5th Grade Fun

Yesterday was AWESOME!

I had the great fortune of visiting Jen Sandland's classroom in the morning.

Such an engaging, energetic morning learning w @mr_stadel Thank you for sharing your love of math w my Ss! @TUSDSTEM pic.twitter.com/4j6wqgsdQU

— Ms. Sandland (@SandScholars) January 27, 2016

Jen is a 5th grade teacher in my district. Her students and I spent an hour having a blast:

• talking number sense
• doing Estimation 180
• doing Clothesline math
• measuring

Jen's students have done a few Estimation 180 challenges this year. Therefore, I assumed they already knew my height. WRONG! So, we started with estimating my height. The best part of the conversation was helping students deliver their answers like 6.2 as 6 foot 2 inches. It was sooooo cool to hear students catch themselves, and work at eliminating the decimal point when referring to feet and inches. Once they found out my height, I took three student volunteers for the class to estimate their heights?
A BLAST!

The tallest student, (we'll call her Jane), came in at a towering 5'2".  I was holding a part of  the clothesline in my hand as the remainder of it was outstretched on the floor. I asked the class:
"How many Janes would make the length of the clothesline?"

Oh, man. You should have seen these kids talking about this? Some made guesses like four or five Janes. Naturally, I asked, "So how long are four Janes? How long are five Janes?"

I wish I took a picture of our model, but it looked something like this:

One student explained his method of adding the feet first and then the inches. It was amazing! So we came up with the length of the clothesline as a range of 20'8" to 25'10". I then had two students help me measure the clothesline against Jane's height and we almost got five Janes. That makes sense because the rope is actually 25 feet long.

We used the clothesline to talk about Day 150 on Estimation 180.
What will be the value of the finished cent sign?

The thinking, strategies, and conversations were so cool. We placed our too lows, too highs, and just rights on the clothesline. We talked about order, magnitude, and spacing. If you do Day 150 with students and you're watching the answer as a class,
PAUSE THE VIDEO WHEN THE "C" IS COMPLETED TO MAKE $0.65.

Cent Sign of Pennies from Mr.Stadel on Vimeo.

Give students a chance to revise their initial estimates. It's such a powerful experience. Pause those video answers and let students change their answers once they have more information.

Before my farewell, the students asked me a few questions:
How'd you make the video to the pennies answer?
Take a picture of the complete layout. Subtract a penny. Take another picture. Repeat.

What program do you use to make the counters on Estimation 180 videos?
Apple's Motion

What are your favorite Estimation 180's?
The music challenges. HANDS DOWN!

Did you always like math?
No. I loved music and art in school. I was just good at remembering math rules. Now, I love getting better and understanding numbers.

My question to them:
What is your favorite thing about numbers?

They are expected to answer this when I return to their class. When I return, I'd love to just blend in, if that's possible, while they are doing math centers or other activities and learn from them. Man, these kids were so fun to hang out with for an hour.

Thanks Jen! Keep up the fantastic work you're doing with them!

5th,
924

Tech Tool Criteria

Why get out of bed tomorrow and teach math?
I love student thinking because it helps drive my math instruction.
*this is just one reason for me

So when it comes to tech tools in the math class, I need tech tools that allow me to focus on student thinking because student thinking will better drive my math instruction. This video shares a few more detailed thoughts:

Here's my criteria:

In order to focus on student thinking, my tech tools need to :

• CAPTURE
• SORT
• ASSESS 
• DISCUSS

Let me explain:

• I need tech tools that capture student thinking as best possible. And I mean ALL students.
• I need tech tools that sort the student thinking efficiently and effectively. 
• I need tech tools that allow me to quickly assess what students are thinking. In REAL-TIME.
• I need tech tools that allow the students and me (the teacher) to discuss the thinking and mathematics that has been captured, sorted, and assessed.

My next post will include:

• my rubric
• examples of tools that currently DO and DON'T meet my criteria 

What's your criteria?

Student thinking,

912

Integers [temperatures]

Yesterday, I co-taught an integers activity with a colleague. It was a blast! Before I share the lesson, I'll back up and give the backstory on the context. During winter break, I ventured over to Brian Head, Utah to do some snowboarding. I knew it was going to be cold so I went into the trip with the intention to frequently check my phone's weather app and take screenshots of temperatures. I figured I might be able to make an activity out of it and/or use it with 6th graders at some point when discussing integers. (official lesson page with resources)

My fellow displayed this slide and asked, "What do you notice? What do you wonder?"
(the 3 in the lower right is the slide number)

Students noticed and wondered great things. Here are just a few:

• What's the temperature at 9am?
• Why is it warmer on the days it is supposed to snow?
• Thursday is the only day with a negative temperature.
• It's 4:13 am.
• It's zero degrees at 5am.
• It's cold!
• How cold does it get?

