Dancing with the Functions

I'm honored and humbled to have been a (small) part of Christopher Danielson's online course The Mathematics in School Curriculum: Functions. There were some great tasks, discussions, and contributors. I now have a better misunderstanding of functions. However you interpret that last sentence, let me assure you that this two week course broke me down in order to give me a better perspective and idea of functions. Professor Triangleman moderated the course well, provided challenging tasks and opportunities that took me out of my comfort zone, encouraged us to think differently, and didn't hesitate to whip us into shape as you can see here:

He's referring to beating me down while informing the teacher's pet (Fawn) of his tactic.

Our choices for our final project were:

• a blog post,
• a lesson plan,
• an interpretive dance,
• a work of visual art,
• etc.

I thought writing a blog post was "too easy" in the sense that I could blog about anything ordinary at anytime. This class wasn't ordinary though, and I felt I'd rather try and give something back to the class, professor, and community in exchange for what I have received. No Fawn, not because I'm "too lazy." Therefore, I'm going to give you a lesson idea I have, based on an interpretive dance, which might be a work of visual art, all wrapped up in a blog post.

Interpretive dance really got me thinking. I thought back to the handful of dance lessons my wife (fiance at the time) and I took to practice for the First Dance at our wedding. My wife was a natural. As for me, well let's just say all the dance lessons in a lifetime wouldn't have helped. Here's a dance photo I have of us where it actually looks like I'm doing something worthy. Don't be fooled.

Don't worry, I won't torture you with video. Anyway, our dance instructor taught us many helpful tips and gave us a glimpse of dances like swing, salsa, the waltz, and the two-step box. We only did a few moves in our wedding dance, but it mainly revolved around the two-step box. We had a short song, thank goodness. I'm sure our guests would have taken their gifts back had they seen me dance any longer.

Here comes my lesson idea. I'd like to see the relationship between the number of steps taken in a dance over time. So let's make it a graphing story. Here's the first 30 seconds of a dance. Write a story for it. Even better, can you write the functions (along with any intervals, domains, ranges, etc)? Go here to Desmos to check your answers. I give you my interpretive dance.

Thanks to Sadie, Timon, and Michael Pershan for inviting me to their hangouts. I was honored to collaborate with you guys during one of the hangouts and bounce ideas off of each other. Thanks to Fawn for getting me in trouble, ratting me out to the teacher, and reminding me to submit my final project. Where would I be without you? Probably in class and not in the principal's office.

I would love some feedback on this lesson idea. Would you have your students dance? If so, what dance(s)? Would you have students come up with a function for each type of dance? What kind of relationships would you have your students look for? Would you consider "dancing" an applicable use of functions? I leave you with this clip. You must give these guys (Sean and John Scott) some crazy respect. They're insanely fantastic at tap-dancing. Just watch the first minute. Then make a graphing story.

Dance,
933

Buses

I just returned from taking my son (turns 3 in a month) to preschool. One of the many perks to Spring Break so far! On the way to preschool, my son spotted a city bus.

Son: Ohhhh! A bus!

Me: Right. What type of bus? 

Son: A city bus. 

A little background knowledge here: He loves trucks! Let me rephrase that. He loves anything larger than a car, has an engine, is big, makes a lot of noise, is big, does construction, is big, intakes diesel, etc. I've seen many kids share these interests, especially when the garbage man does his rounds in our neighborhood. You'd think the garbage man was passing out ice cream or something (and he doesn't need that silly Ice Cream truck music either). We have multiple truck books that get frequent use before nap and bedtime. We have a surplus of toy trucks and Legos, recently added to by the most generous, wonderful, and great Fawn. You're the best!

Back to our drive. We had just stopped at a red light and on the other side of the street he spots a school bus.

Son: Ohhh! A school bus!

Me: You're right!

Son: We've seen two buses!

Me: I know. Look what's coming up behind the school bus.

Son: Another bus.

