california career technical education model … and architecture. overview ... the cte model...

California Career Technical Education Model Curriculum Standards

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Architectural Design Pathway

Engineering Technology

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Engineering Design Pathway

Environmental Engineering Pathway

Table of ContentsEngineering and Architecture

Overview ............................................................................................................................................ iii

California Standards for Career Ready Practice ........................................................................... vi

Sector Description .............................................................................................................................1

Knowledge and Performance Anchor Standards ............................................................................2

1.0 Academics ..........................................................................................................................................2

2.0 Communications ...............................................................................................................................2

3.0 Career Planning and Management ..............................................................................................2

4.0 Technology .........................................................................................................................................3

5.0 Problem Solving and Critical Thinking .......................................................................................3

6.0 Health and Safety ............................................................................................................................3

7.0 Responsibility and Flexibility ........................................................................................................4

8.0 Ethics and Legal Responsibilities .................................................................................................4

9.0 Leadership and Teamwork ..............................................................................................................5

10.0 Technical Knowledge and Skills ....................................................................................................5

11.0 Demonstration and Application ...................................................................................................6

Pathway Standards ............................................................................................................................7

A. Architectural Design Pathway ..........................................................................................................7

B. Engineering Technology Pathway ....................................................................................................9

C. Engineering Design Pathway ..........................................................................................................12

D. Environmental Engineering Pathway ............................................................................................14

Academic Alignment Matrix ..........................................................................................................18

Contributors .....................................................................................................................................36

References ........................................................................................................................................37

EA | California Career Technical Education Model Curriculum Standardsii

Overview

The Career Technical Education (CTE) Model Curriculum Standards publication is organized for use as a complete document or for access to individual industry sectors and pathways. The document includes Standards for Career Ready Practice—which describe the knowledge and skills that students need prior to entering a career technical education program—as part of the career technical educa-tion sequence or as integrated elements of other course work in preparation for careers and college.

Each of the 15 industry sector sections includes a description, anchor standards, pathway standards, and an academic alignment matrix. The standards can be adjusted to be part of the curriculum (grades seven through twelve), provided through adult education, or included in community col-lege programs. The document also lists the representatives who participated in each sector’s content development and the references that were consulted to revise the CTE standards.

Standards for Career Ready PracticeCalifornia’s Standards for Career Ready Practice, which follow this overview, are based on the Career Ready Practices of the Common Career Technical Core (CCTC), a state-led initiative sponsored by the National Association of State Directors of Career Technical Education Consortium (NASDCTEc):

Career Ready Practices describe the career-ready skills that educators should seek to develop in their students. These practices are not exclusive to a Career Pathway, program of study, discipline or level of education. Career Ready Practices should be taught and reinforced in all career exploration and preparation programs with increasingly higher levels of complexity and expectation as a student advances through a program of study. (NASDCTEc 2012, 2)

California’s 12 Standards for Career Ready Practice align with the state’s CTE anchor standards and reflect the expectations from business and industry, labor and community organizations, and second-ary and postsecondary education representatives from 42 participating states.

Anchor StandardsThe 11 anchor standards build on the Standards for Career Ready Practice and are common across the 15 industry sectors. Content for these standards was drawn from several documents: “Preparing Students for the 21st Century Economy” (American Association of Colleges for Teacher Education and the Partnership for 21st Century Skills 2010); How Should Colleges Prepare Students to Succeed in Today’s Global Economy? (Association of American Colleges and Universities and Peter D. Hart Research Associates, Inc. 2006); “Importance of Skills and Knowledge for College and Career Readiness,” from The MetLife Survey of the American Teacher: Preparing Students for College and Careers (MetLife, Inc. 2011); and Are They Really Ready to Work? Employers’ Perspectives on the Basic Knowledge and Applied Skills of New Entrants to the 21st Century U.S. Workforce (The Conference Board et al. 2006).

Each anchor standard is followed by performance indicators using action verbs from the Beyond Knowledge Construct, presented in a hierarchical progression of simple tasks to more complex tasks. Performance indicators provide guidance for curriculum design and standards measurement.

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EA | California Career Technical Education Model Curriculum Standards

The industry-sector anchor standards have been customized with selected additions to better reflect the needs and special conditions of each industry sector.

Anchor Standard 1 (Academics) guides users to sector-specific core academic standards related to each industry sector, which are listed in the alignment matrix at the end of each sector section. Anchor standards 2–10 are deliberately aligned with one of the Common Core English language arts standards, using similar language demonstrating the natural connections between the two subjects. Anchor Standard 11 (Demonstration and Application) highlights classroom, laboratory, and workplace learning specific to the individual sector and pathways.

Pathway StandardsAll 15 industry sectors contain multiple pathways. In order to be identified and listed for an industry sector, each pathway had to meet the following criteria:

• unique to an industry sector

• has an occupational focus

• consistent in size and scope

• composed of similar functions

• inclusive of all aspects of the industry

• includes 8–12 pathway-specific standards

• demonstrates sequence potential

• reasonable and appropriate for high school

• leads to high-skill, high-wage, or high-demand jobs

• sustainable and viable over the next 10 years

Academic Alignment MatrixEach sector includes an academic alignment matrix that displays where a natural, obvious alignment occurs. Compiled by five teams of academic content experts in collaboration with industry-sector consultants, teachers, and other advisers, the alignment was selected if it was determined that the pathway standard would enhance, reinforce, or provide an application for a specific academic subject standard.

The alignment matrices include the subjects of Common Core English language arts and mathemat-ics standards, history/social studies standards, and Next Generation Science Core Ideas. To assist with further review and implementation, each academic alignment is notated with specific pathway standards codes.

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Engineering and Architecture | EA

ImplementationThe Standards for Career Ready Practice can be integrated with a course or incorporated into several courses over multiple school years (grades seven through twelve). The practices are expectations for all students, whether they are enrolled in a CTE program or following a more generalized course sequence. It is expected that all students who exit high school will be proficient in these practices.

The anchor standards are the basis for each of the pathways within each sector. These standards are designed to assist with the development of course curricula and instructional lesson plans; they describe what is to be taught and measured. In most cases, the teacher determines the sequence and strategies to be used to meet the needs of the student population he or she is serving.

The performance indicators that follow each standard offer guidance for both course design and student assessment. They are intended to guide course work as it is developed. The pathways organize the standards with a career focus, but they are not designed to be offered as single courses. Rather, the standards from each pathway are collected and organized into a sequence of learning. To meet local demands of business and industry and particular student populations, standards can be collected from more than one sector to create a course.

Using the academic alignment matrices as a resource, academic and CTE teachers can see where enhancements and support for both sets of standards can be initiated. CTE teachers can quickly iden-tify academic standards that have a substantial relationship to their instruction. Likewise, academic teachers can specify individual academic standards and quickly identify related CTE standards, which will assist them in incorporating application and technology in their curricula and lessons.

The CTE Model Curriculum Standards are intended to serve the entire education community—from middle schools and high schools to postsecondary colleges and career training programs. A major aim of these standards is to prepare students for postsecondary education and training and to help them make a smooth transition into the workforce. In order for both the people and the economy of Cali-fornia to prosper, it is essential for all students to emerge from schools ready to pursue their career and college goals. Equipping all high school students with the knowledge and skills necessary to plan and manage their education and careers throughout their lives will help to guarantee these important outcomes. Strong CTE programs will continue to provide important educational opportunities to assist students as they pursue their dreams and strive for economic prosperity. The CTE Model Curriculum Standards are a resource for educators and the business world for ensuring high-quality CTE learning experiences and improved student outcomes in the twenty-first-century economy.

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California Standards for Career Ready Practice

Standards for Career Ready Practice describe the fundamental knowledge and skills that a career-ready student needs in order to prepare for transition to postsecondary education, career training, or the workforce. These standards are not exclusive to a career pathway, a CTE program of study, a par-ticular discipline, or level of education. Standards for Career Ready Practice are taught and reinforced in all career exploration and preparation programs with increasingly higher levels of complexity and expectation as a student advances through a program of study. Standards for Career Ready Practice are a valuable resource to CTE and academic teachers designing curricula and lessons in order to teach and reinforce the career-ready aims of the CTE Model Curriculum Standards and the Common Core State Standards.

1. Apply appropriate technical skills and academic knowledge.Career-ready individuals readily access and use the knowledge and skills acquired through experience and education. They make connections between abstract concepts with real-world applications and recognize the value of academic preparation for solving problems, communicating with others, calcu-lating measures, and other work-related practices.

2. Communicate clearly, effectively, and with reason.Career-ready individuals communicate thoughts, ideas, and action plans with clarity, using written, verbal, electronic, and/or visual methods. They are skilled at interacting with others, are active listen-ers who speak clearly and with purpose, and are comfortable with the terminology common to the workplace environment. Career-ready individuals consider the audience for their communication and prepare accordingly to ensure the desired outcome.

3. Develop an education and career plan aligned with personal goals.Career-ready individuals take personal ownership of their own educational and career goals and man-age their individual plan to attain these goals. They recognize the value of each step in the educa-tional and experiential process and understand that nearly all career paths require ongoing education and experience to adapt to practices, procedures, and expectations of an ever-changing work envi-ronment. They seek counselors, mentors, and other experts to assist in the planning and execution of education and career plans.

4. Apply technology to enhance productivity.Career-ready individuals find and maximize the productive value of existing and new technology to accomplish workplace tasks and solve workplace problems. They are flexible and adaptive in acquir-ing and using new technology. They understand the inherent risks—personal and organizational—of technology applications, and they take actions to prevent or mitigate these risks.

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5. Utilize critical thinking to make sense of problems and persevere in solving them.Career-ready individuals recognize problems in the workplace, understand the nature of the problems, and devise effective plans to solve the problems. They thoughtfully investigate the root cause of a problem prior to introducing solutions. They carefully consider options to solve the problem and, once agreed upon, follow through to ensure the problem is resolved.

6. Practice personal health and understand financial literacy.Career-ready individuals understand the relationship between personal health and workplace per-formance. They contribute to their personal well-being through a healthy diet, regular exercise, and mental health activities. Career-ready individuals also understand that financial literacy leads to a secure future that enables career success.

7. Act as a responsible citizen in the workplace and the community.Career-ready individuals understand the obligations and responsibilities of being a member of a com-munity and demonstrate this understanding every day through their interactions with others. They are aware of the impacts of their decisions on others and the environment around them and think about the short-term and long-term consequences of their actions. They are reliable and consistent in going beyond minimum expectations and in participating in activities that serve the greater good.

8. Model integrity, ethical leadership, and effective management.Career-ready individuals consistently act in ways that align with personal and community-held ideals and principles. They employ ethical behaviors and actions that positively influence others. They have a clear understanding of integrity and act on this understanding in every decision. They use a variety of means to positively impact the direction and actions of a team or organization, and they recognize the short-term and long-term effects that management’s actions and attitudes can have on produc-tivity, morale, and organizational culture.

9. Work productively in teams while integrating cultural and global competence.Career-ready individuals positively contribute to every team as both team leaders and team members. They apply an awareness of cultural differences to avoid barriers to productive and positive interac-tion. They interact effectively and sensitively with all members of the team and find ways to increase the engagement and contribution of other members.

10. Demonstrate creativity and innovation.Career-ready individuals recommend ideas that solve problems in new and different ways and con-tribute to the improvement of the organization. They consider unconventional ideas and suggestions by others as solutions to issues, tasks, or problems. They discern which ideas and suggestions may have the greatest value. They seek new methods, practices, and ideas from a variety of sources and apply those ideas to their own workplace practices.

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11. Employ valid and reliable research strategies.Career-ready individuals employ research practices to plan and carry out investigations, create solu-tions, and keep abreast of the most current findings related to workplace environments and practices. They use a reliable research process to search for new information and confirm the validity of sources when considering the use and adoption of external information or practices.

12. Understand the environmental, social, and economic impacts of decisions.Career-ready individuals understand the interrelated nature of their actions and regularly make deci-sions that positively impact other people, organizations, the workplace, and the environment. They are aware of and utilize new technologies, understandings, procedures, and materials and adhere to regulations affecting the nature of their work. They are cognizant of impacts on the social condition, environment, workplace, and profitability of the organization.

Note: As stated previously, California’s Standards for Career Ready Practice are based on the CCTC Career Ready Practices posted at https://careertech.org/ (accessed June 8, 2016).

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https://careertech.org/


Engineering and Architecture

Sector DescriptionThis sector is designed to provide a foundation in engineering and architecture

sector pathways and occupations for students in California. Students are engaged

in an instructional program that integrates academic and technical preparation

and focuses on career awareness, career exploration, and career preparation in

four pathways that emphasize real-world, occupationally relevant experiences of

significant scope and depth: Architectural Design; Engineering Technology; Engi-

neering Design; and Environmental Engineering. To prepare students for continued

training, advanced educational opportunities, and direct entry to a career,

the Engineering and Architecture programs offer the following components:

classroom, laboratory, and hands-on contextual learning; project- and

work-based instruction; and leadership and interpersonal skills development.

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Engineering and ArchitectureKnowledge and Performance Anchor Standards

1.0 AcademicsAnalyze and apply appropriate academic standards required for successful industry sector pathway completion leading to postsecondary education and employment. Refer to the Engineering and Architecture academic alignment matrix for identification of standards.

2.0 CommunicationsAcquire and accurately use Engineering and Architecture sector terminology and protocols at the career and college readiness level for communicating effectively in oral, written, and multimedia formats. (Direct alignment with LS 9-10, 11-12.6)

2.1 Recognize the elements of communication using a sender–receiver model.

2.2 Identify barriers to accurate and appropriate communication.

2.3 Interpret verbal and nonverbal communications and respond appropriately.

2.4 Demonstrate elements of written and electronic communication, such as accurate spelling, grammar, and format.

2.5 Communicate information and ideas effectively to multiple audiences using a variety of media and formats.

2.6 Advocate and practice safe, legal, and responsible use of digital media information and communications technologies.

3.0 Career Planning and ManagementIntegrate multiple sources of career information from diverse formats to make informed career decisions, solve problems, and manage personal career plans. (Direct alignment with SLS 11-12.2)

3.1 Identify personal interests, aptitudes, information, and skills necessary for informed career decision making.

3.2 Evaluate personal character traits, such as trust, respect, and responsibility, and understand the impact they can have on career success.