We established that -4 degrees Fahrenheit is cold, below zero, and the temperature at 4:13 am. Let's plot this on a vertical number line today, just like a thermometer. Does -4 degrees go above or below -5 on the vertical number line?

I told students that we're going to show them five more times and their temperatures throughout the day. Most importantly, I asked students to first predict the temperatures at those given times (tap into student intuition). Here are the times:

• 6:00 am
• 7:00 am
• 9:30 am
• 2:30 pm
• 8:00 pm

Essentially, we're tapping into student intuition, a free resource in our classrooms. I want them to predict the story of temperatures and degree change for the remainder of the day. If anyone has experienced winter weather, they know it gets cold at night and warmer during the day, possibly peaking midday. It's a small part of the activity to keep it moving along and gain student investment.

Here come the temperatures. For each time and temperature revealed, here's what were going to do:

• Plot the temperature on your vertical number line.
• Find the degree change between the last temperature given.
• At the end, we'll find the largest difference in temperature during the day.

Here's a few of our whiteboard representations:

This was a simple and fun context to work with integers and the vertical number line. I also took screenshots of the temperatures in Celsius and might be able to make a Math 8 activity out of it. Here's the desmos rough draft.

The best part for me (as a teacher) was listening to students make sense of the temperature changes and explaining their thinking. There were so many opportunities to help students with their vocabulary. For example, when asked, "what's the difference between 12 degrees and -8 degrees?" it was interesting to hear how students wanted to change -8 to a positive in order to add it to 12. There was our intro to absolute value and a number's distance from zero. Love it!

One student came up to me on his way out and showed me his paper,
"Hey Mr. Stadel, I predicted the temperature correctly for each time!"
High-five!
I asked, "Do you want to pick my Powerball lottery numbers for this week?"
He declined. Drat.

Again, official lesson page with resources here.

Brrrrrrr! it's cold,
225

Make It Happen

"This could have easily been a two- or three-day activity."

I literally just met with a fellow who made this comment after we debriefed on an activity she prepared for her sixth grade students. This comment was the result of how rich the activity was. The math was rich, students were collaborating, there was student thinking, great visual representations and she did a wonderful job facilitating the activity based on 6.NS.C.6.A.

I'm sure you can relate with the sentiments expressed by this teacher. You had an activity where students would benefit from it and you wish it could go on forever. I remember experiencing this too. Here are two solutions to this [great] challenge:

Short-term:
Subtract your homework, guided practice, and housekeeping stuff from your Classroom Clock for that day (and maybe the next day).
*I'll blog more about my definition of a Classroom Clock soon.

Long-term:
Do bits and pieces of this type of activity most days of the year so students are more and more familiar with these concepts and practices.

I prefer the long-term goal! (and assigning extremely little-to-no homework EVERY day)

Example:
In this case, the teacher prepared a Pear Deck activity where students would drag colored lines to represent the placement of fractions and their opposites on a number line.

The ratio of students to devices was 4:1. After each Pear Deck slide, the teacher provided a validation slide displaying the correct placement of each line. In addition to the pear Deck activity, she also had a clothesline number line across her room where students interacted with these same fractions in a different yet still dynamic way.

The teacher's learning objectives were met with this activity, but let's move toward retention. We talked about doing this more each day. (long-term solution). Here are some specific ways:

• Make these activities the two-three minute warm-up at the beginning of class each day. 
• Do them as a transition in your class. For example, "I need you to put your notebook away, get your whiteboards out, and when you're ready, place 3/10 and 7/5 on a number line." 
• Make them an exit activity before student leave for the day.

If you agree to provide students with access to rich math, find ways to make it happen more often.

Long-term,
159

Productive Struggle [part 2]

Recently, I started thinking more about productive struggle:

• Blogged part 1 here
• Desmos activity here
• Comments and questions contributed here

Thanks to all (approximately 100) who participated. Here's an overlay of the Desmos activity:

I noticed (of those who participated):

• there isn't necessarily a one-to-one relationship of struggle to frustration.
• most participants will struggle for a bit before getting frustrated.
• some participants thought their frustration was logarithmic or exponential

Here are a few of the graphs.