Me: And what type of bus is that?

Son: A city bus.

Me: So how many buses have we seen?

Son: Three!

Me: That's right. We've seen 2 city buses and 1 school bus, so we've seen a total of...

I pause for him to fill in the blank.

Son: Three!

We're still stopped at the red light and have a little time before the green light. I turn around and illustrate this again with my fingers, because lately he's been doing really well identifying the numbers one through five on a single hand. Since we saw two different types of buses, I use two hands. I hold up on hand with two fingers up and say, "We've seen two city buses" and on the other hand I hold up one finger saying, "and we've seen one school bus. So we've seen a total of how many buses?"
I expect him to say "three" because it's fresh in his mind, but he pleasantly surprises me and I can see his eyes moving across my fingers and mentally counting the fingers to verify the word 'three' matches up with Dad's fingers. "Three." he says.

The light turns green and we're on our way. We have less than five minutes until we get to preschool. Of course, I'm keeping my eyes peeled for more buses. No buses. Shucks. However, we pull into the parking lot of the preschool and park. Before I exit the car to get him out, I turn around and want to try something. Simply for fun.

Me: So we saw two city buses [I'm holding up two fingers on one hand]. What if we saw two school buses [I hold up two fingers on my second hand]. How many buses would we have seen?

Son: Three.

Me: Are you sure? Count my fingers.

Son: One... two... three... four, five, six, seven, eight, nine, te...

Me: Okay, silly. [holding up two fingers on each hand again] If we saw two city buses and two school buses, how many total buses would we see?

Son: Three.

I left it at that. He's content with the concrete. It's not about future counting for him. It's about what he just experienced, what's relevant, what's applicable and what's associated with his interests. I made a small attempt at the abstract, just for fun. There's no need to push this any further. He's convinced we saw three buses and he's right. He doesn't care about a fourth bus that we didn't see. Plus, it's time for preschool. Man, I love vacation. I get to have conversations like this with my son. It doesn't get any better than that.

Buses,
1047

[UPDATE]
*Read what happened two days later in Buses [Day 2].

Not Drawn to Scale

I hope you'll allow me to vent for a bit. I have been encouraging my students to be in tune with the 8 Mathematical Practices by Standard of the CCSS for some time now. It's pretty safe to say that my students know I really favor Mathematical Practice Standard 6, Attend to Precision. However, some of the resources I occasionally use in class are beginning to play tricks with everyone's minds, including mine. Here's a resource I have, Cooperative Learning and Geometry by Becky Bride.

Don't get me wrong, I like this book. It has some great explorative exercises that have appropriately challenged my students. For example, look at this exercise to help students derive the 30-60-90 triangle relationships. Take an equilateral triangle, its altitude, and the Pythagorean Theorem to find out the special relationships between the shorter leg, longer leg, and hypotenuse. Great.

Here's where I start to beat my head against the wall. The book uses diagrams that simply shouldn't be used, especially in the context of 30-60-90 triangles. Look closely...

That's right, the 30 degree angle is opposite the longer (drawn) leg for questions 1, 3, and 4. My students get bothered by this contradiction. I do too. I have no problem admitting this to them. I'm honest with them saying, "I know guys. It goes against everything we strive to do in here. I encourage you guys to attend to precision and check for reasonableness. Yet, I give you this. I'm sorry. It says at the top 'not drawn to scale', but they should be drawn to scale. Right guys?!"

I think this about sums it up. Students will come up and ask about the dimensions they've solved for and whether or not they're reasonable. I'm proud of my students for making sense of their answers and checking for reasonableness.  I know something is a skew when my response to those students is,

"I never assume those things are drawn to scale." 

I feel rotten saying this to students. I feel like I've just provided them with a worthless and menial task. I've let them down. I feel dirty. Mr. Stadel's quality control group hasn't done their job. What message are we sending students? Do they think we're out to trick them? Do the directions read, "Find the mistakes?" They should. It's times like these that force me to (gladly) keep a closer eye on the content I provide my students with. Don't just throw some triangles at them with random angles and units. Make sure they're reasonable.

