"Mathematical objects are present in many natural occurring chemical substances. Studying the molecular shape of objects, one finds pentagons in the shape of deoxyribose, tetrahedrons in silicates molecules, double helices in DNA, polyhedron shapes in crystals and other molecular formations."
This is the only page of a new section, "Mathematical Models & Chemistry." Last week, I wrote that during these Pappas pages in the science chapter, I'll reflect on how I taught science last year -- or should I say, how I didn't teach science last year.
Chemistry, the subject of this section, falls under the umbrella of physical science. As such, it was part of eighth grade science under the old California standards. In the NGSS, however, some of the chemistry-related topics are now considered seventh grade standards. I've written before that I should have stuck to the old California Science Standards in Grades 7-8 and introduced the NGSS only to the sixth graders. This meant that the eighth graders should have received the chemistry lessons.
Of course, there was that Edible Molecule Project -- the first project in the Illinois State science project text. As you may recall, a huge argument between me and the "special cousin" -- the new girl transferring in from another school -- surrounded that project. First, she stated that the previous year, her science teacher had assigned an Edible Cell Project, which she'd enjoyed. She also told me that I was wrong to teach anything other than physical science -- since the previous year had been life science -- and ignored me when I tried to explain the NGSS. Finally, when I did finally assign the Edible Molecule Project, she continued to complain and didn't want to complete the project.
Although the new girl was just being oppositional, she did make some valid points. Chances are that if I'd taught physical science strongly from the start of the year -- as well as treated her cousin (the "special scholar") with more respect -- she'd have been willing to learn science from me. Notice that if I really had taught science from the start of the year, I probably would have been past the chemistry projects in the Illinois State text and been ready to work on those that leaned towards physics.
During the Edible Molecule Project, I didn't really say much about the shapes of the molecules -- the focus of the Pappas page. I just told the students that for a molecule like H2O, each hydrogen atom is bonded to the oxygen atom, not to the other hydrogen. I didn't say, for example, that the bond angle in H2O is 105 degrees.
It's a shame that I wasn't able to teach chemistry to my eighth graders better. After all, I wrote before that I prefer physical science to life science -- and in fact, I have a special affinity for chemistry. Back in February 2016, I explained why:
One last thing I want to mention in this post -- when I was young, I remember being fascinated by an old college chemistry text. Some of the problems in this text required algebra, and one of them was a slope question which used the notation slope = delta-y / delta-x -- where the symbol "delta" stands for something like "difference" or "the change in." So when my Algebra I teacher assigned some slope problems, I started writing "delta" in all of my answers. I still remember her response: "Delta is one of my favorite Greek letters." Believe it or not, I've since noticed that nowadays, some Algebra I teachers actually use "delta" when teaching slope!
And then eleven months later, I wrote about how well I did in my chemistry classes:
I think back to my own days as a science student -- which contain many highs and lows. As a high school freshman, my general science teacher saw some promise in me and wanted to promote me to an Applied Bio/Chem class, but I moved to another school before the end of the first quarter. Two years later, my Integrated Science III teacher at that new school similarly thought I was gifted and not only recommended me for Chemistry, but convinced the magnet at our school to accept me!
But unfortunately, I didn't extend my chemistry fascination to my eighth graders. I could have had fun telling them about tris, a molecule Pappas describes as having the shape of a Mobius strip:
"Tris is composed of chains of carbon and oxygen atoms and ends in alcohol groups, which lend themselves to being clipped easily together after the chain is given a half-twist."
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 whose calendar I used three years ago -- the first year of this blog.
I could have used another calendar -- a charter school who might also hire me as a sub. This calendar is closer to the one used at LAUSD. In particular, the charter's first day of school was yesterday. The reason I favor the district calendar is that it's more convenient for my purposes.
The two calendars more or less agree (staying within one day of each other) until winter break. But the charter follows the LAUSD three-week winter break and completes the first semester on December 15th with 80 days. The other district calendar agrees that December 15th is Day 80, but its winter break is only two and a half weeks long. After December 15th there are more days of school before winter break -- and these are the days for finals.
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 Days 79-80 can be review days for the final, to be given on Days 81-83.
On the other hand, following the charter calendar forces Days 78-80 to be finals days. One could argue that the SAS Inequality isn't that important (and I often skipped it myself in the past), but Lesson 7-7, "Sufficient Conditions for Parallelograms," really is important. The charter calendar would force this lesson to share Day 77 with review for the final -- and Lesson 7-6, "Properties of Special Figures," would also be affected by finals review. Therefore the district calendar, with 83 days in the first semester, is more convenient for my purposes.
Of course, notice that the district calendar starts the second semester with Day 84, which would be the day for Lesson 8-4. But Lessons 8-1 through 8-3 can be waved away. After all, Lesson 8-1, "Perimeter Formulas," can be summed up in a single sentence ("Just add up all the sides!") Then Lesson 8-2, "Tiling the Plane," can be skipped entirely. Lesson 8-3, "Fundamental Properties of Area," does give the formula for the area of a rectangle, but then this can easily be sneaked into Lesson 8-4 ("Areas of Irregular Regions"). So I still prefer the district calendar because I find Lessons 7-6 and 7-7 to be more valuable than Lessons 8-1 and 8-2.
In the end, this is the only true difference between the calendars. The two day counts remain within three days of each other the entire year, and both stay within three days of LAUSD. You can refer to my posts from my first blog year (2014-15) to see this district calendar in action. But for future reference, here is a pacing guide for the entire year:
Chapter 0: August 16th-29th
Chapter 1: August 30th-September 13th
Chapter 2: September 14th-27th
Chapter 3: September 28th-October 11th
Chapter 4: October 12th-26th
Chapter 5: October 27th-November 9th
Chapter 6: November 13th-December 1st
Chapter 7: December 4th-15th
Semester 1 Finals: December 18th-20th
Chapter 8: January 8th-17th
Chapter 9: January 18th-31st
Chapter 10: February 1st-15th
Chapter 11: February 16th-March 2nd
Chapter 12: March 5th-16th
Chapter 13: March 19th-April 9th
Chapter 14: April 10th-23rd
Chapter 15: April 24th-May 9th
State Testing Window: May 10th-June 1st
Semester 2 Finals: June 4th-6th
Notice that Day 14 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 1-4, "Points in Networks" -- which was my traditional first day of school lesson for the first three years of this blog.
But at the district whose calendar I'm following on the blog, today is the first day of school. Actually, there was a "Freshman First Day" yesterday, so ninth graders attend 181 days of school. We could thus count yesterday as "Day 0" -- but if I were a regular Geometry teacher in this district, I wouldn't bother to teach any math on Day 0 anyway. Some of the Geometry students might be freshmen, but many would be sophomores, and so the first real lesson would be today, Day 1.
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.
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. Serra begins:
"Nature displays an infinite array of geometric shapes, from the small atom to the greatest of the spiral galaxies. Crystalline solids..."
Atoms -- hey, this sounds exactly like what Pappas is writing about! It's fitting, then, that this Pappas page landed on the same day as this lesson. Then again, Serra focuses more on macroscopic shapes rather than microscopic shapes. His other examples, including honeycombs, snowflakes, and pine cones, appear earlier in Pappas.
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.
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).
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.
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