Westside High School Algebra 2 Advisor

Westside City 2050: Our Mall of the Future as a Mathematical System

2007-11-17T12:37:00.001-08:00

For McDougal Littell Units 4, 5, 6 and 7, students will use the concepts underlying

quadratic, polynomial, exponential, rational, radical and non-linear functions (as well as linear functions and systems) to algebraically, graphically, physically, verbally and numerically create and solve real-world models of their businesses developed in Unit 3, in both 2D and 3D. All activities align fully with Pre-AP Algebra 2 TEKS, HISD Planning Guides, and our Power Standards.

The concurrent learning systems of TAKS (Exit level) and Laying the Foundation (and its Big Ideas) will integrate throughout as well.

Students will have two rubrics for completion that determine their grade: one for math content based on 3D completion with relevant solutions, and a second based on instructional teamwork. Each team member must show his or her contributed product to receive a grade!

Algebraic Product: Students will also create 16 appropriate Algebra 2 Pre-AP questions

surrounding the expansion of their businesses (products, store layout, revenue, costs et al) for Units 4, 5, 6 and 7. These math issues will involve quadratics of revenue, exponential decay and growth, complex numbers and electricity, completing the square and construction, parabolic forces and building infrastructure et al. Students will also write at least 4 Laying the Foundation/Applied Free Response questions detailing step by step the mathematics of the specific issues they face and how they used Algebra 2, Geometry and Pre-Calculus to solve them.

Geometric Product: Students will build 2D and 3D models of their business space, hypothetically located in a given lease location within West Oaks Mall. Space and layout solutions will also involve these LTF Big Ideas: 1) Optimization (finding minimum and maximum space/layout); 2) Area and Accumulation (introductions to accumulation and integration as readiness for Pre-AP Pre-Cal and Cal); 3) Transformations (both algebraic and geometric), and other overlapping ideas. Completion of their geometric product also allows students to complete (and apply) preparation for Objectives 5, 6 and 7 of the Exit Level TAKS.

Using McDougal Littell Well: Students will receive a packet of model solutions for all 4 chapters from their Practice Workbook and model solutions from each End of Chapter Practice in McDougal. These practice problems involve different levels of tasks, and students should (systematically begin to) recognize when a question level is basic versus when a question level is more challenging. More challenging questions (like those in LTF tests) are best solved by using more than one problem solving approach.

Understanding more than one problem solving approach is key in 2007-2008, and even more key in the years ahead. Major International Problem Solving Assessments (like PISA 2003) use three very advanced (open-ended) problem solving strategies that US high school testers might never see.

According to the OECD, NCTM and others, 1) decisionmaking; 2) system analysis and design; and 3) troubleshooting are 3 key problem solving approaches for youth today to master for the next century. These complex strategies work alongside covering Bloom's questioning taxonomy (i.e. knowledge, comprehension, application, analysis, synthesis, and evaluation). These complex strategies require our future leaders to understand how mathematically to make decisions, how to more fluidly see systems (in schools, in texts, in and across math) and how effectively to use strategies to troubleshoot if and when problems with their systems arise.

Creating differentiated product and mastering the many mathematical systems at work daily in the management of malls involves all Bloom's questioning levels and all three of the advanced problem solving strategies.

GPVAN also is part of McDougal's Plan: By thematically unifying their LTF and Pre-AP Algebra 2 problems, students will learn that dismissing LTF's GPVAN is to ALSO dismiss McDougal's larger plan, as their new student textbook ALSO asks them to solve graphically, algebraically, numerically, verbally and physically (in keeping with education's Calculus Reform tenets)--in alignment with nationwide research and writing on best mathematics practices.

Additionally, students will receive problems as part of their Final Exam Review that integrate their own PLC's businesses throughout Pre-AP Algebra 2. These problems will also provide a more authentic context for using the math ideas and problems in Units 4, 5, 6, and 7.

Connecting with Quizlab: All Quizlab quizzes for Units 4, 5, 6 and 7 will include free response and multiple choice. For these quizzes, students will be asked to select or create one or more different representations of the answers found in the practice problem model sets, in their TAKS activity packets or in their Laying the Foundation Activity packets or Problems of the Week.

