## Friday, April 25, 2014

### Teaching Math 5HAB: Welcome to AP Calculus Review!

Teaching Math 5HAB
Welcome to AP Calculus Review!

Welcome to all my new AB Caclulus students I'm helping to review for the AP Exam in a couple of weeks! Here's some pointers that may help you.

Good MCQ practice.

Try these FRQs!

2007 AB FRQs 4-6 AP Review with code:

Stuff You Must Know Cold (crib sheet)!

The Mother Function Dance!

All Our Calculus Songs (aka Filks)!

Here's a sample Filk (geeky cover) by Queen (not!) called "Calculus Rhapsody" which is a nice over view of your whole year in AP Calculus AB.

Here's another Calculus Filk by Bruno Mars (not!) singing "Calculus Time" all about the Chain Rule! I even checked his work!!

Hope that helps!

Well, that's all folks!

Sincerely,
A. Jorge Garcia
Applied Math, Physics and CS

Teaching with Technology,
mathforum apcommunity

## Sunday, April 6, 2014

### Teaching Math 5H UNIT 11 Power Series

Teaching Math 5H
UNIT 11 Power Series

Quarter III Weeks 7&8: 3/24-4/04
We started UNIT 11 about MacLaurin Series, Taylor Series, Intervals of Convergence, Alternating Series Error and LaGrange Error terms! Next week, the week before April Break, we'll finish UNIT 11. The week after break we'll do a short unit on Vector/Polar. The week after that is review and the week after that is the AP Exam already!

UNIT11 Power Series

Quarter III Weeks 5&6: 3/10-3/21
We finished UNIT8 about Partial Fractions and By Parts Integration techniques. I skipped UNIT9 about VARSEP DIFFEQUS as we covered that elsewhere and we had to make up time. We only have a few weeks before and a week after April Break to finish the course! Then we only have a week of review!

So, we just started UNIT10 on Convergence of Infinite Series of Constants with all Positive Terms. We'll sneak the Alternating Series Error Theorem somewhere. Then we have 2 weeks on Power Series and 1 week on Vector/Polar.

UNIT10 Series of Constants

Quarter III Weeks 3&4: 2/24-3/7
We didn't get very far this past couple of weeks with all the Snow Days and February Break! We did manage to cover most of UNIT 8 about Integration By Parts and Partial Fractions. We started the unit with a class on L'Hopital's rule using the "Mean Girls Limit" as a Do Now! I also ended that class with a Calculus Carol by one of my students about L'Hopital as a summary. I do this topic now as these limits will start to become an issue soon!

I will finish the unit next week with a discussion of Variable Separable DiffEqus including Logistics, Slope Fields and Euler's Method.

Quarter III Weeks 1&2: 2/3-2/14
We didn't get very far this past couple of weeks with 3 SnowDays and a Delayed Opening in the way! We did somehow manage to finish UNIT 7 focusing on Differential Equations. We talked about Slope Field and Variable Separable solutions for Exponential Growth and Decay, Exponential Approach (aka Newton's Laws of Heating or Cooling) and Logistic Growth models! After February Break we have our last AB Part I MCQ Monday and then we'll talk about L'Hopital's Rule and Indeterminate Forms.

Announcement from the AP Calculus Forum:
FREE! MOOC style AP Review courses at coursera.com only for Calc and Stats at present!

The University of Houston is offering the following FREE courses through Coursera, with start dates of March 17. Registration is currently taking place. Please inform your interested students and colleagues.

Quarter II Weeks 8&9: 1/13-1/24
We started UNIT7: Transcendental Functions! We focused on the derivative of ln(x) and Logarithmic Differentiation. Next week and after Midterm Week, we'll revisit Applications of Derivatives, Applications of Integrals and Variable Separable Differential Equations involving e^x and ln(x).

UNIT 7 Calculus of Transcendental Functions:

Quarter II Week 7: 1/6-1/10
We finished UNIT6: Applications of the AntiDerivative! We focused on Volumes with Known Cross Sections, Arc Length and Surface Area.

Quarter II Week 6: 12/16-12/20
We continued UNIT6: Applications of the AntiDerivative! We focused on Volumes of Revolution with horizontal and vertical strips: Disk, Washer, Shell. Of course, Friday was Calculus Caroling Day!

