Sunday, December 6, 2015

Productive Struggle [part 1]

I want to know more about "Productive Struggle".

Let me be more specific:
If students are allowed to reasonably struggle with a math task, I want to know more about a teacher prescription of actionable steps to:
  • move the learning forward and 
  • avoid a meltdown level of frustration
I built a Productive Struggle Desmos Activity if you would like to share your thoughts and learn from others interested in this topic.

Robert Kaplinksy recently gave a wonderful Ignite Talk on Productive Struggle. Communication was a big part Robert's message. I want to think more (in part 2) about communication as one of the actionable steps in that prescription.


Part 2 is here.

Monday, November 23, 2015

Should 3 Act Tasks Build Literacy?

I went to the Nashville NCTM Regional session by Graham Fletcher and Mike Wiernicki and they showed this slice of awesome:

You'll notice they covered up the text of a [K-5] word problem only to show the question at the bottom of the chart paper. I thought this was a really slick move to get students talking, thinking, and imagining. If you've been to one of my problem-solving sessions lately, you'll know I'm really encouraging math teachers to push student potential by creating a mystery, layering in the clues, and solving the mystery. Therefore, the slide Mike and Graham displayed really resonated with me. Imagine students taking those stickies off one at a time, creating suspense in the process. More importantly, in my opinion, a teacher can scaffold in the context and literacy demand of the word problem.

Imagine reading one sentence (or one part of a sentence) at a time on that chart paper, as a class or with a classmate, working on understanding the context better and better with each sticky that is removed. However, the resonation of their slide didn't stop there with me. It really got me asking myself, "Can we help students simultaneously build math skills and literacy skills with 3 Act tasks?"

As much as I love how 3 Act tasks make the math accessible to more students because the literacy demand is usually removed, I agree with teachers that voice their concern about this actual feature. Understandably, they're concerned about the literacy demand that many of our state tests demand. (*concern should not be limited to state tests)

Essentially, I'm wondering if there's a natural way to work in the literacy demand during Act 1 and Act 2 of a 3 Act task? For example, let's use my File Cabinet task as an example:

Students watch Act 1:

After we gather student thinking (noticing and wondering a la Math Forum) and have students make a guess, I'm feeling the notion to present students with the textual representation of this task at some point. I'm not sure when that point is, since I badly want to test this out with students. The text might look something like this:
Mr. Stadel is using sticky notes to completely cover a file cabinet in his classroom. How many sticky notes will he need to cover the five visible sides of the file cabinet?
Whether we (the teachers) present the text to students or students help compose the text description above, would this benefit both the math and literacy? Would it detract from the math?

Moving into Act 2:
I think it's still important to have students think of information (identify variables) that is important to know in solving this question. Lately, I've been encouraging teachers to have students formulate a plan without any data, numbers, measurements, or other information. Lately, I've been seeing students just grab the numbers from Act 2 and hastily plow into a wrong plan or formula, getting unreasonable answers. My suggestion: Let's sit tight on revealing the information in Act 2. Get students to formulate a plan or representation first. Maybe make a more precise estimate in the process. After going through that process, maybe we can refine our original text description to something like this that now includes the measurements necessary in solving the task:
Mr. Stadel is using 3" x 3" sticky notes to completely cover a file cabinet in his classroom. The file cabinet is a rectangular prism with a 36-inch width, 72-inch height, and an 18-inch depth. How many sticky notes will he need to cover the five visible sides of the file cabinet?
Now that we know more information in this task, I think the original text should be adjusted (updated) accordingly. To me this feels like we have removed all the stickies from the chart paper Mike and Graham gave us.

Similar to Act 1, I question if this would benefit both the math and literacy?

Since I am putting Act 1 and Act 2 under some scrutiny, it would only be fair to address Act 3 as well. Maybe the literacy in Act 3 seems more intuitive (all relative), but would this be a good time for students to write something that represents their plan from Act 2? For example:
We found the surface area of each side by... We figured that we could divide each side by 9 square inches, the area of one sticky. In doing so we predict Mr. Stadel will need X number of stickies to cover the file cabinet. 
There are two big reasons I was initially drawn to these tasks. 3 Act tasks typically:

  1. eliminate the literacy demand, making the math accessible to more students. 
  2. have Act 3 to validate (or break) the mathematical model we used in Act 2.

I still believe in 3 Act tasks, don't get me wrong. However, I believe we might be able to get even more out of them as teachers. I consider this: at what point do we say to our students,
Look, I first want you to access the mathematics without your english language skills (or lack thereof) getting in the way. We have to keep in mind that our state tests (and other math problems) require strong literacy skills. I think you need to see what this task might look like as just plain text.
Or do we say this at all to students? parents? colleagues? administrators?

