Iowa Testing today; students can complete Unit 3 assignments through Quizlab. Day 1
Wesley Westside’s Pre-AP Work Plan (Lessons for the Week of 10.29.2007)
Power Objective(s): additional Power
Standards are also present via Unit 3.
Laying the Foundation Optimization and
Analysis of Functions activities address key
Power Standard “Big Ideas.”
Connect algebraic and geometric processes
with tabular, graphic, pictorial, problem
situations and symbolic representations to
skillfully determine the domain and range of
functions. (P.1.B)
Objective(s): Foundations for functions. The student uses properties and attributes of
functions and applies functions to problem situations, and is expected to:
A.1.D. The student can identify linear equations and inequalities graphically and
algebraically.
2.A.3.A.
The student can solve linear systems by graphing.
2.A.3.B.
The student can solve linear systems algebraically.
2.A.3.A. a2. The student can graph systems of linear inequalities in two or three variables.
2.A.3.A. a.2-a.4 The student can perform basic matrix operations and multiply matrices,
and evaluate determinants.
1. Warm-Up/Engage & Motivate: Real-World Connections Used to review and introduce
concepts of Chapters 3: Entrepreneurs as Equals and the GPVAN 500. Building our Businesses
as Mathematical and Real World “Systems.” How might the concepts of a line, linear equations
and inequalities actually affect the costs, revenue, plan and projections of businesses in daily life?
How might a business I create use these mathematical models to generate a profit? How might
matrices and their properties be harnessed to help me more accurately control costs and inventory
for my business? (Students continue to build their businesses, calculating the requisite functions,
equations and linear inequalities, using AP Extension work in Linear Programming and
Optimization.) (Connections: Business, Linear Programming, Accounting; Business Calculus;
Pre-Calculus and Algebra 2 Pre-AP)
2. Student-Friendly Objective(s) (SO):
 I can use algebraic properties to evaluate and simplify expressions.
 I can use problem solving strategies and verbal models to the goals of making my own
successful business.
 I can solve linear systems by graphing and apply these to my business product.
 I can solve linear systems algebraically and apply these to my business product
 I can graph systems of linear inequalities in two or three variables and apply these to my
business product.
 I can perform basic matrix operations and multiply matrices, and evaluate determinants,
and apply these to my business product.
3. High-Yield Strategies Used: Setting Objectives (SO); Identifying Similarities and
Differences (ISD); Summarizing & Notetaking (SNT); Nonlinguistic Representations
(NLR); Cooperative Learning (CL); Financial Frayer is Used to Set forth business
characteristics. Scholars and Knowledge Research Skills also are used to sculpt Business
Goals.
1
* Student Product in Terms of Bloom’s Taxonomy & Higher Level Thinking Skills Used:
K, A, A, S, E (Students respond to a Bloom’s-aligned hierarchy of questions related to this
activity.)
4. Checking For Learning Embedded Into Lesson: teacher circulates the work and is in the
work, listening to discussion on process and outcome. Students reciprocally discuss and
check processes used amongst themselves. Reciprocal teaching is used alternately amongst
groups and shoulder partners. PLC Managers also model and teach Unit 3 problems from
McDougal Littell, and solicit input and mastery from other PLC members.
* Differentiated Instruction (VAKS Learners):
 Visual Learners: Students can use pictorial, graphic and nonlinguistic representations to
master Unit 3 objectives for inequalities and systems.
 Auditory Learners: Students orally communicate, review and contribute within the group
both their and their group’s problem solving processes.
 Kinesthetic Learners: Students can physically simulate both linear inequalities and their
solutions, using a range of tools, simulations and transformations.
5. TEKS-Aligned Assessment (Piece Described): Aligned with Region IV ESC Performance
Rubrics (Focus A.1.D. Exit-Level TAKS Objective 1-4 www.mathbenchmarks.org
 Procedural Skills: student-friendly rubric (accompanying project and setting forth
details for performance – See GPVAN 500 document.)
 Conceptual Skills: students analyze and identify attributes of linear functions and
inequalities. Students also review mastery of transformations.
 Communicative Skills: Students will present, describe and explain the processes chosen
to determine the business outcomes, costs, revenue and profit.
Guiding Questions:
1. Now that I have built a store, what other constraints must I understand and analyze to
ensure the most efficient and profitable use of my capital and other resources? (A, S, E)
2. Which business constraints and equations must I solve to have a profitable business?
Justify your explanation algebraically and graphically and verbally. (LTF GPVAN)
3. Describe how changes in your business might draw upon graphical transformations to
illustrate changes in profit, cost and revenue. Justify your description graphically and
algebraically.
Key Math Terms to Master (through Frayer, Semantic, Concept Maps): Aligns with HAPG,
MDL, DAA and LTF.
Materials: Instructions, colored pencils, pegboards, graphing paper, technology and
Powerpoint, rulers and/or straightedges, rubric, TI-83 and 84 calculators, other tools.