Quarter II Weeks 4&5: 12/2-12/13
We started UNIT6: Applications of the AntiDerivative! We focused on the Betty Sue problem and the importance of adding a constant C. We talked about horizontal and vertical strips in our Riemann Statements for finding area between curves and Volumes of Revolution.

UNIT 6 Applications of AntiDerivatives:

Quarter II Week 3: 11/25-11/29
This week we continued our discussion of AntiDerivatives by introducing The Fundamental Theorem Parts I and II! We went over a MCQ Monday on Monday and did the Fundamental Theorem on Tuesday. This was a short week due to Thanksgiving, so we had GAMEDAY on Wednesday. Fun was had by all!

Since we were covering Indefinite Integrals this week, we had to do the Betty Sue FRQ and sing the song

Also, next week is December already, so we start practising our preCalculus and Calculus Carols!

Quarter II Week 2: 11/18-11/22
This week we continued our discussion of AntiDerivatives and Riemann Sums! We focused on Scientific Computing. IE: we wrote programs in TI89 BASIC demostrating the Numerical Methods for definite integration: LSUM, RSUM, MSUM, TRAP and SIMP!

Quarter II Week 1: 11/11-11/15
This week was all about AntiDerivatives and Riemann Sums! We talked about Right Riemann Sums as exact limits. Next week we'll have to right some TI89 code! We also started talking about solving Variable Separable Differential Equations.

UNIT 5 AntiDerivatives and Riemann Sums:

Quarter I Week 9: 11/4-11/8
We finally finished with UNIT 4: Application of Differentiation this week. We programmed Newton's Method in TI89-BASIC. We also covered related rates. Next week is all about AntiDerivatives and Reimann Sums!

Quarter I Week 8: 10/28-11/1
We're nearly finished with UNIT 4: Application of Differentiation this week. We programmed Newton's Method in TI89-BASIC. We also started related rates this week.

Quarter I Week 7: 10/21-10/25
We started UNIT 4: Application of Differentiation this week. We started talking about IVT, MVT, Min/Max and Optimization!

UNIT 4 Applications of Derivatives:

Quarter I Week 6: 10/14-10/18
This week we finished UNIT 3 with a discussion of the Chain Rule, Implicit Differentiation, Min/Max and Related Rates.

Quarter I Week 5: 10/07-10/11
Out sick.... However, I did start using DropBox, see above!

Quarter I Week 4: 9/30-10/04
We started UNIT 3 about Differentiation! We derived the Product and Quotient Rules. We did all 6 Trig Rules. We started talking about the Chain Rule.

UNIT 3 Differentiation Rules:

Quarter I Week 3: 9/23-9/27
We finished UNIT 2 with a test! Our last topic concerned the existence of the derivative. BTW, we start with UNIT 2 since UNIT 1 is just a review of PreCalculus. We did a bit of that in 106 and 107 on Conics and Polar Notation.

Quarter I Week 2: 9/16-9/20
We are almost finished with UNIT 2: Continuity and Differentiablility! We demostrated the Power Rule using the Definition of the Derivative as the limit of the Difference Quotient. We even started the Trig Rules!

Quarter I Week 1: 9/9-9/13
AP Calculus BC started with a preCalc review in the form of the topic of Conic Sections! This is a great topic to review Cartesian and Polar Coordinates, as well as some algebra, trig and TI89 usage!

UNIT 2 Limits and Derivatives:

Well, that's all folks!

Sincerely,
A. Jorge Garcia
Applied Math, Physics and CS

Teaching with Technology,
mathforum apcommunity

### Teaching Math 4R: Calculus UNIT3: Derivatives!

Teaching Math 4R:
Calculus UNIT3: Derivatives!

Quarter III Weeks 7&7: 3/24-4/04
We finished UNIT2 of Calculus with the Definition of the Derivative as the limit of the Difference Quotient. We also started UNIT3 about the Product Rule and the Quotient Rule. We had fun on April Fool's day (see video 302). Chain rule in next week!