3.3 Explore how information and communication technologies are used in career planning and decision making.

3.4 Research the scope of career opportunities available and the requirements for education, training, certification, and licensure.

3.5 Integrate changing employment trends, societal needs, and economic conditions into career planning.

3.6 Recognize the role and function of professional organizations, industry associations, and organized labor in a productive society.

3.7 Recognize the importance of small business in the California and global economies.

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3.8 Understand how digital media are used by potential employers and postsecondary agencies to evaluate candidates.

3.9 Develop a career plan that reflects career interests, pathways, and postsecondary options.

4.0 TechnologyUse existing and emerging technology to investigate, research, and produce products and services, including new information, as required in the Engineering and Architecture sector workplace environment. (Direct alignment with WS 11-12.6)

4.1 Use electronic reference materials to gather information and produce products and services.

4.2 Employ Web-based communications responsibly and effectively to explore complex systems and issues.

4.3 Use information and communication technologies to synthesize, summarize, compare, and contrast information from multiple sources.

4.4 Discern the quality and value of information collected using digital technologies, and recognize bias and intent of the associated sources.

4.5 Research past, present, and projected technological advances as they impact a particular pathway.

4.6 Assess the value of various information and communication technologies to interact with constituent populations as part of a search of the current literature or in relation to the information task.

5.0 Problem Solving and Critical ThinkingConduct short, as well as more sustained, research projects to create alternative solutions to answer a question or solve a problem unique to the Engineering and Architecture sector using critical and creative thinking; logical reasoning, analysis, inquiry, and problem-solving techniques. (Direct alignment with WS 11-12.7)

5.1 Identify and ask significant questions that clarify various points of view to solve problems.

5.2 Solve predictable and unpredictable work-related problems using various types of reasoning (inductive, deductive) as appropriate.

5.3 Use systems thinking to analyze how various components interact with each other to produce outcomes in a complex work environment.

5.4 Interpret information and draw conclusions, based on the best analysis, to make informed decisions.

6.0 Health and SafetyDemonstrate health and safety procedures, regulations, and personal health practices and determine the meaning of symbols, key terms, and domain-specific words and phrases as related to the Engi-neering and Architecture sector workplace environment. (Direct alignment with RSTS 9-10, 11-12.4)

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6.1 Locate, and adhere to, Material Safety Data Sheet (MSDS) instructions.

6.2 Interpret policies, procedures, and regulations for the workplace environment, including employer and employee responsibilities.

6.3 Use health and safety practices for storing, cleaning, and maintaining tools, equipment, and supplies.

6.4 Practice personal safety when lifting, bending, or moving equipment and supplies.

6.5 Demonstrate how to prevent and respond to work-related accidents or injuries; this includes demonstrating an understanding of ergonomics.

6.6 Maintain a safe and healthful working environment.

6.7 Be informed of laws/acts pertaining to the Occupational Safety and Health Administration (OSHA).

7.0 Responsibility and FlexibilityInitiate, and participate in, a range of collaborations demonstrating behaviors that reflect personal and professional responsibility, flexibility, and respect in the Engineering and Architecture sector workplace environment and community settings. (Direct alignment with SLS 9-10, 11-12.1)

7.1 Recognize how financial management impacts the economy, workforce, and community.

7.2 Explain the importance of accountability and responsibility in fulfilling personal, community, and workplace roles.

7.3 Understand the need to adapt to changing and varied roles and responsibilities.

7.4 Practice time management and efficiency to fulfill responsibilities.

7.5 Apply high-quality techniques to product or presentation design and development.

7.6 Demonstrate knowledge and practice of responsible financial management.

7.7 Demonstrate the qualities and behaviors that constitute a positive and professional work demeanor, including appropriate attire for the profession.

7.8 Explore issues of global significance and document the impact on the Engineering and Architecture sector.

8.0 Ethics and Legal ResponsibilitiesPractice professional, ethical, and legal behavior, responding thoughtfully to diverse perspectives and resolving contradictions when possible, consistent with applicable laws, regulations, and organizational norms. (Direct alignment with SLS 11-12.1d)

8.1 Access, analyze, and implement quality assurance standards of practice.

8.2 Identify local, district, state, and federal regulatory agencies, entities, laws, and regulations related to the Engineering and Architecture industry sector.

8.3 Demonstrate ethical and legal practices consistent with Engineering and Architecture sector workplace standards.

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8.4 Explain the importance of personal integrity, confidentiality, and ethical behavior in the workplace.

8.5 Analyze organizational culture and practices within the workplace environment.

8.6 Adhere to copyright and intellectual property laws and regulations, and use and appropriately cite proprietary information.

8.7 Conform to rules and regulations regarding sharing of confidential information, as determined by Engineering and Architecture sector laws and practices.

9.0 Leadership and TeamworkWork with peers to promote divergent and creative perspectives, effective leadership, group dynamics, team and individual decision making, benefits of workforce diversity, and conflict resolution as practiced in the SkillsUSA career technical student organization. (Direct alignment with SLS 11-12.1b)

9.1 Define leadership and identify the responsibilities, competencies, and behaviors of successful leaders.

9.2 Identify the characteristics of successful teams, including leadership, cooperation, collabora-tion, and effective decision-making skills, as applied in groups, teams, and career technical student organization activities.

9.3 Understand the characteristics and benefits of teamwork, leadership, and citizenship in the school, community, and workplace setting.

9.4 Explain how professional associations and organizations and associated leadership develop-ment and competitive career development activities enhance academic preparation, promote career choices, and contribute to employment opportunities.

9.5 Understand that the modern world is an international community and requires an expanded global view.

9.6 Respect individual and cultural differences and recognize the importance of diversity in the workplace.

9.7 Participate in interactive teamwork to solve real Engineering and Architecture sector issues and problems.

10.0 Technical Knowledge and SkillsApply essential technical knowledge and skills common to all pathways in the Engineering and Architecture sector, following procedures when carrying out experiments or performing technical tasks. (Direct alignment with WS 11-12.6)

10.1 Interpret and explain terminology and practices specific to the Engineering and Architecture sector.

10.2 Comply with the rules, regulations, and expectations of all aspects of the Engineering and Architecture sector.

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10.3 Construct projects and products specific to the Engineering and Architecture sector requirements and expectations.

10.4 Collaborate with industry experts for specific technical knowledge and skills.

11.0 Demonstration and ApplicationDemonstrate and apply the knowledge and skills contained in the Engineering and Architecture anchor standards, pathway standards, and performance indicators in classroom, laboratory and workplace settings, and through the SkillsUSA career technical student organization.

11.1 Utilize work-based/workplace learning experiences to demonstrate and expand upon knowledge and skills gained during classroom instruction and laboratory practices specific to the Engineering and Architecture sector program of study.

11.2 Demonstrate proficiency in a career technical pathway that leads to certification, licensure, and/or continued learning at the postsecondary level.

11.3 Demonstrate entrepreneurship skills and knowledge of self-employment options and innovative ventures.

11.4 Employ entrepreneurial practices and behaviors appropriate to Engineering and Architecture sector opportunities.

11.5 Create a portfolio, or similar collection of work, that offers evidence through assessment and evaluation of skills and knowledge competency as contained in the anchor standards, pathway standards, and performance indicators.

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Engineering and ArchitecturePathway Standards

A. Architectural Design PathwayThe Architectural Design pathway provides learning opportunities for students interested in preparing for careers in such areas as architecture, industrial design, and civil engineering.

Sample occupations associated with this pathway:

Drafter

Architect

Structural Designer

Building Department Plan Examiner

City Planner

A1.0 Understand how history shaped architecture and know significant events in the history of architectural design.

A1.1 Know significant historical architectural projects and their effects on society.

A1.2 Understand the development of architectural systems in relation to aesthetics, efficiency, and safety.

A2.0 Compare the theoretical, practical, and contextual issues that influence design.

A2.1 Describe the influence of community context and zoning requirements on architectural design.

A2.2 Understand the ways in which sociocultural conditions and issues influence architectural design.

A2.3 Compare the theoretical and practical effects of human and physical factors on the development of architectural designs.

A2.4 Analyze project design and compile a cost analysis.

A3.0 Understand the sketching processes used in concept development.

A3.1 Apply sketching techniques to a variety of architectural models.

A3.2 Produce proportional two- and three-dimensional sketches and designs.

A3.3 Present conceptual ideas, analysis, and design concepts using freehand graphic communication techniques.

A4.0 Understand the use of computer-aided drafting (CAD) in developing architectural designs.

A4.1 Develop a preliminary architectural proposal using CAD software.

A4.2 Analyze viability of a project as the design is developed using Building Information Modeling (BIM).

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A5.0 Compare the relationship between architecture and the external environment.

A5.1 Understand the significance of sustainable building design practices that incorporate beneficial energy and environmental design policies.

A5.2 Develop a site analysis that considers passive energy techniques, sustainability issues, and landscaping.

A5.3 Create a building design that incorporates passive and/or active energy-efficient technologies.

A6.0 Understand methods used to analyze simple structures.

A6.1 Understand load transfer mechanisms.

A6.2 Understand stress-strain relationships of building structures.

A6.3 Interpret structural design considerations, including load-bearing relationships of shear walls, columns, and beams.

A6.4 Design a simple structure by using structural analysis principles.

A7.0 Understand the properties of structural materials.

A7.1 Understand the integration of architectural factors, such as soil mechanics, foundation design, engineering materials, and structure design.

A7.2 Develop a stress analysis chart of typical structural components.

A7.3 Evaluate available building materials (e.g., steel, concrete, and wood) by considering their properties and their effect on building form.

A7.4 Develop a preliminary building plan using the appropriate materials.

A8.0 Systematically complete an architectural project.

A8.1 Describe the various components of structures, including lighting; heating, ventilating, and air-conditioning (HVAC); mechanical; electrical; plumbing; communication; security; and vertical transportation systems.

A8.2 Develop a preliminary proposal for presentation of an architectural design.

A8.3 Read and interpret architectural and construction plans, drawings, diagrams, and specifications.

A8.4 Develop a complete set of architectural plans and drawings.

A8.5 Estimate the materials needed for a project by reading an architectural drawing.

A8.6 Plan a project using site and building restrictions imposed by various entities (e.g., Planning, Zoning, Building, and Home Owners Association [HOA]).

A8.7 Plan the sequence of events leading to an architectural project.

A9.0 Using various methods create both written and digital portfolios to represent architectural renderings.

A9.1 Develop a binder or digital portfolio representative of completed work for presentation.

A9.2 Prepare an effective oral presentation of the portfolio content.

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B. Engineering Technology PathwayThe Engineering Technology pathway provides learning opportunities for students interested in preparing for careers in the design, production, or maintenance of mechanical, electrical, electronics, and computer and electromechanical systems and products.


Surveyor

Research and Development Analyst

Engineering Technologist

Field Engineer

Operations Engineer

B1.0 Communicate and interpret information clearly in industry-standard visual and written formats.

B1.1 Explain the classification and use of various components, symbols, abbreviations, and media common to technical drawings.

B1.2 Describe the current industry standards for illustration and layout.

B1.3 Draw flat layouts of a variety of objects by using the correct drafting tools, techniques, and media.

B1.4 Organize and complete an assembly drawing using information collected from detailed drawings.

B1.5 Create reports and data sheets for writing specifications.

B2.0 Demonstrate the sketching process used in concept development.

B2.1 Understand the process of producing proportional two- and three-dimensional sketches and designs.

B2.2 Apply sketching techniques to a variety of architectural and engineering models.

B2.3 Present conceptual ideas, analysis, and design concepts using freehand graphic communication techniques.

B3.0 Identify the fundamentals of the theory, measurement, control, and applications of electrical energy, including alternating and direct currents.

B3.1 Understand the characteristics of alternating current (AC) and how it is generated; the characteristics of the sine wave; and of AC, tuned, and resonant circuits; and the nature of the frequency spectrum.

B3.2 Analyze relationships between voltage, current, resistance, and power related to direct current (DC) circuits.

B3.3 Calculate, construct, measure, and interpret both AC and DC circuits.

B3.4 Understand how electrical control and protection devices are used in electrical systems.

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B3.5 Calculate loads, currents, and circuit-operating parameters.

B3.6 Classify and use various electrical components, symbols, abbreviations, media, and standards of electrical drawings.

B3.7 Analyze, repair, or measure electrical and electronic systems, circuits, or components using appropriate electronic instruments.

B3.8 Predict the effects of circuit conditions on the basis of measurements and calculations of voltage, current, resistance, and power.

B4.0 Understand the concepts of physics that are fundamental to engineering technology.

B4.1 Describe Newton’s laws and how they affect and define the movement of objects.

B4.2 Explain how the laws of conservation of energy and momentum provide a way to predict and describe the movement of objects.

B4.3 Compare the effects and applications of heat transfer and thermal dynamic processes.

B4.4 Explore the fundamentals and properties of waveforms and how waveforms may be used to carry energy.

B4.5 Analyze how electric and magnetic phenomena are related and know common practical applications.

B5.0 Understand how the principles of force, work, rate, power, energy, and resistance relate to mechanical, electrical, fluid, and thermal engineering systems.

B5.1 Differentiate between scalars and vectors.

B5.2 Solve problems by using the concept of vectoring to predict resultants.

B5.3 Compare and explore the six simple machines and their applications.

B5.4 Evaluate how energy is transferred and predict the effects of resistance in mechanical, electrical, fluid, and thermal systems.

B5.5 Formulate and solve problems by using the appropriate units applied in mechanical, electrical, fluid, and thermal engineering systems.

B6.0 Employ the design process to solve analysis and design problems.

B6.1 Understand the steps in the design process.

B6.2 Determine what information and principles are relevant to a problem and its analysis.

B6.3 Choose between alternate solutions in solving a problem and be able to justify the choices made in determining a solution.

B6.4 Translate word problems into mathematical statements when appropriate.

B6.5 Demonstrate the process of developing multiple details, within design constraints, into a single solution.

