*Teaching Math 5H:*

*UNITs 11+12*

__Power Series + Polar!__

*April + May 2015*

*(LAST POST)*
It's our last post of the school year and I think it safe to say that our TI nSpire CX CAS in AP Calculus BC class project was a great success! To paraphrase those Car Talk guys on NPR, "Well, now you've done it again! You've wasted another perfectly good school year with me at ShadowfaxRant on BlogSpot as well as CalcPage2009 on YouTube!"

Please see the new nSpire ScreenCasts for UNIT11 Power Series and UNIT12 Vector/Polar below. You may have noticed that I had to condense a few of these topics as we were running out of time before the AP Exam! Next year, I may redo some of these ScreenCasts. I hope you found our new nSpire ScreenCasts helpful this year. Have a great Summer and see you next school year!

Fare thee well AP Calculus BC class of 2014-2015! You will be missed. I hope you go on to fulfill your dreams! Each and every one of you has the potential for greatness. Don't let anyone tell you different and don't settle for less in yourself. Most people are just like lemmings, all they do is follow the leader. Why be a follower when you can be a leader? You can be a leader in your school, your place of worship, your community, your office, your profession, your field. Don't be a lemming just complaining about your lot in life or flaws in the system at large without trying to fix it yourself. You can effect change for the greater good! Life is short and time is precious. Don't let a day go by where you don't make the most of your talents and contribute something to society. You are the true dreamers, and dreams accomplish wonderful things! I won't say goodbye, let me just say: Until we meet again. Summer Assignment: Watch all 3 Lords Of The Ring in one sitting!

NB01: I may start a new YouTube PlayList for Life After Calculus 2015 (LAC2015) before long. I'll just redo LAC2014 which was the TI-89's swan song with the nSpire instead. I'm thinking of doing a Life After Computer Science 2015 (LACS2015) PlayList too! Also, I hope to have a class at the local college this Summer, so there may be a new course blog for that too.

NB02: Sorry I haven't been able to update the blog much these past few weeks. I've been dealing with some medical issues that have made it hard to write: aka grade and type. I've been saving my hand for grading tests ans writing finals. As a result, next year I will probably be cutting back to one or two posts per month per course blog.

YOUTUBE WEDNESDAYS:

All of April: Cliff Stoll's Cuckoo's Egg!

There will be no more YouTube Wednesdays during May and June as we have our AP Movie Marathon (all 3 Hobbits) every other day with LAC2015 in between....

*NEW AP Calculus BC + nSpire***:**

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

*Teaching Math 5H:*

*UNIT10*

__Quarter III Weeks 7-10 Series!__

*03/23/15-04/10/15*
These past 4 weeks have all been about Convergence of Series with all Positive Constants. We talked about Harmonic and Geometric Series. We touched on the Comparison Test and p-Integrals leading into the Integral Test next week. There is no UNIT09 anymore as I combined Improper Integrals with Series as one unit. We'll be playing with Power Series in UNIT12 really soon!

YOUTUBE WEDNESDAYS:

All of March: Vi Hart Channel and PI Day!

*NEW AP Calculus BC + nSpire***:**

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

*Teaching Math 5H:*

*UNIT08*

__Quarter III Weeks 3-6 DiffEqus!__

*02/23/15-03/20/15*
These past 4 weeks have all been about Variable Separable Differential Equations. We talked about solving DiffEqus Graphically using Slope Fields, Numerically with Euler's Method and Analytically using advanced integration techniques! So, we also focused on Integration By Parts and Partial Fractions Decomposition as well as other anti-derivative quotient rules involving ln(x), arcsin(x) and arctan(x). Have a look at all our new TI nSpire CX CAS based ScreenCasts below finishing UNIT07 and covering all of UNIT08. We pushed the UNIT08 preTest and Test to Monday and Tuesday next week.

YOUTUBE WEDNESDAYS:

All of March: Vi Hart Channel and PI Day!

*NEW AP Calculus BC + nSpire***:**

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

*Teaching Math 5H:*

*UNIT07*

__Quarter III Weeks 1-2 Exponentials!__

*02/02/15-02/13/15*
The first 2 weeks of Quarter III focused on derivatives and anti-derivatives involving e^x and ln(x). Firstly, however, we had a lesson on measuring work when the Force is not constant!