Answering the free response questions created in each quiz is critical in order to receive an "A."

Westside 2050 Extension: An extension project to Westside City 2050 asks Pre-AP PLCs to decide, systematically analyze and/or redesign the space most appropriate for learning and teaching at Westside High School in the year 2050. By 2050, Westside City becomes an interconnected community where business and education combine like goals and optimize their interactions--at least in terms of Algebra 2 and Pre-AP mathematics. Today's Westside students in Pre-AP Algebra 2 become the community leaders who solve and see these mathematical systems through--whose contributions in the future will help with educational goals, too.

[Links to Rubrics, Model Solutions and other materials will follow.]

Entrepreneurs As Equals: Presenting Our Linear Programming Businesses

2007-11-12T11:37:00.000-08:00

Greetings Noble Superstars, Parents and Members of the Westside Family:

Our Pre-AP Professional Learning Corporations (PLCs) are in the process of sharing the many interesting businesses, stores and services they have created while studying linear systems, matrices, linear programming, and optimization in Unit 3.

Please find attached a link to the Invitation for Judges of Our Business Projects.
Enjoy, and again congratulations to all our entrepreneurs!

Our Judges' Invitation to An Investment Celebration

Wesley's Pre-AP Lesson Plans for The Week of November 5th-13th, 2007

2007-11-04T19:18:00.000-08:00

Synopsis of Lessons Plans for the Week of November 5-13th, 2007 (20 page lesson plans will follow):

Greeks, Romans and "Modern Romans": I Can Apply Linear Programming In Two Variables and/or in Three to My Prepare My Future Path As Pre-AP
[Student Superstars complete Two Systems Tests for Pre-AP and Present Their Businesses]

1. MONDAY: Our "TEKS" Message (TEKS a.1, a.4, 2A.3.A, 2A.3.B)
Student-Friendly Objective: I can evaluate determinants of matrices and apply them to my business and its constraints.

Linear Programming Extension in McDougal Littell;
LTF Algebra 2 Activities: Systems of Linear Inequalities (Activity 5) and Optimization;
TI-Youniversity (Technological Applications of Determinants). Class work:
Using Matrices and Determinants to Decode and Solve our Sweet 16 (Problems).
Homefun, MDL Notetaking Guide Section 3.7 Quizzes on Quizlab, Part I and Part II.
LTF Algebra 2 Activities; Homefun: Solving Linear Systems of Inequalities with Solids.
Y-Axis Homefun for Tutoring Algebra 1: "My Teaching Script"; Algebra 1 LTF Activities on Rate of Change and Slope (Linear Functions).
PLC Practice with McDougal: 3.7 - Unit 3.7 Practice Problems (Led by Student Managers)

2. TUESDAY: Our "TEKS" Message (TEKS 2A.2.A, 2A.3.A, 2A.3.B, 2A.3.C)
Student-Friendly Objective: I can solve linear systems using inverse matrices and apply them to secret messages, cryptography, digital photo pixels and/or to my business and its constraints.

Class work: Sweet Sixteen Problems (Pre-AP, LTF, TAKS and SAT Questions)
LTF Activities: linking Analysis of Functions with Optimization, . Review Homefun (3.7)
Unit 3.8 Notetaking Guide (my teaching script), Pre-AP 3.8 Quizzes available on Quizlab. LTF Homefun: Activities from Algebra 2 (Review and Analysis of Inverse Functions)
3-Variable System Pop Quiz (3.4).
McDougal Littell PLC Practice: pg. 214 – 217 #3, 5, 13, 15, 25, 27, 51 – 533

3. WEDNESDAY or 11/07 (PLC Presentations; Entrepreneurs as Equals: GPVAN 500 and our Businesses through Linear Programming)

Our "TEKS" Message: (2A.1.A, 2A.3.A, 2A.3.B, 2A.3.C)
Student-Friendly Objective: I can solve linear programming problems and apply them either to my business and/or to that of my colleagues.

Warm-Up: GT applications and connections: Math systems, business systems, Math rules and Math patterns, business patterns.
Managers transition to Pre-AP Sweet 16 Questions.
Class work: Review Sweet Sixteen of Problems (3.3-3.8);
LTF Activity Connections to Optimization as Big Idea.
McDougal, Cumulative Review Questions, End Chapter 3.

