Substitute days are tricky for a teacher.B A successful lesson for the sub is one where these things happen:
B Students are productive (Read: BUSY) the whole period doing something mathematical
…yet are happy to see me when I return.
The sub is happy that the class worked hard.
And my classroom is intact, nothing stolen, punched, or burned down.
To that end, this was a successful lesson, just like last year. I left a sample list of some words they could use and they got to work.
Here are some of my favorites:
And, as usual, a Valentine for my wife using stolen lines from the student work:
Dear Andrea,
The formula of love is Me + You.B You are theB solution to all my problems. Your expressions are the cutest ever. You addB happiness to my soul, youB intersect my heart. You give me theB power to do anything I desire.
You’re the numerator to my fraction. You and I equal a perfect square. You’re so radical; I want us to be binomials.
Roses are red, Violets are blue, But the only flower I choose…
After our Start-of-the-Period Routine, my first period sat quietly as we made a foldable together. They asked pertinent questions about the Discriminant as we colored, cut, and took notes on colored paper.
I then gave them options for two different activities, one of which involves walking around the class and submitting answers on digital responders. The instant I put on Pandora[1], the entire class…
…went to work. Every one of them started one of the activities, grabbed whiteboards to show their work, and murmured quiet calculations in pairs or trios.
“Class, please return to your sea-! Oh… never mind.”
I looked around the class for something to do and I noticed…
…they don’t need me.
And that is how I define a successful class.
The class average for the responders was 90%. All that’s missing to make my class complete heaven is Han Solo giving me a high-five.
[1]The Pandora stations that I use for quiet studying are Penguin Cafe Orchestra, Ludovico Einaudi, and City and Colour (make sure explicit content is turned off).
I added that last line to the slide because I had 4 or 5 students who finished the Daily Doozy and proclaim, “That wasB easy!” I reminded them that it probably isn’t easy forB allB the students. Instead, they can proclaim, “My, what an appropriate challenge!”
I do declare!
UPDATE 17 April 2013: Per Dan’s request, hereB are a few more.
When I was six, I had a birthday party at Lincoln Heights Pizza Parlor. Four friends and I spent the afternoon whacking moles, earning tickets, spending tokens, eating pizza, and finding diapers in the ball pit.
Documenting the day are several grainy, indoor photos characteristic of the late 80s. My friends and I are smiling and happy in every shot in our striped shirts and shaggy haircuts.
“Michael’s cheating! Daaaaaad!”
A few years later, I had a surprise 16th birthday, put on by my girlfriend in conjunction with my sisters and youth pastor. Every photo is happy (that is, nobody is crying), but some photos are without smiles as people chat or eat cake.
Yesterday, we celebrated my birthday by carving pumpkins with a few friends. My wife and baby and I hung out with our guests on the couch and we spent a long time discussing the Pacific Northwest. We printed out stencils for our pumpkins and put on some relaxing autumn music and had a great afternoon.
Yes, that is Boba Fett and a high-speed drill.
This leads me to my thesis, ready?
If you’re reading this, your best birthdays are behind you.
As you can see, the fun increases as a child, then is inconsistent during teenage years (as is everything) before a brief spike at 21 and a rapid decline until death. Some people get a small jump in fun at 50, unless you have heart problems, in which case it’s about the same.
My birthday was yesterday, and today I had to leave work early because I had a back spasm.
I got a back spasm for my birthday.
Mother Nature gave me the gift of awareness; my vitality is weakening every year, and I’m one year closer to the grave.
Dear Matt, you become a worse athlete every year. Love, Gaia
Without revealing too much, my birthday ranked less than 30 on the scale above, which is a great score for my age bracket. I had a great day with friends, carved pumpkins, spent time outside, had great food, and then went on a date with my wife. Despite all that, a birthday (for people my age) is just another Sunday between Labor Day and Thanksgiving.
Here’s the difference, though. As an adult, every other day is way more fun.
Students in middle school absolutely hate Mondays. But Saturdays? Oh, man! Saturdays are like a mini-Christmas 36 times a school year.
As an adult, I’m not a huge fan of Mondays, but they’re qualitatively no worse than Thursdays; I still have to go to work. Friday is marginally better, and the weekend is great.
