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r an s p o r t a t i o

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Operations Systems Diagnostics, Service, and Repair

Structural Repair and Refinishing

California Career Technical Education Model Curriculum Standards

Table of ContentsTransportation

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 ...................................................................................................5

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

A. Operations Pathway ............................................................................................................................7

B. Structural Repair and Refinishing Pathway ................................................................................10

C. Systems Diagnostics, Service, and Repair Pathway .................................................................13

Academic Alignment Matrix ..........................................................................................................16

Contributors .....................................................................................................................................35

References ........................................................................................................................................36

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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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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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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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Transportation

Sector DescriptionThis sector is designed to provide a foundation in transportation services for all

industrial technology education students in California. There are eight focus areas

that fall under the Transportation sector, each with different career opportunities.

The focus areas are On-Road; Off-Road; Stationary; Rail; Water/Sea; Air; Space;

and Small Engines and Specialty Equipment.

The pathways in the Transportation sector emphasize real-world, occupationally

relevant experiences of significant scope and depth in three areas: Operations,

Structural Repair and Refinishing, and Systems Diagnostics, Service, and Repair. The

standards are designed to integrate academic and technical preparation and focus

on career awareness, career exploration, and skill preparation in the three pathways.

Integral components include classroom, laboratory, and hands-on contextual learn-

ing; project- and work-based instruction; and leadership development. The standards

in this sector prepare students for continued training, postsecondary education, and

entry to a career.

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TransportationKnowledge 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 Transportation academic alignment matrix for identification of standards.

2.0 CommunicationsAcquire and accurately use Transportation sector terminology and protocols at the career and col-lege 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.

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.

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4.0 TechnologyUse existing and emerging technology to investigate, research, and produce products and services, including new information, as required in the Transportation 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 to create alternative solutions to answer a question or solve a problem unique to the Transportation 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 Trans-portation sector workplace environment.(Direct alignment with RSTS 9-10, 11-12.4)

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.

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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 Transportation 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 Transportation 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 organiza-tional 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 Transportation industry sector.

8.3 Demonstrate ethical and legal practices consistent with Transportation sector workplace stan-dards.

8.4 Explain the importance of personal integrity, confidentiality, and ethical behavior in the work-place.

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 Transportation sector laws and practices.

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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 Transportation sector issues and problems.

10.0 Technical Knowledge and SkillsApply essential technical knowledge and skills common to all pathways in the Transportation 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 Transportation sector.

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

10.3 Construct projects and products specific to the Transportation 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 Transportation 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 knowl-edge and skills gained during classroom instruction and laboratory practices specific to the Transportation sector program of study.

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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 innova-tive ventures.

11.4 Employ entrepreneurial practices and behaviors as appropriate to the Transportation 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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TransportationPathway Standards

A. Operations PathwayThe Operations pathway prepares students for postsecondary employment and education in a variety of career opportunities in the transportation industry, including but not limited to harbors, ports, warehousing, marine applications, airplanes, trains, vehicles, and specialty equipment.

Sample occupations associated with this pathway:

Warehouse Worker/Dispatcher

Production, Planning, and Expediting Clerk

Storage, Warehouse, and Distribution Manager

Container Crane Operator

Inspectors and Planners

A1.0 Evaluate and assess all aspects of facilities and facility planning for efficient and effective processing/handling of people, goods, and services in the transportation industry (housing, storage, maintenance, parts).

A1.1 Recognize the importance of space and location of equipment.

A1.2 Define and understand highway, rail, harbor, port, and airport controls.

A1.3 Identify where to place equipment for effective and efficient processing.

A1.4 Explain the difference between office area and processing areas.

A1.5 Design a/an processing center/office/shop.

A2.0 Describe and identify tools, techniques, and systems used to plan, staff, lead, and organize human resources as it relates to the transportation sector.

A2.1 Define the role of management and the responsibility and importance that are required to hold or maintain a position.

A2.2 Describe the production and use of industry-generated documents, records, and forms as well as related management skills used in the transportation industries.

A2.3 Understand work-related systems of the transportation industries.

A2.4 Maintain accurate records as applicable.

A2.5 Understand how guidelines, rules, regulations, and laws control transportation-industry practices and how they are overseen by local, state, federal, and international agencies.

A2.6 Explore career paths and opportunities within the transportation industry.

A2.7 Analyze asset acquisition and procurement needs.

A2.8 Research the various types of communication systems needed.

A3.0 Demonstrate an understanding of the concepts and processes needed to move, store/house, locate, and/or transfer people, goods, and services.

A3.1 Identify and understand transportation options such as rail, air, road, and sea.

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A3.2 Define the different types of process controls available.

A3.3 Describe hazardous and nonhazardous materials handling.

A3.4 Understand process controls, from planning to completion.

A3.5 Determine the uses of information systems in the order fulfillment process.

A3.6 Determine the effects of government regulations on stock handling techniques and warehousing.

A3.7 Explore the functions of the shipping and receiving process in the success of the distribution function.

A3.8 Evaluate types of inventory controls.

A4.0 Demonstrate an understanding of business fundamentals, uses and application of technologies, communications, and basic management functions.

A4.1 Describe current business and marketing trends.

A4.2 Identify and analyze the risks associated with obtaining business credit.

A4.3 Identify considerations in planning and implementing marketing/business strategies.

A4.4 Identify target audience for specific marketing and sales needs.

A4.5 Identify the legal aspects of sales contracts and warranties.

A4.6 Explain the nature of sales forecasting and marketing needs.

A4.7 Understand the practices of acceptable customer relations services.

A4.8 Compare and contrast advantages and disadvantages of business ownership.

A5.0 Analyze and evaluate the design advantages and disadvantages of transportation-industry systems and the effects of those systems on people and the environment.

A5.1 Identify environmental conditions that would impact various aspects of the transportation industry.

A5.2 Identify steps necessary to design a specific mode of transportation using aerodynamics.

A5.3 Research the effects of ergonomics on the health and safety of workers and customers.

A5.4 Create a model of a vehicle (train, airplane, railroad, car) incorporating ergonomics and aerodynamics in the design.

A6.0 Demonstrate safety practices pertaining to the transportation industry, including requirements of the Occupational Safety and Health Administration (OSHA), Environmental Protection Agency (EPA), Air Quality Management Districts (AQMDs), and other regulatory agencies.

A6.1 Extract information from Material Safety Data Sheets (MSDS) pertaining to chemicals used in the workplace.

A6.2 Locate regulatory information and manufacturer recalls.

A6.3 Conform to federal, state, and local regulations and manufacturers’ specifications when handling, storing, and disposing of chemicals and equipment, including necessary certifications.

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A6.4 Adhere to ergonomic and environmental safety regulations in the workplace.

A6.5 Participate in compliance training activities and exercises.

A6.6 Determine the safe and correct application and use for chemicals used in the transportation industry.

A7.0 Describe and identify the infrastructures required and used in the transportation industry.

A7.1 Identify the infrastructure needed to move people, goods, and equipment from one location to another (highways, bridges, waterways, railways).

A7.2 Recognize the need for traffic signals, signs, and markings.

A7.3 Define fueling infrastructure needed to move vehicles, equipment, goods, and services from one location to another.

A7.4 Explain the importance of infrastructure in transporting vehicles, goods, and/or equipment in our everyday lives.

A7.5 Evaluate the need to safely move fluids from one location to another.

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TransportationPathway Standards

B. Structural Repair and Refinishing PathwayThe Structural Repair and Refinishing pathway prepares students for postsecondary education and employment in the transportation industry, including but not limited to body and frame straighten-ing, estimating, painting, and refinishing (included but not limited to airplanes, trains, vehicles, and equipment).

Sample occupations associated with this pathway:

Estimator

Claims Adjuster

Technician

Insurance Company/Manufacturer’s Representative

Investigator/Inspector

B1.0 Students practice personal and occupational safety and understand the environmental effects of collision repair and refinishing practices.

B1.1 Describe industry environmental conservation practices and their applications.

B1.2 Practice the safe handling and storage of chemicals and hazardous wastes as required by the Occupational Safety and Health Administration (OSHA), Air Resources Board (ARB), Air Quality Management Districts (AQMDs), and other regulatory agencies.

B1.3 Understand the generation of waste products and other environmentally destructive substances.

B1.4 Use appropriate materials and repair technologies.

B1.5 Understand the environmental implications of using new and emerging materials, resources, and technologies.

B1.6 Demonstrate the safety practices applied when servicing vehicle-body electronics and other vehicle systems.

B2.0 Practice the safe and appropriate use of tools, equipment, and work processes.

B2.1 Understand how certain tools and equipment are used to perform maintenance and repair operations.

B2.2 Use tools, equipment, and machines to safely measure, test, diagnose, and analyze components and systems (e.g., electrical and electronic circuits, alternating- and direct-current applications, fluid/hydraulic and air/pneumatic systems).

B3.0 Apply measurement systems and the mathematical functions necessary to perform required fabrication, maintenance, and operation procedures.

B3.1 Use industry-standard measurement scales, devices, and systems to perform design, fabrication, diagnostic, maintenance, and repair procedures.

B3.2 Use technical vocabulary, technical reports and manuals, electronic systems, and related technical data resources, as appropriate, to determine repairs and estimates.

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B3.3 Demonstrate the different types of welding and heat processes used in repair processes and procedures.

B3.4 Understand the mathematical functions associated with collision repair and refinishing.

B4.0 Apply scientific principles in relation to chemical, mechanical, and physical functions and in relation to industry and manufacturer standards.

B4.1 Identify and understand the physical and chemical characteristics of metals, plastics, and other materials.

B4.2 Describe the basic terms, characteristics, and concepts of physical and chemical processes.

B4.3 Apply the principles of mechanical, electrical, hydraulic, and pneumatic power in relation to collision repair and refinishing.

B4.4 Practice the principles of electricity and electronics.

B4.5 Understand body and frame construction.

B4.6 Know the importance of calibration processes, systems, and techniques in using various measurement and testing devices.

B5.0 Perform and document repair procedures in accordance with manufacturer recommendations and industry standards.

B5.1 Explain and practice the recommended procedures and practices of various manufac-turers.

B5.2 Use reference books and materials, technical service bulletins, and other related documents to determine repairs and rate of pay.

B5.3 Document repair procedures accurately as required by the Bureau of Automotive Repair and other regulatory agencies.

B6.0 Demonstrate basic business practices.

B6.1 Know the laws and regulations applicable to the recordkeeping and handling of hazardous materials.

B6.2 Use and understand work-related systems.

B6.3 Practice and understand the importance of, and procedures for, maintaining accurate records.

B6.4 Discuss and apply the concept and application of accepted ethical business practices.

B6.5 Use and understand the concept and application of acceptable customer relations services.

B7.0 Understand structural and nonstructural analysis and damage repair.

