Today I subbed in a freshman English class. It's in my new district. Since it's a high school class that isn't math, there's no need for "A Day in the Life" today.
At this school, even classes meet on Thursdays. Second period is a regular English 9 class while the other two classes are honors. The non-honors class (which has an aide) is reading To Kill a Mockingbird, while the honors classes are studying Fahrenheit 451.
Unusually for this level, this teacher provides a ten-minute break during class. The aide and I lead the class downstairs to get some fresh air -- and one guy requests that we take a short walk around the campus as well. I decide that this is a great time to sing my song for today. Since I've performed "Mousetrap Car Song" and "Meet Me in Pomona" too often lately, I choose "Earth, Moon, and Sun" for the walking song.
Hmm, on one hand, there recently was a new moon, so this song makes sense. On the other hand, this new moon marks Eid-al-Fitr, the end of Ramadan -- and it might be considered incongruous to sing a Hebrew tune (recall this is my "Hava Nagila" parody) to celebrate a Muslim holiday. (Some of the students online have possible Arabic last names -- they might have been offended, especially since there is ongoing violence between Israel and Palestine right now.) Perhaps one of these days I should write a parody of an Arabic tune for balance (lute index finger, anyone?).
During tutorial, I let the students choose some more songs for me to sing -- they end up choosing "Nine Nine Nine" from Square One TV and "U-N-I-T Rate! Rate! Rate!"
In fourth period, I must remain quiet because next door there is an AP Capstone Project going on. Hmm, speaking of Eid al-Fitr, I heard that the AP exams scheduled for today -- including AP Stats -- were delayed to Monday in deference to the Muslim holiday. I probably wouldn't have known this, had it not affected one of the math AP's. (Due to the purely lunar Islamic calendar, Eid al-Fitr falls about 10-11 days earlier each year on the Gregorian Calendar. Next year, the holiday might fall on Monday, May 2nd or Tuesday, May 3rd -- the first two days of the AP's. If it's the latter, that would be AP Calculus.)
And so for sixth period, I walk the students away from the building before singing. I headed for the special ed classrooms (as these students are unlikely to be studying for AP today).
Today is Eightday on the Eleven Calendar:
Resolution #8: We follow procedures in the classroom.
In second period, the aide tells the students to turn on cameras. Not all high schools enforce the camera procedure, but these students are taking a quiz on Chapter 22, and I'm definitely strict on cameras during a quiz or test. Three online students refuse to turn them on -- and I inform them that by not turning them on during a quiz, they might be suspected of cheating.
During fourth period, Krispy Kreme doughnuts were served to all students. Of course, the procedure is that students can't remove masks to eat in the classroom during the pandemic. Fortunately, one student reminds me to pass them out during the ten-minute walking break.
In sixth period, one guy kept removing his mask (and he wasn't even eating a doughnut or anything). So I had to give him a warning.
Today is Thursday, and so it's time for my weekly series on COVID-97 and high school Track. This week, my alma mater participated in the fifth dual meet of the season -- held on our home track. But this isn't a league meet -- instead, it's our second nonleague meet.
There was a dual meet originally scheduled for this week. But the other school isn't competitive -- our first Cross Country race was also against them, and so we basically ended up running unopposed. So for Track, the coaches apparently replaced this opponent with two nonleague opponents. Thus this is more like a tri-meet (or triangular meet).
And unlike most of our league opponents, these opponents decided to contest almost all of the running events as relays. This often happens at weekend invitationals, but rarely at midweek meets.
When I arrived at my home campus, there were the usual 4 * 100 races interspersed with two Distance Medley relays -- first girls, then boys. The Distance Medley is called this because it consists of a medley of distances -- each of the four racers runs a different length. The traditional order of this particular race (also called DMR for short) is 1200, 400, 800, 1600.
Aha, you might say -- so the 400 really is a "distance" race since it's part of the Distance Medley, and so "Distance Carnivals" are justified in contesting the 400. Well, not so fast there -- there's also a race called a Sprint Medley, and it's anchored by a 400. Meanwhile, the 1200 is a race that's almost never contested except as the first leg of a DMR.
I admit that I've never participated in a DMR, nor have I ever watched one. It's difficult to follow because Varsity and Frosh Soph ran in one race -- it was easy for the Varsity to lap Frosh Soph. For some reason, the bell (marking one lap to go) was rung when there was one lap left on the 1200 leg. I thought I heard the bell with one lap to go for the 1600 leg in the girls race, but not the boys race -- it's possible that the coaches, including the bell ringer, were also confused.
As it turned out, the best way to tell the teams apart was to watch the hip numbers -- only the anchor (the last leg -- the one running 1600) wore one. Thus I should have paid more attention to them -- count to see when the teammate with the hip number has circled the track four times.
