The Infinite Chocolate Trick, Tangrams, and Area on the Coordinate Plane

With 2 months to go in this semester, it'll be time this week to begin the work on the last big project in my Applied Math class where the kids use tangrams to study area, the distance formula, and linear equation writing. Usually I hook the kids with a day of playing tangrams to practice the spatial reasoning, but before that, I played this video of "The Infinite Chocolate Trick," where the user supposedly breaks off a chocolate bar, moves the pieces around, and winds up with an extra piece of chocolate, which if its true, would mean extra surface area just materialized out of nothing.

I didn't know how much the chocolate video would pull them in, but I'd declare it was a huge success! Kids were jumping out of their seats to come to the smartboard and try to explain their hypothesis on where the chocolate was coming from, several theories were floating around the room, and kids were asking me to play the clip over and over so they could try and catch what was happening. It set up so well for the essential question, someone actually REMEMBERED it today without me even asking. :)

For the next layer of the learning I started class with a Do Now of a triangle, circle, and rectangle on a coordinate plane, but with the relevant sides laying horizontal or vertical so the lengths could be determined just by counting units.

After we reviewed the solutions, I had to students focus on the example projects above the whiteboard and asked, "Looking at the projects up there, why do you think we started with these specific problems today?"

A student jumped right into, "So that we can prove that area of a shape is the same even if you move the pieces around..." Granted, that wasn't really why we started with that specific Do Now (I was setting up the distance formula), but I was glad that EQ stuck with her!

The official essential question for this unit is:

"How can you prove that the area of a given polygon is constant, no matter how its parts are arranged?"

Practically, the kids will be thinking, "Can I show that the area of my tangram goose (or sailboat, candle, fox, etc) is the same as the square my shapes came from?"

This project covers:
Area on the coordinate plane
Distance formula
Linear equation writing
Parallel and perpendicular lines/equations
Spatial reasoning
Using tools appropriately (measuring with a ruler, setting up their grid paper)

Here are some examples of previous years' work:

Instruction/example handout

An example of a kid who had all the required elements, but it WASN'T pretty.

If you've listened to either of the podcast episodes about our statistics based project based learning unit, you'll remember I was very frustrated with how little buy in my students showed behind what I thought was a highly relevant, meaningful project. This one is less relevant, so I wanted to make an extra effort to start with a strong hook and have an experience to draw from when the kids seemed to be lost on the connection or purpose of our work in this unit.  

5 Ways to Respond to a Students' Phone Being Out Besides Smashing It

You've seen a video like this, right?

I don't want to get on a high horse and pretend there hasn't been a time or two through the years that it hasn't been a dreamy proposition, but is this ever justifiable when you're awake, and of sober mind?

I had a Facebook friend propose this should happen to any student that has their phone out. Who does this help? Is there a follow-up to this video where the student whose phone was destroyed (or anyone else in the room for that matter) comes to see the errors of their ways and begins proselytizing in the name of luddites everywhere?

I had one of my "good" students in a class of several that cause me trouble who I caught FaceTiming with her friend. Was I frustrated? You bet. Does she need a consequence? Of course! But the only thing an over-reaction does (even a referral, I think) is take a student that is much more often than not an ally in the room and turn her against me. So I had her shut it down immediately when I found it, then as she was about to leave for lunch, I called her over to conference with her and asked her what she thought her consequence should be. (Believe it or not, I did not yet have one ready for "FaceTiming in class instead of working on guided practice" LOL)

So, I'm still working out what exactly this students' consequence will be for today, (although I'm leaning toward some kind of essay on appropriate tech use/PSA/fix all the iPads backgrounds back to normal work), but until then, here's a few other ideas. 

1. Treat it like you would if the student were your own child. Especially if its an isolated incident, do your best to laugh it off, tell them to put it away, and move on to the next battle.

This is easier if you actually ARE a parent, but teachers are great at empathy, so I'm sure you'll make due. Besides the fact that you probably would have had a hand in paying for that device (or the replacement), you would also have to parent and have a relationship with this teenager after your moment of phone-smashing passion. Its tough to recover from things you say/promise/or do in moments of frustration. 

2. Call/email home and let the parents know that their son or daughter is using class time to Insta-tweet-book instead of asking a question about the course content or getting in extra practice.

 If your student is obsessive about it in your room, their parents are probably equally annoyed by the behavior and they will no doubt have your back. Make sure you back up the threat, but in my experience, kids will do a lot to avoid an effective call/email home. 