YOUTUBE WEDNESDAYS:

All of February: 15mins/week

*NEW AP Calculus BC + nSpire***:**

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

*Teaching Math 5H:*

*UNIT06*

__Quarter II Weeks 7-10 More Applications!__

*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 Unit 6 all about Applications of the AntiDerivative: Area, Volume, Arc Length and Surface Area as well as Variable Separable Diff Equs (see below).

YOUTUBE WEDNESDAYS:

Week7: Phil Plait and Apophos

Week8: Michio Kaku and Extinction

Week9: Carl Sagan's "Pale Blue Dot"

*NEW AP Calculus BC + nSpire***:**

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

*Teaching Math 5H:*

*UNIT06*

__Quarter II Weeks 4&6 Applications!__

*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 UNIT05 about AntiDerivatives and started UNIT06 about Applications of AntiDerivatives!

YOUTUBE WEDNESDAYS:

Week4: #HourOfCode!

Week6: preCalc and Calculus Carols!

*NEW AP Calculus BC + nSpire***:**

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

*Teaching Math 5H:*

*UNIT05*

__Quarter II Weeks 1&2 AntiDerivatives!__

*11/10/14-11/21/14*
Yeah, Quarter II has begun! After playing with some TI nSpire BASIC programming, we did a lot of LSUM, RSUM, TRAPSUM and ERRORTRAP as well as MIDSUM and SIMPSUM! Now we're working on Definite vs. Indefinite Integrals. Our last topic in this unit will by U-Substitution next week.

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?

*NEW AP Calculus BC + nSpire***:**

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

*Teaching Math 5H:*

*UNIT05*

__Quarter I Weeks 9&10 AntiDerivatives!__

*10/27/14-11/07/14*
Yeah, Quarter I is done! We finally finished Applications of the Derivative with Related Rates. Then we started AntiDerivatives! After playing with AntiDerivatives and DiffEqus analytically, we started to evaluate some Riemann Sums arithmetically by hand. Soon, we're going to program the TI nSpire CX CAS to do them for us! We are about to write LRTE and MTSE. LRTE will output LSUM, RSUM, TRAPSUM and ERRORTRAP. MTSE will add MIDSUM and SIMPSUM!

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.

*NEW AP Calculus BC + nSpire***:**

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

*Teaching Math 5H:*

*UNIT04*

__Quarter I Weeks 7&8 Applications!__

*10/13/2014 - 10/24/2014*
In UNIT04 we turn our attention to the Applications of the Derivative. We developed the ideas behind Rolle's Theorem and the Mean Value Theorem as well as Optimization problems! We also learned how to program the TI nSpire CX CAS with TI-BASIC. We wrote a program to solve Quadratic Equations for practice. Then we wrote a function for Newton's Method for finding Roots!

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).

*NEW AP Calculus BC + nSpire***:**

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

*Teaching Math 5H:*

*UNIT03*

__Quarter I Weeks 5&6 Differentiation Rules!__

*9/29/2014 - 10/10/2014*
During these past couple of weeks we finished UNIT03 covering the Product, Quotient and Chain Rules. We finished by working with Implicit Differentiation. UNIT04 will cover applications of differentiation including the use of Implicit Differentiation in Related Rates problems. We'll also cover optimization!

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.

*NEW AP Calculus BC + nSpire***:**

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

*Teaching Math 5H:*

*UNIT03*

__Quarter I Weeks 3&4 Differentiation Rules!__

*9/15/2014 - 9/26/2014*
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 UNIT02 on Limits and Continuity. Then we started UNIT03 on the Algebraic Rules of Differentiation. I think you will get a lot out of our new ScreenCasts (see below) featuring the TI nSpire CX CAS!

We also celebrated "The Great TI NSPIRE UnBoxing of 2014!" We unboxed and distributed 22 out of the 24 nSpires that were donated to our class. I'm still waiting on some calculator rental forms to give out the remaining 2 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). We are also waiting for a our DonorsChoose Project to be funded to get another 14 GCs! So, over the past several years we've upgraded our emulators from Hal and Colossus (VTI-83/89 and TIEMU-89) to Castiel (KARMTI-nSpire)!

YOUTUBE WEDNESDAYS:

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

Week4: Lobachevsky channeling Danny Kaye!

**:**

*NEW AP Calculus BC + nSpire SCREENCASTS*YouTube desciptions include links to handouts and notes if you need them.