B6.6 Construct a prototype from plans and test it.

B6.7 Evaluate and redesign a prototype on the basis of collected test data.

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B7.0 Understand industrial engineering processes, including the use of tools and equipment, methods of measurement, and quality assurance.

B7.1 Know the structure and processes of a quality assurance cycle.

B7.2 Describe the major manufacturing processes.

B7.3 Use tools, fasteners, and joining systems employed in selected engineering processes.

B7.4 Estimate and measure the size of objects in both Standard International and United States units.

B7.5 Apply appropriate geometric dimensioning and tolerancing (GD&T) practices.

B7.6 Calibrate precision measurement tools and instruments to measure objects.

B8.0 Understand fundamental control system design and develop systems that complete preprogrammed tasks.

B8.1 Identify the elements and processes necessary to develop a controlled system that performs a task.

B8.2 Demonstrate the use of sensors for data collection and process correction in controlled systems.

B8.3 Perform tests, collect data, analyze relationships, and display data in a simulated or modeled system using appropriate tools and technology.

B8.4 Program a computing device to control systems or process.

B8.5 Use motors, solenoids, and similar devices as output mechanisms in controlled systems.

B8.6 Assemble input, processing, and output devices to create controlled systems capable of accurately completing a preprogrammed task.

B9.0 Understand the fundamentals of systems and market influences on products as they are developed and released to production.

B9.1 Understand the process of product development.

B9.2 Understand decision matrices and the use of graphic tools in illustrating the develop-ment of a product and the processes involved.

B10.0 Design and construct a culminating project effectively using engineering technology.

B10.1 Use methods and techniques for employing all engineering technology equipment appropriately.

B10.2 Apply conventional engineering technology processes and procedures accurately, appropriately, and safely.

B10.3 Apply the concepts of engineering technology to the tools, equipment, projects, and procedures of the Engineering Technology Pathway.

B11.0 Understand the methods of creating both written and digital portfolios.

B11.1 Develop a binder or digital portfolio representative of student work for presentation.

B11.2 Give an effective oral presentation of a portfolio.

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C. Engineering Design PathwayThe Engineering Design pathway provides learning opportunities for students interested in preparing for careers in the design and production of mechanical, electrical, and computer systems.


Mechanical/Electrical Drafter

Design Engineer

Manufacturing Design Engineer

Project Architect

C1.0 Understand historical and current events related to engineering design and their effects on society.

C1.1 Know historical and current events that have relevance to engineering design.

C1.2 Interpret the development of graphic language in relation to engineering design.

C2.0 Understand the effective use of engineering design equipment.

C2.1 Employ engineering design equipment using the appropriate methods and techniques.

C2.2 Apply conventional engineering design equipment procedures accurately, appropriately, and safely.

C2.3 Apply the concepts of engineering design to the tools, equipment, projects, and procedures of the Engineering Design Pathway.

C3.0 Understand the sketching process used in concept development.

C3.1 Apply sketching techniques to a variety of architectural models.

C3.2 Produce proportional two- and three-dimensional sketches and designs.

C3.3 Present conceptual ideas, analysis, and design concepts using freehand, graphic, communication techniques.

C4.0 Understand measurement systems as they apply to engineering design.

C4.1 Know how the various measurement systems are used in engineering drawings.

C4.2 Understand the degree of accuracy necessary for engineering design.

C5.0 Use proper projection techniques to develop orthographic drawings.

C5.1 Understand the concepts and procedures necessary for producing drawings.

C5.2 Develop multiview drawings using the orthographic projection process.

C5.3 Understand the various techniques for viewing objects.

C5.4 Use the concepts of geometric construction in the development of design drawings.

C5.5 Apply pictorial drawings derived from orthographic multiview drawings and sketches.

12


C6.0 Understand the applications and functions of sectional views.

C6.1 Understand the function of sectional views.

C6.2 Clarify hidden features of an object using a sectional view and appropriate cutting planes.

C7.0 Understand the applications and functions of auxiliary views.

C7.1 Understand the function of auxiliary views.

C7.2 Use auxiliary views to clarify the true shape and size of an object.

C8.0 Understand and apply proper dimensioning standards to drawings.

C8.1 Know a variety of drafting applications and understand the proper dimensioning standards for each.

C8.2 Apply dimension to various objects and features.

C9.0 Understand the tolerance relationships between mating parts.

C9.1 Understand what constitutes mating parts in engineering design.

C9.2 Interpret geometric tolerancing symbols in a drawing.

C9.3 Use tolerancing in an engineering drawing.

C10.0 Understand the methods of applying text to a drawing.

C10.1 Describe the processes of lettering and/or text editing.

C10.2 Implement standard methods of title block creation and use.

C10.3 Develop drawings using notes and specifications.

C10.4 Plan, prepare, and interpret drawings and models through traditional drafting or computer-aided design (CAD) techniques.

C11.0 Understand the methods of creating both written and digital portfolios.

C11.1 Develop a binder or digital portfolio representative of completed work for presentation.

C11.2 Give an effective oral presentation of a portfolio.

13



D. Environmental Engineering PathwayThe Environmental Engineering pathway includes design and development processes, equipment, and systems that are used to create, monitor, prevent, or correct environmental events and conditions.


Environmental Safety Technician

Environmental Specialist

Environmental Analyst

Environmental Scientist

Air Pollution Control Engineer

D1.0 Communicate and interpret information clearly in industry-standard visual and written formats.

D1.1 Know the current industry standards for illustration and layout.

D1.2 Understand the classification and use of various electronic components, symbols, abbreviations, and media common to electronic drawings.

D1.3 Organize and complete site plans.

D2.0 Understand the design process and how to solve analysis and design problems.

D2.1 Understand the steps in the design process.

D2.2 Determine what information and principles are relevant to a problem and its analysis.

D2.3 Choose between alternate solutions in solving a problem and be able to justify choices in determining a solution.

D2.4 Understand the process of developing multiple details into a single solution.

D2.5 Translate word problems into mathematical statements when appropriate.

D2.6 Build a prototype from plans and test it.

D2.7 Evaluate and redesign a prototype on the basis of collected test data.

D3.0 Understand the fundamentals of earth science as they relate to environmental engineering.

D3.1 Know the fundamental stages of geochemical cycles.

D3.2 Understand the effects of pollution on hydrological features.

D3.3 Classify the three major groups of rocks, according to their origin, on the basis of texture and mineral composition.

D3.4 Analyze the importance and use of soil and evaluate how soil may be preserved and conserved.

D3.5 Assess and evaluate geological hazards.

14


D3.6 Interpret and evaluate topographical maps and images.

D3.7 Locate and evaluate soil or geological conditions or features using global positioning systems equipment and related technology.

D3.8 Analyze soil erosion and identify the causes.

D4.0 Understand the effects of the weather, the hydrosphere, and the atmosphere on the environment.

D4.1 Know the common causes of atmospheric contamination.

D4.2 Understand the effects of weather fronts on regional air pollution.

D4.3 Understand the relationship between the health of the marine environment and climate control.

D4.4 Understand the effects of human activity on the atmospheric environment.

D4.5 Analyze and predict conditions of meteorological events.

D4.6 Analyze the mechanisms for air mass movement.

D4.7 Analyze atmospheric pressure and weather systems.

D5.0 Understand how the principles of force, work, rate, power, energy, and resistance relate to mechanical, electrical, fluid, and thermal engineering systems.

D5.1 Know the six simple machines and their applications.

D5.2 Know how energy is transferred and the effects of resistance in mechanical, electrical, fluid, and thermal systems.

D5.3 Understand scalars and vect

D5.4 Solve problems by using the concept of vectoring to predict the resultant forces.

D5.5 Solve problems by using the appropriate units applied in mechanical, electrical, fluid, and thermal engineering systems.

D6.0 Evaluate regional interactive systems and elements that create harmful environmental effects.

D6.1 Describe the sources of, and impacts attributable to, pollution and contamination.

D6.2 Recognize the actions that cause resource depletion.

D6.3 Define the causes of erosion and soil depletion.

D6.4 Describe the attributes and proliferation of hardscape.

D6.5 Identify the sources of, and impacts attributable to, habitat alteration.

D7.0 Understand the concepts of physics that are fundamental to engineering technology.

D7.1 Understand Newton’s laws and how they affect and define the movement of objects.

D7.2 Understand how the laws of conservation of energy and momentum provide a way to predict and describe the movement of objects.

15


D7.3 Understand how electric and magnetic phenomena are related and know common practical applications.

D7.4 Analyze the fundamentals and properties of waveforms and how waveforms may be used to carry energy.

D8.0 Understand the effective use of environmental and natural science equipment.

D8.1 Use appropriate methods and techniques for employing environmental and natural science equipment.

D8.2 Apply conventional environmental and natural science processes and procedures accurately, appropriately, and safely.

D8.3 Apply the concepts of environmental and natural science to the tools, equipment, projects, and procedures of the Environmental Engineering Pathway.

D9.0 Identify the role and impact of waste management systems, and their operations, on the environment.

D9.1 Understand the role of waste and storm water management systems, their operation, and their impact on the environment.

D9.2 Explore the causes and effects of pollution linked to wastewater treatment facilities.

D9.3 Identify wastewater treatment processes that lessen environmental impacts and improve water reuse.

D9.4 Explain the types and sources of hazardous waste and associated safety practices and legal requirements for handling and disposing of such waste.

D9.5 Design solid waste disposal processes that lessen environmental impacts and improve recycling.

D10.0 Understand the field of land use management and its potential for environmental impact.

D10.1 Describe the need for and role of habitat preservation.

D10.2 Describe the composition, role, and function of ecosystems, including trends affecting viability.

D10.3 Explain the laws and regulations pertaining to ecosystem preservation and use.

D10.4 Demonstrate the need for, and methods of, land use planning.

D10.5 Identify the aspects of land use planning and describe current trends.

D10.6 Summarize the relationship between land use planning and energy use and distribution.

D10.7 Explain the laws and regulations pertaining to land use planning.

D10.8 Develop strategies to maximize the effectiveness of land use planning.

D11.0 Research the role of air quality management and systems, their operations, and their impact on the environment.

D11.1 Understand the elements that create outdoor air quality.

16


D11.2 Summarize the causes of air pollutants and their chemical composition.

D11.3 Research air pollutants and their threat to human health.

D11.4 Understand U.S. and California laws and regulations related to air pollution control programs and health effects of air pollution.

D11.5 Describe the basic U.S. Environmental Protection Agency (EPA) and California Air Resources Board (ARB) roles and regulations.

D12.0 Implement processes to support energy efficiency.

D12.1 Understand the relationship between power and energy efficiency.

D12.2 Outline how domestic and industrial appliances and systems affect the environment, such as water units and heating and cooling systems.

D12.3 Compare costs of alternate/renewable energy sources, systems, and appliances and traditional energy sources, systems, and appliances.

D12.4 Conduct an energy audit.

D13.0 Research drinking-water sources, systems, treatment, and conservation.

D13.1 Understand water reuse: issues, strategies, technologies, and applications.

D13.2 Analyze strategies for improving energy efficiencies in water collection and distribution.

D13.3 Describe the role of environmental engineering and green energy in water systems.

D13.4 Understand the functions and operations of water storage, reservoirs, aqueducts, and dams.

D13.5 Identify and explain the applicable codes and regulations.

D14.0 Evaluate the impact and flow management of storm water, rivers, and groundwater.

D14.1 Understand the designs and tools used in water flow management.

D14.2 Describe watershed modeling.

D14.3 Understand the principles and applications of drainage engineering.

D14.4 Use the Hydrologic Engineering Centers River Analysis System (HEC-RAS).

D14.5 Analyze and interpret contaminated harbor and river sediment.

D14.6 Describe the concerns and strategies for catastrophic storm water events and management.

17


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

ENGL

ISH

LA

NGU

AGE

ART

S

Lang

uage

Sta

ndar

ds –

LS

(Sta

ndar

d A

rea,

Gra

de L

evel

, Sta

ndar

d #)

11-1

2.1.

Dem

onst

rate

com

man

d of

the

con

vent

ions

of s

tand

ard

Engl

ish

gram

mar

and

usa

ge

A9.0

B1.0

C11.

0D1

.0w

hen

writ

ing

or s

peak

ing.

11-1

2.2.

Dem

onst

rate

com

man

d of

the

con

vent

ions

of s

tand

ard

Engl

ish

capi

taliz

atio

n,

A9.0

B1.0

C11.

0D1

.0nc

tuat

ion,

and

spe

lling

whe

n w

ritin

g.

Read

ing

Stan

dard

s fo

r In

form

atio

nal T

ext

– RS

IT (

Stan

dard

Are

a, G

rade

Lev

el,

Stan

dard

#)

11-1

2.2.

Det

erm

ine

two

or m

ore

cent

ral i

deas

of a

tex

t an

d an

alyz

e th

eir d

evel

opm

ent

over

the

A1

.0, A

2.0,

co

urse

of t

he t

ext,

incl

udin

g ho

w t

hey

inte

ract

and

bui

ld o

n on

e an

othe

r to

prov

ide

a co

mpl

ex

B1.0

C1.0

D1.0

A5.0

, A8.

0an

alys

is; p

rovi

de a

n ob

ject

ive

sum

mar

y of

the

tex

t.

11-1

2.7.

Inte

grat

e an

d ev

alua

te m

ultip

le s

ourc

es o

f inf

orm

atio

n pr

esen

ted

in d

iffe

rent

med

ia o

r fo

rmat

s (e

.g.,

visu

ally

, qua

ntita

tivel

y) a

s w

ell a

s in

wor

ds in

ord

er t

o ad

dres

s a

ques

tion

or s

olve

A1

.0a

prob

lem

.

Read

ing

Stan

dard

s fo

r Li

tera

cy in

His

tory

/Soc

ial S

tudi

es –

RH

SS (

Stan

dard

Are

a,

Grad

e Le

vel,

Stan

dard

#)

11-1

2.2.

Det

erm

ine

the

cent

ral i

deas

or i

nfor

mat

ion

of a

prim

ary

or s

econ

dary

sou

rce;

pro

vide

A1

.0, A

2.0

C1.0

an a

ccur

ate

sum

mar

y th

at m

akes

cle

ar t

he r

elat

ions

hips

am

ong

the

key

deta

ils a

nd id

eas.

