, September 28, 2012

Estimation vs. guessing Part 2

Yesterday I blogged (part 1) about visiting a fourth grade classroom and their lesson on estimation. After her lesson and her students left for lunch, the teacher and I debriefed. I really hope I complimented her enough. I was inspired. She asked me for some feedback. To remind you, she started the lesson by picking up a small cup, about half full of cubes, somewhat concealing it and asked students how many cubes were inside. She wanted to demonstrate that their initial answer would be a "guess" and not an "estimate". However, she had many observant students who already saw the size of the cup, the fact that it wasn't full of cubes, and even from my seat in the back I could tell that the cubes were small enough to fit inside the small cup. I told her I loved everything. The only additional thing I would have done was this:
Don't even show the kids anything. Don't go and pick up the cup. Simply say to the students:
Students, I will have a cup in my hands very soon. There will be cubes inside. How many cubes do you think will be in the cup?

Okay, look how simple this uninformative setup was. If I were a student, a bunch of questions would have just popped into my head: Hey teacher, what size is the cup? Is it a small paper cup? A medium coffe cup? or a large Big Gulp cup? What size are the cubes? As a fourth grader, I know what base ten cubes look like. Are they bigger like the size of snap cubes? Are they the size of ice cubes? and how about the amount of cubes in the cup, teacher? Are there just two at the bottom? Is the cup half full (or over half empty for you pessimists)? Is the cup full of cubes?

Any number the students produce would simply be a guess. It's a low-entry point, but doesn't hold much strength for long. How many cubes are in the cup? It could be two. It could be two hundred. Two thousand. You get the point. This strategy reminds me of a couple engineering classes I took in which we discussed a black box. In other words, there's something inside this black box that serves a purpose or function. However, you have no idea what's inside or the parts that make it function.
Students are guessing blindly at this stage. However, I wouldn't want them to just guess. I want them to beg for more information. Even better, I want them to think what information would help them solve this question. Let's move to the next stage.

Let's spiffy up our description, but still refrain from showing students the cup, cubes, or content level:
Students, I have a small drinking cup in my hand that's about 8 oz. Inside are cubes that are slightly smaller than six-sided dice. The cup is a little less than half full. How many cubes are inside?
By this time, I hope students would be falling out of their seats trying to sneak a peek at the cup. They're lusting after more information to make a more accurate assessment. You're simply adding some labels to the black box. Heck, put the cup inside a brown paper bag for this part.
What stage is this? I think this is the in-between stage. Shall we call it guesstimating? I used to really loathe this term as I want my students to use estimation. I thought it was a silly verb and should be eliminated from our vocabulary. I no longer think that. A guesstimate implies we could make a better attempt. We could use better clues. It's the bridge between guessing and using sufficient clues and observations to make a reasonable estimate. In other words, we must encourage our students to demand better information. Demand facts. Demand relevance. Don't SETTLE! Okay, so what takes us to that next stage, estimation?

Reveal the cup. Take it out of the black box and put it in the display case. That's right, put it in the display case. Don't let them touch it.
Demand they use their intuition, their available senses, and rely less on the sense of touch. Show a picture of the cup, a cube, and a birds eye view of the cup. Remember, it's in a display case. An even greater challenge to your display case would be to put the cup on the students's desks, but don't allow them to touch anything. Hold onto any last shred of information you could provide them with. Guard it. Be stingy. Let them use their sense of sight and intuition to build their number sense. Help students build up a thirst for relevant information. Build a problem solving plan or strategy. Don't be mean about it or covet the information for malicious reasons. Give students time to respond to the clues provided. The display case is a prime stage for estimation. Students have many context clues from either a picture or physical model. This should be enough for students to really build a strong theory and/or problem solving plan. As we saw in yesterday's post, students came up with a couple of theories on how to more accurately estimate the cubes in the cup by counting the top layer or cubes on the sides. The teacher didn't just hand her students the cup. She helped them climb the ladder of abstraction.  I think the key to this is encouraging students to demand more information. Don't inundate them with all of the context clues immediately. Make them demand the clues.

Hands-On is the last stage of estimation. Without counting, allow the students to pick up the cup. I'm not saying students will change their estimate. However, it will give them opportunities to consider another perspective of the task. They are including another component: weight, size, etc. There's only one place to go from the hands-on stage and that's revealing the answer: the payoff.

1-Black box: Keep that description minimal. Avoid a visual.
2-Label the black box: gradually reveal some information
3-Display case: Look but don't touch
4-Hand-On: incorporate one last sense in order to bring one last perspective to the estimate.

