Today is the first day of a new middle school teaching assignment. This one is very different from my previous assignment -- I start my day in a seventh grade math classroom, move to a sixth grade English classroom, and finish in a seventh grade AVID classroom. It will be very tough having to teach three different subjects in three different rooms everyday for the rest of the school year, but in the end, gaining this experience is worth it -- or is it?
APRIL FOOL!
You fell for my old trick again -- whatever class I sub in on April 1st, I claim that this is my assignment from April to June. And it seems as if I always have some weird schedule that day, so that it really makes my "long-term" schedule look ridiculous.
But yes, I really do work in three different classrooms today. Let's do "A Day in the Life" today to see exactly what happens:
8:45 -- When I arrive on campus, I'm expecting to be placed in a seventh grade English class. The office manager informs me that I'll be in more than one classroom today -- and as it works out, none of those classrooms will be the original English 7 classroom.
This is the same school -- in my new OC district -- where I subbed last Friday. So we recall that the two cohorts attend Periods 0-4 and 5-9. Since today is Thursday, it's periods 0-4 today.
Zero period arrives. This is the first of two Math 7 Honors classes. Students who are successful in this class will move on to Algebra I as eighth graders -- that is, the SteveH track.
This is the only class where I attempt to play an April Fool's Day prank on this students. I work in tandem with the morning announcements -- on the board, I write down a possible schedule for the upcoming expansion of in-person learning (that I briefly mentioned on the blog yesterday). Except instead of April 26th, I claim that it starts next week -- that is, in lieu of spring break. Then the same claim is made over the intercom. Only one boy figures out that it's an April Fool's Day joke before it's revealed over the intercom (although others claim that they knew it all along).
The students are learning about percent. They have a project where they calculate percent increase or decrease -- first they work it out on paper, and then they take a picture and post it on Canvas.
Although this class is talkative, most of the students appear not to need my assistance. Indeed, the only help I give the students today is through my song. It's the percent song from Square One TV. Believe it or not, I've never posted the lyrics on the blog, nor did I ever write it in either of my songbooks.
The reason for this is tricky -- it goes back to my percent lessons at the old charter school. Notice that there are percent standards in both Math 6 and Math 7:
CCSS.MATH.CONTENT.6.RP.A.3.C
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
CCSS.MATH.CONTENT.7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
But here's the problem -- that year, I started the year by covering the first four RP standards in both Grades 6-7 -- that is, through 6.RP3b and 7.RP2c. In each case, I was just shy of reaching the percent standards before I started jumping around the curriculum, (improperly) letting the STEM text guide which standards to teach.
In seventh grade, I never made it to a percent lesson. In sixth grade, I did reach a project, and hence a lesson, on RP3c. I did sing parts of the percent song with my sixth graders, but I didn't choose it as the official song of the week -- Math 7 was learning integer addition at the time, and so "Same Song Add and Keep" became the official song that I wrote on the blog and in my songbook.
Since I don't have the full lyrics, I sing only the parts that I remember. Then I continue my usual Easter pencil and candy incentive. I accidentally say "pizza" instead of pencil -- April Fool! But this year, April Fool's Day is the same as Maundy Thursday, and so I start my very real Easter incentive.
I have enough pencils and candy to give rewards to the top four students in each class -- that is, the kids with the most progress towards completing the percent assignment. Two girls are tied for fourth (as they were working together), and so I end up giving out a fifth pencil and candy.
9:40 -- Zero period leaves and first period arrives. This is the second of two Math 7 Honors classes.
While most students in this class are seventh graders, one boy is only a sixth grader. This means that he's working at the Bruce William Smith level -- on pace to reach Algebra I next year and Geometry as an eighth grader (just as I did as a young student).
This class is a bit quieter than zero period.
10:35 -- Before this class leaves for snack break, another sub arrives, and it's time for me to move on. I wish I could stay in this classroom the entire day since I'm a math teacher, but that's not how things work today. I do have time to sing the percent song and hand out rewards to the top four students before I leave.
Before I depart the math classroom, I glance at the rosters of the three remaining math classes that I don't get to cover. Two of them are regular Math 7 classes, and the last class is a Geometry class. The Geometry class has a test today on conic sections. This is usually an Algebra II (if not Precalculus) topic, yet it appears in the geometry strand of the Common Core standards:
Derive the equation of a parabola given a focus and directrix.
(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
Notice that the high school math strands don't necessarily correspond 1-1 to math courses, yet many publishers assume that the entire geometry strand must be in high school Geometry class. The U of Chicago text teaches circle equations in Lesson 11-3 (and only briefly mentions conic sections in Lesson 9-4), yet some text apparently teaches conics fully in Geometry.
And while most of the students in this Geometry class are eighth graders, one student is, believe it or not, a seventh grader. This student is working beyond Bruce level, on pace to make Calculus AB as a sophomore -- provided, of course, that the kid can take Algebra II in eighth grade next year.
I never do get to meet this student or inquire about next year's math class. Indeed, I wonder how well this seventh grader did on today's conics test -- and yes, this is the first time I've ever used the words "seventh grader" and "conics" in the same sentence. (I'm not sure whether I even knew what conic sections were as a young seventh grader -- and I thought I was smart at math!)
10:45 -- Second period arrives in my new classroom. This is the first of two sixth grade English classes.
It turns out that this is another one of those classes where the regular teacher is able to teach at home using Zoom, and so all I need to do is supervise the in-person students. One of the students in this class is the sixth grader from Math 7 Honors.
