Should I do "A Day in the Life" today? That's a tough one. On one hand, a Spanish class isn't quite representative of what I want to teach someday, since I don't even speak Spanish. But on the other, it is a multi-day assignment, which means that I want to focus on my classroom management.
In the end, I decided that I will do "A Day in the Life" today, but not tomorrow or Friday. At least by doing so, today you'll be familiar with these Spanish classes. Then you'll be ready for my quick overview of my day in tomorrow's and Friday's posts.
7:55 -- Second period (recall that at high schools, "first period" is like zero period) is the first of the Spanish II classes. These students have three tasks -- first they must answer some questions out of the textbook, then they complete two pages in the workbook, and finally they have a worksheet.
8:50 -- Second period leaves and third period arrives. This is the other Spanish II class.
9:50 -- Third period leaves for snack.
10:00 -- It is now tutorial. One student is working on her Algebra I assignment, and so I am able to do some actual math today. Her assignment is on putting equations in standard form and graphing them using intercepts. I notice that the Glencoe text does something here that I wish other Algebra I texts would do -- admit that in the form Ax + By = C, A should be positive, and A, B, and C should all be integers with no common factor other than 1. Other texts don't state this assumption directly -- but they make this unstated assumption when giving the answers at the back of the text. Then students get confused as to why their equation of -2x + (1/2)y = 3 doesn't match the answer in the book.
10:30 -- Tutorial leaves and fourth period arrives. This is the first Spanish I class. These students have a one-page lesson to read, and then their assignment is similar to that of Spanish II -- they do about 4-5 pages on a worksheet, two page in the workbook, and six questions in the textbook.
11:30 -- Fourth period leaves and fifth period arrives. This is the second Spanish I class. Some of these students were in yesterday's P.E. class. I let them know about yesterday's sub report (third period was the best behaved, sixth period the best walking the track, fourth period had issues). One student was in yesterday's fourth period P.E. -- fortunately he wasn't one of the troublemakers. He tells me that the P.E. teacher has scolded the five students whose names I listed. He wasn't sure exactly what their punishment was -- it might have been just a one- or two-point deduction, or it could have been a detention.
12:25 -- Fifth period leaves for lunch.
1:10 -- Sixth period arrives. This is the last Spanish I class.
2:00 -- Sixth period leaves. Officially, seventh period is the teacher's conference period. For the teacher, this means that he teaches five straight periods followed by a break. For me, it means that I get to go home early.
As you might expect, the more mature Spanish II classes are the hardest-working classes. I name third period to be the best class of the day, since this class is the most hard-working. Once again, there's a trade-off, as second period might have been slightly quieter. (Also, there are more tardies in third period than in second, a bit of a surprise.)
I also decide to name a best Spanish I class of the day. This is tricky -- fifth period is the quietest, but only because this class is much smaller than the other two first-year classes. In fact, fifth period becomes even smaller today, as one student transfers from fifth to fourth period. He is shocked when he finds only two open seats for him to choose from in his new class (as opposed to his old class, where there are two open rows).
But here's the problem I have with both Periods 4-5 today. As I write down names for my good list, I notice that most of the hard-working students in fourth period are guys -- while in fifth period, most of the diligent students are girls.
Therefore I name sixth period as the best Spanish I class of the day, since both guys and girls are listed among the hard-working. I hope that I can inspire the fourth period girls and fifth period guys to work harder tomorrow and Friday.
This is what I wrote last year about today's lesson:
Normally, I'd be posting today's worksheet, but today is just Day 2 of yesterday's activity. I feel guilty for making a school-year post without a worksheet. But then again, I felt even guiltier for never posting multi-day activities and thereby never giving students an opportunity to continue a worksheet before posting the next one.
So there's no worksheet for me to post today. The students should continue working on yesterday's "Corresponding Parts in Congruent Figures" assignment.
And now I feel even guiltier because I mentioned no Geometry at all in today's post -- the only math I wrote about today is Algebra I. Let me make up for it by at least linking to some Geometry. Here is a blog post I found by retired teacher Henri Picciotto on this week's Geometry topics -- glide reflections and congruence:
https://webcache.googleusercontent.com/search?q=cache:-MJhnBMrEjIJ:https://blog.mathedpage.org/2016/01/glide-reflection-and-symmetry.html+&cd=10&hl=en&ct=clnk&gl=us
I had to use the Google cache to find this post, so let me cut and paste it again here:
In my previous post, I introduced glide reflections, and explained their importance from the point of view of congruent figures: in the most general cases, given two congruent figures in the plane, one is the image of the other in a rotation or a glide reflection. (In some special cases, one is the image of the other in a translation or a reflection.) Another way to state the same thing, as commenter Paul Hartzer pointed out, is that if the composition of two of the well-known rigid transformations (rotation, translation, reflection) is not one of those three, then it is a glide reflection.
In this post, I will give an additional argument in defense of the glide reflection: its importance in analyzing symmetric figures. The Common Core does not have much to say about symmetry (see my analysis.) This is unfortunate, because symmetry provides us with connections to art and design, as well as to abstract algebra, and is very interesting to students.
Symmetry is deeply connected to rigid transformations, and can be defined in terms of those: a figure is symmetric if it is invariant under an isometry. (In other words, if it is its own image in an isometry.) In the most familiar example, bilateral symmetry, the isometry in question is a line reflection. Another well-known symmetry is rotational symmetry. In these examples (from my Geometry Labs), the stick figure is its own reflection in the red line, and the recycling symbol is its own image in a 120° rotation around its center:
But what if we have a figure that is its own image under a translation? That is the case for this infinite row (or frieze) of evenly spaced L's. It is its own image under a translation to the left or to the right by a whole number of spaces:
...L L L L L L L L L L L L...
A frieze can be thought of as an infinitely wide rectangle, with a repeating pattern. A symmetry group is the set of isometries that keep a figure invariant. As it turns out, there are only seven possible frieze symmetry groups. In the example above, translation is the only isometry that keeps the group unchanged. But look at this one:
It is invariant under the composition of a horizontal translation and a reflection in a horizontal mirror. In other words, a glide reflection. If you want to analyze frieze symmetry, the glide reflection is absolutely necessary.
Likewise, if you want to analyze wallpaper symmetry. In this Escher design, for example, the light-colored birds are images of the dark ones in a glide reflection (the reflection lines and translation vectors are vertical.)
Do all students need to know this? Probably not. But to some of us, this is a lot more interesting than many of the "real world" applications of math I have the opportunity to present.
--Henri
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