B7.1 Perform frame inspection and repair.

B7.2 Demonstrate applications, installations, and removal of fixed and moveable glass and hardware.

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B7.3 Demonstrate the principles of metal welding and cutting.

B7.4 Prepare and analyze vehicles for repair.

B7.5 Perform outer body panel repairs, replacements, and adjustments.

B7.6 Prepare vehicles for metal finishing and body filling.

B8.0 Demonstrate an understanding of mechanical and electrical components in relation to industry and manufacturer standards.

B8.1 Identify and communicate the operation of drivetrain, fuel, intake, and exhaust systems.

B8.2 Perform steering and suspension analysis and repairs.

B8.3 Perform electrical repairs.

B8.4 Perform brake analysis and repairs.

B8.5 Perform heating, air-conditioning, and cooling system repairs.

B8.6 Explain and demonstrate the operation of restraint systems.

B9.0 Demonstrate the concepts, principles, and practices of painting and refinishing.

B9.1 Identify, use, and repair plastics and adhesives.

B9.2 Prepare surfaces for painting and finishing.

B9.3 Practice operation of spray guns and related equipment.

B9.4 Practice mixing, matching, and applying paint.

B9.5 Prepare vehicles for final detail.

B9.6 Analyze the causes and cures of paint defects.

12

Transportation | T

TransportationPathway Standards

C. Systems Diagnostics, Service, and Repair PathwayThe Systems Diagnostics, Service, and Repair pathway prepares students for postsecondary education and employment in the transportation industry, which includes but is not limited to motor vehicles, rail systems, marine applications, and small-engine and specialty equipment.

Sample occupations associated with this pathway:

Service Technician/Maintenance Worker/Shop Foreman

Technical Writer

Dispatcher

Engineer

Investigator/Inspector

C1.0 Demonstrate the practice of personal and occupational safety and protecting the environment by using materials and processes in accordance with manufacturer and industry standards.

C1.1 Know and understand common environmental conservation practices and their applications.

C1.2 Practice the safe handling and storage of chemicals and hazardous wastes in accor-dance with Material Safety Data Sheets (MSDS) and the requirements of local, state, and federal regulatory agencies.

C1.3 Understand the way in which waste gasses, emissions, and other environmentally destructive substances are generated and the effects of these substances on the environment.

C1.4 Use appropriate personal protective equipment and safety practices.

C1.5 Evaluate the advantages and disadvantages of existing, new, and emerging systems and the effects of those systems on the environment.

C2.0 Practice the safe and appropriate use of tools, equipment, and work processes.

C2.1 Recognize the importance of calibration processes, systems, and techniques using various measurement and testing devices.

C2.2 Demonstrate and use appropriate tools and equipment—such as wrenches, sockets, and pliers—to diagnose, service, repair, and maintain systems and components.

C2.3 Use tools, equipment, and machines to safely measure, test, diagnose, and analyze components and systems (e.g., electrical and electronic circuits, alternating- and direct-current applications, fluid/hydraulic and air/pneumatic systems).

C2.4 Select and use the appropriate measurement device(s) and use mathematical functions necessary to perform required fabrication, maintenance, and operation procedures.

C2.5 Use measurement scales, devices, and systems, such as dial indicators and micrometers, to design, fabricate, diagnose, maintain, and repair vehicles and components following recommended industry standards.

13

T | California Career Technical Education Model Curriculum Standards

C2.6 Demonstrate how to access technical reports, manuals, electronic retrieval systems, and related technical data resources.

C2.7 Test and analyze the elements of precision measuring using standard and metric systems.

C3.0 Use scientific principles in relation to chemical, mechanical, and physical functions for various engine and vehicle systems.

C3.1 Describe the operating principles of internal and/or external combustion engines.

C3.2 Describe the function and principles of air-conditioning and heating systems.

C3.3 Describe the basic principles of pneumatic and hydraulic power and their applications.

C3.4 Describe the applications of alternative power sources.

C3.5 Practice the basic principles of electricity, electronics and electrical power generation, and distribution systems.

C3.6 Explain the principles of converting energy from one form to another.

C3.7 Perform necessary procedures to maintain, diagnose, service, and repair vehicle systems and malfunctions.

C4.0 Perform and document maintenance procedures in accordance with the recommendations of the manufacturer.

C4.1 Communicate the procedures and practices of various manufacturers regarding service, repair, and maintenance schedules.

C4.2 Demonstrate how to properly document maintenance and repair procedures in accordance with applicable rules, laws, and regulations (e.g., Bureau of Auto Repair [BAR], Occupational Safety and Health Administration [OSHA], and the California Air Resources Board [ARB]).

C4.3 Use reference books, technical service bulletins, and other documents and materials related to the service industry available in print and through electronic retrieval systems to accurately diagnose and repair systems, equipment, and vehicles.

C4.4 Complete a work order, including customer information, description of repairs, and billing information, in accordance with applicable rules, laws, and regulations.

C5.0 Apply and understand appropriate business practices.

C5.1 Identify work-related systems common to the transportation service industry.

C5.2 Know the laws and regulations applicable to recordkeeping and the appropriate handling and disposal of hazardous materials.

C5.3 Explain the importance of and the procedures for maintaining accurate records (e.g., business licenses, repair orders, billing and tax records).

C5.4 Practice the concept and application of accepted ethical business practices.

C5.5 Practice the concept and application of acceptable customer relations practices.

C5.6 Recognize, analyze, and evaluate the need for maintenance of components and systems and the conditions under which service and maintenance are required.

14

Transportation | T

C6.0 Demonstrate the application, operation, maintenance, and diagnosis of engines, including but not limited to two- and four-stroke and supporting subsystems.

C6.1 Perform general engine maintenance, diagnosis, service, and repair in accordance with portable national industry standards, such as the National Automotive Technicians Education Foundation and the Equipment and Engine Training Council.

C6.2 Maintain, diagnose, service, and repair lubrication and cooling systems.

C6.3 Practice how to maintain, diagnose, and repair computerized engine control systems and other engine-related systems.

C6.4 Maintain, diagnose, service, and repair ignition, electronic, and computerized engine controls and fuel management systems.

C7.0 Demonstrate the function, principles, and operation of electrical and electronic systems using manufacturer and industry standards.

C7.1 Practice maintenance, diagnosis, and repair of electrical systems.

C7.2 Maintain, diagnose, repair, and service batteries.

C7.3 Demonstrate maintenance, diagnosis, service, and repair of starting and charging systems.

C7.4 Diagnose, service, and repair lighting systems.

C7.5 Diagnose, service, and repair heating and air-conditioning systems and components.

C7.6 Diagnose, service, and repair horns, wipers/washers, and other accessories.

C7.7 Perform necessary procedures to maintain, diagnose, service, and repair vehicle electrical and electronic systems and malfunctions.

C8.0 Demonstrate the function and principles of automotive drivetrain, steering and suspension, brake, and tire and wheel components and systems in accordance with national industry standards.

C8.1 Describe how to maintain, diagnose, service, and repair hydraulic and power assist systems.

C8.2 Describe the function and operation of automatic and manual transmissions and transaxles.

C8.3 Diagnose, service, and repair disc brakes, drum brakes, antilock brakes, and other brake systems as developed.

C8.4 Diagnose, service, and repair steering and suspension systems.

C8.5 Interpret tire and rim sizing to select appropriate wheels and tires for vehicles.

C8.6 Maintain, diagnose, service, and repair under-vehicle systems and malfunctions.

15

T | California Career Technical Education Model Curriculum Standards

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

TR

AN

SPO

RTA

TIO

NO

pera

tion

sSt

ruct

ural

Rep

air

Syst

ems

Diag

nost

ics,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

ENGL

ISH

LAN

GUAG

E A

RTS

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

2.3

Follo

w p

reci

sely

a c

ompl

ex m

ultis

tep

proc

edur

e w

hen

carr

ying

out

exp

erim

ents

, B1

.0, B

2.0,

B3.

0, B

4.0,

ta

king

mea

sure

men

ts, o

r per

form

ing

tech

nica

l tas

ks; a

naly

ze t

he s

peci

fic r

esul

ts b

ased

on

A6.0

C1.0

, C2.

0, C

5.0

B6.0

, B7.

0, B

8.0,

B9.

0ex

plan

atio

ns in

the

tex

t.

11-1

2.10

By

the

end

of g

rade

12

read

and

com

preh

end

scie

nce/

tech

nica

l tex

ts in

the

gra

des

A1.0

, A2.

0, A

3.0,

B1

.0, B

2.0,

B3.

0, B

4.0,

C1

.0, C

2.0,

C3.

0, C

4.0,

11

-12

text

com

plex

ity

band

inde

pend

ently

and

pro

ficie

ntly

.A4

.0, A

5.0,

A6.

0,

B5.0

, B6.

0, B

7.0,

B8.

0,

C5.0

, C6.

0, C

7.0,

C8.

0A7

.0B9

.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

A5

.0B5

.0C5

.0va

lid r

easo

ning

and

rel

evan

t an

d su

ffici

ent

evid

ence

.

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

A7

.0B5

.0C5

.0an

alys

is o

f con

tent

.

11-1

2.4

Prod

uce

clea

r and

coh

eren

t w

ritin

g in

whi

ch t

he d

evel

opm

ent,

orga

niza

tion,

and

sty

le

A3.0

, A4.

0B5

.0C4

.0ar

e ap

prop

riate

to

task

, pur

pose

, and

aud

ienc

e.

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

B2

.0, B

3.0,

B5.

0, B

6.0,

or

sha

red

writ

ing

prod

ucts

in r

espo

nse

to o

ngoi

ng f

eedb

ack,

incl

udin

g ne

w a

rgum

ents

or

A1.0

, A3.

0, A

4.0

C6.0

, C7.

0B8

.0, B

9.0

info

rmat

ion.

11-1

2.9

Draw

evi

denc

e fr

om li

tera

ry o

r inf

orm

atio

nal t

exts

to

supp

ort

anal

ysis

, refl

ectio

n, a

nd

A1.0

, A2.

0C8

.0re

sear

ch.

11-1

2.10

Writ

e ro

utin

ely

over

ext

ende

d tim

e fr

ames

(tim

e fo

r res

earc

h, r

eflec

tion,

and

re

visi

on) a

nd s

hort

er t

ime

fram

es (a

sin

gle

sitt

ing

or a

day

or t

wo)

for

a r

ange

of t

asks

, A1

.0B5

.0C4

.0pu

rpos

es, a

nd a

udie

nces

.

