Lesson 4.4.1: Solving Linear Inequalities (Day 73)

Today is Tuesday, and so as usual, our focus today is on the seventh grade class.

As I mentioned in yesterday's post, the Math 7 lesson that day didn't go that well. I tried to squeeze in working backwards and p(x + q) = r into 15 minutes so that the students would pass APEX Quiz 4.3.5. I point out that for a lesson titled "Solving Two-Step Equations," there were precious few two-step equations in APEX for students to solve.

It didn't work -- most students didn't even attempt the quiz, and most attempting it didn't pass it. The department head suggested moving on to APEX Lesson 4.4.1 today anyway, on inequalities.

Well, I arrive at school today thinking that I would teach the lesson on APEX. But when I speak to the department head today, she tells me that she's changed her mind yet again. We won't teach the APEX lesson or giving the quiz at all -- fed up with how APEX teaches equations, we decide to use a non-APEX resource to teach equations.

My colleague has previously compiled something she calls a "Digital Notebook," which, like an actual paper notebook, contains notes and problems to solve. Two pages of this notebook are devoted to solving equations, and another two pages are for solving inequalities. And so she shares her notebook on Google Drive with my students so that they can work on it as well.

So for the first half of class, I go over the equations with the students. As expected, some students struggle a little with Two-Step Equations -- this is to be expected, since they worked on it so little on APEX. Then for the second half, I begin inequalities. I just barely make it to the infamous "multiply/divide both sides by a negative" problems.

The department chair has also set up a matching activity for the students on Google Slides. Students solve several inequalities (including some with negative coefficients) and match their solutions to the graphs on another slide. This assignment is to be graded. I tell my students about this, but I'm not sure whether the students truly understand inequalities enough to be successful on this assignment.

After school (but before a special ed meeting), my colleague tells me that she didn't reach inequalities with negative signs either. But unfortunately, our two classes aren't comparable. I teach Math 7 third period, but her Math 7 classes are either even periods or fifth period (the class that meets twice a week for 50 minutes rather than once for 100 minutes). Thus she teaches only 50 minutes of Math 7, while I teach it for 100 minutes -- so of course she doesn't make it very far.

I wouldn't be surprised if on Thursday, she'll tell me that her class easily gets negative inequalities and are very successful with the matching activity. It helps that she's had a Digital Notebook all along, so she doesn't waste time trying to explain it. Also, she played a video on solving two-step equations yesterday while I spent time on working backwards, p(x + q) = r, and APEX 4.3.5 for my Conjectures Game.

For the song of the week, I choose "U-N-I-T Rate! Rate! Rate!" -- a parody of the UCLA fight song, in honor of my alma mater playing USC at the Rose Bowl this Saturday:

To find the mighty unit rate,

All you do is divide.

The answer, two dots, and then a one,

Right on the other side.

And if you have a fraction,

There's no need to hate.

Flip the second and then you'll find,

The mighty unit rate!

U! N! I! T!

U-N-I-T! Rate! Rate! Rate!

This is the original "seventh grade verse" that I wrote years ago. Originally, I also wrote an eighth grade verse on the Laws of Exponents, since Math 8 usually teaches exponent standards (NS or the first part of EE) at around the same time that Math 7 teaches unit rates (RP).

But making the second verse be about slope is more logical, since slope is actually related to unit rates (unlike exponents). Yet slope (later in EE) is usually taught a month or so later in Math 8 than unit rates are in Math 7, so I wouldn't be able to sing this for both classes at the same time.

Then again, this year I'm singing this song well later than when these standards are taught. And so I feel justified in singing a slope verse this month in the eighth grade classes:

To find the slope isn't tough,

It's positive the line goes up.

For a vertical line, you'll find,

That slope is undefined.

Zero slope is fun,

For across the line will run.

If it's negative, don't frown,

For then the line will move down.

U! N! I! T!

U-N-I-T! Rate! Rate! Rate!

Speaking of UCLA, three days ago was the first Saturday in December. My blog tradition on the following Tuesday is to discuss the annual Putnam exam -- the world's hardest math test, and a test I took twice at UCLA. Well, this year's Putnam exam was postponed due to the coronavirus. It will be given in February -- "unofficially," with no prizes or winner.

Still, just as I watched 42 twice and will watch McFarland USA twice, I'm mentioning the Putnam twice in my classes -- this week and again in February. I prefer talking about it only in my highest class, Math 8, since they're closer to actually taking the Putnam. And so I'll wait until tomorrow's post (my eighth grade post) to mention how this goes.

In the Math 7 classes, instead of the Putnam, I discuss placement for eighth grade math. It's possible for students in ordinary Math 7 (as opposed to an Honors class) to advance into Algebra I (the SteveH track), but to do so, they must earn at least A/A/A/B across the four quarters in Math 7.

There's one more thing to say about songs here. Remember the Benchmark Tests song -- "The teacher sees our Benchmark Tests, Knows what to teach now more or less." Well, this is part of what the math department discussed at yesterday's meeting. Today I'll mention from the department head's summary which topics the teachers need to teach more or less.

Math 8:

• Determining and comparing slopes (rate of change) from a table

• Identifying functions/non-functions in graphs

Math 7:

     -    Collecting like terms

     -    Conversions between fraction to decimal (includes identifying the dividend and divisor

          properly)

     -    Distributive Property

     -    Fractions Operations with unlike denominators.

By the way, when I ask her whether she had graded the Tasks yet, she tells me that she's asked the district to give her an extra day to grade. Considering that yesterday was my birthday, perhaps I should have lobbied for a one-day extension -- but then again, she's the department chair while I'm nothing more than a long-term sub, so she has more cachet. There's no guarantee that I would have been granted the extension.