Many online colleagues gave input on building literacy into an Act 4. You can read more in the thread here. I support extended opportunities for more literacy like our colleagues suggest (or practice). However, my focus is during Act 1 and Act 2 right now. Help me think this through. Add some thoughts in the comments.


Friday, November 13, 2015

Are You A Mathematician?

I flew out to New York last Sunday. An older gentleman on the airplane sitting next to me saw me working on this idea in Desmos and simply asked, "Are you a mathematician?"

I hesitated. Not sure I know why

I think my hesitation roots from me having this impression that mathematicians exist only at the college level. They do math all the time. On chalkboards. Wear white coats. Have frizzy hair. Stand in front of chalkboards full of symbols and equations. Yes, I know. Very stereotypical.

Why did I hesitate?

Yes, I am a mathematician.
I love thinking critically. 

Yes, I’m a mathematician.
I love building number sense.  

Yes, I’m a mathematician.
I'm scared of math problems in which I lack the skills to solve. 

Yes, I'm a mathematician. 
I love being challenged by a good [math] problem.

Yes, I'm a mathematician.
I love using numbers to make sense of the world around me.

Are you a mathematician?
Yes. Don’t hesitate. 


Monday, October 26, 2015

2015 Ignite at NWMC

I delivered my second Ignite Talk at the 54th Annual Northwest Mathematics Conference in Whistler, Canada this past weekend.

I start my Ignite saying:
Take 10 seconds to think of the most forgettable parts of your math class.

I am so grateful for the wonderful BCAMT program committee (<---follow them). They worked extremely hard to put a great conference together. Thank you Chris, Marc, Sandra, and Selina for inviting me out. Whistler is so beautiful this time of year and I learned a lot from the great sessions and speakers. It was a pleasure to hang with some old math friends and make new ones too!

There were some other great Ignite talks and I hope that someone part of the BCAMT was able to record them in order to post online. To the entire Ignite team: Marian, Ron, Robert, Allison, Janice, Carole and Marc (emcee). WE DID IT!


*P.S. Here's my first Ignite talk.

Sunday, October 18, 2015

OCMC Keynote: Tools for Student Thinking

The wonderful people at Orange County Math Council have asked me to be the Keynote speaker tomorrow night, Monday, October 19, 2015.

OCMC is hosting the 2015-16 Math Tech Night in Tustin, CA a la EdCamp Style. Math teachers will have the chance to share with and learn from other teachers their math tech tools, secrets, and favorites.

The title of my Keynote is: Tools for Student Thinking.

I've scheduled my TweetDeck to tweet out parts of my Keynote during the keynote, starting at 5:00 pm (PST). Hopefully you can follow along or tune into the #OCMC15 hashtag at your convenience. I'm really pumped.


Sunday, October 4, 2015

Cheeseball Estimation 180

Earlier this week, I tweeted out a new Estimation 180 challenge:
How many cheeseballs will cover the plate?

Thanks for playing along. The video reveal is below.
Here is the latest Estimation 180 series: Cheeseballs!
Days 206-210

Enjoy getting your hands dirty (with orange cheese dust).


Tuesday, September 29, 2015

Plate of Cheeseballs

I might be the only one excited about this Estimation 180 challenge. And that's okay. If you want to play along and test out at the same time, click here.

How many cheeseballs will fit on the plate?
*a single layer of cheeseballs

Enter your estimate, work, and reasoning here. Play along.


Sunday, September 20, 2015

Is Your Math Class Forgettable or Memorable?

A little over three days ago, I tweeted the following:
I highly recommend you read everyone's response. I truly appreciate everyone who responded. This question definitely can be revealing and/or create vulnerability. You will be my biggest ammunition as I attempt to inspire teachers at the Northwest Math Conference in October to create more memorable times in their math classes.

Here is my takeaway from your responses:

If you (the teacher) want your class to be FORGETTABLE (to both yourself and students), do the following:
  • TALK a lot
  • LECTURE a lot
  • make sure students are silent
  • have students take a lot of NOTES
  • ask closed questions
  • have students sit and get, then forget
  • give meaningless homework
  • focus on grades
  • discipline students because the math wasn't engaging
  • be bored with your own work
  • assign a lot of WORKSHEETS

If you (the teacher) want your class to be MEMORABLE (to both yourself and students), do the following:
  • make a math song to "Can't Touch This"
  • be kind
  • build relationships
  • tell stories
  • have students work collaboratively
  • have discussions about identity, character, and equality
  • allow students to propose methods that you never considered
  • build a class community
  • allow shy students to present
  • engage even the negative students
  • have students work in small groups
  • have students share their thinking
  • believe in your students
  • use stuff from the MTBoS like 3 Acts, whiteboarding, visual patterns, estimation 180, barbie bungee, number talks, etc.
  • build relationships
A few of you were kind enough to email me and share some amazing stories. A fourth grade teacher emailed me about two of her students writing a letter to Swingline asking them why their box of staples says 5000 staples, when their math class calculated it to be 5040. All because of Days 14 & 15 at Estimation 180. Those students probably won't remember the worksheet they had last week in any class, but I guarantee they'll remember writing those letters. Now I hope Swingline does the right thing and replies to those students.

