Lesson 0.2 of Michael Serra's Discovering Geometry is called "Line Designs." In this lesson, students learn to draw amazing designs with nothing but straight lines. Serra writes:
"The symmetry and the proportions in geometric designs make them very appealing. Geometric designs are easy to make when you have the tools of geometry."
Serra explains to the students that there are many tools used in geometry -- including the compass, straightedge, ruler, and protractor. As a second day of school assignment, this is a great time to tell students to purchase these tools for use in this class.
Today's assignment officially requires only a ruler. Technically, the compass or protractor could be used to ensure that the angles are right angles, but I expect the students to have access only to rulers for this assignment.
The first question directs students to re-create two designs using only lines. Notice that the first one can also be completed using graph paper. The last two can be drawn on isometric graph paper if it is turned sideways. (Yes, I still recall the problems my class had with isometric graph paper.) One of these is Sierpinski's Triangle, a famous fractal.
Serra also writes about several famous architects -- Ustad Ahmad Lahori, the designer of the Taj Mahal (and a mathematician!), as well as Frank Lloyd Wright. I include the project based on architecture on today's worksheet.
Meanwhile, I skipped Serra's question on the symmetries of the benzene molecule.
As today is the fifteenth, let's look at the 15th prompt on Shelli's Blaugust list:
Something I struggle with as a teacher/in the classroom.
And that's an easy one to answer. Three years ago, I was hired as a math and science teacher, yet I struggled to teach science. Last year, I wrote about this in my Blaugust post -- and since I'm cutting and pasting that post anyway, I might as well cut and paste this story in.
When I first wrote that post, I referred to two particular students in my old class -- the "special scholar" and her cousin, the "special cousin." The previous summer I'd written a post explaining who those two girls are, but those posts were lost in the Great Post Purge of 2017. I then repeated who they are in my January 6th post. (I won't cut and paste from that post, but it's another post that's all about my struggles in the classroom.)
Now I'll retell this story, now that you know exactly whom I'm talking about:
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. 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 described as having the shape of a Mobius strip.
Today's Blaugust poster is Denise Gaskins:
https://denisegaskins.com/
https://denisegaskins.com/2019/08/15/updated-geometric-coloring-designs-free/
I actually mentioned Denise Gaskins on the blog in an earlier Blaugust post. That's because I used her "Tax Collector" activity as a "rich task" for my sixth graders at the old charter school.
In today's Blaugust post, Gaskins posted some "Geometric Coloring Designs." Hey -- this fits today's Serra lesson like a glove. Here's a link to her 42-page coloring book:
https://tabletopacademy.files.wordpress.com/2019/08/geometric-coloring-designs.pdf
I'll include Denise's disclaimer here:
You have permission to print and use these game boards and worksheets in your own local classroom, home school, math circle, co-op class, etc. But you may not post them as your own or sell them. If you’re not sure how copyright works on the Internet, check out Daniel Scocco’s Copyright Law: 12 Dos and Don’ts.
(And I'm not posting this as my own right here -- the credit completely goes to Denise Gaskins.)
This coloring book also contains pages for lessons that appear later in Serra's book, such as mandalas (Lesson 0.5) and tessellations (Lesson 8.4). And in today's blog post, she also refers to her Islamic Art page (Lesson 0.7).
The brilliance of Denise's coloring book makes me almost not want to post my puny worksheets, which refer to Lesson 0.2 only. In fact, this worksheet doesn't even say to color the designs. Of course, students can color them.
Here are the worksheets for today:
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