November+Algebra+I+Honors+07-08

November 1, 2007 November 2, 2007 November 5, 2007 November 6, 2007 November 7, 2007 November 8, 2007 November 9, 2007 November 13, 2007 November 14, 2007 November 15, 2007 November 16, 2007 November 19, 2007 November 20, 2007 November 21, 2007 November 26, 2007 November 27, 2007 November 28, 2007 November 29, 2007 November 30, 2007

November 1, 2007

Objectives: YWBAT solve systems of equations involving quadratic and linear functions YWBAT piecewise functions involving quadratic and linear elements

Agenda: 1. Provide several possible graphical representations of a linear and quadratic system 2. Determine which algebraic outcomes match a given set of graphical representations and state why. 3. Create piecewise rather than systems of quadratic and linear functions.

HW: Handout

November 2, 2007

Objective: YWBAT solve using a variety of methods in a variety of purely mathematical and real-world scenarios

Agenda: Problem set to be done in duos

HW: Problem Solving Handout

November 5, 2007

Objectives: YWBAT apply exponent rules to complete operations with constants and variables YWBAT simplify expressions using exponent rules and factoring

Agenda: 1. What is a "property"? Include concepts of a property that have been developed in other disciplines. 2. What would one want to have properties describing operations involving expressions with exponents? 3. Why are addition and muliplication (or subtraction and division) related in these properties? 3. List the properties in your notes including examples of each property.

HW: Exponent Handout 1

November 6, 2007

Objectives: YWBAT apply property of negative exponents to rewrite and simplify algebraic expressions

Agenda: 1. What does the word consensus mean? 2. Using numerical expressions and your calculator derive the meaning of a negative exponent. 3. In what contexts would writing algebraic and number expressions with negative exponents be useful?

HW: Exponent Handout 2

November 7, 2007

Objectives: YWBAT simplify complex expressions using all properties of exponents YWBAT present and explain the process of simplification to your peers

Agenda: 1. Describe the process of simplification including its purpose. 2. Devise a presentation on a particular problem from your packet to present to the class. 3. Provide constructive professional feedback to your peers.

HW: Exponent Handout 3

November 8, 2007

Objectives: YWBAT translate fractional exponents into radical form and vice versa. YWBAT simplify numeric and algebraic radical expressions

Agenda: 1. Using the properties we have alread learned, why is the .5 power the same operation as a square root? 2. What does mathematical fluency mean? 3. How do properties of exponents aid in the factoring process?

HW: Exponent Handout 4

November 9, 2007

Objectives: YWBAT apply properties of exponents with fluency YWBAT use properties of exponents to rewrite equations in terms of a desired variable

Agenda: 1. In what contexts do we usually see equations with exponents? 2. How can properties of exponents help us rearrange or rewrite these equations to meet new needs? 3. Physics Case Study

HW: Exponent Handout 5

November 13, 2007

Objectives: YWBAT interpret and explain functions using appropriate notation and vocabulary YWBAT perform operations with functions, including composition

Agenda; 1. What is the purpose of function notation? 2. How, if at all, do operations change between functions rather than between terms or numbers? 2. What does composition of functions accomplish?

HW: p. #387, 17-46

November 14, 2007

Objective: YWBAT apply operations with functions in real-world contexts

Agenda: 1. What is assumed or stated to be true that allows for operations between functions? 2. Describe how the changes in y related to the functions from which it was assembled? 3. What does an operation like composition accomplish in a real-world context?

HW: p. 388, #47-59

November 15, 2007

Objective: YWBAT find and interpret the inverse of a function algebraically, verbally, and graphically

Agenda: 1. Explain the meaning of inverses using notation and the concepts of input vs. outpute 2. What does finding the inverse accomplish? Why might it be useful to do this? 3. How does graphical approaches to inverse functions reinforce, support, and even broaden algebraic methods?

HW: p. 393 #14-37

November 16, 2007

Objective: YWBAT interpret functions graphically and algebraically using operations, composition, and inverses

Agenda: Worksheet incorporating operations and inverses

November 19, 2007

Objective: YWBAT interpret linear and quadratic function using concepts grounded in the concept of a function

Agenda: 1. What advantage or import is there to saying that a linear or quadratic equation is a function? 2. Why would humans care about functions? 3. How do inverses apply to linear and quadratic equations? similarities? differences?

HW: Handout

November 20, 2007

Objective: YWBAT recall and demonstrate mastery of the basic skills involving linear and quadratic equations

Agenda: Review Packet

November 21, 2007 Objective: YWBAT recall and demonstrate mastery of the basic skills involving linear and quadratic equations

Agenda: Review Packet

November 26, 2007

Objective: YWBAT classify polynomial functions and describe their overall behavior

Agenda: 1. Compare and contrast linear, quadratic, cubic, quarter, and quintic functions. 2. What patterns in end behavior emerge? 3. What do odd functions have in common? 4. What do even functions have in common?

HW: p. 350 #16-44

November 27, 2007

Objective: YWBAT articulate the fundamental theorem of algebra and apply it to polynomials

Agenda: 1. How does factoring methodology change as it is applied to higher order polynomials? 2. How does the degree of a particular factor apply to its graph and behavior? 3. What knowledge from quadratic equations can be applied to all polynomials regardless of degree

HW: p.356 #13-25

November 28, 2007

Objective: YWBAT determine verbally, graphically, and algebraically what the factors of a polynomial can tell you about the life of a particular curve

Agenda: 1. What does the word "root" mean? Where have you heard the word root before in math? 2. What does the word "intercept" mean? Where have you heard the word intercept before in math? 3. What does the word "solution" mean? Where have you heard the word solution before in math? 4. Explain how the words roots, intercept, and solution are related.

HW: p. 368 #13-30

November 29, 2007

Objective: YWBAT graph polynomial functions and identify key points in the life of the curve including loca maxima and minima

Agenda: 1. How are non-graphing calculator and approaches to graphing and graphing involving a calculator related? 2. List the key points of a curves life. 3. Why are maximia and minima important points on the life of a curve? 4. How does the concept of a maxima differ for odd degree and even degree polynomials?

HW: p. 357 #27-39

November 30, 2007

Objective: YWBAT interpet a graph and determine the likely number and nature of roots that compose the given function YWBAT write a possible equation for a given graph of a polynomial.

Agenda: 1. What information can you gather from graphs about the identity of the given function? 2. What does the end behavior provide us about the nature of the given function? 3. What does the intercepts provide about the nature of the given function? 4. What do the undulations of the graph tells us about the given function? 5. What kind of educated guess can we make about the identify of a function given its graph? 6. What are the limitations in analyzing a graph of a higher degree polynomial.

HW: Polynomial Handout