*Teaching Math 4R:*

*Calculus UNIT02*

__Quarter III Weeks 7-10 Limits!__

*03/23/15-04/10/15*
We finished off UNIT02 on Limits as an introduction to Calculus. We continued the discussion from preCalc CH03 about Limits at Infinity and Limits at a Point. We also developed the Difference Quotient definition of the Derivative. We applied this definition to several functions such as Power Functions as well as Sin(x) and Cos(x). The next unit will focus on Algebraic Rules of Differentiation such as the Product Rule, the Quotient Rule and the Chain Rule!

YOUTUBE WEDNESDAYS:

All of March, Vi Hart Channel and PI Day:

*Math 4R: preCalculus + SAGECELL***:**

*SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 3*

__Quarter III Weeks 3-6 Rationals!__

*02/23/15-03/20/15*
We finished off some loose ends in CH04 about Polynomial InEqualities. Then we spent most of the last 4 weeks in CH03 reviewing Power and Quadratic Functions. This review lead to the study of Rational Functions. Our focus in this part of the chapter was the introduction of Limits and Limit Notation when discussing Horizontal, Slant and Vertical Asymptotes as well as points of Removable Discontinuity. This marks the end of our preCalculus adventures. We just started our first unit in Calculus about Limits and The Difference Quotient! Enjoy the following ScreenCasts with all new SageCell notes attached! This SageCells are also available on the right hand sidebar of this blog.

YOUTUBE WEDNESDAYS:

All of March, Vi Hart Channel and PI Day:

*Math 4R: preCalculus + SAGECELL***:**

*SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 4*

__Quarter III Weeks 1-2 Polynomials!__

*02/02/15-02/13/15*
The first 2 weeks of Quarter III were devoted to solving Polynomial Equations. We talked about the Fundamental Theorem of Algebra, the Rational Roots Theorem and the Remainder Theorem. We figured out how to deal with Real and Complex Roots as well as how to factor the Sum and Difference of Perfect Cubes! All this factoring and solving is a great warm up for Chapter 3 on Rational Functions. In Chapter 3 we can start talking about Limits at a Point and Limits at Infinity. So, an intro to AP Calculus AB cannot be far off!

YOUTUBE WEDNESDAYS:

All of February, 15mins/weeks:

*Math 4R: preCalculus + SAGECELL***:**

*SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 5*

__Quarter II Weeks 7-10 More Inverses!__

*01/05/15-01/30/15*
This post is mostly about weeks 7&8. Week 9 was all about review for MidTerms and in-class Midterms. Week 10 was for formal Midterms and NYS Regents Exams so we had no classes! During Weeks 7&8 we finished up Chapter 5 all about solving equations using inverse functions as well as a lot of work with exponential and logarithmic functions (see below).

YOUTUBE WEDNESDAYS:

Week7: Phil Plait and Apophos

Week8: Michio Kaku and Extinction

Week9: Carl Sagan's "Pale Blue Dot"

*Math 4R: preCalculus + SAGECELL***:**

*SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 5*

__Quarter II Weeks 4&6 Inverses!__

*12/01/14-12/19/14*
OK, you can't make me blog about Week 3 (11/24-11/28) since it was a 2 day week right before Thanksgiving Break. Monday we had tests and Tuesday was a make up day. Actually, Monday was also a make up lab day for APCS.

Also, I'm not blogging about Week 5 (12/08-12/12) since I focused on telling the whole school about the #HourOfCode! So, my regular classes just had a lot of review sheets.

Finally, I'm not blogging about Week 7 (12/22-12/26) since it's also a 2 day week before XMas Break! Monday we have tests and Tuesday is preCalculus and Calculus Carols plus a game day in APCS. Monday is also a make up day for APCS.

So, what am I blogging about? Well, I'll let the YouTube ScreenCasts speak for themselves. Suffice it to say that we completed all of CH09 about Vectors and started CH05 about Inverse Functions!

YOUTUBE WEDNESDAYS:

Week4: #HourOfCode!

Week6: preCalc and Calculus Carols!

*Math 4R: preCalculus + SAGECELL***:**

*SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 9*

__Quarter II Weeks 1&2 Vectors!__

*11/10/14-11/21/14*
Yeah, Quarter II has begun! We started the unit on vectors by talking about complex numbers in CIS(theta), aka polar form, and 2D vector form. We also talked about adding, subtracting and multiplying, via the dot product, 2D vectors. Next week, we'll talk about 3D vectors and the cross product!

Don't forget to start rehearsals!

YOUTUBE WEDNESDAYS:

Since we're doing Conic Sections and Planet Orbits in preCalculus, it's time for our Astronomy related YouTubes! We had 2 guest speakers talk about the Asteroid Apophos and its flyby in 2029!

Week1: Neil deGrasse Tyson!

Week2: Bill Nye the Science Guy?