16

Transportation | T

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

TR

AN

SPO

RTA

TIO

NO

pera

tion

sSt

ruct

ural

Rep

air

Syst

ems

Diag

nost

ics,

an

d Re

finis

hing

Serv

ice,

and

Rep

air

MAT

HEM

ATIC

S

Alge

bra

– A-

SSE

– Se

eing

Str

uctu

re in

Exp

ress

ions

Inte

rpre

t the

stru

ctur

e of

exp

ress

ions

1. In

terp

ret

expr

essi

ons

that

rep

rese

nt a

qua

ntit

y in

ter

ms

of it

s co

ntex

t.

a. In

terp

ret

part

s of

an

expr

essi

on, s

uch

as t

erm

s, f

acto

rs, a

nd c

oeffi

cien

ts.

B3.0

, B4.

0, B

9.0

b. In

terp

ret

com

plic

ated

exp

ress

ions

by

view

ing

one

or m

ore

of t

heir

part

s as

a s

ingl

e en

tity.

Fo

r exa

mpl

e, in

terp

ret P

(1+r

)’ as

the

prod

uct o

f P a

nd a

fact

or n

ot d

epen

ding

on

P.

2. U

se t

he s

truc

ture

of a

n ex

pres

sion

to

iden

tify

way

s to

rew

rite

it. F

or e

xam

ple,

see

x4 –

y4 a

s (x

2 )2 - (y

2 )2 , thu

s re

cogn

izin

g it

as a

dif

fere

nce

of s

quar

es t

hat

can

be f

acto

red

as (x

2 – y

2 ) (x

2 + y

2 ).

a. U

se th

e di

strib

utiv

e pr

oper

ty to

exp

ress

a s

um o

f ter

ms

with

a c

omm

on f

acto

r as

a m

ultip

le

of a

sum

of t

erm

s w

ith n

o co

mm

on f

acto

r. Fo

r exa

mpl

e, e

xpre

ss x

y2 + x

2 y as

xy

(y +

x).

B3

.0, B

9.0

(Com

mon

Cor

e St

anda

rd A

-SSE

-2a)

b. U

se th

e pr

oper

ties o

f ope

ratio

ns t

o ex

pres

s a

prod

uct o

f a s

um o

f ter

ms

as a

sum

of

prod

ucts

. For

exa

mpl

e, u

se th

e pr

oper

ties o

f ope

ratio

ns to

exp

ress

(x +

5)(

3 –

x +

c) a

s –x

2 +

cx -

2x

+ 5c

+ 1

5. (C

omm

on C

ore

Stan

dard

A-S

SE-2

b)

2.1

Appl

y ba

sic

fact

orin

g te

chni

ques

to

seco

nd-

and

sim

ple

third

-deg

ree

poly

nom

ials

. The

se

tech

niqu

es in

clud

e fin

ding

a c

omm

on f

acto

r for

all

term

s in

a p

olyn

omia

l, re

cogn

izin

g th

e

B3.0

, B9.

0di

ffer

ence

of t

wo

squa

res,

and

rec

ogni

zing

per

fect

squ

ares

of b

inom

ials

. (CA

Sta

ndar

d

Alge

bra

I - 1

1.0)

17

T | California Career Technical Education Model Curriculum Standards

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

Tra

nsp

orta

tion

Ope

rati

ons

Stru

ctur

al R

epai

r Sy

stem

s Di

agno

stic

s, an

d Re

finis

hing

Serv

ice,

and

Rep

air

Alge

bra

– A-

SSE

– Se

eing

Str

uctu

re in

Exp

ress

ions

(con

tinue

d)

Writ

e ex

pres

sion

s in

equi

vale

nt fo

rms t

o so

lve

prob

lem

s

3. C

hoos

e an

d pr

oduc

e an

equ

ival

ent

form

of a

n ex

pres

sion

to

reve

al a

nd e

xpla

in p

rope

rtie

s of

the

qu

antit

y re

pres

ente

d by

the

exp

ress

ion.

a. F

acto

r a q

uadr

atic

exp

ress

ion

to r

evea

l the

zer

os o

f the

fun

ctio

n it

defin

es.

b. C

ompl

ete

the

squa

re in

a q

uadr

atic

exp

ress

ion

to r

evea

l the

max

imum

or m

inim

um v

alue

of t

he

func

tion

it de

fines

.

c. U

se t

he p

rope

rtie

s of

exp

onen

ts t

o tr

ansf

orm

exp

ress

ions

for

exp

onen

tial f

unct

ions

. For

exa

mpl

e th

e ex

pres

sion

1.1

5t can

be

rew

ritte

n as

(1.1

5 1/

12)1

2T = 1

.012

12t t

o re

veal

the

app

roxi

mat

e eq

uiva

lent

B3

.0, B

9.0

mon

thly

inte

rest

rat

e if

the

annu

al r

ate

is 1

5%.

d. P

rove

sim

ple

law

s of

loga

rithm

s. (C

A St

anda

rd A

lgeb

ra II

- 1

1.0)

e. U

se t

he d

efini

tion

of lo

garit

hms

to t

rans

late

bet

wee

n lo

garit

hms

in a

ny b

ase.

(CA

Stan

dard

Al

gebr

a II

- 13

.0)

f. U

nder

stan

d an

d us

e th

e pr

oper

ties

of lo

garit

hms

to s

impl

ify

loga

rithm

ic n

umer

ic e

xpre

ssio

ns a

nd

to id

entif

y th

eir a

ppro

xim

ate

valu

es. (

CA S

tand

ard

Alge

bra

11-

14.0

)

4. D

eriv

e th

e fo

rmul

a fo

r the

sum

of a

fini

te g

eom

etric

ser

ies

(whe

n th

e co

mm

on r

atio

is n

ot 1

), an

d B3

.0, B

9.0

use

the

form

ula

to s

olve

pro

blem

s. F

or e

xam

ple,

cal

cula

te m

ortg

age

paym

ents

.

Alge

bra

– A-

CED

– Cr

eatin

g Eq

uati

ons

Crea

te e

quat

ions

that

des

crib

e nu

mbe

rs o

r rel

atio

nshi

ps

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

sol

ve p

robl

ems

in a

nd o

ut o

f con

text

, inc

ludi

ng e

quat

ions

aris

ing

from

line

ar f

unct

ions

.C2

.0, C

3.0,

C5.

0, C

6.0,

B3

.0, B

4.0,

B6.

01.

1 Ju

dge

the

valid

ity

of a

n ar

gum

ent

acco

rdin

g to

whe

ther

the

pro

pert

ies

of r

eal n

umbe

rs, e

xpo-

C7.0

nent

s, a

nd lo

garit

hms

have

bee

n ap

plie

d co

rrec

tly a

t ea

ch s

tep.

(CA

Stan

dard

Alg

ebra

II -

11.

2)

2. C

reat

e eq

uatio

ns in

tw

o or

mor

e va

riabl

es t

o re

pres

ent

rela

tions

hips

bet

wee

n qu

antit

ies;

gra

ph

C2.0

, C3.

0, C

5.0,

C6.

0,

B3.0

, B4.

0, B

6.0

equa

tions

on

coor

dina

te a

xes

with

labe

ls a

nd s

cale

s.C7

.0

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

ities

, an

d 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

rese

nt

A4.0

B3.0

, B6.

0C5

.0in

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

.

18

Transportation | T

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

Tra

nsp

orta

tion

Ope

rati

ons

Stru

ctur

al R

epai

r Sy

stem

s Di

agno

stic

s,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

Alge

bra

– A-

CED

– Cr

eatin

g Eq

uati

ons

(con

tinue

d)

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

B3.0

, B6.

0C2

.0, C

5.0,

C7.

0eq

uatio

ns. F

or e

xam

ple,

rea

rran

ge O

hm’s

law

V =

IR t

o hi

ghlig

ht r

esis

tanc

e R.

Alge

bra

– A-

REI –

Rea

soni

ng w

ith

Equa

tion

s an

d In

equa

litie

s

Unde

rsta

nd so

lvin

g eq

uatio

ns a

s a p

roce

ss o

f rea

soni

ng a

nd e

xpla

in th

e re

ason

ing

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

A1.0

solu

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

A1

.0, A

4.0

B4.0

C3.0

, C4.

0ex

tran

eous

sol

utio

ns m

ay a

rise.

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.A1

.0, A

5.0

B4.0

, B5.

03.

1 So

lve

equa

tions

and

ineq

ualit

ies

invo

lvin

g ab

solu

te v

alue

. (CA

Sta

ndar

d Al

gebr

a I -

3.0

and

CA

Sta

ndar

d Al

gebr

a II

- 1.

0)

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 A1

.0, A

2.0,

A4.

0B6

.0C5

.0is

an

elem

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

gr

aph

of f

is t

he g

raph

of t

he e

quat

ion

y =

f(x)

.

2. U

se f

unct

ion

nota

tion,

eva

luat

e fu

nctio

ns f

or in

puts

in t

heir

dom

ains

, and

inte

rpre

t st

ate-

A1.0

, A2.

0B6

.0C5

.0m

ents

tha

t us

e fu

nctio

n no

tatio

n in

ter

ms

of a

con

text

.

3. R

ecog

nize

tha

t se

quen

ces

are

func

tions

, som

etim

es d

efine

d re

curs

ivel

y, w

hose

dom

ain

is

a s

ubse

t of

the

inte

gers

. For

exa

mpl

e, t

he F

ibon

acci

seq

uenc

e is

defi

ned

recu

rsiv

ely

by

B6.0

f(0)

= f

(1) =

1, f

(n+1

) = f

(n) +

f(n-

1)fo

r n

1.

19

T | California Career Technical Education Model Curriculum Standards

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

Tra

nsp

orta

tion

Ope

rati

ons

Stru

ctur

al R

epai

r Sy

stem

s Di

agno

stic

s, an

d Re

finis

hing

Serv

ice,

and

Rep

air

Func

tion

s –

F-IF

– In

terp

retin

g Fu

ncti

ons

(con

tinue

d)

Inte

rpre

t fun

ctio

ns th

at a

rise

in a

pplic

atio

ns in

term

s of t

he c

onte

xt

4. F

or a

fun

ctio

n th

at m

odel

s a

rela

tions

hip

betw

een

two

quan

titie

s, in

terp

ret

key

feat

ures

of

grap

hs a

nd t

able

s in

ter

ms

of t

he q

uant

ities

, and

ske

tch

grap

hs s

how

ing

key

feat

ures

giv

en a

A1

.0, A

2.0,

A5.

0,

verb

al d

escr

iptio

n of

the

rel

atio

nshi

p. K

ey f

eatu

res

incl

ude:

inte

rcep

ts; i

nter

vals

whe

re t

he f

unc-

B6.0

C5.0

A4.0

tion

is in

crea

sing

, dec

reas

ing,

pos

itive

, or n

egat

ive;

rel

ativ

e m

axim

ums

and

min

imum

s; s

ymm

e-tr

ies;

end

beh

avio

r; an

d pe

riodi

city

.