Note that the beginning and end of the weekends are common for both data sets.
So, kids: you can have your birthdays. We adults quite enjoy our lives for the other 364 days of the year quite a bit as well.
Even though child birthdays clearly are way more fun than adult ones, but adult Mondays are much more fun than child ones.
Man! My life has been a blur the last 2 week! A few things before I start:
I’m unaccustomed to writing math-centered posts (which you’ve noticed if you read anything prior to the Mullet Ratio). Though I’m still pretty green, I’m thrilled to be involved in the “mathblogosphere”, for which, there must be a better name.
The Barbie Bungee lesson was planned in way less time than the Mullet Lesson, which was in the works for weeks. I was saving pictures, constructing the worksheets, planning my own mullet since April, and it still makes me a little embarrassed to know that people are downloading it. I would have changed this color, updated that picture, or tweaked this font. And the Barbie Bungee lesson was largely planned the morning of. Polished and perfect, it’s not.
In the last week, I got a few thousand hits on the Mullet Lesson, a few dozen tweets about it from people I’ve never met, and it’s been taught in Orange County, the Netherlands, and maybe some places in between. Plus, I got tagged to teach an iPad class with digital textbooks next year and I finished BTSA. Now I’m writing this post, finally. Again, polished and perfect, it’s not.
So, like a proctologist about to scope, I ask that you keep #2 in mind. Remember that teaching and learning are both about improvement over time, and this lesson will likely improve.
Prologue
Saturday, for the TEAMS grant at UC-Riverside, a couple teachers talked about Barbie Bungee and I figured I could call the ante and raise the stakes. I sketched some schematics for a bungee platform and began testing prototypes a few days before the Bungee lesson (Thursday/Friday). I finished up building 9 more of them last night.
It’s not too hard. It’s exactly how it looks. Those angles are 45 degrees and each one hooked onto the chain-link fence outside my class so students could raise and lower the platform to various heights.
Students’ only homework this week was for their group to bring in a doll. I advised them on size, weight, and clothing (one student gel-painted a bikini because she couldn’t find Barbie’s shirt), and stored them in class, tagged by period.
Late last night, I wondered in a panic, “Do I have enough content to fill the 90 minutes for two days?”
I turned to my teaching advisor, Google. It turns out I’m nowhere near the first teacher (as I found out via Twitter) to try a Barbie Bungee lesson.
…and many of them more epic than my plan.
NCTM’s Illuminations had some good questions for students. The Math Lab obviously planned their blog post, with pictures and stuff. Mr. Pederson filmed his class doing the bungee off the bleachers. Fawn Nguyen has been doing it for years, and even planned hers for the same day as me! Talk about being born under the same geeky star! I hope someday my Barbie Bungee lesson will be as involved and pointed as hers. You nailed it, Fawn! Fabulous work.
Seriously, teachers. If you’re interested in this lesson, go to her page first. I guarantee it’s worth your time.
Day 1
After the warm-up, announcements, and whatever, I show these two videos:
Purists will note that the second video (a Russian Missile silo) isn’t technically bungee jumping; they’re using what rock climbers call static rope, which doesn’t stretch. Meaning that they fall about 15-20 meters and are yanked at the bottom. Russians have a different meaning for fun, I suppose.
This is the front row at a KISS concert in Moscow.
But back to Barbies.
I started a discussion first (low-entry point, everybody’s involved).
What do you think the world’s first bungee jumpers thought about?
What makes a bungee jump exciting?
What are the dangers in a bungee jump?
I framed our plan for the day, passed out the pink papers (attached below) and set them to work.
This part was pretty easy. They began building bungee cords, threading their platforms and heading outside to bunge. The GATE (Honors) students finished fairly quickly, some even wanting to go higher (which I saved for day 2).
Memorable quotes:
“What if they don’t hit the ground on the first try?”
“It’s okay to smash their face a little bit, right?”
And my favorite:
“Can I tape her dress down? She’s flashing the goodies with every jump.”
Day 2:
Students were notified that Barbie was to jump 203 centimeters today.
Before we go further, here’s what yesterday’s pink worksheet looked like (Attachment below):
Mathematicians, you’ll note that this is a good time to talk about Ceiling Functions (because you can’t have a 6.3 rubber bands), but I glossed over that for this year.
