Being the Answer Key (or not)

After reading through the Pimm Quotes that Dan selected, some type of bittersweet emotion about teachers being the answer key was rekindled within me. I left a few comments/questions and I appreciate Dan's timely and thoughtful responses.

For the following questions, I'll define "yourself" to include you, your students, and your classroom culture.

• Where would you place yourself today?
• Where would you place yourself at the beginning of this year?
• Where would you place yourself last year? 
• Where would you place yourself during your first year?
• Where would you like to be placed at the end of this year? 
• Where would you like to be next year?

*I'll share mine at the end.

There's way more to talk about here. I did not fully capture the essence of Pimm's quote, Dan's response, nor my own thoughts. I just wanted to toss this around as is.

I challenge you to blog about this too.

• Reflect. 
• Label your axes how you want. 
• Should it just be two axes? 
• Either way, create/add some type of visual.

Stadel this school year:

Stadel last school year (I went overboard and it was not enjoyable for anyone.):

AVOID quadrant IV

Stadel in the past (pre #MTBoS):

Stadel as a rookie:

Answer key,

609

NEW JOB!!! and some fraction ideas

I recently accepted a new teaching position with a middle school where I'll be teaching 6th and 7th grade math. I was fortunate to be at my last school for about 10 years exploring 7th and 8th grade math: Pre-Algebra, Algebra 1, Algebra 1A, Algebra Honors, and Geometry. I'm extremely grateful for the opportunities, experiences, friendships, and professional growth opportunities the school afforded me. As I advance in my teaching career, I'm very excited about my new position, new school, new students, and new everything. There are many differences between my previous school and my future school... and I welcome them wholeheartedly.

As my future school transitions to Common Core, I'm giddy at the thought of exploring so many wonderful concepts in 6th and 7th grade math. However, I will be working with students that have typically struggled when it comes to understanding math. Therefore, I had a few ideas about fractions I thought I'd like to explore with you.

I'll include all the visuals here, but feel free to go to my "fractions test page" at Estimation 180 to get the full experience. Please offer me some feedback. I'd like to pursue these "fraction" ideas with other items; some easier, some more difficult. Is this something you could use? Is this something worth pursuing?

Question: Where would the cylinder be one-third full?
(Image 1)

We're estimating here. I did not provide any choices because I want students to formulate ideas on their own. Look at their screen and move their finger up and down the screen to find one-third. Come up to the board at the front of the classroom and put a post-it note on the board.

Offer some choices: When ready, click on the image for choices.

Notice I said, "when ready"? Did you have students discuss? point with their fingers? place a few sticky notes on the screen at the front of the room? or something else to get students invested? Because of the restrictions at Estimation 180, this image will currently serve as the next viable step. Now students have a choice. I'm not the biggest fan of this, but it's something. Were there students who were way off because their sticky or initial guess didn't even fall within the given range?

Make a choice and demand reasoning: Why did a student choose "C" instead of "D"? Have students try and convince each other. Argue! Egg them on a little bit. Have students choose a line in which they think the cylinder will reach one-third its capacity.

Do some math? I provide you with the capacity of the glass: 1,170 milliliters. Find one-third of that. Encourage different strategies in your class. Doing the math won't tell students if the answer is choice A, B, C, D, or E, but it might help with later parts of this activity.

Reveal the answer: a really short video.

I have additional video for two-thirds, fourths, and a full cylinder (when using thirds or fourths). I haven't inserted the choices, added a counter, or other after effects. Would this be something you'd be interested in? Please let me know.

Two things:

1. I also set this up as Red Dot (Active Prompt) activity and it'd be fun to see how students would approach this activity without multiple choice. Then, show the class their results before watching the answer (video).
2. I'd love to see Dave Major make a slider so students could slide a bar up and down the cylinder. Using a computer or tablet, students could place the bar where they want and without a given range of choices. Then we could see who was actually correct.

What feedback do you have for me? Again, is this something you could use? Should I prepare more at Estimation 180? Would you like to see the remaining fractions and other ideas?