11-1

2.7.

Inte

grat

e an

d ev

alua

te m

ultip

le s

ourc

es o

f inf

orm

atio

n pr

esen

ted

in d

iver

se f

orm

ats

and

med

ia (e

.g.,

visu

ally

, qua

ntita

tivel

y, a

s w

ell a

s in

wor

ds) i

n or

der t

o ad

dres

s a

ques

tion

or

A1.0

C1.0

solv

e a

prob

lem

.

11-1

2.10

. By

the

end

of g

rade

12,

rea

d an

d co

mpr

ehen

d hi

stor

y/so

cial

stu

dies

tex

ts in

the

A1

.0, A

2.0

C1.0

grad

es 1

1-12

tex

t co

mpl

exit

y ba

nd in

depe

nden

tly a

nd p

rofic

ient

ly.

Read

ing

Stan

dard

s fo

r Li

tera

cy in

Sci

ence

and

Tec

hnic

al S

ubje

cts

– RL

ST

(Sta

ndar

d A

rea,

Gra

de L

evel

, Sta

ndar

d #)

11-1

2.2.

Det

erm

ine

the

cent

ral i

deas

or c

oncl

usio

ns o

f a t

ext;

sum

mar

ize

com

plex

con

cept

s,

A1.0

, A5.

0,

B4.0

, B5.

0, B

7.0,

C1

.0, C

4.0,

D2

.0, D

3.0,

pr

oces

ses,

or i

nfor

mat

ion

pres

ente

d in

a t

ext

by p

arap

hras

ing

them

in s

impl

er b

ut s

till a

ccur

ate

A9.0

B8.0

, B9.

0C1

1.0

D4.

0, D

6.0

term

s.

18


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

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En

gine

erin

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gine

erin

g En

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tal

Desi

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Desi

gnEn

gine

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Read

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Stan

dard

s fo

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tera

cy in

Sci

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and

Tec

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ubje

cts

– RL

ST

(Sta

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d A

rea,

Gra

de L

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, Sta

ndar

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(con

tinue

d)11

-12.

4. D

eter

min

e th

e m

eani

ng o

f sym

bols

, key

ter

ms,

and

oth

er d

omai

n-sp

ecifi

c w

ords

and

ph

rase

s as

the

y ar

e us

ed in

a s

peci

fic s

cien

tific

or t

echn

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con

text

rel

evan

t to

gra

des

11-1

2 A9

.0B1

1.0

C11.

0te

xts

and

topi

cs.

11-1

2.7.

Inte

grat

e an

d ev

alua

te m

ultip

le s

ourc

es o

f inf

orm

atio

n pr

esen

ted

in d

iver

se f

orm

ats

B9.0

, B10

.0,

and

med

ia (e

.g.,

quan

titat

ive

data

, vid

eo, m

ultim

edia

) in

orde

r to

addr

ess

a qu

estio

n or

sol

ve a

A1

.0, A

9.0

C1.0

, C11

.0B1

1.0

prob

lem

.

11-1

2.10

. By

the

end

of g

rade

12,

rea

d an

d co

mpr

ehen

d sc

ienc

e/te

chni

cal t

exts

in t

he g

rade

s D1

.0, D

2.0,

B1

.0, B

4.0,

B5.

0,

11-1

2 te

xt c

ompl

exit

y ba

nd in

depe

nden

tly a

nd p

rofic

ient

ly.

A1.0

, A5.

0C1

.0, C

4.0

D3.0

, D4.

0,

B7.0

, B8.

0, B

9.0

D3.0

, D6.

0

Writ

ing

Stan

dard

s –

WS

(Sta

ndar

d A

rea,

Gra

de L

evel

, Sta

ndar

d #)

11-1

2.1.

Writ

e ar

gum

ents

to

supp

ort

clai

ms

in a

n an

alys

is o

f sub

stan

tive

topi

cs o

r tex

ts, u

sing

B1

1.0

valid

rea

soni

ng a

nd r

elev

ant

and

suffi

cien

t ev

iden

ce.

11-1

2.2.

Writ

e in

form

ativ

e/ex

plan

ator

y te

xts

to e

xam

ine

and

conv

ey c

ompl

ex id

eas,

con

cept

s,

and

info

rmat

ion

clea

rly a

nd a

ccur

atel

y th

roug

h th

e ef

fect

ive

sele

ctio

n, o

rgan

izat

ion,

and

A9

.0B1

1.0

C11.

0an

alys

is o

f con

tent

.

11-1

2.4.

Pro

duce

cle

ar a

nd c

oher

ent

writ

ing

in w

hich

the

dev

elop

men

t, or

gani

zatio

n, a

nd s

tyle

A9

.0C1

1.0

are

appr

opria

te t

o ta

sk, p

urpo

se, a

nd a

udie

nce.

11-1

2.5.

Dev

elop

and

str

engt

hen

writ

ing

as n

eede

d by

pla

nnin

g, r

evis

ing,

edi

ting,

rew

ritin

g, o

r tr

ying

a n

ew a

ppro

ach,

foc

usin

g on

add

ress

ing

wha

t is

mos

t si

gnifi

cant

for

a s

peci

fic p

urpo

se

A9.0

C11.

0an

d au

dien

ce.

11-1

2.6.

Use

tec

hnol

ogy,

incl

udin

g th

e In

tern

et, t

o pr

oduc

e, p

ublis

h, a

nd u

pdat

e in

divi

dual

or

shar

ed w

ritin

g pr

oduc

ts in

res

pons

e to

ong

oing

fee

dbac

k, in

clud

ing

new

arg

umen

ts o

r inf

or-

A9.0

C11.

0m

atio

n.

11-1

2.7.

Con

duct

sho

rt a

s w

ell a

s m

ore

sust

aine

d re

sear

ch p

roje

cts

to a

nsw

er a

que

stio

n (in

clud

ing

a se

lf-ge

nera

ted

ques

tion)

or s

olve

a p

robl

em; n

arro

w o

r bro

aden

the

inqu

iry

whe

n A9

.0C1

1.0

appr

opria

te; s

ynth

esiz

e m

ultip

le s

ourc

es o

n th

e su

bjec

t, de

mon

stra

ting

unde

rsta

ndin

g of

the

su

bjec

t un

der i

nves

tigat

ion.

19


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

Writ

ing

Stan

dard

s –

WS

(Sta

ndar

d A

rea,

Gra

de L

evel

, Sta

ndar

d #)

(con

tinue

d)11

-12.

8. G

athe

r rel

evan

t in

form

atio

n fr

om m

ultip

le a

utho

ritat

ive

prin

t an

d di

gita

l sou

rces

, usi

ng

adva

nced

sea

rche

s ef

fect

ivel

y; a

sses

s th

e st

reng

ths

and

limita

tions

of e

ach

sour

ce in

ter

ms

of t

he

task

, pur

pose

, and

aud

ienc

e; in

tegr

ate

info

rmat

ion

into

the

tex

t se

lect

ivel

y to

mai

ntai

n th

e flo

w o

f A9

.0C1

1.0

idea

s, a

void

ing

plag

iaris

m a

nd o

verr

elia

nce

on a

ny o

ne s

ourc

e an

d fo

llow

ing

a st

anda

rd f

orm

at f

or

cita

tion

incl

udin

g fo

otno

tes

and

endn

otes

.

Writ

ing

Stan

dard

s fo

r Li

tera

cy in

His

tory

/Soc

ial S

tudi

es, S

cien

ce, a

nd T

echn

ical

Su

bjec

ts –

WH

SST

11-1

2.2.

Writ

e in

form

ativ

e/ex

plan

ator

y te

xts,

incl

udin

g th

e na

rrat

ion

of h

isto

rical

eve

nts,

sci

entifi

c A9

.0C1

1.0

proc

edur

es/e

xper

imen

ts, o

r tec

hnic

al p

roce

sses

.

11-1

2.5.

Dev

elop

and

str

engt

hen

writ

ing

as n

eede

d by

pla

nnin

g, re

visi

ng, e

ditin

g, re

writ

ing,

or t

ryin

g

B1.0

a ne

w a

ppro

ach,

focu

sing

on

addr

essi

ng w

hat i

s m

ost s

igni

fican

t for

a s

peci

fic p

urpo

se a

nd a

udie

nce.

11-1

2.6.

Use

tec

hnol

ogy,

incl

udin

g th

e In

tern

et, t

o pr

oduc

e, p

ublis

h, a

nd u

pdat

e in

divi

dual

or s

hare

d A9

.0B1

.0, B

11.0

C11.

0w

ritin

g pr

oduc

ts in

res

pons

e to

ong

oing

fee

dbac

k, in

clud

ing

new

arg

umen

ts o

r inf

orm

atio

n.

11-1

2.7.

Con

duct

sho

rt a

s w

ell a

s m

ore

sust

aine

d re

sear

ch p

roje

cts

to a

nsw

er a

que

stio

n (in

clud

-in

g a

self-

gene

rate

d qu

estio

n) o

r sol

ve a

pro

blem

; nar

row

or b

road

en t

he in

quir

y w

hen

appr

opri-

B1.0

ate;

syn

thes

ize

mul

tiple

sou

rces

on

the

subj

ect,

dem

onst

ratin

g un

ders

tand

ing

of t

he s

ubje

ct u

nder

in

vest

igat

ion.

11-1

2.8.

Gat

her r

elev

ant

info

rmat

ion

from

mul

tiple

aut

horit

ativ

e pr

int

and

digi

tal s

ourc

es, u

sing

ad

vanc

ed s

earc

hes

effe

ctiv

ely;

ass

ess

the

stre

ngth

s an

d lim

itatio

ns o

f eac

h so

urce

in t

erm

s of

the

sp

ecifi

c ta

sk, p

urpo

se, a

nd a

udie

nce;

inte

grat

e in

form

atio

n in

to t

he t

ext

sele

ctiv

ely

to m

aint

ain

B1.0

the

flow

of i

deas

, avo

idin

g pl

agia

rism

and

ove

rrel

ianc

e on

any

one

sou

rce

and

follo

win

g a

stan

dard

fo

rmat

for

cita

tion.

MAT

HEM

ATIC

SAl

gebr

a –

A-CE

D –

Crea

ting

Equa

tion

sCr

eate

equ

atio

ns th

at d

escr

ibe

num

bers

or r

elat

ions

hips

1. C

reat

e eq

uatio

ns a

nd in

equa

litie

s in

one

var

iabl

e in

clud

ing

ones

with

abs

olut

e va

lue

and

use

them

to

solv

e pr

oble

ms

in a

nd o

ut o

f con

text

, inc

ludi

ng e

quat

ions

aris

ing

from

line

ar f

unct

ions

.A

2.0,

A6.

0B6

.0, B

10.0

D2.0

1.1

Judg

e th

e va

lidit

y of

an

argu

men

t ac

cord

ing

to w

heth

er t

he p

rope

rtie

s of

rea

l num

bers

, exp

o-ne

nts,

and

loga

rithm

s ha

ve b

een

appl

ied

corr

ectly

at

each

ste

p. (C

A St

anda

rd A

lgeb

ra II

- 1

1.2)

20


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

Alge

bra

– A-

CED

– Cr

eatin

g Eq

uati

ons

(con

tinue

d)2.

Cre

ate

equa

tions

in t

wo

or m

ore

varia

bles

to

repr

esen

t re

latio

nshi

ps b

etw

een

quan

titie

s; g

raph

A

2.0,

A6.

0B6

.0, B

10.0

D2.0

equa

tions

on

coor

dina

te a

xes

with

labe

ls a

nd s

cale

s.

3. R

epre

sent

con

stra

ints

by

equa

tions

or i

nequ

aliti

es, a

nd b

y sy

stem

s of

equ

atio

ns a

nd/o

r ine

qual

i-tie

s, a

nd in

terp

ret

solu

tions

as

viab

le o

r non

viab

le o

ptio

ns in

a m

odel

ing

cont

ext.

For e

xam

ple,

rep

-A

2.0,

A6.

0B6

.0, B

10.0

D2.0

rese

nt in

equa

litie

s de

scrib

ing

nutr

ition

al a

nd c

ost

cons

trai

nts

on c

ombi

natio

ns o

f dif

fere

nt f

oods

.

4. R

earr

ange

for

mul

as t

o hi

ghlig

ht a

qua

ntit

y of

inte

rest

, usi

ng t

he s

ame

reas

onin

g as

in s

olvi

ng

equa

tions

. For

exa

mpl

e, r

earr

ange

Ohm

’s la

w V

= IR

to

high

light

res

ista

nce

R.A6

.0

Alge

bra

– A-

REI –

Rea

soni

ng w

ith

Equa

tion

s an

d In

equa

litie

sUn

ders

tand

solv

ing

equa

tions

as a

pro

cess

of r

easo

ning

and

exp

lain

the

reas

onin

g

1. E

xpla

in e

ach

step

in s

olvi

ng a

sim

ple

equa

tion

as f

ollo

win

g fr

om t

he e

qual

ity

of n

umbe

rs

asse

rted

at

the

prev

ious

ste

p, s

tart

ing

from

the

ass

umpt

ion

that

the

orig

inal

equ

atio

n ha

s a

solu

-A

2.0,

A8.

0B3

.0, B

10.0

tion.

Con

stru

ct a

via

ble

argu

men

t to

just

ify

a so

lutio

n m

etho

d.

2. S

olve

sim

ple

ratio

nal a

nd r

adic

al e

quat

ions

in o

ne v

aria

ble,

and

giv

e ex

ampl

es s

how

ing

how

A

2.0,

A8.

0B3

.0, B

10.0

extr

aneo

us s

olut

ions

may

aris

e.

Solv

e eq

uatio

ns a

nd in

equa

litie

s in

one

varia

ble

3. S

olve

line

ar e

quat

ions

and

ineq

ualit

ies

in o

ne v

aria

ble,

incl

udin

g eq

uatio

ns w

ith c

oeffi

cien

ts

repr

esen

ted

by le

tter

s.A

2.0,

A8.