Quarter III Weeks 5&6: 3/10-3/21
We finished CH3 Rational Functions. I always like to end preCalculus this way as Rational Functions is a rich topic for introducing limits at infinity and limits at a point. Then we started UNIT2 of Calculus with the Definition of the Derivative as the limit of the Difference Quotient.

We already figured out the Power Rule as well as the derivatives of sin(x), cos(x) and exp(x) not to mention 1/x and sqrt(x) which are really Power Rule anyway!

Take a look at our SagePub directory above. We've been using SAGECELL in class a lot lately. I've been saving these cells as worksheets on the Clemson server to share here.

SAGE Calculus UNIT2 Limits:

Quarter III Weeks 3&4: 2/24-3/7
We didn't get much accomplished these past few weeks with all the Snow Days and February Break! We did, nevertheless, get to finish the PreCalc text doing CH3 Rational Functions. We also talked about Linear, Quadratic, Power and Polynomial Functions. I love to end on this topic as its a nice intro to Limits! Next unit starts Calculus! We also started using the SAGECELL server (see video).

SAGE Chapter 3 Rational Functions:

Quarter III Weeks 1&2: 2/3-2/14
We didn't get much accomplished these past few weeks with a Delayed Opening and so many SnowDays of late! We did somehow finish CH4: Polynomials. We talked about Real Roots, Complex Roots and InEqualities. After February Break we'll cover CH3 Rational Functions before starting Calculus!

NOTE TO SELF:
BTW, we had problems scheduling our Midterm this year. I think that next year I'll leave CH5 for after Midterms so we have more time for Review! So, we will cover Chapters 12,11,10,9,4. Then we Review and have an in class Midterm. After Midterm week, we can cover CH5 and CH3 and then Calculus! We can be a bit more SAGE intensive next year too, now that I have all my SAGE worksheets. Maybe we'll try using http://cloud.sagemath.org or http://sagecell.sagemath.org too.

SAGE Chapter 4 Polynomials:

TI83 Chapter 4 Polynomials:

Quarter II Weeks 8&9: 1/13-1/24
We finished Chapter 5 all about Inverse Functions like Exponential and Logarithmic Functions. This week we worked on solving exponential and logarithmic equations as well as real world problems aka word problems and problem solving.

Next week is the last week of the quarter and then we have midterm week. As I look over Quarter II, I find that we had precious little time for SAGE in class. We focused on the basics of SAGE and python during Quarter I. This Quarter, I still used SAGE, but I posted my SAGE WorkSheets on Edmodo after class for those who still wanted to follow along any new topic with SAGE.

Our in class midterm was delayed until the week after midterms. So, there won't be much new here until 2/10/14!

Quarter II Week 7: 1/6-1/10
We continued Chapter 5 all about Inverse Functions like Exponential and Logarithmic Functions. We focused on using exponents to cancel logs and visa versa in order to solve equations!

Quarter II Week 6: 12/16-12/20
We started Chapter 5 all about Inverse Functions like Exponential and Logarithmic Functions. Of course, Friday was PreCalculus Caroling Day!

SAGE Chapter 5 Inverses:

TI83 Chapter 5 Inverses:

Quarter II Weeks 4&5: 12/2-12/13
We finished Chapter 9 all about CIS(theta) and Vectors. We focused the last week or so on dot products and cross products (see below)!

Quarter II Week 3: 11/25-11/29
We started Chapter 9 all about Vectors. Actually, we started with CIS(theta) and Complex Arithmetic! We stuck to reference angles mostly and no tech was harmed in the making of our screencast (as yet). It was a short week due to Thanksgiving. So, we had Take Home Tuesday on CIS(theta) and GAMEDAY on Wednesday. Fun was had by all!

SAGE Chapter 9 Vectors:

TI83 Chapter 9 Vectors:

Quarter II Week 2: 11/18-11/22
We finished Chapter 10 all about Conics. This week we focused on Parametric graphs and Word Problems. Next we will cover CH9 Vectors starting with CIS(theta).

Quarter II Week 1: 11/11-11/15
We continued Chapter 10 all about Conics. This week we focused on Polar graphs. We talked about converting General Form Conics to Polar Form instead on Completing the Square in the case of rotated graphs! Next weeks now is about Parametrics.

