Summer Learning

Why summer packets? I'm glad you asked. Every summer students lose ground in both reading and mathematics, especially among students in less affluent households. These packets (taken from supplementary materials associated with our Algebra textbook) are to serve as one way we to keep you mentally active over the summer and to help you retain what you have learned. Click the tab for the packet that pertains to you!



In addition, I hope that you all will take advantage of all the web has to offer. I encourage you to start or continue working through the practice exercises at Khan Academy, to watch and work through problems on Brightstorm, to engage the latest and greatest TED videos, or to create a game or animation using Scratch .

I just read this article on why nerds win!

Here is an updated list of what I think is cool on the web as a I discover it. Let me know if you agree or if you thought something I found was particularly interesting.



This is my twitter feed and the #mathchat feed. Yes, I think about education and math all the time and am listening and discussing it all the time! If you like, follow what is recently going on in #mathchat or with me.

The Final Four

We are now in "The Final Four" days of school! Please find the weeks in-class review that we will be doing as well as the links to other study materials available online and on this blog! Please make a study plan and remember to check-in with me during the study sessions being offered after and during school. Special thanks to CCS for their excellent curriculum materials!



Do Nows for the week (with solutions at the end of each tab)!

Systems of Equations (Monday) Quadratics (Tuesday) Polynomials (Wednesday) Rationals (Thursday)

FYI:

Finals Review Packets:

Final Review Packet 1	Final Review Packet 2	Final Review Packet 3

Please remember that on the FINALS tab above I have placed online exams as well as other study aids to help you prepare finals.

In addition, your peers in precalculus have posted sample problems, videos, and presentations that can help you prepare for your final. Check out there website too!

Lastly for finals resources, you have all the video resources posted at BrightStorm and KhanAcademy to help you review the material when you are not with myself or someone else who can review the math with you.

SCRATCH BONUS: Scratch projects are due June 17th. You must send me a link to your scratch e-mail by the end of the school day on June 17th to be considered for credit.

KHAN BONUS: I will check Khan Academy one last time on the 20th of June. You have until then to log in your practice!

Week 39

This is the last week of radical functions and we will be focusing on their graphs (square root and cube root functions only). June 9th we will have our last exam of the quarter!!! Prepare, prepare.




Here is a complete review of radicals with answers at the end for your perusal (will be worked on in class Wednesday)



Blank Guided Notes (special thanks to CCS):











Reference Sheet:


Videos:
*Khan Academy Videos
Simplifying Radical Expressions 1
Simplifying Radical Expressions 2
Simplifying Radical Expressions 3
Solving Radical Equations 1
Solving Radical Equations 2
Solving Radical Equations 3
*Brightstorm Videos
Roots and Radicals (set of videos)

Homework: (odd answers at end of document!)

Week 37-38

Our build up to radical functions continues with an exploration of operations with radical expressions as well as how to solve radical equations algebraically. Please find a copy of the guided notes as well as the current smartboard snapshots of the completed notes. IF anybody can tell me what this picture is demonstrating I will give you mega bonus!

Blank Guided Notes (special thanks to CCS):









Reference Sheet:


Videos:
*Khan Academy Videos
Simplifying Radical Expressions 1
Simplifying Radical Expressions 2
Simplifying Radical Expressions 3
Solving Radical Equations 1
Solving Radical Equations 2
Solving Radical Equations 3
*Brightstorm Videos
Roots and Radicals (set of videos)

Homework:

Global Studies Layered Assessment LOGO Contest Help: http://skyje.com/2010/03/drawing-tools/

Scratch Project:

Reference Guide	Project Outline

Week 36

Algebra II embarks on a new and what will be our final function, the radical function. It is another example of a function with a restricted domain as well as a different pattern of growth than our family of polynomials. We will work this week on our exponent rules and try to solidify your ability to accurately perform operations with expressions that contain rational exponents. Please find guided notes below as well as relevant videos and online resources. For online practice or general resources please check the tabs at the top of the screen entitled, "online practice" and "online resources". Every week until June 17th, I will post the Scratch project guidelines and a link to a scratch reference guide. This project is available to all juniors for bonus.