0B3

.0, B

10.0

3.1

Solv

e eq

uatio

ns a

nd in

equa

litie

s in

volv

ing

abso

lute

val

ue. (

CA S

tand

ard

Alge

bra

I - 3

.0 a

nd

CA S

tand

ard

Alge

bra

II -

1.0)

4. S

olve

qua

drat

ic e

quat

ions

in o

ne v

aria

ble.

a. U

se t

he m

etho

d of

com

plet

ing

the

squa

re t

o tr

ansf

orm

any

qua

drat

ic e

quat

ion

in x

into

an

equa

tion

of t

he f

orm

(x -

p)2 =

q t

hat

has

the

sam

e so

lutio

ns. D

eriv

e th

e qu

adra

tic f

orm

ula

from

th

is f

orm

.B3

.0, B

4.0,

A8

.0D7

.0B1

0.0

b. S

olve

qua

drat

ic e

quat

ions

by

insp

ectio

n (e

.g.,

for x

2 = 4

9), t

akin

g sq

uare

roo

ts, c

ompl

etin

g th

e sq

uare

, the

qua

drat

ic f

orm

ula

and

fact

orin

g, a

s ap

prop

riate

to

the

initi

al f

orm

of t

he e

qua-

tion.

Rec

ogni

ze w

hen

the

quad

ratic

for

mul

a gi

ves

com

plex

sol

utio

ns a

nd w

rite

them

as

a ±

bi

for r

eal n

umbe

rs a

and

b.

21


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

Alge

bra

– A-

REI –

Rea

soni

ng w

ith

Equa

tion

s an

d In

equa

litie

s (c

ontin

ued)

Solv

e sy

stem

s of e

quat

ions

5. P

rove

tha

t, gi

ven

a sy

stem

of t

wo

equa

tions

in t

wo

varia

bles

, rep

laci

ng o

ne e

quat

ion

by t

he s

um

A8.0

of t

hat

equa

tion

and

a m

ultip

le o

f the

oth

er p

rodu

ces

a sy

stem

with

the

sam

e so

lutio

ns.

6. S

olve

sys

tem

s of

line

ar e

quat

ions

exa

ctly

and

app

roxi

mat

ely

(e.g

., w

ith g

raph

s), f

ocus

ing

on

A8.0

B3.0

, B10

.0pa

irs o

f lin

ear e

quat

ions

in t

wo

varia

bles

.

7. S

olve

a s

impl

e sy

stem

con

sist

ing

of a

line

ar e

quat

ion

and

a qu

adra

tic e

quat

ion

in t

wo

varia

bles

al

gebr

aica

lly a

nd g

raph

ical

ly. F

or e

xam

ple,

find

the

poi

nts

of in

ters

ectio

n be

twee

n th

e lin

e y

= -3

x A8

.0an

d th

e ci

rcle

x2 +

y2 =

3.

Func

tion

s –

F-IF

– In

terp

retin

g Fu

ncti

ons

Unde

rsta

nd th

e co

ncep

t of a

func

tion

and

use

func

tion

nota

tion

1. U

nder

stan

d th

at a

fun

ctio

n fr

om o

ne s

et (c

alle

d th

e do

mai

n) t

o an

othe

r set

(cal

led

the

rang

e)

assi

gns

to e

ach

elem

ent

of t

he d

omai

n ex

actly

one

ele

men

t of

the

ran

ge. I

f f is

a f

unct

ion

and

x is

A3

.0B2

.0, B

10.0

C3.0

an e

lem

ent

of it

s do

mai

n, t

hen

f(x)

den

otes

the

out

put

of f

corr

espo

ndin

g to

the

inpu

t x.

The

gra

ph

of f

is t

he g

raph

of t

he e

quat

ion

y =

f(x)

.

Anal

yze

func

tions

usi

ng d

iffer

ent r

epre

sent

atio

ns

7. G

raph

fun

ctio

ns e

xpre

ssed

sym

bolic

ally

and

sho

w k

ey f

eatu

res

of t

he g

raph

, by

hand

in s

impl

e ca

ses

and

usin

g te

chno

logy

for

mor

e co

mpl

icat

ed c

ases

.

a. G

raph

line

ar a

nd q

uadr

atic

fun

ctio

ns a

nd s

how

inte

rcep

ts, m

axim

a, a

nd m

inim

a.

b. G

raph

squ

are

root

, cub

e ro

ot, a

nd p

iece

wis

e-de

fined

fun

ctio

ns, i

nclu

ding

ste

p fu

nctio

ns a

nd

abso

lute

val

ue f

unct

ions

.

c. G

raph

pol

ynom

ial f

unct

ions

, ide

ntif

ying

zer

os w

hen

suita

ble

fact

oriz

atio

ns a

re a

vaila

ble,

and

A3

.0B2

.0, B

10.0

C3.0

show

ing

end

beha

vior

.

d. (+

) Gra

ph r

atio

nal f

unct

ions

, ide

ntif

ying

zer

os a

nd a

sym

ptot

es w

hen

suita

ble

fact

oriz

atio

ns

are

avai

labl

e, a

nd s

how

ing

end

beha

vior

.

e. G

raph

exp

onen

tial a

nd lo

garit

hmic

fun

ctio

ns, s

how

ing

inte

rcep

ts a

nd e

nd b

ehav

ior,

and

trig

o-no

met

ric f

unct

ions

, sho

win

g pe

riod,

mid

line,

and

am

plitu

de.

22


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

8. W

rite

a fu

nctio

n de

fined

by

an e

xpre

ssio

n in

dif

fere

nt b

ut e

quiv

alen

t fo

rms

to r

evea

l and

ex

plai

n di

ffer

ent

prop

ertie

s of

the

fun

ctio

n.

a. U

se t

he p

roce

ss o

f fac

torin

g an

d co

mpl

etin

g th

e sq

uare

in a

qua

drat

ic f

unct

ion

to s

how

zer

os,

extr

eme

valu

es, a

nd s

ymm

etry

of t

he g

raph

, and

inte

rpre

t th

ese

in t

erm

s of

a c

onte

xt.

A3.0

B2.0

, B10

.0C3

.0

b. U

se t

he p

rope

rtie

s of

exp

onen

ts t

o in

terp

ret

expr

essi

ons

for e

xpon

entia

l fun

ctio

ns. F

or

exam

ple,

iden

tify

perc

ent

rate

of c

hang

e in

fun

ctio

ns s

uch

as y

= (1

.02)

t , y =

(0.9

7)t , y

= (1

.01)

12t ,

y =

(1.2

)t/10

, and

cla

ssif

y th

em a

s re

pres

entin

g ex

pone

ntia

l gro

wth

or d

ecay

.

Func

tion

s –

F-LE

– L

inea

r, Q

uadr

atic

, and

Exp

onen

tial M

odel

s

1. D

istin

guis

h be

twee

n si

tuat

ions

tha

t ca

n be

mod

eled

with

line

ar f

unct

ions

and

with

exp

onen

tial

func

tions

.

a. P

rove

tha

t lin

ear f

unct

ions

gro

w b

y eq

ual d

iffe

renc

es o

ver e

qual

inte

rval

s, a

nd t

hat

expo

nen-

tial f

unct

ions

gro

w b

y eq

ual f

acto

rs o

ver e

qual

inte

rval

s.D5

.0b.

Rec

ogni

ze s

ituat

ions

in w

hich

one

qua

ntit

y ch

ange

s at

a c

onst

ant

rate

per

uni

t in

terv

al r

ela-

tive

to a

noth

er.

c. R

ecog

nize

situ

atio

ns in

whi

ch a

qua

ntit

y gr

ows

or d

ecay

s by

a c

onst

ant

perc

ent

rate

per

uni

t in

terv

al r

elat

ive

to a

noth

er.

Func

tion

s –

F-TF

– T

rigon

omet

ric F

unct

ions

Exte

nd th

e do

mai

n of

trig

onom

etric

func

tions

usin

g th

e un

it ci

rcle

1. U

nder

stan

d ra

dian

mea

sure

of a

n an

gle

as t

he le

ngth

of t

he a

rc o

n th

e un

it ci

rcle

sub

tend

ed b

y th

e an

gle.

B3.0

, B4.

0,

A6.0

C4.0

D6.0

, D7.

01.

1 U

nder

stan

d th

e no

tion

of a

ngle

and

how

to

mea

sure

it, i

n bo

th d

egre

es a

nd r

adia

ns. C

onve

rt

B10.

0be

twee

n de

gree

s an

d ra

dian

s. (C

A St

anda

rd T

rigon

omet

ry -

1.0

)

2. E

xpla

in h

ow t

he u

nit

circ

le in

the

coo

rdin

ate

plan

e en

able

s th

e ex

tens

ion

of t

rigon

omet

ric

B3.0

, B4.

0,

func

tions

to

all r

eal n

umbe

rs, i

nter

pret

ed a

s ra

dian

mea

sure

s of

ang

les

trav

erse

d co

unte

rclo

ckw

ise

A6.0

D7.0

B10.

0ar

ound

the

uni

t ci

rcle

.

23


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

Func

tion

s –

F-TF

– T

rigon

omet

ric F

unct

ions

(con

tinue

d)

3. (+

) Use

spe

cial

tria

ngle

s to

det

erm

ine

geom

etric

ally

the

val

ues

of s

ine,

cos

ine,

tan

gent

for

/3

, /4

and

/6

, and

use

the

uni

t ci

rcle

to

expr

ess

the

valu

es o

f sin

e, c

osin

e, a

nd t

ange

nt f

or

-x,

+x, a

nd 2

-x in

ter

ms

of t

heir

valu

es f

or X

, whe

re x

is a

ny r

eal n

umbe

r.B3

.0, B

4.0,

3.

1 Kn

ow t

he d

efini

tions

of t

he t

ange

nt a

nd c

otan

gent

fun

ctio

ns a

nd g

raph

the

m. (

CA S

tand

ard

A6.0

D7.0

B10.

0Tr

igon

omet

ry -

5.0

)

3.2

Know

the

defi

nitio

ns o

f the

sec

ant

and

cose

cant

fun

ctio

ns a

nd g

raph

the

m. (

CA S

tand

ard

Trig

onom

etry

- 6

.0)

Mod

el p

erio

dic

phen

omen

a w

ith tr

igon

omet

ric fu

nctio

ns

5. C

hoos

e tr

igon

omet

ric f

unct

ions

to

mod

el p

erio

dic

phen

omen

a w

ith s

peci

fied

ampl

itude

, B3

.0, B

4.0,

D2

.0, D

6.0

freq

uenc

y, a

nd m

idlin

e.B1

0.0

6. (+

) Und

erst

and

that

res

tric

ting

a tr

igon

omet

ric f

unct

ion

to a

dom

ain

on w

hich

it is

alw

ays

incr

easi

ng o

r alw

ays

decr

easi

ng a

llow

s it

s in

vers

e to

be

cons

truc

ted.

D6.0

6.1

Know

the

defi

nitio

ns o

f the

inve

rse

trig

onom

etric

fun

ctio

ns a

nd g

raph

the

fun

ctio

ns. (

CA

Stan

dard

Trig

onom

etry

- 8

.0)

Geom

etry

– G

-CO

– C

ongr

uenc

e

Mak

e ge

omet

ric c

onst

ruct

ions

12. M

ake

form

al g

eom

etric

con

stru

ctio

ns w

ith a

var

iety

of t

ools

and

met

hods

(com

pass

and

st

raig

hted

ge, s

trin

g, r

eflec

tive

devi

ces,

pap

er f

oldi

ng, d

ynam

ic g

eom

etric

sof

twar

e, e

tc.).

Cop

ying

A3

.0, A

5.0,

a

segm

ent;

cop

ying

an

angl

e; b

isec

ting

a se

gmen

t; b

isec

ting

an a

ngle

; con

stru

ctin

g pe

rpen

dicu

lar

B2.0

, B10

.0C3

.0, C

5.0

A7.0

, A8.

0lin

es, i

nclu

ding

the

per

pend

icul

ar b

isec

tor o

f a li

ne s

egm

ent;

and

con

stru

ctin

g a

line

para

llel t

o a

give

n lin

e th

roug

h a

poin

t no

t on

the

line

.

13. C

onst

ruct

an

equi

late

ral t

riang

le, a

squ

are,

and

a r

egul

ar h

exag

on in

scrib

ed in

a c

ircle

.C5

.0

Geom

etry

– G

-GM

D –

Geom

etric

Mea

sure

men

t an

d Di

men

sion

s

Expl

ain

volu

me

form

ulas

and

use

them

to so

lve

prob

lem

s

5. D

eter

min

e ho

w c

hang

es in

dim

ensi

ons

affe

ct t

he p

erim

eter

, are

a, a

nd v

olum

e of

com

mon

geo

-B6

.0, B

7.0,

C8

.0D2

.0m

etric

figu

res

and

solid

s.B1

0.0

24


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

Geom

etry

– G

-MG

– M

odel

ing

wit

h Ge

omet

ryAp

ply

geom

etric

con

cept

s in

mod

elin

g sit

uatio

ns

3. A

pply

geo

met

ric m

etho

ds t

o so

lve

desi

gn p

robl

ems

(e.g

., de

sign

ing

an o

bjec

t or

str

uctu

re t

o sa

t-A3

.0, A

5.0,

B6

.0, B

10.0

C8.0

, C9.

0D2

.0is

fy p

hysi

cal c

onst

rain

ts o

r min

imiz

e co

st; w

orki

ng w

ith t

ypog

raph

ic g

rid s

yste

ms

base

d on

rat

ios)

.A7

.0, A

8.0

Geom

etry

– G

-SRT

– S

imila

rity,

Rig

ht T

riang

les,

and

Trig

onom

etry

Unde

rsta

nd si

mila

rity

in te

rms o

f sim

ilarit

y tr

ansf

orm

atio

ns

1. V

erif

y ex

perim

enta

lly t

he p

rope

rtie

s of

dila

tions

giv

en b

y a

cent

er a

nd a

sca

le f

acto

r:

a. A

dila

tion

take

s a

line

not

pass

ing

thro

ugh

the

cent

er o

f the

dila

tion

to a

par

alle

l lin

e, a

nd

A3.0

, A5.

