Tacos For (almost) Everyone

Do you remember when I blogged about the Ultimate Task for Vertical Planning: Stacking Cups? If not, feel free to check it out at your convenience. I've got another task for you that can be used at multiple grade levels: Dan Meyer's Taco Cart.

When asking:

Who will reach the taco cart first?

there are so many mathematical opportunities awaiting us. Here are a few:

Math 6 (maybe Math 7)
Pass out this handout during Act 2 and tell students you will only give them one dimension. Choose wisely.

Read more about this great technique on Fawn's blog post about Mr. Meyer's Taco Cart.
It simply is brilliant. Students are measuring the dimensions (distances) on the paper and using proportional reasoning to figure out the real life distances. I recommend students use centimeters when measuring the dimensions of the triangle on the handout. I really enjoy this technique.

Math 8
If you're a math teacher and you see the picture Dan provided for Act 2, your intuition will most likely steer you in the direction of the Pythagorean Theorem. Go for it!

Geometry (HS)
Let's say you have already used Taco Cart during the year to apply the Pythagorean Theorem or Distance Formula (Desmos). How about we extend the mathematics and look for more right triangle relationships in Taco Cart. I noticed that the hypotenuse is about twice the length of the shorter leg. Let me connect that to the context of the story: Ben's distance is about twice the distance Dan travels in sand. That's right, Dan gave us a 30-60-90 right triangle. Pro skills there, Dan.
*I'm not saying the 30-60-90 relationship is the most intuitive, but we'd be helping students make connections with previous learning. 

Algebra and Beyond
As you move into the sequels provided on the website, there's a lot of higher level math. Depending on the question, the problem-solving is fun. I worked with a high school group of math teachers who found it extremely challenging to solve the question:

What path to the taco cart would take the least amount of time?

Overall, this is such a fun and meaningful task. Dan has given us a treat! Today, my students did such a great job arguing, sharing theories, identifying variables, and using their intuition even before I unveiled any information from Act 2. It was awesome! I'm avoiding the use of the Pythagorean Theorem this round. I went Fawn-style by giving students only one dimension on their Act 2 handout. So good!

Tacos por favor,
942

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

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

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

Cent-ed Whiffle Balls

Want to know how to make Cent-ed Whiffle Balls? Here are the ingredients:

1. Bookmark this picture at 101qs.com
2. Do coin estimation with your students.
3. Go to the bank and withdraw a few dollars worth of pennies.
4. Get some Gorilla Glue.
5. Take whiffle balls from your son's collection (source of whiffle balls may vary). 

Show your students the picture from Step 1. Do the estimation task from Step 2. Show them the following slide! 

*If you don't know yet, we covered surface area of spheres in Geometry this week.

We just completed Nathan Kraft's Soccer Ball 3 Act lesson which was spectacular for volume of a sphere! (Nathan, post act 2 and act 3 for everyone NOW!) The Cent-ed Whiffle Ball is a simple task. You know you have a keeper when you hear the following come out of students:

"This is fun!"

"This is stressful!" 

Students first started this task by using a tape measure to find the circumference of their whiffle ball. Thankfully, I've finally won them over on using centimeters. Shooosh! Don't tell those people who like inches. Students then used the circumference to find the radius of the whiffle ball. Well done, kiddos! Next, students either used a tape measure or ruler to get the circumference or diameter of a penny, respectively. Ultimately, they wanted the radius of the penny. Then they got stuck.

"Mr. Stadel, what's the surface area formula for a sphere?"

Sweet! They want it. They need it. They crave it. I didn't write it on the board or give it to them on a handout. Here's where I wish I had an additional hour with these kids to explore this formula. Instead, I had a demonstration ready for them. I took our Nerf basketball we use for Math Basketball Review. I told students that I measured the circumference of the ball in order to construct a circle that has the same circumference. Before class, I cut out a second congruent circle and cut it into eight congruent sectors. I then played this game with students:

Me: How many of these circles will it take to cover the entire ball?

Student 1: Three

Student 2: Four 

Student 3: Three and a half

Student 4: Five

Me: Let's find out!

I pinned the sectors onto the Nerf ball with thumbtacks, covering a fourth of the ball.

Student 2: I was right! It's four!

