8:00 -- Once again, I begin with morning duty. At least the weather is dry today.
8:15 -- It is now homeroom. This time, the rotation begins with fourth period -- while homeroom still matches third period. So we don't have homeroom feeding directly into class time.
8:20 -- Fourth period is the teacher's conference period. But as often happens, my free period was taken away since I must cover an eighth grade English class. I've subbed in this room before, often as part of either period coverage or co-teaching.
These students also begin with a Warm-Up, except it's DOL, Daily Oral Language. The questions involve the root -lum- (light). The main lesson is reading Frankenstein -- yes, it's a story more suitable for Halloween, yet the class is reading it in December.
And since the class is reading a Halloween story, my song for this period is Square One TV's "Ghost of a Chance." I decide that the class has earned three out of five verses since some students haven't finished the assignment yet -- these kids eventually do enough to stay off of my bad list, but it's too late to sing any more verses.
9:15 -- I return to the seventh grade math class for fifth period.
After the usual agenda, Warm-Up, and homework check, we begin the main activity. This activity is called "Whodunnit" -- a murder mystery where the clues are given by solving equations. Notice that "Whodunnit" isn't an original activity by any stretch -- in fact, here's a link to Cindy Flim, another middle school math teacher who's used something similar in her classroom:
https://cindyflim.wordpress.com/2017/09/16/favorite-math-task/
I was considering composing an original song to play today in class -- in fact, last night I ran the Mocha program to get a tune, and even took home some of the "Whodunnit" clues in order to create lyrics for a song to go with the activity. My plan was to finish writing the song during conference period and then be ready to perform it in class.
But then my free period was taken away, and so I never finished composed the song. Instead, I just repeated "Ghost of a Chance" -- we can imagine that perhaps the murder took place in the haunted house mentioned in the song. I make sure to reach at least the third verse in every class -- the verse that mentions a hallway full of rattlesnakes. One of the possible murder methods in "Whodunnit" is a venomous snakebite.
Even though I didn't finish the song, preparing the song does come in handy today. I had hung the third clue poster up on the hooks above the whiteboard -- but then it fell behind the whiteboard, impossible to reach without unscrewing the entire board! Fortunately, in preparing for the song, I had written down the equation and correct clue, so I was able to make my own third clue poster.
Meanwhile, even before the third clue gets missing, the eighth clue contains an error. The correct solution eliminates drowning as the murder method -- but on the worksheet, drowning isn't even one of the choices. Because of this, both "eaten by a cougar" and "stubbed toe" remain as possibilities after all ten clues are solved.
I end up "killing two birds with one stone" here -- I created a third clue poster and added a statement that eliminates one of the methods: "Professor Delta stubbed her toe lifting gym equipment" (that is, Delta isn't the culprit, the gym isn't the scene of the crime, and the toe-stubbing was in lifting rather than in killing).
Even so, since it takes me so long to put up the replacement clue, only one student in this period successfully solves the mystery.
10:10 -- Fifth period leaves for snack.
10:20 -- Sixth period arrives. This is the first of two classes with the co-teacher.
The co-teacher checks the website that is the source of this "Whodunnit" activity, and verifies what I wrote for my third clue poster. She also suggests that, even though the regular teacher specifies this as a group activity, it works better as an individual activity, even though the kids may congregate at each of the clues in groups.
11:10 -- Sixth period leaves and first period arrives. This is the other class with the co-teacher.
The co-teacher must punish two boys for disturbing others -- she moves one student to another seat during the Warm-Up and the other to the hallway just as "Whodunnit" begins. I decide to place both names on my bad list.
12:05 -- First period leaves for lunch.
During lunch, I meet another math teacher in the hallway. He tells me that back when he was a young college student, his trig professor was an actual rocket scientist. During his lectures, he calculates how fast the wind is blowing -- and has access to a red button which, when pushed, cancels the next rocket launch! Of course, this story immediately reminds me of Ottaviani's moon book.
12:50 -- Second period arrives.
At this school, the period after lunch begins with silent reading. And so as the students take out their silent reading books, I take out my own reading book -- Ottaviani's T-Minus, of course. During the last few minutes of silent reading, I read my book aloud to the students. When silent reading time is over, I tell them the other teacher's story of the rocket trig professor -- and, of course, use both stories to drive home the relevance of math equations to the real world (and beyond).
I believe that the students enjoy these stories. They remain quiet throughout my telling them -- and beyond through the Warm-Up until it's "Whodunnit" time.