Blank Guided Notes (special thanks to CCS):





Reference Sheet:


Videos:
Simplifying Radical Expressions 1
Simplifying Radical Expressions 2
Simplifying Radical Expressions 3


Homework:


Scratch Project:

Reference Guide	Project Outline

Precalculus is reviewing for finals and getting geared up for a strong finish. The link below are some self-practice tests on the topics we covered this year. There are alse paper and pencil tests that have keys as well if you don't want to stay online to take the web-based exams. Also, don't forget about Khan Academy--a good place to review those basic skills.

Practice Exams, 1
Practice Exams, 2
Practice Exams, 3

Week 35

Algebra II will be doing some exploration of rational functions from The College Board. One is intended to review their prior knowledge of rational functions and apply it to solve a problem. The other is a review of polynomials applied to running a business and analyzing profit, revenue, and cost. I hope they enjoy it!! See the graph at right from the Rodale Institute explanation of effective pricing.

As promised, I have included a fourth quarter bonus project that allows interested students to get credit as well as learn some of the basics of computer programming using MIT's Scratch. Here is a on all aspects of the program as well as a wiki hosted by scratch that contains examples for blocks of code. Please find the project outline attached below. If you have any further questions just e-mail me!


Algebra II and Precalculus both have exams on Monday!!! Please take some time this weekend to prepare. Use the information on the blog from previous posts to help guide your studies.

Algebra II review packet:


The homework for this week is solving rational equations, which will help you review all the basic operations involved with rational expressions as well as solve them.


Precalculus is reviewing for finals and getting geared up for a strong finish. The link below are some self-practice tests on the topics we covered this year. There are alse paper and pencil tests that have keys as well if you don't want to stay online to take the web-based exams.

Practice Exams, 1
Practice Exams, 2
Practice Exams, 3

 Here are two previous exams from early in the year to start reviewing!

Week 34

Precalculus will be exploring the law of sines and cosines and working through the ever challenging "ambiguous case" for law of sines. To review trigonometry for the upcoming exam try this online set of tutorials and practice or this set of videos. Let me know if it helps!

Homework with odd answers:*

Bonus:
Khan Academy



Algebra II is moving from operations with rational expressions to solving rational equations. We will again apply all modalities to solve these equations: numeric, graphic, and algebraic. It is important to be able move between these modalities and use each to help you solve the more difficult problems.

Examples for Simplifying Complex Rational Expressions:


Videos of the Week:
Adding and Subtracting Rational Expressions 1
Adding and Subtracting Rational Expressions 2
Adding and Subtracting Rational Expressions 3
Solving Rational Equations 1
Solving Rational Equations 2
Solving Rational Equations 3

Reference Sheets:



Homework* with odd answers:



*Modified from University of Houston

Week 33

First and foremost, have a great Spring Break. I know I will.

Secondly, take this extended time to do some work on Khan Academy. It is an excellent tool for you to practice and prepare for finals. In addition, you can take your math skills to new heights and new topics. Enjoy.

Algebra II is moving into basic operations with rational functions. As always, the basics of multiplication, division, addition, and subtraction of fractions comes back to haunt us all. I think the reference sheet for this one could be of real help to keep you organized, focused, and always pointed in the right direction.






Reference Sheet:


Completed Notes on Adding and Subtracting Rational Expressions:


Operations with Rational Expressions Videos:
Multiplying and Dividing Rational Expressions 1
Multiplying and Dividing Rational Expressions 2
Multiplying and Dividing Rational Expressions 3
Adding and Subtracting Rational Expressions 1
Adding and Subtracting Rational Expressions 2
Adding and Subtracting Rational Expressions 3


Homework (with odd solutions):

Final Review Packets:



Precalculus will graph the other 4 trigonometric functions with all their pecularities and nuances. I highly recommend watching some of the videos I have posted below. Remember to pause and rewatch them to get a true idea of how these functions behave.