Student 5: Cool!

BOOM! We had our formula: 4 areas of a circle with the same circumference as the sphere. Simply put: 4πr^2. Most groups immediately found the surface area of the whiffle ball and penny, dividing the two to get something like 88 pennies. One group of girls immediately came up to me and asked for their pennies. Before giving students their pennies, I drilled each group, asking them to explain their number and show their work.

Me: Now girls, if we've learned anything in here this year, we know that our answer on paper isn't always the actual answer. Have you accounted for everything? Look at this picture again (from the ingredients). Did you account for everything?

Devon: There's spaces between the pennies. 

Me: Yup. Why don't you go back and mathematically show me a different number of pennies, now accounting for those spaces.

I had this conversation with each group, or some variation of it. This is where the magic begins. Remember, students were allowed a maximum of six pennies. Here's what they came up with. I'll let the pictures do the talking:

 

 Chris asked for a compass to draw a circle having the same circumference as the sphere.

Elle found the area of a rectangle formed by six pennies. She then subtracted the area of six pennies to get the area of the space created by six pennies. 

Noelle used a parallelogram of pennies to execute the same idea as Elle.

Groups started coming back with revised numbers. They quietly told me their amount. Remember, there's a CASH PRIZE on the line! Im still not sure what that is yet. Groups came in with the following amount of pennies to cover their whiffle ball:
70 pennies
65 pennies
69 pennies
62 pennies

Good luck to them all. They are almost done gluing their pennies. Two groups are done and the other two are close. Here's a few pics!

This group used 71 pennies versus a theoretical 69.

I highly suggest you make Cent-ed Whiffle Balls in class! If not, here are the dimensions:

Whiffle Ball circumference: 28 centimeters
Penny diameter: 1.9 centimeters

Cent-ed,
1050

P.S. Help me make this task better.

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

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

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,
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Be the 'student' at 101qs.com

*Disclaimer: Im not a professional cinematographer! I haven't taken any film lessons! I consider myself a novice with film editing. However, I'm passionate. I want to improve my craft with film almost as much as improving my craft of teaching!

Dan Meyer was kind enough to invite me to the beta testing of 101qs.com after seeing my Fake Money - Act 1.

I was both flattered an honored that he dug my exponential growth video and wanted to include me in the beta testing before his site went live. One of the best pieces of advice Dan gave me was, "Buy yourself a tripod for Christmas, Andrew." His feedback from Sand Vase - Act 1. I totally agreed with him and didn't wait for Santa. A tripod makes the experience much easier on the viewer. Plus, no matter how perplexing you might think your tire rolling down a hill is, you run the risk of losing your audience from a shaky camera or poor camera work. (Hits forehead with palm, D'oh)

Look, I've read many blogs and comments that challenge Dan's objective with 101qs, the perplexity rating, the lack of comments/feedback, the initial question versus the discussion, and on and on. My objective here is not to rehash any of that. Hands down! It's a solid site and beneficial to us teachers! Embrace its ingenuity! My goal is to offer some observations and advice that might contribute to making the viewing experience even better for you and your students. Here's how:

1. Have measurable acts.
2. Be the 'student' during both the staging and viewing portions.
3. Have fun!

Make sure it's measurable:
I've thrown some pics up on 101qs.com, but they were flops because it's not measurable or epic. I can discuss it with my class, but that's it. If we can't measure it, we're done. Maybe we can create a small scale project, but that could detract from the amazement of the initial media. John Golden's Largest Land Vehicle in the World pic is epic. But how do you measure it? I don't have a giant earth mutating blade in my backyard. Do you? However, one of my all-time favs is Nathan Kraft's Tuba Echo. There are definitely some measurable parts here. Plus, it's really simple!

Be the 'student':
Before pressing record or taking a plethora of pictures. Before sitting down to create, to plan, or to stage your first act, stop and think as a 'student'. Be every student you have! Be the die-hard learner. Be the mediocre student who goes with the majority. Be the smart-aleck kid who loves any opening for a joke or wise comment. Get some candles, some incense, channel them all... okay you get the point! Let the 'student' critique, trash, beat up, and make fun of your mere idea! Take the rose-colored glasses off.
This doesn't count for off-the-cusp pictures you can take with a digital camera while experiencing some majestical moment on vacation. However, be the 'student' before uploading said pictures. Would this really be something a student would be interested in, be perplexed by, have a question about, wonder about? Be honest. Your student doesn't necessarily think like you. Amazement and perplexity are two different things.
*My goal is to allow my classes to experience 101qs.com next week and see what they think. Seeing other teachers do this inspired me.

