San Diego Conversions

I was in San Diego, California the past few days doing the whole San Diego Zoo and SeaWorld thing with the family. We had a great time, but that's not the point of the post. There were definitely a handful of opportunities to capture some math moments, but I've found it more important to contain myself (mathematically) when I'm with family and make the most of our time together. Here are the two things I captured and want to share.

Number 1: 
We were waiting to board the Wild Arctic Ride (virtual helicopter ride) at SeaWorld and watched this video. There were subtitles in Spanish for our spanish-speaking (reading) friends. However, they go along with the helicopter pilot.

Here's Act 1:

When I saw the the number behind the black box, I thought, "Is that right? Is 400 miles per hour really ### kilometers per hour?"
Are they correctly converting for our Spanish speaking friends? It turns out that 400 miles per hour is about 643.7 kilometers per hour.

Here's act 3:

What do you think? Should I keep the black box there? Should I delete it?
I feel this is one of those moments where I don't insert a black box and we simply ask students:
Is 400 miles per hour really 600 kilometers per hour?
I'm curious about students arguing about this one? or would they even care?
What difference would 40 kilometers per hour make?
Where do you stand, on any of it?

Number 2: 
The great thing about San Diego is there are tons of people from many different places of the world. San Diego has an international airport and many places of interest besides SeaWorld and the zoo to contribute to this melting pot. I loved listening to all the different languages being spoken throughout the day. Therefore, it didn't surprise me when I walked into the pool area for the first time on our trip and noticed a few interesting things. I couldn't help but think how wonderful it would be to use these in any math classroom, specifically Math 6. The first thing you see as you enter the pool area is the jacuzzi. I couldn't help but notice the depth:

Okay class, check this conversion. It ends up making sense and I appreciate the use of meters for pretty much everyone outside of the United States. Seriously, I simply have such a hard time understanding why the United States uses inches, feet, yards, miles, etc. I digress.

Here's the (very shallow) pool:

Let's look a little closer at the depth signs around the pool. The deepest part of the pool is 4 feet or 1.2 meters. Okay class, check this conversion. Looks pretty legit, right?

So, if you saw a depth sign with 3.5 feet, what would you put the meters conversion at? How would you order these pictures with your students? Which would you present first? second? third? or would you give them all to your students at the same time? Would you cover up one of the measurements (like feet) and only show them one measurement so they work on finding the conversion. Here's the 3.5 ft depth sign.

Okay, if you do the conversion, 3.5 feet is 1.0668 meters. Obviously, someone was following their rounding rules. A few questions pop into mind here:
Should we round up?
Would it be wiser to round to 1 meter?
How much of a difference does roughly 4 centimeters make?
Could they not use a slightly larger tile and put 1.07 meters?
These questions aren't the only questions, nor the most profound, but I'm still curious.

There's one more crazy thing about this pool I had to capture and share. How did they get away with this? 

Look closely. Inside the pool is a depth of 4 feet (1.1 meters). Outside the pool is a depth of 3.5 feet (1.1 meters). WHAT?!!! Now reflecting, I should have had my wife take a picture of me next to the sign to get the water level and measure how deep it actually is here. I don't know about you, but 6 inches is definitely more significant than the 4 centimeters we discussed earlier.
At what point does an error like this matter significantly enough to change it? 6 inches? 2 inches? 12 inches? and in what direction: shallower or deeper?

How would you use any of these images or video in your class to help facilitate discussions or arguments regarding conversions?

SD conversions,
906

A Few Updates

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

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

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

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

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

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

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

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

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

Updates,
243

SBAC on Steroids?

California is an SBAC (Smarter Balanced Assessment Consortium) state. This last week my school started the SBAC Field Tests and I was a Test Administrator for my 7th grade classes. Before I continue, let me post part of the Security Affidavit I had to sign.

That's right, I will not divulge the contents of the field test. However, I will first refer you to last year's post where I made a video comparing released CST questions and SBAC practice questions.  Here's a reminder (screen shot), comparing just two questions. 

This week, I felt like my students were looking at SBAC practice questions that were on steroids. Since I can't speak about the SBAC Field Test questions, I took my Deodorant 3 Act task and put what I think the SBAC steroid version might look like. I have nothing against SBAC. I tried to create a similar task that had rigor, complexity, and mathematical modeling.

First, my Deodorant task goes like this:

Act 1: How long will it take to use all of that deodorant?

Act 2: Data from the first 4 sticks. 

Act 3: The answer is still in the works. 

Sequel: How many sticks of deodorant would a person use in one lifetime?

Here's how I'd see this same task presented SBAC-on-steroids-style. 