Thanks again. Keep creating memorable times in your math classes. 


Monday, August 24, 2015


Dear Chris Shore,

Thanks for introducing Tustin Unified to Clothesline during your awesome professional development workshop!
You, Math Projects Journal, and Clothesline rock (David Lee Roth style)!

With all of my math heart,

*Check out Chris' post on Clothesline (link coming soon).
**I highly recommend inviting Chris to your district/school for math workshops.

Where do I begin?
I used to have a number line in my old class. But it was static. All of the benchmark numbers were taped to the wall. I used it often, but not often enough.

Flash forward to Chris' workshop last week. He introduced Clothesline using this great quote from Tim McCaffrey:
You better believe my ears perked up when I heard "master number sense maker". Check it out!

When I worked with teachers in Irvine today, my ice breaker was asking the teachers,
"How long does Dyson think it should take you to dry your hands with their machine?" 
I've never posted this picture online because it's my favorite ice breaker to do with teachers at conferences and workshops. However, I will use the context to illustrate how I introduced Clothesline to about 150 teachers, coaches, administrators today.

As teachers were discussing, I went around and asked
  • two teachers for a guess that's too low (3 and 5 seconds)
  • two teachers for a guess that's too high (30 and 40 seconds)
  • four teachers for a guess that's just right
I used a big black marker to write the numbers on the red papers for the first four teachers with their "wrong" answers. I then had them place the red papers on the 25 feet long clothesline hanging on the side wall. I had the last four teachers write their "just right" guesses on the green slips. 

You'll notice the green slips might be hard to read from a distance. I did this on purpose so that we could get the visual effect (from a distance) of placing their green slips accurately on the clothesline using correct spacing (sorry, no pictures), based on where the red slips were originally placed. I reminded the teachers that this is a dynamic number line. You can move the numbers along the clothesline as you please. Please note that the teachers (in this case) were doing all the work, thinking, critiquing, and adjusting. In other words, students should be doing the same in my class as I help facilitate the conversations.

Throughout the rest of the day, I worked with teachers grades 7-12 during three breakout sessions. Therefore, I made a handful of cards for each breakout session to correspond to numbers or expressions relevant to them and their content area. Here's a sample:

I love when Chris used colored papers to focus on the numbers being placed (or in question). Notice the "benchmark" numbers are on white paper.

The clothesline is 25 feet long. I think this is plenty long. I went to Home Depot and bought a 100 ft. clothesline. I made three cuts to make four lines of 25 feet. I used a flame to burn the ends of the rope so they stay in tact.

I noticed Chris used these to stack equivalent values together vertically. Brilliant. See above for examples that could stack.

THE NUMBERS (or expressions)
NCTM suggests using 3x5 cards, but then you have to use more clothespins, making the number line more static. Chris suggested using strips of paper. Using strips of paper allows the number line to be way more dynamic, allowing the numbers to slide along the clothesline or making it easy to place the numbers or take them off without the use of clothespins.

Many teachers loved the idea of using variable expressions. Here's how I determined x for each group. I asked the three teachers in possession of the variable expressions to share how long they had been working in the district. For example, three teachers shared 12, 13, and 15 years. Therefore, 40 was the value of our variable, x.

Whenever I give a professional development workshop for teachers from now on, I will be using Clothesline. IT'S AWESOME! It is a master number sense maker. If I happen to be at your district or school doing PD, I'll bring a handful of clotheslines to raffle off (or give away). At the end of my last session today, it was awesome to have two excited calculus teachers be extremely thankful for receiving a clothesline. One walked away saying, "I'm going to use this Wednesday." Their first day of school! Calculus!

Last, but not least, test it out at home if you have the chance. My five-year-old son and I had fun this past weekend. He threw me a few surprises.

Clothesline 1
I just tossed up a few numbers on the clothesline for him to first get acquainted with the idea of numbers on the clothesline. "Move the pieces of paper so they make sense to you."

Clothesline 2
My son caught me off guard when he pursued something he was interested in. 1, 2, 3, 6.

Clothesline 3
I wanted to see how my son did with spacing the numbers.
"Show me where four and five go."

I'd love to hear about your Clothesline experiences.
Check out Kristin Gray's great post from the other day. I love how much she anticipates student thinking in preparing for a successful Clothesline activity.