Have you ever felt this way? Have you ever been caught in this situation? What did you do? How do we avoid these situations again? How do we demand better quality content from publishers? How do we make sure we provide our students with content that matches the CCSS and Mathematical Practices? Maybe you're okay with these types of diagrams, so please explain why. I want to hear from you all on this.

nOt tO sCAlE,
939

Race Car Math

If you've looked at any of Dan Meyer's Algebra or Geometry curricula on his blog, you'll notice he has "Race Car Math" throughout many of his Keynote slides. Since I couldn't put two and two together on this one nor find anything on his blog explaining it, I simply asked him.

My loving wife bought my son and me an RC Ferrari car for Christmas 2011 (featured in the 3 Act lesson Ferrari Ride), but I figured I'd invest a few bucks in a classroom RC car for Mr. Stadel's room. I made my way over to Toys "R" Us and spent less than $15 on this bad boy. The remote is about the size of a crayon box and the car is about the size of a cantaloupe. It doesn't go crazy fast. It's just the right size and speed for a middle school student, boy or girl. This might be one of the best $15 I've ever spent.

This week, we spent Wednesday reviewing linear systems in algebra and quadrilaterals in geometry. We have reviewed with Math Basketball numerous times this year and the ground rules are very similar. Check out Dan's Math Basketball directions if you need some guidance. Here's how I roll in my class. I toss a slide up with the following information. *The slide for my students is less text-heavy.

1. Work individually in your notebook (unless I announce "GROUP ANSWER" meaning students work with their group/table on their giant whiteboard).
2. Show all work.
3. Talking = DQ  (*talking during "group answer" is allowed)
4. One person stands with answer (all members of a group must stand before standing again).
5. 10 seconds with car:
1. Big box = 1 point
2. Medium box = 2 points
3. Small box = 3 points

When students are done solving a question you've thrown up on the board and most (if not all) groups have a representative standing, I usually call on the last person that stands up. They explain and/or give their answer. If any other person agrees with the answer, they sit down. I've already been circulating the room checking student work, so mentally I have a decent idea who has the correct work (answer) or not. If anyone is still standing, that means they disagree and have a different answer. I repeat this until every student sits down. If all groups have the same correct answer, I announce that. If there's one different answer, I (for time reasons) will demonstrate the correct solution while students watch in suspense to see who's correct.

Whoever stood and got the answer correct comes to the front of the room to represent their group in driving the car. If a person got it wrong, they are to stay at their desk and study the board so they can write down the correct solution or talk with someone around them for the correct solution. Since students must drive the car along an L-shaped path, they can follow it to the finish line. Here's what's at the finish line.

Students can drive the car into the largest box worth 1 point, or two other boxes with narrower openings worth two and three points. The 3-point box is the narrowest. In order for the team to get their points, they must enter the box (cross the plane) with the two FRONT tires before the end of 10 seconds. I count down. Ready. Set. GO!

We had a couple of groups somehow get two tires on the same side of the car in the box, but it didn't count. Set up your own rules. Whatever they are, stick to them. Many kids said they liked this better than math basketball. I can't blame them. You should see some of their shooting form. On second thought, you might not want to see their basketball form when shooting a nerf basketball. Scary!

My favorite exchange came from Chase in geometry who scored three points for his team with ease.

Student 1: "Chase, you're really good at that."

Chase: "Yea, I'm part of an RC car club."

Student 2: "Really?"

Chase: (sarcastically) "Yes, after school I practice driving RC cars."

Student 3: "Really Chase? Wow! Do you really?"

Chase: "Yes, I'm part of an RC car club." and sat down.