5. R

elat

e th

e do

mai

n of

a f

unct

ion

to it

s gr

aph

and,

whe

re a

pplic

able

, to

the

quan

titat

ive

rela

-tio

nshi

p it

desc

ribes

. For

exa

mpl

e, if

the

fun

ctio

n h(

n) g

ives

the

num

ber o

f per

son-

hour

s it

take

s A1

.0, A

2.0,

A5.

0B6

.0C5

.0to

ass

embl

e n

engi

nes

in a

fac

tory

, the

n th

e po

sitiv

e in

tege

rs w

ould

be

an a

ppro

pria

te d

omai

n fo

r the

fun

ctio

n.

6. C

alcu

late

and

inte

rpre

t th

e av

erag

e ra

te o

f cha

nge

of a

fun

ctio

n (p

rese

nted

sym

bolic

ally

or a

s A1

.0, A

2.0,

A4.

0,

B6.0

C5.0

, C6.

0, C

7.0

a ta

ble)

ove

r a s

peci

fied

inte

rval

. Est

imat

e th

e ra

te o

f cha

nge

from

a g

raph

.A5

.0

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

and

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,

A1

.0, A

2.0

B6.0

C5.0

and

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

onom

etric

fun

ctio

ns, s

how

ing

perio

d, m

idlin

e, a

nd a

mpl

itude

.

20

Transportation | T

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

Tra

nsp

orta

tion

Ope

rati

ons

Stru

ctur

al R

epai

r Sy

stem

s Di

agno

stic

s, an

d Re

finis

hing

Serv

ice,

and

Rep

air

Func

tion

s –

F-IF

– In

terp

retin

g Fu

ncti

ons

(con

tinue

d)

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

ze

ros,

ext

rem

e va

lues

, and

sym

met

ry o

f the

gra

ph, a

nd in

terp

ret

thes

e in

ter

ms

of a

con

text

.B6

.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

.97)

t, y

= (1

.01)

12t,

y =

(1.2

)t/1

0, a

nd c

lass

ify

them

as

repr

esen

ting

expo

nent

ial g

row

th o

r dec

ay.

9. C

ompa

re p

rope

rtie

s of

tw

o fu

nctio

ns e

ach

repr

esen

ted

in a

dif

fere

nt w

ay (a

lgeb

raic

ally

, gr

aphi

cally

, num

eric

ally

in t

able

s, o

r by

verb

al d

escr

iptio

ns).

For e

xam

ple,

giv

en a

gra

ph o

f one

A1

.0, A

2.0

B6.0

C5.0

quad

ratic

fun

ctio

n an

d an

alg

ebra

ic e

xpre

ssio

n fo

r ano

ther

, say

whi

ch h

as t

he la

rger

max

imum

.

10. D

emon

stra

te a

n un

ders

tand

ing

of f

unct

ions

and

equ

atio

ns d

efine

d pa

ram

etric

ally

and

gra

ph

A1.0

, A2.

0B6

.0C5

.0th

em. (

CA S

tand

ard

Mat

h An

alys

is -

7.0

)

Func

tion

s –

F-BF

– B

uild

ing

Func

tion

s

Build

a fu

nctio

n th

at m

odel

s a re

latio

nshi

p be

twee

n tw

o qu

antit

ies

1. W

rite

a fu

nctio

n th

at d

escr

ibes

a r

elat

ions

hip

betw

een

two

quan

titie

s.

a. D

eter

min

e an

exp

licit

expr

essi

on, a

rec

ursi

ve p

roce

ss, o

r ste

ps f

or c

alcu

latio

n fr

om a

con

-te

xt.

b. C

ombi

ne s

tand

ard

func

tion

type

s us

ing

arith

met

ic o

pera

tions

. For

exa

mpl

e, b

uild

a fu

nc-

tion

that

mod

els t

he te

mpe

ratu

re o

f a c

oolin

g bo

dy b

y ad

ding

a c

onst

ant f

unct

ion

to a

dec

ayin

g A1

.0, A

2.0

B6.0

C5.0

expo

nent

ial,

and

rela

te th

ese

func

tions

to th

e m

odel

.

c. (+

) Com

pose

fun

ctio

ns. F

or e

xam

ple,

if T

(y) i

s th

e te

mpe

ratu

re in

the

atm

osph

ere

as a

fun

c-tio

n of

hei

ght,

and

h(t)

is t

he h

eigh

t of

a w

eath

er b

allo

on a

s a

func

tion

of t

ime,

the

n T(

h(t)

) is

the

tem

pera

ture

at

the

loca

tion

of t

he w

eath

er b

allo

on a

s a

func

tion

of t

ime.

2. W

rite

arith

met

ic a

nd g

eom

etric

seq

uenc

es b

oth

recu

rsiv

ely

and

with

an

expl

icit

form

ula,

use

A1

.0, A

2.0

B6.0

C5.0

them

to

mod

el s

ituat

ions

, and

tra

nsla

te b

etw

een

the

two

form

s.

21

T | California Career Technical Education Model Curriculum Standards

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

Tra

nsp

orta

tion

Ope

rati

ons

Stru

ctur

al R

epai

r Sy

stem

s Di

agno

stic

s, an

d Re

finis

hing

Serv

ice,

and

Rep

air

Func

tion

s –

F-BF

– B

uild

ing

Func

tion

s (c

ontin

ued)

Build

new

func

tions

from

exi

stin

g fu

nctio

ns

3. Id

entif

y th

e ef

fect

on

the

grap

h of

rep

laci

ng f(

x) b

y f(

x) +

k, k

f(x)

, f(k

x), a

nd f(

x +

k) f

or s

peci

fic

valu

es o

f k (b

oth

posi

tive

and

nega

tive)

; find

the

val

ue o

f k g

iven

the

gra

phs.

Exp

erim

ent

with

cas

es

and

illus

trat

e an

exp

lana

tion

of t

he e

ffec

ts o

n th

e gr

aph

usin

g te

chno

logy

. Inc

lude

rec

ogni

zing

eve

n A1

.0, A

2.0

B6.0

C5.0

and

odd

func

tions

fro

m t

heir

grap

hs a

nd a

lgeb

raic

exp

ress

ions

for

the

m.

3.1

Solv

e pr

oble

ms

invo

lvin

g fu

nctio

nal c

once

pts.

suc

h as

com

posi

tion.

defi

ning

the

inve

rse

func

-tio

n an

d pe

rfor

min

g ar

ithm

etic

ope

ratio

ns o

n fu

nctio

ns. (

CA S

tand

ard

Alge

bra

II -

24.0

)

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

nent

ial

func

tions

gro

w b

y eq

ual f

acto

rs o

ver e

qual

inte

rval

s.A

2.0

B5.0

C5.0

b. R

ecog

nize

situ

atio

ns in

whi

ch o

ne q

uant

ity

chan

ges

at a

con

stan

t ra

te p

er u

nit

inte

rval

rel

ativ

e to

ano

ther

.

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.

2. C

onst

ruct

line

ar a

nd e

xpon

entia

l fun

ctio

ns, i

nclu

ding

arit

hmet

ic a

nd g

eom

etric

seq

uenc

es, g

iven

a

A2.

0B6

.0C5

.0gr

aph,

a d

escr

iptio

n of

a r

elat

ions

hip,

or t

wo

inpu

t-ou

tput

pai

rs (i

nclu

de r

eadi

ng t

hese

fro

m a

tab

le).

3. O

bser

ve u

sing

gra

phs

and

tabl

es t

hat

a qu

antit

y in

crea

sing

exp

onen

tially

eve

ntua

lly e

xcee

ds a

A

2.0

B6.0

C5.0

quan

tity

incr

easi

ng li

near

ly, q

uadr

atic

ally

, or (

mor

e ge

nera

lly) a

s a

poly

nom

ial f

unct

ion.

4. F

or e

xpon

entia

l mod

els,

exp

ress

as

a lo

garit

hm t

he s

olut

ion

to a

bct =

d w

here

a, c

, and

d a

re n

um-

B6.0

C5.0

bers

and

the

bas

e b

is 2

, 10,

or e

; eva

luat

e th

e lo

garit

hm u

sing

tec

hnol

ogy.

Inte

rpre

t exp

ress

ions

for f

unct

ions

in te

rms o

f the

situ

atio

n th

ey m

odel

5. In

terp

ret

the

para

met

ers

in a

line

ar o

r exp

onen

tial f

unct

ion

in t

erm

s of

a c

onte

xt.

A2.

0B6

.0C5

.0

6. A

pply

qua

drat

ic e

quat

ions

to

phys

ical

pro

blem

s, s

uch

as t

he m

otio

n of

an

obje

ct u

nder

the

for

ce o

f B6

.0C5

.0gr

avit

y. (C

A St

anda

rd A

lgeb

ra 1

- 23

.0)

22

Transportation | T

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

Tra

nsp

orta

tion

Ope

rati

ons

Stru

ctur

al R

epai

r Sy

stem

s Di

agno

stic

s, an

d Re

finis

hing

Serv

ice,

and

Rep

air

Geom

etry

– G

-CO

– C

ongr

uenc

e

Expe

rimen

t with

tran

sfor

mat

ions

in th

e pl

ane

1. K

now

pre

cise

defi

nitio

ns o

f ang

le, c

ircle

, per

pend

icul

ar li

ne, p

aral

lel l

ine,

and

line

seg

men

t, ba

sed

on t

he u

ndefi

ned

notio

ns o

f poi

nt, l

ine,

dis

tanc

e al

ong

a lin

e, a

nd d

ista

nce

arou

nd a

A1

.0, A

2.0

B6.0

C5.0

circ

ular

arc

.

2. R

epre

sent

tra

nsfo

rmat

ions

in t

he p

lane

usi

ng, e

.g.,

tran

spar

enci

es a

nd g

eom

etry

sof

twar

e;

desc

ribe

tran

sfor

mat

ions

as

func

tions

tha

t ta

ke p

aint

s in

the

pla

ne a

s in

puts

and

giv

e ot

her

A1.0

, A2.

0B6

.0C5

.0po

ints

as

outp

uts.

Com

pare

tra

nsfo

rmat

ions

tha

t pr

eser

ve d

ista

nce

and

angl

e to

tho

se t

hat

do

not

(e.g

., tr

ansl

atio

n ve

rsus

hor

izon

tal s

tret

ch).

3. G

iven

a r

ecta

ngle

, par

alle

logr

am, t

rape

zoid

, or r

egul

ar p

olyg

on, d

escr

ibe

the

rota

tions

and

A1

.0, A

2.0

B6.0

C5.0

refle

ctio

ns t

hat

carr

y it

onto

itse

lf.

4. D

evel

op d

efini

tions

of r

otat

ions

, refl

ectio

ns, a

nd t

rans

latio

ns in

ter

ms

of a

ngle

s, c

ircle

s,

A1.0

, A2.