I walked away this week, thinking our students need to do many things.

1. Read the story. 
2. Decode the text.
3. Understand the question.
4. Organize the data.
5. Retrieve and access the correct skill(s) or skill set.
6. Apply the necessary skills.
7. Perform the correct operations with the above skills.
8. Interpret their answer.
9. Explain (and articulate) their answer.

As a teacher of many ELD students, I can safely say that the following steps are already challenging; 1, 2, 3, 8, and 9. Don't get me wrong. I believe in literacy, but I wouldn't want language to be a barrier when assessing a student's mathematical abilities.

Hear this though: Students must make sense of the problem before they can use mathematical modeling to predict the answer. Then, they must articulate how they got their answer. I would consider this expectation the new norm.

I'm not done. I could totally see SBAC taking this deodorant task and creating an additional question that would complete my 3 Act. Check out this doozy.

We're looking for students to drag numbers to both axes, use a line of best fit, make a mathematical prediction, and explain everything again. The only thing I left out of this question was for students to write an equation for the line they draw. 

I have more to say about this, but that's enough for now. I'm already thinking about how to better prepare my students for these types of questions, which should be my next post. If you have any thoughts, please share. If you've made it this far, here's a preview of Act 3 for my deodorant task. Don't worry, I keep my shirt on!

Steroids,

1158

Explain that, please.

Recently, I've given a few teacher workshops/conferences and have had the luxury of reflecting on teacher moves as I facilitate a lesson with the attendees. One of the many things we talk about are teacher responses to students.

Me: Did anyone hear me say, "No. That's wrong. You're wrong. I don't like your answer."

Attendees: No.

Me: Right. Instead, you'll hear me say things like, "Can you explain what you did here? Explain that, please. I noticed you did [this] here, please share how you got [that]. I'm curious how you came up with that. Walk me through what you did."  

I tell teachers that I'm taking the emphasis away from right versus wrong answers and placing an interest on the student's thought process and problem-solving. I continue with teachers:

Me: By telling a student they're wrong, a student can have the tendency to shutdown [I make the sound effect of a machine shutting down, "BOOOOvvvvvvvv"]. By asking a student to explain things, it shows that I'm more interested in how they arrived at their answer. 

As teachers, we know a student can be told they're wrong and it's easy for them to give up. On the flip side, when we validate a kid by telling them they're right, the student can also shut down and never reach the higher levels of Depth of Knowledge.

Recently, a workshop attendee asked me how I respond to students who have nailed the answer to a 3 Act task. First, I have them explain their problem-solving plan to me. Second, I question any details that were unclear, encourage them to be more precise, or have them explain their units of measurement. Third, I ask them if they feel confident in their answer after explaining it to me. Fourth, I validate them by simply saying, "That makes sense to me."

I don't tell them they're correct. I treat them just like as if they got the answer wrong. If that doesn't satisfy them, I respond with, "We'll find out soon if you're correct, but that (their explanation and work) makes sense to me." At this point, I offer them an extension to the task. I'd like to talk more about this later, but usually the extension revolves around the students creating something with the new knowledge or skills they have just recently gained.

After all that, please add your favorite lines when questioning students to this Google doc. I think it's also helpful we create a list of lines we avoid using with students as they explore math.

Here are a few people with other stellar teacher moves/lines to support students.
Max Ray: 26 Questions You Can Ask Instead
Dan Meyer: You Don't Have To Be The Answer Key
David Cox: Creating A Culture Of Questions
Steve Leinwand: Accessible Mathematics

BOOOOvvvvvvvv,
645

Estimation 180 has Lessons!

Head over to Estimation 180 and you'll see this lovely new option in the menu bar.

LESSONS!

That's right! 

LESSONS!

I've added a "Lessons" page with many lessons I've created, sorting them by their CCSS. I'd like to thank Dan Meyer and Robert Kaplinsky for their friendly suggestions (nudging) to tag my lessons in an attempt to make it easier for other teachers to find and use. Plus, I'm tired of my lessons collecting digital dust and hope that teachers can find and use them.

I was honored to give a workshop for teachers in my district today. The workshop became the motivating factor for making this Lessons page. Right now, most of the lessons are 3 Act lessons that can be found at Dan's 101qs.com A few other lessons are ones I've blogged about. However, I have added two test pages at Estimation 180 where the entire lesson is available for teachers to use. Right now. At Estimation 180.

Pay close attention to my File Cabinet and Stacking Cups lesson PAGES!.

These two full-on lessons are ready for you and your students. You'll see all three acts, teacher notes, student work, student handout (if you like/need), and downloadable videos. Let me know if you have any thoughts, advice, or questions.