Staging:
Face it, we have a demographic. When staging your videos or pictures, keep students in mind; your students, my students, someone else's students. Sit in their desk, put their glasses on, be your demographic. Sorry John Hanks, is your Dirt really going to interest your students? Maybe yours. It wouldn't perplex mine. What might be perplexing for you or the general majority of the users of 101qs.com is not necessarily perplexing for your student. So how do you effectively stage an act? I'm going to use Chris Hunter's Big Box o' Krispies. It's my new favorite.
I think the intended question was 'how many?' Hence all the skips. Longtime users are for the most part...done with 'how many?' But c'mon, they're Rice Krispies! SNAP! CRACKLE! POP! Think outside the box here (I can't pass up a good pun!) I'm going for another audio clip here, "How loud would the Snap Crackle Pop be if they were poured into a barrel of milk?" Can you imagine that? If I had a box that big, here's how I'd stage it:
Use a tripod, put a small bowl on a table, pour some Krispies in, and then pour in some milk. Record the audio up close. Cut to a picture of a barrel, a few or many gallons of milk, and the huge box of Rice Krispies. Cut. Act 1!
Think about the sequel? If it's not loud enough, how much cereal should we add? How quickly? What type of milk will yield the loudest response? How much longer will the barrel snap crackle pop compared to the bowl? What's the perfect ratio of milk to cereal for the highest decibel? Maybe invest in a decibel meter? You can still cover your volume question and more... I love it! So what about the 101qs.com viewing experience?

Viewing:
When viewing the uploads on 101qs.com, think like a 'student'. Sometimes the expected questions are staring you in the face. I've commented to Dan that some users are abusing their power with the 'Skip' button, but I respect their autonomy. I can't force or coerce a student into what I think is perplexing so I'm not going to bash a 101qs.com user. However, I would encourage that user or student to still offer some feedback. Why is this boring? Why did you press 'skip'? I don't care if I'm on the top ten (no, that's not loser talk). I don't. I care that I hit my intended mark. I care that I get constructive feedback from a flop and improve upon it. I care that my students are perplexed.  Lastly, I believe I can offer feedback to those on 101qs.com if I pretend to be that smart-aleck kid in your class. Perplexity in math is a natural component of classroom management. If you can't engage me, the smart-aleck, I'm cracking jokes and off-task. Here's how I'd make Abbie's Oatmeal slightly more student friendly. There's too much text. Students don't want to read much or dig through text after they've become accustomed to you showing them epic pictures. Crop this picture. Zoom in on what you want the student to question. I almost skipped this, but offered Abbie some feedback because this picture has great potential.

Have fun:
If you're not having fun, your students aren't having fun. It was fun to put Post-Its on a huge File Cabinet. The students had fun making estimates. They had fun writing the numbers on the Post-Its. They had fun doing the math to figure out the actual number. They wanted to know how many Post-Its to write numbers on. I said, "You tell me." They didn't blink. They took ownership of both the writing of numbers and the math. Keep these fun moments in mind when you are channeling the student. If it's fun for them, it'll be fun for you while you plan, stage, record, and edit your media.

Have fun,
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FIle Cabinet

By far, File Cabinet has got to be my favorite 3 Act lesson to date!

I am proud of my newfound passion for 3 Act lessons and the final product for my File Cabinet lesson. However, I am even more proud of:

• My students for their interest, critical thinking, and assistance with Post-Its and filming
• My family, friends, and colleagues who took an interest in the project/lesson
• Fawn Nguyen for using the lesson, providing feedback, and sharing her dynamic results, classroom and students with us
• Dan Meyer for calling me 'Crazy Bananas.' I deserve it. I own it proudly!

Here's the story:
In previous years, a Mr. Stadel Geometry class sounded something like this during the surface area unit, "If we covered this object in wrapping paper, we'd need to figure out the total surface area of the solid so we know how much paper to use. Let's use this formula. Blah, blah, blah!"

