Friday, August 30, 2019

Lesson 1-3: Ordered Pairs as Points (Day 13)

Today I subbed in a seventh grade science class. This marks my first day of subbing of the new school year.

In my old district, today is Day 13, but in my new district, it's only Day 5. This is the first time that I've ever subbed as early in the year as Day 5 in my district. And it's only the second time that I've ever subbed before Labor Day -- in 2015 I also subbed on the Friday before the holiday, but in that district, it was Day 8. Last year, I started subbing on Day 7. (You can refer to my posts in September 2015 and 2018 to read about those subbing days.)

We return to "A Day in the Life" format for blogging days on which I sub. I'm inconsistent when it comes to "A Day in the Life" -- I always try to blog when subbing a math class, but for other classes it often depends on the situation.

Since my focus is on classroom management, I try to post on middle school days unless there is a special aide who manages most of the classes. Today there's an aide for two of the five classes, which isn't a majority. Therefore I will post "A Day in the Life" today.

But before we start, here is the Blaugust prompt for today -- the thirtieth from Shelli's list:

A Day in the LIfe  (#DITL)

Hey, that's very convenient! I want to post "A Day in the Life" for today's subbing, and today's Blaugust prompt is also "A Day in the Life." And so let's just begin "A Day in the Life":

8:15 -- This is homeroom. Ordinarily there is a video to watch during homeroom, but today the online link isn't ready until it's too late. So instead, I lead the Pledge of Allegiance, and then an eighth grader from ASB gives the announcements.

8:20 -- Homeroom ends. This is the middle school where all classes rotate, and today the rotation begins with fourth period. In case you're wondering why the rotation begins with fourth period on Day 5, it's because the rotation starts with Period 1 on the first two days.

Anyway, fourth period is an honors science class. But since today is only Day 5, it's still the first week of school. And you know what that means -- first week activities! Thus many of the activities suggested by other bloggers actually appear in this class.

First of all, the students do have name tents. These aren't exactly the same as VanDerWerf name tents, where students ask a question or leave a comment everyday during the first week and the teacher must respond. But in addition to the name, students write their goals for science on the back and write something inside too. So it's likely these tents were inspired, directly or indirectly, by VanDerWerf.

Each day this week there's supposed to be some sort of "seating challenge" where students must complete a challenge and then take a seat based on the results of the challenge. I don't have a clue what the seating challenge is supposed to look like. But because it's a sub day, the seating challenge is cancelled, and kids are free to sit wherever (as they don't have assigned seats due to the challenges).

Finally, we reach the main activity of the day. I write the instructions to the activity on the board:

  1. Choose one picture of a beaker.
  2. Write first name and initial of last name on the beaker.
  3. Draw items that represent you, in color with no white or pencil showing.
  4. Cut it out after it is completed.
  5. Turn it over and write full name and period on the back.
This activity is due on Tuesday. Completed projects will be hung on the walls. Oh, and any names I write on the bad list will receive detention. Of course, this is an honors class, so there's no behavior issues at all.

9:15 -- Fourth period leaves and fifth period arrives. This is the first of two classes with an aide.

10:05 -- A lock down drill is announced. I don't wish to turn this post into politics, but what does it say about recent events that there needs to have a lock down drill during the first week of school?

Some students are talkative during the lock down drill. Notice that this isn't an honors class -- and the special aide had already left for another classroom before the drill began.

10:20 -- The lock down drill ends, and it's time for snack.

10:30 -- Sixth period begins. This is the second of two classes with the aide. This is not an honors class -- in fact, one of the students is absent because she's already been suspended. Notice that not even my seventh grade boys at the old charter school -- some of whom were extremely defiant -- managed to get themselves suspended that fast! What's more unsettling is that this girl has just arrived this week from her (K-6) elementary school.

11:15 -- Sixth period leaves and first period arrives. This is the second of two honors classes. Of course, there are no behavior issues in this class.

