Saturday, March 25, 2017

It's March MATH MADNESS!

Welcome to March Madness...

The MATH behind the MADNESS!

Students came in talking about the NCAA brackets and how that would be the focus for the week before spring break.  First things, first: What is a tournament and how are they set up?

I set up a mini-tournament in the classroom.  8 students were put head-to-head in a critical game of coin flipping.  I had students complete a bracket and discuss how many different ways this bracket could be filled out



There can be only one!

Students came up with many different theories: 2*8, 2*7, 8*7*6*5*4*3*2*1, 2^8, 8^2... It was a good check in for me since we already had covered calculating outcomes of independent events.

Finally students realized this is the same as flipping a coin 7 times and settled on 2^7, or 128 possible outcomes.

"So, Mr. Taylor, the probability of two of us filling it out the same is 1 in 128?"
That was a good eye-opening realization for many of them: in this small bracket of just 8 teams there were 128 different possible ways to complete this.

From there I introduce a region of the tournament. We review what the rankings mean as well as how the tournament runs.  Students were randomly assigned one of four regions.  Students were told there were 16 teams in each region and were asked to make predictions as to how many ways those could be arranged. Many, understandably, made the jump that if there are twice as many teams, there should be twice as many outcomes.  They quickly checked the math and realized how far off they were.

Instead of 256 outcomes, it actually explodes to 32,768 possible outcomes!

Their homework night one is to complete a regional bracket and think about why companies will put up $1 million as a prize for a perfect bracket.

Students come in the next day and discuss their picks - they meet in their region and discuss similarities and differences.  They notice while many picks are the same (everyone took my advice and picked the one over the 16 seed), nobody matches exactly.

On day two we talk about the whole tournament.  Students pick up the pattern that there is one fewer game than number of teams (an 8 team bracket had 7 games, a 16 team region had 15 games.)  They use Wolfram Alpha to calculate this value.

They discover that the number is big.  Like really big.  Good thing we have reviewed scientific notation.... because the answer is 9.22 x 10^18, or 9,220,000,000,000,000,000... over 9 quintillion.

The question the becomes how to QUANTIFY a number that big?  Many students talk about having that much money, but is that even possible?

How big is big?

First, let's look at space.  Space is really big.  That should be a good place to find 9 quintillion.  The distance from the Sun to Neptune is 2.8 billion miles.  Billion is too small, so lets figure out how many INCHES it is from the Sun to Neptune.  Will that reach 9 quintillion?

Not quite:

Tournament: 9,220,000,000,000,000,000
 Distance in inches: 176,400,000,000,000

(I make sure to line up the place values to emphasize the SIZE difference. In this case the tournament value is over 51,000 times bigger.)

In other words: if you picked a random inch between the sun and Neptune, and I picked a random inch between the sun and Neptune, we are 51,000 times more likely to pick the same inch as someone picking every game in the NCAA tournament correctly.

Let that sink in a moment or three..



Not big enough, Solar System!


OK. Let's try this.  The accepted scientific age of the universe is about 14 billion years.  How many SECONDS has the universe been in existence?  TO WOLFRAM ALPHA!

 Tournament: 9,220,000,000,000,000,000
Seconds of the universe: 441,500,000,000,000,000

Wait. So not even that is a big enough number?  Well how close are we talking? Let's figure out the part of the whole:

441,500,000,000,000,000 ÷ 9,220,000,000,000,000,000 = .047

.047? That is LESS THAN 5%?  DO YOU KNOW WHAT THIS MEANS? 

The students sure did...  

"So wait. That means if Jeremiah filled out one tournament since the universe started, he'd only be 5% done?"

Yes.  5%  This number, 5 quintillion, is so ASTRONOMICALLY HUGE, that if you had a large supply of pencils, blank tournaments sheets, came into existence the same moment as the universe, and filled one out tournament per second, every second, since the universe started... you would be 5% finished. 

I love the madness. And Math.

