Once again, it's in my old district, where today really is Day 119. The pattern for January/February continues -- I keep subbing for English classes in my old district and non-English in my new district.
Also, this is the lone school in the old district that does not have a block schedule. Therefore all classes meet today. The first class of the day is actually P.E., followed by two sophomore English and one senior English. All students have Chromebooks, with the younger students working on a "Sophomore Project" and the older students on a "Senior Project." I glance at some of the Sophomore Projects -- the rough drafts are 5-10 pages in length. I'm not sure what the project topic is -- some of the students write about their future careers, while another tells the history of music and technology.
The last class of the day is coaching -- this regular teacher is in charge of the water sports (that is, swim and water polo). Assistant coaches run the practice, and so I'm able to go home right after "interventions" (a sort of cross between "embedded support" at the block schedule schools in this district and "tutorial" in my new district).
Going into today, I choose "The Need for Speed" (mousetrap cars) as my song for the day. But during P.E., the other teacher decided to have the kids go on a "nature walk" around the campus. Thus I couldn't resist singing my walking song, "The Big March," emphasizing the verse for Week 2 of the current calendar stretch.
Today is Elevenday on the Eleven Calendar. This means that I get to choose which of the ten rules that I'd like to focus on. Obviously, I don't do much math today, but I am able to help a student during tutorial gain confidence as he leaves to make up his unit circle test for trig. This is indirectly related to the first rule. (We are good at math but need to improve at other things.)
His friend tells him a mnemonic for the unit circle: 2, 4, 5 -- 3, 5, 7 -- 5, 7, 11. This allows him to recall which radian values belong on the circle. For example, 2, 4, 5 is for pi/3, so the multiples of pi/3 on the unit circle are 2pi/3, 4pi/3, 5pi/3. Then 3, 5, 7 are the multiples of pi/4, and so on.
I've also been using Elevendays to focus on the millennium resolutions, which state that I should improve communication skills with my fellow teachers as well as students. Today I don't really eat lunch with my fellow teachers because my day ends after tutorial -- while the teachers are eating lunch, I'm already halfway home. The only communication I make with a colleague is during P.E., when another teacher helps me out with the "nature walk." (Oh, and I do speak with some of the special one-on-one aides who are there to help certain students in English.)
Since this particular school is the only one in my old district without a block schedule, I've argued that this is the lone school whose calendar I've been following on the blog. (The day count follows this district, while I don't follow any block schedule, so bingo! This is the school!) For the most part, my posting schedule does fit the schedule at today's school. But coming up, there's a major point of contention -- the SBAC schedule. I just so happened to see a schedule for the SBAC posted in the P.E. teachers' office today. And here's what it reveals:
- Days 142-145: Math SBAC for juniors
- Days 147-153: ELA SBAC for juniors
- Days 152-153: California Science Test for seniors
Recall that the state science test is to be given during any of the four years of high school. This district is unusual in giving it to seniors -- typically, seniors take no state tests at all. I can see why we'd want to avoid junior year with both math and ELA being assessed this year, but it's interesting that the science test isn't given to sophomores, especially considering that the old pre-NGSS science test was once given in tenth grade.
But our focus on the blog is, of course, the math test. If we follow the blog calendar strictly, then we'll give the Chapter 13 Test on Day 140, just barely before the SBAC. Chapters 14 and 15 aren't taught until after the SBAC -- and both chapters contain material appearing on the exam. (Chapter 14 is on basic trig, while Chapter 15 is on circles, including the Inscribed Angle Theorem in 15-3.) And of course, this also leaves out probability, which is considered part of the Common Core Geometry course here in California.
I probably won't change or deviate from the digit pattern here on the blog despite learning more about my school's SBAC schedule. Still I ask myself, if I were really a teacher at this school, how would I cover the text in order to cover all tested material before the exam?
Well, it would all depend on whether there are many juniors in my Geometry class, since there's no need to bend if most students in my class aren't in the testing grade. I would hope that we'd at least have the Third Edition of the U of Chicago text, with its 14 chapters. Chapter 13 of my Second Edition is incorporated into earlier chapters, so that trig moves down to the new Chapter 13, just in time to be completed before the SBAC. (Of course, I doubt that this district actually uses the U of Chicago text, but this post describes how I'd try to compress any text -- whichever text that the school actually uses -- in order to complete tested material in time for the exam.)
Then I could skip the Chapter 13 Test and proceed directly to Chapter 14 on circles. I wouldn't need to cover all of 14 as long as we reached the important Inscribed Angle Theorem. As for probability, I wouldn't mind squeezing it in with Chapter 8 (as geometric probability is closely related to the areas studied in that chapter), but due to the way we cover Chapter 8 at the start of the semester, it might be better to wait until Chapter 9. (But don't forget that Chapter 9 Third Edition is meatier than that chapter of the Second Edition -- surface area appears in the new Chapter 9.)
On Days 147-153 when the juniors are taking their English test, I complete the circle chapter, but I'd probably make it almost all activities rather than traditional lessons. This serves two purposes -- first, long activities fit the block testing schedule better, and second, by in-class projects means that there's less homework. I like the idea of having no HW during testing week, so that the students have one fewer excuse not to take the SBAC seriously.
Finally, after the SBAC is a great time to teach extracurricular topics, such as my personal favorite, spherical geometry. This can span a few weeks (during AP testing), and then there's still a few weeks left to review for the final.