“CLEAR”-ly-Aligned MDL & DAA Resources: MDL Lesson 3.1– 3.4 emphasizes solving
systems graphically and algebraically. For Chapter 3, Pre-AP-level Best Practices Toolkit
supplements are also used. A2 BPT, See Extension Activities on Linear Programming. See also
MDL Lesson 3.3: Graphing Calculator Activity. Assignments integrate MDL Lessons 3.1-3.7:
Practice Workbook Problems and Notetaking Guide with businesses of students. Students
will complete all sections of Unit 3 on Quizlab as well as apply them to their differentiated
products.
2
LTF Alignments/AP Big Ideas and Activities: AP Calculus [Analysis of Functions:
Transformations; Optimization; Rate of Change: Position, Velocity, Acceleration: ;
Areas and Volumes (Store layout); Accumulation; AP Statistics [Data Gathering and
Simulation; Probability; Graphical Displays: Distributions Measures of Center,
Variability and Shape: Exploring Linear and Non-linear Bivariate Data. All LTF
Activities deal with Inequalities, their Graphing, and Systems of Inequalities from Algebra
2 text.
TAKS & TEKS-Aligned Big Ideas and Objectives: Exit-Level TEKS aligned with TAKS
Objectives 1, 2, 3 and 4. See Quizlab Practice.
TI and Technology Resources Used: Quizlab; Animations; MDL Technology Resources;
TI-Tools and TI-84 Smart View Inequalities Applications; Flash Sites and Blogger Sites;
Parent Companion Site. Blog for Students: www.westsidealg2.blogspot.com
3
Iowa Testing resumes today; students can complete assignments through Quizlab. Day 2
Wesley Westside’s Pre-AP Work Plan (Lessons for the Week of 10.30.2007)
Power Objective(s):
Connect algebraic and geometric processes
with tabular, graphic, pictorial, problem
situations and symbolic representations to
skillfully determine the domain and range of
functions. (P.1.B)
Objective(s): Foundations for functions. The student uses properties and attributes of
functions and applies functions to problem situations, and is expected to:
(A) identify the mathematical domains and ranges of functions and determine reasonable domain
and range values for continuous and discrete situations; and
A.1.D. The student can identify linear equations and inequalities graphically and
algebraically.
2.A.3.A.
The student can solve linear systems by graphing.
2.A.3.B.
The student can solve linear systems algebraically.
2.A.3.A. a2. The student can graph systems of linear inequalities in two or three variables.
2.A.3.A. a.2-a.4 The student can perform basic matrix operations and multiply matrices,
and evaluate determinants.
1. Warm-Up/Engage & Motivate: Real-World Connection Used to review and introduce
concepts of Chapters 1-3: how might the concepts of a line, linear equations and inequalities
actually affect the costs, revenue, plan and projections of businesses in daily life? How might a
business I create use these mathematical models to generate a profit? (Students continue to
specify and create their businesses, calculating the requisite functions, equations and linear
inequalities.) (Connections: Business, Linear Programming, Accounting; Business Calculus;
Pre-Calculus and Algebra 2 Pre-AP)
2. Student-Friendly Objective(s) (SO):
 I can use problem solving strategies and verbal models to the goals of making my own
successful business.
 I can solve linear systems by graphing and apply these to my business product.
 I can solve linear systems algebraically and apply these to my business product.
 I can graph systems of linear inequalities in two or three variables and apply these to my
business product.
 I can perform basic matrix operations and multiply matrices, and evaluate determinants,
and apply these to my business product.
* Student Product in Terms of Bloom’s Taxonomy & Higher Level Thinking Skills Used:
K, A, A, S, E (Students respond to a Bloom’s-aligned hierarchy of questions related to this
activity.)
3. High-Yield Strategies Used: Setting Objectives (SO); Identifying Similarities and
Differences (ISD); Summarizing & Notetaking (SNT); Nonlinguistic Representations (NLR);
Cooperative Learning (CL); Financial Frayer is Used to Set forth business characteristics.
Scholars and Knowledge Research Skills also are used to sculpt Business Goals.
4. Checking For Learning Embedded Into Lesson: teacher circulates the work and is in the
work, listening to discussion on process and outcome. Students reciprocally discuss and
4
check processes used amongst themselves as they explain and model the business cycle.
Reciprocal teaching is used alternately amongst groups and shoulder partners. PLC
Managers model and teach Unit 3 problems from McDougal Littell.
* Differentiated Instruction (VAKS Learners):
 Visual Learners: Students can use pictorial, graphic and nonlinguistic representations to
master the specific objectives for their enterprises vis a vis our learning goals in Unit 3.
 Auditory Learners: Students orally communicate, review and contribute within the group
both their and their business group’s problem solving processes.
 Kinesthetic Learners: Students can physically simulate transformations to their
businesses via manipulatives, technology, LTF GPVAN strategies and through graphing
on the coordinate plane.
5. TEKS-Aligned Assessment (Piece Described): Aligned with Region IV ESC Performance
Rubrics
 Procedural Skills: student-friendly rubric (with 4 categories to evaluate of their
businesses: store description and product; inequalities and equations; graphs relevant to
cost, revenue and profit, reflections on their business and investments).
 Conceptual Skills: students analyze and identify attributes of the coordinate plane and
concepts related to slope, y-intercepts, boundaries and regions, linear functions and linear
inequalities as they apply to business products and their development.