Sunday, August 16, 2015

Counting Dots

A teacher asked me about the Counting Dots activity I did in her teacher workshop I facilitated a couple weeks ago. I did the Counting Dots activity as a follow-up to Max Ray's Ignite talk: Why 2 > 4. I believe we teachers need to experience how valuable it is to listen to each other share strategies. If we're going to do it in our classrooms with students and value student thinking by listening to them, then we need to practice ourselves. You know? Build that muscle memory.

I was inspired by Dan Meyer's 2014 NCTM talk titled Video Games & Making Math More Like Things Students Like. You can find his specific reference to Counting Dots at the 30-minute mark. This link includes Dan's NCTM session and references to Ruth Parker's work, who according to Dan popularized Counting Dots.

I also made a video of the exact slides I used with teachers, a few extensions to counting dots, and a behind-the-scenes for anyone interested in making their own.

Questions? Let me know.


Featured comments:
Graham Fletcher shares an insightful article on Subitizing.

Dan Kearney shares more goodness from Steve Wyborney.

Saturday, August 15, 2015

How Do You Like Your Bacon (Math Modeling)?

During the past few weeks I've had the pleasure to work with and learn from teachers in various places in the country, facilitating district/school workshop trainings as they prepare for their school year. Part of our time together was working on problem-solving tasks and breaking down Mathematical Practice 4: Model with Mathematics. At some point, either before lunch or in the afternoon, I tossed up this Estimation 180 challenge and asked:
How long to cook the bacon, starting with a cold skillet?

I love this estimation challenge because it showcases many parts of the modeling process, especially the two following parts:
  • Identifying variables
  • Formulating a model
Here's why. Teachers instantly start asking questions like:
  • How do you like your bacon?
    • Crispy, charcoal, or like beef jerky?
  • What type of bacon is it?
    • Turkey bacon or real bacon?
  • Is it thick cut or the other stuff?
  • Is the bacon room temperature, cold, or frozen?
  • Is it cooked on a gas or electric stove?
  • How hot is the flame?
  • What is the percent decrease in size of one strip of bacon?
Teachers are identifying variables and asking for information that matters to them in order to formulate a model. I love it. I have also done this Estimation 180 challenge with students before and they have asked many of these same questions too. I love it.

I had a great conversation with Joe Schwartz and others at TMC15 about state tests lacking what the modeling process demands: asking questions. Why do the SBAC and PARCC tests not have students simply ask questions about scenarios? If we're asking students to identify variables and ask/search for information necessary to formulate a model and solve a problem, why don't tests place more of a focus on this? What if we presented students with scenarios a la the Math Forum and simply have students first submit mathematical questions that could be solved. What if we then followed it up with giving students a list of three to four questions they could solve and they pick one?

Another great conversation I had with Nathan Kraft and others at TMC15 was the idea that direct instruction can have a negative connotation in the MTBoS. A similar notion is that the instructional strategy "I do, we do, you do." also has a negative connotation. With problem-solving and mathematical modeling, direct instruction is not the focus. The focus is conceptual understanding. From my experience, I've learned that timing and placement of direct instruction is what matters. I've been catching up on reading NCTM's Principles to Actions and I highly recommend it to anyone; teachers, coaches, parents, administrators, students, and more. It's about 100 pages. Get on it! I think it paints a pretty clear picture why, how, and when conceptual understanding should take place in relationship to procedural fluency.

Principles to Actions really does a great job driving the point home that procedural fluency is important. However, procedural fluency won't stick nor have significant meaning if the students lack the conceptual understanding first. When I'm done with Principles to Actions and have had a chance to let it simmer in my brain, I plan to blog more about it. I also need to explore the Principles to Actions Professional Learning Toolkit.

Last, and certainly not least is literacy. I'm glad that one teacher at a recent workshop voiced her concern about teaching literacy in math and that the use of multimedia in a 3-Act task or an Estimation 180 challenge really doesn't strengthen literacy. I agree.

Trust me, I'm all about building literacy. However, the more I teach and work with teachers, the more I believe in the importance of making the conceptual understanding accessible first as a means to transitioning to procedural fluency and strengthening literacy by scaffolding. If I don't make the conceptual understanding accessible to my students, than I'm not scaffolding both the mathematical procedural fluency and literacy.

