Square Dance

I recently debriefed with a fellow (teacher I support) about two activities focusing on Squares, Square Roots, and Irrational numbers. Let's build number sense. Here are the goods:

• Clothesline activity using these cards
• Square Dance desmos activity

She ran both activities with students, starting with the Clothesline activity. She used the cards linked above for students to first place the visual representations on the number line. It looked something like this:

Followed by:

Students then completed the first 7 screens in the Desmos Square Dance activity. Screen 6 includes a validator when done correctly, compliments of Nathan Kraft.

*Please note that part 1 of the activity uses only whole numbers as rational numbers. I highly recommend using the activity as a launching point for students to know that perfect squares include other rational numbers like fractions and decimals. 

Back to Clothesline:

This week she will use the next set of cards for irrational numbers. It might look something like this on the number line:

Followed by:

Back to Square Dance 

Students can build better conceptual understanding of irrational numbers in the desmos activity. Also look for teachable moments throughout the activity. 

*Please note screens 11 & 15 include non-repeating and non-terminating decimal notations. 

Screen 11

Screen 15

Just like Screen 6, Kraft-y validators are included on screens 12 & 16.

Two closing thoughts:

1) My fellow was so happy to use these conceptual representations with clothesline and desmos. 

2) She hasn't seen students making mistakes like she has in the past. Here's an example (crossed out) of a common mistake she has seen regularly in the past.

If you have time, head over to this post and have your students play War with the Rational-Irrational cards provided.

Dance,

945

Clothesline Cards Hit the Floor

A colleague and I stumbled upon an opportunity to strengthen number sense with students using a double clothesline. The video says it all:

 *For more fun with clothesline math, go to Chris Shore's designated site: clotheslinemath.com

Floor,
831

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

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

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

Pumpkin Seeds

For Halloween, we gutted the larger pumpkin from Day 197 for two reasons:
1) To carve it and
2) To roast the seeds

*Little did I know this pumpkin would produce many number sense opportunities beyond Day 197's weight estimate.

My 4.5 year-old son helped gut the pumpkin with me. We gathered as many seeds as possible and set them aside for the roasting process. The recipe I use can be found here. Before mixing the seeds in olive oil and seasonings, I lowered the pan down to my son and asked how many seeds he thought there were. [How many do you think there are?]

 

Me: How many seeds do you think there are?

Son: Well, ...[thinking for a few seconds]... there's definitely more than a hundred.

Me: How do you know it's more than a hundred?

Son: It just looks like more than a hundred.

Me: Make me a pile of seeds that would be about 100. 

He takes his hands and makes a pile toward the bottom of the pan. I can't contain my excitement to see what he has done.

His pile actually makes sense to me and definitely looks close to 100, give or take. Now that we've made a pile of his "one hundred" seeds. I ask:

Me: How many piles of 100 seeds do you think we can get?

I see he's a little confused by my question, so I ask it differently.

Me: How many piles do you think we could make where each pile has 100 seeds?

He starts to think, but by this time, my almost two year-old daughter sees the pan of seeds is now at her level, so she comes running over and wants in on the action of moving seeds. I thought our conversation was derailed as I brought the pan back up to counter height. But my son keeps it going. He didn't necessarily attempt to answer my question (which is fine by me). He took it in a different, pleasantly unexpected direction:

Son: What if we could get 10 piles?

Me: Do you mean ten piles of one hundred?

Son: Yes!

Me: Are you asking me how many seeds we would have if we had ten piles of 100?

Son: Yes.

This blew me away. Where'd this come from?

Me: Well, ten piles of one hundred seeds would mean we have a thousand seeds.

Son: A thousand??!!

Me: Yes.

Son: What if we had twenty?

Me: Twenty piles of 100 seeds?

Son: Yes.

Me: Well, what two numbers make twenty? Ten and...

Son: Ten!

Me: Right. So if ten piles make a thousand and another ten piles make a thousand, we would now have two th...

Son: ...ousand! 

Me: Right.

Son: What's 100 piles? 

Me: You mean, what's one hundred piles of one hundred? 

Son: Yea.

Me: That would be ten thousand.

My wife chimes in.

Wife: No. 

Me: One hundred piles of one hundred? Ten thousand.

Wife: Wait. You're right.

And our kids are now off in the other room playing and getting ready for going outside and looking at Halloween decorations before trick or treating. So many cool things happened:

1. I love how we pursued my son's questions and not mine. 
2. I love that he was fascinated by the word "thousand" even if it didn't make sense.
1. Because he thinks a "hundred" is big.
3. I love how we started with actual seeds (concrete) and went way more abstract.
4. I love how my wife had the best estimate in the house [375 seeds].
5. I love how the "pumpkin seeds" estimation challenge is just large enough so you can't accurately eyeball the amount and it's just small enough where it wouldn't take me an absurd amount of time to accurately count.