Cosecant	Secant	Cotangent

Graphing Trigonometric Functions Videos:
Graphs of Trig Functions
Graphing Trig Functions
More Trig Graphs
Determining an equation of a trig graph

Homework:


Final Review Packets:

Week 32

Algebra 2 finalizes their investigation and construction of the graphs of rational functions. It is absolutely essential to make the connection between the algebraic manipulations and understandings of these functions and their graphs. I will be away from school both Thursday and Friday of next week trying to learn how to better use the SmartBoard (you know I need that). Remember to take advantage of the exercise practice at www.khanacademy.org. Please find a rather complicated rational function below. The steps to graphing it can be found here.

Graphing Rational Functions Powerpoint:


Operations with Rational Expressions Guided Notes:



Reference Sheets:




Rational Function Videos:
Asymptotes of Rational Functions
Rational Function Example
Another Rational Function Example!


Homework with odd solutions:


Final Review Packets:



Precalculus is going to continue with sine and cosine functions in the attempt at mastering all the different transformations that result in changes in amplitude, vertical shift, phase shift and period. The change in one parameter, amplitude, is captured in the image below:

Applet:
Transformations of sine functions



Khan Academy videos:
Graphs of trigonometric functions
More graphs of trig functions!

Precalculus Homework:


Final Review Packets:

Week 31

Fourth Quarter is now here. Your grade from the first three quarters cannot be changed--the only thing you can control, as a student, is your grade fourth quarter. Please, scholars, do thy best to finish strong. A great way to keep your basic skills up as we move through fourth quarter and prepare thyself for finals is to login at www.khanacademy.org and keep marching through the exercises.

*For Parents: I added an e-mail subscription to the sidebar so that you can receive an e-mail everytime the blog is updated. Just type your e-mail in and follow the steps that follow. It should take about 20 seconds.

Algebra II begins rational functions, which are graphically somewhat different than previous functions, but they nevertheless require a great deal of the skills we have been building all year. Factoring fun will remain a large part of our life. Here are two graphical examples of rational functions:


To explore the graphs of rational functions try this applet.

Videos:
Rational Expressions and Functions, part I
Rational Expressions and Functions, part II

Rational Functions Blank Note Guide and Graphing Powerpoint:



Reference Sheet:




Homework:


Saturday School:


Precalculus is ending the year with a bang. We are investigating the graphs of the six trigonometric functions and the unique types of behavior they can model. The coming week we will start with graphing sin(x), cos(x), and possibly tan(x). We will be relying on a curriculum that can be found online here. Here is a graph of sin(x):

To explore transformations of sine functions try this applet.

Videos:
Trigonometry Videos

Homework:


Saturday School:

Week 30

The Abel prize was awarded last week to John Milnor for his work in topology. It is an annual prize that recognizes innovative thinkers in mathematics and comes with a $1,000,000 award. The two-dimensional picture of a seven-dimensional sphere below demonstrates some of the work for which Milnor was recognized.

Algebra II's month long journey deep into the heart of polynomials is coming to an end this Thursday. Please find the test review posted below. We will be completing this in class on Tuesday and Wednesday--answers are at the end of this document! The exam will be answering some essential questions about polynomials, which will only be posted here for your perusal--start thinking.

1. How many max's or min's could an even degrees polynomial have? How few can it have?
2. Could a polynomial have two max's, but no local minimums?
3. If a polynomial has two max's and two min's, can it be of odd degree? can it be of even degree?
4. Can a polynomial have local max's or min's without having any real zeros?
5. Why must every polynomial of odd degree have at least one real zero?
6. Can a polynomial have two distinct real zeros and no local max's or min's?
7. Can an x-intercept yield a local max or min? Can it yield an absolute max or min?
8. If the y-intercept yields is the lowest point the polynomial reaches, what can we say about the degree of the polynomial and the sign of the leading coefficient?

Test Review

Homework:

Saturday School 5.2:

Precalculus will finish with solving trigonometric equations and have an exam over basic trig identities, the unit circle, and trigonometric equations! The homework is short this week, but be diligent. Exam Thursday!!