*Math 4R: preCalculus + SAGECELL***:**

*SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 10*

__Quarter I Weeks 9&10 Conics!__

*10/27/14-11/07/14*
Yeah, Quarter I is done! We finally finished Conic Sections using the Completing The Square algorithm to get Standard Forms for Parabolas, Ellipses and Hyperbolera! For those graphs that we could not use the Completing The Square algorithm, we used SAGE and polar_plot(). We also talked about parametrically defined trajectories and SAGE's parametric_plot().

YOUTUBE WEDNESDAYS:

Since we're doing Conic Sections and Planet Orbits in preCalculus, it's time for our Astronomy related YouTubes! We started by talking about really big and really small numbers and metric prefixes.

Week9: NEW Powers of Ten.

Week10: Original Powers of Ten.

*Math 4R: preCalculus + SAGECELL***:**

*SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 10*

__Quarter I Weeks 7&8 Conics!__

*10/13/14-10/24/14*
We finished the Matrix unit (CH11) with nonLinear Systems and Linear Programming. Then we started Conic Sections (CH10). In fact, we're having a quiz right now, as I type, on the Standard Form Equations for Parabloas, Ellipses and Hyperbolera! We are focusing on conics with horizontal or vertical symmetry right now. Next week, we'll deal with what I call Twisted Conics using Polar Mode. Then, the following week, we'll revisit the concept of foci and do some real world problem solving!

YOUTUBE WEDNESDAYS:

If it's October, it's gotta be Admiral Grace Murray Hopper!

Week7: Letterman interview.

Week8: Walter Isaacson on CBS Sunday Morning (from my DVDR).

*Math 4R: preCalculus + SAGECELL***:**

*SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 11*

__Quarter I Weeks 5&6 Matices!__

*9/29/14-10/10/14*
During these past 2 weeks, we started solving 2D and 3D Systems using Matrix Arithmetic and Matrix Algebra! In fact, we are having a quiz this week using Cramer's Rule of Determinants as well as Matrix Inverses to solve these systems. I make a point of doing 2D problems totally by hand (no calculator or CAS). We are doing 3D systems on SAGE!

YOUTUBE WEDNESDAYS:

If it's October, it's gotta be Admiral Grace Murray Hopper!

Week5: CBS Rewind 60 Minutes interview.

Week6: Full interview on DVD.

*Math 4R: preCalculus + SAGECELL***:**

*SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 11*

__Quarter I Weeks 3&4 Systems!__

*9/15/14-9/26/14*
OK, let me go back to my weekly or biweekly summaries. The day by day summary is too time consuming to write and I think too tedious to read! So, this will be a 2 week

summary as this past week was quite short

(Thursday and Friday was Rosh Hashanah).

We finished Chapter 12 on Sequences and Series with the Binomial Expansion Theorem. Then we started Chapter 11 on solving 2D and 3D Systems of Equations. Next week, this will lead to the development of Matrix Arithmetic and Matrix Algebra. We will even get into some Linear Programming! I hope you are getting a lot out of our ScreenCasts (see below) which include SageCell WorkSheets in the YouTube Descriptions.

We also celebrated "The Great TI 84+ UnBoxing of 2014!" We unboxed and distributed 24 out of the 48 84s that were donated to our class. I'm still waiting on some calculator rental forms to give out the remaining 24 GCs. BTW, these are not really rental forms as no one pays a dime until the end of the year if the GC is lost or damaged (like a book card really). So, over the past several years we've upgraded our emulators from Ziggie (VTI-83 and TILEM-83) to Frodo (WABBIT-84) to SAGE!

YOUTUBE WEDNESDAYS:

If it's September, it's gotta be Tom Lehrer!

Week4: Lobachevsky channeling Danny Kaye!

**:**

*Math 4R: preCalculus + SAGECELL SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 12*

__Quarter I Week 2 Sequences and Series!__

*9/8/14-9/12/14***:**

*MONDAY*__Lesson 1201A Recursion__

Now we redo 1201 by looking at sequences and series defined recursively.

**:**

*TUESDAY*__Lesson 1202 Arithmetic Seqs__

Today we talked about adding finite arithmetic sequences.

**:**

*WEDNESDAY*__Lesson 1203__

__Geometric Seqs__

Then we derived a formula for summing finite and infinite geometric sequences. BTW, if it's September, YouTube Wednesday must include Tom Lehrer's New Math!

**:**

*THURSDAY*__Lesson 1204 Induction Proofs__

Finally, used Peano's Postulates to prove sums by induction!

**:**

*FRIDAY*__Lesson 1204 Induction Practice__

We went over the homework as a review for a QUiz on Monday.

**:**

*Math 4R: preCalculus + SAGECELL SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Chapter 12*

__Quarter I Week 1 First Week Back!__

*9/1/14-9/5/14*
I don't usually do a day by day rundown of the week, but here goes nothing!

