Showing posts with label 4R-2016. Show all posts
Showing posts with label 4R-2016. Show all posts

Tuesday, June 27, 2017

preCalculus 2016-2017: Final Review, Final Exam, Game Day! (June)

preCalculus 2016-2017:
Final Review, Final Exam, Game Day!
(June)

Bye Bye Period 4 preCalc, U will b missed!

Bye Bye Period 9 preCalc, Have a great Summer!

Final Review!
We had Part01 and Part02 of the Final in-class. The Midterm already covered Trig, Vector and Polar Notation, Conics, Matrices and Series. The Final emphasized Polynomial, Exponential and Rational Functions, Limits, Derivatives and Integrals. Below you will find a number of ScreenCasts reviewing all these topics. Above you will find class pictures taken the last day of school on Game Day after the Final! Hope you guys learned alot. Have a great summer and good luck next year!

Final Review preCalculus 2017!


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Sunday, May 21, 2017

preCalculus 2016-2017: 8 Week Calculus Crash Course (May)

preCalculus 2016-2017:
8 Week Calculus Crash Course
(May)





Calculus Units 2,3 & 5!
As you can see above, my Calculus Crash Course starts with CH03 Rational Functions (2 weeks) about Limits. This is actually the last chapter we cover in the preCalculus text. I add the concept of Limits at a Point and Limits at Infinity when graphing Rational Functions. When we talk about horizontal, slant and non-linear asymptotes, we are really talking about Limits at Infinity. When we talk about vertical asymptotes and holes in the graph, we are really talking about Limits at a Point. 

UNIT02 (2 weeks) is from my Calculus class. Here we extend the idea of Limits at a Point to finding the limiting slope of a secant line as it approaches a tangent line. Then we introduce limits involving the Difference Quotient! We also talk about continuity and differentiability.

UNIT03 (2 weeks) is all about developing and applying the algebraic rules for derivatives: Power Rule, Trig Rules, Product Rule, Quotient Rule and Chain Rule. If we have time, we even touch on part of UNIT04 about Implicit Differentiation and Related Rates!

UNIT05 (2 weeks) is about AntiDerivitives. We first work with AntiDerivatives analytically. Then we play around with Definite Integrals and Reimann Sum estimates. We even write a program for LSUM, RSUM and TRAP when calculating areas with large numbers of rectangles! If we have time, we touch on UNIT06 and Volumes of Revolution! 

I don't do UNIT01 as it's preCalculus review! We don't really do justice to UNIT04 (applications of derivatives) nor do we have a lot of time for UNIT06 (applications of antiderivatives). Hopefully, my students will take a full semester of Calculus in college next year or a full year in High School and get a lot more practice with these concepts. However, my 8 week crash course is a good introduction to the concepts of Calculus! We barely scratch the surface, but my students could probably pass the AP Calculus AB exam if it were given in June!


YouTube Wednesday: SymphomyOfScience!



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Saturday, April 29, 2017

preCalculus 2016-2017: Polynomials & Rational Functions (April)

preCalculus 2016-2017:
Polynomials & Rational Functions
(April)



CHAPTERS 3&4
Wow, we finished preCalculus! We're starting Calculus soon, stay tuned. We did Chapter 4 about polynomial factoring first. Then we did Chapter 3 about Rational functions. I like to end the course this way as a warm up to Calculus. I get to start talking about limits at a point (holes and vertical asymptotes) and limits at infinity (horizontal asymptotes) before we actually start doing Calculus with the limit of the Difference Quotient! 

 BTW, if I had my druthers, I'd do the whole course backwards starting with Chapter 12 about Sequences and Series. That's a great way to start if you are using a Computer Algebra System like SAGE (like Mathematica but based on lists and python) or Octave (like MATLAB based on arrays). I've done that in prior years, I may do that next year with some extra python coding!
YouTube Wednesday: What is Apophis?









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Wednesday, March 29, 2017

preCalculus 2016-2017: Conic Sections (March)

preCalculus 2016-2017:
Conic Sections
(March)


CHAPTER10
Chapter 10 was great fun. It was about Conic Sections! We learned about the graphs of Parabolas, Ellipses and Ellipses in General Form and in Standard Form. We played with planet orbits and whisper gardens. We found out about degenerate conics and used polar notation to graph Twisted Conics too!
YouTube Wednesday: Was it Archimedes?











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Sunday, February 26, 2017

preCalculus 2016-2017: Matrices & Linear Programming (February)

preCalculus 2016-2017:
Matrices & Linear Programming
(February)


CHAPTER11
In this chapter we talked about how to add, subtract and multiply matrices! We even talked about division via multiplication by inverse matrices. We solved systems of linear equations using Guass-Jordan Elimination, Cramer's Rule and Matrix Algebra. We even talked about the simple case of John Nash's Theorem: Linear Programming.

YouTube Wednesday: Antikythera on Nova!

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Sunday, January 29, 2017

preCalculus 2016-2017: Exponential & Logarithmic Functions (January)

preCalculus 2016-2017:
Exponential & Logarithmic Functions
(January)


CHAPTER5
This chapter was all inverse functions. We focused on Exponential and Logarithmic functions and their properties. We talked about graphing these functions and their transformations. We used inverse functions to solve equations. Then we had Midterm Review and in-class Midterms!

YouTube Wednesday: Fractals on Nova!

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Wednesday, December 28, 2016

preCalculus 2016-2017: Sequences & Series (December)

preCalculus 2016-2017:
Sequences & Series
(December)


CHAPTER12
This chapter was all about Sequences and Series! We talked about summing Arithmetic and Geometric sequences analytically and graphically! We derived the formula for finite Arithmetic and Geometric Series as well as infinite Geometric Series. We graphed sequences and sequences of partial sums using Sequence Mode on the TI-84C. We played around with Pascal's Triangle, Binomial Expansion Theorem and Binomial Probability Distributions. We even looked at Recursively Defined Sequences modeling Annuities and Mortgages!