I hope this "Lessons" page is useful and/or better than that silly unorganized spreadsheet I've got lingering. You'll notice a few links are under construction, but many links deliver the goods. Check in often for updates.

LESSONS!
1023

P.S. Thanks to Fawn, Nathan, Robert, and Eric for your feedback.

Your Eyes Are Amazing

This Centrum television commercial caught my ear for a few reasons. I tracked it down on the Internet tonight and edited it for Act 1. You can find the entire lesson here at 101qs.com. It's a quick little lesson for Math 6 (6.RP.3d).

Act 1:

Question: How many football fields is 10 miles?

Act 2:
I'm not giving much information for Act 2 as I'm leaving this part of the mathematical modeling process up to the teachers and the students (mainly students). I think there's an essential part to the classroom discussion and I hint at it with the following questions (if necessary) left in the teacher notes:

• Ask students, "What information would be helpful here?"
• Ask students, "How are football fields measured and with what unit of measurement?"
• Allow your students to decide the length of a football field.

I'd like you to do the math right now. Go ahead. I'll wait. It won't take you long.

10 miles. How many football fields is that?

Act 3:

Wait!
Timeout!
Is this commercial's math wrong???

Should it be 176 football fields or 146 football fields?

What did you use as your football field length? Did you use 100 yards? Did you account for the end-zones being 10 yards each, making the total length of the football field 120 yards?

On a related note, I'm a little surprised the Centrum didn't use 100 yards so they could claim 176 football fields for a more dramatical pitch in their commercial. I also think it's fun to talk about what it would take for human eyes to actually see that candle 10 miles away. Darkety-dark-dark probably. No light pollution. No obstructions. Maybe a desert? No bright moon (which the commercial includes for some weird reason).

I'll be using this with my sixth graders this year when we get to conversions. It's a fun little task. Let me know if you have anything to add.

Candle Eyes,
1059

Snail's Pace

Last post, I shared a lesson (Woody's Raise) that included both Act 1 and Act 3. I asked you all to collaborate and design Act 2. Many of you came through like champs in the comments.
THANK YOU!

For this post, I only have an Act 1, leaving Act 2 even more open-ended. I'll admit, I only have Act 1 because I haven't invested the time necessary for Act 2 and Act 3. Here's my current Act 1.

I thought of this lesson many months ago while out walking in the morning, but wanted to capture it on video... no joke. So until that time actually comes along, I'll give you what I envisioned for Act 1, the video version. We start with Bill Conti's Gonna Fly Now (Theme from Rocky) as we take a couple close-up shots of the snail. The camera pans out to a bird's eye view of the snail starting at one side of the sidewalk, letting time elapse for about 15-20 seconds.

Back to the picture of the snail who has an increasingly long road ahead of him. I notice that he isn't taking the shortest path to the other side. I notice that there aren't any other snails to avoid. I notice the sidewalk is wet. I wonder what his path will be. Will his path be linear? curved? circular? other? I wonder what his rate will be. I wonder what the dimensions of the sidewalk are. I wonder if the Pythagorean Theorem could be used here. What do you wonder?

Head over to Dan Meyer's 101qs.com and enter a question (or skip it) so you can see my Teacher Notes for Act 2. You might need to log in. Thanks to Ignacio Mancera for linking a site with Speed of Animals. This will help assist our Act 2 adventure.

Here's what I have so far if you can't get into 101qs.

What initial conversation(s) would you have with students?
How would you have students work with Act 2 information (dimensions, rate of snail)?
Is this a waste of time?
Should we (I) shelf this idea for now? (or even toss it in the trash can?)

Slowly,
333

Woody's Raise

We decided to get Netflix recently and I was excited to see that Cheers episodes are available. I occasionally put an episode on in the background while I get work done. I came across this episode that literally snuck in some math (money, raises, time, rate) right before the end of the episode. Sam Malone, the owner of the bar in the tie (played by Ted Danson), is talking with Woody Boyd, a bartender (played by Woody Harrelson), about a raise. Roll Act 1:

After consulting with my man, Nathan Kraft, I bleeped out a part of Woody's last line. The two of us discussed the tendency a bleep can have in implying some profanity was removed. So if this lesson goes horribly wrong, blame Nathan! All those toothpicks finally caught up with him. Here's how the exchange goes between Sam and Woody:

Sam: We were talking about your 50 dollar a month raise.

Woody: Sam, it was a hundred a month.

Sam is caught for trying to pull a fast one on Woody. Woody appears to let it slide, but something occurred to Woody. He turns to Sam and the exchange continues:

Woody: I think a hundred a month is too steep. I'll settle for [BLEEP] a week. 