 Communicative Skills: Students have a 4-part rubric that details how they might exceed
expectations in terms of their business product and its application to Linear Programming
and Matrices.
Guiding Questions:
1. If I build a store, what sorts of constraints must I understand and analyze to ensure the
most efficient and profitable use of my capital and other resources? (A, S, E)
2. Which business constraints and equations must I solve to have a profitable business?
Justify your explanation algebraically and graphically and verbally. (LTF GPVAN)
3. Describe how changes in your business might draw upon graphical transformations to
illustrate changes in profit, cost and revenue. Justify your description graphically and
algebraically.
Materials: Instructions, colored pencils, pegboards, graphing paper, technology and
PowerPoint, rulers and/or straightedges, rubric, TI-83 and 84 calculators, other tools.
“CLEAR”-ly-Aligned MDL & DAA Resources: MDL Lesson 3.1– 33 emphasizes solving
systems graphically and algebraically. For Chapter 3, Pre-AP-level Best Practices Toolkit
supplements are also used. A2 BPT, See Extension Activities on Linear Programming. See also
MDL Lesson 3.3: Graphing Calculator Activity. Assignments: focus on MDL Lessons 3.1-3.7:
Practice Workbook Problems and Notetaking Guide. Students will complete all sections of
Unit 3 on Quizlab as well as through their differentiated products.
LTF Alignments/AP Big Ideas and Activities: AP Calculus [Analysis of Functions:
Transformations; Optimization; Rate of Change: Position, Velocity, Acceleration: ;
Areas and Volumes (Store layout); Accumulation; AP Statistics [Data Gathering and
Simulation; Probability; Graphical Displays: Distributions Measures of Center,
Variability and Shape: Exploring Linear and Non-linear Bivariate Data. All LTF
5
Activities deal with Inequalities, their Graphing, and Systems of Inequalities from Algebra
2 text.
TAKS & TEKS-Aligned Big Ideas and Objectives: Exit-Level TEKS aligned with TAKS
Objectives 1, 2, 3 and 4. See Quizlab Practice.
TI and Technology Resources Used: Quizlab; Animations; MDL Technology Resources;
TI-Tools and TI-84 Smart View Inequalities Applications; Flash Sites and Blogger Sites;
Parent Companion Site; Blog for Students: www.westsidealg2.blogspot.com
6
LTF Meeting Day (Associate Teacher)
Day 3
Wesley Westside’s Pre-AP Work Plan (Lessons for the Week of 10.31.2007)
Power Objective(s):
Connect algebraic and geometric processes
with tabular, graphic, pictorial, problem
situations and symbolic representations to
skillfully determine the domain and range of
functions. (P.1.B)
Objective(s): Foundations for functions. The student uses properties and attributes of
functions and applies functions to problem situations, and is expected to:
(A) identify the mathematical domains and ranges of functions and determine reasonable domain
and range values for continuous and discrete situations; and
A.1.D. The student can identify linear equations and inequalities graphically and
algebraically.
2.A.3.A.
The student can solve linear systems by graphing.
2.A.3.B.
The student can solve linear systems algebraically.
2.A.3.A. a2. The student can graph systems of linear inequalities in two or three variables.
2.A.3.A. a.2-a.4 The student can perform basic matrix operations and multiply matrices,
and evaluate determinants.
1. Warm-Up/Engage & Motivate: Real-World Connection Used to review and introduce
concepts of Chapters 1-3: how might the concepts of a line, linear equations and inequalities
actually affect the costs, revenue, plan and projections of businesses in daily life? How might a
business I create use these mathematical models to generate a profit? (Students continue to
specify and create their businesses, calculating the requisite functions, equations and linear
inequalities.) (Connections: Business, Linear Programming, Accounting; Business Calculus;
Pre-Calculus and Algebra 2 Pre-AP)
2. Student-Friendly Objective(s) (SO):
 I can use algebraic properties to evaluate and simplify expressions.
 I can use problem solving strategies and verbal models to the goals of making my own
successful business.
 I can solve linear systems by graphing and apply these to my business product.
 I can solve linear systems algebraically and apply these to my business product
 I can graph systems of linear inequalities in two or three variables and apply these to my
business product.
 I can perform basic matrix operations and multiply matrices, and evaluate determinants,
and apply these to my business product.
3. High-Yield Strategies Used: Setting Objectives (SO); Identifying Similarities and
Differences (ISD); Summarizing & Notetaking (SNT); Nonlinguistic Representations
(NLR); Cooperative Learning (CL); Financial Frayer is Used to Set forth business
characteristics. Scholars and Knowledge Research Skills also are used to sculpt Business
Goals.
* Student Product in Terms of Bloom’s Taxonomy & Higher Level Thinking Skills Used:
K, A, A, S, E (Students respond to a Bloom’s-aligned hierarchy of questions related to this
activity.)
7
4. Checking For Learning Embedded Into Lesson: teacher circulates the work and is in the
work, listening to discussion on process and outcome. Students reciprocally discuss and
check processes used amongst themselves. Reciprocal teaching is used alternately amongst
groups and shoulder partners. PLC Managers model and teach Unit 3 problems from
McDougal Littell.