Here's an oldie but goodie featuring the TI-89. I was sick last week and could not re-record this ScreenCast, sorry.

OK, I just recorded a new version of 302!

*Teaching Math 5H:*

*UNIT02*

__Quarter I Week 2 Limits and Continuity!__

*9/8/2014 - 9/12/2014***:**

*MONDAY*__Lesson 107 Functions vs Relations__

We talked about graphing General Form Conic Sections by Completing The Square and using Polar Notation!

Now we look at Limits at Infinity and limits on either side of points of discontinuity.

Now we define Continuity and use the Intermediate Value Theorem. BTW, if it's September, YouTube Wednesday must include Tom Lehrer's New Math!

Nothing new today, we just went over the homework in groups on our mini marker boards from http://whiteboardsusa.com

Finally, we defined the Derivative as the limit of the secant line slopes!

YouTube desciptions include links to handouts and notes if you need them.

If you are having trouble running KARMTI at home, you may need to reinstall the OS. Enter this line:

/1=boot1.img /MXC /PB=boot2.img /PO=TI-NspireCXCAS-3.6.0.550.tcc /K4 /N /R

in

(FILE)(BOOT OPTIONS)(COMMANDLINE)

Then enter

myFlash.bin

in

(FILE)(SAVE FLASH AS)

Then enter this line:

/1=boot1.img /F=myFlash.bin /K4

in

(FILE)(BOOT OPTIONS)(COMMANDLINE)

Then do

(FILE)(EXIT)

UPDATE: You may also have to goto (FILE)(SKINS) to enable a skin!

The next time you run KARMTI, it should default to "/1=boot1.img /F=myFlash.bin /K4" using the new OS without you having to enter anything as it works in class. BTW, the new OS file "TI-NspireCXCAS-3.6.0.550.tcc" is already in the KARMTI folder I gave you. What we do in class requires OS 3.1 or greater, I'm using 3.6 OS. To get the latest TI nSPire CX CAS OS goto http://education.ti.com/en/us/home Good Luck!

**:***TUESDAY*__Lesson 201 1-Sided Limits__Now we look at Limits at Infinity and limits on either side of points of discontinuity.

**:***WEDNESDAY*__Lesson 202 Continuity__Now we define Continuity and use the Intermediate Value Theorem. BTW, if it's September, YouTube Wednesday must include Tom Lehrer's New Math!

**:***THURSDAY*__Lesson 202____Continuity__Nothing new today, we just went over the homework in groups on our mini marker boards from http://whiteboardsusa.com

**:***FRIDAY*__Lesson 203 Definition of f'(x)__Finally, we defined the Derivative as the limit of the secant line slopes!

**:***NEW AP Calculus BC + nSpire SCREENCASTS*YouTube desciptions include links to handouts and notes if you need them.

*TECHNOTE:*If you are having trouble running KARMTI at home, you may need to reinstall the OS. Enter this line:

/1=boot1.img /MXC /PB=boot2.img /PO=TI-NspireCXCAS-3.6.0.550.tcc /K4 /N /R

in

(FILE)(BOOT OPTIONS)(COMMANDLINE)

Then enter

myFlash.bin

in

(FILE)(SAVE FLASH AS)

Then enter this line:

/1=boot1.img /F=myFlash.bin /K4

in

(FILE)(BOOT OPTIONS)(COMMANDLINE)

Then do

(FILE)(EXIT)

UPDATE: You may also have to goto (FILE)(SKINS) to enable a skin!

The next time you run KARMTI, it should default to "/1=boot1.img /F=myFlash.bin /K4" using the new OS without you having to enter anything as it works in class. BTW, the new OS file "TI-NspireCXCAS-3.6.0.550.tcc" is already in the KARMTI folder I gave you. What we do in class requires OS 3.1 or greater, I'm using 3.6 OS. To get the latest TI nSPire CX CAS OS goto http://education.ti.com/en/us/home Good Luck!

*Teaching Math 5H:*

*UNIT01+UNIT02*

__Quarter I Week 1 First Week Back!__

*9/1/2014 - 9/5/2014*
I don't usually do a day by day rundown of the week, but here goes nothing!