Cue the sigh, the yawn, the head tilting back, and eyes closing. The class would use a bland formula to trudge through a static textbook question so that they could arrive at some theoretical answer that meant absolutely nothing to everyone, including me at times.

Not this year... Dan Meyer's 3 Act lesson format is here to breathe life into applied math. I was staring at this file cabinet at the back of my room, saw a stack of Post-Its on my desk and thought, how many Post-Its would it take to cover this rectangular son-of-a-prism... and so it began.

Forget wrapping paper, Post-its FTW! 

I filmed File Cabinet - Act 1 (watch video here before Act 3) last Monday, posted it to 101qs.com and every day I chipped away at sticking Post-Its for about 40-60 minutes after school. Yes, it was a lot of work, but totally worth it! This math lesson/project instantly became a huge conversation piece in my classroom. Students came in completely intrigued by what was going on in the back of my room. They stared at it. They did weird finger, arm, and eyeball measurements. They walked around it numerous times before I finally said, "Make an estimate. It's free! Write it on the board." My whiteboard at the front of the class had about 30 kids' names on it with their estimates. It was so invigorating to hear them discuss or argue their estimate. One student made an estimate within 1 Post-It of the actual result.
Going beyond estimates, students wanted to help and the only thing I felt comfortable having them do was write numbers on the Post-Its and tape down Post-Its that were sticking out.  My students were a HUGE HELP! Thanks guys! Knowing I will post my math videos online, I will not include my students in my videos for what I think are obvious reasons.

The math lesson went extremely well. My students calculated the theoretical answer for homework after we watched Act 1, made estimates, and discussed the necessary information in order to answer the question, "How many Post-Its will cover the file cabinet?" The next day we discussed the differnt ways my students calculated. NONE of them used any formula from the textbook. I love it! Students either:

1. Found the total amount of Post-Its on each face and found the total sum or 
2. Found the sum of the areas of each face and divided it by 9 square inches.

I was impressed by their ingenuity, resourcefulness, and independent thinking process. Bottom line: I didn't help. I didn't force-feed them a formula that means nothing to them. Instead, I allowed them to derive the answer. Little voice in my head says, "Derive the answer or formula on your own!" We also discussed potential problems with the theoretical answer as they walked around the cabinet. Check out Act 3 to get a 'handle' on the potential problem. Here's a hint:

Get a handle on the potential problem.

I asked my new online math teacher friend Fawn Nguyen if she had done surface area with her Geometry kiddos and I was glad to share File Cabinet - Act 1 with her. Check out Fawn Nguyen's blog here for an exciting read about how her kids responded, their inquisitiveness, ingenuity, and the depth in which Fawn took the lesson. One of my favorite parts was seeing the kids come up to her board and measuring the video display in order to make estimates. They also estimated my height while they were at it... classic! I was flattered and happy that the lesson sparked such a great interest with her and her students. They were so kind to send me a 'thank you' picture. I love it! I shared the story with my class.

Another new online math teacher friend Nathan Kraft simply said, "I'm using this."
I'm glad! I hope you do too! and send me some feedback.

I also sent out the video link to family and friends and got a healthy amount of intriguing responses. My brother, who has great insight regarding the furniture business, was able to eyeball two-thirds of the file cabinet dimensions and had a blast calculating the number of Post-Its. It was fun to go back and forth with him about this. When asking friends what their first question was after watching Act 1, one family friend shared a perspective I wouldn't have thought of in a milion years. Her husband underwent chemotherapy years back and they used Post-Its to count down the days left. They had a pack of Post-Its in the car and counted down each of the 33 days of radiation treatment. This was an extremely touching email as I learned a life-impacting fact, all because of a math video about Post-Its.

As I was busy sticking Post-Its on the cabinet all week, staging the next camera angle, stop motion setup, or editing the video, I was honored to see Dan Meyer's blog post of his weekly Five Favorites - 101Questions [4/28/12]. Yes, Dan is correct that I'm 'Crazy bananas.' I am proud of that title and fully embrace it. I also got this tweet from him:

I don't think I'll be using a Post-It for awhile... and every time I use a Post-It I will think of this math lesson. Enjoy File Cabinet - Act 3.