Sunday, March 12, 2017

Washington D.C. Marathon Race recap

On Saturday, March 11th I completed the Washington D.C. Saint Jude Children's Hospital. This was my 3rd marathon and my 7th marathon-or-longer event. It was also the toughest road event I've attempted.

I have been training for this run for nearly 12 weeks. I put in the miles, did the speed work, ran the hills, bought the Gu. I was ready. Then I checked the weather. 12 degrees with winds of 15 miles an hour... ouch. It certainly wouldn't be the coldest race I've ever experienced, but it presented another challenge to an already challenging distance.

The day before the run I got an e-mail from the race organizers. It warned us of the cold weather and included this advice:

Manage your expectations. This may not be the race to run a PR. Slow down according to the conditions and consider switching down distances if you are not feeling prepared. 


Here is the deal: Running is an outdoor sport. There are no rain delays, no cancelled due to snow. I'm not letting 'weather' be an excuse for not hitting my goal.




Five top layers. Worked perfectly! 

The day started in my typical fashion: I got lost. Seriously. Bree was so amazing and agreed to drive me to the start line at 5:30 AM since the metro did not start up until 7 am. I programmed the start in my GPS and off we went. The only problem was that I programmed the FINISH LINE into the GPS. Luckily I realized my error and Bree was SUPER patient with me. I was dragging her all around a pre-dawn city that we'd never driven in before and she never did anything but reassure me. I am so thankful for her.

Eventually we got to the right location, she dropped me off, and I was off to the start line. I got myself ready, dropped off my bag with a change of clothes and some post-run food, and did a little light running to warm up. I also got to take a group picture with other St. Jude Heroes. The start was actually quite well done. Marathoners started at 7:00 and Half-marathoners didn't start until 8:30, which meant the start was (relatively) small.

It took me a few miles, but I managed to warm up and was feeling really good. The wind wasn't too bad and before I knew it I was at mile six: CRAZY HILL! Still, after running so many hills I knew how to approach it and felt good when I got to the top. A couple miles later I got to see Bree, Sam, and Alexa. A mile later I got to see Wendi and Jason as well! My pace through the first half of the marathon was 10:54 minutes per mile, right at my 11:00 minute pace goal.

The second half of the marathon started well. Bands were still playing, the course was smooth and fast, and the weather, while cold, was still not crazy cold or windy. There were fewer historical spaces to see, but I pressed on and crossed the 20-mile mark at a pace of 11:07 minutes per mile.

This is where things got rough. The wind really started to kick up and gusts were very noticeable. Some course volunteers said gusts were close to 30 miles per hour. Running began to be challenging, but I kept moving forward. Still the grind of 20 miles and the weather were starting to take its toll.

Then came mile 22. I had previewed the course and knew there was a bit of a climb at 22, but after four hours of running my body decided it needed a break and I had to do some considerable walking. About half way up the hill, the 5-hour pacer passed me. I forced my body to run, but couldn't keep pace with her.


 Four hours of running? Perfect time for a climb!


 I have been involved in sports nearly all my life. I can honestly say none of them have been as emotional or frustrating as distance running. You train for weeks and literally can watch your goal pass you by.

 I do so much reflecting after an event. What could I have done better? Did I give it my all? What did I miss? Here is what I know: All that training made me run my strongest road race of my life. I left nothing out there. Usually when I cross the finish line I collect my 'goodies', meet anyone that is at the finish, and hang out a bit. After this run, I crossed the line, had someone put a medal around my neck, and then sat down and couldn't move. My legs were cramping and in pain. My body was hurting badly and I was pretty emotionally devastated that I didn't finish under 5 hours.

As it turns out I did set a personal record (PR) for a marathon distance (26.2 miles), but I ended up running 26.6 miles total and crossed at 5:02:52, 40 seconds slower than the Columbus Full, but at a slightly faster overall pace.

If I did this event this time last year I would have finished in a much slower time. I would have given up running much earlier. Given the conditions there is a chance I may not have even finished. I've learned so much and look forward to busting that official 5 hour barrier in the future. I know it is in me.