**: 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 101 Intro to TI-nSpire__

Finally, we say goodbye to Hal (TI-89) and play around with the KARMTI emulator on each PC as we don't have all our TI nSpire CX CAS Graphing Calculators from DonorsChoose as yet. The students are still trying to get some FREE Google Gift Cards from Codecademy!

**TECH NOTE**: I was ScreenCasting Lesson 101 from the front of the room at the SmartBoard using SmartNotebook with my USB Mic attached to the SmartBoard. This was all well and good until the keys on the emulator started sticking. So, I had to go to my PC in the back of the room to use a standard keyboard and mouse instead of the SmartBoard for input on the emulator.

**:**

*FRIDAY*__Lesson 106 Implicit Graphs__

I used to do a whole UNIT1 on preCalculus Review. Now I just sneak in a few of those lessons before UNIT2 on Limits. These UNIT1 Lessons are mainly an intro to the calculator and review of a bit of Algebra and Trig. We play around with Function, Parametric, DiffEqu and Polar modes all in the first few days of class!

**TECH NOTE**: I was ScreenCasting Lesson 106 from the back of the room at my PC with the USB Mic attached to the PC to fix the problems I listed in the last technical note. I still had a problem late in the ScreenCast when xournal, the pen app I was using, started drawing random lines all over the SmartBoard whenever I put the stylus down on my tablet. I was using xournal instead of SmartNotebook and a DROID Tablet over WiFi instead of the SmartBoard like the old days when all I had was a PC Projector. Maybe I'll try using SmartNotebook with the Tablet on Monday to see if that's a bit better. The problem with this setup is that when I use SmartNotebook with aconv, my ScreenCaster, and SplashTop (to connect the tablet over WiFi) then SmartNotebook is a bit laggy.

**UPDATE**: Today is Monday and I recorded ScreenCast 107 as above. I got a lot of lag between writing with the stylus and seeing what I wrote on SmartNotebook. So, I moved every thing back up front next to the SmartBoard. I attached an extra USB keyboard and USB mouse as well as the USB Mic directly to the SmartBoard. Luckily there's 3 USB ports! So, Tuesday I'll record ScreenCast 201 from the front of the room using the SmartBoard with SmartNotebook which worked well the first day (101). When I need to use the nSpire emulator, I can now use the keyboard and mouse at the front of the room to avoid the sticky keys! Neither will I need SpalshTop nor the Tablet. I still have the standard keyboard and mouse on the teacher/smartboard PC at the back of the room.

**:**

*NEW AP Calculus BC + nSpire SCREENCASTS*YouTube desciptions include links to handouts and notes if you need them.

*Teaching Math 5H:*

*Hal Must Die - No More TI-89!*

__Quarter I Week 0 August Preparation__
AP Calculus BC is switching gears this year. We're leaving our TI-89s behind for the first time in 20 years! We will go forth and conquer with our new TI nSpire CX CAS Graphing Calculators! We've been running project after project on Donorschoose and nearly have a class set of nSpires to loan out.

We used to call the TI-89 "Hal," hence the title of this post: Hal Must Die - No More TI-89! It shouldn't be a tough transition, however, as the 89 and the nSpire are very similar Computer Algebra Systems aka CAS. However, the nSpire has a nicer color, hi-res, bright interface and a document system to save our work. It also has the LUA programming environment, but I think we'll stick to TI-BASIC when writing programs for Calculus class!

Whenever I change textbooks or technology, I have to rerecord the course for YouTube. So, I'll record AP Calculus BC all over again with a bunch of new screencasts featuring the nSpire! This was the first course I ever recorded, so it's about time.

Here's a taste of the nSpire (not my video):

Here's a taste of the TI-89 (this is mine):

We used to call the TI-89 "Hal," hence the title of this post: Hal Must Die - No More TI-89! It shouldn't be a tough transition, however, as the 89 and the nSpire are very similar Computer Algebra Systems aka CAS. However, the nSpire has a nicer color, hi-res, bright interface and a document system to save our work. It also has the LUA programming environment, but I think we'll stick to TI-BASIC when writing programs for Calculus class!

Whenever I change textbooks or technology, I have to rerecord the course for YouTube. So, I'll record AP Calculus BC all over again with a bunch of new screencasts featuring the nSpire! This was the first course I ever recorded, so it's about time.

Here's a taste of the nSpire (not my video):

Here's a taste of the TI-89 (this is mine):

**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*