__________________________________________________________
BONUS ASSIGNMENT FOR ALL-
Step 1: Go to www.khanacademy.org
Step 2: Login with a gmail account or a facebook account
Step 3: Once your logged in, at the bottom of the screen is a link to "Add a Coach"--click it!
Step 4. Add me as your coach! My ID is my e-mail address is darren.burris@gmail.com
Start with addition and advance!

Week 29

Algebra II will begin to reverse the flow on polynomials. We have been driving from the algebraic to the graphic, and now we will start with the graphic and drive toward the algebraic. It should be both fascinating and mind-blowing. Here is the summary of the week in two pages!


BTW: Answers for

We will continue to plough through our guided notes. I have placed the notes from the previous weeks below.
Blank Note Guide:

Completed Note Guides:












Polynomial Notes Supplement:
Polynomial Note Guide, part 14 (this week)

Polynomial Note Guide, part 15 (this week)


Homework with odd answers:


__________________________________________________________
Precalculus will do a brief unit on trigonometric identities before heading into trigonometric ratios as functions. Please don't forget the development of the unit circle as we take a slight detour through identities.



Guided Notes:
Trigonometric Identities

Trigonometric Functions

Homework:

__________________________________________________________
BONUS ASSIGNMENT FOR ALL-
Step 1: Go to www.khanacademy.org
Step 2: Login with a gmail account or a facebook account
Step 3: Once your logged in, at the bottom of the screen is a link to "Add a Coach"--click it!
Step 4. Add me as your coach! My ID is my e-mail address is darren.burris@gmail.com
Start with addition and advance!

Week 28

Algebra II will continue investigating polynomials and fully merge the graphical with the algebraic. It should be exciting. Please remember to bring your graphing calculators to class everyday. We are going to rely on them an increasing amount from her to the end of the unit. This coming Thursday we will have an exam in order to break up this large unit a bit. Reference sheets will be able to be used!

Blank Polynomial Notes:


Completed Polynomial Notes from previous weeks:












Polynomial Notes Supplement


Reference Sheets:




Videos on Polynomials
Polynomials, part I
Polynomials, part II
Imaginary Numbers

Algebra II HW with odd answers

_________________________________________________________________

Precalculus will be continuing their work with the unit circle and increasing their level of comfort with it. By the end of next week we will begin to develop the idea of a trigonometric function through our new unit circle informed eyes. It should be awesome, really!
Reflect on the following widget--it is the whole of trigonometry.





Unit Circle Notes:


Trigonometric Identities Notes:


Homework:


Trigonometry Videos:
Trigonometry

BONUS ASSIGNMENT FOR ALL-
Step 1: Go to www.khanacademy.org
Step 2: Login with a gmail account or a facebook account
Step 3: Once your logged in, at the bottom of the screan is a link to "Add a Coach"--click it!
Step 4. Add me as your coach! My ID is my e-mail address is darren.burris@gmail.com
Start with addition and advance!

Week 27

Algebra II will continue with our examination of polynomial functions, and start to integrate the algebraic, tabular/numeric, and graphical dimensions more directly. Please find a two summary documents on polynomials below that will help us structure the conversation in a concise user-friendly way.

Factoring a Polynomial Using its Graph


Finding Zeros of Polynomials


Polynomial Guided Notes:


Completed Polynomial Notes in the previous week:








Completed Polynomial Notes for this week:
Polynomial Note Guide, part 9

Polynomial Note Guide, part 10

Polynomial Note Guide, part 11


Homework with odd answers:


Saturday School work:


Links to videos on Polynomials
Polynomials, Part I
Polynomials, Part II
_________________________________________________________________

Precalculus will start to build the unit circle and develop their concept of trigonometric ratios beyond that of 180 degrees. This will serve as the building block for our transition to trigonometric functions.