By the way, did you know that Stevie Wonder played many of the instruments on his Innervisions album. I read somewhere that he virtually played all the instruments on about six of the nine songs. That's one of my favorite Stevie Wonder albums. If he can do that without the use of sight, imagine what we can do with all of our senses. 

Part 3: Why should we be the gatekeeper of information for our students? How can you help your students build their number sense and demand more information to make a reasonable estimation? How do I incorporate estimation in my classroom?

Part 2,

Wednesday, September 26, 2012

Estimation vs. guessing Part 1

Estimation vs. guessing and the space between, let's talk about it.

If you've been following my thoughts lately, via Twitter (#estimation180) or this blog, I've really been investigating the relevance of estimation for some time now. However, the past few days have really had a great impact on my approach with students, leaving me even more intrigued with the relevance and application of estimation with students. Over the next few days, I plan to share a few of the interactions: here's part 1.

Today, I visited a fourth grade classroom at my school. It's a personal goal of mine this year to visit as many classrooms as possible during my prep period and learn, learn, learn from other teachers, especially elementary teachers. I love observing elementary classrooms and seeing how so many children are still excited about learning. I'm constantly looking for strategies to bring back to my own classroom that will create a sense of excitement with my middle schoolers. The fourth grade teacher and I will be working on creating and implementing 3 Act lessons this year, so I was getting acquainted with the climate of her classroom. It was destiny: the class was discussing estimation and guessing.

First off, she's a fantastic teacher. Second, she did a wonderful job comparing and contrasting what the students thought estimation and guessing meant in their own words. She created a list for each on a huge giant sheet of paper, like a giant Post-It note. She does this often and sticks them around the class for students to refer to. The fourth graders decided that guessing could be something:
  1. you don't know
  2. you think could be the answer
  3. 50% sure
  4. or anything
As for estimation, the fourth graders decided it could be something:
  1. you round
  2. you think is close to the answer and reasonable
  3. you look at and use clues to carefully give an answer
This last definition was very insightful for a fourth grader.  The teacher proceeded to pick up a cup in front of the class and tell the class there were cubes inside. She asked them to make a guess and students were stretching their necks to gather any information about the cup in her hands. She did a great job concealing it, but many students had already mentally logged characteristics of the cup. She had a low-entry point for the students. They all wanted to know how many cubes were in the cup. They wrote down guesses in their journals and she took them to the next level. She showed the students how full the cup was with the cubes and asked them if this would be a good time to keep guessing or make an estimate. Students agreed, they had more information to make an estimate and they jotted this new number down in their journal. Lastly, she passed out cups, requesting students to not touch, but think of a strategy with their small group to get an even better estimate of the cubes in the cup. Students shared their theories:
  • I counted the cubes in the top layer and then counted the layers down and multiplied the two numbers.
  • I counted the number of cubes around the cup on each layer and made a reasonable guess for the hidden cubes inside.
The teacher asked the class who had similar theories and many of them chose the first. I really enjoyed how the teacher didn't once offer her theory on how to estimate. She let the students take ownership. As the lesson drew to a close, she requested the students work together to quickly count the cubes inside their cup and compare it to both their guess and estimate. The teacher had a low-entry point for all students, she let the students define their own vocabulary, she took them up the ladder of abstraction with gradually revealing information they needed/wanted and going from guessing to estimation. Lastly, the payoff was huge as she allowed students go hands-on with the cup and cubes to validate their learning for the day. I left her class inspired. But before I left, the teacher and I had a valuable brief discussion. A few things came out of that conversation I will touch base on in part 2.

Part 2 will connect estimation with guessing and the space between, sometimes referred to as a guess-timation. I want to create a low-entry point that's even more inviting for students. Lastly, I want to discuss how number sense can be strengthened as we transition from guessing to estimation before the payoff.

Part 1,

Sunday, September 23, 2012

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!

Andrew Stadel

Monday, September 17, 2012

Estimation 180

Estimation initiative:
[*UPDATE: 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 )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: is live. Forget the spreadsheet!]

Number sense,

Thursday, August 23, 2012


I finally recorded my PEMDAS song!
Listen/Download here.

*[Update] Here's a video for those visual learners: Vimeo or YouTube.
I know, I know, I know... math teachers need another PEMDAS song just as much as we need another Michael Bolton ballad. Oh well! I wrote this song a few years ago and brought it into my students at the beginning of the year. I think I had reached the point as a teacher where I didn't like any other PEMDAS song I came across (sure, call me a snob). I was getting more comfortable as a teacher, making a fool of myself in front of my students. And if there was one math concept to write a song about, Order of Operations was it!  I had a couple of lines that made sense lyrically. I picked up my acoustic guitar, threw down a few chords, and put some lyrics to PEMDAS. I wanted to keep it short, to the point, have a call and response feel, and something my students could remember for the rest of the year. Mastering Order of Operations at the beginning of the year pays dividends throughout the year.