NEW,
723

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

Zero Olives

My two-and-a-half year old son loves black olives just as much as I do. Tonight at dinner, my wife placed two olives on our son's napkin. Surprisingly, the olives remained untouched for a few minutes. He made some descriptive comments like, "The rice is delicious. The egg is delicious. The milk is delicious." You can tell what vocabulary we use around him, right? Quite the eclectic dinner, I know. Unbeknownst to me as I was taking a bite, he grabbed an olive with his hand so he could put it on his finger to eat and says, "There's one olive left, Dad!" Here's how the rest of this played out:

Me: "Yes, after you eat the one on your finger."

(we've had this conversation before)

He quickly shoves the finger-olive into his mouth.

Not wasting anytime, the olive-gobbler grabs the lonesome olive on the napkin and exclaims, "Now there's zero olives!"

WOAH!!!

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

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

Our dinner conversation didn't end there. Let's see if this olive-gobbler has some depth. I held up two fingers and asked, "How many fingers do you see?"

Olive-gobbler: Two

(I take down one finger)

Me: How many fingers do you see?

Olive-gobbler: One

(I take down the last finger)

Me: How many fingers do you see?

Olive-gobbler just sits there......... "hmph"
He holds up his hand with all fingers extended and says, "Five!" (Wise-guy!)

I start over by holding up two fingers and repeat my questioning. Same exact response from the olive-gobbler. So it didn't work with the fingers. Later on during our dinner I put one of my olives on his napkin. He grabbed it.

Olive-gobbler: Zero olives left!

Me: You're right.

I put our workout on zero to rest for the night. We're getting there.

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

Olive-gobbler's dad,

936

When does a rock stop being a rock?

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

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

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

So many questions... here's more:
Living in the USA, our customary units system of measurements seems counterproductive with inches, feet, yards, fathoms, miles, ounces, cups, pints, quarts, gallons, barrels, etc. Terminology can be difficult enough for students and to throw all these different measurements at kids (nay, humans) can only seem daunting. When should we use feet to measure something instead of inches or yards? I envy the metric system and, well, let's leave it at that. These measurement questions become even more relevant as I dive into estimation with my students and as I update estimation180.com each week.

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

Rocky,
858

Estimation is Key

First Day of summer school.
This morning, I snapped a picture of a portion of our school parking lot. My intention: use it as the daily estimation question included in the warm-up.
Q: How many total parking spaces are in the parking lot?

We did our warm-up. I first asked for numbers that were too low and didn't make sense. Then too high. Finally, I asked for their estimates, but didn't validate any responses. We then jumped into our lesson for the day: ESTIMATION.
Opening the lesson, I asked my students to think of one good thing and one bad thing about estimation. Here's what they listed.

Good:

• Doesn't have to be correct
• It's easy
• Can be made mentally
• It's an educated guess
• "It's free! It doesn't cost you anything." (Oh, I added that one)

Bad:

• Not precise
• Could be wrong

After comparing the pros and cons, the good guys won! Estimation FTW!
Why?
It gives anyone a chance to cast an answer based upon specific information. It's a starting point. It keeps your number sense in check. It allows the brain to think abstractly for a brief moment. It's free!

We went outside and delegated the work. Students counted staff, reserved, preschool, handicap, and ordinary (unlabeled) spots. We got a total of 141 parking spaces. One kid was two away with 143 as his estimate. Go figure. Another kid was in the five hundreds. Go figure. After the empirical data produces the answer, we always circle back to our original estimates. It's important for students to see the difference so they can improve their number sense and estimation skills for next time.

Tomorrow, we extend the lesson: convert those itemized numbers into percentages in order to make a pie chart of the allocation of parking spaces.

Check it: Steve Leinwand Case 4: Number Sense
He hits some great points at 2:25. It's worth watching the whole thing in my opinion.
Steve exclaims about estimation, "We need to build that into ALL the things that we do!"