That said, I tried to imagine what Day 185's bacon estimation challenge might look like. I still love the visual and simple question and would still start with the current setup as the introduction to the task. Once students and teachers voice their questions, Act 2 information might be presented in text. Here's what I came up with (I know it could be better):
I have 20 minutes to prepare and eat breakfast before leaving for work. I need to cook 12 pieces of bacon for my family and the skillet only holds 6 pieces at a time. We like our bacon crispy, but not like charcoal. The gas stove will be at a medium to high heat. The first batch of bacon starts to sizzle one and a half minutes after I put the skillet on the lit stove. Five and a half minutes after the bacon starts to sizzle, it is about 65% cooked. Will I have enough time to cook all 12 pieces of bacon?
I'm not sure this blog post brings much closure. However, it has brought a greater focus for me as I prepare for the school year. I am more focused on
  • students asking questions
  • students building conceptual understanding first
  • teachers making conceptual understanding more accessible (as much as possible) 
  • teachers scaffolding their classroom activities and direct instruction to strengthen procedural fluency by building upon conceptual understanding
Does this sound reasonable?
How do you like your bacon?
Let me know. I'm on my way to finishing Principles to Actions.


Saturday, August 1, 2015

CA Teachers Summit Ed Talk

I had the honor and privilege to give an Ed Talk at the California Teachers Summit held on Friday, July 31, 2015. Across the state of California, teachers attended college campuses for breakout sessions, Ed Talks, and keynote speakers. I gave an Ed Talk at the Pasadena Convention Center titled, Estimation: A Gateway To Better Number Sense. Check it out.

I gave an Ed Talk at the California Teachers Summit on July 31, 2015.

I also had the privilege of meeting the other two inspiring Ed Talk presenters, Nicol R. Howard and Thema Bryant-Davis. The highlight of the day for me (and my son) was that I got to meet one of the Keynote speakers, astronaut Leland Melvin!
Nicol, Leland, and me
Ed Talk,

Thursday, July 16, 2015

Turning 3 Challenges Into 3 Charges

My next three weeks are slammed with opportunities, via conferences and teacher trainings, to work with fellow teachers, learn from them, and share resources and thoughts about what I'm most passionate about in math education. The great thing about this two-way learning environment is that it will make me even stronger and better equipped for the upcoming school year as I support my fellows in their classroom.

If we're at the same conference or teacher training, you will be hearing me drive home the importance of the following three challenges we face as teachers of students and students of teachers:
  • Problem solving
  • Student thinking
  • Number sense
  • Why are these three challenges so important?
  • Why am I so passionate about lesson design and tech tools that meaningfully support these three challenges?
  • What resources are available to teachers to support students?
  • How do we implement said resources to support problem solving, student thinking, and number sense?
At the end of our time together during a workshop or conference, I hope you become better equipped with strategies, tools, resources, ideas, and inspiration to make them your charges for the upcoming school year.

Thanks in advance for letting me be part of your valuable PD time and for allowing me to absorb your insight and knowledge at the same time.  


Sunday, July 5, 2015

Open House: Week 1, Day 2

Last week was the first week of a four-week summer academy. I teach a 110-minute class, four days a week, and it's designed as an enrichment course: no homework, no tests, no grades. The class is titled Get Ready for Algebra and here's the working schedule for the four weeks.

It's a great opportunity for me to practice some of my skills; skills I once possessed and skills I learned this past year, but didn't practice enough. Initially I thought I'd be keeping some of my skills sharp, but I soon found out how rusty I am at various moves, ranging from facilitation, to instructional, to questioning. How do I know, I recorded three of the four days last week.

Before I break down an 8-minute video clip from the second day, I want to be clear:

1) It's Open House everyday in my classroom. Anyone is welcome at anytime. I observed so many teachers this year and am extremely grateful for the opportunity. I learned a lot by being an observer. Being an observer allows me to reflect on my own practices, not necessarily the person being observed.

2) Recording my Open House classes allows me to identify certain skills and improve them.
These are NOT self-fulfilling, self-righteous, self-absorbed, self-promoting attempts at my own teaching. If I am to encourage other teachers at video-recording their teaching in the name of professional development, I need to do it too.

3) What professions record themselves (or other professionals) as a means to strengthen their craft? I recently tweeted some professions that benefit from recording their craft, ranging from athletes to musicians to dancers to doctors to comedians to teachers. You can only get better, right?
4) I need to be vulnerable, humble, and open to improve. I intend to keep my video clips to segments shorter than 10 minutes. I picked a specific part of the class I wanted to focus on improving. Even if no one else sees your video, I hope you'll prop up a camera in your room and record 10-15 minutes of your class. Play it back and reflect. Go in the next day and make those changes (improvements) you want to make.

5) One more time: These are NOT self-fulfilling, self-righteous, self-absorbed, self-promoting attempts at my teaching. Nor do I pretend to be perfect at this stuff. I just know I can be better and video recording helps immensely. If you have the stomach to continue, you'll see my notes as I reflect on my facilitation of this Estimation 180 challenge: my wife's height.


I ask the class to share a "too low" for Mrs. Stadel's height.
I try to get the class' attention about writing down 4'10" and how it's confusing... because I know students typically write feet and inches using decimal notation (4.10).