Chase remained straight-faced the entire exchange. Hilarious! I'm not sure if some students were still convinced he was part of an RC club, but he's not. Since this was my first time with Race Car Math, I'm happy how I kept fine-tuning it throughout the day to make it more efficient and student-friendly. For instance, with larger classes I said we would solve two questions first before racing the car. If they got both questions correct, their team would simply double the points of the box their car entered. If a team only got one question correct, they would get the box's points at face-value. This also allowed students to send up who they thought could best drive the RC car. For round two, that person could not drive again.

I found that the classroom dynamic and energy to be better when I did more "group answer" questions and students collaborated on their giant whiteboards. It's a win-win. They get to stand up, talk to each other, and collaborate just like any other day in class. Plus, I get to listen to them problem-solve, argue, agree, and cheer each other on.

*[Update] Here's an idea for the to-do list: Another way to play is have students accumulate correct answers for a sequence of approximately three questions. Each group earns 10 seconds with the car for every correct answer. Set the boxes up like goals on a soccer field, maybe 15 feet apart. If the group got three questions correct, they have 30 seconds to drive the car between boxes to score as many points as possible. If you test this one out before me, let me know how it goes.

Ready-Set-Go!
411

Trashketball (2013 Pi Day task)

It all started with an episode of Suits on USA Network from January 31, 2013 (episode 213: Zane vs. Zane) where the opening scene has the two main characters (Harvey and Mike) playing a round of H-O-R-S-E trashketball in Harvey's office.  I jotted this one down on my digital "task ideas" list and knew it might have some potential later this year in Geometry. Here's Act 1:

Dan Meyer has thrown us some wonderful updates on 101qs.com. Head over to the Trashketball task where you will get all the goods when you sign in:
Act 1: video to wonder and notice about
Act 2: teacher notes, and visual data/information to help solve the task
Act 3: visual confirmation of the practical answer
Sequel: additional tasks to explore (especially for early finishers) and teacher notes

I was going to chip away at this task until I realized Pi Day was coming up. Needless to say, I started working a little quicker. Ironically, in calculating the answer to the task, Pi can actually be divided by itself or "cancelled." I grabbed (bought, not shoplifted) two trashcans from Bed Bath & Beyond. I found the exact trashcan from Suits. Woohoo!!!! That circular truncated cone trashcan is so dreamy and transparent. I also found a cylindrical trashcan for my Geometry class. As you can see from Act 1, it's not transparent, but it'll get the job done. Measuring each dimension of the can was simple. Measuring the diameter of the trashketballs is a different story. I'm open to suggestions here. You'll find this in the "Teacher Notes"

How do you find the diameter of a trashketball? Have your students come up with ideas. Test those ideas. Make conjectures.

I crumpled up 8.5"x11" paper and made it as compact as possible. I took a handful of trashketballs and put them down on a ruler to get a rough mental mean of the diameters. Then I traced the best-fitting circle to measure the best-fitting diameter of each trashketball. I took the mean of these five diameters.

An extension to the task would be to explore the difference one-tenth the radius makes in your calculated answer.

Seriously, I'm open to ideas. I quickly discovered that trashketballs are like snowflakes: no two are the same. However, I really started to perfect the form and process of making a trashketball. I'll admit, there's some buy-in with the trashketballs being perfect spheres. I'm okay with that. So maybe spend some time with your students perfecting the trashketball. Anyway, leave some ideas about measuring the diameter of the trashketballs in the comments, won't ya?

I'm looking forward to this task. My students occasionally play trashketball in my class with their scratch paper or class handouts (not necessarily mine) contributing to their idea of going paperless. I see this happening a lot on Thursday. Happy Pi Day!

Next up! The circular truncated cone trashcan. I'll start chipping away at having enough trashketballs for the circular truncated cone. Thanks in advance to the following people for helping with the volume of the circular truncated cone trashcan:
@mjfenton, @absvalteaching, @MaryBourassa, and @RobertKaplinsky.