Sorry, I'm not here to discuss where Order of Operations came from, why does it exist, or what underground math cult magically persuaded the entire universe to evaluate mathematical expressions in the way we do. My twitter cohorts @MrPicc112, @jreulback, @druinok, @ChrisHunter36, @fnoschese, and @ray_emily had a fantastic discussion the other week. It would be nice to know why, where, and how Order of Operations came to be. However, I've reached the point of acceptance. Honestly! I've learned to accept acceptance. So, on with the show.

I get together with my nephew (16 years younger and still in HS) and we jam out to our favorite bands in my garage every once in a while. This last time we jammed, I asked him to throw a beat down for my PEMDAS song since I actually wanted to record it. Being the phenomenal young drummer that he is, he was happy to do so! He did a fantastic job in about 10 minutes. Every other noise you hear is me... guitar, bass, and vocals. So at least the drumming is good. You don't dig it, blame everything on me. I dig it! Many of my former students dig the song and sometimes sing it back to me in class. Very cool. Many times throughout the year, all I have to say is, "Parentheses" and without skipping a beat, the students respond, "Start with these."

If you decide to torture your students with the PEMDAS song, here are a few tips:
1. Do a 'call & response.' You start each line of the verse and they finish it:
Teacher: Parentheses
Students: Start with these
2. Tell your students it will only take a minute to learn and a lifetime to forget!
3. Hire me and I'll come perform at your school. Ha!
4. Don't forget to actually teach them how to simplify/evaluate expressions.

If you're looking for an extension to torturing your students with learning the song, have them rewrite the lyrics of the second verse. Have them write lyrics for the Left to Right rule that applies to Multiplication/Division and Addition/Subtraction. I did this one year and really received some cool lyrics. I also received some terrible ones because those kids could have given a rip about the assignment. Guess what though! They remembered the Left to Right rule. Who's laughing now?

This was a labor of love. I hope you get some mileage out of it, no matter what grade you teach. Lastly, not all your students are the biggest fans of cheesy songs like this. I never was! Hence, my reluctance to record and share. I'm seriously thinking about making a video to accompany the song for those visual learners. Stay tuned!


P.S.  Apologies to my Canadian and British readers! PEMDAS is kind of limited to the States. Let me know and maybe I'll upload an instrumental version and you guys can change the lyrics to suit your needs.

Sunday, August 19, 2012

In the Name of Efficiency

See anything weird about this?