3. Have a charging station in your room away from everyone's seat. 

I have a strip by my desk where kids can plug in their chargers and put it in a box.  Time/space to charge a device is a hot commodity in my buildings, and when its in the box, its not a student's desk, distracting them with notifications every 3 minutes. 

4. Give them something to do USING IT PRODUCTIVELY.

Recording audio notes, setting a reminder for homework, responding to a backchannel discussion, pulling up a video related to their work, sending them to a page like thatquiz.org with some readymade practice (math, science, and geography). Redirecting their thumb swiping to a positive activity is an easy redirect.

5. Start a conversation about your favorite educational/learning/productivity app.

Once I put the TED app on my class iPads, my favorite question has always been from students assuming it was related to a Seth McFarland movie by the same name. :) People don't know better until they know any better - maybe your student will delete one of their 5 messaging apps and make space for your recommendation. 

What else have you done effectively? Leave a comment!

NCAA Tourney Simulation 2015

Following a process similar to last year's, I used the fan picks on Yahoo Fantasy Pick 'Em as a "true proportion," assigned integers according to those percentages for each team, and then used the randInt( function on my TI-84 to generate a number.

As an example, in the 2nd round game of Butler vs Texas, I assigned the numbers 1-60 to Butler (as the higher seed), and 61-100 to Texas. The number generated was between 1 and 60, so I chose Butler.

This year's simulation had Arizona upsetting Kentucky in the Final Four and Duke taking the championship in the final.

Here's the whole simulated bracket. Click the image for a larger view.

Do Your Students DESERVE Technology?

"Well, its they fault for having iPads..."

This was a students' response a couple weeks ago when I told everyone we were putting their project on hiatus because someone in their class walked out with an iPad yesterday. (The day after someone walked out with the class fish to be "funny.")

"The school should have known they'd be stolen - this is the hood."

I'm not oblivious to my own white privilege, and my school is definitely not Pleasantville High, but to describe our setting as "the hood" is laughable at best and disrespectful to the students in cities who have to go to schools across the country where their safety IS obviously in question.

But... maybe my school is more authentically ghetto than I thought. In a real, Webster's Dictionary kind of way, many of  my students are at least CULTURALLY isolated and trapped. When I announced their class would be going back to worksheets, there were some kids who started making contingency plans to finish their project work after school or on their cellphones, but no one really expressed the same outrage at the injustice I was about to enact on this class as I was feeling myself. I wonder how aware they are of the creative, cool, relevant projects kids with more access to technology are doing every day in other schools?

Some of my students may have even been relieved - completing a worksheet requires much less of them than a student-paced, open-ended statistics project like we've been doing. Worksheets eventually go away because the teacher moves on to the next teacher-centered, teacher-directed activity. The sheeple can follow along.

When relevance is a CLASSROOM-SPECIFIC focus, it sends the message organizationally that its only something that happens in so-and-so's class. Something THAT TEACHER is doing extra. (I had a kid tell me today after he told me he couldn't enter his answers into a Google Form that he was going to just go to credit recovery so he could get a math class that doesn't use technology. His teacher last semester that he failed with was heavy on flipping the class and using Study Island for some assessment.) When student-centered, relevance-seeking technology use is only in pockets, students can escape (and slip through the cracks). Students can blame THAT TEACHER on bad experiences. When relevance is a school-level or district-level emphasis, it starts to shift the CULTURE, which can then change the students' mindsets.

So what did do the next day? I kept the iPads locked up for that class for several more days after the fact, but they're back out now. I don't want to manage two different lesson plans for the same course, nor do can I bear intentionally making the decision to leave the iPads in the cart. I believe the only thing to fight my students' ignorance is with knowledge and exposure, and the only way to ever know and expect better is to see and experience better. 

He REALLY Said That! - Episode 7 - Debriefing 5 Best Practices for PBL

In this episode, the Algebra 1 PLC debriefs the end of their project-based learning unit, "The Lemonade Hustle" using a recent Edutopia article, "5 PBL Best Practices for Refining the Teacher's Role"

The PBL Best Practices listed in the post are:

1. Framing the Learning
2. Idea Development
3. Consultation and Revision
4. Peer Feedback
5. Presentation

Subscribe to the He REALLY Said That Podcast! iTunes | other devices

Median - The Resistant Little Bugger

One of my most favorite things to discuss in a stats lesson about measures of central tendency is the value or situational advantages of uses mean or median to tell the story YOU want to tell when analyzing data.

While preparing a different post about Google Classroom and Edmodo, I dredged up this old assignment from my Edmodo archives and was smitten by my own work. LOL

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Median was described in class as being resistant to change from outliers.  Find a news or blog article online discussing "average" (mean or median) and

1.  Give the url of your article.
2.  Summarize the article - include the variables being discussed
3.  Determine if the article is using median or mean for "average".
4.  Was the article's use of median or mean correct?  Why or why not?