Swish,
1140

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

Wooden Balance Game Pt. I

Let's play a game! Actually, you're welcome to invite your students to join in the fun here as well. Here's what you do:

1. Watch the video below.
2. Check out the specs.
3. Submit your order.

1. Video:

2. Wooden Solids and specs:

Make estimates of the dimensions.

What do you notice? What do you wonder?

3. Submit:  goo.gl/naDhr

Good luck! I'll tally your submissions for the week and stack the top configuration.

Balance,
327

Quotes of the Week [QOTW]

Have your students said something that completely moved you?
Was it insightful?
Was it relative?
Was it an epiphany?
Was it a proclamation?
Ok, let's not get carried away.

I hope you know what I'm talking about. Those comments become even more powerful when students see you acknowledge them and they didn't even think you were paying attention. I'm talking about those insightful things students say while they're collaborating with their peers, discussing solutions, or completing tasks. They blurt out something that catches you off guard (in a good way). The first semester has come to a close and I'm reflecting on student quotes. Quotes of the week: QOTW.

My students have said some great stuff and I was lucky enough to start telling myself to capture it on our front whiteboard. Why are there so many opportunities to hear what they say? Because we do a lot of group work and collaboration so they're bound to say something sensational. It's not about me. It's about them. They don't think I'm listening, but I am.

There's a section now carved out on my whiteboard for student quotes. It happened out of happenstance. This wasn't planned. I didn't find this idea somewhere on the wild internet (although it'd be cool if someone started a site for student quotes). A couple of students said something toward the beginning of the year and I wrote it on the board to share with all my classes throughout the day. They went nuts. Students were quoting the quote. I snapped a picture of it to make room for the next big quote and away we went. I'd like to share some of my favorites with you as I shared them with my students today.

"There has to be an easier way!" This is the one that started it all! In response to solving a weekly PS (Lucky 7’s) given to me by Fawn Nguyen, a group of students was filling their pages with numbers as they worked through exponential rules. Shawn continued the pattern for a long time on his paper, badly wanting to figure out the nth term in the pattern, lifted his head and let out this gem. The rest is history.

"Do it really neat so no one writes any bad stuff." After getting our new whiteboards and whiteboarding for a few days, students walked the room dishing out some harsh criticism to each other and their work. After addressing this criticism with them, students realized the importance of keeping their work clean, organized, and neat. Before beginning their task, Will verbalized his desire to be neat as to motivate his group. Good idea!

"We're actually learning." Yes, girls we’re actually learning. That’s because you’re actually thinking on your own while exploring math and not being told some procedure to regurgitate back to me. This was the result of my geometry class exploring parallel and perpendicular lines in a coordinate plane. These two girls were struggling for a day or two without any intervention from me and on the third day they had their shining moment. 

"That's upsetting me!" A quote is only as good as the context that goes with it. If you look at this quote, it could be your typical math student after doing the typical math question, resulting in typical frustration. However, Elle was working with her group on my Transversals, Tape, and Stickies task where they were given limited clues and had to identify twelve angles created by three intersecting lines. The bell rang and as she was heading back to her desk, let this one rip. She wanted resolution and was upset she didn't complete her task before leaving for the day. She came in the following day and conquered it with her group! Tenacious!

"Is that the opposite of PEMDAS?" In solving equations using inverse operations, James asks if the procedure is basically the opposite of PEMDAS (order of operations). Why, yes James it is. This was an "a-ha" moment for him. I couldn’t let this one escape.

"I plugged mine in. It worked! It's ALIVE!" You know those stories where someone says, "You had to be there." This is one of those stories. Elijah was checking his answer to an algebraic equation. Sure he could've just got a number for his answer and stopped, but he didn't. This is Elijah plugging in and verifying that his answer is the only solution. His excitement that the solution worked is hard to capture with an EXPO marker, but he took on the persona of a mad scientist, a la Frankenstein. I didn't write it on the board, but his "It's ALIVE!" was followed by "MWOOHAHAHA!" I love it!

