Tuesday, July 24, 2012

Distance, Rate, & Time [Giddy Up!]

Last week I finished Steve Leinwand's Accessible Mathematics. It's a quick, easy, informative, realistic, and applicable read. Get on that!
This week I planned on diving into Standards Based Grading while restructuring some things for next school year. Well, there's still time for SBG. Instead, I've been churning out some new 3 Act lessons with:
  1. Some outtakes to the hexagonal Pencil Cup lesson and...
  2. The beginning of some distance, rate, and time lessons
There's a plethora of resources out there dealing with d = rt. Therefore, I thought I'd try and put my little spin on the whole roundabout. Keep checking my Distance, Rate, & Time album for updates.
Giddy up to summer!

Go the distance,

Thursday, July 12, 2012

Elmo's Microwave Travel

Summer school has been a fantastic testing ground for 3 Act lessons with incoming 6th & 7th graders. I'm constantly reassessing my deployment of the lesson format. If you have any improvements to offer, go for it. Check out Dan's whole catalog. Here's a few I used this summer:
  • Print Job: Talk about rate and breach theoretical v. practical discrepancies.
  • Nana's Chocolate Milk: Ratios, Fractions, Proportions, Equivalencies, do it!
  • Popcorn Picker: Do identical rectangular papers have the same volume?
  • Super Bear: Unit rate, ratios. Discuss Percent Error (genius)!
Dan's lessons are wrapped up in a neat little package, following his own framework for digital media. It's up to us to deliver. Today, I used my Elmo's Microwave Travel lesson. Keep in mind this was with incoming 6th graders. I'm more generous with them than my 8th graders. I continue to learn about the 3 Act lesson format (here's Act 1):

Act 1 (go get that Q):
View and immediately get those Q's (questions) in the air.
I don't perseverate anymore over having at least one student ask the intended Q. Let students ask what they wonder and state observations. If they hit your intended mark, don't jump for joy. Act as if it's just another Q in the mix. Summarize the questions and observations before revealing the Q. I usually say something like, "I'm right there with (insert name) on this and I also want to know (state question)." Luckily, there was at least one kid form each class who wanted to know how many rotations Elmo makes in the microwave. Get that Q on the board immediately along with any other questions that could be answered during the lesson. Have students write the Q's at the top of their paper, notebook, handout (whatever you use). Everyone needs an objective, something to work toward. Once it's scribbled down, encourage your students to make an estimate for each Q and pencil it in near the Q. We came up with:
  1. How many rotations does Elmo make? (They nailed this Q!)
  2. What distance does Elmo travel around the microwave? (Extension of the 1st Q)
  3. Will he melt? (Some students really worried about him melting. How considerate.)
* Using their wording for the Q's, I encouraged them to put it in relation to one minute.
Students do all the thinking, questioning, noticing, etc. but in the past I wasn't writing the Q on the board. Big mistake. Now it's monkey see, monkey do! Get the Q on the board. Go!

Act 2 (muy importante!):
Ask the students to discuss, "What do we already know?" Here are some responses from students:
Elmo travels for a minute. (Me: "How does that help?")
He's on a circular plate. (Me: "What do we know about circles or can do with that?")

Write the facts on the board. Now I ask, "What information would help you answer those Q's on the board?" or "What would you want to know in order to answer the Q's?"
Really make students think here. Don't make it easy. I have to keep working at this tactic. Allow students to struggle with the notion that they need to determine what's relevant before you divulge any new information. This allows students to be better critical thinkers. Here's what they thought:
Maybe we could see how far he goes in 10 seconds (Me: "Interesting.")
The plate is a circle. Can we know the circumference? (Me: "Is that easy to measure?")
Then can we have the radius? (Me: "I'll give you the diameter. How's that?")