Visual Learners: Students can use pictorial, graphic and nonlinguistic representations to
master the specific objectives for their enterprises vis a vis our learning goals in Unit 3.
Auditory Learners: Students orally communicate, review and contribute within the group
both their and their group’s problem solving processes.
Kinesthetic Learners: Students can physically simulate transformations to their
businesses via manipulatives, technology, LTF GPVAN strategies and through graphing
on the coordinate plane.
5. TEKS-Aligned Assessment (Piece Described): Aligned with Region IV ESC Performance
Rubrics
 Procedural Skills: student-friendly rubric (with 4 categories to evaluate of their
businesses: store description and product; inequalities and equations; graphs relevant to
cost, revenue and profit, reflections on their business and investments).
 Conceptual Skills: students analyze and identify attributes of the coordinate plane and
concepts related to slope, y-intercepts, boundaries and regions, linear functions and linear
inequalities as they apply to business products and their development.
 Communicative Skills: Students have a 4-part rubric that details how they might exceed
expectations in terms of their business product and its application to Linear Programming
and Matrices.
Guiding Questions:
1. If I build a store, what sorts of constraints must I understand and analyze to ensure the
most efficient and profitable use of my capital and other resources? (A, S, E)
2. Which business constraints and equations must I solve to have a profitable business?
Justify your explanation algebraically and graphically and verbally. (LTF GPVAN)
3. Describe how changes in your business might draw upon graphical transformations to
illustrate changes in profit, cost and revenue. Justify your description graphically and
algebraically.
Materials: Instructions, colored pencils, pegboards, graphing paper, technology and
Powerpoint, rulers and/or straightedges, rubric, TI-83 and 84 calculators, other tools.
“CLEAR”-ly-Aligned MDL & DAA Resources: MDL Lesson 3.1– 33 emphasizes solving
systems graphically and algebraically. For Chapter 3, Pre-AP-level Best Practices Toolkit
supplements are also used. A2 BPT, See Extension Activities on Linear Programming. See also
MDL Lesson 3.3: Graphing Calculator Activity. Assignments: focus on MDL Lessons 3.1-3.7:
Practice Workbook Problems and Notetaking Guide. Students will complete all sections of
Unit 3 on Quizlab as well as through their differentiated products.
LTF Alignments/AP Big Ideas and Activities: AP Calculus [Analysis of Functions:
Transformations; Optimization; Rate of Change: Position, Velocity, Acceleration: ;
Areas and Volumes (Store layout); Accumulation; AP Statistics [Data Gathering and
8
Simulation; Probability; Graphical Displays: Distributions Measures of Center,
Variability and Shape: Exploring Linear and Non-linear Bivariate Data. All LTF
Activities deal with Inequalities, their Graphing, and Systems of Inequalities from Algebra
2 text.
TAKS & TEKS-Aligned Big Ideas and Objectives: Exit-Level TEKS aligned with TAKS
Objectives 1, 2, 3 and 4. See Quizlab Practice.
TI and Technology Resources Used: Quizlab; Animations; MDL Technology Resources;
TI-Tools and TI-84 Smart View Inequalities Applications; Flash Sites and Blogger Sites;
Parent Companion Site. Blog: www.westsidealg2.blogspot.com
9
Day 4
Wesley Westside’s Pre-AP Work Plan (Lessons for the Week of 11.1.2007)
Power Objective(s):
Connect algebraic and geometric processes
with tabular, graphic, pictorial, problem
situations and symbolic representations to
skillfully determine the domain and range of
functions. (P.1.B)
Objective(s): Foundations for functions. The student uses properties and attributes of
functions and applies functions to problem situations, and is expected to:
(A) identify the mathematical domains and ranges of functions and determine reasonable domain
and range values for continuous and discrete situations; and
A.1.D. The student can identify linear equations and inequalities graphically and
algebraically.
2.A.3.A.
The student can solve linear systems by graphing.
2.A.3.B.
The student can solve linear systems algebraically.
2.A.3.A. a2. The student can graph systems of linear inequalities in two or three variables.
2.A.3.A. a.2-a.4 The student can perform basic matrix operations and multiply matrices,
and evaluate determinants.
2. Student-Friendly Objective(s) (SO):
 I can solve linear systems by graphing and apply these to my business product.
 I can solve linear systems algebraically and apply these to my business product
 I can graph systems of linear inequalities in two or three variables and apply these to my
business product.
 I can perform basic matrix operations and multiply matrices, and evaluate determinants,
and apply these to my business product.
3. Intended Learner Outcomes: By producing a graphical representation of cost and
revenue functions, and by solving linear business systems algebraically and graphically,
students enhance their abilities to algebraically understand how to apply and use linear
functions for practical application and in ways that connect them with both Pre
* Student Product in Terms of Bloom’s Taxonomy & Higher Level Thinking Skills Used:
K, A, A, S, E (Students respond to a Bloom’s-aligned hierarchy of questions related to this
activity.)