Places to find links with statistics in them:
http://www.freakonomics.com
http://www.census.gov
http://www.espn.com
http://fedstats.sites.usa.gov/
http://www.baseball-reference.com
http://fivethirtyeight.com/

OR - you could Google "average _______", anything really, and get a news article about it.  "Average salary" gave a lot of hits.

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To give you more info on the way I graded this assignment, I was looking for some understanding of how students might pick out the difference in use between the two. (Whether or not the article actually said average or middle, using an actual data set to pick that out, searching for clues in the context, i.e. an article discussing how athletes are overpaid would probably use a mean.)

I used this assignment more to generate discussion and thought than as an assessment, but I suppose if you were confident that your students would be successful at this, I don't know why it couldn't be the basis of a performance event or graded writing prompt.

Do you think there are any consistent sources of "stats" articles that I've left off?

Defining Students' Capabilities (What Happened on the Scientific Notation Project?)

What do you think defines more of your students' capabilities to create, the tools you give them, or the content you teach?

Which builds more capacity in our students to solve (their own) real problems, teaching them to ask better questions, or teaching the content necessary to attack those problems?

I had a great conversation with +Jeff Horwitz from Chesterfield Day School in December about continuing to push myself to think out of a box about what problems kids can solve and what products they can create in 2015 with the technology and information available to them. There are skills we teach at the high school level in our career and technical ed and arts courses that 15 years ago a kid may have needed to make a professional-ish product.

When I was a kid...

• I "published" stories and books by using a printer, our best markers, and those little metal brads and giving them to my parents. One day, I even got invited to an city-wide event where I got to read my story in a classroom of TWENTY-FIVE other kids and parents who were attending the same event.
  
• I "produced" songs by recording myself singing along to the radio on a casette recorder.
  
• I "interviewed" people from other cultures by making up fake languages and talking into my casette recorder.
  
• I "published" a newspaper by drawing a picture in the box and writing on the lines of a pre-printed template on newsprint that my parents bought one time. (And just once. So, the fun was over in an evening.)
  
• I saw my grandparents on my mother's side fewer times than I can count on my hands, because they lived more than a day's drive away.
  

My 5 year old...

• Has published an interactive ebook and shared it on my facebook with her friends (okay, my friends, their parents, but you know what I mean.)
  
• Without even being given the idea, recorded music videos on a Leapfrog Leappad with songs she makes up herself.
  
• Has a "fashion" blog with images of her designs that she'll request we post to so she can show her friends her pictures of "horse braids", "tags for charming babies," necklaces, and more
  
• Can Facetime her Mimi and Poppa almost whenever she wants, sharing all the latest news from STL to ATL. 
  

Its hard for me to even imagine what she'll be capable of once she starts reading, but I have a feeling it will only be limited by our ability to get the tools into her hands, and her own imagination. 

I think in a lot of ways, I expect greater creativity and imagination from my preschool-aged children than I might from the high-schoolers in my classroom. Is there a chance our expectations of what they may be capable of is what defines the end product? If something is an "11th-grade" project, what makes it so? Is it the math content from a course they haven't yet taken, or is it a complexity limitation? 

Once you raise your expectations of the quality that students are capable of producing, how do you sell that to your students that have a fixed mindset of what they can accomplish? 

Two weeks ago I gave my Applied Math students a mini-project about multiplying or dividing numbers in scientific notation. I gave them the choice of 4 different questions to research and solve, and a choice of poster, collage, video, or whatever else cool they could come up with as their product. Several students steered toward poster, which was fine, but the disparity between quality was what rattled me for the better part of a weekend. Choosing to work by herself, one student finished her work in 2 class periods (and most of the 2nd was filled with coloring in block letters and graphics on her poster.) I had a group of 4 boys "finish" the same question in 4 class periods with what was probably a level of quality I could have produced in 3rd grade. 

What happened with these boys (the 2nd photo above)? Is it a matter of their teacher accepting this poster as "done," even as I already know that it will barely pass muster on my rubric? Can we mandate creativity in core classes? Do I have to put quality measures in my rubric that really should be assessing a student's learning of the content? 

From my experience, its not enough to give the option of creativity in the classroom and producing cool, quality work. Some students will flourish under that setting, but it cheats that ones who will continue to function at the lowest common denominator. I don't think its enough to show our students what they can do - we have some level of responsiblity to push and encourage them to make it happen.