Here's what I wish I did (or could have done):
If I had done a better job of checking student work while they're working, I would have known how the student wrote 4 feet 10 inches on her paper.
I wish I asked the student how to write 4 feet 10 inches on the whiteboard.
I could have had the student write it up on the board while all the students were working.
I should have asked her why 4'10" was a reasonable "too low".
Having her share her reasoning would strengthen her voice and mine at the same time.

I received 7'10" from another student for the "too low" and asked "Is that taller than me?"
Like the previous student, I should have asked her to share her reasoning.

"Did anyone put 6'4" as their 'too high'?"
I need to capitalize on why 6'4" would be an extremely reasonable "too high".
Five students raised their hand on camera and I remember about two others students (off camera) raised their hand as well.
I should have followed up with at least one of these seven students as to why 6'4" makes sense here.
*I usually do this... argh.

"Don't share with me, share with your neighbor. Share with your group."
Why did I not say, "I would also like you to explain your reasoning behind your answer."
This would have also bought me an extra minute to check in with at least one more student. When checking in with students, I typically have them rehearse on me so I can encourage them to share whole group in a few minutes.

I began to take four estimates.
"I'm totally forgetting something."
I forgot to introduce the idea of students filling out their number lines.

I like the idea of the class filling out the same number line together on the first estimation challenge.

I explain that it's a common student misconception to put their estimate right smack in the middle of the number line, even if it's wrong.
Instead of being abstract in my explanation, I could have been more concrete by showing them an example. Let's say a student thinks Mrs. Stadel is exactly 5 feet tall (5'0"), they would still put there answer right smack in the middle. I should have put 5'0" in the middle.
Ask students: What's wrong with this?
Ask students: How can we use this number line more accurately?

I was truly lucky to get a difference of three feet between 4'10" and 7'10".
I didn't explain my thinking to students: I knew it was three feet, but didn't explain that I knew that half of 3 feet is one and a half. I should have modeled my thinking for students.

"For time reasons, I'm going to help you out"... look at me, the clock watcher. Am I really helping students out? I feel more like I'm helping me out by bailing them out. For about a minute, it's me doing the math, not the students.

How silly of me, I could have simply marked 5'10" and 6'10" on my number line breaking the distance between 4'10" and 7'10" into thirds. And again, explain my thinking.

I'll start taking your guesses.
I like when I ask students to stop me when I get to their guess on the number line.
Should I take the average? or should I have students argue it out?
I think the latter.
Here's why: that initial placeholder on the number line impacts EVERY estimate afterwards. Make it count.

I just got done taking four estimates and didn't ask for one single reason behind them...
I say, "A lot of good guesses here." because I already know the answer. I can see that the four estimates I took are in the ballpark. However, I never called on one of those four students to convince me.

I tried to dig myself out of this hole by saying, "I'm going to keep you guys in suspense."
I wouldn't say this is the best move. However, it was better than completely ignoring (or forgetting) the reasoning behind their estimates.
I went with two reasons. Half the number of guesses I received just a few minutes prior. BUMMER.

Once I revealed the answer, you can hear the "ohhs." because they were actually pretty close.
I say, "If you are within one or two inches, you should be really proud of yourself."

A student says, "Dude! I was off one inch!"
Same student, "I'm so happy!"

Maybe I missed it (or forgot by now), but a couple kids had a huge sigh of relief and were even excited about this. Seriously, that's awesome. If all we did was worry about our "answer" being exact every time, then we've lost focus on the process of estimating. Doesn't it feel absolutely awesome to have an estimate within a couple inches?

For my second day, I've seen how rusty I am and what needs improving. Moving forward:
Goal #1:
I want to cheat when placing my "too low" and "too high" on my number line from now on. Once I place my "too low", I will choose a "too high" that allows me to easily partition my number line into reasonable spacings.

Goal #2:
While students are filling out their handouts, look for 8 different students and prepare them that I'd like them to share with the class (and include reasoning):
Too low: 2 students
Too high: 2 students
Actual estimate: 4 students

Goal #3:
Ask the class who agrees or disagrees with the first estimate given.
For example, "Who disagrees with the estimate of 5'9" and would like to share why?"
Continue this with the second and third estimates given.

If you made it this far, feel free to offer any suggestions to help me get better. Thanks in advance.

Open house,

Thursday, July 2, 2015

Barbie Zip Line (2015) Part 1

Last summer I tried Barbie Zip Line and reported the experience here. I also supported a handful of Math 8 teachers interested in Barbie Zip Line during the school when they explored the Pythagorean Theorem. I have to admit, with every experience, it always felt like it could be different, possibly better.  This year, I went a different route and Part 1 just documents what I've done so far. Part 2 will be the conclusion.