4. Checking For Learning Embedded Into Lesson: teacher circulates the work and is in the
work, listening to discussion on process and outcome. Students reciprocally discuss and
check processes used amongst themselves. Reciprocal teaching is used alternately amongst
groups and shoulder partners. PLC Managers model and teach Unit 3 problems from
McDougal Littell.
* Differentiated Instruction (VAKS Learners):
 Visual Learners: Students can use pictorial, graphic and nonlinguistic representations to
master the specific objectives for their enterprises vis a vis our learning goals in Unit 3.
 Auditory Learners: Students orally communicate, review and contribute within the group
10
both their and their group’s problem solving processes.
 Kinesthetic Learners: Students can physically simulate transformations to their
businesses via manipulatives, technology, LTF GPVAN strategies and through graphing
on the coordinate plane.
5. TEKS-Aligned Assessment (Piece Described): Aligned with Region IV ESC Performance
Rubrics
 Procedural Skills: student-friendly rubric (with 4 categories to evaluate of their
businesses: store description and product; inequalities and equations; graphs relevant to
cost, revenue and profit, reflections on their business and investments).
 Conceptual Skills: students analyze and identify attributes of the coordinate plane and
concepts related to slope, y-intercepts, boundaries and regions, linear functions and linear
inequalities as they apply to business products and their development.
 Communicative Skills: Students have a 4-part rubric that details how they might exceed
expectations in terms of their business product and its application to Linear Programming
and Matrices.
Guiding Questions:
1. If I build a store, what sorts of constraints must I understand and analyze to ensure the
most efficient and profitable use of my capital and other resources? (A, S, E)
2. Which business constraints and equations must I solve to have a profitable business?
Justify your explanation algebraically and graphically and verbally. (LTF GPVAN)
3. Describe how changes in your business might draw upon graphical transformations to
illustrate changes in profit, cost and revenue. Justify your description graphically and
algebraically.
“CLEAR”-ly-Aligned MDL & DAA Resources: MDL Lesson 3.1– 33 emphasizes solving
systems graphically and algebraically. For Chapter 3, Pre-AP-level Best Practices Toolkit
supplements are also used. A2 BPT, See Extension Activities on Linear Programming. See also
MDL Lesson 3.3: Graphing Calculator Activity. Assignments: focus on MDL Lessons 3.1-3.7:
Practice Workbook Problems and Notetaking Guide. Students will complete all sections of
Unit 3 on Quizlab as well as apply them to their differentiated products.
Materials: Instructions, colored pencils, pegboards, graphing paper, technology and
PowerPoint, rulers and/or straightedges, rubric, TI-83 and 84 calculators, other tools.
LTF Alignments/AP Big Ideas and Activities: AP Calculus [Analysis of Functions:
Transformations; Optimization; Rate of Change: Position, Velocity, Acceleration: ;
Areas and Volumes (Store layout); Accumulation; AP Statistics [Data Gathering and
Simulation; Probability; Graphical Displays: Distributions Measures of Center,
Variability and Shape: Exploring Linear and Non-linear Bivariate Data. All LTF
Activities deal with Inequalities, their Graphing, and Systems of Inequalities from Algebra
2 text.
TAKS & TEKS-Aligned Big Ideas and Objectives: Exit-Level TEKS aligned with TAKS
Objectives 1, 2, 3 and 4. See Quizlab Practice.
TI and Technology Resources Used: Quizlab; Animations; MDL Technology Resources;
TI-Tools and TI-84 Smart View Inequalities Applications; Flash Sites and Blogger Sites;
Parent Companion Site; Blog: www.westsidealg2.blogspot.com
11
Day 5
Wesley Westside’s Pre-AP Work Plan (Lessons for the Week of 11.2.2007)
Power Objective(s):
Connect algebraic and geometric processes
with tabular, graphic, pictorial, problem
situations and symbolic representations to
skillfully determine the domain and range of
functions. (P.1.B)
Objective(s): Foundations for functions. The student uses properties and attributes of
functions and applies functions to problem situations, and is expected to:
(A) identify the mathematical domains and ranges of functions and determine reasonable domain
and range values for continuous and discrete situations; and
A.1.D. The student can identify linear equations and inequalities graphically and
algebraically.
1. Warm-Up/Engage & Motivate: Real-World Connection Used to review and introduce
concepts of Chapters 1-3: how might the concepts of a line, linear equations and inequalities
actually affect the costs, revenue, plan and projections of businesses in daily life? How might a
business I create use these mathematical models to generate a profit? (Students continue to
specify and create their businesses, calculating the requisite functions, equations and linear
inequalities.) (Connections: Business, Linear Programming, Accounting; Business Calculus;
Pre-Calculus and Algebra 2 Pre-AP)
2. Student-Friendly Objective(s) (SO):
 I can solve linear systems by graphing and apply these to my business product.
 I can solve linear systems algebraically and apply these to my business product
 I can graph systems of linear inequalities in two or three variables and apply these to my
business product.
 I can graph systems of linear inequalities in two or three variables and apply these to my
business product.
 I can perform basic matrix operations and multiply matrices, and evaluate determinants,
and apply these to my business product.