Unit Circle Exact Values

function	sincostancscsecantcot
angle
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Radians, arc length, and the area of a sector:


Central angles, arcs, and angular velocity


Unit Circle Notes:


Precalculus HW:


Precalculus Saturday School:


Precalculus videos on TRIGONOMETRY

Week 26

Algebra II will continue to dig deeper into polynomials and head directly in to synthetic division and an introduction to both the Factor Theorem and the Remainder Theorem. While this will seem "difficult" and "new" it is only a restatement of how division fundamentally works only with variables. So, consider it a return to 5th and 6th grade when you first explored division and apply what you learned then to what you are learning now! I have included reference sheets that summarize much of the concepts in order to focus your attention on the most important skills.

Polynomial Guided Notes:


Completed Polynomial Notes in the previous week:






Polynomial Note Guide, part 7

Polynomial Note Guide, part 8


Reference Sheets:
Factoring

Quadratic Formula and Completing the Square:


Friday HW CP:

Friday HW H:


Precalculus will continue to lay the foundations of trigonometry by returning to special right triangles and the six trigonometric ratios they learned in Geometry. We will begin to build the unit circle by the end of the week. Here are the notes that will enable you to engage the homework and which we will review at the beginning of the week.

Special Right Triangls and the Six Trigonometric Ratios:

Radians Arc Length, and the Area of a Sector


Homework:

Week 25

Algebra II has started to delve into the vast topic of polynomials and have been reviewing the basic skills associated with them (operations, substitution, and classification). We will start to move into more unchartered waters as we look at their behavior graphically as well as continue to emphasize and develop the skill of factoring. It is crucial during our investigation of polynomials that students become increasingly comfortable with their graphing calculators and its capabilities. Please find the guided notes we started last week below as well as the portions we have already completed below. Reference sheets and homework are also found below--become comfortable with those reference sheets and how you can use them to help you navigate this topic.

Guided Notes:


Complete Guided Notes:
Part 1

Part 2

Part 3

Part 4

Part 5

Part 6


Reference Sheets:
Factoring, Completing the Square, and the Quadratic Formula

Factoring Flow Diagram:

Polynomial Graphical and Algebraic Behavior:


Homework:


Videos:
Polynomial Videos

Precalculus is heading into Trigonometry! We will start with trigonometry as you have already engaged it in Geometry and begin to extend into the arena of functions and periodic behavior. It will be a long road that will extend across the entire third quarter so it is important to get the foundational concepts early so that as the develop and become more complex you will find it much easier! Please find notes, homework, and videos below!

Notes:


Homework:


Videos:
Trigonometric Functions

Week 24

Everyone is back! Third quarter is in full swing and you all currently have a clean slate.

Please find the lengthy Algebra II guided notes attached below. I will, as we complete it in class, post the completed version online as well. These notes will serve as the backbone of the coming weeks and hopefully will give you the ability to both review what we are doing as well as preview what is coming up (The guided notes come from Mrs. Brown at Carmel High School--Thank you!) I will also post a link to videos that deal with all aspects of polynomials so that you can progress through the next few weeks with other voices on these topics.

Guided Notes:


Complete Guided Notes:
Part 1

Part 2

Part 3

Part 4


Homework:


Polynomial Videos

Algebra II Honors is wrapping up conic sections! I'm sure everyone is happy about that. Please find next weeks homework below:

Homework:


Precalculus is wrapping up exponential and Logarithmic functions! Please find the application problem set and test review below. We will be doing a great deal of application problems over the next few weeks, so get prepared.

Application Problem Packet:


Test Review Packet:


Exponential and Logarithmic Functions Videos

Week 23

The juniors will be preoccupied with more midterms (due to the snow days) and finalizing their internship presentations. Good luck with both of them.

Algebra II Honors will complete the brief adventure into conic sections and be examined on them Friday. The final conic section to be explored is the Hyperbola. The powerpoint and hyperbola problem set can be found below.

Powerpoint:


Hyperbola Problem Set:


Precalculus will continue their exploration of exponential and logarithmic functions and move toward applications of them in real-world contexts. Banking and biology will be our primary focus for applications of these two functions.