4. THURSDAY 11 /08 (PLC Presentations; Entrepreneurs as Equals: GPVAN 500 and our Businesses through Linear Programming)
Our "TEKS" Message: (2A.1.A, 2A.3.A, 2A.3.B, 2A.3.C);

Student-Friendly Objective: I can solve linear programming problems and apply them either to my business and/or to that of my colleagues.

Warm-Up: GT applications and connections to Pre-AP: Math systems, business systems, Math rules; and math patterns, business patterns.
Managers "teach" and touch on Sweet 16 Questions and Solutions.
Class work: Sweet Sixteen Problems and Our Businesses (3.3-3.8);
LTF Algebra 2 Activity Connections to Optimization.
McDougal, Cumulative Review Questions, End Chapter 3.

5. FRIDAY 11/09
Our "TEKS" message: (TEKS 2A.1.A, 2A.3.A, 2A.3.B, 2A.3.C)
Student-Friendly Objective: I can apply concepts of matrices to solve various business and applied problems.

Warm-Up: Sweet 16 questions and pop quiz.
Class work: Final Presentations and Questions.
Homefun: LTF Algebra 2 Activity due: Solving Linear Systems of Inequalities
Introduction to Optimization via Non-Linear Functions.

4a. "YOUNIVERSITY AS INTERVENTION" : Review and Mastery of Matrix Multiplication: Inventory Control and Enhancements, Total Sales, and Other Applied Uses.

4b. "YOUNIVERSITY AS ENRICHMENT" - PLCS JUDGE BUSINESS NEEDS: LINEAR PROGRAMMING PRESENTATIONS: ENTREPRENEURS AS EQUALS: GPVAN 500; Building Our Business System of Linear Inequalities and Equations =- Rubric based, classroom-readiness presentations of our businesses (I. Store and product descriptions; II. Graphs; III. Inequalities and Equations; IV. Reflections on business investments and strategies). Differentiated Homefun: Make up your own Sweet Sixteen of 16 Unit 3-related problems: 3.1 (2); 3.2 (4); 3.3 (2); 3.4 (2); 3.5 (2); 3.6 (2); 3.7 (1); and 3.8 (1). Problems should be applied, and relate both to the Chapter Subsection Big Ideas and to the specific businesses set forth by your colleagues throughout our PLCs.

4c. Integrated throughout this week: TI-"YOUNIVERSITY": Students learn both Greek (classical formulas and their application) and Modern Roman (Graphing calculator) methods for solving matrices, determinants, inverse and identity matrices.

Business Funding For PLCs-List One

2007-10-31T08:21:00.001-07:00

Congratulations to all teams for
your good work!

More to come!

PowerPoint Template for Your Business Presentations

2007-10-19T17:56:00.000-07:00

Greetings Noble Superstars:

My outside Google server links you to the PPT template for download. You can connect to the template through this link.

If you need the file sent, please share an email address that allows for large transfers.

Make sure that we see your equation for R and your equation for C for both products. Good luck!

Lesson Plans for Week of October 29, 2007

2007-10-18T20:28:00.000-07:00

Lesson Plans for Week of October 29, 2007 (Pre-AP Algebra 2)

Lesson Plans for the Week of October 1st, 2007

2007-09-30T18:58:00.000-07:00

Lesson Plans for the Week of October 1st are here.

Lesson Plans - Week of 9.17. 2007 (Second link)

2007-09-17T05:35:00.001-07:00

http://westsidealg2.blogspot.com/2007/09/pre-ap-algebra-2-lesson-plans-week-of.html

Pre-AP Algebra 2 Lesson Plans--Week of 9.17.2007

2007-09-17T05:21:00.000-07:00

Welcome To All Our New Noble Superstars!

We are pleased to have you. We will review as we go through Chapter 2.

Best to you, C. Jones

Lesson Plans for Week of 9.17.2007

Capital Won Credits Are Coming Tonight!

2007-09-12T05:21:00.001-07:00

Noble Superstars: Stay Tuned! Any new students will be updated hereafter.