3. Intended Learner Outcomes: By producing a graphical representation of cost and revenue
functions, and by solving linear business systems algebraically and graphically, students enhance
their abilities to algebraically understand how to apply and use linear functions for practical
application and in ways that connect them with both Pre-Calculus and College Math.
3. High-Yield Strategies Used: Setting Objectives (SO); Identifying Similarities and
Differences (ISD); Summarizing & Notetaking (SNT); Nonlinguistic Representations (NLR);
Cooperative Learning (CL); Financial Frayer is Used to Set forth business characteristics.
Scholars and Knowledge Research Skills also are used to sculpt Business Goals
4. Checking For Learning Embedded Into Lesson: teacher circulates the work and is in the
work, listening to discussion on process and outcome. Students reciprocally discuss and
check processes used amongst themselves. Reciprocal teaching is used alternately amongst
groups and shoulder partners. PLC Managers model and teach Unit 3 problems from
12
McDougal Littell.
* Differentiated Instruction (VAKS Learners):
 Visual Learners: Students can use pictorial, graphic and nonlinguistic representations to
master the specific objectives for their enterprises vis a vis our learning goals in Unit 3.
 Auditory Learners: Students orally communicate, review and contribute within the group
both their and their group’s problem solving processes.
 Kinesthetic Learners: Students can physically simulate transformations to their
businesses via manipulatives, technology, LTF GPVAN strategies and through graphing
on the coordinate plane.
5. TEKS-Aligned Assessment (Piece Described): Aligned with Region IV ESC Performance
Rubrics
 Procedural Skills: student-friendly rubric (with 4 categories to evaluate of their
businesses: store description and product; inequalities and equations; graphs relevant to
cost, revenue and profit, reflections on their business and investments).
 Conceptual Skills: students analyze and identify attributes of the coordinate plane and
concepts related to slope, y-intercepts, boundaries and regions, linear functions and linear
inequalities as they apply to business products and their development.
 Communicative Skills: Students have a 4-part rubric that details how they might exceed
expectations in terms of their business product and its application to Linear Programming
and Matrices.
Guiding Questions:
1. If I build a store, what sorts of constraints must I understand and analyze to ensure
the most efficient and profitable use of my capital and other resources? (A, S, E)
2. Which business constraints and equations must I solve to have a profitable business?
Justify your explanation algebraically and graphically and verbally. (LTF GPVAN)
3. Describe how changes in your business might draw upon graphical transformations to
illustrate changes in profit, cost and revenue. Justify your description graphically and
algebraically.
“CLEAR”-ly-Aligned MDL & DAA Resources: MDL Lesson 3.1– 33 emphasizes solving
systems graphically and algebraically. For Chapter 3, Pre-AP-level Best Practices Toolkit
supplements are also used. A2 BPT, See Extension Activities on Linear Programming. See also
MDL Lesson 3.3: Graphing Calculator Activity. Assignments: focus on MDL Lessons 3.1-3.7:
Practice Workbook Problems and Notetaking Guide. Students will complete all sections of
Unit 3 on Quizlab as well as apply them to their differentiated products.
LTF Alignments/AP Big Ideas and Activities: AP Calculus [Analysis of Functions:
Transformations; Optimization; Rate of Change: Position, Velocity, Acceleration; Areas
and Volumes (Store layout); Accumulation; AP Statistics [Data Gathering and Simulation;
Probability; Graphical Displays: Distributions Measures of Center, Variability and Shape:
Exploring Linear and Non-linear Bivariate Data. All LTF Activities deal with Inequalities,
their Graphing, and Systems of Inequalities from Algebra 2 text.
Materials: Instructions, colored pencils, pegboards, graphing paper, technology and
Powerpoint, rulers and/or straightedges, rubric, TI-83 and 84 calculators, other tools.
TAKS & TEKS-Aligned Big Ideas and Objectives: Exit-Level TEKS aligned with TAKS
Objectives 1, 2, 3 and 4. See Quizlab Practice:
TI and Technology Resources Used: Quizlab; Animations; MDL Technology Resources;
13
TI-Tools and TI-84 Smart View Inequalities Applications; Flash Sites and Blogger Sites;
Parent Companion Site. Blog for Students: www.westsidealg2.blogspot.com
14
Enrichment+
Wesley Westside’s Pre-AP Work Plan (Lessons for the Week of 11.1.2007)
Power Objective(s):
[This section draws upon AP Best Practices
Resources from both LTF and McDougal
Littell, extending them to Pre-Cal.]
Connect algebraic and geometric processes
with tabular, graphic, pictorial, problem
situations and symbolic representations to
skillfully determine the domain and range of
functions. (P.1.B)
Objective(s): Foundations for functions. The student uses properties and attributes of
functions and applies functions to problem situations, and is expected to:
(A) identify the mathematical domains and ranges of functions and determine reasonable domain
and range values for continuous and discrete situations; and
A.1.D. The student can identify linear equations and inequalities graphically and
algebraically.