My wife and son watched the video answer this morning. My wife's response:

This is perfect for my [1st grade] students!

We paused the video when we saw ten groups of ten and paused it again when I made a larger pile of one hundred seeds. He struggled with making sense of final amount. 

Me: How would you say that number?

Son: Forty-eight eight? 

Me: How many piles of one hundred are there? 

Son: Four.

Me: So we say "four hundred" and let's count the piles of ten together. Ten, twenty,..

Together: thirty, forty, fifty, sixty, seventy, eighty,  

Me: And. Wait. There are only eight in this last group. So we say eighty-eight. Four hundred eighty eight. Say that.

Son: Four hundred eighty eight.

Me: Great. Let's go make breakfast.

Here's the recipe again and some pictures of the process.

Seasonings!

Ready for the oven.

Roasted and ready to eat!

Seeds,
225

P.S. Thanks to Christopher Danielson and all he does at #tmwyk!

Number Sense Conversations

I've put the elevator speeches to rest. Today's two minute speech went well... I think. As one event concludes, I'm excited to resume my ongoing thoughts about number sense and students.

Working with teachers and students, I can't help but be inundated with thoughts about things I miss, look forward to, and will be challenged with this year in and out of the classroom. However, there's one thing I crave more than anything else, and that's working with students, which usually entails having number sense conversations with students.

Today, I had rich number sense conversations with students in Math 7, Math 8, and high school Algebra classes. As I sit here and put the finishing touches on the slides for my upcoming conference workshop, Get Students to Argue in Class With Number Sense Activities, I can't put to words how valuable it is to allow students to talk about math in math class. That's an oversimplification, but we seriously need to provide our students with opportunities to talk to each other, even argue with each other. Mathematical Practice 3:

Construct viable arguments and critique the reasoning of others.

Steve Leinwand sums it up best:

These nine words may be the most important words in the entire Common Core effort. 

Last December at CMC North, I was honored to give an Ignite talk about something I'm passionate about: number sense and student conversations. It's titled: Number Sense: I Don't Like This Game Anymore.

Students are hungry for number sense conversations in math class. I really do believe. If you don't believe me, just put up this picture in your class and ask your students, "How long would it take to use all of that?" Then ask them to convince you of their conclusion.

As October quickly approaches, I look forward to seeing you at an upcoming conference this school year. In the meantime, I hope to post more about number sense.

Number Sense,
1005

San Diego Conversions

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

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

Here's Act 1:

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

Here's act 3:

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

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

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

Here's the (very shallow) pool:

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

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

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

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

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

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

SD conversions,
906

180 Ways to Use Estimation 180

New challenge: Find 180 ways to use Estimation 180. Wait a minute. That's seems a little extreme, yet I still love the idea. Here's one use I came up with this week: inequalities.  Click on any picture to enlarge.

Me: Hey guys, here's a piece of paper. Fold it into fourths for me like this.

Me: Great. Now, who remembers how tall I am?

I know, silly question, right? If these guys don't know my height by now, I'll send them back a few grades. Then I show them this picture and ask: What's the height of Mrs. Stadel compared to Mr. Stadel?

I take about 4-6 guesses and write them on the whiteboard. It’s been awhile since we’ve done this specific estimation challenge in class. Many have forgotten my wife’s height. Great! However, it’s quite obvious her height is less than mine.

Me: Let me step back. Let’s all look at these guesses. Is it safe to say that all of your guesses put her height less than mine?

Class: Yes.

Me: Okay, so before I reveal the answer let’s put this in our notes for today.

Me: Before I reveal the answer, who can remind me why we used an open circle?

Student: Because we know her height is not the same as yours.

Reveal Mrs. Stadel's height. Wait for it... Wait for it... Here it comes... Student responses: 

“Yes, I was right!” 

“Ohh, I was close.”

“Ohh, I was off by an inch.”

Next up, our beloved Mr. Meyer.

“Woah! He’s tall!”

“Someone is actually taller than you, Mr. Stadel?”

Again, toss 4-6 guesses up on the whiteboard. Step back. What do we notice? Yes, all the guesses should be greater than my height.

Walk through the notes on this new section with more student confidence and participation.

Ask students:

• What type of circle should we use this time?
• If we’re talking about guesses that are greater than my height, how will that affect the inequality symbol?
• What are ways to remember this inequality as greater than?
• Which direction will we shade now?
• Someone give me a variable we can use for Mr. Meyer's height.

