Lesson 0-1: Geometry in Nature and in Art (Day 1)

Today is the first day of school according to the blog calendar. The blog calendar is based on one of the districts from which I hope to receive subbing calls. This district is not LAUSD, but in fact is the district where I receive the majority of my calls, in Orange County. This is the first year that I'm following this calendar.

I could have used another calendar -- the other district where I currently sub. This district, in LA County, had the calendar that I've followed the past three years on the blog. But I decided this year to follow the Orange County district.

Recall that I'm following the digit pattern for days in the U of Chicago text. Chapter 7 is the last chapter of the first semester, and it contains eight sections. Following the district calendar puts Lesson 7-8 ("The SAS Inequality" or Hinge Theorem) on Day 78. Then finals will be given afterward, on Days 79-81.

Notice that the district calendar starts the second semester with Day 82, which would be the day for Lesson 8-2. Lesson 8-1, "Perimeter Formulas," can be summed up in a single sentence ("Just add up all the sides!") and so it's fine to start with Lesson 8-2, "Tiling the Plane," on the day after winter break.

For future reference, here is a pacing guide for the entire year:

Chapter 0: August 17th-28th
Chapter 1: August 31st-September 15th
Chapter 2: September 16th-30th
Chapter 3: October 1st-14th
Chapter 4: October 15th-28th
Chapter 5: October 29th-November 12th
Chapter 6: November 13th-December 3rd
Chapter 7: December 4th-15th
Semester 1 Finals: December 16th-18th
Chapter 8: January 4th-15th
Chapter 9: January 19th-February 1st
Chapter 10: February 2nd-17th
Chapter 11: February 18th-March 3rd
Chapter 12: March 4th-17th
Chapter 13: March 18th-31st
Chapter 14: April 1st-21st
Chapter 15: April 22nd-May 5th
State Testing Window: May 6th-28th
Semester 2 Finals: June 1st-3rd

Comparing the calendars in my two districts, notice that my old district started last Wednesday while my new district starts today. The last day of school is the same in both districts, June 3rd.

Meanwhile, the first semester in my new district is very similar to the LAUSD calendar. Indeed, except for the fact that my new district starts today and LAUSD starts tomorrow, the two calendars are identical for the first semester. Thus Days 2-81 in my new district are the same as Days 1-80 in LAUSD. This includes a change to one PD day in my new district that was just announced last week (and technically hasn't been approved by the board yet). 

Notice that Day 15 is the day after Labor Day. This means that teachers at schools that have a Labor Day Start, but wish to follow my pacing guide, can simply pick it up at Lesson 1-5, "Drawing in Perspective." (This is one of several worksheets that I had once set up as a possible first day of school lesson during the earliest years of this blog.)

Speaking of which, I have more to say about the Labor Day Start vs. Early Start Calendars. For years, schools have started after Labor Day. My new district is the latest to join the growing Early Start Calendar movement.

But the Early Start calendar has been criticized more this year due to the pandemic. Some people wonder whether schools are truly ready for the new school year -- and whether they'd finally be ready by Labor Day, in which case a Labor Day Start Calendar this year is better.

Also, some people claim the reason for the Early Day Start Calendar is so that there's more time in school before the state tests. Yes, the reason for the calendar change is testing, but no -- it's not the state tests, but rather high school finals. The idea is to have the fall semester end before Christmas so that finals can be given before winter break, before the students have a chance to forget what they learned over the holidays.

But temperature and air conditioning remain concerns. It's unfortunate that, due to seasonal lag, the hottest day of the year (sometimes called the "summer thermistice") is well after the summer solstice, while Christmas is tied to the winter solstice. Thus the first semester must begin before the summer thermistice in order to end before the winter solstice. (I don't know the exact date of the summer thermistice, but it definitely feels hot outside where I am today -- oh, and also Death Valley here in California recorded a temperature of 130 degrees yesterday!)

I've seen some people suggest that even after the pandemic is over, the school year should always start online from now on -- now that we've seen that it can work -- until Labor Day. Then students can avoid being stuck in a classroom during the heat of the summer thermistice. I haven't decided whether I agree with this proposal or not, but I understand the reasoning behind it.

(In my last post, I wrote that school should start no more than two weeks before Labor Day, but that was in reference to the Andrew Usher Calendar, and for a different reason. But two weeks before Labor Day is just about the latest the first semester can credibly begin and still have finals before Christmas. Oh, and speaking of Usher, let me wish you a Happy Leap Week!)