Students, predictably, added the 60 cm to the 140 cm “then added a little more” to plan for the 203 cm jump. Okay, fine.
Then we took them outside to video as the Barbies jumped 203 cm.
Some classes were very successful, pushing the limits of how close they could get. (and getting frustrated when their doll’s skull cracked the ground).
Then, back inside to answer questions on the back and make calculations for the roof jump.
The janitor had agreed earlier to climb up to the roof and toss the dolls off, two at a time. Of course, I had to build a separate launching platform for the Pavilion roof.
I must really love my job, because I hate drilling pilot holes.
We also taped two yardsticks to the wall, so we could play back the footage and see who “won”. For the more cautious classes, it wasn’t really necessary. Here are all the jumps put together.
Bundle the rubber bands in 20s, then make sure to get all 20 back. (Way easier than counting each group.)
Show that the 60 cm jump is the distance downfrom the ledge, not up to the fence.
For heavy dolls, double up the bungee
Go very slowly to show the class a slipknot for Barbie’s legs.
All told, it was an excellent activity, but not yet a great lesson. Check out Fawn’s post on this. It’s awesome. Mine can get close, but for now it’s just a good year-end activity.
I admit, I would love for my 8th graders to remember a sweet lesson about Systems of Equations (when we used math to convince my wife to buy skis rather than rent them) or something more mathematical than what we did yesterday. But this will probably be the one they tell their parents about.
Mulletude: Just How Mullety Is It?
I was browsing Mr. Piccini’s blog a few weeks ago and came across a simple question: “Who has the more Mullety mullet?”
We’re done with state testing, so why not explore it? Here’s how it went down.
Prologue:
I gave myself a mullet. It was totally worth it; every student came into class with a smile, already curious. It also felt good to say, “Good morning! We’re studying Mullets today.”
A student, certain I was lying, exclaimed to her friend:
“Omigod! Look at the Agenda! It’sB allB about Mullets!”
Part 1: Warm-up
To get them thinking, I started with this mullet question (#1). No numbers, no right answer, just taking a risk and interacting with a foreign subject.
One student said, “No solution. They’re both terrible.” I loved it.
Part 2: What is a Mullet?
I previously discussed the lesson plan with my teammates, and discovered that some of them didn’t know what a mullet was. After the usual start-up business, I went to this slide.
I threw these two beauties on the board and asked, “Which is more Mullety?”
The best part is that students immediately began using the terms I introduced.
Kelsey: The hillbilly has a little too much Party in the back, even though his Business is the same as the cute guy.
Susy: I think the cute guy has the better mullet because it’s more even.
John: Yeah, his Business and Party are moreB B proportional.
“Hold on to that word for later.” I said to John.
Part 3
I then started introducing different mullets, asking which is more Mullety. I knew I’d baited the hook when a student said, “Can we rank their mulletude?”
Yes! Yes, student! Yes, you can! High five!
Part 4: The Mullet Ratio
Students already recognized the vocab from before, so this transition was very smooth. And (here’s the best part) they all jumped on the math with no groaning. Students lunged for their calculators like they were bagels at a hunger strike.
As a sample, I guided the class as we calculated my mullet ratio on the board (See above; it’s 4.73).
“Show me a thumbs up if you got 4.73… okay, good. You’re ready to go.”
Then I took a seat, moved through the slides with a clicker, called on students (using my random cards), and let them discuss.
The above slide (Lionel Richie vs. me in 1989) led to a great discussion on the differences between mullet, afro, and Jerry Curl.
With calculators, they weren’t afraid of large numbers, and they realized that the ratios were still comparable, even when the units were nanometers and miles. After a few slides, we got into a groove, and I could start asking key questions:
“Mark, you calculate the hockey player, Dariana, you get Uncle Jesse”
“Does that answer make sense?”
“Why do you think his ratio is so much higher?”
I also wanted to emphasize that the measurement doesn’t matter; it’s a ratio between two things. This slide and the one above it really drove that home. The Mullet Family caused a fit of giggles in every period, but who cares? It was fun for me.
Highlights: “This is the best homework we’ve ever had.”