0B6

.0C5

.0pe

rpen

dicu

lar l

ines

, par

alle

l lin

es, a

nd li

ne s

egm

ents

.

5. G

iven

a g

eom

etric

figu

re a

nd a

rot

atio

n, r

eflec

tion,

or t

rans

latio

n, d

raw

the

tra

nsfo

rmed

figu

re

usin

g, e

.g.,

grap

h pa

per,

trac

ing

pape

r, or

geo

met

ry s

oftw

are.

Spe

cify

a s

eque

nce

of t

rans

form

a-A1

.0, A

2.0

B6.0

C5.0

tions

tha

t w

ill c

arry

a g

iven

figu

re o

nto

anot

her.

Prov

e ge

omet

ric th

eore

ms

9. P

rove

the

orem

s ab

out

lines

and

ang

les.

The

orem

s in

clud

e: v

ertic

al a

ngle

s ar

e co

ngru

ent;

whe

n a

tran

sver

sal c

ross

es p

aral

lel l

ines

, alte

rnat

e in

terio

r ang

les

are

cong

ruen

t an

d co

rres

pond

ing

A1.0

, A2.

0B6

.0C5

.0an

gles

are

con

grue

nt; p

aint

s on

a p

erpe

ndic

ular

bis

ecto

r of a

line

seg

men

t ar

e ex

actly

tho

se

equi

dist

ant

from

the

seg

men

t’s e

ndpo

ints

.

10. P

rove

the

orem

s ab

out

tria

ngle

s. T

heor

ems

incl

ude:

mea

sure

s of

inte

rior a

ngle

s of

a t

riang

le

sum

to

180°

; bas

e an

gles

of i

sosc

eles

tria

ngle

s ar

e co

ngru

ent;

the

seg

men

t jo

inin

g m

idpo

ints

of

two

side

s of

a t

riang

le is

par

alle

l to

the

third

sid

e an

d ha

lf th

e le

ngth

; the

med

ians

of a

tria

ngle

A1

.0, A

2.0

B6.0

C5.0

mee

t at

a p

oint

.

1

0.1

Know

and

use

the

tria

ngle

ineq

ualit

y th

eore

m. (

CA S

tand

ard

Geo

met

ry -

6.0

)

11. P

rove

the

orem

s ab

out

para

llelo

gram

s. T

heor

ems

incl

ude:

opp

osite

sid

es a

re c

ongr

uent

, op

posi

te a

ngle

s ar

e co

ngru

ent,

the

diag

onal

s of

a p

aral

lelo

gram

bis

ect

each

oth

er, a

nd

A1.0

, A2.

0B6

.0C5

.0co

nver

sely

, rec

tang

les

are

para

llelo

gram

s w

ith c

ongr

uent

dia

gona

ls.

23

T | California Career Technical Education Model Curriculum Standards

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

Tra

nsp

orta

tion

Ope

rati

ons

Stru

ctur

al R

epai

r Sy

stem

s Di

agno

stic

s,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

Geom

etry

– G

-CO

– C

ongr

uenc

e (c

ontin

ued)

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

y-in

g 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

r-A1

.0, A

2.0

B6.0

C5.0

pend

icul

ar li

nes,

incl

udin

g th

e pe

rpen

dicu

lar 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

.

Num

ber

and

Qua

ntit

y –

N-V

M –

Vec

tor

and

Mat

rix Q

uant

itie

s

Perf

orm

ope

ratio

ns o

n m

atric

es a

nd u

se m

atric

es in

app

licat

ions

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

A1

.0, A

2.0

B6.0

C5.0

rela

tions

hips

in a

net

wor

k.

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

A1

.0, A

2.0

B6.0

C5.0

gam

e ar

e do

uble

d.

8. (+

) Add

, sub

trac

t, an

d m

ultip

ly m

atric

es o

f app

ropr

iate

dim

ensi

ons.

A1.0

, A2.

0B6

.0C5

.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

atri-

A1.0

, A2.

0B6

.0C5

.0ce

s is

not

a c

omm

utat

ive

oper

atio

n, b

ut s

till s

atis

fies

the

asso

ciat

ive

and

dist

ribut

ive

prop

ertie

s.

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-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

A1

.0, A

2.0

B6.0

C5.0

nonz

ero

if an

d on

ly if

the

mat

rix h

as a

mul

tiplic

ativ

e in

vers

e.

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-

A1.0

, A2.

0B6

.0C5

.0si

ons

to p

rodu

ce a

noth

er v

ecto

r. W

ork

with

mat

rices

as

tran

sfor

mat

ions

of v

ecto

rs.

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

A1

.0, A

2.0

B6.0

C5.0

valu

e of

the

det

erm

inan

t in

ter

ms

of a

rea.

Stat

isti

cs a

nd P

roba

bilit

y –

S-IC

– M

akin

g In

fere

nces

and

Jus

tify

ing

Conc

lusi

ons

Unde

rsta

nd a

nd e

valu

ate

rand

om p

roce

sses

und

erly

ing

stat

istic

al e

xper

imen

ts

1. U

nder

stan

d st

atis

tics

as a

pro

cess

for

mak

ing

infe

renc

es a

bout

pop

ulat

ion

para

met

ers

base

d A1

.0, A

2.0,

A4.

0B6

.0C5

.0on

a r

ando

m s

ampl

e fr

om t

hat

popu

latio

n.

24

Transportation | T

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

Tra

nsp

orta

tion

Ope

rati

ons

Stru

ctur

al R

epai

r Sy

stem

s Di

agno

stic

s,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

Stat

isti

cs a

nd P

roba

bilit

y –

S-IC

– M

akin

g In

fere

nces

and

Jus

tify

ing

Conc

lusi

ons

(con

tinue

d)2.

Dec

ide

if a

spec

ified

mod

el is

con

sist

ent

with

res

ults

fro

m a

giv

en d

ata-

gene

ratin

g pr

oces

s,

e.g.

, usi

ng s

imul

atio

n. F

or e

xam

ple,

a m

odel

say

s a

spin

ning

coi

n fa

lls h

eads

up

with

pro

babi

lity

A1.0

, A2.

0B6

.0C5

.00.

5. W

ould

a r

esul

t of

5 t

ails

in a

row

cau

se y

ou t

o qu

estio

n th

e m

odel

?

Mak

e in

fere

nces

and

just

ify c

oncl

usio

ns fr

om sa

mpl

e su

rvey

s, ex

perim

ents

, and

obs

erva

tiona

l st

udie

s

3. R

ecog

nize

the

pur

pose

s of

and

dif

fere

nces

am

ong

sam

ple

surv

eys,

exp

erim

ents

, and

obs

erva

-A1

.0, A

2.0,

A4.

0B6

.0C5

.0tio

nal s

tudi

es; e

xpla

in h

ow r

ando

miz

atio

n re

late

s to

eac

h.

5. U

se d

ata

from

a r

ando

miz

ed e

xper

imen

t to

com

pare

tw

o tr

eatm

ents

; use

sim

ulat

ions

to

A1.0

, A2.

0B6

.0C5

.0de

cide

if d

iffe

renc

es b

etw

een

para

met

ers

are

sign

ifica

nt.

6. E

valu

ate

repo

rts

base

d on

dat

a.A1

.0, A

2.0,

A4.

0,

B6.0

C1.0

, C5.

0A5

.0, A

6.0

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

).A1

.0, A

2.0,

A4.

0B6

.0C5

.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,

A1.0

, A2.

0, A

4.0

B6.0

C5.0

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

A1.0

, A2.

0, A

4.0

B6.0

C5.0

for p

ossi

ble

effe

cts

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 A1

.0, A

2.0

B6.0

C5.0

is n

ot a

ppro

pria

te. U

se c

alcu

lato

rs, s

prea

dshe

ets,

and

tab

les

to e

stim

ate

area

s un

der t

he n

orm

al

curv

e.

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

-tiv

e fr

eque

ncie

s in

the

con

text

of t

he d

ata

(incl

udin

g jo

int,

mar

gina

l, an

d co

nditi

onal

rel

ativ

e A1

.0, A

2.0

B6.0

C5.0

freq

uenc

ies)

. Rec

ogni

ze p

ossi

ble

asso

ciat

ions

and

tre

nds

in t

he d

ata.

25

T | California Career Technical Education Model Curriculum Standards

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

Tra

nsp

orta

tion

Ope

rati

ons

Stru

ctur

al R

epai

r Sy

stem

s Di

agno

stic

s,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

Stat

isti

cs a

nd P

roba

bilit

y –

S-ID

– In

terp

retin

g Ca

tego

rical

and

Qua

ntit

ativ

e Da

ta

(con

tinue

d)6.

Rep

rese

nt d

ata

on t

wo

quan

titat

ive

varia

bles

on

a sc

atte

r plo

t, an

d de

scrib

e ho

w t

he v

aria

bles

are

re

late

d.

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 the

dat

a.

Use

giv

en f

unct

ions

or c

hoos

e a

func

tion

sugg

este

d by

the

con

text

. Em

phas

ize

linea

r, qu

adra

tic, a

nd

A1.0

, A2.

0B6

.0C5

.0ex

pone

ntia

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.

Inte

rpre

t lin

ear m

odel

s

7. In

terp

ret

the

slop

e (r

ate

of c

hang

e) a

nd t

he in

terc

ept

(con

stan

t te

rm) o

f a li

near

mod

el in

the

con

text

A1

.0, A

2.0,

B6

.0C5

.0of

the

dat

a.A4

.0, A

5.0

8. C

ompu

te (u

sing

tec

hnol

ogy)

and

inte

rpre

t th

e co

rrel

atio

n co

effic

ient

of a

line

ar fi

t.A1

.0, A

2.0

B6.0

C5.0

9. D

istin

guis

h be

twee

n co

rrel

atio

n an

d ca

usat

ion.

A1.0

, A2.

0B6

.0C5

.0

Stat

isti

cs a

nd P

roba

bilit

y –

S-CP

– C

ondi

tion

al P

roba

bilit

y an

d th

e Ru

les

of P

roba

bilit

y

Unde

rsta

nd in

depe

nden

ce a

nd c

ondi

tiona

l pro

babi

lity

and

use

them

to in

terp

ret d

ata

1. D

escr

ibe

even

ts a

s su

bset

s of

a s

ampl

e sp

ace

(the

set

of o

utco

mes

) usi

ng c

hara

cter

istic

s (o

r cat

ego-

A1.0

, A2.

0B6

.0rie

s) o

f the

out

com

es, o

r as

unio

ns, i

nter

sect

ions

, or c

ompl

emen

ts o

f oth

er e

vent

s (“

or,”

“and

,” “n

ot”)

.