Quarter I Week 9: 11/4-11/8
We started Chapter 10 all about Conics. This week we focused on Completing The Square as a method to convert General Form conics into Standard Form Parabolas, Ellipses and Hyperbolas. We also focused on graphing Standard Form Conics without any tech! Next week is about Polar graphs and 2 weeks from now is about Parametrics. We're going to need TI83s or SAGE for that....

SAGE Chapter 10 Conics:

TI83 Chapter 10 Conics:

Quarter I Week 8: 10/28-11/1
We are finished with Chapter 11 about Matrices! We had a test on Friday. We are starting Chapter 10: Conics next week.

Quarter I Week 7: 10/21-10/25
We are almost finished with Chapter 11 about Matrices. This week focused on nonLinear Systems. Then we reviewed solving Linear Systems using Determinants or Matrix Inverses. We even had a preQuiz on Thursday and a Quiz on Friday on Linear Systems. Next week we cover the last topic in CH11: Linear Programming. The preTest this Thursday and Test this Friday will include all the nonLinear and Linear Systems as well as Linear Programming.

Quarter I Week 6: 10/14-10/18
We continued Chapter 11 about Matrices. This week focused on Matrix Arithmetic and Matrix Algebra. First we need to know how to add, subtract, multiply and divide before we can do the Algebra, aka Arithmetic backwards! BTW, we aren't really dividing, we're multiplying by the reciprocal. So, we used reciprocals to solve Matrix Equations.

Quarter I Week 5: 10/07-10/11
Out sick.... However, I did start using DropBox, see above!

Quarter I Week 4: 9/30-10/04
We started Chapter 11 about Matrices this week! We started by reviewing 2x2 Systems Algebraically and Graphically. Then we introduced Guass-Jordan Elimination using Augmented Matrices!

SAGE Chapter 11 Matrices:

TI83 Chapter 11 Matrices:

Quarter I Week 3: 9/23-9/27
We finished CH12 this week with a test! Our last topics included Proof By Induction and The Binomial Expansion Theorem!

Quarter I Week 2: 9/16-9/20
This week we covered Geometric Sequences and Induction! Included below you will find ScreenCasts based on TI83 and SAGE. I also have SmartNotes from the TI83 ScreenCasts as well as SAGE Worksheets for the SAGE ScreenCasts!

Quarter I Week 1: 9/9-9/30:
PreCalculus is all new this year:
(1) My preCalculus for Juniors classes started 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 TI83. The grand experiment this year is to see how well students learn the Math while learning to code in python at the same time!

(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!

I actually have 2 different preCalculus classes. PreCalculus 4R and preCalculus 4H cover the same material and is comprised mostly of Juniors. The difference between these to groups is that 4R takes AP Calculus AB next year and 4H takes AP Calculus BC. Also, we cover material a little more in-depth for the 4H student and our tests may be a bit more challenging.

SAGE Chapter 12 Sequences:

TI83 Chapter 12 Sequences:

Well, that's all folks!

Sincerely,
A. Jorge Garcia
Applied Math, Physics and CS

Teaching with Technology,
mathforum apcommunity

### Teaching AP CompSci: More CH8/LAB7 Arrays!

Teaching AP CompSci:
More CH8/LAB7 Arrays!

Quarter III Weeks 7&8: 3/24-4/04
We're about finished with LAB7 about static arrays, ArrayLists, 1D and 2D arrays and the for each loop. We'll finish this up next week, the week before April Break. The week after break we'll do a short lab on Recursion. Then we have to finish GridWorld the following week. We won't have a lot of time for review since the week after is the AP Exam already!

new LAB7:

Quarter III Weeks 5&6: 3/10-3/21
We finished LAB6 about for, while and do loops. We started LAB7 about static arrays, ArrayLists, 1D and 2D arrays and the for each loop. New ScreenCasts are coming soon!

old LAB7:

Quarter III Weeks 3&4: 2/24-3/7
I'm only posting every 2 weeks lately as we've had so many Snow Days plus February Break, so we haven't been able to cover a lot of material. We did finish GridWorld Part II and we did start CH7/LAB6 Iteration!

new LAB6:

Quarter III Weeks 1&2: 2/3-2/14
OK, we finally got around to starting GridWorld! We did all the readings and questions in Parts I&II. We started the exercises at the end of Part II on p13. After February Break we'll finish these exercises and start CH7/Lab6 Iteration!

Here's a free MOOC at udacity.com based on the Computer Science textbook by Cay Horstmann from San Jose State U. My students have covered the equivalent of Lessons 1-5 (Intro, Objects, Classes, Types, Decissions) already. So, I told them to try these on their own as a review
They could probably skip the Video Lessons and try the Problem Sets which give plenty of feedback in the case of errors.

We did some of Lessons 8&9 (More Classes, Interfaces and Inheritance). But I told my students not to try these on their own yet as about half of these Problem Sets are based on Lessons 6&7.

I'm covering GridWorld right now, but there's nothing on GridWorld, I'm afraid!

After GridWorld we are doing the equivalent to Lessons 6&7 (Loops, Arrays). I told my students that, if they want a head start, they could watch these Video Lessons!

GridWorld Parts I&II:

Quarter II Weeks 8&9: 1/13-1/24
We finished CH5 this week about Conditional Statements, Boolean Expressions and Predicate Methods. In fact, we went a bit nuts this last couple of weeks or so on Line.java, C5X15. This project was about abstracting a line of the form y=mx+b by encapsulating m and b. The lab question wanted us to write isParallel(Line other), intersects(Line other) and equals(Line other) predicates. I went ahead and extended the Object class by overriding equals(Object other) and toString(). I even implemented the Comparable interface with the compareTo(Line other) method. So, we started talking about Inheritance and Polymorphism. The project also asked us to overload the constructors: Line(m,b), Line(m,x1,y1) and Line(x1,y1,x2,y2) with out rewriting code. We also added graphics! Next week is the last week before midterms, so the students can finish their labs and hand them in by Friday. I think we'll start GridWorld soon after midterms.

Finishing new LAB5, Line.java:

Quarter II Week 7: 1/6-1/10
We continued CH5 this week about Conditional Statements, Boolean Expressions and Predicate Methods. We even started talking about OOPs concepts such as ReUsable Code, Extending the Object Class and Implementing the Comparable Interface! YouTubes on these OOPs topics are still in the works.

Oh, apparently, this is what we do between periods before AP CompSci:

Quarter II Week 6: 12/16-12/20
We continued CH5 this week about Conditional Statements, Boolean Expressions and Predicate Methods. We also finished Number Systems and Chip Logic! I did the #HourOfCode again on Monday as an in school field trip for our Honors 9th Grade Math classes to advertise AP Computer Science. Due to budgetary constraints, we're not offering an intro CompSci course anymore. So, Honors 9th and 10th Graders won't have that option anymore. Friday was, of course, GAMEDAY!

Quarter II Weeks 4&5: 12/2-12/13
We started CH5 this week about Conditional Statements, Boolean Expressions and Predicate Methods. We also finished Number Systems and Chip Logic!

Chip Logic:

new LAB5:

Quarter II Week 3: 11/25-11/29
We finally finished CH4 this week. We have Take Home 4 due this Tuesday. We printed Lab 4. This was a short week due to Thanksgiving, so that's about it! Next week we'll start CH6+Lab5 on Conditional Statements. Of course, Wednesday was GAMEDAY!

Quarter II Week 2: 11/18-11/22
We continued CH4 this week. We went nuts with "Can you name that number?" aka Number Systems. We converted to Base 10. We converted from Base 10. We counted, added and subtracted in various bases: BIN, OCT, HEX. See ScreenCasts below!

Quarter II Week 1: 11/11-11/15
We continued CH4 this week. We also continued "Numeral of the Day!" aka "Can you name that number?" For example, 111BIN, 222TRI, 777OCT and FFFHEX=? We wrote several classes where finals were useful such as the CashRegister class which had public static final double QUARTER_VALUE=0.25 listed after the private instance fields. We also dealt with various forms of input from main: JOptionPane, Scanner and args[0]. When using JOptionPane and args[0] we had to use Double.parseDouble() or Integer.parseInt() quite a bit!

