Polynomials

Higher Order Polynomial
https://www.desmos.com/calculator/1jrm9svty1

Polynomials from Constants to x^5
https://www.desmos.com/calculator/ve1lwttlmo

The broad family of functions called polynomials allows us to investigate the behavior of functions in depth and hone all previous skill sets we have started to develop.  The graphs above represent polynomials of differing degrees: linear, quadratic, cubic, quartic, quintic, sixth degree, etc.  This unit will serve as a culmination and an extension of what you have already done with linear and quadratic functions.

(Pre)Review Materials:
Here are some of the skills you should have mastered that are available to you on Khan Academy.  Please let me know if you are going to start using this as a way to remediate, review, practice, or push ahead!
Khan Academy Practice workflow sheets:
Creating and Solving Linear Equations
Linear Functions
Systems of Equations and Inequalities
Quadratic functions
Functions

TenMarks Passwords
Period 2 Login Information
Period 5 Login Information

PowerPoint and Guided Notes:
This unit on polynomials will largely develop through two key documents that are both embedded below.  The first is a PowerPoint presentation that provides much of the meat of polynomials and provides you a resource to review and reference as we cover this topic together.

 The second is a set of guided class notes that will walk through some of the skills we will need to work through together.  We will fill this out together as we move through this unit.
Polynomial Videos:
Here is the link to the list all of the Khan Academy videos on Polynomials.  
Below are two more videos that may be helpful to preview or use as review some of the big ideas.


Homework (stay tuned, more to come):

• Homework: Homework Due Friday November 30th are Functions and Function Notation and Quadratic Tasks (from the Dana Center Assessments)

Reference Sheets:

Function Notation and Intrerpretation

After reviewing the basics of linear equations, linear systems of equations and inequalities, and quadratic equations, we are going to step by back and look at the larger idea of function.  Here is Salman Khan's (of Khan Academy) introduction to functions video (you can continue to watch his series on functions by clicking here):
Introduction to functions: An introduction to functions.


Here is the basic presentation of the technical side of functions and function notation that we will be navigating over the next 8-10 days:
Here are the series of conceptual tasks we will be going through over the next week that build the general idea of a function from understanding points to understanding the relationship between two values. Please click on the link below to see or print the class tasks we will be investigating (scaffolded document from Language of Functions and Graphs):
Tasks 1 - 4:  Interpreting Points and Sketching Graphs from Words
Tasks 1 - 4:  Interpreting Functions in Situations

Please find the homework embedded in the folder below:
Homework due Friday November 2nd are the files "Space Station," "Painted Cubes," and "Distance and Time"
Homework due Friday November 9th are the files "Community Park," "Bathing the Dog," "Walking the Yo-Yo," "Extracurricular Activities, and "Nesting Rectangles."
Homework Due Friday November 16th are Tasks 2 and 3 of Interpreting Functions in Situations.
Homework Due Friday November 30th are Functions and Function Notation and Quadratic Tasks (from the Dana Center Assessments)

Basics of Functions Powerpoint:


Those pursuing Khan Academy Practice may reference these workflow sheets based on topics of interest to help you "know" which ones to do!
Creating and Solving Linear Equations
Linear Functions
Systems of Equations and Inequalities
Quadratic functions
Functions

Quadratics!

See at  https://www.desmos.com/calculator/tzgpvgn8p2 

Our next unit will be a brief exploration of quadratics with an emphasis on three things (click each for a short video on the topic):
1. Completing the Square
2. Complex Numbers
3. Applying quadratics to solve geometric problems

Prior Knowledge Alert:
We should be building on the work you have already done in Algebra 1 on quadratics and we will largely assume the following three things (click each for a short video on the topic):
1.  Factoring
2.  Quadratic Formula
3.  Graphing Quadratic Functions

Please find a couple videos that introduce the big concepts from this short unit on quadratics below as well as the presentations, reference sheets, problem sets, and homeworks for the coming weeks.

Here is our collective brainstorm on Linear and Quadratic Functions as well as some factor by grouping and sum and difference of cube examples from class.

Linear-Quadratic Brainstorm Summary
Grouping and Sum and Difference of Cubes Class Examples
Completing the Square Class Examples
Solving Quadratic Equations Class Examples (practice problems with answers)

Homework Due October 19th

Complex Roots from the Quadratic Formula:


Linear, Quadratic, and Exponential Models: Linear, Quadratic, and Exponential Models

Systems of Linear Equations and Inequalities

The first week and a half we reviewed linear functions as tools to model the relationship between two quantities with an emphasis on distance vs. time relationships.  This week we are moving into a brief review systems of linear equations, which will culminate in exploration of linear programming.  The picture at left is an example of what we will eventually will be building, interpreting, and using to solve real-world problems.