File Cabinet - Act 3 from Mr.Stadel on Vimeo.

If you'd like the information for Act 2, email me or post a comment. I'm working on making Act 2 files more accessible or downloadable. Until then, drop me a line!
[UPDATE] Check my 3 Act catalog for Act 2 information and more!

Best,
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Rolling Tires

It started a little over a month ago when I had to get my car tires aligned. As my car was being worked on, I killed 30 minutes worth of time walking around the industrial park with my son and came across this goldmine:

a dumpster full of used and abandoned tires 

Mentally, I started mapping out some math application(s) for the tires and figured Spring Break would be a prime opportunity to record a 3Act lesson for my geometry class. I'm proudly addicted to Dan Meyer's 3 Act lesson format. I can only hope I'm doing it justice. After trial and error, self reflection, and feedback from both students and online colleagues I'm starting to see the strength in 3 Act lessons, if done correctly. It requires planning, objectives, patience, and of course... time.

Have an objective, a lesson in mind, a real-world example, (maybe use a word problem from a textbook to jumpstart your direction), start training your eye to always look for lessons you can bring to your students...

Make sure it's measurable: Yes, it's fun to throw a picture at students and ask them, "What's the first question that comes to mind?" Both you and your students might agree on the same perplexing question, but if there isn't measurable data or a realistic solution, your media might simply reduce to a fun picture you both were perplexed by, predicted an answer to, and discussed a path to the solution. That fact alone might be valuable enough without the actual construction and implementation of a class activity/lesson.
This Lego pic I snapped is a great example of something difficult to measure: it might open up a discussion, students might make a prediction, but measuring it would be very difficult because of the numerous variables. However, something like my JUMBO and mini stop sign staging is very measurable and a lesson can be constructed beyond the discussion and prediction arena. Therefore, with Rolling Tires, I made sure everything was measurable before pressing record.

Act 1: A video of me rolling a tire (a friend was disappointed it wasn't a supermodel in a bikini). What's the first question that comes to mind? Hitting the initial mark during Act 1 is imperative to the overall success of the lesson.


Act 2: A keynote and/or video to reveal information my students might find necessary to solve the question agreed upon.

Act 3: The video payoff to see how the calculated (theoretical) answers compare to the actual (practical) results.

Please feel free to download and use all three videos. Give me some feedback. Ask me some questions. The necessary information is included in Act 2. I thought, great an actual way to apply circumference. I will try to post any handouts or graphic organizers used. Lastly, if time permits I might make a sequel to include a couple different scenarios.

Possible Sequel: I heard a long time ago that some taxi drivers put smaller wheels on their cabs so the car tires would produce more revolutions, yielding a higher cab fare. Check the tires of that cab before you get in it.

Best,
930

Survey your students

Spring Break Questionnaire 2012:

I believe in the importance of feedback, whether it's:

1. Customer feedback regarding a product
2. Feedback about a restaurant, their food, service, cleanliness, etc.
3. Feedback from colleagues, administrators, students in your class or 
4. The feedback Jimi Hendrix produced wailing on guitar (that's definitely a topic for another day).

I gave my students this questionnaire last week, right before we went to Spring Break:

The feedback I received from my students is invaluable. My favorites were:

1. A student that responded to question 5 and a difficult concept: "I need more space, there were too many."
2. A high percentage of students used the same verbiage for question 6 regarding the warm-up: "It helps get my brain ready for math and I like the second question because it's fun."

So here's the how, why, and when I do questionnaires.

How: 
Keep it simple. Type up a one page questionnaire your students can finish in about 5-8 minutes. Give it to them on the first day of school or at the end of a short test or quiz. Give your students the premise, don't just throw it at them. Tell them their feedback is important to you (because it is). Explain that their honesty and constructive feedback helps you (the teacher) help them (the students). Again, tell them again that their input is important to you (because it is).

Why:
I don't feel much explanation is necessary here as we could come up with a million reasons, but hopefully the reasons are instinctive, logical, genuine, and simple.

