There's not much to say here. Indeed, there's no "A Day in the Life" since at high schools, I usually do it only for math classes.
Today I cover one freshman, two sophomore, and two junior classes. All classes begin with 25 minutes of silent reading, followed by five minutes of stamping a Warm-Up sheet where students answer a question related to whichever book they choose to read.
Recall that in this district, most schools have a block schedule with one all-classes day each week. At this school, the all-classes day is on Fridays -- and this is also the late day. (Since my day starts with conference period, I don't actually have a class today until 9:55!) Anyway, 25 minutes of reading and a five-minute Warm-Up make sense on block days, but on Fridays -- with 45-minute classes -- silent reading and the Warm-Up take up fully two-thirds of the period! There's only a few minutes left to do any other tasks (which aren't even worth mentioning on the blog).
And so I must consider the silent reading and Warm-Up to be the main tasks of the day. Most of my classroom management is devoted to keeping the class silent during the reading, and my good and bad lists of names are based on completing the Warm-Up.
Meanwhile, I'm still thinking about yesterday's science classes -- and what I could have done at the old charter school to make my classes resemble yesterday's (and hence be more successful).
Part of my problem that year was my confusion regarding whether I should have taught from the STEM text (which isn't actually a science text) or the actual Illinois State science text. I ended up leaning towards the STEM text, mainly because I had printed copies of this text (as opposed to the fully-online science text).
But even sticking to the STEM text, there are some activities that I could have taught better. For example, we consider "Show Me the Numbers," the second project of the year. This project contains a mini-lesson on graphing. But unfortunately, I just glossed over this mini-lesson (which the possible exception of my sixth graders).
Instead, I should have emphasized the step-by-step process more, just as the co-teacher and student teacher did yesterday. We follow each step as a class (in all three grades), and I perhaps show them other examples of data for the student to graph. If I have had interactive notebooks (as I should have), then I could have had them glue these graphs there as a reference.
Of course, I wouldn't have used the DRY-MIX mnemonic since I didn't learn it until yesterday. It's possible that DIXI-ROYD, which I already knew then, might have fit here (except that D = domain and R = range might not have been appropriate in a science setting). These graphs are linear, as opposed to yesterday's bar graphs (though other graphs are mentioned).
In past posts, I suggest that perhaps I should have taught only the first STEM activity and then jumped to the online science text. But as this lesson shows, perhaps this second lesson (which I taught around this time of year three years ago) has a useful purpose.
Today on her Mathematics Calendar 2019, Theoni Pappas writes:
What is the area of this oddly-shaped kite?
(Here's the given info from the diagram: the diagonals are 4 and 10.)
In the U of Chicago text, kites are taught in Lesson 5-4, while areas appear in Chapter 8. Yet nowhere in our text does the area of a kite appear. In other texts, the area is:
A = (1/2)d_1 d_2
that is, half the product of the diagonals. It's proved by dividing the kite into two triangles and then using the Triangle Area Formula.
But Pappas describes this as an "oddly-shaped kite" -- that is, this kite (which can be flown in the sky) doesn't have the symmetry of the kite quadrilateral of Lesson 5-4. But as it turns out, the formula applies to any quadrilateral whose diagonals are perpendicular, not just kites. And since our diagonals are indeed perpendicular, we can use the formula.
(It's possible that two of our sides just happen to be parallel, which would make it a trapezoid. But this isn't necessary for our purposes.)
It remains only to plug the values into our formula:
A = (1/2)d_1 d_2
A = (1/2)(4)(10)
A = 20
Thus the desired area is 20 square units -- and of course, today's date is the twentieth.
Lesson 2-7 of the U of Chicago text is called "Terms Associated with Polygons." (It appears as Lesson 2-6 in the modern edition of the text.)
This is what I wrote last year about today's lesson:
This is what I wrote last year about today's lesson:
Lesson 2-7 of the U of Chicago text deals with polygons. Notice that this lesson consists almost entirely of definitions and examples. But this chapter was setting up for this lesson, since a polygon is defined (Lesson 2-5, Definitions) in terms of unions (Lesson 2-6, Unions and Intersections) of segments:
A polygon is the union of three or more segments in the same plane such that each segment intersects exactly two others, one at each of its endpoints.
It follows that this section will be very tough on -- but very important for -- English learners. I made sure that there is plenty of room for the students to include both examples and non-examples of polygons. The names of n-gons for various values of n -- given as a list in the text -- will be given in a chart on my worksheet.
The text moves on to define a polygonal region. Many people -- students and teachers alike -- often abuse the term polygon by using it to refer to both the polygon and the polygonal region (which contains both the polygon and its interior). Indeed, even this book does it -- when we reach the chapter on area. Technically, triangles don't have areas -- triangular regions have areas -- but nearly every textbook refers to the "area of a triangle," not the "area of a triangular region." Our text mentions polygonal regions to define the convexity of a polygon -- in particular, if the polygonal region is convex (that is, if any segment whose endpoints lie in the region lies entirely in the region), then the polygon itself is convex.
The text then proceeds to define equilateral, isosceles, and scalene triangles. A triangle hierarchy is shown -- probably to prepare students for the more complicated quadrilateral hierarchy in a later chapter.
Many math teachers who write blogs say that they sometimes show YouTube videos in class. Here is one that gives a song about the three types of triangle. It comes from a TV show from my youth -- a PBS show called "Square One TV." This show contains several songs that may be appropriate for various levels of math, but I don't believe that I've ever seen any teacher recommend them for the classroom. I suspect it's because a teacher has to be exactly the correct age to have been in the target demographic when the show first aired and therefore have fond memories of the show. So let me be the first to recommend this link:
Another song from Square One TV that's relevant to this lesson is "Shape Up." Notice that many geometric figures appear on the singer's head -- though not every shape appearing on her head is a polygon:
Today is an activity day. Last year right after Lesson 2-7, I posted activities for the Daffynition Game and Jeopardy, and so I repeat those activities today. This is what I wrote two years ago about these activities:
And now I present my worksheet for the Daffynition Game. Remember that only one of these worksheets need to be given to each group -- in particular, to the scorekeeper in each group. The students write their guesses for Rounds 1-4 (or 5) on their own separate sheet of paper. I recommend that it be torn into strips so that they are harder to recognize. And the teacher provides the index cards, one for each student. Make sure that the students give back the index cards so you can reuse them for the next period. The students may keep their "guess cards," so there should be one for every student in every period.
The second page is for the Jeopardy game -- just as with the Daffynition game, there should be index cards, with the number of points on one side and the question (um, the answer, since the response is the question) on the other. In my class the questions were taped to the front board. In this version of the game, the categories correspond to the four lessons covered earlier this week. Of course, some lessons, such as Lessons 3-1 and 3-2 on angles, are tailor-made for Jeopardy, but unfortunately we haven't quite covered the lesson. Of course, we'll get there next week. I didn't include a Final Jeopardy Question, but here's a tricky one:
Final Jeopardy Category: Types of Polygons
If two points lie in the interior of this type of polygon, then the segment joining them lies in the interior.
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