Thank you to all of you for your support. I had so many people check in with me about how things were going with training and how the run went. I am so blessed to have so many people in my life that care about me.

To those of you that donated any amount to my run: I was proud to represent all of you! With your help we raised over $700 for the Children of Saint Jude.

To those of you that donated songs to my run through St. Jude Children's Hospital: I had great conversations with all of you. You will never know how much those help me get through the miles. It is funny how my player knows exactly what song to play when I need to hear it. Seriously, nobody's song came up before mile 7 (after that first climb) despite the fact I had it on random.

To my amazing family: Thank you SO MUCH for trekking all over D.C. and the metro, putting up with the stupid coldness of the day, and supporting me on my runs. This day would have been so much more difficult without you there. Sam and Alexa: your signs were great, and I LOVED seeing you on the jumbotron! Bree: you are amazing. Thank you for everything you do for me. I love you.

What's next? That's always the question. Currently I'm registered for a half-marathon in April and then two 50km (31 mile). I'm looking forward to getting back on trails! Outside of that, we'll see where the rabbit hole takes me!

Love you all,

Michael

Monday, February 20, 2017

The Infection Spreads!

Last week an infection got introduced to my classroom. How to what it was, how to catch it, how it spreads - none of that was known. Throughout the week students completed problems to receive clues as to the nature of the infection. 

This past week it was revealed: the infection is a virus which affects the midichlorians. When infected, the virus turns the midichlorians to favor the dark side. By the time this was known, half of the class was on the light side and half was on the dark side. There is also a ‘secret agent’ on the light side: someone that is infected, but that does not show any signs. There is also one student in the class that is immune to the infection. 

Both of those came out randomly based on the cards students drew from a deck last week.

 For the past week students have continued to push their cause's side by earning points to win mini-challenges. Students had probability challenges, number challenges, and other games. Light side students got a chance to retry, while dark side students were ‘tossed’ into the Pit of Sarlak. The most recent one was a kahoot battle. Students signed into kahoot as normal, but labeled their side: 

Sides have been set. 

Many of them wanted to name themselves “Darth”, but I told them there are only two sith lords, and they are currently held by the two teachers in the classroom. I also told them they were welcome to challenge us in a math competition to take the title. None have done so yet. 

During the game, students saw the top 5 but also knew EVERY point mattered so they focused on getting answers right.  They reminded each other that getting answers right is better than answering fast and incorrectly. 

Light side leads, but the force is strong with the dark forces. 

When the game was over I totaled the dark and light sides and averaged their scores. That became their points for “final” kahoot (just like final jeopardy.) The leader from each team (the one with most points) got to decide how many points to risk. Other students could help, ask, and beg, but ultimately that student decided the wager. 

From there, students were told one random person from each team would represent their answer. Collaboration during that question could not have been higher as teammates checked in with each other about both the process and the final answer. 

In the end, the light side won this battle, but the war is not over yet.

How will episode II end?

Sunday, February 5, 2017

Explore Like A Pirate: Pandemic Based Game!

Last week a dangerous infection was let loose in math. Nobody knows the source or the cure (well except the teachers, of course), but class has been on edge trying to solve the mystery.

Students walked in on Monday and saw they had a 1 in 5 chance of being infected. They had no idea what this meant, but they were told that by completing problems in class they could start to find clues as to who is infected and how to cure it.

One of my favorites. Why not put it into class?

It was interesting to watch because even though they figured out the theoretical number of students currently infected (four), most chose to work alone because they didn’t want to risk sitting by someone that was infected. This led to a great social studies connection about how fear creates walls.

Students worked on problems related to simple and compound probability and were told that they could draw 2 cards for every 5 problems they got correct (which allowed them to connect ratios from a previous unit.)  If the student draws a heart card, they would get some information about the game.  This allowed students to complete work at their own pace while still being engaged.  Work could be done at home optionally for draws the next morning.  I have never had more students do optional homework than that night.

The right column is very filled with names now.

