Wednesday, February 8, 2017

Student Journal: More on Equations (Day 97)

Here is today's Pappas question of the day:

7.571 liters = __________ quarts U.S.

One liter is slightly more than one quart, so 7.571 liters is slightly more than 7.571 quarts. It's safe to assume that 7.571 is just about eight quarts -- and of course today's date is the eighth.

This is the sort of conversion problem that my sixth graders worked on recently. The tricky part is to convert from metric to U.S. measurement. This is why I prefer this question for my class:

2 gallons = __________ quarts U.S.

By the way, you may wonder why the "U.S." part is there -- after all, doesn't the word "quarts" imply American measurement already? Actually, there used to exist Imperial quarts in the U.K., and their quarts were larger than ours. In fact, 7.571 liters works out to be 6.662 Imperial quarts.

Today the eighth graders continued working on solving equations:

Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

As I said earlier, this is tricky for those students who need more help on one-step equations, but we must proceed in the Illinois State text.

Today my predecessor -- the teacher who taught this class before me -- was on campus. He decides to pull students whose current grade is 60-75% to provide them with extra help. So again, today I have learning centers, but not the official Illinois State centers.

Again, my predecessor gives me some tips on how to cover the material. He warns me that the upcoming units on systems of equations and slope will be tricky. Indeed, it may be a good idea to make the Warm-Up question be on one of these standards everyday, even after we've moved on to other topics. I may reflect this in my Pappas questions posted to the blog, but it's tricky to convert the solution (x, y) to a date. Sometimes I'll have to ask for just x, just y, or even x + y or xy -- the latter allowing us to convert pairs with negative values of x and y to positive dates.

My predecessor tells me that he is currently a tutor at Kumon. He says that many of his students are well above grade level, even ahead of the top students here at our school whom he remembers. This reminds me of the traditionalists, who are fond of bringing up Kumon. The claim is that school systems hold the brightest students back, and so the parents must take their young prodigies to Kumon to get accelerated work.

Anyway because he mainly works after school these days, my predecessor is willing to come back to his old school from time to time. He'll continue to work with those borderline students who can use the extra help.

The music break song is Weird Al's "Patterns," another Square One TV song. This is an anniversary song, as today marks ten years since its posting. I actually sang the song in class yesterday, since I don't have music break on Wednesdays:

Barry Carter, who has transcribed the lyrics to many Square One TV songs, doesn't have the lyrics to this particular song. But Weird Al is famous enough that his lyrics appear at other websites:


Everywhere, I see them there
I stop and stare at patterns
I don't care, I must declare
I've got a flair for patterns

On my hair, the clothes I wear
My savoir faire is patterns
All I see is patterns
The patterns that repeat

Let's go into the bathroom
I know we're in a room where you would not expect much math
Usually you're in here for a shower or a bath
But if you gaze upon the floor, and if you're kinda smart
You'll see the repetition is like geometric art

Wow, haha

Everywhere, I see them there
I stop and stare at patterns
I don't care, I must declare
I've got a flair for patterns

On my hair, the clothes I wear
My savoir faire is patterns
All I see is patterns
The patterns that repeat


A polkameister like myself never has to be bored
I just grab my ax and play some patterns on my keyboard
Now's the time for earplugs if you care about your health
So stand back, everybody, I'm gonna express myself

Look at this, patterns
I've got blisters on my fingers
Woo, hey, aw, get down
Yeah, help me, somebody, woo

Still there? Okay

Next time you find yourself at an exciting polka party
You can make some patterns with your feet and with your body
If you don't know the steps yet, here's the gang with all the answers
Ladies and gentlemen, introducing, the "Weird Al" Polka Dancers

Here they are

Everywhere, we see them there
We stop and stare at patterns
We don't care, we must declare
We've got a flair for patterns

On our hair, the clothes we wear
Our savoir faire is patterns
All we see is patterns
The patterns that repeat

Wallpaper, skyscrapers, funny papers, patterns
Evergreens, nouvelle cuisine, human beings, patterns
Garden rakes, wedding cakes, rattlesnakes, patterns
Golden wheat, little feet, my heartbeat

I gotta stop

Patterns, patterns, patterns, patterns

This song was a good song to sing yesterday, as students had to search for patterns while performing the STEM projects. But the lyrics of this particular song were a bit awkward for me.

First, Weird Al calls himself a polkameister, and the "ax" he plays is short for "accordion," an instrument often played by polkameisters. I, of course, don't have an accordion -- but I do have a guitar, which, for some reason, also has the slang term "ax" (though usually spelled "axe"). But if I want to pretend that "ax(e)" really means "guitar," I'd have to change the "keyboard" line, since accordions, unlike guitars, have keyboards.

So I skipped the accordion verse -- but since I didn't want to skip any more verses, that left me singing the verse about polka dancing. I can't polka dance either -- all I did was swing my legs the way the "Weird Al" Polka Dancers do in the video. I suppose I could have changed the words even more and pretend that "polka" refers to "polka dots" -- which really do form a pattern!

My sixth graders are now learning about percents today -- which means that I could have sung another Square One TV song, the Percents song. But I did keep repeating that song's bridge:

The number of parts of one hundred
Is what a percent is
Let’s take two:
Can be said as a fraction, two-one-hundredths
Or a decimal, point-zero-two; that’s true

You may notice that it's awkward to teach percents when, if you recall, I've hardly taught my students any decimals. But in the Illinois State text, percents are converted to fractions, not decimals. So to find 25% of 40, we multiply 25/100 by 40/1. The percent is over 100 and the whole is over 1.

