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)

Harvard Medical School Opportunity, More Linear Programming and Linear Functions

HPREP is a free 9-week program that takes place at the Harvard Medical School campus on Longwood Ave, Boston, on Saturday mornings from 10:00AM to 2:00PM. The program will begin on November 19th, 2011 and end in early February 2012. The application, along with more information, can be found at http://sites.google.com/site/hmshprep/application-deadlines. The application is also attached to this email. Applications are due October 19, 2011 by email to HPREP@hms.harvard.edu.

From http://news.discovery.com/space/nobel-prize-physics-111004.html

The pictures above represent a few images from the work of Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess, the most recent recipients of the Nobel Prize in Physics. If you are interested in their work on the accelerating universe, here is a link to an approachable summary on the topic.  Mathematics is at the heart of their discovery and reiterates the central role of math in understanding our world.


 We have yet another short week ahead of us, but I hope that we can really engage the material and deepen our understanding of mathematics.

Algebra II will be examining linear equations within the context of functions and addressing any and all misconceptions about linear relationships.  We will spend these four days solidifying linear equations as a basis for a brief but rigorous investigation of systems of equations as well as the basis of our exploration of polynomials.
Homework is due in two weeks, October 21st.

Slides:	Classwork (from eMathInstruction):	Homework (from XYZ Custom Plus):	Linear Equations Reference Sheet

________________________________________________________________________________________ Precalculus is zeroing in on linear programming. We started our investigation with a modified version of the National Council for Teacher's of Mathematics "Dirt Bike Dilemma" and will continue to explore it over the next six days. Homework is due in two more Fridays!  A great deal of graphing and interpreting is involved so work steady and check-in with me regularly.Here is the link to the chapter from which the problem set came.
Please find the slides related to linear programming here as well and some exemplar problems to help guide you on your way.

Slides:	Text Examplars:	Homework	Reference Material

Video resources:
Brightstorm Videos on solving and graphing inequalities
Khan Academy on graphing inequalities
Youtube Video 1 on Linear Programming
Youtube Video 2 on Linear Programming
________________________________________________________________________________________ Remember, you all have ongoing Khan Academy assignments with the first installment due November 1st, and the ability to practice and get immediate feedback at TenMarks. If you have forgotten your password for TenMarks just e-mail me.

Solving Systems with Matrices and All Things Linear

     From Pearson Education

Algebra II will be putting algebra basics behind them and moving on to linear equations with a coordinate geometry twist and an introduction to the concept function.  The goal of this week is to recall all you have learned about linear equations and really push your understanding of linearity to the limit.  Please find the Pearson PowerPoint slides below, a collection of videos on lines, the homework, and a linear equations reference sheet!

Slides:	Homework (from University of Houston):	Linear Equations Reference Sheet

Brightstorm Videos:
These videos are aligned to the sections from your textbook, so as you are completing homework from your textbook you can easily locate the most relevant videos for you!
_______________________________________________________________________________ Precalculus will continue to develop the properties of matrices and apply them to solving systems of equations. We will complete the final investigation of this unit on mixtures and solidify our ability to organize and manipulate information using matrices and apply them in problem-solving contexts.

Slides:	Text Examplars:	TI-83 Guide (see ch. 10-pp.167-182)

Homework: Handout from Finite Mathematics and Calculus with Applications Khan Academy Video:
Matrices to solve a system of equations


Brightstorm Video:
Solving linear systems using matrices  (this is a link to four videos that start with previous topics and build to the final topic of solving systems with matrices)

Solving Systems with Matrices and Factoring Expressions

                                         Factoring Flowchart Image Link




Precalculus will begin applying matrices to the solution of systems of equations.  It is an exciting week!  Please find the slides for the upcoming week below (starting with ppt5), a keystroke guide for matrices, as well as the homework.  We will have another investigation from the College Board's Springboard materials.  We completed "Gems in the Matrix" and "How Much Wood Do You Need," and will end with an investigation of mixtures.  Continue to focus on argument and explaining how matrices can help us manage and manipulate large sets of information.

Slides:	Text Examplars:	TI-83 Guide (see ch. 10-pp.167-182)

Khan Academy Video:
Matrices to solve a system of equations


Brightstorm Video:
Solving linear systems using matrices  (this is a link to four videos that start with previous topics and build to the final topic of solving systems with matrices)


Homework:
pp. 103-104 #27-52, pp. 119-122 #1-48, pp. 124-125 #1-10
_________________________________________________________________________________
Algebra II will hone their factoring skills and will be introduced to the basics of rational expressions.  After next week algebraic basics is over and we will be moving onto linear functions and piecewise functions.  Please find the notes from the week below (factoring is ppt2), factoring reference sheets, and the homework.