Reveal answer. Same responses as my wife, but usually a different kid was right this time.

Okay, great. Now what? What about those other two inequalities, right?

Me: Before I show you this next picture, last year the 6^th grade English teacher (@mrkubasek) at my old school read this novel with his students and came across these two books he found interesting. I found it interesting too and took a picture so we could talk about it in math.

Show picture.

Me: How many pages in the book on the LEFT?

No need to write anything down. Just get 6-8 guesses out loud. Don’t spend much time here. Reveal the answer. Give some math love [one clap on three: 1, 2, 3, CLAP!] to the closest student. Seriously, it’s pure gut instinct here people.  

NOW, show this picture and ask how many pages in the book on the RIGHT.

They don't know it yet, but you just broke their brains for a bit. Yup, you’ll get a lot of guesses below 307. But wait for it. I guarantee in a class of 35-40 students like mine, one student will say 307. If you do, treat it like every other guess you've gotten.

...and if no one guesses 307, step back after about 6-8 guesses and...

Me: You know all of your guesses make sense to me. I'm curious though guys. This is the same novel here, right? What if? I mean, WHAT IF? What if these books had the same amount of pages? Do you think that's possible? Do I have your permission to add it to your guesses?

Step back again. Look at all those beautiful guesses. 

Me: So if I'm looking at this right, you guys think the number of pages could be equal to 307, or could be less than 307? I wonder how we could represent this mathematically?

BAM! Focus here on the circle. Why are we shading it in this time? What's up with that line under the less than inequality?

Me: Okay, before I reveal the answer, someone remind me why we shaded in the circle. 

Reveal!

Brains broken! Now repair. 

Me: What's up with that? Anyone have any ideas/theories why they have the same amount of pages?

Alright. That fourth and final inequality. Here are the goods. Repeat all the other moves from above. 

Initial guess of one bar.

Take some guesses out loud. Reveal the answer.

Toss up new picture.

Write down some guesses on the board. Play up the "what if" again. Complete the notes. Ask a few questions before revealing the answer.

BAM!

That was fun. Boy, I wish it didn't have to end. But it did. Okay, let's find other ways to use Estimation 180 in the curriculum. The full lesson will soon be is available on the lessons page at Estimation 180.

180 ways,

957

Daily Something [WCYDWT]

#WCYDWT

What can you do with this?

Why would a teacher use this?

How would you use this in your class?

What would you add? subtract? replace? other?

How would you use the information from student performance on this?

How could this be used as a pre-assessment? an assessment? an intervention?

Take a few minutes to complete each day. What do you notice?

Hint:
*  **  ***  ****  *****  ******  *******  ********  *********

Answer as many or as few of these questions... or feel free to add your own.

This:

Thanks in advance!
843

CMC North 2013

Here's a recap of my CMC North experience from last weekend. 

Friday:

Fawn Nguyen and I flew up to Monterey Bay, checked in, and found the Fishwife restaurant for lunch. It was within walking distance of the conference grounds. Thank goodness because it was a little chilly outside. We enjoyed lunch so much we made a trip back there for the 4-6 p.m. Happy Hour so we could fine-tune our Saturday presentation. We checked in with the CMC people, and if you ever make it up to Pacific Grove for the conference, don't forget the badge they mail you. It'll cost you $5 if you forget it, right Fawn?

Later that night, we attended the opening keynote by Dr. David Dockterman where he discussed the importance of a growth mindset.  Afterward, it was great to see and meet up with Fawn, Dan Meyer, Avery Pickford, and Breedeen Murray for some pizza. Good times. Good company.

Saturday:
Session 1:
The first session I attended was titled Using Formative Assessment to Create Equitable Practices by Karen Mayfield-Ingram. We diagnosed some student work and left with the following reminders:
1) Make a concerted effort to give students detailed feedback on any assessment.
2) Try and ask students questions that will encourage them to analyze their work better.

Session 2:
I showed up early at Larry Armstrong's session titled Flip Instruction to Transform Learning. I'm interested to know more about the flipped classroom. Not because I'm sold on the idea, but because my district is getting iPads the second semester and I have a feeling we will be encouraged to implement some type of flipped classroom model. Who knows? Again, I'm not sold on the idea, but I want more information just in case. Well, it's 5 minutes before the start of the session and the front of the room is empty: no computer plugged into the projector, no one is setting up, no Larry Armstrong. Nothing!
A CMC helper comes to the front to inform us Armstrong won't be presenting and we have time to catch another session if we want. I saw Brad Fulton come in at the back of the room and I got up to ask him if he'd present, but he said he was only coming to drop his stuff off for presenting at the following session. I turned to the CMC helper and offered to present my Number Sense session I gave at CMC South. She took me up on my offer and we had ourselves an impromptu Number Sense session. It was fun! For the forty to fifty attendees that stuck around, we had a blast doing estimation challenges and talking number sense for about 50 minutes. I will blog more about my presentation over the next few weeks. Stay tuned! I was honored when Rebecca Lewis, the Program Chair, gave me this token of appreciation for stepping in at this session. This proudly sits on my desk.