Please find a video on systems of equations in three variables below as well as one on systems of inequalities immediately below.  I encourage you to take a moment and critically view them, pausing and re-watching when needed.The documents for our first unit are embedded beneath that, including the next two homework assignments.  

Systems of Three Variables:

Graphical Systems Application Problem:

Linear Programming Example:

Documents from our first unit:

Modeling Linear Functions

The emphasis of Algebra 2 this year will be mathematics and modeling.  Here is a general diagram that overviews the modeling cycle:

Here are some examples of modeling to get you thinking about mathematical models:

• Estimating how much water and food is needed for emergency relief in a devastated city of 3 million people, and how it might be distributed.
• Planning a table tennis tournament for 7 players at a club with 4 tables, where each player plays against each other player.
• Designing the layout of the stalls in a school fair so as to raise as much money as possible.
• Analyzing stopping distance for a car.
• Modeling savings account balance, bacterial colony growth, or investment growth.
• Engaging in critical path analysis, e.g., applied to turnaround of an aircraft at an airport.
• Analyzing risk in situations such as extreme sports, pandemics, and terrorism.
• Relating population statistics to individual predictions.

The first week and a half will be reviewing linear functions as tools to model the relationship between two quantities with an emphasis on distance vs. time relationships.  Please find the syllabus, course overview, and self assessment embedded below.

Documents from our first unit are embedded below:

Please do not forget to complete the following things listed in the syllabus by Friday of this week:

Required Online Registration for the following:

• Create gmail account (or know login and password for existing account)
• Register for Khan Academy with your gmail account and only your gmail account AND add me as your coach using darren.burris@gmail.com
• Complete Student Information Form (click link or it is embedded below)

Summer Packets 2012

Greetings Scholars!
You have likely been out of school a few weeks and are starting to feel a bit rusty with some of your basic math skills . . . Well, you are in luck, because your summer packets are here for your to keep your mathematical skills primed and ready for a successful fall.
Note: They are two files for AP Statistics students and Algebra 2 for 9th Grade and for 11th Grade have the same file!

From Functions to Finals!

Algebra 2 is wrapping up a review of functions and heading into finals.  Please find our functions review embedded below and the associated homework as well as tools to start studying for finals!  Please remember to check out the fact sheets, problem sets, and Prezi's made by the seniors for you here:  A2toPrecalc.



Finals Resources!

●Review Popplet:


●Khan Academy: Khan Academy Practice
●Online Practice Exams: Self-Mastery Tests
●Final Topic List and Review Packets:

Finals, finalizing Rationals, and looking toward Circles

Thinking about finals may be overwhelming, but hopefully these two review packets with answers will help you negotiate the basic skills required to succeed on the final.

 

 In addition, please find some online exams on a variety of topics to help you prepare for the final. Click to the appropriate topic and get some practice--also, don't forget about your TenMarks account!

Web-based Practice Tests

Starting Trigonometry and Rational Functions

Precalculus is starting the descent into the intricate, beautiful, and wonderful world of trigonometry.  We will spend the remaining time this year exploring triangles and how they become a window into the periodic behavior of tides, light, and even crankshafts!  The two applets above capture the conceptual essence of what we are building together over the next week--reflect on them and start to SEE the trigonometry.



The homework is due Monday the 9th of April and should generally be a review of trigonometric ratios with a couple twists.


Algebra II begins the brief introduction to rational functions and will focus on the interconnections between the graphical, algebraic, and tabular representations of this function. Please find some of the powerpoints on these topics below:

The homework is centered on graphing of rational functions and requires more time than it looks! Be diligent.

End of Polynomials and Logarithms

 www.math.montana.edu

Both Algebra II and Precalculus are wrapping up lengthy units in polynomials and logarithms respectively. Precalculus will move onto trigonometric functions and Algebra II will move onto a small unit on rational functions.  As the functions come and go, it appears that students are understanding the basic but sometimes conceptually complicated life of functions.

Algebra II will complete one more week focused on "modeling."  I am hoping to be explicit and use the rich and full framework developed in the common core state standards:

http://www.meaningfulmath.org 

The homework is from your textbook:  pp. 375-377 #1-53 and pp. 380-382 #1-45.  If you are still feeling a bit lost when it comes to polynomials you can check your textbook and the accompanying video series.  Algebra 2 Videos linked to your textbook (we are in chapter 7!).