The first day of every quarter starts with the "Ceremony Of The Seats" (new seating assignments). The students come into a dark room except for the PC monitors and the SmartBoard. On the SmartBoard I'm playing an MP3 of the sound track to "A Beautiful Mind" over VLC. Since this isn't an MP4, VLC adds some wild special effects on the SmartBoard so it's all cool. Then I walk to each seat and call each student using my SmartPhone as a flashlight as if I'm an usher in the Movie Theater. It's all very dramatic. Then we hand out books and book cards, go over the syllabus and fill out some biographical forms. Sorry, there's no instruction the first day of classes.

Finally, we say goodbye to Ziggie (TI-83) and play around with SAGECELL! All we did was some basic Arithmetic and Algebra but I think we got across the power of a robust Computer Algebra System, aka CAS, such as SAGE!

We dive right into sequences and series using for loops and list comprehensions in python!

YouTube descriptions include links to code and notes if you need them.

**: Labor Day (nothing to report)***MONDAY***: Superintendent's Conferences where we spent all day in meetings except for the last 2 hours of the day when we finally got to set up our rooms. I spent those 2 hours moving 100 textbooks, arranging and tweeking 25 PCs, finding 25 chairs and placing 6 tables. Then I found that my SSH server's RAID drive crashed, so I had to setup openSSH on an alternate server I used to have for FTP. That's OK since I don't need the FTP server much anymore. I use the SSH sever for my AP Computer Science students to login from home and finish their Java projects. I share files with my students through Edmodo. I upload my files on DropBox, SageCell and YouTube aka my cloud!***TUESDAY***: First Day of Classes***WEDNESDAY*The first day of every quarter starts with the "Ceremony Of The Seats" (new seating assignments). The students come into a dark room except for the PC monitors and the SmartBoard. On the SmartBoard I'm playing an MP3 of the sound track to "A Beautiful Mind" over VLC. Since this isn't an MP4, VLC adds some wild special effects on the SmartBoard so it's all cool. Then I walk to each seat and call each student using my SmartPhone as a flashlight as if I'm an usher in the Movie Theater. It's all very dramatic. Then we hand out books and book cards, go over the syllabus and fill out some biographical forms. Sorry, there's no instruction the first day of classes.

**YOUTUBE**: Since it was Wednesday, after all, I had to show a FILK or two! So, at the end of the period I snuck in our own student made Frozen and then the infamous Mathmaticious!**:***THURSDAY*__Lesson 1200 Intro to SAGE__Finally, we say goodbye to Ziggie (TI-83) and play around with SAGECELL! All we did was some basic Arithmetic and Algebra but I think we got across the power of a robust Computer Algebra System, aka CAS, such as SAGE!

**:***FRIDAY*__Lesson 1201 Sequences & Series__We dive right into sequences and series using for loops and list comprehensions in python!

**TECH NOTE**: I recorded these ScreenCasts last year. The audio isn't great as I was using a BlueTooth Mic I inherited after Hurricane Sandy. It took me a while to get all my equipment replaced, sorry.**:***Math 4R: preCalculus + SAGECELL SCREENCASTS*YouTube descriptions include links to code and notes if you need them.

*Teaching Math 4R:*

*Ziggie must die - No more TI-83!*

__Quarter I Week 0 August Preparation:__
PreCalculus is all new this year:

(1) My preCalculus for Juniors classes will start the school year with Chapter 12 this year! We start with Chapter 12 so we don't waste a lot of time reviewing topics from Chapters 1 and 2 which are about solving Linear Equations and Quadratics! So, when midyear is upon us, we can switch to Calculus without skipping important topics at the end of the preCalculus text. As such, we cover as much preCalculus as we can in the Fall Semester and as much AP Calculus AB material as we can in the Spring in preparation for Calculus next year!(2) We are using a Computer Algebra System called SAGE instead of the TI-83. We used to call the TI-83 "Ziggie." Hence the title of this post: Ziggie must die! The grand experiment this year is to see how well students learn the Math while learning to code in python at the same time! Well, it's not such a grand experiment as we've been using SAGECELL for several years now. What's different is that we won't be using the TI-83 this year as we just don't need it anymore!

(3) We will be learning a lot of python in class. You can learn some python code on your own too with this online, interactive textbook!

(4) Here's a taste of our first day:

Well, that's all folks!

*Sincerely,*

*A. Jorge Garcia*

*Applied Math, Physics and CS*

*http://shadowfaxrant.blogspot.com*

http://www.youtube.com/calcpage2009

2015 NYS Secondary Math PAEMST Nomineehttp://www.youtube.com/calcpage2009

2015 NYS Secondary Math PAEMST Nominee

*Teaching with Technology,*

*pastebin youtube slideshare*

*mathforum apcommunity*

*sage ebay*
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