Unlike yesterday's regular teacher, this teacher works until the end of the period. I definitely don't have time to sing any songs -- and it's difficult just to decide which four students get the Easter pencils and candy that I'm prepared to hand out. In the end, I do a very quick "Who Am I?" with my usual questions on my age and weight -- as the dismissal bell rings -- and hand out the prizes to the winners.
11:40 -- Second period leaves and third period arrives. This is the second of two English 6 classes.
Since there's nothing else for me to do during the teacher's lesson, I grab some headphones and listen to the percent song on YouTube. Now I finally have the full lyrics.
12:35 -- Third period leaves for lunch.
1:15 -- It is now time for tutorial. Just as tutorial begins, my classroom phone rings. Another teacher must leave for an emergency, and so I must cover her tutorial, which leads directly into fourth period.
This is an AVID class. I haven't covered AVID since before the pandemic. Back then, AVID classes often used VNPS -- vertical non-permanent surfaces -- but I see nothing like that today.
During tutorial, I perform my typical tutorial "concert." I start with the "The Percent Song" now that I have the lyrics, and then let the students choose the rest of the songs. It turns out that all the songs they select are from Square One TV -- "Less Than Zero," "Wanna Be," and "Draw a Map."
1:45 -- In fourth period proper, the students must write a reflection of their third quarter grades, and set goals for fourth quarter. I do sing one more song for fourth period proper -- I revert to my usual "Big March," song since it's still the Big March (which thankfully, won't be extended -- the cancellation of spring break being an April Fool's Day joke).
One boy is also enrolled in the Math 7 Honors class that I covered earlier. I glance at his assignment -- he writes that while he has mostly A's and B's on his report card, he failed Math 7 Honors (despite at some point being good enough at math to get into the class in the first place). I remind him that yes, he was once successful at math, and he can regain that success. The Square One TV songs that I perform today remind him of the importance of learning math, and need to recognize patterns in math.
This guy becomes one of the top four students in the class -- so he earns the Easter reward, after having missed the reward in math class.
2:35 -- Fourth period leaves, thus ending my day.
And this fits perfectly today. The one student I help in Math 7 Honors and AVID understands that he must work hard in order to excel in his math class.
Today on her Daily Epsilon on Math 2021, Rebecca Rapoport writes:
0/0
The answer is obviously 1 -- and of course, today's date is the -- hold on a minute! This is an indeterminate form, so it has no solution.
APRIL FOOL!
This is the first of three joke days on the Rapoport calendar this year. (Last year, April Fool's Day was the second of three joke days -- this year, she didn't post a special Pi Day joke.)
And while today's date may be 4-1, it's all about 14-1 -- Lesson 14-1 in the U of Chicago text, that is.
Lesson 14-1 of the U of Chicago text is called "Special Right Triangles." In the modern Third Edition of the text, special right triangles appear in Lesson 8-7 (as I explained in yesterday's post).
This is what I wrote two years ago about today's lesson:
Chapter 14 of the U of Chicago text is on Trigonometry and Vectors. Here's the plan:
Today, April 1st -- Lesson 14-1: Special Right Triangles
Friday, April 2nd -- Pandemic-Friendly Activity (includes Lesson 14-2: Lengths in Right Triangles)
Monday, April 12th -- Lesson 14-3: The Tangent Ratio
Tuesday, April 13th -- Lesson 14-4: The Sine and Cosine Ratios
Wednesday, April 14th -- Lesson 14-5: Vectors
Thursday, April 15th -- Lesson 14-6: Properties of Vectors
Friday, April 16th -- Pandemic-Friendly Activity (includes Lesson 14-7: Adding Vectors Using Trig)
Monday, April 19th -- Activity (as explained in posts from two years ago)
Tuesday, April 20th -- Review for Chapter 14 Test
Wednesday, April 21st -- Chapter 14 Test
So the plan for this chapter is straightforward. I've noticed how many texts, including the U of Chicago, discuss the tangent ratio in a separate lesson from sine and cosine. I suppose that in many ways, sine and cosine are alike in a way that tangent isn't. The sine or cosine of any real number is between -1 and 1, while the tangent can be any real number. Therefore the graphs of sine and cosine resemble each other. The tangent ratio involves two legs, while the sine and cosine ratios involve one leg and the hypotenuse. Even the name "cosine" includes the word "sine," while the name "tangent" doesn't include "sine."
But that's for next week -- how about today's lesson? Lesson 14-1 of the U of Chicago text is on Special Right Triangles -- that is, the 45-45-90 and 30-60-90 triangles. The text emphasizes how these triangles are related to the regular polygons. In particular, the 45-45-90 and 30-60-90 triangles are half of the square and the equilateral triangle, respectively. We can obtain these regular polygons, in true Common Core fashion, by reflecting each right triangle over one of its legs. The regular hexagon is also closely related to the 30-60-90 triangle.
The questions that I selected from the text refers to these regular polygons and using the triangles to measure lengths related to the regular polygons. I mentioned today how I like to watch baseball over summer break -- well, a baseball "diamond" (really a square) appears on the worksheet. Also, a honeycomb, with its hexagonal bee cells, also appears.
The review questions that I selected are also preview questions. Two of the questions involve similar right triangles in preparation for geometric means in Lesson 14-2, and the other one is about how to simplify radicals, so we can explain in Lesson 14-4 why the sine and cosine of 45 degrees are usually written as sqrt(2)/2.
This lesson used to be given as an activity. The new pandemic-friendly activity will appear tomorrow.
As we begin Chapter 14, notice that the Laws of Sines and Cosines might appear in the Pre-Calc classes, but not most Geometry texts. [2021 update: On the other hand, these new Geometry texts apparently include conic sections!]
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