YouTube Wednesday: Fractals on Nova!

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Monday, November 28, 2016

preCalculus 2016-2017: Vector & Polar Notaion (November)

preCalculus 2016-2017:
Vector & Polar Notaion
(November)


CHAPTER09
This chapter was all about using the Trig we learned in chapters 6-8 in order to talk about vector and polar notation! We started with some Polar Graphs. Then we talked about Complex Numbers as Vectors on the Complex Plane. Last, but not least, we played with Vector Arithmetic in 2D and 3D. We worked with sums, differences, dot products and cross products too. Please see the YouTube Playlist above.

YouTube Wednesday: Mathematicious!

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Saturday, October 29, 2016

preCalculus 2016-2017: More Trigonometry (October)

preCalculus 2016-2017:
More Trigonometry
(October)

Chapter 7 ScreenCasts
We were still finishing up some loose ends in chapter 7 talking about Proving Identities vs. Solving Equations. We graphed y=sec(x), y=csc(x), y=cot(x) and their transformations. We learned about the inverse trig functions arcsin(x), arccos(x) and arctan(x) and how to use inverse functions to solve equations.


 Chapter 8 ScreenCasts
We also covered Chapter 8 about Law of Sines and Cosines. We talked about completing triangles, navigation, triangle areas, Heron's Formula and even Simple Harmonic Motion!

Grace Hopper YouTube Wednesday 10/12/16



Grace Hopper YouTube Wednesday 10/26/16


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Well, that's all folks,
A. Jorge Garcia
Applied Math, Physics and CS
2017 NYS Secondary Math PAEMST Nominee


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Monday, September 26, 2016

preCalculus 2016-2017: Trigonometry (September)

preCalculus 2016-2017:
Trigonometry 
(September)
We are currently reviewing all of Trigonometry! September was all about CH06: Unit Circle and Trig Graphs plus UNIT07: Trig Identities and Equations. We start with Trigonometry because some students didn't take Algebra 2 and Trig last year. CC Algebra II does not have a lot of Trig.

This year I'm trying something new:
MCQ Mondays,
TakeHome Tuesdays,
YouTube Wednesdays,
ThinkPairShareThursdays,
FRQ Fridays.

MCQ Mondays will start in October. Even months we will do practice MCQ Exams using Formative Assessments via Socrative. On odd months we will have actual Mock MCQ Exams as Summative Assessments.

TakeHome Tuesday is when I collect TakeHome Exams. Most tests will be TakeHomes given on Friday and collected on Tuesday.

YouTube Wednesday is infamous for STEAM related Filks as well as month long Documentaries from National Geographic or Nova on PBS.

ThinkPairShare Thursday is when the students get into groups of 2 or 3 with a WhiteBoard to review HomeWork questions they had trouble with.

FRQ Fridays occur at the end of every 2-3 week unit. On Friday I give a preTEST review sheet. We go over it using ThinkPairShare again. The real TEST, similar to the preTEST, is then given at the end of the period as a TakeHome Exam due the following Tuesday.

Chapter 6 ScreenCasts
We talked about "SOHCAHTOA East of Java!" In other words, we developed the idea of finding exact values for the sin(x), cos(x), tan(x), sec(x), csc(x) and cot(x) of certain reference angles, in degrees and radians, in all 4 quadrants! We also graphed y=sin(x), y=cos(x), y=tan(x) and their transformations! Last, but not least, we worked with non-Linear Regressions!

Chapter 7 ScreenCasts
Now we talk about Proving Identities vs. Solving Equations. We graphed y=sec(x), y=csc(x), y=cot(x) and their transformations. We learned about the inverse trig functions arcsin(x), arccos(x) and arctan(x) and how to use inverse functions to solve equations.


Tom Lehrer YouTube Wednesday 9/7/16
Tom Lehrer YouTube Wednesday 9/14/16
Tom Lehrer YouTube Wednesday 9/21/16
Tom Lehrer YouTube Wednesday 9/28/16
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Well, that's all folks,
A. Jorge Garcia
Applied Math, Physics and CS
2017 NYS Secondary Math PAEMST Nominee


Sage Ebay
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Friday, September 2, 2016

BSHS 2016-2017 Week 1: Welcome Back!

BSHS 2016-2017 Week 1:
Welcome Back!

It's our first week of classes back from Summer! Tuesday was all about Seating Charts and Book Cards and Syllabi and the Original Sound Track of a A Beautiful Mind playing in the background. I tried posting everything I could on Edmodo so as not to kill trees and have time to start a lesson! PreCalc was amazed by Radian Mode. AP Calc was floored by 2-Sided Limits. AP CompSci managed to log into the server from class, begin HelloWorld.java and login from home via TeamViewer!
Wednesday was our first YouTube Wednesday. Of course, we had to start with Tom Lehrer's New Math with an explanation of base 8 numbers and positional arithmetic!
Thursday was a regular day of class but we did celebrate Star Trek Day 9/8/16. This day marks the 50th anniversary of the live broadcast of the first ever Star Trek episode on NBC at 8:30 pm! I am told that I saw it live when I was 4 years old....
I know it's not YouTube Wednesday, but Friday I had to start with the "Frozen PreCalc" Filk by one of my students. She wrote this filk to show that even though you may struggle at first in this class, there is hope if you work at it!

 OK, here's some of the handouts from the first day:
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Well, that's all folks,
A. Jorge Garcia
Applied Math, Physics and CS
2017 NYS Secondary Math PAEMST Nominee


Sage Ebay
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