I started college as a Mechanical Engineer major since some college advisor (who knew nothing about me) thought ME (Mechanical Engineering) would be the most fitting major based on some test I completed coupled with my interest in math and science. As I was taking my prerequisite courses in math and science I switched gears to Electrical Engineering because my love for music swayed me into thinking I could design amplifiers and effects pedals (stompboxes) for musicians. I took a couple of EE classes and really didn't enjoy it. I wasn't passionate about it and saw many others in the same boat who kept making comments such as, "I have to finish this [major] now" or "I can't not major in electrical engineering" or "It's what my [insert parent gender] does." As for me, I really enjoyed my introductory Philosophy classes because they allowed me to explore some pretty radical thinkers and we had all these wonderful debates about logic, God, metaphysics, existentialism, human rights, medical rights, law, etc. I became a Philosophy major and the rest is history... I think. My point is, if anyone (me included) knew me well enough, they should have highly suggested I major in Civil Engineering.
Here's why CE:
I'm one of those people who drives by construction (road, building, bridges, pipes, etc.) and is always trying to figure out what is being built, modified, or enhanced in the name of efficiency. I'm also that person that drives by an area and will vocalize how inefficient the lane configurations are, or offramp, or stoplight sequence, etc. That's usually followed by a suggestion on how to improve it. My poor wife gets an earful at times. I'm also that guy that looks at products and either loves and respects an efficiently designed product or will completely be baffled that a company releases a product so poorly engineered and wreaking of inefficiency. Then, I spend the next 30 minutes thinking of ways to make it a better product or design while restraining myself from emailing the company. I know the latter example isn't necessarily classified as CE. However, I could see myself out there designing things to help improve civilian efficiency. Thank goodness I'm not. Instead, I'm in the classroom with normal adolescent  middle schoolers who are always are in a good mood and never have social problems or woes. Right? One can dream. I love my job. I love teaching those wonderful teenagers. There's never a dull moment with middle schoolers. As their teacher, my objective is to strengthen their young impressionable minds and help them be better critical thinkers.
Enough about me, the point of this post [In the Name of Efficiency] is I have an idea for my class this year. Dare I say 'theme'! And if it goes well, could easily become a staple for the remainder of my teaching career. That's how much I value this idea! We look for products that fit one of two categories:
  1. The product is very efficiently designed. We explore everything about it that makes it a superbly designed product. What math is involved? How is math involved?
  2. The product is inefficiently designed in one or more ways. Identify the area(s) of inefficiency and propose a well-thought out modification/enhancement. Again, how would math be involved? 
Here's a simple one for the first category: efficient.
A modern ketchup bottle.
The ketchup bottle that rests on its lid uses gravity to its advantage and you rarely have to shake the dang thing. Plus, your burger, dog, or fries will actually still be warm when you're done getting ketchup out of the bottle. Why did it take someone so long to think if this, right?
Here's an example that fits the second category: inefficient.
A depleted salt container.
Take that salt container at the top of this post. Granted, it took a couple of years to deplete the salt in the container, and maybe there's a new design out there, but I got to the end and there's still salt in it. No matter what angle I hold the container, or shake the cylindrical container, it won't pour out every little grain of salt. My question would be: How could we better design the spout? Should its location change? What would happen if the spout were closer to the rim? What would be the easiest, yet most effective change?
Companies do this all the time (or at least should). They reassess the efficiency of their products. Why can't a classroom full of students do the same? We/they complain about things all the time. I want my students to bring in stuff: pictures, products, construction site pictures, machines, etc. We discuss it for a week. We make a bulletin board of ideas. We split the board in half for efficient vs. inefficient. I want each student to be responsible for at least one contribution throughout the year. They do a brief write-up. Pick from a collection of modifications/enhancements submitted by their peers. Sketch or draw a new design. I'm ranting here because I want to flesh this out... I want this to work!
I want my students to bring things in that drive them bonkers. Fine, if you don't like it, think of something better. How would you design it? What would you want it to do? On the other hand, I want my kids to bring in things that they absolutely adore. Things they couldn't live without. Things that they take for granted on how awesome they are. This might require them to give it more thought. Usually something that is efficient, well-designed, well-made, and awesome can be overseen because of how great it is. The second it stops working, is gone, or replaced with an inferior product we pine. Talk about an opportunity for students to appreciate many of the wonderful, amazing, and unbelievable inventions of our time. I think this would foster a sense of gratitude for some of the cool things we experience every single day. It's not just about complaining and finding things that could be better. 
This is one thing I'll be doing differently this year. Am I off base here? This wouldn't be the foundation of my teaching, but it sure feels naturally appropriate to a math class. Aren't we teaching our kids to be better problem solvers? better critical thinkers? better contributors to society? I always tell them to better problem solvers and not better problem complainers. Don't we have things that drive us nuts? Within reason. I'm not talking about losing your internet in the middle of an airplane ride. Your life will go on without the internet for a few hours. Yes, it will! Don't even start with me. If you got a problem with losing the internet on a plane, read a book, pay attention to your kid for a few minutes, or talk to the person next to you. Everybody has a story to tell. Ask them what their story is. If you're not convinced, talk to my man Louis CK. Tell 'em CK:


Tuesday, July 24, 2012

Distance, Rate, & Time [Giddy Up!]

Last week I finished Steve Leinwand's Accessible Mathematics. It's a quick, easy, informative, realistic, and applicable read. Get on that!
This week I planned on diving into Standards Based Grading while restructuring some things for next school year. Well, there's still time for SBG. Instead, I've been churning out some new 3 Act lessons with:
  1. Some outtakes to the hexagonal Pencil Cup lesson and...
  2. The beginning of some distance, rate, and time lessons
There's a plethora of resources out there dealing with d = rt. Therefore, I thought I'd try and put my little spin on the whole roundabout. Keep checking my Distance, Rate, & Time album for updates.
Giddy up to summer!

Go the distance,

Thursday, July 12, 2012

Elmo's Microwave Travel

Summer school has been a fantastic testing ground for 3 Act lessons with incoming 6th & 7th graders. I'm constantly reassessing my deployment of the lesson format. If you have any improvements to offer, go for it. Check out Dan's whole catalog. Here's a few I used this summer:
  • Print Job: Talk about rate and breach theoretical v. practical discrepancies.
  • Nana's Chocolate Milk: Ratios, Fractions, Proportions, Equivalencies, do it!
  • Popcorn Picker: Do identical rectangular papers have the same volume?
  • Super Bear: Unit rate, ratios. Discuss Percent Error (genius)!
Dan's lessons are wrapped up in a neat little package, following his own framework for digital media. It's up to us to deliver. Today, I used my Elmo's Microwave Travel lesson. Keep in mind this was with incoming 6th graders. I'm more generous with them than my 8th graders. I continue to learn about the 3 Act lesson format (here's Act 1):

