Find x.
[All the given info is in an unlabeled diagram once again, so I must invent my own labels. In Triangle ABC, P is between A and B, and Q is between A and C.
Finally, I'm doing a Geometry problem from the calendar rather than highlighting an error. This is a case of the Side-Splitting Theorem. We set up the proportion:
AP = AQ
PB QC
18 = x
12 18
12x = 324
x = 27
Therefore the desired length is 27 -- and of course, today's date is the 27th. The Side-Splitting Theorem appears in Lesson 12-10 of the U of Chicago text.
Fortunately there are no errors in this problem -- except possibly for the diagram itself. It is drawn so that
This is what I wrote last year about today's lesson:
Lesson 0.9 of Michael Serra's Discovering Geometry is labeled "Chapter Review." In the Second Edition, chapter reviews have their own lesson numbers, but in the modern editions (just as in the U of Chicago text), the chapter reviews are unnumbered.
At this point, we may wonder, should there be a Chapter 0 Test? If there were a Chapter 0 Test tomorrow, then this would allow us to start Lesson 1-1 of the U of Chicago text on Day 11, which would be Monday.
Some teachers may point out that Chapter 0 consists of just introductory activities and so it shouldn't be tested -- and besides, a Chapter 0 test would be so soon after the first day of school, when many students are still requesting schedule changes from their counselors.
On the other hand, without a Chapter 0 Test, the first test would be the Chapter 1 Test on Day 20. At some schools, grades must be submitted every quaver (i.e., twice a quarter). Day 20 would be very close to the end of the first quaver -- and at many schools, grades are due a few days before the mathematical end of the quaver. So whether or not there should be a Chapter 0 Test depends on how often a school issues progress reports, as well as whether a teacher wants to give a solid test before those first progress reports are issued.
As far as this blog is concerned, my decision is to follow what my old school did four years ago. If you recall from that year, the first test I gave my students was called a "Benchmark Test." This was, of course, a diagnostic pre-test to determine what the students already knew, and what they would need to learn in the coming year.
Therefore tomorrow I will post some Benchmark Tests for Geometry. It will preview lessons to be covered the entire year. Nonetheless, today's worksheet is based on review questions from Lesson 0.9 of Serra's text.
Here is the Blaugust prompt for today:
How do you support struggling students? What intervention strategies have you used?
To respond to today's Blaugust prompt, as usual, I think back to four years ago. Let's look at old some posts from around that time.
January 12th, 2017:
I need to mention my eighth grade class today, especially since they're learning about transformations on this Common Core Geometry blog. In the end, I decided to delay the science lesson to tomorrow and teach transformations today.
This means that this week I had three full days to cover the three transformations. On the first two days, the translations and reflections went well, and most students appeared to understand. But I worried as today's lesson approached, because rotations are probably the most difficult of the three transformations for students to understand.
Now keep in mind that I'm using the Student Journals that are part of the Illinois State text. We know that rotations can be centered either at the origin or away from the origin. Rotations centered at the origin have easier formulas -- for example, the rotation of 180 degrees centered at the origin maps the point (x, y) to the point (-x, -y).
But none of the rotations mentioned in the Illinois State text are centered at the origin. Most of the questions direct a student to rotate a line segment around one of its endpoints. This at least makes it a little easier, since every rotation maps its center to itself.
And so here's what I did today -- on the first page, the students are asked to rotate
Of course the students are confused by this at first, but in the end, I believe that they're starting to get the hang of this. I like teaching rotations this way because it sets them up nicely to learn the slopes of perpendicular lines later on. By the end of class, I think the most confusion came from changing all the questions in the Illinois State text, which were geared towards the rotation centered at A rather than the origin.
So that's one possible answer to the Blaugust prompt -- I help struggling students by making the questions in the text easier.
January 23rd, 2017:
Meanwhile, today is a coding Monday. In case you're curious, sixth graders create logos for an imaginary company, while seventh graders learn about spreadsheets. The students learn about various Excel functions, including mean, median, and mode. I don't normally have music break on coding Mondays, but I couldn't help singing the Measures of Center song from last month to jog the students' memory.
I notice that often when I wrote that my class "struggled" on something, that something was actually the Monday coding assignment, not math! But in this case, the coding lesson was math-related -- and my solution was to sing a song to remind them of what they had learned.
I admit that in both of these cases, the students simply shut down. They didn't realize why learning math was worth the effort. I used the field trip to inspire them -- I reminded them (especially the girls) that if they studied hard in math, they could become the next Katherine Johnson.
Today Shelli, the leader of the Blaugust challenge, posted:
http://statteacher.blogspot.com/2020/08/mtbosblaugust-reflecting-on-week-1.html
We started back to school on Monday in a Distance Learning format, so here's our schedule:
Monday - Odd hours are synchronous / Even hours are asynchronous
Tuesday - Even hours are synchronous / Odd hours are asynchronous
Tuesday - Even hours are synchronous / Odd hours are asynchronous
Wednesday - All classes are asych ; teachers have "office hours"
Thursday - same as Monday
Friday - same as Tuesday
However, you are only required to be synchronous once a week, but since I teach AP, I'm requiring both days, although it may be for a short check-in instead of a lesson.
Notice that this isn't quite like distance learning in my districts. First of all, the day that all classes meet in my districts is Monday, not Wednesday -- and all Mondays are synchronous. The rest of the week, when three classes meet, there is both synchronous and asynchronous instruction. Office hours are after lunch everyday.
Of course, I'm not completely familiar with the distance learning since I'm just a sub -- and once again, while subbing during this stage is theoretically possible, in reality I haven't had opportunities to sub at all so far.
Shelli mentions Google Meet, but she also says that it's possible to use Desmos for distance learning:
OMG, can I sing the praises of Desmos from the rooftops? I simply cannot imagine life with Desmos. Desmos allows me to create an async (or even sync) lesson that flows similar to what I would do in class, so I think it will provide a wonderful transition back to the classroom
Sue Jones has also posted today:
https://resourceroomblog.wordpress.com/2020/08/27/details/
Jones mentions the Wisconsin incident in her post, so you may proceed to that blog if you wish to read more about it from a teachers' perspective.
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