0,

B2.0

, B10

.0C3

.0le

aves

a li

ne p

assi

ng t

hrou

gh t

he c

ente

r unc

hang

ed.

A7.0

, A8.

0

b. T

he d

ilatio

n of

a li

ne s

egm

ent

is lo

nger

or s

hort

er in

the

rat

io g

iven

by

the

scal

e fa

ctor

.

Num

ber

and

Qua

ntit

y –

N-Q

– Q

uant

itie

sRe

ason

qua

ntita

tivel

y an

d us

e un

its to

solv

e pr

oble

ms

1. U

se u

nits

as

a w

ay t

o un

ders

tand

pro

blem

s an

d to

gui

de t

he s

olut

ion

of m

ulti-

step

pro

blem

s;

A2.

0, A

6.0,

B3

.0, B

4.0,

ch

oose

and

inte

rpre

t un

its

cons

iste

ntly

in f

orm

ulas

; cho

ose

and

inte

rpre

t th

e sc

ale

and

the

orig

in

D7.0

A8.0

B10.

0in

gra

phs

and

data

dis

play

s.

2. D

efine

app

ropr

iate

qua

ntiti

es f

or t

he p

urpo

se o

f des

crip

tive

mod

elin

g.A

2.0,

A6.

0,

B3.0

, B4.

0,

D7.0

A8.0

B10.

0

3. C

hoos

e a

leve

l of a

ccur

acy

appr

opria

te t

o lim

itatio

ns o

n m

easu

rem

ent

whe

n re

port

ing

A

2.0,

A6.

0,

B3.0

, B4.

0,

C4.0

D7.0

quan

titie

s.A8

.0B1

0.0

Num

ber

and

Qua

ntit

y –

N-V

M –

Vec

tor

and

Mat

rix Q

uant

itie

sRe

pres

ent a

nd m

odel

with

vec

tor q

uant

ities

1. (+

) Rec

ogni

ze v

ecto

r qua

ntiti

es a

s ha

ving

bot

h m

agni

tude

and

dire

ctio

n. R

epre

sent

vec

tor q

uan-

titie

s by

dire

cted

line

seg

men

ts, a

nd u

se a

ppro

pria

te s

ymbo

ls f

or v

ecto

rs a

nd t

heir

mag

nitu

des

A6.0

B5.0

, B10

.0C8

.0D

4.0,

D5.

0(e

.g.,

v, lv

l, Ilv

ll, v

).

2. (+

) Fin

d th

e co

mpo

nent

s of

a v

ecto

r by

subt

ract

ing

the

coor

dina

tes

of a

n in

itial

poi

nt f

rom

the

A6

.0B5

.0, B

10.0

C8.0

D4.

0, D

5.0

coor

dina

tes

of a

ter

min

al p

oint

.

3. (+

) Sol

ve p

robl

ems

invo

lvin

g ve

loci

ty a

nd o

ther

qua

ntiti

es t

hat

can

be r

epre

sent

ed b

y ve

ctor

s.A6

.0B5

.0, B

10.0

C8.0

D4.

0, D

5.0

25


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

Num

ber

and

Qua

ntit

y –

N-V

M –

Vec

tor

and

Mat

rix Q

uant

itie

s (c

ontin

ued)

Perf

orm

ope

ratio

ns o

n ve

ctor

sD

4.0

4. (+

) Add

and

sub

trac

t ve

ctor

s.

a. A

dd v

ecto

rs e

nd-t

o-en

d, c

ompo

nent

-wis

e, a

nd b

y th

e pa

ralle

logr

am r

ule.

Und

erst

and

that

the

m

agni

tude

of a

sum

of t

wo

vect

ors

is t

ypic

ally

not

the

sum

of t

he m

agni

tude

s.

b. G

iven

tw

o ve

ctor

s in

mag

nitu

de a

nd d

irect

ion

form

, det

erm

ine

the

mag

nitu

de a

nd d

irect

ion

of t

heir

sum

.A6

.0B5

.0, B

10.0

C8.0

D4.

0, D

5.0

c. U

nder

stan

d ve

ctor

sub

trac

tion

v –

w a

s v

+ (-

w),

whe

re -

w is

the

add

itive

inve

rse

of w

, with

th

e sa

me

mag

nitu

de a

s w

and

poi

ntin

g in

the

opp

osite

dire

ctio

n. R

epre

sent

vec

tor s

ubtr

actio

n

grap

hica

lly b

y co

nnec

ting

the

tips

in t

he a

ppro

pria

te o

rder

, and

per

form

vec

tor s

ubtr

actio

n co

mpo

nent

-wis

e.

5. (+

) Mul

tiply

a v

ecto

r by

a sc

alar

.

a. R

epre

sent

sca

lar m

ultip

licat

ion

grap

hica

lly b

y sc

alin

g ve

ctor

s an

d po

ssib

ly r

ever

sing

the

ir di

rect

ion;

per

form

sca

lar m

ultip

licat

ion

com

pone

nt-w

ise,

e.g

., as

c(v

, v,)

= (c

v, c

v).

xy

x2y

A6.0

B5.0

, B10

.0C8

.0D

4.0,

D5.

0b.

Com

pute

the

mag

nitu

de o

f a s

cala

r mul

tiple

cv

usin

g llc

vll =

lclv

. Com

pute

the

dire

ctio

n

of c

v kn

owin

g th

at w

hen

lclv

0

, the

dire

ctio

n of

cv

is e

ither

alo

ng v

(for

c >

0) o

r ag

ains

t v

(for

c <

0).

Perf

orm

ope

ratio

ns o

n m

atric

es a

nd u

se m

atric

es in

app

licat

ions

D4.

0, D

5.0

6. (+

) Use

mat

rices

to

repr

esen

t an

d m

anip

ulat

e da

ta, e

.g.,

to r

epre

sent

pay

offs

or i

ncid

ence

B5

.0, B

9.0,

A6

.0D

4.0,

D5.

0re

latio

nshi

ps in

a n

etw

ork.

B10.

0

7. (+

) Mul

tiply

mat

rices

by

scal

ars

to p

rodu

ce n

ew m

atric

es, e

.g.,

as w

hen

all o

f the

pay

offs

in a

B5

.0, B

9.0,

A6

.0D

4.0,

D5.

0ga

me

are

doub

led.

B10.

0

8. (+

) Add

, sub

trac

t, an

d m

ultip

ly m

atric

es o

f app

ropr

iate

dim

ensi

ons.

B5.0

, B9.

0,

A6.0

D4.

0, D

5.0

B10.

0

9. (+

) Und

erst

and

that

, unl

ike

mul

tiplic

atio

n of

num

bers

, mat

rix m

ultip

licat

ion

for s

quar

e m

atric

es

B5.0

, B9.

0,

A6.0

D4.

0, D

5.0

is n

ot a

com

mut

ativ

e op

erat

ion,

but

stil

l sat

isfie

s th

e as

soci

ativ

e an

d di

strib

utiv

e pr

oper

ties.

B10.

0

10. (

+) U

nder

stan

d th

at t

he z

ero

and

iden

tity

mat

rices

pla

y a

role

in m

atrix

add

ition

and

mul

ti-B5

.0, B

9.0,

pl

icat

ion

sim

ilar t

o th

e ro

le o

f 0 a

nd 1

in t

he r

eal n

umbe

rs. T

he d

eter

min

ant

of a

squ

are

mat

rix is

A6

.0D

4.0,

D5.

0B1

0.0

nonz

ero

if an

d on

ly if

the

mat

rix h

as a

mul

tiplic

ativ

e in

vers

e.

26


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

Num

ber

and

Qua

ntit

y –

N-V

M –

Vec

tor

and

Mat

rix Q

uant

itie

s (c

ontin

ued)

11. (

+) M

ultip

ly a

vec

tor (

rega

rded

as

a m

atrix

with

one

col

umn)

by

a m

atrix

of s

uita

ble

dim

en-

B5.0

, B9.

0,

A6.0

D4.

0, D

5.0

sion

s to

pro

duce

ano

ther

vec

tor.

Wor

k w

ith m

atric

es a

s tr

ansf

orm

atio

ns o

f vec

tors

.B1

0.0

12. (

+) W

ork

with

2 x

2 m

atric

es a

s tr

ansf

orm

atio

ns o

f the

pla

ne, a

nd in

terp

ret

the

abso

lute

val

ue

B5.0

, B9.

0,

A6.0

D4.

0, D

5.0

of t

he d

eter

min

ant

in t

erm

s of

are

a.

B10.

0

Stat

isti

cs a

nd P

roba

bilit

y –

S-ID

– In

terp

reti

ng C

ateg

oric

al a

nd Q

uant

itat

ive

Data

Sum

mar

ize,

repr

esen

t, an

d in

terp

ret d

ata

on a

sing

le c

ount

or m

easu

rem

ent v

aria

ble

1. R

epre

sent

dat

a w

ith p

lots

on

the

real

num

ber l

ine

(dot

plo

ts, h

isto

gram

s, a

nd b

ox p

lots

).B1

.0, B

8.0,

A

2.0

B10.

0

2. U

se s

tatis

tics

appr

opria

te t

o th

e sh

ape

of t

he d

ata

dist

ribut

ion

to c

ompa

re c

ente

r (m

edia

n,

A2.

0B1

.0, B

10.0

mea

n) a

nd s

prea

d (in

terq

uart

ile r

ange

, sta

ndar

d de

viat

ion)

of t

wo

or m

ore

diff

eren

t da

ta s

ets.

3. In

terp

ret

diff

eren

ces

in s

hape

, cen

ter,

and

spre

ad in

the

con

text

of t

he d

ata

sets

, acc

ount

ing

for

A2.

0B1

.0, B

10.0

poss

ible

eff

ects

of e

xtre

me

data

poi

nts

(out

liers

).

4. U

se t

he m

ean

and

stan

dard

dev

iatio

n of

a d

ata

set

to fi

t it

to a

nor

mal

dis

trib

utio

n an

d to

es

timat

e po

pula

tion

perc

enta

ges.

Rec

ogni

ze t

hat

ther

e ar

e da

ta s

ets

for w

hich

suc

h a

proc

edur

e A

2.0

B1.0

, B10

.0is

not

app

ropr

iate

. Use

cal

cula

tors

, spr

eads

heet

s, a

nd t

able

s to

est

imat

e ar

eas

unde

r the

nor

mal

cu

rve.

Sum

mar

ize,

repr

esen

t, an

d in

terp

ret d

ata

on tw

o ca

tego

rical

and

qua

ntita

tive

varia

bles

5. S

umm

ariz

e ca

tego

rical

dat

a fo

r tw

o ca

tego

ries

in t

wo-

way

fre

quen

cy t

able

s. In

terp

ret

rela

tive

B1.0

, B8.

0,

freq

uenc

ies

in t

he c

onte

xt o

f the

dat

a (in

clud

ing

join

t, m

argi

nal,

and

cond

ition

al r

elat

ive

freq

uen-

B10.

0ci

es).

Reco

gniz

e po

ssib

le a

ssoc

iatio

ns a

nd t

rend

s in

the

dat

a.

6. R

epre

sent

dat

a on

tw

o qu

antit

ativ

e va

riabl

es o

n a

scat

ter p

lot,

and

desc

ribe

how

the

var

iabl

es

are

rela

ted.

a. F

it a

func

tion

to t

he d

ata;

use

fun

ctio

ns fi

tted

to

data

to

solv

e pr

oble

ms

in t

he c

onte

xt o

f th

e da

ta. U

se g

iven

fun

ctio

ns o

r cho

ose

a fu

nctio

n su

gges

ted

by t

he c

onte

xt. E

mph

asiz

e lin

ear,

B1.0

, B10

.0qu

adra

tic, a

nd e

xpon

entia

l mod

els.

b. In

form

ally

ass

ess

the

fit o

f a f

unct

ion

by p

lott

ing

and

anal

yzin

g re

sidu

als.

c. F

it a

linea

r fun

ctio

n fo

r a s

catt

er p

lot

that

sug

gest

s a

linea

r ass

ocia

tion.

27


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

Stat

isti

cs a

nd P

roba

bilit

y –

APP

S –

Adva

nced

Pla

cem

ent

Prob

abili

ty a

nd S

tati

stic

s1.

0 St

uden

ts s

olve

pro

babi

lity

prob

lem

s w

ith fi

nite

sam

ple

spac

es b

y us

ing

the

rule

s fo

r add

ition

, m

ultip

licat

ion,

and

com

plem

enta

tion

for p

roba

bilit

y di

strib

utio

ns a

nd u

nder

stan

d th

e si

mpl

ficia-

B5.0

D5.0

tions

tha

t ar

ise

with

inde

pend

ent

even

ts.

2.0

Stud

ents

kno

w t

he d

efini

tion

of c

ondi

tiona

l pro

babi

lity

and

use

it to

sol

ve f

or p

roba

bilit

ies

in

B5.0

D5.0

finite

sam

ple

spac

es.

3.0

Stud

ents

dem

onst

rate

an

unde

rsta

ndin

g of

the

not

ion

of d

iscr

ete

rand

om v

aria

bles

by

usin

g th

is c

once

pt t

o so

lve

for t

he p

roba

bilit

ies

of o

utco

mes

, suc

h as

the

pro

babi

lity

of t

he o

ccur

renc

e B5

.0D5

.0of

five

or f

ewer

hea

ds in

14

coin

tos

ses.

4.0

Stud

ents

und

erst

and

the

notio

n of

a c

ontin

uous

ran

dom

var

iabl

e an

d ca

n in

terp

ret

the

pr

obab

ility

of a

n ou

tcom

e as

the

are

a of

a r

egio

n un

der t

he g

raph

of t

he p

roba

bilit

y de

nsit

y

B5.0

D5.0

func

tion

asso

ciat

ed w

ith t

he r

ando

m v

aria

ble.

5.0

Stud

ents

kno

w t

he d

efini

tion

of t

he m

ean

of a

dis

cret

e ra

ndom

var

iabl

e an

d ca

n de

term

ine

the

B5.0

D5.0

mea

n fo

r a p

artic

ular

dis

cret

e ra

ndom

var

iabl

e.

