operations systems diagnostics, service, and repair ... · transportation | t. 5. utilize critical...
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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