2. U

nder

stan

d th

at t

wo

even

ts A

and

B a

re in

depe

nden

t if

the

prob

abili

ty o

f A a

nd B

occ

urrin

g to

geth

er

B6.0

is t

he p

rodu

ct o

f the

ir pr

obab

ilitie

s, a

nd u

se t

his

char

acte

rizat

ion

to d

eter

min

e if

they

are

inde

pend

ent.

3. U

nder

stan

d th

e co

nditi

onal

pro

babi

lity

of A

giv

en B

as

P(A

and

B)/P

(B),

and

inte

rpre

t in

depe

nden

ce o

f A

and

B as

say

ing

that

the

con

ditio

nal p

roba

bilit

y of

A g

iven

B is

the

sam

e as

the

pro

babi

lity

of A

, and

A1

.0, A

2.0

B6.0

the

cond

ition

al p

roba

bilit

y of

B g

iven

A is

the

sam

e as

the

pro

babi

lity

of B

.

5. R

ecog

nize

and

exp

lain

the

con

cept

s of

con

ditio

nal p

roba

bilit

y an

d in

depe

nden

ce in

eve

ryda

y la

n-gu

age

and

ever

yday

situ

atio

ns. F

or e

xam

ple,

com

pare

the

cha

nce

of h

avin

g lu

ng c

ance

r if y

ou a

re a

A1

.0, A

2.0

B6.0

smok

er w

ith t

he c

hanc

e of

bei

ng a

sm

oker

if y

ou h

ave

lung

can

cer.

26

Transportation | T

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

Tra

nsp

orta

tion

Ope

rati

ons

Stru

ctur

al R

epai

r Sy

stem

s Di

agno

stic

s, an

d Re

finis

hing

Serv

ice,

and

Rep

air

Stat

isti

cs a

nd P

roba

bilit

y –

S-CP

– C

ondi

tion

al P

roba

bilit

y an

d th

e Ru

les

of

Prob

abili

ty (c

ontin

ued)

Use

the

rule

s of p

roba

bilit

y to

com

pute

pro

babi

litie

s of c

ompo

und

even

ts in

a u

nifo

rm p

roba

bilit

y m

odel

6. F

ind

the

cond

ition

al p

roba

bilit

y of

A g

iven

B a

s th

e fr

actio

n of

B’s

outc

omes

tha

t al

so b

elon

g to

A, a

nd

A1.0

, A2.

0B6

.0in

terp

ret

the

answ

er in

ter

ms

of t

he m

odel

.

7. A

pply

the

Add

ition

Rul

e, P

(A o

r B) =

P(A

) + P

(B) -

P(A

and

B),

and

inte

rpre

t th

e an

swer

in t

erm

s of

the

A1

.0, A

2.0

B6.0

mod

el.

Stat

isti

cs a

nd P

roba

bilit

y –

S-M

D –

Usin

g Pr

obab

ility

to

Mak

e De

cisi

ons

Calc

ulat

e ex

pect

ed v

alue

s and

use

them

to so

lve

prob

lem

s

1. (+

) Defi

ne a

ran

dom

var

iabl

e fo

r a q

uant

ity

of in

tere

st b

y as

sign

ing

a nu

mer

ical

val

ue t

o ea

ch e

vent

in

A1.0

, A2.

0,

a sa

mpl

e sp

ace;

gra

ph t

he c

orre

spon

ding

pro

babi

lity

dist

ribut

ion

usin

g th

e sa

me

grap

hica

l dis

play

s as

for

B6

.0C5

.0A4

.0da

ta d

istr

ibut

ions

.

2. (+

) Cal

cula

te t

he e

xpec

ted

valu

e of

a r

ando

m v

aria

ble;

inte

rpre

t it

as t

he m

ean

of t

he p

roba

bilit

y A1

.0, A

2.0,

B6

.0C5

.0di

strib

utio

n.A4

.0

3. (+

) Dev

elop

a p

roba

bilit

y di

strib

utio

n fo

r a r

ando

m v

aria

ble

defin

ed f

or a

sam

ple

spac

e in

whi

ch

theo

retic

al p

roba

bilit

ies

can

be c

alcu

late

d; fi

nd t

he e

xpec

ted

valu

e. F

or e

xam

ple,

find

the

the

oret

ical

A1

.0, A

2.0,

pr

obab

ility

dis

trib

utio

n fo

r the

num

ber o

f cor

rect

ans

wer

s ob

tain

ed b

y gu

essi

ng o

n al

l five

que

stio

ns o

f B6

.0C5

.0A4

.0a

mul

tiple

-cho

ice

test

whe

re e

ach

ques

tion

has

four

cho

ices

, and

find

the

exp

ecte

d gr

ade

unde

r var

ious

gr

adin

g sc

hem

es.

4. (+

) Dev

elop

a p

roba

bilit

y di

strib

utio

n fo

r a r

ando

m v

aria

ble

defin

ed f

or a

sam

ple

spac

e in

whi

ch p

rob-

abili

ties

are

assi

gned

em

piric

ally

; find

the

exp

ecte

d va

lue.

For

exa

mpl

e, fi

nd a

cur

rent

dat

a di

strib

utio

n A1

.0, A

2.0,

B6

.0C5

.0on

the

num

ber o

f TV

sets

per

hou

seho

ld in

the

Uni

ted

Stat

es, a

nd c

alcu

late

the

exp

ecte

d nu

mbe

r of s

ets

A4.0

per h

ouse

hold

. How

man

y TV

set

s w

ould

you

exp

ect

to fi

nd in

100

ran

dom

ly s

elec

ted

hous

ehol

ds?

Use

prob

abili

ty to

eva

luat

e ou

tcom

es o

f dec

ision

s

5. (+

) Wei

gh t

he p

ossi

ble

outc

omes

of a

dec

isio

n by

ass

igni

ng p

roba

bilit

ies

to p

ayof

f val

ues

and

findi

ng

expe

cted

val

ues.

a. F

ind

the

expe

cted

pay

off f

or a

gam

e of

cha

nce.

For

exa

mpl

e, fi

nd t

he e

xpec

ted

win

ning

s fr

om a

A1

.0, A

2.0,

st

ate

lott

ery

ticke

t or

a g

ame

at a

fas

t-fo

od r

esta

uran

t.B6

.0C5

.0A4

.0, A

5.0

b. E

valu

ate

and

com

pare

str

ateg

ies

on t

he b

asis

of e

xpec

ted

valu

es. F

or e

xam

ple,

com

pare

a h

igh

dedu

ctib

le v

ersu

s a

low

-ded

uctib

le a

utom

obile

insu

ranc

e po

licy

usin

g va

rious

, but

rea

sona

ble,

cha

nces

of

hav

ing

a m

inor

or a

maj

or a

ccid

ent.

27

T | California Career Technical Education Model Curriculum Standards

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

TR

AN

SPO

RTA

TIO

NO

pera

tion

sSt

ruct

ural

Rep

air

Syst

ems

Diag

nost

ics,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

Stat

isti

cs a

nd P

roba

bilit

y –

S-M

D –

Usin

g Pr

obab

ility

to

Mak

e De

cisi

ons

(c

ontin

ued)

6. (+

) Use

pro

babi

litie

s to

mak

e fa

ir de

cisi

ons

(e.g

., dr

awin

g by

lots

, usi

ng a

ran

dom

num

ber

A1.0

, A2.

0B6

.0C5

.0ge

nera

tor)

.

7. (+

) Ana

lyze

dec

isio

ns a

nd s

trat

egie

s us

ing

prob

abili

ty c

once

pts

(e.g

., pr

oduc

t te

stin

g, m

edic

al

A1.0

, A2.

0, A

4.0

B6.0

C5.0

test

ing,

pul

ling

a ho

ckey

goa

lie a

t th

e en

d of

a g

ame)

.

SCIE

NCE

Scie

ntifi

c an

d En

gine

erin

g Pr

acti

ces

– SE

P

1. A

skin

g qu

estio

ns (f

or s

cien

ce) a

nd d

efini

ng p

robl

ems

(for

eng

inee

ring)

2. D

evel

opin

g an

d us

ing

mod

els

3. P

lann

ing

and

carr

ying

out

inve

stig

atio

nsA1

.0, A

2.0,

A3.

0,

B1.0

, B2.

0, B

3.0,

4.

Ana

lyzi

ng a

nd in

terp

retin

g da

taC1

.0, C

2.0,

C3.

0,

A4.0

, A5.

0, A

6.0,

B4

.0, B

5.0,

B6.

0,

5. U

sing

mat

hem

atic

s an

d co

mpu

tatio

nal t

hink

ing

C4.0

, C5.

0, C

7.0

A7.0

B7.0

, B8.

0, B

9.0

6. C

onst

ruct

ing

expl

anat

ions

(for

sci

ence

) and

des

igni

ng s

olut

ions

(for

eng

inee

ring)

7. E

ngag

ing

in a

rgum

ent

from

evi

denc

e

8. O

btai

ning

, eva

luat

ing,

and

com

mun

icat

ing

info

rmat

ion

Cros

scut

ting

Con

cept

– C

C

1. P

atte

rns

2. C

ause

and

eff

ect:

Mec

hani

sm a

nd e

xpla

natio

n

3. S

cale

, pro

port

ion,

and

qua

ntit

yA1

.0, A

2.0,

A3.

0,

B1.0

, B2.

0, B

4.0,

C1

.0, C

2.0,

C3.

0,

4. S

yste

ms

and

syst

em m

odel

sA4

.0, A

5.0,

A6.

0,

B5.0

, B6.

0, B

7.0,

C4

.0, C

5.0

A7.0

B8.0

, B9.

0S.

Ene

rgy

and

mat

ter:

Flow

s, c

ycle

s, a

nd c

onse

rvat

ion

6. S

truc

ture

and

fun

ctio

n

7. S

tabi

lity

and

chan

ge

28

Transportation | T

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

TR

AN

SPO

RTA

TIO

NO

pera

tion

sSt

ruct

ural

Rep

air

Syst

ems

Diag

nost

ics,

an

d Re

finis

hing

Serv

ice,

and

Rep

air

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

rB1

.0, B

4.0,

B7.

0,

C1.0

, C2.

0, C

3.0,

A5

.0, A

6.0,

A7.

0PS

1.B:

Che

mic

al R

eact

ions

B8.0

C4.0

, C5.

0

PS1.

C: N

ucle

ar P

roce

sses

PS2:

Mot

ion

and

Stab

ility

: For

ces

and

Inte

ract

ions

PS2.

A: F

orce

s an

d M

otio

nB1

.0, B

4.0,

B7.

0,

A2.

0, A

3.0,

A6.

0C1

.0, C

2.0,

C3.

0, C

4.0

PS2.

B: T

ypes

of I

nter

actio

nsB8

.0

PS2.

C: S

tabi

lity

and

Inst

abili

ty in

Phy

sica

l Sys

tem

s

PS3:

Ene

rgy

PS3.

A: D

efini

tions

of E

nerg

yA

2.0,

A3.