I love that there's a story behind each graph. I love that the graphs are practically all different. Looking at the responses of math educators, it convinces me that we are just like a classroom of math students. Not surprisingly, we're all different and the relationship between struggle and frustration is different for everyone, much like the students in our classes. So what's next?

As teachers, we need actionable steps when working with math students who might be at various levels of struggle and frustration during an activity or task. From my experience, I believe the best actionable step is communication. Communication is what's next.

This idea of communication was shared by many math educators in the Desmos activity. At the conclusion of the activity, I asked for some final thoughts. If students are allowed to reasonably struggle with a math task, what would be a teacher prescription of actionable steps to:

• move the learning forward and 
• avoid a meltdown level of frustration?

Here are a few responses:

• using well-timed and small hints as needed
• humor helps
• constructive feedback that promotes reflection on the students thought processes
• have a set of scaffolded supports easily available and in multiple mediums
• hints and scaffolds are appropriate, preferably after significant struggle has already been felt
• reminders that everything worthwhile takes work 
• look at mistakes together and see what we can learn collectively
• let students explain their thinking, then discuss as a class
• turn and talk to your neighbor about this problem.
• develop a series of hints/question schemes to use with students
• determine the "breaking point" where the teacher should use whole group/small group instruction to address misconceptions to alleviate frustration
• remind yourself to ask questions before dispensing information
• remind your students that taking a break and coming back to the problem is sometimes a great idea
• pair them with someone else, ask them to break the problem down
• chunk the task or you can take a break and come back to it later
• learn to judge frustration level, have some strategies ready for each level
• I like using VNPSs so that they can look at other groups for ideas.

In my teacher mind, these all include some form of communication. Communication is happening either visually, orally, conversationally, or with questions and hints. THANK YOU for sharing these ideas so we all can make our classrooms a better environment for communicating. Many of these resonate with me, especially the scaffolded hints and questions. I'd like to share a few from my experience with students (and adults in workshops):

• be sincere in your communication and questioning
• anticipate student mistakes/misconceptions before students do the task
• compliment a strategy/idea/mistake students make that might nudge them forward
• ask another student to explain the task or sticking point to a struggling student
• explore a list of 26 questions to ask students (from Max Ray-Riek)
• listen to student thinking, not for the right explanation (see Max's Ignite)
• reassure students that you're confident they can solve it (or progress before the end of class)
• give hints that might refocus their energy on a small part of the task that's solvable or might gain them some momentum
• don't game students
• don't ask, "what do you think you did wrong?"
• don't ask, "do you think that's correct?"
• don't ask, "does that make sense to you?" (about the student's work)
• don't let students work too long on an incorrect strategy

These are two LOOONG lists and I could add even more to them. These lists are not for every student or teacher in every situation. The length of the lists and their variety convince me that it's best we know our students best when communicating with them during a math task in which they most likely will struggle. Some of these steps might appear as though I'm bailing a kid out or robbing them from some learning experience. Maybe. However, I believe we all have students that need strong encouraging hints that will give them momentum instead of me letting them struggle for too long and take the chance of losing them for good. Likewise, I don't see any point in letting students work too long on an incorrect strategy if I spot it while they're working. I'd rather use that valuable time to ask them questions and redirect them. 

I thought about writing a few conversations I've had with students, but every conversation is different because every student is different and their mathematical thinking can be different. The result is that conversations with students during a math task are many times like fingerprints; they're identifiable and we can learn a lot from them, but no two are the same.  Therefore, our communication with students should be customized to that moment. Does it help to have some "go-to" responses? Absolutely! Here are mine.

When walking up to a student for the first time, you can find me initiating the conversation with:

• Show me what you've tried so far.
• Tell me about what you've done.
• Do you know where you're stuck? If so, show and tell me about it.
• Where are you confused?
• I noticed you did this [something in their work]. I'm curious why you did that.
• I noticed you have something circled here. Explain that to me or tell me why that makes sense to you.

I try to ask questions or give commands that allow the student to communicate to me what they've tried, what they're frustrated with, or what sense they've made of the task. More often than not, I will try and ask the most-efficient and revealing question. In other words, the question that tells me the most information about their thinking in the shortest amount of time. The goal is to use this ice-breaker question/command as a quick formative assessment while I look at their work (or lack thereof). Okay, so what's next?