In the end, I name second period the best class of the day. Although only four students complete the task successfully (paling in comparison to sixth and third periods), this class is much quieter.
2:00 -- Second period leaves and third period arrives.
As usual, this class is noisy. I must write down one name on the bad list -- this guy enters the classroom and takes the wrong seat, then he answers "your mama" after I ask "Whodunnit," and then he plays with hand sterilizer instead of solving equations and getting clues.
In all classes, when I see someone with a low grade on the homework, I follow that student around during the activity. The goal is to make sure that this student is prepared for the upcoming quiz.
2:55 -- Third period leaves, thus ending my day.
One day remains for me in this class. It's interesting how much I was able to incorporate Ottaviani's book into my teaching this week. In fact, in this post we will focus on the exact pages that I read today to the class.
Let's look at pages 109-117 of Jim Ottaviani's T-Minus: The Race to the Moon. We left off just as we were preparing to launch Apollo 11 to the moon:
Russian: Get the computers out!
Comrade: They're coming!
Russian: Koff! If Korolev were here...
Comrade: No, no, the N-1 was his design. So this would still have happened, but it would have happened years ago. So if Sergei Pavlovich were here, perhaps I... we... maybe we'd still be in the race.
(One week later...)
Gene: All components now on site. Begin countdown for the "G Mission"... on my mark. And... start the clock!
As Ottaviani explains, the countdown for Apollo 11 -- the "G Missions" -- began on July 10th, six days before launch.
Let's proceed after a few buttons are flipped, pushed, slide, and tick-tocked:
Gene: Coming in, Max?
Max: Nah... after Glenn's flight, it's pretty clear you don't want guys like me in the Trench.
Ottaviani explains, "Remember, Max argued with Flight (Chris Kraft) during John Glenn's Mercury mission. Arguing in Mission Control was a bad idea -- even if it turned out okay -- so they changed the mission rules so it wouldn't happen again."
Gene: Chris, what about? --
Chris: Nah, I'm going with Max. It's your show now, Gene -- I mean, "Flight."
We're now introduced to "the Trench" -- the engineers working on the ground:
Gene: AGC.
Apollo Guidance Computer Jack Garman: Go, Flight.
Gene: FIDO.
Flight Dynamics Officer Jerry Bostick: Go!
Gene: LM CONTROL.
Lunar Module Control Bob Carlton: Go!
Gene: GUIDO.
Guidance Officer Steve Bales: We are go.
Gene: CAPCOM.
Capsule Communicator Astronaut Charlie Duke: Go, Flight.
Gene: All right then. Launch Control... we are go for Apollo 11.
The three astronauts, Michael Collins, Neil Armstrong, and Buzz Aldrin, board the bus at NASA -- Cape Kennedy, FL. 8 miles later, at Pad 39A:
Michael: There's nobody here. God... maybe they know something I don't.
Fredo Haise (alternate pilot to prepare the spacecraft): ...and that's 417 -- give or take. Your turn to flip those switches, guys.
Michael: Thanks, Fredo. Here you go, Gunter.
As Ottaviani explains, it was tradition for astronauts to give "Pad Leader" Gunter Wendt a parting gift, since he was the last person they saw on Earth.
Gunter: Ja, vill do, Mike.
Mike: Catch me something while I'm up there.
It was a fish. Ottaviani explains, "Michael Collins and Gunter fished together." A few clicking sounds are heard as the safety belts are fastened, and then Apollo is launched.
Let's skip up to T-minus 7 hours, 27 minutes. (At this point, Ottaviani counts the time backwards from the actual moon landing, not the launch.)
Michael: All right, let me... let me do my rain dance with the DSKY here. Okay.
Ottaviani explains, "DSKY = Display/keyboard for the AGC. AGC = Apollo Guidance Computer, which all the astronauts loved... and relied on."
(T-minus 6 hours, 54 minutes)
Buzz: Hit verb 77?
Neil: Okay, OMNI's in.
Ottaviani explains, "OMNI = Omni-directional antenna, which Buzz and Neil can point wherever they want."
Charlie: Columbia, Houston, we've lost them.
Buzz: They've lost you... use the OMNI again.
Neil: Roger, copy. ...PGNS. We got good lock-on. Altitude lights out. Delta-H is minus...
Michael: Program alarm. It's a 1202.
Charlie: ...1202. Ack! People?
Steve: Wait. Wait! We... we...
Charlie: Simulated this. Yes. Software error, right? But it's not... got a list, got a list, gotalistsomewhere.