First, I avoided the Pythagorean Theorem (for now). On Monday, my students already knew we would be starting Barbie Zip Line on Thursday. That was about as much information as I revealed. Everything else was structured to elicit as much student insight, information, and ideas as possible.

I started by projecting this slide:
Students discussed in their groups and a few shared whole group. I jotted down a few quick notes:
I love this informal language. Would this be an opportunity to work in slope? Maybe. I wouldn't force it as I'm confident we'll have plenty of other opportunities.
Me: Has anyone her gone zip lining before. 
A few hands go up.
Me: How would you describe it to someone in the class who has never been?
Katherine: Awesome!
Me: How would you describe what zip lining is to someone unfamiliar to it?
Katherine: You wear this harness. You ride down a line...
Mateo: You have two cables attached to you in case one of them breaks, there's a backup. Someone pushes you at the beginning and you ride along a cable...
Me: Great. Thanks. Would it help if we saw pictures or video of someone zip lining to give everyone a better perspective?
Everyone: YES!
Me: Here's what Google Images has for "zip line pictures". 
Me: A good business model will provide their customers with a safe and thrilling experience. Therefore, I'd like you all to fill out this Google Form with the following prompts and questions:
  • Briefly describe the characteristics of a DEATH zip line.
  • Briefly describe the characteristics of a BORING zip line.
  • Briefly describe the characteristics of a JUST RIGHT zip line. 
  • What information would be useful to know when building a zip line?
  • If we had a small scale zip line in class, what data can we collect from the small scale? 
I'm fascinated by the results. I learned I need to truly value, trust, and use my students' intuition way more often and when launching a lesson/activity. Check out their results here. These results will help guide Desmos Part 2. However, first we need to do Desmos Part 1.

The actual zip line quad.
Desmos Part 1
Students go to this Desmos graph and quickly create three zip lines.

Once they are done, they head over to this Padlet page and post their Desmos graph for their classmates (and me) to see.

Desmos Part 2
*I will post what students do in Barbie Zip Line (2015) Part 2.
Before going outside, students begin doing a small scale version of the zip line inside the classroom. Here are the materials:
  • 3 paper clips
  • 2 measuring tapes
  • 1 string (100 inches)
  • iPad (for Desmos part 2)
  • iPad or phone timer
Record their data inside of this pre-made Desmos template.
*If you go the route of the Pythagorean Theorem, adjust your table accordingly.

Here's a handout for each student. After collecting their data, students will be expected to draw a pretty descriptive scale picture of their zip line on this handout. They'll also need to predict how long it will take their doll to complete her zip line ride.

As you can see from the handout and expectations, I'm placing a big emphasis on the following:
  • Scale
  • Proportional reasoning
  • Rate of change (or slope)
  • Rate
No mention of Pythagorean Theorem. Find out if it stays that way in my Barbie Zip Line (2015) Part 2 post, next week.

Zip 1,

P.S. Most importantly, my son was really excited to visit my class today and partake in the Barbie Zip Line adventure. I was really excited too. DUH!

Wednesday, July 1, 2015

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,

Thursday, June 25, 2015

How Much Is Your Name Worth?

Starting next week, I'll be back in the classroom with my own roster of students. I'm super pumped and plan to be really active on this blog...  I plan to do a mixture of blogging about ideas before I use them with students and after I use them.

I need to quickly learn the names of my students on Day 1, especially since I'll only be with them for only 20 days. I'll probably do the Name Tent activity and Class Height activities found here. However, I want to establish some mathematical tones as well. For example, most tasks/activities will require students to:
  • make guesses (too low, too high, just right)
  • submit data
  • collect data
  • sort data
  • use the data
  • measure
  • problem-solve
  • make predictions
  • use technology
How much is your name worth?
If each letter of the alphabet was worth its place in the alphabet, how much is your name worth?
For example:
A-N-D-R-E-W would be 1 + 14 + 4 + 18 + 5 + 23 = 65

Figure out how many points your name is and submit it here:

What name will have the lowest points?
What name will have the highest points?
What will be the class average?

If this is golf, the lowest wins.
If this is basketball, the highest wins.
If I want the class average, what would that be?
  • Students will submit their values using Google Forms.
  • We learn how to sort the data in Google Sheets.
  • We can answer our questions.
  • We can use the data to predict the value of the next person that walks into our class, or the principal, or a parent, a stranger, etc.
This should not necessarily last that long, but there will be parts of the process that will be important to being more successful and efficient during our time together.

Name value,

Tuesday, June 16, 2015

Classroom Visit in New Hampshire

Yesterday, I had the great fortune to Skype with a second grade class and their teachers in New Hampshire.