Slides:	Factoring Reference Sheet	Factoring Flowchart

Brightstorm Videos:
These videos are aligned to the sections from your textbook, so as you are completing homework from your textbook you can easily locate the most relevant videos for you!


Homework:

Handouts taken from XYZ Custom+.  Completes the multiples of three, please.

Matrices and more algebra basics

Precalculus will venture from algebraic manipulation of three variable linear systems using "elimination" and "substitution" and venture into the properties, characteristics, and application of matrices to multivariable linear systems. This adventure will be facilitated by a good dose of reasoning and technology. The basic key strokes associated with entering and solving matrices can be found here. We will go over instructions for this in class in greater detail. Please find both the PowerPoint slide shows for the coming week as well as relevant fact sheets and homework.

Slides:	Text Examplars:	TI-83 Guide (see ch. 10-pp.167-182)	Class Examples

Brightstorm Videos:
Systems of Linear Equations and Matrices


Homework:

pp. 76-77 #8-22; pp. 82-85, #1-54; pp. 102, #14-26

________________________________________________________________________________________

Algebra II will continue their review of basic algebra concepts by steaming on into the concept of factoring. We will loop back to concepts of number, especially as it pertains to exponents and radicals, and apply these concepts to sums and differences of terms as they emerge in polynomials. The image above is the factorization of a fifth degree polynomial, which shows that the expression has three distinct factors with one factor having a multiplicity of two. The irreducible factorization of the polynomial will not be covered in this basics review, but we will emerge in our study of polynomials over the coming months. Please find the PowerPoint slides as well as reference sheets and homework below:

Slides:	Factoring Reference Sheet	Factoring Flowchart

Brightstorm Videos:
These videos are aligned to the sections from your textbook, so as you are completing homework from your textbook you can easily locate the most relevant videos for you!


Homework:

pp. 260-261 #1-63; pp.242-243 #1-45; pp. 247-248#1-59.

Graphical Solutions and Algebra Basics

In Precalculus we will finish our brief overview of lines and modeling and move onto a conceptual analysis of solutions in all of their many forms.  As shown in the pictures above we will be leaning on technology to conceptualize solutions to equations primarily in their tabular and graphical forms.

We will be finishing some of the remaining PowerPoint slides* from last week and moving onto a new set.  Please find both of them below (start with the tab ppt1 for both) as well as two reference sheets on systems of linear equations:

Video Resources at Brightstorm:
Graphs of Linear Equations
Systems of Equations

Exemplars from Textbook (start with Exemplar 1)
Homework (due September 9, 2011): 
pp. 41-44, #1-19 evens; pp. 54-56, #1-22; pp. 70-72, #1-45. 

_________________________________________________________________________________

In Algebra II we will continue with our algebra basic review* and move onto a review of factoring, rational expressions, and radicals. I have included the set of powerpoints below as well as resources on the "rules" around these different basic algebra concepts. The algebra cheat sheet is from Paul's Online Math Notes.

Video Resources at Brightstorm:
Factoring Methods
Rational Exponents
Exponent Rules
More on Exponent Rules

Homework (due September 9, 2011): 
 pp. 226-228, #1-65 all; pp. 37-39, #1-58 all

 *Powerpoints are modified from 2007 Pearson text.

Linear Functions, Equations, and Inequalities for ALL

Numbers are a great place to begin the school year.  For Algebra II honors we are going over the number system and thinking through the implications this has for our work this year.  In precalculus we are thinking of these numbers as different values that give each function its peculiar meaning.  As we move forward we will broaden our ideas of the number system to help us explain mathematical statements that require a new set of numbers to include the complex numbers.
I look forward to a great year as we see what we can do with numbers.  Please find a flowchart of the number system below as well as a reference sheet on exponent rules:

Precalculus
Please find the Powerpoint slides provided for week 1 below (start with the tab ending with ppt1).

These slides are slightly modified versions of a 2007 Pearson Precalculus text.

Homework due Friday 2, 2011:
pp. 8-12, #1-57 odds, pp. 23-25, 1-39 evens, pp. 27-31, #1-29, evens, pp. 35-37 #1-34 evens
(approximately 70 problems)



Algebra II H
Please find the Powerpoint slides for week 1 below (start with tab ending with ppt 1)

These slides are slightly modified versions of a 2007 Pearson College Algebra text.

Homework due Friday 2, 2011:
pp. 8-10, #1-66 evens, pp. 14-18, #1-86 evens, pp. 24-25 #1-89 evens


Please post or e-mail me any questions you might have.