CLEAR-ly-Aligned Weekly Lesson Plans (Fall 2007)

2007-09-09T04:26:00.000-07:00

Weekly Lesson Plans

1. The TEKS Message: Lesson Plans for Pre-AP Algebra 2

Week of September 10th, 2007

Week of September 17th, 2007 (http://westsidealg2.blogspot.com/2007/09/pre-ap-algebra-2-lesson-plans-week-of.html)

2. Clearly-Aligned Lessons and Focus: HISD Horizontal Alignment Planning Guides

Week 2 Assignments (9.4.2007)

2007-09-04T08:38:00.000-07:00

Week 2: Assignments: Complete your Frayer model for the term "function" using your Math Dictionary in Class to define it and then providing your own examples (graphs, pictures, words, equations and numbers) to personalize it. The Frayer Model can be downloaded here.

Welcome to Westside High School Algebra 2!

2007-08-14T17:49:00.000-07:00

Syllabus for Pre-AP Algebra 2 - 2007-2008

2007-08-13T14:55:00.001-07:00

1. Syllabus for Pre-AP Algebra 2 (2007-2008)

2. So What? Go Ahead and See What & How You'll Learn Math in AP (Topics Outline for AP Calculus - College Board)

3. Course Outline for Pre-AP Algebra 2 (2007-2008)(Updated: 9.2.2007)

4. AP Avenue: Model TEKS-Aligned Projects That You Can Do To Master Parts of Algebra 2

5. Precalculus Links and Resources for All (2007-2008)

HISD HAPG Materials - High School Math Year At A Glance

2007-08-13T14:47:00.000-07:00

Year at a Glance - High School Math

Assignments for Week 1 (August 27th-31st) and Week 2 (9.4.2007-9.8.2007)

2007-08-13T08:14:00.000-07:00

Week 1

1. McDougal Littell Resources for Week 1: Two Assignments: 1) AP- Working with Irrational Numbers; 2) Pre-AP Algebra Review * Summer Packet Diagnostic & Test Prep

Week 2: Assignments: Complete your Frayer model for the term "function" using your Math Dictionary in Class to define it and then providing your own examples (graphs, pictures, words, equations and numbers) to personalize it. The Frayer Model can be downloaded here.

2. Daily Work and Warm-Up Problems (GPVAN & The Sweet Sixteen by ROYGBIV)

3. Virtual Enrichment For Algebra 2 Assignments (Quizlab et al)

[Each Pre-AP student has his or her own electronic Quizlab account customized and TEKS-aligned to his or her Algebra 2 needs. All McDougal Littell Assignments Can Be Completed Through Quizlab.]

How to logon to Quizlab:
Go to http://www.quizlab.com/
Click on the Student login link on upper left side.
Then click on Single Class login.
Your Classword will be "Pre-AP#" (i.e. your class period number). If this does not work, type in your ID number.
This is not a breach of confidentiality to give you a general clue. Your current password will be your first initial and some combination of last name letters (see your individual information). You may change your password after tonight. Let me know in advance, please.
Click on the links for Assigned Quizzes et al. Complete the test assigned to you for tonight.
Blog comment or e-mail if there are further questions or wait for the tutorial during class.

4. SAT Fat Cat

5. Laying The Foundation - Activities & Problems of the Week:

Week 1 Activities: Introducing Interval Notation

6. Discovering Advanced Algebra (Key Curriculum Press)

7. Mastery of Linear Functions: Welcome to Market Browser (Download)

Quiz & Other Credits (Listed by Student Selected Alias)

2007-08-13T03:18:00.000-07:00

Week One Credits (Cumulative and Itemized)

1. Students Receiving Summer Packet Credit (By Period)

2. Students Receiving Pre-AP Summer Packet Test Credit (Indicates if Passed)

Model Algebra 2 Benchmark Test (Foundation of Functions)(Form A)

2007-08-12T22:17:00.000-07:00

Greetings Noble Colleagues, Parents and Students:

The attached offers a sample of what a current
Algebra 2 benchmark might include, based on both TEKS and CLEAR sequencing. Please note that subsequent quizzes, tests and diagnostics will be aligned with both curriculum and client needs and expectations. In any case, hope this helps!