12:10 -- First period ends and it's time for lunch. My break extends to second period conference.

2:05 -- The homeroom class returns for third period. This class is labeled as a "sheltered" class, which indicates that there are many English learners in this class. As often happens in such classes, this class is quieter than Periods 5-6 (since students are reluctant to speak due to language issues), but not as quiet as the honors classes. There's also a second girl who's been suspended from this class.

2:55 -- Third period leaves, thus ending my day.

I've been making it a habit to sing some of my old songs in class as an incentive. Today I choose a song that's (somewhat) related to science from this time three years ago -- "The Need for Speed" (aka the mousetrap car song -- see yesterday's post for pictures of the mousetrap cars). In fifth period -- longer due to the lock down drill -- I sing another science song, "Meet Me in Pomona, Mona" (on this opening day of the LA County Fair). This is just before the lock down, not during the drill itself (when everyone needs to be silent to hear instructions over the intercom).

Another habit I wish to develop this year is emphasizing the positive. Of course, it's easy to say positive things about the two honors classes, since those students are so quiet and hardworking.

But I have to push myself to say good things about students in the other three classes. Today, I praise students who are making nice drawings or coloring them in neatly. Also, when the class is noisy, I remind the students that most of them are being quiet, except for those few who are clearly doing something wrong (like speaking loudly or faking knocks at the door). There's still room for me to grow here, but at least I was able to avoid arguments or writing anyone on the detention list.

Normally, whenever I sub in a science class, I lament seeing all the wonderful lessons that I could have taught at the old charter school, but didn't. Today's lesson really wasn't much science-y -- but it does remind me of some opening week activities that might have improved my classes. Indeed, I discussed many of these earlier this month while reading Blaugust posts (including yesterday).

For example, the seating challenges seem awkward during the first week of school, when the teacher is still trying to learn student names. But then again, that's what the name tents are for -- with name tents, the teacher doesn't need a seating chart to learn the names. Thus we can have activities that don't require a seating chart -- and hence avoid arguments about seating during the first week.

Among other Blaugust participants, Denise Gaskins posts what she calls a carnival -- dozens and dozens of links to math teachers of all levels, from elementary to high school:

https://denisegaskins.com/
https://denisegaskins.com/2019/08/30/playful-math-education-carnival-130/

Under "Teaching with Wisdom and Grace" she links to both Sara(h)s as well as a few others who post opening week activities.

And Beth Ferguson also adds some activities for Algebra I/II and Statistics, though these aren't necessarily for the first week:

http://algebrasfriend.blogspot.com/
http://algebrasfriend.blogspot.com/2019/08/data-collection-labs-to-model-functions.html

But it's Ferguson's post from yesterday that reminds me of how in some ways, I blew the first week of school almost as much as I blew it in science.

I tried to find a link to a blog that describes what a "seating challenge" might be. I found this old 2014 post describing what it might be. (This link might appear in the Ferguson or Gaskins lists, but I just used Google since searching all of their links might take too long.)

https://mathinate.wordpress.com/2014/08/24/first-week-plan/

Notice that the author of this post just happens to be named Sarah -- but of course, it's not VanDerWerf or Carter:

Tuesday:
To get started, students will find their seat by solving a simple math problem; the seats are numbered 1 – 24. 

Wednesday:
For this first day, students will seat themselves by alphabetical order of first name.

Thursday:
Students will seat themselves by birthday, January to December.

Friday:
Students will seat themselves in order by height, shortest to tallest. They have to do this one silently, which is an extra challenge.

Except for the math problem, I can easily see a science teacher doing something like this. And once again, I could have done this in my own classroom three years ago.