0, A

5.0,

C2

.0, C

3.0,

C4.

0,

PS3.

B: C

onse

rvat

ion

of E

nerg

y an

d En

ergy

Tra

nsfe

rB1

.0, B

4.0,

B8.

0A6

.0, A

7.0

C5.0

, C7.

0PS

3.C:

Rel

atio

nshi

p Be

twee

n En

ergy

and

For

ces

PS3.

D: E

nerg

y in

Che

mic

al P

roce

sses

and

Eve

ryda

y Li

fe

PS4:

Wav

es a

nd T

heir

Appl

icat

ions

in T

echn

olog

ies

for I

nfor

mat

ion

Tran

sfer

PS4.

A: W

ave

Prop

ertie

sB4

.0, B

8.0

C2.0

, C3.

0, C

4.0,

C7.

0PS

4.B:

Ele

ctro

mag

netic

Rad

iatio

n

PS4.

C: In

form

atio

n Te

chno

logi

es a

nd In

stru

men

tatio

n

Life

Sci

ence

s –

LS

LSI:

From

Mol

ecul

es t

o O

rgan

ism

s: S

truc

ture

s an

d Pr

oces

ses

LS1.

A: S

truc

ture

and

Fun

ctio

n

LS1.

B: G

row

th a

nd D

evel

opm

ent

of O

rgan

ism

sA5

.0, A

6.0

B4.0

C3.0

, C4.

0

LS1.

C: O

rgan

izat

ion

for M

atte

r and

Ene

rgy

Flow

in O

rgan

ism

s

LS1.

D: I

nfor

mat

ion

Proc

essi

ng

29

T | California Career Technical Education Model Curriculum Standards

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

TR

AN

SPO

RTA

TIO

NO

pera

tion

sSt

ruct

ural

Rep

air

Syst

ems

Diag

nost

ics,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

Life

Sci

ence

s –

LS (c

ontin

ued)

LS2:

Eco

syst

ems:

Inte

ract

ions

, Ene

rgy,

and

Dyn

amic

s

LS2.

A: In

terd

epen

dent

Rel

atio

nshi

ps in

Eco

syst

ems

LS2.

B: C

ycle

s of

Mat

ter a

nd E

nerg

y Tr

ansf

er in

Eco

syst

ems

B1.0

C1.0

LS2.

C: E

cosy

stem

s D

ynam

ics,

Fun

ctio

ning

, and

Res

ilien

ce

LS2.

D: S

ocia

l Int

erac

tions

and

Gro

up B

ehav

ior

LS3:

Her

edit

y: In

herit

ance

and

Var

iatio

n of

Tra

its

LS3.

A: In

herit

ance

of T

rait

sA6

.0B1

.0

LS3.

B: V

aria

tion

of T

rait

s

LS4:

Bio

logi

cal E

volu

tion:

Uni

ty a

nd D

iver

sity

LS4.

A: E

vide

nce

of C

omm

on A

nces

try

and

Dive

rsit

y

LS4.

B: N

atur

al S

elec

tion

A4.0

B1.0

LS4.

C: A

dapt

atio

n

LS4.

D: B

iodi

vers

ity

and

Hum

ans

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

ESS2

.B: P

late

Tec

toni

cs a

nd L

arge

-Sca

le S

yste

m In

tera

ctio

nsB1

.0C1

.0ES

S2.C

: The

Rol

es o

f Wat

er in

Ear

th’s

Surf

ace

Proc

esse

s

ESS2

.D: W

eath

er a

nd C

limat

e

ESS2

.E: B

ioge

olog

y

ESS3

: Ear

th a

nd H

uman

Act

ivit

y

ESS3

.A: N

atur

al R

esou

rces

B1.0

, B4.

0, B

8.0,

ES

S3.B

: Nat

ural

Haz

ards

A5.0

C1.0

, C2.

0, C

4.0,

C5.

0B9

.0ES

S3.C

: Hum

an Im

pact

s on

Ear

th S

yste

ms

ESS3

.D: G

loba

l Clim

ate

Chan

ge

30

Transportation | T

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

TR

AN

SPO

RTA

TIO

NO

pera

tion

sSt

ruct

ural

Rep

air

Syst

ems

Diag

nost

ics,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

Engi

neer

ing,

Tec

hnol

ogy,

and

the

App

licat

ions

of

Scie

nce

– ET

S

ETS1

: Eng

inee

ring

Desi

gnB1

.0, B

2.0,

B3.

0,

ETS1

.A: D

efini

ng a

nd D

elim

iting

an

Engi

neer

ing

Prob

lem

A1.0

, A2.

0, A

4.0,

C1

.0, C

2.0,

C3.

0,

B4.0

, B7.

0, B

8.0,

ET

S1.B

: Dev

elop

ing

Poss

ible

Sol

utio

nsA5

.0, A

6.0,

A7.

0C4

.0, C

5.0

B9.0

ETS1

.E: O

ptim

izin

g th

e De

sign

Sol

utio

n

ETS2

: Lin

ks A

mon

g En

gine

erin

g, T

echn

olog

y, S

cien

ce, a

nd S

ocie

tyB1

.0, B

2.0,

B3.

0,

A1.0

, A2.

0, A

4.0,

C1

.0, C

2.0,

C3.

0,

ETS2

.A: I

nter

depe

nden

ce o

f Sci

ence

, Eng

inee

ring,

and

Tec

hnol

ogy

B4.0

, B5.

0, B

7.0,

A5

.0, A

6.0,

A7.

0C4

.0, C

5.0,

C7.

0B8

.0, B

9.0

ETS2

.B: I

nflue

nce

of E

ngin

eerin

g, T

echn

olog

y, a

nd S

cien

ce o

n So

ciet

y an

d th

e N

atur

al W

orld

HIS

TORY

/SO

CIAL

SCI

ENCE

Prin

cipl

es o

f A

mer

ican

Dem

ocra

cy a

nd E

cono

mic

s –

AD

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

lo

cal g

over

nmen

ts.

12.7

.2. I

dent

ify

the

maj

or r

espo

nsib

ilitie

s an

d so

urce

s of

rev

enue

for

sta

te a

nd lo

cal g

over

n-B1

.0, B

2.0

C1.0

, C2.

0m

ents

.

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

A6.0

, A7.

0B1

.0, B

2.0,

B9.

0C1

.0, C

2.0

impl

emen

tatio

n of

it t

hrou

gh r

egul

atio

ns a

nd e

xecu

tive

orde

rs.

12.7

.7. I

dent

ify

the

orga

niza

tion

and

juris

dict

ion

of f

eder

al, s

tate

, and

loca

l (e.

g., C

alifo

rnia

) A6

.0, A

7.0

B1.0

, B9.

0co

urts

and

the

inte

rrel

atio

nshi

ps a

mon

g th

em.

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.

12.1

.1. E

xam

ine

the

caus

al r

elat

ions

hip

betw

een

scar

city

and

the

nee

d fo

r cho

ices

.C1

.0, C

2.0,

C5.

0, C

7.0,

A4

.0B6

.0C8

.0

12.1

.2. E

xpla

in o

ppor

tuni

ty c

ost

and

mar

gina

l ben

efit

and

mar

gina

l cos

t.C1

.0, C

2.0,

C5.

0, C

7.0,

A4

.0B1

.0, B

2.0,

B6.

0C8

.0

12.1

.3. I

dent

ify

the

diff

eren

ce b

etw

een

mon

etar

y an

d no

n-m

onet

ary

ince

ntiv

es a

nd h

ow

B1.0

, B2.

0, B

6.0

C5.0

, C7.

0, C

8.0

chan

ges

in in

cent

ives

cau

se c

hang

es in

beh

avio

r.

31

T | California Career Technical Education Model Curriculum Standards

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

TR

AN

SPO

RTA

TIO

NO

pera

tion

sSt

ruct

ural

Rep

air

Syst

ems

Diag

nost

ics,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

Prin

cipl

es o

f Ec

onom

ics

– PE

(con

tinue

d)

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

B1

.0, B

2.0,

B6.

0C5

.0, C

7.0,

C8.

0re

sour

ces,

incl

udin

g re

new

able

and

non

rene

wab

le n

atur

al r

esou

rces

.

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.

12.2

.5. U

nder

stan

d th

e pr

oces

s by

whi

ch c

ompe

titio

n am

ong

buye

rs a

nd s

elle

rs d

eter

min

es a

mar

ket

B6.0

C5.0

, C7.

0, C

8.0

pric

e.

12.2

.6. D

escr

ibe

the

effe

ct o

f pric

e co

ntro

ls o

n bu

yers

and

sel

lers

.B6

.0C5

.0, C

7.0,

C8.

0

12.2

.9. D

escr

ibe

the

func

tions

of t

he fi

nanc

ial m

arke

ts.

A6.0

B6.0

C5.0

, C7.

0, C

8.0

12.2

.10.

Dis

cuss

the

eco

nom

ic p

rinci

ples

tha

t gu

ide

the

loca

tion

of a

gric

ultu

ral p

rodu

ctio

n an

d in

dus-

A1.0

, A6.

0B6

.0C5

.0, C

7.0,

C8.

0tr

y an

d th

e sp

atia

l dis

trib

utio

n of

tra

nspo

rtat

ion

and

reta

il fa

cilit

ies.

12.3

Stu

dent

s an

alyz

e th

e in

fluen

ce o

f the

fed

eral

gov

ernm

ent

on t

he A

mer

ican

eco

nom

y.B6

.0

12.3

.1. U

nder

stan

d ho

w t

he r

ole

of g

over

nmen

t in

a m

arke

t ec

onom

y of

ten

incl

udes

pro

vidi

ng

C1.0

, C2.

0, C

5.0,

C7.

0,

for n

atio

nal d

efen

se, a

ddre

ssin

g en

viro

nmen

tal c

once

rns,

defi

ning

and

enf

orci

ng p

rope

rty

right

s,

A4.0

B1.0

, B2.

0, B

6.0

C8.0

atte

mpt

ing

to m

ake

mar

kets

mor

e co

mpe

titiv

e, a

nd p

rote

ctin

g co

nsum

ers’

right

s.

12.3

.2. I

dent

ify

the

fact

ors

that

may

cau

se t

he c

osts

of g

over

nmen

t ac

tions

to

outw

eigh

the

ben

efits

.C1

.0, C

2.0,

C5.

0, C

7.0,

A7

.0B1

.0, B

2.0

B6.0

C8.0

12.3

.3. D

escr

ibe

the

aim

s of

gov

ernm

ent

fisca

l pol

icie

s (t

axat

ion,

bor

row

ing,

spe

ndin

g) a

nd t

heir

influ

-B6

.0C5

.0, C

7.0,

C8.

0en

ce o

n pr

oduc

tion,

em

ploy

men

t, an

d pr

ice

leve

ls.