Roll Act 2 Elmo. Students, get solving. Start discussing, debating, testing, calculating, etc. If you come up with something let the class know. If we agree on it, we'll write it on the board. If not, we'll erase it. Hey Frank Noschese, now I'm starting to see the importance of those student whiteboards. WWFSD? (What would Frank's students do?) Can we still jot down necessary info at the front while students collaborate? Of course.
This is all student derived. I was simply the scribe.
Okay students, you got a solution? What does that number mean? Does it make sense? Did you check it for reasonableness? Did you give a unit of measurement? Did he travel in miles, feet, inches, millimeters? Does it make sense? I bombard them with questions. I'm almost getting to the point where I forget about Act 3. I want to see their work during Act 2. I want to hear their rationale. I want to learn from my students and their thought process. I enjoy that. Lately, the big driving force for me to actually leave Act 2 behind and attack Act 3 is the discussion that follows after viewing Act 3

Act 3 (theoretical v. practical):
On paper, many 6th graders miscalculated that Elmo travels 37.68 inches for one minute. Even after asking them if it made sense, they stuck with their answer (I let it go). There were a couple who got the correct answer! I didn't tell them; we watched Act 3. The students who had the correct answer and saw that 37.68 inches was quickly ruled out, watched intently as the time wound down. The anticipation on their face was priceless. The video ended and one girl was both happy and confused at the same time as she awkwardly asked, "Is it okay that my answer is one inch off?" Hello! Here's our opening for discussion. Theoretical v. Practical. I was so happy. First we discussed why 37.68 inches was incorrect. They didn't multiply their circumference by the number of rotations in a minute. Then we tackled the theoretical v. practical results. My microwave plate is kind of wiggly. It doesn't rotate at a constant speed the entire time: it slows down and speeds up. That one inch could be accounted for a few reasons. Their world was rocked, but Elmo's world made sense.

[Sequel to come] Dan contacted me for some video footage of Elmo traveling for 30 seconds in real time so he could use it at a workshop. He wanted his attendees to graph:
  1. Elmo's distance from the center of the plate over time [Update: Video]
  2. Elmo's distance from the glass door over time [Update: Video]
  3. Elmo's total distance traveled over time [Update: Video] *My recent addition
I plan on doing the video sequel and will experiment with it in Motion this week. My kids enjoyed the sequel discussion, but missed a video to back it up. Great sequel idea Dan, thanks.


Sunday, July 8, 2012

Rock, Paper, Scissors

A few weeks ago I was out with my family and caught a glimpse of two kids playing Rock, Paper, Scissors. I immediately made a note of it on my phone for a 3 Act lesson. Here's what I came up with for Act 1:

In my mind, Rock, Paper, Scissors (RPS from here on out), is such a powerful way to decide something between two people. I think of all the times it decided who got to ride shotgun, who got the last piece of pizza, who got to go first, etc. We're talking a huge playground staple (at least I think it still is). I have no idea if the two kids were deciding something or just playing RPS for fun. It doesn't matter! I wanted to know who would win? Were they playing straight up to one? Were they playing the best 2 out of three? Who has the advantage: rock, paper, or scissors? What are the chances of a tie? A lesson was born... I have to get it down on paper or make a digital note of it somewhere. Imagine the class activity that could result from this... that will be a future post.
I'll admit, I was proud of this Act 1. I thought I had a slam dunk. Feedback from some tweeps said they preferred the scoreboard (thank you twitter and online colleagues). As you can see only 7 people have viewed it on 101qs.com so far and 3 of them skipped it. Usually those first 7 people are the regular 101qs users who post first. I admire them. I dig their attentiveness. I could list them, but I won't. They're awesome!

I'm over the initial bewilderment that it barely passes 50% perplexity. There's a bigger, more important element here besides my state of mind: comments. That said, I'm excited with Dan Meyer's most recent update to 101qs.com, specifically the option to leave Comments. I would love to hear from those 3 people and what prompted them to skip it? How could I improve it? What about RPS did not perplex them? Bottom lime: I look forward to receiving constructive feedback on 101qs.com just as much as giving it. Our students, classrooms, and craft of teaching all benefit from it. I think Vimeo sums it up nicely when leaving comments, "Be cool and play nice."
What do you think?


Thursday, July 5, 2012

Why? How? and What?

Inspired by Simon Sinek's TED talk (at least the first 6 minutes of it), The Teaching Gap (Stigler & Heibert), and you... I'm reevaluating some teaching ideas & restructuring some classroom details in preparation for next year. What are your thoughts, using
One sentence for Why?
One sentence for How?
One sentence for What? about:
  • Learning
  • Teaching
  • Estimating
  • Exploring
  • Discussing
  • Assessing
  • Improving
*PLEASE send me a CONFIRMATION TWEET when you take the poll, verifying your twitter handle.


Results here.

Thanks in advance!

*Gold star for @fawnpnguyen for first post!