On Friday I conferenced with students one-on-one while they took a formative assessment. The meeting gave me an opportunity to do many things. I asked them how they felt about the learning targets, how comfortable they were, where they needed to improve. I also informed them whether they were infected or not.  Students that were infected had two choices: They could work for the light side and try to discover a cure to help the class, or they can play the role of antagonist and join the dark side to spread the infection.

Tomorrow they will come into class with a list of actions on the board, some for the light side and some for the dark side.  Actions include trying to cure the disease, spread the disease, mutate the disease to make it stronger, or protect someone from becoming infected.

The Game ends when one of these things occur:

  • Everyone is cured (light side wins) 
  • 80% of the class is infected (dark side wins) 
  • Mr. Taylor or Mrs. Menker says “the game is over”

(that last option allows us to end the game should students lose sight of the objectives or forget rules about physical and emotional safety.)

Students will complete problems (this will be a general review of the term so far) and after each problem they will fill out a google form to choose one action. From there teachers will discern the outcome and let them know the result.

We’re right in the heart of the game and I have no idea how it will turn out. Will students unite to destroy the infection, or will darkness win? I’m excited to see what happens!


Saturday, January 14, 2017

The Importance of Routine

Many of you know I’m in the middle of marathon training. Last week I almost missed a speed run. It wasn’t because of injury or family reasons. It was because I couldn’t find my Garmin watch. Instead of following my routine of putting it back on the charging station, I put it… well somewhere else. I searched for that thing for nearly 40 minutes, even enlisting my daughters to help, but no luck.

I still went on my run, using my cell phone and a couple of apps to help time my splits, but knew that this mistake could cost me serious money. Luckily my wife ended up finding it… in the pocket of a sweater that was lying on my bed. Not following my routine ended up costing me time and raised my anxiety.

#MyLife

Routines are important for students as well. Well run classrooms thrive on routine. They build muscle memory, allow students to feel comfortable and confident in the classroom, lower anxiety, and uncertainty, and give teachers the full allotment of classroom learning time.

That isn’t to say teachers can’t be spontaneous, but basic routines as far as what to do when entering the classroom, sharpening pencils, or handing in homework are essential.

Over winter break our school moved into a brand new building. We went from a one-floor, two hallway school to a 64,000 square foot, 2-floor, multi-hallway building. Despite it being January, my teaching partner and I treated Monday and Tuesday as if it were the first day of school – no academics, no tests, all routines and procedures.

My new home away from home

Students came in the first day and we talked about their winter break, what they did, and gave students some time just to be middle school chatter boxes. We went over schedules, took a tour of the building as a class, and gave them a classroom scavenger hunt. They had to sharpen pencils, hand in assignments written on index cards, sign out to use the water fountain, and even staple papers together.

Our classroom also has two standing desks and six wiggle stools which students can use instead of standard chairs. We reviewed procedures and expectations of how to move to standing tables or how to get a wiggle stool. Students then practiced doing this.

These are amazing! I use them in staff meeting now.

By taking time and actively teaching the expectations in the new space we let students reflect on their anxieties in the new building and determine how to best adjust to the new space. On Wednesday students handed in assignments quickly and efficiently, moved furniture around the classroom without disturbing other students, and felt they had ownership of a classroom. By Friday students were fully confident in coming into classrooms and following procedures, leaving plenty of time for education to happen.

Even with a full mooned Friday the 13th.
(yes I know the full moon was the 12th and it was technically waining gibbous the 13th. I also know the century started in 2001 not 2000.  But sometimes pretending is fun.)

Monday, January 2, 2017

My 2017 Word: Risk

Risk is a scary word. It implies injuries. It implies danger. Risk implies failure. I have worked at Camp Mary Orton for a number of years and when I run groups there we always talk about risk. There is risk in everything you do. When groups are doing the ropes course I remind them while the course looks dangerous, they have done the most dangerous thing already that day - they drove to camp. Statistically there are more injuries on the road then there are on ropes courses.

My summer playground :) 

Risk is more though. Risk is about exploring, if not conquering the unknown. Risk is aiming for greatness, but not always succeeding.

