CTE Model Curr Stds: Business and Finance - Standards and

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Business Management Pathway

International Business Pathway

Financial Services Pathway

California Career Technical Education Model Curriculum Standards

Table of ContentsBusiness and Finance

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A. Business Management Pathway ......................................................................................................7

B. Financial Services Pathway .............................................................................................................10

C. International Business Pathway.....................................................................................................14

Academic Alignment Matrix ..........................................................................................................17

Contributors .....................................................................................................................................34

References ........................................................................................................................................35

BF | California Career Technical Education Model Curriculum Standardsii

Overview

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

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

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

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

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

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

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

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BF | California Career Technical Education Model Curriculum Standards

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

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

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

• unique to an industry sector

• has an occupational focus

• consistent in size and scope

• composed of similar functions

• inclusive of all aspects of the industry

• includes 8–12 pathway-specific standards

• demonstrates sequence potential

• reasonable and appropriate for high school

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

• sustainable and viable over the next 10 years

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

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

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Business and Finance | BF

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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http://www.careertech.org/


Business and Finance

Sector DescriptionPersons trained in fields such as business management, international trade, and

various financial services specialties (e.g., accounting, banking, and investing)

will find that their skills are highly marketable. Students master basic business

principles and procedures before proceeding to the career path specializations.

The specializations emphasize concepts of accounting and finance, including

computer applications, taxes, investments, and asset management as well as

pathways in international business and business management. Because almost

every business and organization has a financial and management component,

students will find that opportunities exist in many career paths in addition to

those in business and finance.

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Business and FinanceKnowledge 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 Business and Finance academic alignment matrix for identification of standards.

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

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

2.2 Identify barriers to accurate and appropriate communication.

2.3 Interpret verbal and nonverbal communications and respond appropriately.

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

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

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

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

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

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

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

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

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

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

3.7 Recognize the importance and impact small businesses have on our state, nation and world 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 Business and Finance 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 Business and Finance 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 Business and Finance 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.

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

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

6.6 Maintain a safe and healthful working environment.

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

7.0 Responsibility and FlexibilityInitiate, and participate in, a range of collaborations demonstrating behaviors that reflect personal and professional responsibility, flexibility, and respect in the Business and Finance 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 Business and Finance 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 Business and Finance industry sector.

8.3 Demonstrate ethical and legal practices consistent with Business and Finance sector workplace standards.

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

8.5 Analyze organizational culture and practices within the workplace environment.

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

8.7 Conform to rules and regulations regarding sharing of confidential information, as determined by Business and Finance 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 prac-ticed in the Future Business Leaders of America (FBLA) 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 Business and Finance sector issues and problems.

10.0 Technical Knowledge and Skills Apply essential technical knowledge and skills common to all pathways in the Business and Finance 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 Business and Finance sector.

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

10.3 Construct projects and products specific to the Business and Finance sector requirements and expectations.

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

10.5 Interpret financial data, analyze results, and make sensible business decisions to promote a financially reliable business.

10.6 Evaluate the variety, nature, and diversity of investment vehicles and the elements that contribute to financial growth and success.

10.7 Adapt the distribution concepts and processes needed to move, store, locate, and transfer ownership of goods or services.

10.8 Integrate the techniques and strategies used to foster positive, ongoing relationships with customers, suppliers, investors, and community.

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10.9 Evaluate the impact of local, state, federal, and/or international regulations on business and financial management decisions.

10.10 Apply the economic principles and concepts fundamental to business operations.

10.11 Recognize the importance of marketing in a global economy.

10.11 Develop a system for keeping and using financial records and a personal financial plan to manage cash flow and maintain creditworthiness.

11.0 Demonstration and ApplicationDemonstrate and apply the knowledge and skills contained in the Business and Finance anchor standards, pathway standards, and performance indicators in classroom, laboratory, and workplace settings, and through the Future Business Leaders of America (FBLA) 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 Business and Finance sector program of study.

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

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

11.4 Employ entrepreneurial practices and behaviors appropriate to Business and Finance 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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Business and FinancePathway Standards

A. Business Management PathwayManagement consists of planning, leading, and controlling an organization or effort to accomplish a goal. In the Business Management pathway, students learn entrepreneurship and business funda-mentals, goal-setting, resource allocation, organizational structure and management techniques, economics, financial data, risk management, information technology, and supply chain management.

Sample occupations associated with this pathway:

Human Resources Specialist

Education Administrator

Purchasing Agent

Office Manager

Chief Financial Officer

A1.0 Explain entrepreneurship and the fundamentals of developing a new business.

A1.1 Recognize personal traits and leadership styles of entrepreneurs and business leaders.

A1.2 Analyze management theories and their application within the business environment.

A1.3 Develop personal management skills to function effectively, efficiently, and collabora-tively in a business environment.

A1.4 Determine the type of business organization most appropriate for various business profiles.

A1.5 Construct and defend a business plan (components may include an executive summary, organizational structure, market analysis, Strengths Weaknesses Opportunities and Threats (SWOT) analysis, marketing plan, operating procedures, financial data, and feasibility and supporting documentation).

A2.0 Plan, organize, secure, and manage resources of a project to achieve specific goals.

A2.1 Determine Specific, Measurable, Achievable, Realistic and Time-bound (SMART) goals for a specific project.

A2.2 Develop a project schedule, including the constraints of cost, time, and scope, to illustrate project structure using Gantt, Program Evaluation Review Technique (PERT), or other project planning tools.

A2.3 Optimize allocation of resources necessary to achieve predefined objectives.

A2.4 Evaluate beneficial change, or added value, of a specific project.

