Tuesday, January 24, 2017

Similarity (Days 86-87)

Here is the Pappas question for today:

lim (n->oo) (6) lim (n->oo) (4)

The limit of a constant is the constant. So it's six times four or 24, and today's date is the 24th. Of course, this isn't a middle school problem but the simplest possible Calculus problem. But today I gave Illinois State questions as a warm-up, so this is the question for the blog.

The Oscar nominations have been released. Hidden Figures received three nominations -- for Best Picture, Best Adapted Screenplay, and Best Supporting Actress Octavia Spencer (Dorothy). Some people believe that Taraji Henson (Katherine) was snubbed for Best Leading Actress. While most experts expect La La Land to dominate the awards, I hope that Hidden Figures will at least win something at the Academy Awards.

All classes today at least officially are assigned to work on STEM projects. Learning Module 9 of the Illinois State text is called "Similarity," but this is a misnomer. The main topic of this module is in fact the Pythagorean Theorem.

I can't explain the title of the module, but I do know the link between similarity and the Pythagorean Theorem -- the preferred proof of the theorem in the Common Core Geometry. But notice that in eighth grade, the connection between similarity and right triangles usually isn't emphasized.

This is a good time to take a step back and discuss how I'm using transformations to teach geometry to my eighth graders. The first week, when I introduced the transformations, was fine, but the second week led to problems. There were several arguments about science and the way I'm teaching it -- and I'm still saving it for Friday's post. Suffice it to say that I only taught math once last week -- on Friday, I discussed parallel lines cut by a transversal. As I promised on the blog, I used translations and rotations to show why corresponding and alternate interior angles respectively are congruent.

Last week was also supposed to contain a lesson on dilations -- which I skipped for science. So now any attempt to connect dilations to the Pythagorean Theorem is doomed to failure. I still want to introduce dilations at some point, since I should try to connect similarity to slope. Notice that under the Year View of our pacing plan, all of Expressions and Equations (including slope) appear before Geometry, even though similar triangles are supposed to be used to explain slope.

Today I wanted to have the students work on the STEM project. The students are directed to draw right triangles on dot paper and measure their sides, then draw squares along each side in order to measure their areas. Of course, the goal is for the square on the hypotenuse to equal the sum of the squares on the legs.

But then there was another issue in class. Today was the day that I made the Hidden Figures extra credit assignment due. There are several students failing the class, and I was hoping that I could give the students a little boost.

Recall that at our school there is no D grade, so anyone with a grade below 70% has an F, My sixth grade class had the most F's, but many of those F's are in the 60% range, where the extra credit is enough to raise the students to passing. The eighth grade class had fewer F's, but those F's were more in the 50% range.

And so I ended up spending much of the period trying to come up with an alternative assignment that, in addition to Hidden Figures, would allow students to raise their grade from 50% to 70%. This was problematic because then the students who are already earning good grades start abandoning the project to work on the extra credit assignments. I've read that this is a big cause of grade inflation -- some easy assignment designed to reduce F's ends up raising the grades of the top students too.

Keep in mind that the original cause of all the F's was the zeros received for talking during the tests when they were given. Suddenly, the grades are being detached from levels of knowledge -- first with all the zeros (so smart students who talk a lot have low grades), and then with Hidden Figures being used to raise the zeros. Notice that when I first declared Hidden Figures to be extra credit, I was expecting only one or two students at the most to complete it -- it was before we decided to make the movie into a field trip.

And this is not to mention that my grading scale has gone out of whack anyway. My original plan was for the whole trimester to be worth 1000 points, divided up into sections so that 400 points (or 40%) is for projects and tests, 200 points (20%) for quizzes, and so on. It was easier when I planned on five learning modules per trimester. I knew how many points I needed everything to be worth, but now, with the idea of covering all major content (MC) before the SBAC, there must be more than five modules per trimester, and so all the points are off if I want the total to be 1000.

With all of this worry about grades, not much of the project was completed. But this is not to worry, as I have another Pythagorean Theorem activity already posted to the blog (from last year) -- and I like it more than the Illinois State project. There are some examples in the Student Journal that are similar to my own activity, and so I wouldn't be deviating too much from the prescribed Illinois State lesson if I were to start tomorrow's lesson with my own activity.

So tomorrow, my new schedule has the eighth graders starting with SBAC Math Prep in the morning, then the Student Journals in the middle, and finally science at the end of the day. We'll see how it all turns out tomorrow -- the second day of this two-day post.

Today's song for music break is a parody of TLC's "No Scrubs":


A DREN is a guy that thinks he's fly
And is also known as a buster
Always talkin' about what he wants
So (no)

I don't want your number (no)
I don't want to give you INTERVIEW and (no)
I don't want YOUR RESUME (no)
I don't want none of your time and (no)

I don't want no DREN
A DREN is a guy that can't get no JOB from me
Hanging out the passenger side
Of his best friend's ride
Trying to GET HIRED BY me
I don't want no DREN
A DREN is a guy that can't get no love from me
Hanging out the passenger side
Of his best friend's ride
Trying to GET HIRED BY me

But a DREN is checkin' me
But his MATH is kinda weak
And I know that he cannot approach me
'Cause I'm lookin' like class and he's lookin' like trash
So (no)

I don't want your number (no)
I don't want to give you INTERVIEW and (no)
I don't want YOUR RESUME (no)
I don't want none of your time (no)


The "Day in the Life" poster with a monthly posting date of the 24th is Brian Palacios, a New York high school math teacher:


He hasn't made his January 24th post yet, but here's a link to his December 24th post:


Of course that day was Christmas Eve, so there's not much math teaching in that post. Palacios does answer the reflection questions about several issues on his mind, including the completion of two major applications and a meeting he had with the principal.

Now that the Hidden Figures assignment has been submitted and the Oscar nominations have been released, this will be my last mention of the film for now (at least until Oscar night) after having mentioned it in nearly every post this month. As important are the gender and racial issues raised by the movie are, let's toss those aside. The focus of my blog during the school year is the math.

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