Sam (without blinking): You got it!

I anticipate students noticing that the amount was bleeped out and wondering what was bleeped. I anticipate students not sure if Woody said, "[BLEEP] a week" or something inaudible? I anticipate students noticing that the studio crowd laughs while wondering if Sam was just made a fool by Woody. I would love to first have a leisurely conversation with students about who they think just got the better deal in this exchange, Sam or Woody? Or was there even a better deal to be had? If you've ever watched an episode of Cheers, you know that neither character has a strong IQ. If anything, Woody is portrayed as a real naive, gullible, and takes-you-at-face-value type of character. Sam is about a handful of points above Woody. So what about Act 2 after you take some guesses from the class on who just got the better deal from this exchange?

This might be the first 3 Act lesson in which I don't have any additional information for Act 2. In all fairness, this might not fit my previous rant on measurable acts, but I think the 8 Standards for Mathematical Practice are rubbing off on me (in a good way), especially Practice 4: Model with Mathematics.

I posted the Woody's Raise lesson on 101qs.com with very little in Act 2 because I'd love to know where the teacher would take this with his/her class. This type of teacher discretion can't be packaged in an online portal or catalog of video instruction. Here's what I threw out there for Act 2 (the first edition):

At what "raise" amount per week would Woody "settle" for the:

1. Better deal
2. Equivalent deal
3. Worse deal

I have many questions when thinking about Act 2. Here's a few:
Over time, when does Sam or Woody begin to benefit or suffer from this deal, compared to the $100 raise per month?
Do all months have exactly four weeks? Does that matter or should we use 52 weeks in a year?
How would you anticipate students representing Woody's better deal versus the worse deal?
What would this look like graphically?
What would this look like organized in a table?
What equations could you anticipate students writing? If any?
How does this deal apply to Woody's hourly rate?
In what classroom could you talk about the tips Woody might make? Remember this takes place in a bar. Middle school students? High school students? College? A workshop with teachers? I think there's a lot of fun to be had with this video clip. Let's Roll Act 3 and see what Woody would "settle" for instead of the $100 a month raise:

I'm posting this lesson because I'm thinking out loud. More importantly, I'm curious what you would do in between Act 1 and Act 3 with your students. How would it be different in an elementary classroom? Middle school classroom? High school classroom? Teacher workshop? What would your Act 2 be? Where would you take this lesson with your students? I believe this is a multi-dimensional lesson that can take on some great mathematics. Bleeping out that weekly rate in Act 1 really opens up Act 2 for some rich mathematical discussions and modeling. Toss your Act 2 in the comments. Thanks!

Cheers,
1026

Back to School Ignite Talk

Man, I love a good Ignite talk.
5 minutes.  15 seconds per slide.  20 slides.
Concise.  Succinct.  Compelling.

Why not do my own version of an Ignite talk at Back to School Night next year? I get 10 minutes with parents and would love to change it up a little this coming year. Trust me, after surviving last year, I think the parents deserve a better, improved, and more reassuring version of Mr. Stadel. I'll explain that last sentence in some upcoming blog posts that I'll use to debrief about the 2012-2013 school year. If you're not sure what an Ignite talk is, let me introduce you to my man, Steve Leinwand.

If you like that, check out more Ignite talks by Annie Fetter, Dan Meyer, Max Ray, and Phil Daro. These are my go-to talks when I need a math pick-me-up. Do the math, that will be a little over 20 minutes well spent, being inspired by some key people in our math community. Seriously, check out those four talks.

I'm brainstorming in this space, so feel free to share some input please. At Back to School Night, I'll start by giving a brief 30-60 second introduction of what an Ignite talk is and how they work. I'll give an Ignite talk for 5 minutes, covering any of the following things:

• Standards Based Grading (SBG)
• Noticing and Wondering
• Common Core State Standards (CCSS)
• 8 Standards for Mathematical Practice (8 MPs)
• Problem Solving
• Homework (or No Homework)
• Find my Mistake
• High School Placement Tests
• Desmos
• A healthy balance of mathematical application with procedural and conceptual understanding
• Problems of the Week (PoWs)
• Quotes of the Week (QOTW)
• 3 Act lessons
• Reassessments
• Estimation (Number Sense)
• Tangram Tuesdays
• Whiteboarding

This leaves approximately 4 minutes for parents to ask questions or something else... Have any suggestions for those last 240 seconds?

Who's with me? Does anyone else want to do a Back to School Ignite talk? There's already been some interest generated on Twitter and I started a Back to School Ignite list. Shout at me if you're in. Or is this a really foolish idea? Seth Leavitt, my new online colleague and EnCoMPASS Fellow asked if I'll post it online. I don't see why not. Maybe we can create a space for Back to School Ignite talks.