"That doesn't make any sense." Another quote that could be any math student at any time. We've all been there. We've all heard this before, but what's the story here? Sierra said this after doing her calculations for our Stacking Cups task. She received some weird number of cups to stack as tall as Mr. Stadel. She immediately points out to her group that it doesn't make any sense. I love how students might be getting numbers, but they're checking those numbers for reasonableness before applying them. Back to the drawing board she went.

"We're demanding more information." The classic case of eating your own words. This past week we were exploring both Fawn Nguyen's and Dan Meyer's infamous Graphing Stories. All my classes began asking for more information as we progressed through Dan's videos. I continually praised them for demanding more information. We were working on the MARS lesson "Interpreting Distance-Time Graphs" I stole from Fawn and the students wanted more information as they wrote a story for Tom. I repeatedly refused any help by saying, "no" or "be creative" or "use the information on the page." Sean quickly replied, "But, Mr. Stadel we're demanding more information." You got me Sean! He practically jumped out of his seat when he saw me writing his quote on the board. FUN, right?

Expect a blooper's reel when doing this. you'll have the clowns that want to force something or think they're saying something sensational. That's my George. "I like colors." I don't think so George. You can stop now.

I can't make this up. I'm not paying my students to say this stuff. It's not contrived. It's natural. It's authentic. This board reminds my students that I'm listening. The more I can capture these and write these up, I believe the safer it is for my students to take risks, share their thoughts, and explore math. It's all them, but remember every quote has a story. So keep listening!

QOTW,
909

Tip Jar

Vimeo has a feature where their users can add a "Tip Jar" option to a video. Yes, viewers and users on Vimeo can monetarily tip other users to show their appreciation for a video. Today, I activated that on most of my videos.

I started typing this blog giving some examples in life where I gladly tip, reluctantly tip, and refuse to tip specific services in life. I changed my mind as I'm not here to cause waves, offend people, or get into an argument about tipping when the decision to tip a service is completely subjective.  Bottom line: I gladly tip others for their services when the service was completed in an efficient, professional, and satisfactory way, the service was something I can't do on my own, or they're sharing some passionate artistic talent that touched my heart in a compelling way.

I'm not putting my lessons, videos, or pictures on Teachers Pay Teachers. I don't work for a textbook publisher who pays me to do this stuff. I'm not selling this stuff to teachers, schools, or curriculum writers for profit. I've simply put it out there (on that wild internet) for others (teachers) to use, enjoy, and most importantly use with their students for learning math. Please don't think of this as a tip jar at a restaurant or specialty food service. Think of my Tip Jar as that open guitar case in front of the person pouring their heart out on the street giving you a few seconds of raw talent to brighten your day. I might sing out of key a few times, forget the right chord, or might have a string out of tune, but I'm sharing this stuff because I'm passionate about it, love doing it, and enjoy seeing other students learn math. If you feel obliged to tip, my gratitude will be eternal. If you don't tip, I still love you for taking the time to check out my stuff and possibly use with your students. That's the best tip you could give me!

TJ,
540

Styrofoam Cups

Tuesday, I was on my way to BTSA and my subconscious screamed something at me. Find Dan Meyer's Stacking Cup lesson. Seriously, go read his post right now. I hadn't read this post for over a year now and I had to get my lessons ready for the next couple of days as my Algebra classes finished up Pixel Pattern. I was on the road dreading the idea of sitting through a couple hours of BTSA, so I asked Dan if he had the link to his lesson since it wasn't in my bookmarks (that was silly of me) and he came through like a champ! Seriously, check out his post. I'm promoting his blog post more than anything further I have to say here.

First, by all means, spend about $10 and do the lesson with your kiddos. This is one of those 3 Act lessons that just screams "hands-on" activity with your kids. It's tough to capture the overall excitement and energy with a video. If you can't do the "hands on" with your kids or you want to be environmentally friendly, here's my version of the Styrofoam Cup 3 Act lesson: a cheap backup.