Depending on their response, this is where it gets tricky. Once a student has shared their work, thinking, mistake, or blank paper, we need to be in tune to what the student gives us or doesn't give us. We need to allow the communication thrive. I love the post AND comments in this blog post by Annie Fetter, titled One Example of a "Bad Hint." Bookmark this post and revisit it when you need it. There's some great insight from Annie and everyone in the comments. Since many math educators mentioned hints, it reminded me of her post and how it has helped me get better at questioning/assisting students during math tasks. What if hints don't always work? What's next?

Offer some assistance. There's nothing wrong with this. Yes, I agree with Being Less Helpful. However, we're working with students. Their brains are still developing. They (and some parents) see us as adults in positions to offer assistance in the learning process. I'm not advocating we bail students out. Yes, it's a fine line we have to walk between productive struggle and meltdown frustration with students (and parents) at times. Trust me, I've learned the hard way. I've walked away from students after making some naive comments like, "You'll figure it out." or "Keep working on it." or "Does that make sense to you?" when I knew all too well that they wouldn't figure it out, or working on it more will cause them frustration, or that of course it makes sense to them because they're the one who came up with the answer. DUH! I'm good with offering some assistance to students who really need it because it will save both of us some frustration and I'm not about gaming students. I've tried the following inexpensive response and it's gotten me some mileage so far:

How about we work on this together for about a minute? We'll get started together and then I need to go check in with other students. 

We're knocking at the door of perseverance with everything mentioned above. I should address it a bit. Again, communication is our ally here. I've found I get a lot more from my students when I communicate to them something like, 

I know today's task might be challenging. I'm confident you will work hard individually and together. Most of you will make mistakes, but I've seen how well you learn from mistakes in the past. You know I'll check in with you throughout the task, and might offer some hints if you're stuck. However, remember that I want you to first explain your strategy to me first.

Whatever you tell your students, be sincere and honest. Admit when you know a task will be challenging. Admit when you've given them a task too challenging. Likewise, admit when you've given them a task too easy. We're getting better at this teaching stuff, just like they're getting better at that "student" stuff. Honor the fact that one of your roles as a teacher is to both model and encourage perseverance. A lot easier said than done, right. But that's why we're here (#MTBoS) for each other. We share ideas with each other to make our math classrooms a better place for learning and teaching.

I'm not sitting down to write this post because I'm claiming I know all the answers. I had a few goals when initiating these two posts on productive struggle:

• learn how others perceive the relationship of struggle to frustration
• share actionable steps from other math educators
• share actionable steps that have and have not worked for me
• stress the importance of communication
• encourage others to offer timely assistance without bailing students out or being too helpful
• learn from other math educators how to best communicate with students so that they persevere through struggle

SO there it is. Your turn, please. What is your experience?

What are your go-to responses or actionable steps in moving the learning forward while encouraging students to persevere?

Steps,

840

*Here's the link to the Desmos Activity if you want to adapt it and use with your students.

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.

Struggle,
1128

Part 2 is here.

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.

Literacy,
1020

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.

AND VERY WRONG!

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. 

YES!

834

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!

Ignite,
945

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

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.

Tech,
816

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).

Cheesy
603

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 goformative.com 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.

Cheese!
246

Is Your Math Class Forgettable or Memorable?

A little over three days ago, I tweeted the following:

I’m preparing for an IGNITE talk. What’s the most a) forgettable b) memorable part of your math class? #MTBoS

— Andrew Stadel (@mr_stadel) September 17, 2015

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. 

Memorable,

939

Clothesline

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,
Andrew

*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:

"Clothesline is the master number sense maker." says @timsmccaffrey according to @MathProjects. Good call Tim! pic.twitter.com/bVvvJz7CtX

— Andrew Stadel (@mr_stadel) August 19, 2015

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 ROPE
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.

THE CLOTHESPINS
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.

VARIABLES
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.

FUTURE USE
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.
"What?"

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.

Clothesline,
930

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.

Dots,
1200

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

Dan Kearney shares more goodness from Steve Wyborney.

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.

Bacon,

219

Until Further Notice...

This is me until further notice...

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,
1146

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.  

Charge,

855

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?

What professions record themselves (or other professionals) as a means to strengthen their craft? #thinkingoutloud

— Andrew Stadel (@mr_stadel) July 1, 2015

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.

    

1:45
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.

2:10
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.

2:20
"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.

2:35
"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.

3:15
I began to take four estimates.
"I'm totally forgetting something."
I forgot to introduce the idea of students filling out their number lines.

4:00
I like the idea of the class filling out the same number line together on the first estimation challenge.

4:20
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.

4:55
"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.

5:10
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.

6:10
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.

6:15
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.

7:45
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,
816