6.0

Stud

ents

kno

w t

he d

efini

tion

of t

he v

aria

nce

of a

dis

cret

e ra

ndom

var

iabl

e an

d ca

n de

term

ine

B5.0

D5.0

the

varia

nce

for a

par

ticul

ar d

iscr

ete

rand

om v

aria

ble.

7.0

Stud

ents

dem

onst

rate

an

unde

rsta

ndin

g of

the

sta

ndar

d di

strib

utio

ns (n

orm

al, b

inom

ial,

and

expo

nent

ial)

and

can

use

the

dist

ribut

ions

to

solv

e fo

r eve

nts

in p

robl

ems

in w

hich

the

dis

trib

utio

n B5

.0D5

.0be

long

s to

tho

se f

amili

es.

8.0

Stud

ents

det

erm

ine

the

mea

n an

d th

e st

anda

rd d

evia

tion

of a

nor

mal

ly d

istr

ibut

ed r

ando

m

B5.0

D5.0

varia

ble.

9.0

Stud

ents

kno

w t

he c

entr

al li

mit

theo

rem

and

can

use

it t

o ob

tain

app

roxi

mat

ions

for

pro

babi

li-B5

.0D5

.0tie

s in

pro

blem

s of

fini

te s

ampl

e sp

aces

in w

hich

the

pro

babi

litie

s ar

e di

strib

uted

bin

omia

lly.

10.0

Stu

dent

s kn

ow t

he d

efini

tions

of t

he m

ean,

med

ian

and

mod

e of

dis

trib

utio

n of

dat

a an

d ca

n B5

.0D5

.0co

mpu

te e

ach

of t

hem

in p

artic

ular

situ

atio

ns.

11.0

Stu

dent

s co

mpu

te t

he v

aria

nce

and

the

stan

dard

dev

iatio

n of

a d

istr

ibut

ion

of d

ata.

B5.0

D5.0

12.0

Stu

dent

s fin

d th

e lin

e of

bes

t fit

to

a gi

ven

dist

ribut

ion

of d

ata

by u

sing

leas

t sq

uare

s

B5.0

D5.0

regr

essi

on.

13.0

Stu

dent

s kn

ow w

hat

the

corr

elat

ion

coef

ficie

nt o

f tw

o va

riabl

es m

eans

and

are

fam

iliar

with

B5

.0D5

.0th

e co

effic

ient

’s pr

oper

ties.

28


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

Stat

isti

cs a

nd P

roba

bilit

y –

APP

S –

Adva

nced

Pla

cem

ent

Prob

abili

ty a

nd

Stat

isti

cs (c

ontin

ued)

14.0

Stu

dent

s or

gani

ze a

nd d

escr

ibe

dist

ribut

ions

of d

ata

by u

sing

a n

umbe

r of d

iffe

rent

m

etho

ds, i

nclu

ding

fre

quen

cy t

able

s, h

isto

gram

s, s

tand

ard

line

grap

hs a

nd b

ar g

raph

s,

B5.0

D5.0

stem

-and

-Iea

f dis

play

s, s

catt

erpl

ots,

and

box

-and

-whi

sker

plo

ts.

15.0

Stu

dent

s ar

e fa

mili

ar w

ith t

he n

otio

ns o

f a s

tatis

tic o

f a d

istr

ibut

ion

of v

alue

s of

the

B5

.0D5

.0sa

mpl

ing

dist

ribut

ion

of a

sta

tistic

. And

of t

he v

aria

bilit

y of

a s

tatis

tic.

16.0

Stu

dent

s kn

ow b

asic

fac

ts c

once

rnin

g th

e re

latio

n be

twee

n th

e m

ean

and

the

stan

-da

rd d

evia

tion

of a

sam

plin

g di

strib

utio

n an

d th

e m

ean

and

the

stan

dard

dev

iatio

n of

the

B5

.0D5

.0po

pula

tion

dist

ribut

ion.

17.0

Stu

dent

s de

term

ine

confi

denc

e in

terv

als

for a

sim

ple

rand

om s

ampl

e fr

om a

nor

mal

B5

.0D5

.0di

strib

utio

n of

dat

a an

d de

term

ine

the

sam

ple

size

req

uire

d fo

r a d

esire

d m

argi

n of

err

or.

18.0

Stu

dent

s de

term

ine

the

P- v

alue

for

a s

tatis

tic f

or a

sim

ple

rand

om s

ampl

e fr

om a

B5

.0D5

.0no

rmal

dis

trib

utio

n.

19.0

Stu

dent

s ar

e fa

mili

ar w

ith t

he c

hi-

squa

re d

istr

ibut

ion

and

chi-

squ

are

test

and

B5

.0D5

.0un

ders

tand

the

ir us

es.

SCIE

NCE

Scie

ntifi

c an

d En

gine

erin

g Pr

acti

ces

– SE

P1.

Ask

ing

ques

tions

(for

sci

ence

) and

defi

ning

pro

blem

s (f

or e

ngin

eerin

g)B1

.0, B

3.0,

B6.

0,

A5.0

, A8.

0D5

.0, D

7.0

B8.0

, B9.

0, B

10.0

2. D

evel

opin

g an

d us

ing

mod

els

A4.0

, A5.

0,

B1.0

, B2.

0, B

3.0,

D3

.0, D

4.0,

A6

.0, A

8.0

B6.0

, B8.

0, B

10.0

D5.0

, D7.

0

3. P

lann

ing

and

carr

ying

out

inve

stig

atio

nsB2

.0, B

3.0,

B6.

0,

D5.0

, D7.

0B8

.0, B

10.0

4. A

naly

zing

and

inte

rpre

ting

data

A2.

0, A

4.0,

B1

.0, B

2.0,

B3.

0,

C3.0

, C4.

0, C

7.0,

D2

.0, D

3.0,

A5

.0, A

6.0,

B6

.0, B

7.0,

B8.

0,

C8.0

, C9.

0D5

.0, D

7.0

A7.0

, A8.

0B1

0.0

5. U

sing

mat

hem

atic

s an

d co

mpu

tatio

nal t

hink

ing

A2.

0, A

4.0,

B1

.0, B

3.0,

B4.

0,

C3.0

, C4.

0, C

5.0,

D

4.0,

D5.

0,

A5.0

, A6.

0,

B5.0

, B6.

0, B

7.0,

C6

.0, C

7.0,

C8.

0,

D6.0

, D7.

0A7

.0, A

8.0

B8.0

, B10

.0C9

.0

29


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

Des

ign

Engi

neer

ing

Tech

nolo

gyEn

gine

erin

g De

sign

Envi

ronm

enta

l En

gine

erin

g

Scie

ntifi

c an

d En

gine

erin

g Pr

acti

ces

– SE

P (c

ontin

ued)

6. C

onst

ruct

ing

expl

anat

ions

(for

sci

ence

) and

C2

.0, C

3.0,

C4.

0, C

5.0,

A5

.0B3

.0, B

4.0,

B5.

0, B

6.0,

B10

.0D5

.0, D

7.0

desi

gnin

g so

lutio

ns (f

or e

ngin

eerin

g)C6

.0, C

7.0,

C8.

0, C

9.0

7. E

ngag

ing

in a

rgum

ent

from

evi

denc

eA9

.0B3

.0, B

6.0,

B10

.0, B

11.0

C11.

0D5

.0, D

7.0

8. O

btai

ning

, eva

luat

ing,

and

com

mun

icat

ing

A

2.0,

A4.

0, A

5.0,

B1

.0, B

2.0,

B3.

0, B

4.0,

B5.

0,

C3.0

, C5.

0, C

6.0,

C7.

0,

D1.0

, D2.

0, D

3.0,

D4.

0,

info

rmat

ion

A6.0

, A7.

0, A

8.0,

A9.

0B6

.0, B

7.0,

B9.

0, B

10.0

, B11

.0C8

.0, C

9.0,

C10

.0, C

11.0

D5.0

, D6.

0, D

7.0

Cros

scut

ting

Con

cept

– C

C

1. P

atte

rns

B3.0

, B4.

0, B

5.0,

B6.

0, B

8.0,

D1

.0, D

2.0,

D3.

0, D

4.0,

A

2.0,

A3.

0, A

7.0

B10.

0D5

.0

2. C

ause

and

eff

ect:

Mec

hani

sm a

nd e

xpla

natio

nD2

.0, D

3.0,

D4.

0, D

5.0,

B3

.0, B

4.0,

B5.

0, B

6.0,

B8.

0,

A1.0

, A5.

0, A

7.0

D6.0

B10.

0

3. S

cale

, pro

port

ion,

and

qua

ntit

yA1

.0, A

2.0,

A3.

0, A

4.0,

B1

.0, B

3.0,

B4.

0, B

5.0,

B6.

0,

C2.0

, C4.

0, C

5.0,

C6.

0,

D1.0

, D2.

0, D

3.0,

D4.

0,

A5.0

, A7.

0, A

8.0

B7.0

, B8.

0, B

10.0

C7.0

, C8.

0, C

9.0,

C10

.0D5

.0, D

6.0

4. S

yste

ms

and

syst

em m

odel

sB3

.0, B

4.0,

B5.

0, B

6.0,

B8.

0,

D2.0

, D3.

0, D

4.0,

D5.

0,

A5.0

C7.0

B9.0

, B10

.0D6

.0

5. E

nerg

y an

d m

atte

r: Fl

ows,

cyc

les,

and

con

serv

atio

nD2

.0, D

3.0,

D4.

0, D

5.0,

A5

.0B3

.0, B

4.0,

B5.

0, B

10.0

D6.0

6. S

truc

ture

and

fun

ctio

nA1

.0, A

2.0,

A3.

0, A

5.0,

B6

.0, B

7.0,

B8.

0, B

10.0

C2.0

D2.0

, D5.

0A7

.0, A

8.0

7. S

tabi

lity

and

chan

geA5

.0, A

7.0

B3.0

, B10

.0C2

.0D2

.0, D

3.0,

D5.

0, D

6.0

Phys

ical

Sci

ence

s –

PS

PS1:

Mat

ter a

nd It

s In

tera

ctio

ns

PS1.

A: S

truc

ture

and

Pro

pert

ies

of M

atte

rA7

.0B3

.0, B

4.0,

B5.

0, B

10.0

D2.0

, D6.

0

PS1.

B: C

hem

ical

Rea

ctio

nsB4

.0, B

5.0,

B10

.0D2

.0, D

6.0

PS1.

C: N

ucle

ar P

roce

sses

B4.0

, B5.

0, B

10.0

D6.0

30


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g Te

chno

logy

Engi

neer

ing

Desi

gnEn

viro

nmen

tal

Desi

gnEn

gine

erin

g

Phys

ical

Sci

ence

s –

PS (c

ontin

ued)

PS2:

Mot

ion

and

Stab

ility

: For

ces

and

Inte

ract

ions

PS2.

A: F

orce

s an

d M

otio

nA6

.0, A

7.0

B4.0

, B5.

0, B

10.0

D4.

0, D

5.0,

D6.

0 D7

.0

PS2.

B: T

ypes

of i

nter

actio

nsA6

.0, A

7.0

B4.0

, B5.

0, B

10.0

D4.

0, D

5.0,

D6.

0 D7

.0

PS2.

C: S

tabi

lity

and

Inst

abili

ty in

Phy

sica

l Sys

tem

sA1

.0, A

6.0,

A7.

0B4

.0, B

5.0,

B10

.0D

4.0,

D5.

0, D

6.0

D7.0

PS3:

Ene

rgy

PS3.

A: D

efini

tions

of E

nerg

yA5

.0B3

.0, B

4.0,

B5.

0, B

8.0,

B10

.0D

4.0,

D6.

0

PS3.

B: C

onse

rvat

ion

of E

nerg

y an

d En

ergy

Tra

nsfe

rA5

.0B3

.0, B

4.0,

B5.

0, B

8.0,

B10

.0D

4.0,

D6.

0

PS3.

C: R

elat

ions

hip

Betw

een

Ener

gy a

nd F

orce

sB4

.0, B

5.0,

B8.

0, B

10.0

D4.

0, D

6.0

PS3.

D: E

nerg

y in

Che

mic

al P

roce

sses

and

Eve

ryda

y Li

feA5

.0B4

.0, B

5.0,

B8.

0, B

10.0

D4.

0, D

6.0

PS4:

Wav

es a

nd T

heir

Appl

icat

ions

in T

echn

olog

ies

for

Info

rmat

ion

Tran

sfer

PS4.

A: W

ave

Prop

ertie

sB3

.0, B

4.0,

B5.

0, B

10.0

D6.0

, D7.

0

PS4.

B: E

lect

rom

agne

tic R

adia

tion

B4.0

, B5.

0, B

10.0

D6.0

, D7.

0

PS4.

C: In

form

atio

n Te

chno

logi

es a

nd In

stru

men

tatio

nB3

.0, B

4.0,

B5.

0, B

10.0

D6.0

Eart

h an

d Sp

ace

Scie

nces

– E

SSES

S2: E

arth

’s Sy

stem

s

ESS2

.A: E

arth

Mat

eria

ls a

nd S

yste

ms

B3.0

D2.0

, D3.

0, D

7.0

ESS2

.B: P

late

Tec

toni

cs a

nd L

arge

-Sca

le S

yste

m

B3.0

D2.0

, D3.

0, D

4.0,

D7.

0In

tera

ctio

ns

ESS2

.C: T

he R

oles

of W

ater

in E

arth

’s Su

rfac

e Pr

oces

ses

D2.0

, D3.

0, D

4.0,

D7.

0,

B3.0

D9.

0, D

13.0

, D14

.0

ESS2

.D: W

eath

er a

nd C

limat

eB3

.0D3

.0, D

7.0,

D10

.0

ESS2

.E: B

ioge

olog

yD1

1.0,

D13

.0

31


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g

Engi

neer

ing

Envi

ronm

enta

l De

sign

Tech

nolo

gyDe

sign

Engi

neer

ing

Eart

h an

d Sp

ace

Scie

nces

– E

SS (c

ontin

ued)

ESS3

: Ear

th a

nd H

uman

Act

ivit

y

ESS3

.A: N

atur

al R

esou

rces

A5.0

B3.0

D3.0

, D7.

