Tag: estimation

  • A Great Day

    Today was a great day.

    Linear and Non-linear Functions

    Today, the lesson was on linear and non-linear functions. After plotting points and noticing that a ruler can’t go through all five, we stood up, hands at our sides.

    I stood on a desk. Because it’s my class and I can do what I want to.

    “Elbows out.” [I show them.]
    “Arms out.” [All students are making a T.]
    “Arms down.” [Everyone is giggling, but obeying.]
    “When I say go, show me a linear function with your arms… go!”

    The class snaps into a variety of positions, all with straight arms.

    Kinda like this, but all at the same time.
    Kinda like this, but all at the same time.

    “Awesome. Arms down. Now show me a non-linear function…go!”

    Kinda like this, but all at the same time.
    Kinda like this, but all at the same time.

    When 5th period arrived, the day went from good to great. First, they barely made it to one linear function before they were karate-kicking chairs and each other.

    “Huh… Okay, siddown.” I said, hopping off the desk.
    They froze. “What?”
    “Yeah, I’m not gonna fight you so we can do fun things in class. Siddown.”

    We do some more practice and agree to try again. We make it through a couple successful commands before Lorraine takes it up a notch:

    “Can we play Simon Says?”

    Hell yes, we can!

    (This isn't actually 5th period, but it's the best shot I got today.)

    Simon says ‘show me a non-linear function’.
    Simon says ‘show me a function that makes a vertical line’.
    Arms down. Ah! I didn’t say ‘Simon Says’. You’re out, you’re out, you’re out. Sit.
    Simon says ‘show me the YMCA’.

    Estimations

    The 6th period iPad Intervention class has been taking on Estimations, Visual Patterns, Would You Rather, and Daily Desmos.

    Today, we tackled the Red Vines task, and it was friggin’ awesome.

    Previously, we established that one of Mr. Stadel’s hands holds 18 Red Vines, so our guesses hovered around 100-120 (5-7 handfuls).

    redvines1

    Halfway through the video answer, we’re at 150 and I hear Frank.

    “Goddammit! I only put 130!”

    When’s the last time you found an activity for math class that got kids amped enough to curse about it?

    For the record, Frank thought he was mumbling to his neighbor, and I didn’t discipline him. Judge if you must, but I’d much rather have excitement and foul language than boredom and silence.

    The real highlight of today, however, came when the video slowed down.

    redvines2

     

    …and Donte is out of his seat, pumping both arms in the air, chanting, “Two hundred! Two hundred! Come ooooon, baby! Two hundred!” He’s dancing back and forth as only an amateur pro athlete can.

    Then, Mr. Stadel pulls out the 201st Red Vine, just to taunt Donte.

    redvines3

    ..and Donte’s arms fall to his sides, his jaw drops, and his eyes deaden. He stands transfixed, staring at the wall, crestfallen that he was so close to a perfect guess.

    And I laughed my ass off.


    Months later, I realized what a bummer it was that Donte was so crushed by guessing 201. His previous 7 years of math education had taught him he was wrong, even though he was 0.5% off of the correct answer.

    Thankfully, after a few more months of these, Donte grew confident enough in his process to be content with having hisB product be different from the answer key.

    ~Matt “Hasn’t Eaten Red Vines Since Middle School” Vaudrey

     

  • A Good Day

    When in the course of human events, teachers will sometimes adopt curriculum.

    The best days happen outside of it.

    Gremlins, Speed Dating, and Monomial Cubes

    Before we go further, I should describe what we call “Monster Equations” in my school.

    “Eek!”

    The above equation is a Monster. It has several steps, uses multiple operations, and is terrifying to an 8th grade RSP student. Luckily, we have tools to fight such monsters.

    Our notes for the week

    The acronym DCMAM stands for Don’t Call Me A Monster.
    It also stands for the steps needed (in order) to whittle a “Monster” down to a 2-step equation (with which, the students are modestly comfortable).

    Got it? That’s a Monster Equation and why we call it that. Onward:

    Onward

    Last week, I taught Monster Equations and it bombed. Students didn’t know how to combine like terms, distribute properly, mirror operations on both sides of the equal sign “wall”, or even add two numbers with different signs.

    This isn’t surprising; those are all skills covered in 7th grade, and our adopted curriculum assumes they remember everything.

    The same way that my wife assumes hot dogs are good for you, you just have to eat enough of them.

    So, my class is going back to those basics, and today was “Gremlin Equations”.

    Surprisingly, about 1/3 of each class had seen the movie.

    A “Gremlin” equation isn’t quite a Monster, but still requires delicate handling, because if you break the rules…

    …they get ugly.

    Here enters our activityB for today:

    “Each of you has an expression glued to the bottom of your paper, it’s half of a Gremlin Equation. You and your partner will combine your two expressions to make a Gremlin and solve it together. When you’re done, you both stand and find new partners.”

    As I described it to my department head, I realized what it actually was:

    Equation Speed Dating.

    "I see you checking out my coefficients, baby."
    “I see you checking out my coefficients, baby.”

    In the first classes, one student would fill both sides of the worksheet with about 10 minutes left and proclaim, “I’m done.” At that point, I killed the music, returned students to their seats, and opened up the Pan Balance from NCTM. They dove right into it and burned the last few minutes.

    AutoCrat, a Foldable, and Impromptu Estimation

    After about three hours of attempting to synthesize Google Drive with my district firewall, I was met with a failure sandwich on toasted frustration bread. My digital team-mates–John and Karl–did the best they could to troubleshoot unique solutions:


    Well, 6th period arrived before IT support did, so I pulled a quickB foldable from Sarah’s blogB and followed it with my bag full of monomial cubes, planning to do some random practice.

    Photo Feb 04, 2 55 59 PM

    I held up the bag andB immediately a student called, “How many dice are in the bag?”

    Oh. I thought. This just got much more interesting.
    “What do you think?” I asked.

    A couple students call out guesses before someone yells, “Can we see one of them?”

    Photo Feb 04, 2 56 21 PM

    We pull a few guesses (where the median is about 65) and start counting them together.

    Photo Feb 04, 2 46 17 PM

    “Is there an easier way to arrange them for counting? This is confusing me.”

    Photo Feb 04, 2 49 38 PM

    “Okay, five by five… so we’ve got three 25s plus one… so… ”
    Student: 76! I was close!
    “What if this was on a planet where humans had 4 fingers on each hand instead of 5?”

    Students paused. Thought for a little bit. Then…

    Photo Feb 04, 2 53 59 PM

    Hey! Five 16s with 4 missing! That’s also 76!

    So, yeah. It was a good day.

    Tomorrow, students will finish up their Monster PostersB with this cut-and-paste Monster EquationB activity.

    ~Matt “The Expression Matchmaker” Vaudrey