Even though there is no Day 0 on the blog, there is a Chapter 0, covering Days 1-10. Since the U of Chicago text doesn't have a Chapter 0, we use Michael Serra's Discovering Geometry instead. Don't forget that my copy of Discovering Geometry is an old text, dated 1997 (Second Edition). My old version goes up to Chapter 16. The modern (3rd-5th) editions only go up to Chapter 13. But Chapter 0 is essentially the same in all editions -- the only difference is that Lessons 0.5 and 0.8 no longer exist in any edition later than my Second Edition.

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

Lesson 0.1 of the Discovering Geometry text is called "Geometry in Nature and Art." In this lesson, students learn that Geometry is all around them.

The main theme of this lesson is symmetry. Serra writes about two types of symmetry -- reflectional symmetry and rotational symmetry. And so we are introduced to two of the main Common Core transformations, reflections and rotations, in the very first lesson.

By the way, I've noticed that other teachers use the Serra text as well. For example, here is a link to Lucy Logsdon -- a Michigan Geometry teacher and Blaugust participant:

https://lsquared76.wordpress.com/2018/08/14/honors-geometry-unit-5-polygon-properties/

Logsdon was a Blaugust participant in 2018. She's isn't blogging this year -- in fact, she's made only one post since the one linked to above.

Even though Logsdon never mentions the name Serra or title Discovering Geometry, she's clearly referring to this text. Notice that she begins by discussing "Polygon Angle Conjectures" -- and calling these "conjectures" instead of "theorems" is a giveaway that this is Serra's text. I see that the lessons follow the same order as in Serra -- polygon angle conjectures are in Lessons 6.1 and 6.2, kite and trapezoid properties are in Lesson 6.3, midsegment properties are in Lesson 6.4, and parallelogram properties are in Lessons 6.5 and 6.6. The only reason she calls this "Unit 5" instead of 6 is that in his modern editions, Serra combines his old Chapters 1 and 2. Thus the modern chapter numbers tend to be one less than the Second Edition chapter numbers.

The reason that Serra calls these "conjectures" instead of "theorems" is that officially, nothing is proved until the final chapter. But he does sneak a few coordinate proofs and flow proofs in earlier chapters, which is why these proofs appear on Logsdon's blog as well.

I didn't post on August 17th last year because it was a Saturday, but I did post on that date two years ago, on this same prompt. Here is the Blaugust prompt for today:

#made4math - Create something you can use this semester, such as a tarsia puzzle, question stack, game, card sort, etc.  (Or share one you have previously created)

Well, technically I did make the worksheet for today -- and it's definitely something that can be used this semester (even if just as an opening activity). Then again, you can argue that I didn't really "create" it, as the entire worksheet comes from Logsdon and Serra.

In my 2017 post for the third day of school, I wrote about how I'd attempted to create lessons for my science class. But as you already know, that didn't go too well:

I think back to my own days as a student. A classic project is for the students to construct a model of a DNA molecule, and I did so as a sophomore taking Integrated Science II.

I don't know whether the Illinois State text includes a DNA molecule project or not. The Illinois State science text was divided into three volumes -- earth, life, and physical science -- and the life science text was the last to arrive at my school. Therefore I was less familiar with the projects in this text than in the other two science texts.

In fact, part of the reason for my failure to teach science was the lack of science texts. You see, Illinois State didn't supply us with enough science texts (as opposed to math texts) -- in fact, the students never received science texts. There were teachers editions of the earth and physical science texts -- and they were both delivered to our sister charter school.

The thing about our sister charter is that they didn't have any eighth graders. This made a huge difference when looking at their bell schedule. At both schools, the day was divided into four main blocks followed by P.E. time. Over there, sixth and seventh graders had two blocks with my counterpart teacher -- one for math, the other for science. At my school, meanwhile, I had each grade for one STEM block and the last block was for IXL with one of the grades.

I think this was what confused me about teaching science. The administrators intended me to start teaching science, possibly by going to the Illinois State website for science materials. But I didn't, because I thought that the STEM projects in the Illinois State math text counted as science! Notice that some of the math projects in each text could double as science projects (e.g., research projects in Grades 6-7, solar system project in the eighth grade text). But in reality, I should have taught science using the Illinois State materials -- online only until my teachers editions arrived.

So there was a perfect storm of confusion regarding why I didn't teach science properly:

• lack of science texts at start of year
• nonappearance of science on daily schedule (replaced by mystic "STEM" block)
• projects in math "STEM" text resembling science projects
• lack of other middle school science teachers on campus to ask for info
• counterpart on other campus unhelpful as she didn't teach eighth grade (the critical testing year)
• counterpart on other campus unhelpful as her specialty wasn't science (it was kindergarten!)
• transition from California Science Standards to NGSS

My earth and physical science texts finally arrived at some point -- I don't recall exactly when. Neither my counterpart nor I had a life science text. In fact, she ended up using the earth science text for sixth grade (which she knew matched the old standards) and thus, by default, physical science for seventh grade. (Some physical science topics, such as atoms and molecules, do appear in the seventh grade NGSS.)