Gene: How much fuel is left?
(20 seconds later...)
Michael: Give us a reading on the 1202 program alarm.
And this is exactly where I leave off in second period today -- a mini-cliffhanger. What does the program alarm message mean? Is the Apollo 11 really out of fuel? If so, the spacecraft might still land on the moon, but then it could never leave. You'll have to wait along with my students for tomorrow as well!
Today on her Mathematics Calendar 2019, Theoni Pappas writes:
Find x.
(Once again, we have an unlabeled diagram, so let me fill it in. In Triangle ABC, we have D between A and B, and E between B and C. Angle A = DBE = a, BE = 3, EC = 8.4, AB = 19, DB = x.)
We notice that since A = DBE and Angle B is common to both triangles, we conclude that Triangles ABC and DBE are similar by AA~. We can then set up a proportion -- noting that EC = 8.4 isn't the side of a triangle, but BC = BE + EC = 3 + 8.4 = 11.4 is:
DB/AB = BE/BC
x/19 = 3/11.4
11.4x = 19(3)
11.4x = 57
x = 5
Therefore the desired length is 5 -- and of course, today's date is the fifth. This question can be given after Lesson 12-9 of the U of Chicago text. It also marks the four Geometry problem during the first five days in December.
Lesson 7-4 of the U of Chicago text is called "Overlapping Triangles." In this lesson students will write more sophisticated proofs.
This is what I wrote last year about today's lesson:
Lesson 7-4 of the U of Chicago text covers more proofs. These proofs are trickier, since they involve overlapping triangles.
Because the triangles overlap, it may appear that, in Question 4, we need to show that Triangle SUA is isosceles. But as it turns out, we actually don't need to show this to complete the proof.
The bonus question is somewhat interesting here. It asks whether there is a valid congruence theorem for quadrilaterals, SSASS. Last year I tried to solve it, but got confused, so I want to take the time to set the record straight.
Let's convert this into a multi-day activity -- especially since all the proofs are on the first page, with review on the second page, so we can just replace that second page with this new activity. I added in the Exploration Question from Lesson 7-3, on SSSS, just to put SSASS into perspective -- and it also reflects how I should have set up the projects back at the old charter school, with a simpler question on the first day before the main question on the second day.
As it turns out, SSASS is not a valid congruence theorem for quadrilaterals. A counterexample for SSASS is closely related to a counterexample to SSA for triangles -- we start with two triangles that satisfy SSA yet aren't congruent -- one of these will be acute, the other obtuse. Then we reflect each triangle over the congruent side that is adjacent to the congruent angle. Each triangle becomes a kite -- as the original triangles aren't congruent, the kites can't be congruent either, yet they satisfy SSASS (with the A twice as large as the A of the original triangles).
I tried to prove SSASS by dividing each quadrilaterals into two triangles, then using SAS on the first pair and SSS on the second. The problem with this is that that division doesn't produce two triangles unless the quadrilateral is known to be convex. With our two kites, notice that the acute triangle becomes a convex kite, while the obtuse triangle becomes a nonconvex (or concave) kite -- which is also known as a dart. If both quadrilaterals are already known to be convex, then my proof of SSASS is valid.
One congruence theorem that actually is valid for quadrilaterals is SASAS. We can prove it the same way that we proved SAS for triangles. We put one of the sides -- in this case the congruent side that's between the other two congruent sides -- on the reflecting line. Then we can prove that the two far vertices are on the correct ray, the correct distance from the two vertices on the reflecting line -- this works whether the quadrilateral is convex or concave. We can also prove SASAS by dividing the quadrilateral into triangles. There are separate cases for convex and concave quadrilaterals, but all of them work out.
Other congruence theorems for quadrilaterals are ASASA and AASAS. Another congruence theorem, AAASS, is also valid, but it's similar to AAS in that there's a trivial proof based on the angle-sum that reduces it to ASASA (just as AAS reduces to ASA), only in Euclidean geometry. A neutral proof of AAASS exists, but it's more complicated.
Oh, and if students finish the activity early, it's possible to ask them to solve the Exploration question for Lesson 7-5: Explore this conjecture. If, in quadrilaterals ABCD and EFGH, angles A, C, E, and G are right angles, AB = EF, and BC = FG, then the quadrilaterals are congruent. It turns out that this conjecture is false -- again, a counterexample is a pair of kites, one a square, the other not a square. Then again, if you're tired of giving false conjectures, you can give them one of the valid ones instead like SASAS or ASASA.
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