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.]