Of course, I knew that at the very least, my eighth graders needed science for the state test. One day, some eighth graders complained, "Why aren't you teaching us science? In fact, do we even have any science textbooks?"

There were some old texts near the back of the classroom -- but unfortunately, they were only for sixth (earth) and seventh (life) grades. Then I tried to teach an eighth grade NGSS lesson from the seventh grade text -- but of course they rejected the lesson. And of course, no one accepted my explanation of what NGSS was, or why Illinois State didn't provide any student texts. Interestingly enough, science and math suddenly appeared on PowerSchool just in time for me to assign separate grades at the end of the second trimester (as opposed to the first trimester, when the students received only a "STEM" block grade).

Notice that it was right around the end of the first trimester when the Illinois State teacher texts arrived -- perhaps that should have been the hint that skipping science first trimester was understandable without the texts, but as soon as I had them, that was the time to begin teaching science -- to all three grades.

Well, I did start teaching science to the eighth graders at that point -- the DNA lesson. The shape of the sugars in the molecule is important. It is the pentagonal shape of deoxyribose which makes the shape of the spiral and requires 10 rungs to complete a turn. When gene copying (or DNA replication) takes place the DNA double helix is unwound at breakneck speeds of over 8000 rpm, and splits along the bases separating into two strands. Again, I could have tried to keep the mathematical models of DNA structure and replication in mind as I taught this lesson to the proper grade level -- the seventh graders.

Did I ever actually create anything at all for my classes? Well, for the most part my hands were tied since I was required to use the Illinois State texts and materials. But for the third day of school I did create an opening activity worksheet on number patterns. Even though many of the patterns came from other sources, the collection is still original to me.

Outside of the year that I actually taught, some of my posted Geometry worksheets, while based on the U of Chicago text, present the material in new combinations. A typical example is my worksheet for Lesson 9-2 (from my January 15th post), which combines a list of vocabulary words with two Exploration questions from that lesson to create a short activity worksheet.

But actually, I doubt that Shelli, the Blaugust leader, had worksheets in mind when she came up with the Made 4 Math label and prompt. Indeed, Shelli herself posted today:

http://statteacher.blogspot.com/2020/08/mtbosblaugust-pathways-to-being-better.html

Then again, Shelli doesn't really create much today either. As she tells us:

11:30am - Neighbor teacher goes to run an errand, I grab my bag chair and text a friend to see if she wants to sit outside for a bit for fresh air.  Grab my notebook from last year and a blank calendar to try to figure out some pacing calendars.

Well, I guess that makes two of us, since I posted my pacing calendar for the blog earlier. Notice that even though Shelli hasn't had her first day of school yet, she does use "A Day in the Life" format.

Another Blaugust participant, "Algebra's Friend" Beth Ferguson, really does create something today:

http://algebrasfriend.blogspot.com/2020/08/exploring-patterns-extending-thinking.html

Patterns are EVERYWHERE! Some suggest that the study of mathematics is the study of patterns ... identifying them, categorizing them, generalizing them.

OK, so this is similar to the patterns activity that I gave on the third day at the old charter. I won't link to her worksheet here -- you should get it directly from her blog.

Returning to Serra:

"Nature displays an infinite array of geometric shapes, from the small atom to the greatest of the spiral galaxies. Crystalline solids..."

Atoms -- but then again, Serra focuses more on macroscopic shapes rather than microscopic shapes. His other examples include honeycombs, snowflakes, and pine cones.

I created the first worksheet of the year from questions from Serra's text. Some of these are labeled as Exercises, while others come from his first "Project." And some of these questions ask students to bring objects in to class. This seems awkward for the first day of school -- but then again, this is the very first lesson in Serra (so it's intended for early in the year). It might be good for teachers to find photos on the internet and show them to the class. Or better yet, the students might be able to come up with pictures of their own to draw -- especially the questions about art from various cultures (which include the students' own cultures).

[2020 update: OK, this doesn't quite work with coronavirus distance learning. Then again, they might be able to show the objects to the camera.]

Yet there are two questions that students might enjoy as an opening day activity. One of them asks students to find the line of symmetry in a work by British artist Andy Goldsworthy, who indeed is still alive (hint: H2O). The other asks students to name playing cards with point symmetry. They might want to draw these -- the three of diamonds has point symmetry, but not the three of clubs. Yes, they might want to try drawing the three of clubs with point symmetry to see why it is impossible.