There were about 6 students who came up to the webcam to:
Here are some of their favorite Estimation 180 challenges:
Some of the questions they asked:
  • How do you say your last name?
  • How do I think of the estimation challenges?
  • Who takes the pictures of me?
  • Will you do more Lego estimation challenges?
  • How many estimation challenges are there on the site? (I was asked this twice.)
  • Will I continue to make more estimation challenges?
After finishing Q&A with my six new friends, Ms. Spear asked if anyone else wanted to share something. One girl spoke up and thanked me for
"...helping my brain to think more and not give up."
This warmed my math heart and made my day. I think that's a direct reflection of Ms. Spear and her colleagues who are creating a classroom of curiosity, perseverance, and risk-taking. They're raising the bar high for all of us, so anyone who gets Ms. Spear's students in the future, please continue to carry the torch and never let that flame become extinguished.

Something else warmed my heart. Ms. Spear shared that the class used estimation challenges, mohawks, and the strength of a small school community to raise money for Levi and his fight with cancer. Woah! Cool!

I thanked them for being such a polite, mature, and respectful group. As you can only imagine second graders staying seated for longer than 18 seconds is a small miracle. They were a classy group that has inspired me.

Thank you Ms. Spear and your students for allowing me to briefly visit your classroom.
You're the inspiration!


Monday, June 15, 2015

Fastest Sticky Sticker

It's rare that I post about something I haven't tried in the classroom. Here's an idea that came to me today, inspired by:
I haven't done this activity, yet. If you try it out, please report back or offer suggestions. Thanks!


Who is the fastest Sticky Sticker?
Translated: Who is the quickest at covering a 2-dimensional shape with sticky notes?

  • Whiteboards
  • Stickies
  • Blue painter’s tape
  • Scissors
  • Timers
Break students into groups.
Have them time each other sticking 10(?) stickies somewhere (whiteboard, desk, etc.).
  • Determine who is the fastest Sticky Sticker of the group.
  • Use their cell phone stopwatches as timers
  • Use some type of table to predict how long it will take each person to stick different amounts of stickies and write an equation.

  • Have each student determine their rate.

Reveal the playing fields

  • First, without the dimensions, of course.
  • Muster up some trash-talking
    • I bet you I could beat anyone in here with one-hand behind my back.
    • I might even give you a head start.
    • I could beat you blind-folded.
  • Have them write down guesses as to how many stickies will cover each shape.
  • Have students guess the dimensions.
  • Have measuring tapes out for students to measure their shape.

Have all groups figure out how many stickies are necessary for each shape. All dimensions given in inches.

  • Square (24x24)
  • Rectangle (21x27)
  • Triangle (27x24)
  • Parallelogram (24x18)
  • Trapezoid (b1= 27, b2=21, h=18)
  • Circle (d=18)

*The following is where I start thinking out loud and not entirely sure what makes sense since I haven't tested this out with students. Feel free to try it out and please report back.

Have each group randomly pick a shape.
  • I'm going to predict that some students or groups will complain/gripe about receiving anything other than the square or rectangle. That's where the scissors come in.
  • Give each group the amount of stickies they calculated for their shape
    • Include a couple(?) extra stickies for a mistake?
    • Give scissors to every group, but the square and rectangle groups.
  • Groups who don’t get the square or rectangle must cut their stickies to fit inside
    • The Circle group(s) should maybe get a little bit of a cushion (modification).
    • The square and rectangle groups need to be challenged while they wait.
    • They can help other groups prepare or figure out a reasonable head start.
  • Should certain shapes get a head start?
    • Should the head start be:
      • time?
      • stickies?
    • Can we modify any of our equations from above?

Ready, Set, GO!
I’d love to see each student participate in the competition. At first, it might appear as though each group picks the fastest Sticky Sticker, but I’d love to make this competition a relay race.
  • Have each group divide their total number of stickies by the amount of group members
    • Each group member should stick about the same number of stickies.
  • Groups determine the order (strategy)
  • Could we graph what that might look like?

*At this point, go back to the blog posts by Al and Jon for more tips.

Determine how the head starts will be determined.
Blow the whistle and get kids sticking those stickies.
Congratulate the winners. Take selfies. Play your national anthem...

Round 2
Who can take the sticky notes off the fastest?

Useful Math:

  • Area of various 2-D shapes
  • Ratio of stickies stuck to time (or time to stickies)
  • Rate
  • Unit rate
  • Writing an equation to model the rate
  • Using the rate to predict how long it will take
  • Possibly graphing the data (or “constant of proportionality)
  • Translate (graphically) the equation above to account for the head start
  • Piecewise functions for different members of the group.
  • Decompose square units in a defined area

Let me know if you're going to try this one out. I will probably test it out in a few weeks during my summer course and report back here.

Sticky sticker,