What time -- indeed, what distance -- would I have run in the DMR? In my last post, I was following a certain runner -- a current junior whose times are similar to my senior year times. He ran a distance of 800 this week -- it could have been the third leg of a DMR, but it just as easily could have been part of a 4 * 800 race instead (since I heard that this was run after I left). I don't know for sure -- all I know is what his time was, not whether it was a DMR or 4 * 800. I think I'll place myself in the DMR -- something interesting to put in the COVID-97 timeline, since I never contested it in the original (that is, real) timeline.
This runner's time is a few seconds ahead of my 800 time from last week, so I believe I'll match it:
On May 6th, 1999 (fourth dual meet, second nonleague meet), my 800 time would have been 2:23 (as part of a Distance Medley relay).
By running 800 this week, I follow the pattern I established last week -- 800 during the week, 1600 at a weekend invitational. I don't know much yet about the invite coming up on Saturday -- in particular, I don't know yet what school is hosting it (or whether this school hosted an invite in 1999). I do know that, just like this tri-meet, most of the races will be relays. I'll blog about the invite in my Monday post.
Today on her Daily Epsilon on Math 2021, Rebecca Rapoport writes:
Find the indicated area.
All of the given information is given in an unlabeled diagram. The most obvious way to solve it is using trig, but Uda Vino on Twitter found an elegant solution using pure Geometry, so I'll label it his way:
Squares ABCD and CEFG (with no interior points in common) have areas 36 and 49 respectively, and Triangle BCE has area 13. What is the area of Triangle CDG?
The easy way is by using the SAS formula for area, A = (1/2)xy sin theta. Instead, let me reproduce Vino's geometric solution:
Rotate Triangle CDG 90 degrees counterclockwise with respect to point C (yes, it's indeed a Common Core transformation). We end up with new Triangle CBG' which has C as midpoint of EG'. Thus, Triangles EBC and BCG' have the same area (as they have the same height, congruent bases). Since Triangle BCG' is just rotated DCG, hence DCG has the same area with EBC, which is 13. Therefore the desired area is 13 square units -- and of course, today's date is the thirteenth.
There's just one problem here -- it's not actually given that ABCD and CEFG are squares. Instead, Rapoport only states that all four sides are congruent -- which is sufficient to make them rhombi, not necessarily squares. The assumption that any angle in the original diagram is 90 is unwarranted. Vino's proof requires right angles -- otherwise the 90-degree rotation image of D isn't necessarily C, and the points E, C, G' aren't necessarily collinear.
In fact, if the angles aren't 90, then the area doesn't have to be 13. This is an error on Rapoport's part, not Vino's. (Since I'm now a member of Twitter, I'm considering tweeting this error myself soon!)
This is what I wrote two years ago about today's lesson:
Question 11 of the SBAC Practice Exam is on statistics:
Click above the numbers to create a line plot for the given percent chances of rain in different cities.
65, 65, 70, 70, 80, 80, 80, 80, 85, 95, 95, 95, 100
This is a statistics question -- and as I mentioned in my last post, stats, if it's to be taught in Algebra I at all, is covered in the second semester.
As with many Common Core Statistics questions, this is the first time that I've ever seen a "line plot." Apparently, it's similar to a bar graph. There should be two X's above 65, two X's above 70, no X above 75, four X's above 80, one X above 85, no X above 90, three X's above 95, and one X above 100.
The girl from the Pre-Calc class correctly answers for this question. But unfortunately, the guy from that class skips this question altogether. It doesn't help that the question doesn't print on the packet properly -- rather than before Questions 12-13, it appears on the next page after Questions 16-17.
Question 12 of the SBAC Practice Exam is on dimensional analysis:
The formula for the rate at which water flows is R = V/t, where
* R is the rate,
* V is the volume of water measured in gallons (g), and
* t is the amount of time, in seconds (s), for which the water was measured.
Select an appropriate measurement unit for the rate.
A) gs
B) g/s
C) s/g
D) 1/sg
This question on units could appear in the first half of an Algebra I text, since this is a linear equation (provided t is given or a constant). This problem basically solves itself -- the rate is V/t, and V is in g while t is in s. Thus V/t is in g/s, or gallons per second. The correct answer is B).
Both the girl and the guy from the Pre-Calc class correctly answer B) for this question.
SBAC Practice Exam Question 11
Common Core Standard:
Represent data with plots on the real number line (dot plots, histograms, and box plots).
SBAC Practice Exam Question 12
Common Core Standard:
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Commentary: In the U of Chicago Algebra I text, there is a little stats in the last chapter, but not line plots specifically (even though other plots do appear). Meanwhile, in Chapter 5, the division chapter, there is a lesson on rates. Units are briefly mentioned, but not in detail. Still, this question should be easy enough for our students to answer.
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