Input, Process, Output (Day 91)

Here is today's Pappas question of the day:

.(93)repeating = x / 33

Notice that this decimal is just 93/99, which reduces to 31/33. So the answer is x = 31 -- of course, today's date is the 31st. My eighth graders did a few questions similar to this one earlier -- and more recently, my seventh graders dealt with terminating decimals.

The month of January has come to a close, and with it is the end of the 2017 Blogging Initiative. I do wish to link to some of the other participants, especially the middle school teachers:

Our first teacher is "Mathy" Cathy Yenca, who teaches seventh grade in Pennsylania:

http://www.mathycathy.com/blog/

Here is a link to her Week 4 post:

http://www.mathycathy.com/blog/2017/01/we-all-fall-down-mtbos-mtbosblogsplosion-week-4/

Recall that the Week 4 topic is about our biggest failures. For Yenca, her biggest failure involves problems she's had with projects. Two of her projects involve the concepts of surface area and volume, but her students didn't learn as much from the projects as they should have.

Notice that Yenca's projects come from Dan Meyer -- the King of the MTBoS. I can't use Meyer's projects in my classes, since I must only use Illinois State projects. But I've had some similar issues with these projects as well. In particular, there was an eighth grade project earlier where students had to compare the volume of a cylinder to that of other prisms. And just today, the sixth graders had to find the surface area of a piece of wood.

I write about these projects in my comments to Yenca:

I found this post via the Blogging Initiative — in fact I’m one of the other middle school teachers who participated.

I’m wondering whether your popcorn project would have worked better if Act 1 presented the two completed cylinders — of completely different shapes (one tall/thin, one short/broad) — so that students would have no reason to assume that the volumes are equal. Then in the final act, we cut the cylinders back down to the original rectangles to show that surprise, surprise — they’re the same rectangle!

My own school embraces projects, and just today I gave my sixth graders a project where they had to find the surface area of pieces of wood — which sounds very similar to your projects. I ended up breaking up the project into discovery/direct instruction rather than pure discovery, just as you had to do. Basically, I had the students discover that measuring the wood requires three dimensions — and then I directly told the successful students the formula for surface area.

By the way, one of Yenca's other projects is intended to show the students that doubling the length of a cube quadruples its surface area and increases its volume by a factor of eight. I wonder whether the lesson "Can There Be Giants?" from the U of Chicago Geometry text (alluded to on the blog in past years) might have helped motivate this idea. I guess the problem is that surface area just isn't a very easy topic to engage students in.

The other middle school teacher is New Yorker Anna Pacura:

http://iamamathteacher.blogspot.com/

Here is Pacura's Week 4 entry:

http://iamamathteacher.blogspot.com/2017/01/take-chances-make-mistakes-get-messy.html

Pacura's post title refers to the PBS show Magic School Bus, which is a near-contemporary of Square One TV, as the first Bus episode aired about a year or so after Square One TV ended. Actually, there may be new episodes of the show released on Netflix in 2017.

In her post, Pacura writes about how she used "integer chips" -- that is, manipulatives -- to teach her seventh graders. As a student teacher, I've had mixed success with algebra tiles -- it really helped some students out, while others thought it was a waste of time. Now manipulatives are supposed to be included in one of the "learning centers" that I'm supposed to teach on Thursday.

I write about my experience with manipulatives in my comments to Pacura:

I've had mixed reactions when I've used manipulatives similar to the Integer Chips that you describe. For some students they were helpful, while others were more like you, havingalready mastered algorithms without the need for "tiles" or "chips."

My school embraces manipulatives, and soon I'll be required to use them in my upcoming lessons, including integer lessons.

It's been a pleasure getting to read your posts during the 2017 Blogging Initiative. See you in 2018!

Pacura also submitted an extra post to the challenge -- one where she describes her failures as a math student rather than a math teacher. She writes:

That was also the year that I wasn't just taking 8th grade math, but also 9th grade (Sequential 1) math after school.  For the first time in my life, math wasn't coming easily to me anymore.  But I get through it, and did well on the Sequential 1 Regents that June, which meant that in high school, I would be taking all freshman classes, except for math, where I would be a year ahead. My failure came in my second year of high school, when I was taking Sequential 3 (again a sophomore taking a Junior year math class) and I got lazy.