Act 1 (go get that Q):
View and immediately get those Q's (questions) in the air.
I don't perseverate anymore over having at least one student ask the intended Q. Let students ask what they wonder and state observations. If they hit your intended mark, don't jump for joy. Act as if it's just another Q in the mix. Summarize the questions and observations before revealing the Q. I usually say something like, "I'm right there with (insert name) on this and I also want to know (state question)." Luckily, there was at least one kid form each class who wanted to know how many rotations Elmo makes in the microwave. Get that Q on the board immediately along with any other questions that could be answered during the lesson. Have students write the Q's at the top of their paper, notebook, handout (whatever you use). Everyone needs an objective, something to work toward. Once it's scribbled down, encourage your students to make an estimate for each Q and pencil it in near the Q. We came up with:
  1. How many rotations does Elmo make? (They nailed this Q!)
  2. What distance does Elmo travel around the microwave? (Extension of the 1st Q)
  3. Will he melt? (Some students really worried about him melting. How considerate.)
* Using their wording for the Q's, I encouraged them to put it in relation to one minute.
Students do all the thinking, questioning, noticing, etc. but in the past I wasn't writing the Q on the board. Big mistake. Now it's monkey see, monkey do! Get the Q on the board. Go!

Act 2 (muy importante!):
Ask the students to discuss, "What do we already know?" Here are some responses from students:
Elmo travels for a minute. (Me: "How does that help?")
He's on a circular plate. (Me: "What do we know about circles or can do with that?")

Write the facts on the board. Now I ask, "What information would help you answer those Q's on the board?" or "What would you want to know in order to answer the Q's?"
Really make students think here. Don't make it easy. I have to keep working at this tactic. Allow students to struggle with the notion that they need to determine what's relevant before you divulge any new information. This allows students to be better critical thinkers. Here's what they thought:
Maybe we could see how far he goes in 10 seconds (Me: "Interesting.")
The plate is a circle. Can we know the circumference? (Me: "Is that easy to measure?")
Then can we have the radius? (Me: "I'll give you the diameter. How's that?")

Roll Act 2 Elmo. Students, get solving. Start discussing, debating, testing, calculating, etc. If you come up with something let the class know. If we agree on it, we'll write it on the board. If not, we'll erase it. Hey Frank Noschese, now I'm starting to see the importance of those student whiteboards. WWFSD? (What would Frank's students do?) Can we still jot down necessary info at the front while students collaborate? Of course.
This is all student derived. I was simply the scribe.
Okay students, you got a solution? What does that number mean? Does it make sense? Did you check it for reasonableness? Did you give a unit of measurement? Did he travel in miles, feet, inches, millimeters? Does it make sense? I bombard them with questions. I'm almost getting to the point where I forget about Act 3. I want to see their work during Act 2. I want to hear their rationale. I want to learn from my students and their thought process. I enjoy that. Lately, the big driving force for me to actually leave Act 2 behind and attack Act 3 is the discussion that follows after viewing Act 3

Act 3 (theoretical v. practical):
On paper, many 6th graders miscalculated that Elmo travels 37.68 inches for one minute. Even after asking them if it made sense, they stuck with their answer (I let it go). There were a couple who got the correct answer! I didn't tell them; we watched Act 3. The students who had the correct answer and saw that 37.68 inches was quickly ruled out, watched intently as the time wound down. The anticipation on their face was priceless. The video ended and one girl was both happy and confused at the same time as she awkwardly asked, "Is it okay that my answer is one inch off?" Hello! Here's our opening for discussion. Theoretical v. Practical. I was so happy. First we discussed why 37.68 inches was incorrect. They didn't multiply their circumference by the number of rotations in a minute. Then we tackled the theoretical v. practical results. My microwave plate is kind of wiggly. It doesn't rotate at a constant speed the entire time: it slows down and speeds up. That one inch could be accounted for a few reasons. Their world was rocked, but Elmo's world made sense.

[Sequel to come] Dan contacted me for some video footage of Elmo traveling for 30 seconds in real time so he could use it at a workshop. He wanted his attendees to graph:
  1. Elmo's distance from the center of the plate over time [Update: Video]
  2. Elmo's distance from the glass door over time [Update: Video]
  3. Elmo's total distance traveled over time [Update: Video] *My recent addition
I plan on doing the video sequel and will experiment with it in Motion this week. My kids enjoyed the sequel discussion, but missed a video to back it up. Great sequel idea Dan, thanks.