Applications Problem Set:

Week 22

Precalculus Quiz


Algebra II


Snow everywhere and no Saturday School, except for those who checked here! Please find both Precalculus Saturday school work as well as Algebra II work for those qualifying for normal Saturday School--Turn it in Monday!!!
Precalculus Saturday School Work:
\
Algebra II Saturday School Work:


As for those of you who have stopped in for a midterm review of sorts, I haven't got too much yet for my precalc humans, but you can start with visiting the Saturday school work above. For the Algebra II students, I have a couple things to help you below. Good Luck, and remember you always have your books to study as well!

I hope to have more up tomorrow, but Clara and Gwen are calling.

Week 21

Honors Algebra 2 will continue their exploration of conic sections and branch out to include both the ellipse and the hyperbola. It will be important to develop a critical eye to the differences and similarities between the conic sections.

Ellipse Powerpoint:

Ellipse Examples:


Hyperbola Powerpoint:

Hyperbola Examples:


Problem Sets:


Precalculus will continue with logarithms and begin solving exponential equations using logarithms and vice versa. We will continue to review basic properties and continual return to the graphs of both of these functions.

Solving Powerpoint:


Problem Set:

Problem Set Solutions:

Weekend Quiz

Below is the quiz that I have assigned for 12th grade and 9th grade over the weekend of January 15 and 16th. Enjoy.

Week 20

SNOW INFORMATION!
Due to the snow day on Thursday, Janurary 13th, the following will happen:
Friday, 1/14: English and Math midterms (dismissal 2:00)
Internships for two weeks
Monday, 1/31: A day of review
Tuesday, 2/1: History and French midterms (dismissal at 2:00)
Wednesday, 2/2: NO school (conferences)
Thursday, 2/3: Biology midterm in the morning, normal classes following

Junior Midterms is the big ticket item for the week!
Below are some video links to help you review some old or forgotten concepts as well as some old midterms for your perusal. The first embedded midterm file has answers at the end! Study, study, study!

Three old midterms (remember, they have some differences so focus on the linear and quadratic equations!):




Videos:
Linear Equations Overview
Systems of Linear Equations
Factoring
Quadratic Equations
Functions

Don't forget the links to the right titled "Math Links for Students" they are all websites that explain all the mathematical content we have covered!

Algebra II Honors is exploring conic sections and is struggling through the linkage between coordinate geometry and algebraic representations. Nevertheless, parabolas will continue on Thursday and Ellipses will emerge on Friday!

Here is a link to videos on conic sections.

Here is another link to parabolas (they are proving difficulty, eh?).

Precalculus is exploring the properties of logarithms and are working toward mastery of evaluating, condensing, and expanding them.
Here is a link to videos on exponential and logarithmic functions.

Week 19

Professional Development Day:
The start of our first week back from break begins with all your fantastic teachers preparing for the second half of the year. Unbeknown to many students is the fact that we, teachers, are constantly trying to improve what we do everyday, and here is the kicker, we are trying to improve to help you! So, on Monday, each teacher will try to improve, edit, and/or ponder what they do for YOU.

One group of teachers are going to look at blogs, clickers, and bloom's digital taxonomy. Here is the blogging powerpoint to be shared with teachers, but blogs are also a tool for students as well. Maybe one of you will start a blog?



Here is the link to a glogster version of bloom's taxonomy.

Lastly, here is a "pipe" I constructed to sort feeds on charter news (still a work in progress). Click here.
_____________________________________________________________________

Algebra II CP will be preparing for midterms next week and will focus on function notation for the early part of this week and transition to our set of familiar functions.



The best and easiest review is to return to the previous mammoth homework! Here it is again for you!



Honors Algebra II will be heading into conics in a fast and furious fashion and will start with the most fundamental of the conics, the circle. This will be an entirely new conceptual space given that circles (and nearly all the other conics) are not functional relationships.

Distance and Midpoint Powerpoint:


Circles Powerpoint:


Precalculus will be returning to and expanding upon their ability to interpret the relationship between the formal eqaution of an exponential function and its graph. After firming up our basic understanding of exponential behavior we will redefine exponents using logarithms.

Exponential Functions Powerpoint:


Classwork Exponential Functions Problem Set:


Logarithms Powerpoint:


Logarithms Problem Set due January 14th: