Tuesday, June 28, 2016

How To Part II 2016: SAGE Computer Algebra System!

How To Part II 2016: 
SAGE Computer Algebra System!
We just had our Graduation Day at the High School. I suppose that's my unofficial start to Summer. I will miss my Seniors, we had a great year together. The whole week before graduation I was finishing up a series of YouTube ScreenCasts about solving this year's AP Calculus Exam Part IIA. This playlist serves as a summary of this year's Final Project! 

Part IIA is the first Free Response section of the AP Calculus Exam. This section consists of 2 AB or 2 BC questions requiring the use of a Graphing Calculator. AB1 and BC1 are the same question. AB2 and BC2 are different. Below you will find the solutions to these Free Response Questions in the following order: AB2, AB1/BC1, BC2. In this fashion, we covered AB only questions first, then AB/BC questions and finally BC only questions, ie in order of increasing difficulty.

For over 2 decades, I have been teaching my students to complete this section using a TI89. Most schools still use a TI83 or TI84. These past 2 years, my students have been using a class set of TI nSpire CX CAS graphing calculators that were donated to my classroom via DonorsChoose. Thanx to all my donors, my students are indeed very fortunate!

There are 4 functions a Graphing Calculator needs to perform to be allowed on the AP Exam: 

1) Graphing in an arbitrary window, 
2) Solving for the roots of an equation, 
3) Finding Numerical Derivatives and 
4) Finding Definite Integrals. 

All of these capabilities are demonstrated in the ScreenCasts listed below.

However, in this blog post I wish to demonstrate that the use of a Graphing Calculator is, in fact, not necessary. Why don't we toss out the Graphing Calculators and just a Computer Algebra System like SAGE


I'm waiting for Doc Brown from Back To The Future fame to come by and say, "Calculators? Where we're going, we don't need calculators!"

Below you will find all my solutions using a Computer Algebra System called SAGE. SAGE is a free online Computer Algebra System hosted on Google Compute Engine that you can use with just about any web-enabled device! The 3 ScreenCasts below will take you through the solution of each Free Response Question step by step using SAGE.

BTW, you do need the Internet to use SAGECELL. In a recent post I talked about using python on stand-alone PC without Internet access for testing conditions. However, I don't think that using SAGECELL would be so bad for use in class even under testing conditions. The teacher/proctor should be able to watch what the students do during the test. 

I have my PC Lab/Classroom set up with all monitors facing the rear of the room. So the teacher/proctor can easily see that all students are on task at all times. 

Further, we administer a math placement exam at the local college. This placement exam is computer adaptive and is administered via the College Board website. We have had no problems using these PCs with Internet Access during testing conditions.


2016AB2a) Numerical Derivative
2016AB2b) Numerical Root
2016AB2c) Definite Integral
2016AB2d) Definite Integral


2016AB1c/BC1c) Definite Integral


2016BC2a) Definite Integral
2016BC2d) Definite Integral

PS, here's a shot from the traffic jam I hit going home after the graduation!


Have A Great Summer 2016!!!

Well, that's all folks,

Saturday, June 25, 2016

How To Part II 2016: Pythonic Calculus!

How To Part II 2016: 
Pythonic Calculus!
We just had our Graduation Day at the High School. I suppose that's my unofficial start to Summer. I will miss my Seniors, we had a great year together. The whole week before graduation I was finishing up a series of YouTube ScreenCasts about solving this year's AP Calculus Exam Part IIA. This playlist serves as a summary of this year's Final Project! 

Part IIA is the first Free Response section of the AP Calculus Exam. This section consists of 2 AB or 2 BC questions requiring the use of a Graphing Calculator. AB1 and BC1 are the same question. AB2 and BC2 are different. Below you will find the solutions to these Free Response Questions in the following order: AB2, AB1/BC1, BC2. In this fashion, we covered AB only questions first, then AB/BC questions and finally BC only questions, ie in order of increasing difficulty.

For over 2 decades, I have been teaching my students to complete this section using a TI89. Most schools still use a TI83 or TI84. These past 2 years, my students have been using a class set of TI nSpire CX CAS graphing calculators that were donated to my classroom via DonorsChoose. Thanx to all my donors, my students are indeed very fortunate!

There are 4 functions a Graphing Calculator needs to perform to be allowed on the AP Exam: 

1) Graphing in an arbitrary window, 
2) Solving for the roots of an equation, 
3) Finding Numerical Derivatives and 
4) Finding Definite Integrals. 


All of these capabilities are demonstrated in the ScreenCasts listed below.

However, in this blog post I wish to demonstrate that the use of a Graphing Calculator is, in fact, not necessary. Why don't we toss out the Graphing Calculators and just learn a little bit of coding? 


I'm waiting for Doc Brown from Back To The Future fame to come by and say, "Calculators? Where we're going, we don't need calculators!"

Below you will find all my solutions using a programming language called Python. Python is a great first language to learn and use as it is very intuitive and powerful especially when solving math and science problems! 

The final YouTube ScreenCast is my Pythonic Calculus Executive Summary! This video summarizes everything we figured out in python related to solving Graphing Calculator Active Free Response Questions by coding instead! If you want a slower introduction to these numerical methods, please view the first 3 ScreenCasts. These ScreenCasts will take you through the solution of each Free Response Question step by step using python.


2016AB2a) Numerical Derivative
2016AB2b) Numerical Root
2016AB2c) Definite Integral
2016AB2d) Definite Integral

2016AB1c/BC1c) Definite Integral

2016BC2a) Definite Integral
2016BC2d) Definite Integral

Pythonic Calculus Executive Summary:
Includes plot() command!








PS, here's a shot from the traffic jam I hit going home after the graduation!


Have A Great Summer 2016!!!

Well, that's all folks,

Monday, May 30, 2016

My Senior Cut Day Adventure 2016!

My Senior Cut Day Adventure 2016!
Last Friday was Senior Cut Day once more ... or, as I like to call this time honored tradition, Teacher Cut Day! I didn't actually cut, but I didn't do a whole lot of teaching either. As you can see above, I spent the day catching up on paper work as I also caught up on the last few episodes of Supernatural. That was between periods. During class time, if any Sophomores or Juniors showed up, we played BZFlag in Capture The Flag mode. We were all on one server with the left side of the room playing the Red Team and the right side of the room playing the Green Team. Fun was had by all!


What was even more fun was what happened the night before! I attended the BSHS Spring Concert. The Symphonic Band and the Orchestra are my usual favorites. However, I must say, the Choir stole the show with the help of NickB, MiguelM and DavidZ as seen in the video above from my Instagram.


Then, my luck held true, as I drove home after Senior Cut Day by way of the Ocean Parkway and Jones Beach. The place was jammed. There was no parking anywhere. I stopped by the side of the road, east of the Clock Tower, to watch the Blue Angels practice for the Air Show this Memorial Day Weekend! There were a lot of other air teams doing all sorts of stunts too as you can see in the Instagram video above.


Happy Memorial Day 2016!!!

Well, that's all folks!

Generally Speaking,

A. Jorge Garcia
Applied Math, Physics and CS


http://shadowfaxrant.blogspot.com
http://www.youtube.com/calcpage2009
2015 NYS Secondary Math PAEMST Nominee



Teaching with Technology, 
pastebin youtube slideshare 
mathforum apcommunity
sage ebay

Tuesday, May 24, 2016

preCalculus 2015-2016 May Derivatives and AntiDerivatives (LAST POST)!

preCalculus 2015-2016 May

Derivatives + AntiDerivatives (LAST POST)!

This month we covered our last two units: UNIT03 Derivatives and UNIT05 AntiDerivatives. This was only a brief introduction to Calculus. This past Quarter of the year, we only got to spend 2 weeks of Polynomial Functions (preCalcCH4), then 2 weeks on Rational Functions with Limits (preCalcCH3), then 2 weeks on Limits with the Difference Quotient (introCalcUNIT02), then 2 weeks on Derivatives (introCalcUNIT03)and 2 weeks on Integrals (introCalcUNIT05)

Below you will see 2 playlists. UNIT03 is about Differentiation Rules: Power, Product, Quotient and Chain. UNIT05 is about AntiDifferentiation: Definite Integrals, Indefinite Integrals, Left Riemann Sums, Right Riemann Sums, Trapezoidal Area Estimates as well as the infamous LRTE.T84 TI-BASIC program.

This is our last post for the school year. Next week we start Final Review. So, I hope you learned a lot this year! Have a great Summer!


CLASS PICTURE:  
4R-12 2016 Period 03
Playing BZFlag.
You will be missed!

CLASS PICTURE:  
4R-12 2016 Period 04
Playing BZFlag.
You will be missed!


CLASS PICTURE:  
4R-12 2016 Period 09
Playing BZFlag.
You will be missed!


YOUTUBE WEDNESDAYS: 
The Symphony of Science!
NUMA NUMA Calculus!

Calculus Rhapsody!


NEW preCalculus + TI-84plusC
SCREENCASTS:




Well, that's all folks!

Friday, May 13, 2016

AP CompSci 2015-2016 May: Recursion (LAST POST))!

AP CompSci 2015-2016 May

Recursion (LAST POST)!
After AP Week, we have Game Day every other day. In between, we're finishing the labs we didn't get to before the AP Exam. 

The CollegeBoard recommends 20 hours of labs for the whole year. We do that nearly every month! We had a slow start with netowrking issues all of September. SO, we didn't cover all the labs we usually do. 

However, we did cover all the material on the AP Exam as far as our PPTs, TakeHomes and AP Review. So, as you can see below, we completed a project on Recursion!

We'll that's our last post. Hope you learned a lot! Have great Summer!



CLASS PICTURE:  
APCS 2016 Period 06
Playing BZFlag.
You will be missed!




YOUTUBE WEDNESDAYS: 
Doodling in Math Class?
Anti-PI!

AP Computer Science + JAVA
SCREENCASTS


Well, that's all folks!