Session 3:
Shelly Lawson gave a great hands-on session titled Modeling Lessons Can Work for All Students - Yes, Even Yours.  I was excited about this one because it was geared toward 7th grade curriculum. You know you're in for a good session when you see a bag full of PVC pipes, a stopwatch, a meter stick, a steel ball, and some string. There were 5 different length PVC pipes, and four connecters; two right angles and two at about 135 degrees.

We had to construct a pipe so that the ball, when dropped, would make its way through the pipe at the fastest rate possible. Here's our contraption. It was the fastest because of my teammate's design. Great job Bob!

Shelly also introduced us to the Incredible Egg, Float That Boat, and the Penny Lab. All of these activities allow students to make measurements, mistakes, and formulate conclusions based on observations and data collected. I left with a packet full of hands-on activities that I can incorporate into my curriculum. The structure of the packet gives students pretty detailed steps and instructions. Personally, I will probably revise the activities to leave them a little more open-ended and less structured. Overall, some great activities. Email Shelly for a copy. See the link attached to her name above. By this time, I think I ran into Dittmer about 50 times. Really cool guy!

Session 4:
Fawn and I presented Hotel Snap to the CMC attendees. Fawn is awesome! Tell you something you don't know, right? Okay, chances are good you've already read her blog post on Hotel Snap. If not, go now and read it here. Fawn did an amazing job coming up with this task. You might be surprised, but I have nothing but great things to say about Fawn. Her task is challenging and can be used at numerous grade levels. CHECK IT OUT!

Photo by Dan Meyer

Thanks to Brian and Dan for helping us with the calculations. Thanks John for helping us clean up!

Session 5:
My man, Max Ray, presented Becoming Better Reasoners: Supporting Students to Develop as Problem-Solvers. I was excited since this was my first time seeing Max present.  See how calm he is in this picture?

I love how Max is so patient and allows his students (us CMC attendees) to formulate noticings, wonderings, and other thoughts as we worked through some Math Forum tasks. I enjoyed this last session of the conference because we worked in groups to problem-solve a task, we analyzed student work, and Max charged us with asking students questions that would help them further their problem-solving approach by becoming better reasoners. Well done Max!

Saturday night:
Ignite talks!!! I could write a whole other blog post on these. I was honored and privileged to present with the following mathletes!

The Math Forum organized, hosted, and took over the Ignite talks this year. Thanks Suzanne for all you did! Watch them in January or February 2014 when they post the 10 videos online. It was a lot of work preparing my 5 minute talk, but was great fun! Fawn stole the night! The energy and inspiration from these talks was a great way to cap Saturday night!

Sunday:
Dan Meyer gave the first keynote of the morning titled Fake-World Math. Dan is the man! His presentation was fantastic. I don't want to post any spoilers here, but he talked about the importance of modeling and how CCSS defines modeling. If I could summarize some important points, here's what I want to reflect on for future reference.
Although important to the math classroom at certain times, the following is NOT modeling:

1. I do, we do, you do
2. Using concrete manipulatives
3. Graphs, equations, functions

Furthermore, Dan stressed that the real world is not always greater than a math problem. Vice versa, a math problem is not always greater than a real world situation. He emphasized that strong modeling starts with a simple question and allows students to identify variables, formulate the necessary model to organize and solve the task, and to validate conclusions a la something along the lines of a 3-Act task. He reminded everyone that modeling tasks are out there: Dan, Robert, and here. My summary can't do justice to his presentation, content delivery, and charisma. If you get a chance to see Dan live, DO IT!

*For the record, my initial estimate for Dan's Super Stairs task was over by fifty seconds. Bam!

Dr. Timothy Kanold gave the second keynote titled The Art of Teaching Mathematics: Inspiring Students to Learn. CMC North 2013 ended with Bill Withers' Lean on Me.

Before Fawn and I flew back to Los Angeles, we had brunch with some great math amigos (pictured below).

Left to Right: Stadel, Nguyen, Meyer, Murray, Pickford.

We also said hi to some fish at the Monterey Bay Aquarium.

Thanks Dan, Avery, and Breedeen for driving us around too!

North,
819