Think how many times a day we estimate:
Time to get ready in the morning. Time to get to work. How long is this darn red light? How long before I get my cup of coffee? How many? How many? How many?

Please share with me!
What can I do to make estimation better with my students?
How do you use estimation effectively?
How do your students benefit from it? (or not)
What are some other daily estimations you make?

Estimate,
1128

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,
222

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

Jumbo and mini STOP signs

Friday was the beginning of my spring break!!!
I took my new tripod, measuring tape, and camera assistant (my 22-month old son) with me to stage a few pictures.
Objective: shoot different sized STOP signs found on the road to his Gymboree classes.

*can be found at 101qs.com

I've been itching to do this math shoot for weeks, but have been busy with school and other miscellaneous things. Ironically, I found these STOP signs to serve two purposes:

1. I'll be exploring the area of regular polygons with my geometry class when we return from spring break; exploring the apothem, radius, and eventually using these properties for surface area and volume of solids. 
2. The signs are telling me to STOP, collaborate and listen (sorry, Vanilla Ice). Seriously, I need to:

• STOP and rethink a few key components to a successful learning environment for my math students. 
• Collaborate with my teaching counterparts, online and off, and 
• Listen to the needs of my students, common core standards, technology, the future, and...

I'm working on a vision I had last week regarding the reconstruction of my classroom, how students will come to my class to learn, and the overall learning experience(hint). Stay tuned!

Best,

1,254

Infographics

I want to investigate Infographics.

Are you using them? If you are, how? What's effective about them? Do they help create discussion in your class? Do they create 'perplexity' as Dan Meyer would want. From the little I have seen of infographics tonight, I see some strong potential, especially with 3Acts and discussion based learning.

One of my RSS feeds, Mr. G Online was talking about Infographics and I thought I'd see if there's any gems. I clicked on Cool Infographics, immediately finding a picture of an iPad and usage. Continuously trying to better train my brain to look for potential math lessons, I quickly:

1. Snagged the graphic
2. Added some lovely black boxes and...
3. Poof! A potential math lesson? 
4. Uploaded link to 101qs.com

What's the first question that comes to mind?

Is your question, "What percentage is each activity on the iPad?"
Additionally, I want to know if each colored area actually represents that percentage of the iPad screen?

Off to explore some infographics.

Best,
12% (that's one of the percentages)

The Law of Lego

I went to the Lego Store in my local mall the other day. There weren't many people in the store so I was able to take a picture of their back wall full of bins with those little magical plastic pieces. I don't know about you, but quite a few questions popped into my head:

1. How many Legos are in all those bins?
2. How many pieces could I fit in the quart-sized cup for $14.99 ($15)
3. If I worked there would I be allowed to build anything I wanted?
4. Given an hour, what could I build?
5. Am I dreaming?
6. Is this a tease?
7. ...and so on, you get the idea

Most importantly, I left the store with what I think was the best question:

How can I incorporate Legos into my classroom to have an awesome learning experience and lesson?

There's my new objective, especially with surface area and volume coming up in my Geometry class.

What question comes to mind for you?

Best,
15

Can negative answers equal stealing?

If someone gets a negative answer to a question involving a purchase at a store, is it stealing?

Today, I was grading the tests I gave last week covering linear systems in Algebra. I was actually quite impressed with the majority of students who were successfully solving the mixture, distant, and linear systems questions. Then I came across an answer where the student answered with a negative value to the following question:

Mr. Stadel bought a total of 31 Red Bull drinks. Each individual can is priced at $2 and a 4-pack of Red Bull drinks is priced at $7. Mr. Stadel paid a total of $56 for the energy drinks. How many individual cans did he purchase? How many 4-packs did he purchase?

The student answered -6 for the amount of 4-packs. Checking their work, they accidentally forgot to account for a negative in their solving. Of course this prompts me to encourage my students to analyze their answers even better, considering the practicality of their answer before submitting it...

or maybe -6 meant I stole the Red Bulls.

Best,
-6