“Where did you find all of these?”
Part 5: On Your Own
Then I passed out pipe cleaners and rulers, along with copies of this worksheet:
Students fit the pipe cleaner along the hair, then straightened it onto their rulers to find the measurement of the Party. The Business was usually pretty straight.
Ryan: Jeanine’s is more like a ponytail, is that okay?
Bree: How do I know where the Party ends and the Business begins?
Jose: My uncle has a haircut just like Miguel.
Highlight: For Big Daddy, one student used 0.0001 cm for the Business, and got a mullet ratio of 2.5 million. This led to a great discussion of why that happened. What made the ratio so big?
(Also, I managed to make it the whole day without giggling at “the length of Big Daddy’s Business”.)
Part 6: Your Own Mullet Ratio
After students finished, they found their own ratio, which led to another great mathematical revelation for some of them:
Sara: I don’t evenB have a mullet!
Vaudrey: No, but you do have a Mullet Ratio. So find it. And find the Mullet Ratio of four other people, too.
Students worked for a few minutes, finished up their worksheets, and found each others’ ratios. Now here’s my favorite part of the day:
The Discussion
Oh, and some of them calculated the Mullet Ratio of photos on my Wall of Fame. Joe Jonas isn’t really in my 3rd period.
I quickly recorded all the student ratios into Excel and ranked them, then put it on the board and we had a discussion.
“What does it mean to have a Mullet Ratio of 1.0?”
“What does it mean to have a Mullet Ratio of less than 1.0?”
“Why can’t you have a negative Mullet Ratio?”
Student: “If my hair is longer, how come Karla has a higher ratio than me?”
“What’s the Mullet Ratio for Mr. Krasniak (the bald science teacher)?”
That was my favorite question; the initial yells of “One” and “Zero” turned into “No, wait…B undefined!”
B How I Know It Worked
Look at the Excel chart. Students in other periods got Mullet Ratios in the 20s and 30s, even 40s.
…meaning they falsified their data for a higher mullet ratio, and they knew what they were doing.
Wow. Thank you all for the gushing, I’m humbled.
Thanks to dozens of Twittizens (that’s a real word, right?) who linked this page, to Dan Meyer for his review and kudos, and to Peter Price for his ‘Atta boy.
I got an excellent extension from Mr. Bombastic:
I would like to see some additional questions on this day or the next that do not involve measuring and calculating the ratio (just estimation and mental math). For example, sketch a person with a mullet ratio about half that of Barry; or sketch three different looking people with about the same ratio; or a person whose hair is half as long as Barry with a ratio three times as large; or sketch a person that has a mullet ratio ofb &
Also, from Dan Henrickson:
9. Tom has a Mullet Ratio of 6.2. His party in the back is 19 inches. Find the length of his business in the front.
10. Joe has a mullet ratio of 1.7. Find two possibilities for his hair lengths.
11. Write an equation that models all possibilities for Joeb s business and party. (define the variables used)
12. Graph all possibilities for Joeb s business and party:
Wicked. I’m definitely working those into a warm-up this week, though I’ll probably use the names of students in the class.
I had a sub on Thursday, and the students’ assignment was a Valentine’s Card using math vocabulary (and the math terms underlined).
Here are some of the all-stars. Click on the first one to see a slideshow.
So, I stole a few lines, and here is a letter to my wife, the lovely and talented Andrea Vaudrey (with the math terms underlined):
To my Valentine:
Our love is like an irrationalequation; it can’t be simplified.
You are a factor of my life.
If we distribute our love, we can be together forever. Together, we make a perfect square.
I love you like a coefficient loves its variable.
You are the square to my root, the solution to all of my equations. The slope of my love for you is ever increasing.
We fit together like coordinates on an axis.
You are the solution to my New Year’s resolution. Our love is a slope that increases with all my hope that is so dope.
I less thanthree you.
For my love, like pi, is neverending.
Happy Valentime’s Day.
~Matt
UPDATE February 20, 2012: Thanks to Scoop.it for featuring this post, and for opening my eyes to what a fabulous online magazine you are.
UPDATE February 11, 2013:B And here’s the B Math Valentines Card GuideB thatB I used. I’d give credit… if I knew where I got it.
