Lesson 3.2.1: Division of Rational Numbers (Day 45)

Some of the eighth graders struggle with today's lesson -- but that's for tomorrow's post. Today we take at look at the seventh grade lesson in more detail.

We proceed with division of rational numbers. As I mentioned yesterday, division of signed numbers is straightforward to those who understand multiplication. The product or quotient of two numbers with the same sign is positive, while the product or quotient of two numbers with unlike signs is negative.

Division by zero is also mentioned in this lesson. I decide to tell the students about the mnemonic for when division involving zero is defined -- 0/k is "OK" (defined), while n/0 is "NO" (undefined).

Meanwhile, the hardest part of this lesson is the "rational numbers" part -- students must remember how to divide fractions, including converting mixed numbers to improper fractions, "keep, change, flip," and cross-canceling for multiplication.

Here are a few other things going on with the class. First of all, two more students who are listed as hybrid on the roster show up online instead. If I'm not mistaken, one of the students is ill, while the other has a close relative who is sick. In fact, I suggest that another student consider logging in too -- that student has recently suffered a severe illness.

Grades are about to be finalized in Canvas before being transferred to Aeries -- but the students will get a slight reprieve. The exportation has been delayed due to technical issues -- instead of this afternoon, the grades will be made final tomorrow morning. Let's see whether any of the students (about two or three in each class) try to make up any missing APEX assignments in order to improve the grades before they appear in Aeries.

There is also one more task that we must complete during hybrid. The State of California requires all teachers -- including us long-term subs -- to keep track of how much the students are learning during both synchronous and asynchronous instruction. This is to ensure that we are actually meeting the state minimum minutes requirement of four hours per day.

The weekly log consists of several parts:

• Parts A and B include a lesson plan that shows what content was taught during both synchronous and asynchronous instruction. We must make such a lesson plan for each "prep" -- that is, I must make three lesson plans for my three preps (Math 7, Math 8, Math Skills).
• Part C focuses on attendance -- which students actually did the work in the Part A-B lesson plans from above. If a student has attended less than 60% of the time, then we must document what efforts we made to contact the missing student and encourage attendance.
• Part D is just a section for our signature -- the meat of this task is in Parts A-C.

The weekly log -- due today and every Tuesday hereafter -- is just another one of those tasks that I'll need to complete.

The song for today is Square One TV's "Less Than Zero":

1. A big dive meet at our school,

A diver, Ol' Stanley O'Toole,

Did a horrified flip that the judges scored zip,

The worst ever seen at out pool.

2. Well, the spectators let out a roar,

But Stanley had more thrills in store.

His next dive was poorer, it came such a horror,

They gave him a negative score.

Refrain: He got less than zero, less than zero,

The scores are running in reverse.

Less than zero, he's an anti-hero,

"Watch me go from bad to worse!"

3. A dance comp down by the shore,

Stan tripped and fell on the floor.

The judge cried, "PU, you get -2,"

Said Stan with a grin, "Less is more!"

Refrain: ...he's a negative, negative guy.

..."Worse is nothin', that's my battle cry!"

Bridge: When the skaters went rolling at the roller-rink,

The judges held their noses and said, "Stan, you stink!

You're so bad we had to give you a subzero score.

It added up to -24."

4. Stan entered a hammer throw meet,

He set a record that no one would beat.

He threw it behind him, the score they assigned him was -55 feet.

Refrain: ...No ifs, and no ands, and no buts.

..."I'm a certified nationwide klutz."

I decided to keep the song in the key of D major, even though we can't finger a simple D chord with our guitar tuned to EACGAE. Instead, we might use D7 (xx2232).

The second chord in this song is B minor. We mentioned in earlier posts that a Bm7 chord is playable in EACGAE by using a simple barre (x22222). And so it's easier for me just to use a barre for the D7 chord mentioned earlier. In fact, I often ended up playing (xx2222), which works to be D6, not D7. (In fact, the chords D6 and Bm7 are identical except for the choice of bass note.)

An important chord in this song is A7 -- the dominant seventh in the key of D major. In EACGAE tuning, a plausible A7 chord is x01000 -- one of the simplest chords to play.