If there aren't enough juniors to justify speeding up the last few chapters, then instead we cover probability after the testing blocks are complete. We still can cover Chapter 14 as activities during the testing blocks.
But that's enough talk about Chapter 14 and the Third Edition.
Today is the review for the Chapter 11 Test. This is what I wrote last year about today's lesson:
In particular, this test is based on the SPUR objectives for Chapter 11. As usual, I will discuss which items that I have decided to include and exclude, and the rationale for each:
Naturally, I had to exclude Objective G: equations for circles, which I take to be an Algebra II topic, not a Geometry topic. (If this had been an Integrated Math course, I would have delved more into graphing linear equations, as we covered this week.) Actually, equations of circles really is a Common Core topic, so you might want to cover some circle problems of your own. On the other hand, we may still want to leave out three-dimensional coordinates, since I posted the leprechaun graphing worksheet instead.
One major topic that I had to include is coordinate proof, as this appears in Common Core. I did squeeze in some coordinate proofs involving the Distance or Midpoint Formulas, but not slope. So therefore, the coordinate proofs included on this review worksheet all involve either distance or midpoint, not slope. The only proofs involving parallel lines had these lines either both vertical or both horizontal. Once again, a good coordinate proof would often set it up so that the parallel lines that matter are either horizontal or vertical.
What good are coordinate proofs, anyway? Well, a coordinate proof transforms a geometry problem into an algebra problem. Sometimes I can't see how to begin a synthetic geometry proof, so instead I just start labeling the points with coordinates and see what develops.
So coordinate geometry reduces an unknown problem (in geometry) to one whose answer is solved (in algebra, in this case). Mathematicians reduce problems to previously-solved ones all the time -- enough that some people make jokes about it:
http://jokes.siliconindia.com/recent-jokes/Reducing-the-problem-nid-62964158.html
I ended up including six straight problems -- Questions 8 through 13 from U of Chicago. Most of these questions are from Objective C -- the Midpoint Connector Theorem. The text covers this here in Chapter 11, but we actually covered it early, in our Similarity Unit, because we actually used the Midpoint Connector Theorem to start the proof of the basic properties of similarity. Still, this was recent enough to justify including it on the test.
Next are a few center of gravity problems. This is straightforward, since all we have to do is average the coordinates. Afterwards are a few midpoint problems, including two-step questions where one must calculate the distance or slope from one point to the midpoint of another segment.
Then there are a few more coordinate proofs where one has to set up the vertices -- notice that some hints are given in earlier questions.
On Days 147-153 when the juniors are taking their English test, I complete the circle chapter, but I'd probably make it almost all activities rather than traditional lessons. This serves two purposes -- first, long activities fit the block testing schedule better, and second, by in-class projects means that there's less homework. I like the idea of having no HW during testing week, so that the students have one fewer excuse not to take the SBAC seriously.
Finally, after the SBAC is a great time to teach extracurricular topics, such as my personal favorite, spherical geometry. This can span a few weeks (during AP testing), and then there's still a few weeks left to review for the final.
If there aren't enough juniors to justify speeding up the last few chapters, then instead we cover probability after the testing blocks are complete. We still can cover Chapter 14 as activities during the testing blocks.
But that's enough talk about Chapter 14 and the Third Edition.
Today is the review for the Chapter 11 Test. This is what I wrote last year about today's lesson:
In particular, this test is based on the SPUR objectives for Chapter 11. As usual, I will discuss which items that I have decided to include and exclude, and the rationale for each:
Naturally, I had to exclude Objective G: equations for circles, which I take to be an Algebra II topic, not a Geometry topic. (If this had been an Integrated Math course, I would have delved more into graphing linear equations, as we covered this week.) Actually, equations of circles really is a Common Core topic, so you might want to cover some circle problems of your own. On the other hand, we may still want to leave out three-dimensional coordinates, since I posted the leprechaun graphing worksheet instead.
One major topic that I had to include is coordinate proof, as this appears in Common Core. I did squeeze in some coordinate proofs involving the Distance or Midpoint Formulas, but not slope. So therefore, the coordinate proofs included on this review worksheet all involve either distance or midpoint, not slope. The only proofs involving parallel lines had these lines either both vertical or both horizontal. Once again, a good coordinate proof would often set it up so that the parallel lines that matter are either horizontal or vertical.
What good are coordinate proofs, anyway? Well, a coordinate proof transforms a geometry problem into an algebra problem. Sometimes I can't see how to begin a synthetic geometry proof, so instead I just start labeling the points with coordinates and see what develops.
So coordinate geometry reduces an unknown problem (in geometry) to one whose answer is solved (in algebra, in this case). Mathematicians reduce problems to previously-solved ones all the time -- enough that some people make jokes about it:
http://jokes.siliconindia.com/recent-jokes/Reducing-the-problem-nid-62964158.html
I ended up including six straight problems -- Questions 8 through 13 from U of Chicago. Most of these questions are from Objective C -- the Midpoint Connector Theorem. The text covers this here in Chapter 11, but we actually covered it early, in our Similarity Unit, because we actually used the Midpoint Connector Theorem to start the proof of the basic properties of similarity. Still, this was recent enough to justify including it on the test.
Next are a few center of gravity problems. This is straightforward, since all we have to do is average the coordinates. Afterwards are a few midpoint problems, including two-step questions where one must calculate the distance or slope from one point to the midpoint of another segment.
Then there are a few more coordinate proofs where one has to set up the vertices -- notice that some hints are given in earlier questions.
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