*UPDATE: Each item listed above does not correspond to its own slide. I simply listed ideas that could possibly work their way into the presentation. Some support each other. For example, when talking about the importance of problem solving, I would mention resources such as 3 Act lessons and The Math Forum's PoWs. Feel free to add to or subtract from the list.

Ignite,
930

More Tangrams Please!

This week in Geometry, we did the 3 Act lesson Hedge Trimmer. I'll debrief about that another time. Students needed to find the area of some isosceles trapezoids along the way and I didn't give them access to the area formula for trapezoids. Instead they needed to be resourceful and figure it out on their own. Well, that didn't go too well at first [cue the whining]. Many students had trouble breaking the trapezoid into 3 polygons: a rectangle and two triangles. Their warm-up the next day was to play around with tangrams for the first 5-10 minutes of class.

Me: Use all seven pieces to make any one of the following polygons. Do your best!

I drew a square, rectangle, trapezoid, parallelogram, triangle, and circle. I'm just kidding about the circle. However, I should have drawn one. That's funny. My 8th grade students were terrible at this. I use "terrible" with all the love in the world, knowing this is a learning experience for them.

Me: Have you guys ever messed around with tangrams?

Class: No!

Me: WHAT!!!! Are you guys serious? No one has ever let you mess around with tangrams before? Well, I'm glad we're doing it now. You guys need this. Seriously? You guys have never messed around with tangrams.

Class: Nope.

Me: Okay, well keep trying. [as I began scraping my jaw off the floor]

My request to you all: MORE TANGRAMS PLEASE!

Especially elementary teachers, more tangrams please. Have your students mess around with them. Sure you can download some app onto your tablet or find a web-based site to simulate tangrams, but please do your best to get actual tangrams into the hands of your students. Math formulas come and go for math students. However, if they can visually break apart polygons into more recognizable polygons such as rectangles and triangles, I believe their mathematical proficiency greatly increases. My goal is to get these 8th graders to play around with Tangrams once a week for the rest of the year. At least one of my students was eventually able to put together a trapezoid (top left), which quickly turned into a parallelogram, which quickly turned into a rectangle.

Me: How'd those other shapes come so quickly?

Sean: I just moved this one larger triangle to different spots.

I took a picture of his first configuration so I could share it with the class. I figured I'd give the class a chance to redeem themselves and copy his rectangle configuration.

More tangrams please! 

Repeat after me:

Thanks for listening.

Tangrams,
1104


BTW: Cheat sheet for displaying student work immediately:

1. Sign up for Dropbox.
2. Have the Dropbox app on your phone.
3. Take picture(s) of student work.
4. Allow the app to upload your camera photos.
5. Sync your computer with Dropbox.
6. The pictures arrive on your computer in seconds.

Wablammo!

Capturing Time (musically)

Recently, I had the idea to do a theme of "song lengths" over at Estimation 180. Inspired by a recent comment from Fawn, I chose Santana's Oye Como Va. At first, I opened up iTunes and took a screen shot of the music player.  I threw in an album cover and edited it to look like this, asking "How long is Santana's Oye Como Va?":

I can get away with directly asking the question at Estimation 180. How would you make your estimate? I'd make my estimate based on the time played so far (1:26) and the location of the playhead in the timeline. I absolutely love that students have to use time here, specifically 60 seconds in a minute. Furthermore, I'm hoping students use some type of spatial reasoning with the timeline, either as a fraction, percentage, proportion, or something else. But that's it. Can we go anywhere else with this? This task feels constrained. This doesn't capture the medium of music correctly. There's got to be more, right?

The more I thought about it, I was curious of better ways (or the best way) to capture time and music. Let me rephrase that. If I were going for a more perplexing approach and wanted to create a 3 Act task to share at 101qs.com, how would I go about doing that? I remembered that I own the djay app and experimented with a really lengthy Jethro Tull song titled, Thick As A Brick. This is where I need your help. I'd appreciate you checking out Act 1 and letting me know the first question that comes to mind. Or watch it here and leave a comment/question in the comments.

Based on some initial questions, I'm thinking of revising Act 1 where the virtual record player looks more like this. (notice the record?)

The virtual record player opens up many possibilities with this task. There's a white tape marker on the record for precise tracking when playing the track. I feel there's a lot more math opportunities here, but at the same time it feels a little contrived?
Am I over-thinking this?
What do you see here?
What are your thoughts?
I need some help. Thanks in advance.

Spin it,
339

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

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

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