Yesterday, I explained how 2016 was a big year for posting first day activities -- VanDerWerf, Carter, and Ferguson all posted that year. This was the same year that I was in the classroom and thus could have used some first week activities. But for various reasons, I didn't take any of them into account:

  • Ferguson posted hers too early for me. During Blaugust, I read all of Ferguson's posts during the month of August. But Ferguson's opening week activity post was dated July 22nd.
  • Carter posted hers too late for me. She posted during her first week of school, which was one week after mine. (I did use her "Survival in the Desert" in her first week/my second week.) In 2016, she posted many activities that week since it was the first time that her school stared on Monday rather than Thursday (requiring five days of opening week activities, not just two).
  • VanDerWerf posted hers at the perfect time -- nine days before my first day of school. The problem was that in 2016, I had never heard of VanDerWerf. Although she had been teaching for decades, she didn't start blogging until the winter of 2015/6. Thus 2016 was her first opening week since creating her blog. But I didn't know of her blog until 2017 -- long after my first week of school. I haven't been in a classroom during the opening week of school since -- until today, that is.

Indeed, Carter and Ferguson had labeled their posts "Blaugust," while VanDerWerf never did. But then again, Shelli had invited me to join Twitter, which I ultimately turned down. If I had joined, it's likely that I would have seen VanDerWerf's tweets. Indeed, I decided to search some old 2016 tweets and saw that Shelli herself referenced VanDerWerf that August. Thus if I had accepted Shelli's invite to join Twitter, I would have seen VanDerWerf's tweet and likely used one of her activities -- either name tents or her other famous opening activity (known simply as "1-100").

Let's get to the rest of this post. Today on her Mathematics Calendar 2019, Theoni Pappas writes:

x is a rational number. What must x equal for this triplet to represent the sides of a right triangle?
{30.5, x, 5.5}

This is another one of those Pythagorean triple problems where we don't know whether x is the hypotenuse or a leg. Assume that it's the hypotenuse:

a^2 + b^2 = c^2
30.5^2 + 5.5^2 = x^2
930.25 + 30.25 = x^2
960.5 = x^2

And 960.5 isn't the square of a rational number. Thus x must be a leg:

930.25 - 30.25 = x^2
900 = x^2
x = 30

Therefore the missing member of the triple is 30 -- and of course, today's date is the thirtieth. The Pythagorean Theorem is taught in Lesson 8-7 of the U of Chicago text.

This is what I wrote last year about today's lesson:

Lesson 1-3 of the U of Chicago text is called "Ordered Pairs as Points." (It appears as Lesson 1-2 in the modern edition of the text.) The main focus of the lesson is graphing points on the plane. Indeed, we have another description of a point:

Third description of a point:
A point is an ordered pair of numbers.

The idea of graphing points on a coordinate plane is a familiar one. But sometimes I wonder whether we should make students graph points and lines so soon in their Geometry course.

Once again, here's how I think about it -- the students coming to us just finished Algebra I. Some of them struggled just to earn a grade of C- or D- (whatever the lowest allowable Algebra I grade is in your district is so that the students can advance to Geometry). The students who just barely passed Algebra I are tired of seeing algebra. They may look forward to Geometry where they won't have to see so much algebra -- and then one of the first things we show them is more algebra.

Then there's also the issue, first brought up by David Joyce, that students should use similarity to show why the graph of a linear equation is a line. This idea appears in the Common Core standards for eighth grade, but it's awkward in high school. Graphing linear equations is a first semester Algebra I topic while similarity is a second semester Geometry topic -- and it's difficult to justify delaying graphing linear equations by three semesters just to conform to Joyce's wishes.

In the past, I've tried -- and failed -- to teach linear graphs after similarity. (This includes last year, when I tried to follow the eighth grade standards, but I left the class before graphing equations.) This year, my plan is simple -- I will conform to the order of the U of Chicago text. The U of Chicago text introduces linear graphs in Lesson 1-3, and so that's when I'm teaching it.

The bonus question asks about longitude and latitude. I've already located my own coordinates as being near 34N, 118W.

Thus ends another Blaugust. I'm not posting on the 31st since that's a Saturday. Instead, my next post will be on Tuesday, after the Labor Day holiday.


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