1. Warm-Up/Engage & Motivate: Real-World Connection Used to review and introduce
concepts of Chapters 1-3: how might the concepts of a line, linear equations and inequalities
actually affect the costs, revenue, plan and projections of businesses in daily life? How might a
business I create use these mathematical models to generate a profit? (Students continue to
specify and create their businesses, calculating the requisite functions, equations and linear
inequalities.) (Connections: Business, Linear Programming, Accounting; Business Calculus;
Pre-Calculus and Algebra 2 Pre-AP)
2. Student-Friendly Objective(s) (SO):
 I can use algebraic properties to evaluate and simplify expressions.
 I can solve linear systems by graphing and apply these to my business product.
 I can solve linear systems algebraically and apply these to my business product
 I can graph systems of linear inequalities in two or three variables and apply these
to my business product.
 I can graph systems of linear inequalities in two or three variables and apply these to my
business product.
 I can perform basic matrix operations and multiply matrices, and evaluate determinants,
and apply these to my business product.
3. High-Yield Strategies Used: Setting Objectives (SO); Identifying Similarities and
Differences (ISD); Summarizing & Notetaking (SNT); Nonlinguistic Representations (NLR);
Cooperative Learning (CL); Financial Frayer is Used to Set forth business characteristics.
Scholars and Knowledge Research Skills also are used to sculpt Business Goals
3. Intended Learner Outcomes: By producing a graphical representation of cost and revenue
functions, and by solving linear business systems algebraically and graphically, students
enhance their abilities to algebraically understand how to apply and use linear functions
for practical application and in ways that connect them with both Pre-Calculus and
College Math.
4. Checking For Learning Embedded Into Lesson: teacher circulates the work and is in the
work, listening to discussion on process and outcome. Students reciprocally discuss and
check processes used amongst themselves. Reciprocal teaching is used alternately amongst
15
groups and shoulder partners. PLC Managers model and teach Unit 3 problems from
McDougal Littell and solicit classroom interaction and participation.
* Differentiated Instruction (VAKS Learners):
 Visual Learners: Students can use pictorial, graphic and nonlinguistic representations to
master the specific objectives for their enterprises vis a vis our learning goals in Unit 3.
 Auditory Learners: Students orally communicate, review and contribute within the group
both their and their group’s problem solving processes.
 Kinesthetic Learners: Students can physically simulate transformations to their
businesses via manipulatives, technology, LTF GPVAN strategies and through graphing
on the coordinate plane.
5. TEKS-Aligned Assessment (Piece Described): Aligned with Region IV ESC Performance
Rubrics
 Procedural Skills: student-friendly rubric (with 4 categories to evaluate of their
businesses: store description and product; inequalities and equations; graphs relevant to
cost, revenue and profit, reflections on their business and investments).
 Conceptual Skills: students analyze and identify attributes of the coordinate plane and
concepts related to slope, y-intercepts, boundaries and regions, linear functions and linear
inequalities as they apply to business products and their development.
 Communicative Skills: Students have a 4-part rubric that details how they might exceed
expectations in terms of their business product and its application to Linear Programming
and Matrices.
Guiding Questions:
1. If I build a store, what sorts of constraints must I understand and analyze to ensure the
most efficient and profitable use of my capital and other resources? (A, S, E)
2. Which business constraints and equations must I solve to have a profitable business?
Justify your explanation algebraically and graphically and verbally. (LTF GPVAN)
3. Describe how changes in your business might draw upon graphical transformations to
illustrate changes in profit, cost and revenue. Justify your description graphically and
algebraically.
“CLEAR”-ly-Aligned MDL & DAA Resources: MDL Lesson 3.1– 33 emphasizes solving
systems graphically and algebraically. For Chapter 3, Pre-AP-level Best Practices Toolkit
supplements are also used. A2 BPT, See Extension Activities on Linear Programming. See also
MDL Lesson 3.3: Graphing Calculator Activity. Assignments: focus on MDL Lessons 3.1-3.7:
Practice Workbook Problems and Notetaking Guide. Students will complete all sections of
Unit 3 on Quizlab as well as through their differentiated products.
Materials: Instructions, colored pencils, pegboards, graphing paper, technology and
Powerpoint, rulers and/or straightedges, rubric, TI-83 and 84 calculators, other tools.
LTF Alignments/AP Big Ideas and Activities: AP Calculus [Analysis of Functions:
Transformations; Optimization; Rate of Change: Position, Velocity, Acceleration; Areas
and Volumes (Store layout); Accumulation; AP Statistics [Data Gathering and Simulation;
Probability; Graphical Displays: Distributions Measures of Center, Variability and Shape:
Exploring Linear and Non-linear Bivariate Data:
All LTF Activities deal with
Inequalities, their Graphing, and Systems of Inequalities from Algebra 2 text.
TAKS & TEKS-Aligned Big Ideas and Objectives: Exit-Level TEKS aligned with TAKS
Objectives 1, 2, 3 and 4. See Quizlab Practice.