There are a number of places I have not taken risks. I have a fiction novel that I wrote a number of years back. One copy sits printed on a shelf while the original sits in a cloud. I have a teaching book that I’ve been writing for years. It’s sitting safely in my mind. The risk of writing it and the steps beyond that are too great for me to comprehend.


Quoting one of your favorite authors after that paragraph? Ironic...

This is only one area of my life I have not taken a risk. I plan on taking risks on a number of fronts this year - physically, emotionally, mentally, and professionally. We are about to take off on this great adventure called 2017. I’m hoping to have a number of stops along the way:

  • Risk taking time for myself 
  • Risk being selfish 
  • Risk talking to authors and publishers 
  • Risk running more and further than I ever have before 
  • Risk implementing lessons that may not work 

Every great story starts with risk.  One of my favorite quotes is, “If you don’t risk anything, then you risk everything.” In fact it is the quote by my senior picture. My 2017 will be full of risk. I hope to see you along the way!

This pic will end up in my next kahoot :) 

Thursday, December 29, 2016

Reflections on 2016, Part II: Running

People kept telling me that I ran a lot this year. Like a lot a lot. Upon reflecting, it is probably an accurate statement. I completed 16 different events this year: Rocks and Roots 10k, Brokeman’s Winter Warm up half marathon, Rocks and Roots 20k, Possum 30k, The ORRRC Xenia ½ marathon, Glass City Toledo Marathon, ORRRC Tie Dye 32 miler, Columbus Zoo 5k, Brokemans Wild Things 4 miler, Not Your Momma’s 50 km, Running with Scissors double marathon, Hot Chocolate 15km, New Albany 4 miler, Run Santa Run 5k, Big Foot 10 miler, and the Yeti Run.

They were all my favorite. Especially Yeti. 

Looking at that list I’m pretty much in awe - It was about 3 years ago that I ran my second half marathon and swore I would never run that distance again. It was just over a year ago I finished my first marathon. I found a picture of my 2014 bibs (EDIT: it was actually my bibs from 2013 AND 2014) on facebook and in the comments section I was ecstatic that it had four 5k bibs, a 10k bib and 2 half marathon bibs. Now I have run a marathon distance or more six different times (four of those times in 2016.)

Not Yo Momma's 50k - the most difficult 50k I've run to date.

Oddly enough I became friends with Erika in 2014. Pure coincidence I’m sure. Sidenote, Erika is running the Pistol Ultra 100 miler on New Years eve/day - so proud of her! You can read about her adventure here.

Still, the year was not ‘perfect.’ I had two did not finish results (DNF) this year: The first was at the January Rocks and Roots which was supposed to be a 20k but due to the fact I could not feel my feet (literally) after the first 10k, I chose to stop. The second was the Scissors double marathon where I “only” ran moved forward 41.1 (66km) of the 52.4 miles. You can read more about that here. 

I still gave myself a present.

However, I also fell in love with pacing this year, leading the 11 minute pace group during the Columbus Hot Chocolate 15k. It was great helping people achieve their goals since so many people had helped me achieve mine over the past year. Case in point, I ended the year with my fastest 5k ever thanks to my great friends Becky and Erika. It would have been an even faster time if I could have kept up with them past mile 2.5.

All in all I have logged over 1360 miles (about 2200 km) of running this year. For some perspective, that is about the distance from Cleveland to Denver. Looking forward, I have a number of activities and events in 2017. So far I have at least three half marathons, one full marathon, and two 50 kilometer runs on my calendar by the first week of June. Yes I said at least.

Here we go again.

A big thank you to all of my friends and family that supported me with encouragement, candy, a sarcastic comment, or all of the above. My wife and two daughters are just brilliant.  They push me, encourage me, cheer me on, and fully support me in all of this.  I truly would not be able to do this without them.

I love all of my running buddies and I'm proud of every mile we logged together! I will need all of your support, encouragement, and more in the coming weeks!

I’m looking to share many more miles and stories with all of you in 2017!

Happy Running :)