Seventh graders don't have my class on Wednesdays any more. Instead, eighth graders return for the special science period. I finally have the students do the mystery material experiment. I think it works out okay, but one student decides to mix two of the materials together -- I think it was the alcohol with one of the powders.

For those students who weren't playing around, both yesterday's physics project and today's chemistry project are valuable learning experiences. But I can't assert that either project will lead them to even a single correct answer on the science test in May.

By the way, my predecessor tells me that even though our school had a science teacher last year, there was none two years ago -- so he had to cover the science classes. He tells me that he gave science projects that led to math practice -- for example, in human anatomy, the students can use fractions to measure their body parts.

Right now, though, my biggest worry is tomorrow's learning centers -- and I mean the actual Illinois State centers, not the informal centers with my predecessor or Bruin Corps members. There will be a Dren Quiz on Friday, so there's no excuse not to have centers tomorrow. I'm not risking the students be unprepared for a major quiz or test the next day, since it's only a Dren Quiz.

One of the stations is supposed to be for "art projects," with a die cut machine. But I'm having trouble figuring out what art projects have to do with math. The fifth grade teacher was unable to help me out, as middle school art projects work differently from those in elementary. Indeed, the emphasis in middle school is supposed to be on STEM projects, not art projects -- nonetheless, I'm still required to have a station for art projects! Well, we'll see how things turn out tomorrow.

I know I've fallen out of the habit of linking to Tina Cardone's "Day in the Life" poster, but I defintely want to get back on track today. The "Day in the Life" poster with a monthly posting date of the eighth is Jennifer Fairbanks, a Massachusetts high school teacher:

Surprisingly, I haven't linked to Jennifer Fairbanks yet -- I didn't start blogging about "Day in the Life" until September 8th, and then I just kept missing the eighth in my links. So let me finally do her blog justice and write about it. Here's a link to her February 8th post:

The title of the blog is "8 is my lucky number," so it's easy to imagine why Fairbanks selected the eighth as her posting day. Throughout her post, she writes about her fears that tomorrow will be a snow day, and by the end of the day, it's announced that there'll indeed be no school tomorrow.

Fairbanks writes:

We are at A day in our 7 day cycle, so I have a prep period in my room first - this is heavenly.  Then, I have Accelerated Algebra I and we are reviewing for a quiz that will hopefully happen given tomorrow's snow.  Next up is Accelerated Algebra 2 and we are reviewing for a conics quiz hopefully tomorrow.  During lunch block I have lunch duty, followed by last period in Foundations Algebra 1.  We are working on graphing standard form of a line in there.  I am not sure what I am doing with that yet so I will work on that in prep

I've heard of schools that have schedules similar to the one described by Fairbanks. It's often known as "drop and rotate." Students have seven classes, but only six of them meet in a day. So a different period is skipped each day. The class that is skipped is first the following day, hence there is no relationship between period and time of the day. There also is no relationship between which class is skipped and the day of the week, hence the need for her to call today an "A day."

Back during the time when eighth grade in California was Algebra I, there was a Silicon Valley middle school that actually discouraged eighth graders from taking the class. The reason was that the school had a "drop and rotate" schedule, and the administrators believed that they should wait to take Algebra I at the high school where they could have math everyday. But apparently, the school at which Fairbanks works has no problem with Algebra I -- and accelerated at that -- under the "drop and rotate" schedule.

I assume that "Foundations of Algebra I" is a class for low-level students -- that is, it's a freshman pre-algebra course for those destined to take Algebra I as sophomores. (Sarah Carter also teaches a freshman "Foundations" course.) Since Foundations basically covers middle school math, let's look at what Fairbanks writes about this course in more detail:

12:45-1:50 - Foundations of Algebra 1 - Start by checking and reviewing the homework.  Then it is Estimation 180, 2 Solve Me Puzzles, and Visual Patterns (at the board).  Then, we will do cup stacking.  Any activity we can to make sense of graphing and writing equations of lines.  Update about class.  It didn't go well as usual.  

I'm not quite sure what this "cup stacking" activity is. But recall that nearly two years ago, I wrote about a three-act activity from the King of the MTBoS, Dan Meyer, about a stack of cups. So it's reasonable to assume that this is the same activity. The important thing is that the students were given an activity, and it didn't go well. What Fairbanks writes about activities can easily apply to the various activities in my class -- both STEM/science projects and tomorrow's learning centers:

I will come up with something else.  These are kids who could really benefit from manipulatives and hands on, but their behavior is getting in the way.

I notice that there are actually two bloggers whose monthly posting date is the eighth. The other is Jake Winfield, a high school teacher in Arizona:

He hasn't made his February 8th post yet. Here's a link to his January 8th post -- except it was a Sunday, so there's very little math mentioned in the post:

And I know that today's not the seventeenth, but I wish to link to the January 17th post of Mariam Brunner, a sixth grade teacher in Georgia:

Brunner writes:

One instructional strategy I keep trying to implement is station activities.
[emphasis mine -- dw]

So now you can see why I'm bringing up this post -- Brunner is trying to implement station activities, just like me. So let's see what Brunner has to say about them:

I want to work with small groups of students and allow other students to work independently. I’ve been able to effectively do stations before without having a small group, but when I through in a small group station, my other groups seem to fall apart. I tried again today, and I was happy to see that they worked. I think the change was that there were no new activities at the stations. The students were working on things they had done before, so they could focus on doing the activity rather than “how” to do the activity.
Well, this certainly gives me something to think about as I try to set up my stations tomorrow.

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