12.3

.4. U

nder

stan

d th

e ai

ms

and

tool

s of

mon

etar

y po

licy

and

thei

r infl

uenc

e on

eco

nom

ic a

ctiv

ity

B6.0

C5.0

, C7.

0, C

8.0

(e.g

., th

e Fe

dera

l Res

erve

).

12.4

Stu

dent

s an

alyz

e th

e el

emen

ts o

f the

U.S

. lab

or m

arke

t in

a g

loba

l set

ting.

12.4

.2. D

escr

ibe

the

curr

ent

econ

omy

and

labo

r mar

ket,

incl

udin

g th

e ty

pes

of g

oods

and

ser

vice

s pr

oduc

ed, t

he t

ypes

of s

kills

wor

kers

nee

d, t

he e

ffec

ts o

f rap

id t

echn

olog

ical

cha

nge,

and

the

impa

ct

A4.0

of in

tern

atio

nal c

ompe

titio

n.

12.4

.4. E

xpla

in t

he e

ffec

ts o

f int

erna

tiona

l mob

ility

of c

apita

l and

labo

r on

the

U.S

. eco

nom

y.B6

.0C5

.0, C

7.0,

C8.

0

12.5

Stu

dent

s an

alyz

e th

e ag

greg

ate

econ

omic

beh

avio

r of t

he U

.S. e

cono

my.

B6.0

C5.0

, C7.

0, C

8.0

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, a

nd is

af

fect

ed b

y, e

cono

mic

for

ces

beyo

nd t

he U

nite

d St

ates

’ bor

ders

.

32

Transportation | T

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

TR

AN

SPO

RTA

TIO

NO

pera

tion

sSt

ruct

ural

Rep

air

Syst

ems

Diag

nost

ics,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

Prin

cipl

es o

f Ec

onom

ics

– PE

(con

tinue

d)

12.6

.1. I

dent

ify

the

gain

s in

con

sum

ptio

n an

d pr

oduc

tion

effic

ienc

y fr

om t

rade

, with

em

phas

is o

n th

e A

2.0,

A3.

0,

mai

n pr

oduc

ts a

nd c

hang

ing

geog

raph

ic p

atte

rns

of t

wen

tieth

-cen

tury

tra

de a

mon

g co

untr

ies

in t

he

B6.0

C5.0

, C7.

0, C

8.0

A4.0

A7.

0W

este

rn H

emis

pher

e.

12.6

.2. C

ompa

re t

he r

easo

ns f

or a

nd t

he e

ffec

ts o

f tra

de r

estr

ictio

ns d

urin

g th

e G

reat

Dep

ress

ion

com

pare

d w

ith p

rese

nt-d

ay a

rgum

ents

am

ong

labo

r, bu

sine

ss, a

nd p

oliti

cal l

eade

rs o

ver t

he e

ffec

ts o

f A4

.0fr

ee t

rade

on

the

econ

omic

and

soc

ial i

nter

ests

of v

ario

us g

roup

s of

Am

eric

ans.

12.6

.3. U

nder

stan

d th

e ch

angi

ng r

ole

of in

tern

atio

nal p

oliti

cal b

orde

rs a

nd t

errit

oria

l sov

erei

gnty

in a

A4

.0gl

obal

eco

nom

y.

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-u

rban

m

igra

tion,

and

mas

sive

imm

igra

tion

from

Sou

ther

n an

d Ea

ster

n Eu

rope

.

11.2

.1. K

now

the

eff

ects

of i

ndus

tria

lizat

ion

on li

ving

and

wor

king

con

ditio

ns, i

nclu

ding

the

por

tray

al

A6.0

B1.0

, B2.

0of

wor

king

con

ditio

ns a

nd f

ood

safe

ty in

Upt

on S

incl

air’s

The

Jun

gle.

11.2

.2. D

escr

ibe

the

chan

ging

land

scap

e, in

clud

ing

the

grow

th o

f citi

es li

nked

by

indu

stry

and

tra

de,

A3.0

, A4.

0an

d th

e de

velo

pmen

t of

citi

es d

ivid

ed a

ccor

ding

to

race

, eth

nici

ty, a

nd c

lass

.

11.2

.9. U

nder

stan

d th

e ef

fect

of p

oliti

cal p

rogr

ams

and

activ

ities

of t

he P

rogr

essi

ves

(e.g

., fe

dera

l A1

.0, A

6.0,

re

gula

tion

of r

ailro

ad t

rans

port

, Chi

ldre

n’s

Bure

au, t

he S

ixte

enth

Am

endm

ent,

Theo

dore

Roo

seve

lt,

A7.0

Hira

m J

ohns

on).

11.4

Stu

dent

s tr

ace

the

rise

of t

he U

nite

d St

ates

to

its

role

as

a w

orld

pow

er in

the

tw

entie

th c

entu

ry.

11.4

.4. E

xpla

in T

heod

ore

Roos

evel

t’s B

ig S

tick

dipl

omac

y, W

illia

m T

aft’s

Dol

lar D

iplo

mac

y, a

nd W

ood-

C1.0

row

Wils

on’s

Mor

al D

iplo

mac

y, d

raw

ing

on r

elev

ant

spee

ches

.

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

men

ts o

f th

e 19

20s.

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 t

ech-

A1.0

, A3.

0,

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 Am

eric

an

A5.0

, A6.

0,

C2.0

, C3.

0, C

7.0,

C8.

0la

ndsc

ape.

A7.0

33

T | California Career Technical Education Model Curriculum Standards

Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

TR

AN

SPO

RTA

TIO

NO

pera

tion

sSt

ruct

ural

Rep

air

Syst

ems

Diag

nost

ics,

and

Refin

ishi

ngSe

rvic

e, a

nd R

epai

r

U.S.

His

tory

and

Geo

grap

hy –

US

(con

tinue

d)

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 f

unda

-m

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

Prog

ress

Adm

inis

trat

ion,

Soc

ial S

ecur

ity,

Nat

iona

l Lab

or R

elat

ions

Boa

rd, f

arm

pro

gram

s, r

egio

nal

A7.0

deve

lopm

ent

polic

ies,

and

ene

rgy

deve

lopm

ent

proj

ects

suc

h as

the

Ten

ness

ee V

alle

y Au

thor

ity,

Cal

i-fo

rnia

Cen

tral

Val

ley

Proj

ect,

and

Bonn

evill

e Da

m).

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 A

mer

ican

so

ciet

y.

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

serv

atio

n,

expa

nsio

n of

the

nat

iona

l par

k sy

stem

, and

the

dev

elop

men

t of

env

ironm

enta

l pro

tect

ion

law

s, w

ith

A5.0

, A6.

0B1

.0pa

rtic

ular

att

entio

n to

the

inte

ract

ion

betw

een

envi

ronm

enta

l pro

tect

ion

advo

cate

s an

d pr

oper

ty

right

s ad

voca

tes.

11.11

.7. E

xpla

in h

ow t

he f

eder

al, s

tate

, and

loca

l gov

ernm

ents

hav

e re

spon

ded

to d

emog

raph

ic a

nd

soci

al c

hang

es s

uch

as p

opul

atio

n sh

ifts

to

the

subu

rbs,

rac

ial c

once

ntra

tions

in t

he c

ities

, Fro

stbe

lt-A4

.0, A

5.0,

to

-Sun

belt

mig

ratio

n, in

tern

atio

nal m

igra

tion,

dec

line

of f

amily

far

ms,

incr

ease

s in

out

-of-

wed

lock

A6

.0bi

rths

, and

dru

g ab

use.

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, a

nd

the

Uni

ted

Stat

es.

10.3

.2. E

xam

ine

how

sci

entifi

c an

d te

chno

logi

cal c

hang

es a

nd n

ew f

orm

s of

ene

rgy

brou

ght

abou

t m

assi

ve s

ocia

l, ec

onom

ic, a

nd c

ultu

ral c

hang

e (e

.g.,

the

inve

ntio

ns a

nd d

isco

verie

s of

Jam

es W

att,

Eli

A4.0

B4.0

, B5.

0W

hitn

ey, H

enry

Bes

sem

er, L

ouis

Pas

teur

, Tho

mas

Edi

son)

.

10.3

.3. D

escr

ibe

the

grow

th o

f pop

ulat

ion,

rur

al t

o ur

ban

mig

ratio

n, a

nd g

row

th o

f citi

es a

ssoc

iate

d A

2.0,

A3.

0,

with

the

Indu

stria

l Rev

olut

ion.

A4.0

10.3

.4. T

race

the

evo

lutio

n of

wor

k an

d la

bor,

incl

udin

g th

e de

mis

e of

the

sla

ve t

rade

and

the

eff

ects

A1

.0, A

3.0,

B1

.0, B

3.0,

B4.

0of

imm

igra

tion,

min

ing

and

man

ufac

turin

g, d

ivis

ion

of la

bor,

and

the

unio

n m

ovem

ent.

A4.0

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, t

ech-

A1.0

, A4.

0no

logi

cal,

and

com

mun

icat

ions

rev

olut

ions

(e.g

., te

levi

sion

, sat

ellit

es, c

ompu

ters

).

34

Contributors

Transportation

Lloyd McCabe, Administrator, California Department of Education

Dara Dubois, Education Consultant, California Department of Education

Standards Review TeamArmando Hernandez, Instructor, Montebello Unified School District

Mickey Neilson, Instructor, Ramona Unified School District

Michael Palmer, Owner, Midas of Sacramento

Willard Ripley, Instructor, Alex Xydias Center for Automotive Arts

Glenn Singley, Instructor, Sacramento City Unified School District

John Tarrant, Owner, Chaffey Auto Body

Standards Writing TeamArmando Hernandez, Instructor, Montebello Unified School District

Jennifer Lucero, Owner, EZ Parcel Express

John Overton, President, California Teachers Association

Willard Ripley, Instructor, Alex Xydias Center for Automotive Arts

Steve Tomory, Rio Hondo Community College

Common Core Alignment TeamAutumn Chapman, Instructor, Oakland Unified School District

Pamela Davis, Instructor, Sacramento City Unified School District

Marty Gunn, Instructor, California Air Resources Board

Kristi Leonard, Instructor, Lake Tahoe Unified School District

Marcia McAllister, Instructor, Sacramento City Unified School District

Sofia Paez-Valdez, Instructor, Pasadena Unified School District

Sherry Penaflor, Instructor, Coachella Valley Unified School District

Zach Ronnenberg, Instructor, Davis Joint Unified School District

Russell Wong, Instructor, Pasadena Unified School District

Transportation | T 35

T | California Career Technical Education Model Curriculum Standards

References

ACT. 2010. A First Look at the Common Core and College and Career Readiness. http://www.act.org/research/policymakers/pdf/FirstLook.pdf (accessed December 4, 2012).

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37Published January 2017