1. Model Benchmark Test (PDF Format)

Mu Alpha Theta - Math Honor Society Links

2007-08-11T19:44:00.000-07:00

Properties and Real Numbers

2007-08-02T18:49:00.000-07:00

Review and Intro to Algebra 2

Properties and Real Numbers
Taken together, the rational and irrational numbers make up the set of real numbers.

The following examples illustrate some characteristics and properties of real numbers.
1. Classify Real Numbers
a. Whole numbers: a subset of the real numbers; A whole number is either 0 or one of
the “counting numbers,” 1, 2, 3, . . .
b. Integers: A subset of the real numbers; The integers are the set of whole numbers and
their opposites, . . . 23, 22, 21, 0, 1, 2, 3, . . .
c. Rational numbers: A subset of the real numbers; A rational number can be expressed
as the ratio of two integers, and its decimal form terminates or repeats.
d. Irrational numbers: A subset of the real numbers; An irrational number cannot be
expressed as the ratio of two integers, and its decimal form neither terminates nor repeats.

2. Order of Operations: Established rule for evaluating an expression involving more
than one operation:
Step 1: Evaluate expressions inside grouping symbols.
Step 2: Evaluate powers.
Step 3: Multiply and divide from left to right.
Step 4: Add and subtract from left to right.

Making Meaning of the Code-Packet Process Mastery

2007-08-02T18:40:00.000-07:00

A. Thinking about Definitions

B. Packet Process Part Two: Order of Operations:

The Order of operations is an established rule for evaluating an expression involving more
than one operation:
Step 1: Evaluate expressions inside grouping symbols.
Step 2: Evaluate powers.
Step 3: Multiply and divide from left to right.
Step 4: Add and subtract from left to right.

C. Expressions, Equations, and Inequalities

A variable is a letter used to represent one or more numbers. An algebraic expression
is made from numbers, variables, and algebraic operations.

The following examples describe how expressions can be evaluated, combined, written, and used to write algebraic equations and inequalities.

1. Evaluating Expressions (Part 3 of your review)
Evaluate an expression involves the following process:

Step 1: Substitute a number for the variable,
Step 2: Perform the operation(s), and
Step 3: Simplify the result if necessary.

D. Solving Problems with Variables on 1 Side:
A. Solving Equations in one Variable:
To solve an equation in one variable, isolate the variable on one side of the equation.

The following examples illustrate different ways to isolate the variable.
1. Solve an Equation Using Addition or Subtraction
Inverse operations Two operations that undo each other, such as addition and
subtraction or multiplication and division.
Equivalent equations: Equations that have the same solution(s).
Use addition or subtraction to solve the equation.
a. x + 9 = 3 b. x - 5 = 2 c. x + 4.1 = 6
Solution:
a. x + 9 = 3 S1: Write original equation.
x + 9 - 9 = 3 - 9 S2: Use subtraction property of equality. Subtract 9
from each side.
x=-6 S3: Simplify.
The solution is 26.

b. x - 5 = 2 S1: Write original equation.
x - 5 + 5 = 2 + 5 S2: Use addition property of equality. Add 5 to each side.
x = 7 S3: Simplify.
The solution is 7.

c. x + 4.1 = 6 S1: Write original equation.
x + 4.1 - 4.1 = 6 - 4.1 S2: Subtract 4.1 from each side.
x = 1.9 S3: Simplify.
The solution is 1.9.

Use addition or subtraction to solve the equation.
1. x + 5 = 4 2. c - 3 = 8 3. t + 6 = 10

2. Solving an Equation Using Multiplication or Division

Use multiplication or division to solve the equation.
a. x/6 = 3 b. -7x = -49 c. - 3/8x = 5

Solution:
a. x/6 = 3
Step 1: Write original equation.
Step 2: Multiply each side by 6.
Step 3: Simplify.
The solution is 18.

II. More Packet Process for You (Download a Copy of a Notetaking Guide for Algebra 1)

The Notetaking Guide models important steps to perform. Go the given sections (use the Table of Contents) and see how these steps are done. Fill in the blanks with any info relevant to your given problem.