It felt most natural to stage this so the cups stacked to the top of the door frame. Even then, I'm not convinced my Act 1 screams the question I'm looking for, "How many cups will stack to the top of the door frame?"

Enough about me and the video, to my classroom with the students. Dan's got a great script for you to follow, so do it! One of my classes was actually able to finish writing their rules before the bell on Friday so we had time to actually stack cups. Check out their rules and predictions for stacking cups to my height.

We started stacking with the lowest number and went from there. The kids went bonkers. Each group thought they were the best, but knew that they all couldn't be correct. When we revisit the lesson this next week, we'll be discussing where groups went wrong in order to learn from those mistakes. Watch Styrofoam Cups - Act 3 Stadel to find out who won. But I recommend you watch the door task also.

Styrofoamed out,
813

Best Halves [Square]

A few months ago Dan Meyer reached out to Timon Piccini, Chris Robinson, Nathan Kraft and me to participate in what would eventually become his Best Midpoint, Best Square, Best Triangle, and Best Circle series of 3 Act lessons. I was honored to be part of a stellar group and great lesson. I love the potential of these lessons and can't wait to use them with my geometry kiddos later this year. Currently Dan and Dave Major have kicked it up a notch with some great interactive play/learning for better best squares, also providing us with an interactive teacher's guide. Check it out: I nearly cried tears of joy upon reading their two posts: Dan and Dave.

Recently, I've had conversations with Fawn Nguyen about fractions and although fractions aren't the spotlight of my Algebra and Geometry curriculum, I'm still fascinated by them and in turn want to help students build their number sense or spatial reasoning. I had an idea to extend Dan's Best series into the realm of fractions and emailed him for his blessing, hoping I'd do it justice. Here's what I came up with so far:

You might notice it closely resembles Dan's format with very few stylistic differences. "If it ain't broke, don't fix it." That's my motto here. I called on Dan and a few other comrades to make an appearance and compete in this first installment of Best Fractions. This first installment: "Who drew the best half?"

Thanks to Dan, Fawn, Sadie Estrella, and Shauna Hedgepeth for taking the time to contribute. They were great sports! I still don't know who drew the best half yet.

I see a lot of geometry potential here: area, perimeter, midpoints, distance, coordinates, polygons, etc. I'd love to target primary grades with this activity as well (not just secondary), finding an entry level that elementary kids are capable of exploring. I'm not too sure calculating the area of trapezoids would be appropriate for a 4th and 5th grade classroom, but I might be wrong.

I'm not pretending to nail this 3 Act lesson and I'd love some feedback on how you would apply this in your class or make it better. I'm still working on the Act 2 information and will gradually chip away at it over time.  I gathered enough information from the contestants to keep me busy for the next year. I plan to release other installments of Best Fractions, specifically the best half, third, fourth, and fifth of both a square and circle. Just imagine the fun with circles: area, sector area, arc length, degrees, percentages, and more. Stay tuned!

Test it out on your students in the meantime and give me some feedback. Click here for directions and handouts to use with your students.

Best,
420

Estimation 180 update & RSS

Head over to Estimation 180 and throw the blog in your RSS feed. I usually update the site once every week or two and the RSS feed will alert you of those updates. Don't worry, they're not daily and it's definitely not s-p-a-m, as I despise s-p-a-m.

Huge update of estimates today starting at Day 78 and going through Day 91 (over halfway done). Home Depot was just so fun.

*Can you spot something suspicious on Day 86?

Enjoy!
519

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

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.

Narrative:
"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.

Quesadilla,
405

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

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

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.

Balls,
1026

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?

Jam,
1101

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!"

WOAH!!!

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,

936

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:

Basketball Travel

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 Remind101.com 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.

CHEESE,
942

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 estimation180.com 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?

Rocky,
858