Questionnaires allow student's to take the initial step in the ownership of their learning. They see that you are open and willing to make their learning experience rich, rewarding, and reflective of their interests.  They see that you care. Students can possibly gain a better sense of appreciation for your hard work, but this shouldn't be your main objective. If they see you working hard to meet their expectations, then maybe it will rub off on their work habits in your class and pay dividends towards your expectations of them.

The students (your customer) can give you a perspective that you might miss. They might remember something they enjoy in another teacher's class and want to share it with you. Don't take it as a slight. Take it as a Professional Development opportunity. I'm not saying the students dictate the curriculum, daily agenda, or always know best about their learning behaviors, but their input and perspective keeps you connected and in tune to what they are thinking. Simply put, how does your customer feel about the product you are selling? What can you do to enhance your product and better appeal to your customer base?

This a great opportunity to teach your students that constructive feedback is a life skill that benefits from some etiquette. The questionnaire is not a 'comments' section they can anonymously fill out online, bashing the subject or person while they sit in front of a computer screen. Students are given the opportunity to provide words, explanations, and reasons that are constructive, diplomatic, and appropriate. It's a great opportunity for a teacher to teach a life skill... embrace it.

Don't wait until the end of the school year. IT'S TOO LATE. I always found the rating forms at the end of a college course or graduate class pointless. Why ask me after the fact, especially if the instructor was terrible? How do my classmates and I benefit from taking the survey at the end? How come we didn't benefit from a survey given to this instructor's last class? I digress... However, it's important to me that I survey my students frequently. So when do I poll them for their feedback?

When:

Don't abuse questionnaires. Students will see them more as a task instead of an opportunity to provide meaningful feedback. Don't overuse: 4 times max.

Beginning of the year

It allows you an opportunity to find out information, fun facts, learning styles, and their attitude towards your subject area. What a great way to immediately make connections with your students. Use questions that encourage detailed answers. Avoid 'yes' or 'no' questions. Hey, you're gonna spend the next 180 school days together, don't you want to make a connection with your students immediately that will catapult you together into the subject area you teach? Lastly, ask them what is something they would like to know about you...

Before Winter Break

By this time you have been using various techniques, strategies, learning activities, and have gotten to know the make up of your classes. The newness of the school year has definitely worn off and it's time you get some feedback from your students. Use Winter Break to evaluate their responses and give yourself some New Year's resolutions and an action plan upon your return in January. Your response is pivotal. Return in January reminding them what they did, some common threads, and your action plan. It's imperative you follow through with your plan, or you subject yourself to losing your customers...

Before Spring Break

Spring cleaning, right? It might be time for you to utilize some fresh ideas/activities or maybe trash some that are just ineffective. Maybe there's some concepts you need to reteach before those lovely standardized tests arrive. Use Spring Break to prepare some improved ways of reaching your kids. They're older now. They've seen your best and your worst. Give them something fresh upon their return. Maybe this is where you bring out some 'secret weapons' or some awesome activities you found from a colleague on Twitter, 101qs.com, Teaching Channel, a blog, etc. Do something so both you and your students have something to look forward to as you close the school year. Trust me, by this time, your students will feel comfortable enough to tell you what they like/dislike, and how effective/ineffective activities have been in your class. Plus, if you followed through on your January action plan, they trust you will respond equivalently. 

At the end of the year

This isn't one where you just do it as a formality. You have spent 180 days with your students and hopefully have left a positive impact on their life by now. Hopefully they returned the favor. If you're always looking to improve and be a better teacher, this is your opportunity to take the good with the bad so you can better prepare for next year. I know by this time you are looking forward to summer and the last thing you want to do is think about next year, but it will be here before you know it and guess what? Your current students will help you prepare to have an even better and stronger year next year. Yes, your students might be brutally honest on the final questionnaire because they may never see you again, but take off the rose-colored glasses. It might hurt at first, but it can only make you stronger (sticks and stones..., right?). Take the summer to find ways to better connect with that 'one' student who will be in your class again next year. Decompress over the summer, but keep in mind that your former students have given you a valuable gift. They're feedback, their insight and their words are teaching you now. They have left you with a lesson. Think about it, we expect our students to learn from their mistakes, to take chances, be lifelong learners, and always strive to do their best. Expect that of yourself too. Take their feedback and give back. 

Good luck,
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