16
TI and Technology Resources Used: Quizlab; Animations; MDL Technology Resources;
TI-Tools and TI-84 Smart View Inequalities Applications; Flash Sites and Blogger Sites;
Parent Companion Site. Blog for students: www.westsidealg2.blogspot.com
17
“You-niversity” & Intervention+
Wesley Westside’s Pre-AP Work Plan (Lessons for the Week of 11.2.2007)
Power Objective(s):
Connect algebraic and geometric processes
with tabular, graphic, pictorial, problem
situations and symbolic representations to
skillfully determine the domain and range of
functions. (P.1.B)
Objective(s): Foundations for functions. The student uses properties and attributes of
functions and applies functions to problem situations, and is expected to:
(A) identify the mathematical domains and ranges of functions and determine reasonable domain
and range values for continuous and discrete situations; and
A.1.D. The student can identify linear equations and inequalities graphically and
algebraically.
1. Warm-Up/Engage & Motivate: Real-World Connection Used to review and introduce
concepts of Chapters 1-3: how might the concepts of a line, linear equations and inequalities
actually affect the costs, revenue, plan and projections of businesses in daily life? How might a
business I create use these mathematical models to generate a profit? (Students continue to
specify and create their businesses, calculating the requisite functions, equations and linear
inequalities.) (Connections: Business, Linear Programming, Accounting; Business Calculus;
Pre-Calculus and Algebra 2 Pre-AP)
2. Student-Friendly Objective(s) (SO):
 I can use algebraic properties to evaluate and simplify expressions.
 I can use problem solving strategies and verbal models.
 I can calculate, determine and identify the relevant properties of functions and their
transformations, using varied representations and the coordinate plane.
 I can apply these concepts to contexts involving my own life.
* Student Product in Terms of Bloom’s Taxonomy & Higher Level Thinking Skills Used:
K, A, A, S, E (Students respond to a Bloom’s-aligned hierarchy of questions related to this
activity.)
4. Checking For Learning Embedded Into Lesson: teacher circulates the work and is in the
work, listening to discussion on process and outcome. Students reciprocally discuss and
check processes used amongst themselves. Reciprocal teaching is used alternately amongst
groups and shoulder partners. PLC Managers model and teach Unit 3 problems from
McDougal Littell.
* Differentiated Instruction (VAKS Learners):
 Visual Learners: Students can use pictorial, graphic and nonlinguistic representations to
master the specific objectives for their enterprises vis a vis our learning goals in Unit 3.
 Auditory Learners: Students orally communicate, review and contribute within the group
both their and their group’s problem solving processes.
18

Kinesthetic Learners: Students can physically simulate transformations to their
businesses via manipulatives, technology, LTF GPVAN strategies and through graphing
on the coordinate plane.
5. TEKS-Aligned Assessment (Piece Described): Aligned with Region IV ESC Performance
Rubrics
 Procedural Skills: student-friendly rubric (with 4 categories to evaluate of their
businesses: store description and product; inequalities and equations; graphs relevant to
cost, revenue and profit, reflections on their business and investments).
 Conceptual Skills: students analyze and identify attributes of the coordinate plane and
concepts related to slope, y-intercepts, boundaries and regions, linear functions and linear
inequalities as they apply to business products and their development.
 Communicative Skills: Students have a 4-part rubric that details how they might exceed
expectations in terms of their business product and its application to Linear Programming
and Matrices.
Guiding Questions:
1. Now that I have built my store and business, what other constraints must I understand and
analyze to ensure the most efficient and profitable use of my capital and other resources?
(A, S, E)
2. Which business constraints and equations must I solve to have a profitable business?
Justify your explanation algebraically and graphically and verbally. (LTF GPVAN)
3. Describe how changes in your business might draw upon graphical transformations to
illustrate changes in profit, cost and revenue. Justify your description graphically and
algebraically.
“CLEAR”-ly-Aligned MDL & DAA Resources: MDL Lesson 3.1– 33 emphasizes solving
systems graphically and algebraically. For Chapter 3, Pre-AP-level Best Practices Toolkit
supplements are also used. A2 BPT, See Extension Activities on Linear Programming. See also
MDL Lesson 3.3: Graphing Calculator Activity. Assignments: focus on MDL Lessons 3.1-3.7:
Practice Workbook Problems and Notetaking Guide. Students will complete all sections of
Unit 3 on Quizlab as well as apply them to their differentiated products.
LTF Alignments/AP Big Ideas and Activities: AP Calculus [Analysis of Functions:
Transformations; Optimization; Rate of Change: Position, Velocity, Acceleration: ;
Areas and Volumes (Store layout); Accumulation; AP Statistics [Data Gathering and
Simulation; Probability; Graphical Displays: Distributions Measures of Center,
Variability and Shape: Exploring Linear and Non-linear Bivariate Data. All LTF
Activities deal with Inequalities, their Graphing, and Systems of Inequalities from Algebra
2 text.
Materials: Instructions, colored pencils, pegboards, graphing paper, technology and
PowerPoint, rulers and/or straightedges, rubric, TI-83 and 84 calculators, other tools.
TAKS & TEKS-Aligned Big Ideas and Objectives: Exit-Level TEKS aligned with TAKS
Objectives 1, 2, 3 and 4. See Quizlab Practice.
TI and Technology Resources Used: Quizlab; Animations; MDL Technology Resources;
TI-Tools and TI-84 Smart View Inequalities Applications; Flash Sites and Blogger Sites;
Parent Companion Site; Blog for students: www.westsidealg2.blogspot.com
19