Here is a refresher video on how to enter data, plot data, and calculate a regression:

Precalculus will complete logarithms next week by engaging a series of applied problem scenarios.  The homework is a combination of review and application--see below.

Exponential Functions and Higher Order Polynomials

Please peruse the infographic on exponential growth of facebook and explore exponential growth using the mathematica animation below and to the right(click on it)

Precalculus is currently developing an understanding of exponential functions (and their inverses, logarithms) in a variety of ways over the next few weeks.  We are opening our investigation of exponentials via an exploration of inverse functions using a SpringBoard investigation called "Code Breakers." We will move from this more numerical and algebraic look at the concept of inverses to the graphs of exponential and logarithmic functions.  The first homework on this topic, due February 6th, will be purely dedicated to honing the graph of exponential functions. We will progress through the exponentials using investigations and formative assessments from the work of Mathematics Assessment Project, Dan Meyer, and College Board's Springboard materials.  Please find reference sheets, review packets, and presentations in the embedded folder below:



The homework (for February 12th) is the following two files:



Video Links
Brightstorm Video Links

Algebra II is currently moving from linear and quadratic polynomials to higher order polynomials.  This transition is being driven concretely by exploring distance, area, and volume.  We will progress through the exponentials using investigations and formative assessments from the work of Mathematics Assessment Project, Dan Meyer, and College Board's Springboard materials.  We will build on our work with "Forming Quadratics" and move to "Representing Polynomials" before we move on to an intriguing interpretation and application of numerous theorems (see reference sheets in the embedded folder).  We will culminate with modeling of polynomial behavior.

What degree is the polynomial below? What is its equation?

Please find reference sheets, review packets, and presentations in the embedded folder below:


The homework (for February 12th) is the following:




Video Links:
Brighstorm Videos

Fences and Party Planning

While we catalog the year and review the basic component skills learned thus far, we are going to be doing extended investigations of rational expressions (in Precalc) and of quadratics (in Algebra II) in the contexts of design, projectile motion, and event planning.

Precalculus will be "Planning a Summer Camp" based on a College Board Springboard investigation with the following opening scenario:

"You have been appointed to the finance committee of a nonprofit summer camp for children.  The camp will be held in one-week sessions, beginning with breakfast on Monday morning and ending with dinner on Friday evening, each week throughout the summer.

The fixed cost for the camp, which includes rent, staff salaries, staff meals, and all equipment and materials for the recreational activities, will be $2400 per day.  Although the camp has dining facilities for the staff, ti must pay an outside vendor to provide all meals for the campers.  After contacting  a food service vendor, you learn that this additional cost will be $3 per camper, per meal.

As a nonprofit camp, the camp must cover it costs, but does not need to make a profit.  The finance committee does not know how much to charger for a week at the summer camp, so the director is requesting that the committee submit a proposal for setting the fee for reach camper based on the number of campers who are expected to attend each week."

Homework (from www.jmap.org; feel free to check your answers there!)



Algebra 2 will be working with a variety of area situations involving "Fences" and "Rockets in Flight" (the name of the Springboard investigation), which open as follows:

"You are employed by Fence Me In, a business that specializes in building fenced enclosures for both businesses and residences.  Your job is to build enclosures on your client's properties.  One client has purchased a certain length of fencing and wants to enclose the largest possible rectangular area in her yard." (Fences)

"Cooper is a model rocket enthusiast.  The model rockets in cooper's collection hve single engines and when launched can rise as high as 1000 feet depending upon the size of the engine.  After the engine is ignited, it will burn for 3-5 seconds and the rocket will accelerate upward.  Once the engine burns out, the rocket will be in free fall, because the only acceleration is due to gravity.  The rocket has a parachute that will open as the rocket begins to fall back to Earth.

Cooper decides to track one of his rockets, the Eagle, so that he can investigate its time and height while in flight.  He installs an altimeter into the nose of the Eagle.  The altimeter will record the time and the height of the rocket as it falls back to Earth and will be activated when the parachute opens.  The data for one flight of the Eagle is shown in the table below."

Homework (from www.jmap.org; feel free to check your answers there!)

Happy New Year! Midterms are here!

From here.

Both Precalculus and Algebra II have smallish assignments due this Friday and I hope everyone is diligently working on them.(?)  In case you lost them over the break here they are here for your to print.  In addition please refer to posts throughout the year to review content and find missing notes, etc. from you personal collections!










Algebra 2

Precalculus (compliments of Ms. Scheltz!)
]
Both classes will be mixing the new with the old in the hope of reviewing for the midterm, but also advancing the curriculum. Algebra 2 will continue with quadratics and Precalculus will do a brief dip into rational functions. More to come soon!