Quarter I Week 9: 11/4-11/8
We started CH4 this week about the differences between byte, short, int, long, boolean, char, float, double variables and finals. We also started "Numeral of the Day!"

Number Systems:

new LAB4:

Quarter I Week 8: 10/28-11/1
We finished Lab3 which talks about writing your own classes from scratch. Our first TakeHome Tuesday on this chapter is due next week!

Quarter I Week 7: 10/21-10/25
We continued Lab3 which talks about writing your own classes from scratch. We are doing the end of chapter exercises as labs. We do the odds together so I can model new concepts. I am rerecording the odd exercises  as ScreenCasts for YouTube. The students complete the evens as labwork in groups. New Lab1 ScreenCasts are done. New Lab2 ScreenCasts are almost done. Sorry, there's no new ScreenCasts for Lab 3 yet. I have a link to my old Lab3 ScreenCasts. See my DropBox link for all our code so far. See links below.

Quarter I Week 6: 10/14-10/18
We started Lab3 which talks about writing your own classes from scratch. We have to come up with our own Contructors, Accessors and Mutators for the first time. We also discussed Abstraction and Encapsulation! Sorry, there's no ScreenCasts for Lab 3 yet.

old LAB3:

Quarter I Week 5: 10/07-10/11
Out sick.... However, I did start using DropBox and I added some screencasts for Lab 2, see above!

Quarter I Week 4: 9/30-10/4
This week we finished Lab2 by introducing the StdDraw class from Princeton's CS101 course. Here we used Object Based Programming to draw Rectangles, Ellipses and Lines! See all the code linked below from my PasteBin account (last link). I've also been redoing my ScreenCasts in the APCS Shorts playlist on my YouTube channel (see below too)!

Quarter I Week 3: 9/23-9/27
This week we started Lab2 based on Chapter 2. In this chapter we discuss constructing objects from existing classes: Rectangle, Color, Random and String. We started talking about Constructors, Accessors and Mutators as well a Private Instance Fields. I'm reworking the ScreenCasts as short summaries after class. I have a new playlist (see below) with only HelloWorld so far.

new LAB2:

Quarter I Week 2: 9/16-9/20
We had a good week this week! We finished Lab1 based on Chapter 1 Exercises 1-8 (see Code and ScreenCasts below). We basically covered everything you ever wanted to know about main() methods and println()! We just started talking about Chapter 2 and Lab 2, Object Based Programming (using existing classes, constructors, objects, accessors) at the end of the week.

Our networking and various hardware issues are all corrected now (except the HP Color LaserJet is still down). My networking issues required setting up a static IP on the SmartBoard or Teacher PC. So, I have access to all my sites at school, finally!

dns: 10.1.1.19
proxy: NONE! (was 10.0.0.125)

There's a bit of lag on the LAN. So, I think I'll make Static IPs for the students too as there may be a DHCP conflict. However, the student stations are required to have the proxy.

Also, most students can access the ssh server from home. Some of us have Linux running at home which makes accessing java files the same as in class. Some students are logging in using putty from WIN but cannot use GUI applications from home (WIN graphics engine does not recognize the LIN graphics engine). Some have Mac at home and find that the MAC terminal works just like the Linux terminal at home including GUI ssh tunnels using: "ssh -Y userid@173.251.48.56"

Quarter I Week 1: 9/9-9/13
APCS had a slow start this year with a lot of networking and server issues. I think we're up to snuff now. We're in Chapter 1 of Cay Horstmann's fabulous text. All we did was write serveral versions of HelloWorld. This is a fine way to become familiar with our Linux based system.

We talked about how to use our server from home using putty in Windows or a terminal in Mac and Linux land.

We also talked about CLI vs GUI, ASCII and Unicode, SSH vs FTP, javac vs java, etc. We also talked about the importance of comments and self-documenting code!

What's new this year is that I'm trying to stick to a CLI for coding in java all day every day! All we need is a shell or terminal to run javac, java and a text editor. This way we call login from home and do our work the same way we do in class even from a Mac terminal or by using putty in Windows!

new HelloWorld:

new LAB1:

Well, that's all folks!

Sincerely,

A. Jorge Garcia
Applied Math, Physics and CS

Teaching with Technology,