0, D

9.0

ESS3

.B: N

atur

al H

azar

dsB3

.0D2

.0, D

7.0

ESS3

.C: H

uman

Impa

cts

on E

arth

Sys

tem

sD2

.0, D

3.0,

D7.

0, D

9.0,

A5

.0B3

.0D1

0.0,

D12

.0

ESS3

.D: G

loba

l Clim

ate

Chan

geD3

.0, D

7.0,

D10

.0,

A5.0

B3.0

D11.

0, D

12.0

Engi

neer

ing,

Tec

hnol

ogy,

and

the

App

licat

ions

of

Scie

nce

– ET

SET

S1: E

ngin

eerin

g De

sign

ETS1

.A: D

efini

ng a

nd D

elim

iting

an

Engi

neer

ing

Prob

lem

A5.0

, A6.

0, A

8.0

B3.0

, B6.

0, B

8.0,

B10

.0D5

.0

ETS1

.B: D

evel

opin

g Po

ssib

le S

olut

ions

A5.0

, A6.

0, A

8.0

B3.0

, B6.

0, B

8.0,

B10

.0D5

.0

ETS1

.C: O

ptim

izin

g th

e De

sign

Sol

utio

nA5

.0, A

6.0,

A8.

0B3

.0, B

6.0,

B8.

0, B

10.0

D5.0

ETS2

: Lin

ks A

mon

g En

gine

erin

g, T

echn

olog

y, S

cien

ce, a

nd S

ocie

ty

ETS2

.A: I

nter

depe

nden

ce o

f Sci

ence

, Eng

inee

ring,

and

Tec

hnol

ogy

C2.0

, C3.

0, C

4.0,

C5

.0, C

7.0,

C8.

0,

A5.0

, A6.

0, A

7.0

B3.0

, B4.

0, B

5.0,

B10

.0D2

.0, D

4.0,

D6.

0C9

.0, C

10.0

, C1

1.0

ETS2

.B: I

nflue

nce

of E

ngin

eerin

g, T

echn

olog

y, a

nd S

cien

ce o

n So

ciet

y A1

.0, A

2.0,

A5.

0,

B9.0

, B10

.0C1

1.0

and

the

Nat

ural

Wor

ldA8

.0

HIS

TORY

/SO

CIAL

SCI

ENCE

Prin

cipl

es o

f A

mer

ican

Dem

ocra

cy a

nd E

cono

mic

s –

AD12

.3 S

tude

nts

eval

uate

and

tak

e an

d de

fend

pos

ition

s on

wha

t th

e fu

n-da

men

tal v

alue

s an

d pr

inci

ples

of c

ivil

soci

ety

are

(i.e.

, the

aut

onom

ous

sphe

re o

f vol

unta

ry p

erso

nal,

soci

al, a

nd e

cono

mic

rel

atio

ns t

hat

are

not

B9.0

C1.0

D2.0

part

of g

over

nmen

t), t

heir

Inte

rdep

ende

nce,

and

the

mea

ning

and

im

port

ance

of t

hose

val

ues

and

prin

cipl

es f

or a

fre

e so

ciet

y.

32


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

Prin

cipl

es o

f A

mer

ican

Dem

ocra

cy a

nd E

cono

mic

s –

AD (c

ontin

ued)

12.7

Stu

dent

s an

alyz

e an

d co

mpa

re t

he p

ower

s an

d pr

oced

ures

of t

he n

atio

nal,

stat

e, t

ribal

, and

A1

.0, A

2.0,

A5.

0B9

.0C1

.0D2

.0lo

cal g

over

nmen

ts.

12.7

.5. E

xpla

in h

ow p

ublic

pol

icy

is f

orm

ed, i

nclu

ding

the

set

ting

of t

he p

ublic

age

nda

and

D10.

0, D

11.0

, A

2.0

impl

emen

tatio

n of

it t

hrou

gh r

egul

atio

ns a

nd e

xecu

tive

orde

rs.

D13.

0

Prin

cipl

es o

f Ec

onom

ics

– PE

12.1

Stu

dent

s un

ders

tand

com

mon

eco

nom

ic t

erm

s an

d co

ncep

ts a

nd e

cono

mic

rea

soni

ng.

A1.0

, A2.

0, A

5.0

B9.0

C1.0

D2.0

, D3.

0

12.1

.4. E

valu

ate

the

role

of p

rivat

e pr

oper

ty a

s an

ince

ntiv

e in

con

serv

ing

and

impr

ovin

g sc

arce

D1

0.0,

D11

.0,

reso

urce

s, in

clud

ing

rene

wab

le a

nd n

onre

new

able

nat

ural

res

ourc

es.

D13.

0

12.2

Stu

dent

s an

alyz

e th

e el

emen

ts o

f Am

eric

a’s

mar

ket

econ

omy

in a

glo

bal s

ettin

g.A

2.0,

A5.

0B9

.0C1

.0D3

.0

12.6

Stu

dent

s an

alyz

e is

sues

of i

nter

natio

nal t

rade

and

exp

lain

how

the

U.S

. eco

nom

y af

fect

s,

A1.0

B9.0

and

is a

ffec

ted

by, e

cono

mic

for

ces

beyo

nd t

he U

nite

d St

ates

’ bor

ders

.

U.S.

His

tory

and

Geo

grap

hy –

US

11.2

Stu

dent

s an

alyz

e th

e re

latio

nshi

p am

ong

the

rise

of in

dust

rializ

atio

n, la

rge-

scal

e ru

ral-

to-

A1.0

C1.0

urba

n m

igra

tion,

and

mas

sive

imm

igra

tion

from

Sou

ther

n an

d Ea

ster

n Eu

rope

.

11.5

Stu

dent

s an

alyz

e th

e m

ajor

pol

itica

l, so

cial

, eco

nom

ic, t

echn

olog

ical

, and

cul

tura

l dev

elop

-A1

.0C1

.0m

ents

of t

he 1

920s

.

11.5

.7. D

iscu

ss t

he ri

se o

f mas

s pr

oduc

tion

tech

niqu

es, t

he g

row

th o

f citi

es, t

he im

pact

of n

ew

tech

nolo

gies

(e.g

., th

e au

tom

obile

, ele

ctric

ity)

, and

the

res

ultin

g pr

ospe

rity

and

effe

ct o

n th

e C1

.0Am

eric

an la

ndsc

ape.

11.6

Stu

dent

s an

alyz

e th

e di

ffer

ent

expl

anat

ions

for

the

Gre

at D

epre

ssio

n an

d ho

w t

he N

ew D

eal

A1.0

, A5.

0C1

.0fu

ndam

enta

lly c

hang

ed t

he r

ole

of t

he f

eder

al g

over

nmen

t.

11.6

.4. A

naly

ze t

he e

ffec

ts o

f and

the

con

trov

ersi

es a

risin

g fr

om N

ew D

eal e

cono

mic

pol

icie

s an

d th

e ex

pand

ed r

ole

of t

he f

eder

al g

over

nmen

t in

soc

iety

and

the

eco

nom

y si

nce

the

1930

s (e

.g.,

Wor

ks P

rogr

ess

Adm

inis

trat

ion,

Soc

ial S

ecur

ity,

Nat

iona

l Lab

or R

elat

ions

Boa

rd, f

arm

pro

-C1

.0gr

ams,

reg

iona

l dev

elop

men

t po

licie

s, a

nd e

nerg

y de

velo

pmen

t pr

ojec

ts s

uch

as t

he T

enne

ssee

Va

lley

Auth

orit

y, C

alifo

rnia

Cen

tral

Val

ley

Proj

ect,

and

Bonn

evill

e Da

m).

33


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

U.S.

His

tory

and

Geo

grap

hy –

US

(con

tinue

d)

11.8

Stu

dent

s an

alyz

e th

e ec

onom

ic b

oom

and

soc

ial t

rans

form

atio

n of

pos

t-W

orld

War

II A

mer

ica.

A1.0

, A2.

0,

B9.0

C1.0

A5.0

11.11

Stu

dent

s an

alyz

e th

e m

ajor

soc

ial p

robl

ems

and

dom

estic

pol

icy

issu

es in

con

tem

pora

ry

A1.0

, A2.

0,

B9.0

C1.0

D3.0

Amer

ican

soc

iety

.A5

.0

11.11

.5. T

race

the

impa

ct o

f, ne

ed f

or, a

nd c

ontr

over

sies

ass

ocia

ted

with

env

ironm

enta

l con

ser-

vatio

n, e

xpan

sion

of t

he n

atio

nal p

ark

syst

em, a

nd t

he d

evel

opm

ent

of e

nviro

nmen

tal p

rote

ctio

n D1

0.0,

D11

.0,

law

s, w

ith p

artic

ular

att

entio

n to

the

inte

ract

ion

betw

een

envi

ronm

enta

l pro

tect

ion

advo

cate

s D1

3.0

and

prop

erty

righ

ts a

dvoc

ates

.

Wor

ld H

isto

ry, C

ultu

re, a

nd G

eogr

aphy

– W

H

10.3

Stu

dent

s an

alyz

e th

e ef

fect

s of

the

Indu

stria

l Rev

olut

ion

in E

ngla

nd, F

ranc

e, G

erm

any,

Jap

an,

A1.0

, A2.

0,

B9.0

C1.0

and

the

Uni

ted

Stat

es.

A5.0

10.9

Stu

dent

s an

alyz

e th

e in

tern

atio

nal d

evel

opm

ents

in t

he p

ost-

Wor

ld W

orld

War

II w

orld

.A1

.0B9

.0C1

.0

10.1

0 St

uden

ts a

naly

ze in

stan

ces

of n

atio

n-bu

ildin

g in

the

con

tem

pora

ry w

orld

in a

t le

ast

two

of t

he f

ollo

win

g re

gion

s or

cou

ntrie

s: t

he M

iddl

e Ea

st, A

fric

a, M

exic

o an

d ot

her p

arts

of L

atin

A5

.0B9

.0C1

.0Am

eric

a, a

nd C

hina

.

10.11

Stu

dent

s an

alyz

e th

e in

tegr

atio

n of

cou

ntrie

s in

to t

he w

orld

eco

nom

y an

d th

e in

form

atio

n,

A1.0

, A2.

0,

B9.0

C1.0

tech

nolo

gica

l, an

d co

mm

unic

atio

ns r

evol

utio

ns (e

.g.,

tele

visi

on, s

atel

lites

, com

pute

rs).

A3.0

, A5.

0

Chro

nolo

gica

l and

Spa

tial R

easo

ning

– C

SR

1. S

tude

nts

com

pare

the

pre

sent

with

the

pas

t, ev

alua

ting

the

cons

eque

nces

of p

ast

even

ts a

nd

A1.0

C1.0

deci

sion

s an

d de

term

inin

g th

e le

sson

s th

at w

ere

lear

ned.

2. S

tude

nts

anal

yze

how

cha

nge

happ

ens

at d

iffe

rent

rat

es a

t di

ffer

ent

times

; und

erst

and

that

so

me

aspe

cts

can

chan

ge w

hile

oth

ers

rem

ain

the

sam

e; a

nd u

nder

stan

d th

at c

hang

e is

com

pli-

A1.0

cate

d an

d af

fect

s no

t on

ly t

echn

olog

y an

d po

litic

s bu

t al

so v

alue

s an

d be

liefs

.

4. S

tude

nts

rela

te c

urre

nt e

vent

s to

the

phy

sica

l and

hum

an c

hara

cter

istic

s of

pla

ces

and

regi

ons.

C1.0

34


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

D.

EN

GIN

EE

RIN

G A

ND

AR

CH

ITE

CT

UR

EA

rchi

tect

ural

En

gine

erin

g En

gine

erin

g En

viro

nmen

tal

Desi

gnTe

chno

logy

Desi

gnEn

gine

erin

g

His

toric

al R

esea

rch,

Evi

denc

e, a

nd P

oint

of

View

– H

R

4. S

tude

nts

cons

truc

t an

d te

st h

ypot

hese

s; c

olle

ct, e

valu

ate,

and

em

ploy

info

rmat

ion

from

mul

tiple

A1

.0pr

imar

y an

d se

cond

ary

sour

ces;

and

app

ly it

in o

ral a

nd w

ritte

n pr

esen

tatio

ns.

His

toric

al In

terp

reta

tion

– H

I

1. S

tude

nts

show

the

con

nect

ions

, cau

sal a

nd o

ther

wis

e, b

etw

een

part

icul

ar h

isto

rical

eve

nts

and

A1.0

C1.0

larg

er s

ocia

l, ec

onom

ic, a

nd p

oliti

cal t

rend

s an

d de

velo

pmen

ts.

3. S

tude

nts

inte

rpre

t pa

st e

vent

s an

d is

sues

with

in t

he c

onte

xt in

whi

ch a

n ev

ent

unfo

lded

rat

her

A1.0

than

sol

ely

in t

erm

s of

pre

sent

-day

nor

ms

and

valu

es.

35


Contributors

Engineering and Architecture

Lloyd McCabe, Administrator, California Department of Education

John Dunn, Education Consultant, California Department of Education

Standards Review TeamMark Martin, Director, Laney College

Arnold Ruskin, Instructor, San Diego Union High School District

Barbara Worden, Instructor, Liberty Union High School District

Standards Writing TeamChris Alburn, Instructor, Elk Grove Unified School District

Debra Crane, Instructor, Galt Joint Union High School District

Chris Schlesselman, Instructor, Sacramento City Unified School District

Barbara Worden, Instructor, Liberty Union High School District

Common Core Alignment TeamCurtis Earle, Instructor, Los Angeles Unified School District

Jeff Kamansky, Instructor, Oceanside Unified School District

Sheryl Roccoforte, Instructor, Oceanside Unified School District

Zach Ronnenberg, Instructor, Davis Joint Unified School District

Frank Zuidema, Instructor, Oceanside Unified School District

36


References

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. 2007. Career Technical Education Framework for California Public Schools, Grades Seven Through Twelve. http://www.cde.ca.gov/ci/ct/sf/documents/cteframework.pdf (accessed December 4, 2012).

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37


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