I know that "Regents" means New York State tests -- I'm not an expert on them, but I've seen so many New Yorkers refer to these tests before. From context clues, I gather that "Sequential 1" in the Empire State is what other states call "Integrated Math I." I've written about the similarities between Common Core 8 and Integrated Math I. Naturally, Pacura was in high school well before Common Core -- I wonder whether the double would have worked better if her eighth grade class was Common Core 8, as this class and Integrated Math (Sequential) I are so similar.

Of course, the failures mentioned by Yenca, Pacura, and the other participants pale in comparison to my mistake, where I fail to teach an entire subject. My problems with science became an issue again in class today -- especially after one of the other teachers reminds the eighth graders today that there is a California science test coming up. One of my students sits in the teacher's chair, and when I tell her to leave my chair, her response is essentially that I'm not really the teacher, since I don't even teach a subject that they have a big test on.

Once again, my science failures creep into classroom management. It would be simplistic to say that all of my classroom management problems go back to science failures -- indeed, I reckon students would just find other excuses not to obey me. But still, each day I don't teach science means another day that students can use the lack of science instruction to justify not respecting me.

I don't need to repeat my entire Week 4 post to detail my science failures. But after today's latest argument, I doubt that giving my kids a Study Island will be acceptable. The idea of giving my students one science lesson per week might have been OK had I started it in August, but with Wednesday (the science day) already being February, students rightfully feel that they aren't being adequately prepared for the test.

Again, I feel that nothing short of a science project tomorrow will quell the concerns. But now I must figure out what project to give. I already gave the first project from the Illinois State physical science text (on molecules). The second project has the students investigate six "mystery powders and liquids" in order to discover some of their properties. But that means I have to find and gather six mystery chemicals, plus figure out where some of the materials (such as a magnet) are located. And this says nothing about the California/NGSS confusion whether I should even be taking lessons out of the physical science text in the first place.

This is another reason why I wasn't looking forward to teaching science -- all of the materials needed for a successful project. I suspect that the projects that the students will enjoy the most are the ones with the more materials and prep time needed, and any project I can easily prepare by tomorrow will be considered too boring. Again, the day for science is tomorrow, and I'm in trouble. In fact, I feel that I need a real Magic School Bus to take my students on a science field trip, as that's the only way I can come up with a good lesson! But I'm definitely no Ms. Frizzle....

I haven't said anything about the eighth grade STEM project for today. Well, Learning Module 10 of the Illinois State eighth grade text is called "Input, Process, Output." It introduces students to functions as well as the graphing calculator. Seventh graders had a project on exercise and how it affects both calories burned and the heart rate.

In fact, I saw that today was the perfect day for a Square One TV song at music break. There is a song called "Count the Ways," performed by the country duo the Judds. This song prominently mentions the normal human heart rate, 70 beats per minute (or 100,000 beats per day). It is not posted on YouTube except as part of a full Square One TV episode (song starts about 5 1/2 minutes in):

Here is a transcription of the lyrics -- which can't be found on Barry Carter's site. My version changes it up a bit so that I, the singer, am the "mystery man" referred to in the song:

COUNT THE WAYS

My love is three-dimensional, it has width, depth, and length,
I'll run that by you one more time.
Like an equilateral triangle, my love has special strength.
Yes, I have mathematics on my mind.

Refrain:
Let me count the ways that I love you,
I'll calculate the rhythm of my heart.
Let me count the ways that I love you,
And count each fraction of a second we're apart.
My heart beats for you 70 times a minute.
My heart beats for you 4200 times an hour.
My heart beats for you 100,000 times a day.
Three million times a month, 36 million times a year.

Yes, I want you to know that I'm not your average guy.
I'm the missing factor in your equation.
I'll multiply your happiness 'til your love equals mine,
Hey, you don't need any more persuasion,

(Repeat Refrain)

It's also a great song to sing because of the opening line about how love is three-dimensional -- it has width, depth, and length. All I have to do was change "love" to "wood," and it fits the sixth grade project on surface area.

(By the way, notice that the heartbeats in a day is close to the fifth power of 10. There have been some Calendar Reform proposals -- more accurately, Clock Reform -- that take full advantage of this near equivalence. They introduce metric time by using "beat," as in heartbeat, to refer to 10^-5 day.)

Well, the 2017 Blogging Initiative is now complete. But my science adventures are just beginning.