## Sunday, January 12, 2014

### Teaching Math 4R: Continuing Chapter 5 Inverse Functions! Quarter II Week 7

Teaching Math 4R:
Chapter 5 Inverse Functions

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,