A3.0 Investigate the functions and techniques of management and organizational structure and distinguish between small and large companies.

A3.1 Explain the organizational structure of various business environments.

A3.2 Describe management’s role in demonstrating leadership, motivating employees, resolving conflict, addressing stress, and recognizing formal and informal employee groups.

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A3.3 Recognize a business’ responsibility to employees, shareholders, society, and the environment.

A3.4 Summarize techniques for managing human resources to maximize operational efficiencies and effectiveness.

A3.5 Describe the role of organized labor and its influence on government and businesses.

A3.6 Apply operations management principles and procedures to the design of an operations plan.

A4.0 Apply economic concepts as they relate to business.

A4.1 Identify factors of production needed to create wealth.

A4.2 Explain the role of business in a free-enterprise system.

A4.3 Recognize the determinants of supply and demand and their impact on pricing.

A4.4 Calculate productivity with various levels of input.

A4.5 Illustrate the business cycle elaborating on leading, coinciding, and lagging economic indicators.

A4.6 Show the relationship between economic conditions and financial markets, including exchange rates.

A5.0 Analyze financial data in order to make short-term and long-term decisions.

A5.1 Describe factors that affect the value of an asset, inflation, interest rates, risk, and return.

A5.2 Determine investment and finance options available at different stages of a business or product life cycle.

A5.3 Compare and interpret financial reports for internal and external use to analyze risk and return to make business decisions.

A5.4 Analyze how credit reports quantify credit worthiness.

A5.5 Assess how types of financial markets influence interest rates, inflation, balance of trade, and unemployment and the impact on business decisions.

A5.6 Create and use budgets to guide financial decision making.

A6.0 Explain the importance of risk management and regulatory compliance in business.

A6.1 Identify, assess, and prioritize risks.

A6.2 Describe the concept and process of risk management, including the use of risk management tools such as insurance.

A6.3 Compare and contrast the various types of taxes in terms of the business structure.

A7.0 Utilize information and technology tools to conduct business effectively and efficiently.

A7.1 Describe appropriate computer hardware used in business.

A7.2 Apply appropriate software used in business.

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A7.3 Examine technological trends and analyze the impact of technological innovations on the marketing and distribution of goods and services.

A7.4 Integrate appropriate use of the Internet in business.

A7.5 Investigate data security systems for business.

A8.0 Construct a Marketing Plan.

A8.1 Describe effective marketing techniques.

A8.2 Explore how products and services are conceived, developed, maintained, and improved in response to market opportunities.

A8.3 Conduct market analysis and assess the business organization’s position within their industry.

A8.4 Interpret how market research is used to develop strategies for marketing.

A8.5 Differentiate the components of a promotional plan (e.g., advertising, public relations, and sales promotion) and describe how the plan is used to achieve a stated outcome.

A8.6 Practice selling techniques used to aid customers and clients in making buying decisions.

A9.0 Apply principles of supply chain management and SCM 2.0 to a business model.

A9.1 Describe Logistics Management systems.

A9.2 Illustrate the management of the complete flow of materials and activities in the supply chain from suppliers to customers.

A9.3 Summarize materials management, including effective inventory management practices, E= Procurement, and continuous control practices.

A9.4 Create a master plan for resources that addresses market demand, sales, and operations planning.

A9.5 Change variables in a master plan for resources, analyze its effect, and recommend corrective actions.

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B. Financial Services PathwayFinancial services are an essential aspect of every business institution and organization. Students in this pathway investigate the field of financial management, including how it is impacted by industry standards as well as economic, financial, technological, international, social, legal, and ethical factors. Students formulate and interpret financial information for use in financial management decision making, such as compliance and risk management. This pathway may include programs of study for accounting, banking, securities and investments, and other financial specializations.


Accounts Payable Clerk

Investment Consultant

Tax Preparer

Auditor

Accountant

B1.0 Create and use budgets to guide financial decision making.

B1.1 Identify various forms of income and analyze factors that affect income as part of the career decision making process.

B1.2 Evaluate the opportunity costs of savings and investment options to meet short and long term goals.

B1.3 Apply a decision making model to maximize consumer satisfaction when buying consumer goods and service.

B1.4 Analyze factors that affect the choice, cost, and legal aspects of using credit.

B1.5 Develop and defend a spending/savings plan.

B1.6 Develop tax planning strategies for financial planning.

B1.7 Devise a plan to protect against identity theft.

B2.0 Explain how the application of Generally Accepted Accounting Principles (GAAP) impacts the recording of transactions and the preparation of financial statements.

B2.1 Describe the two methods of accounting (cash and accrual) and the different account-ing concepts (financial, tax, cost, nonprofit and auditing) used to report a business’ financial position as it pertains to sole proprietorships, corporations, and partnerships.

B2.2 Complete the steps in the accounting cycle in order to prepare financial statements and communicate how accounting procedures affect financial statements.

B2.3 Use planning and control principles to evaluate the performance of an organization.

B2.4 Discuss state and federal regulation of the accounting industry.

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B2.5 Discuss International Financial Reporting Standards (IFRS) and the convergence between IFRS and GAAP.

B2.6 Develop a working knowledge of individual income tax procedures and compliance with tax laws and regulations.

B3.0 Interpret financial formulas commonly found in financial institutions to aid in the growth and stability of financial services.

B3.1 Identify key ratios and banking calculations such as interest and annual percentage rate.

B3.2 Identify strategies and systems in real-world situations to maintain, monitor, control, and plan the use of financial resources.

B3.3 Use equations, graphical representations, and other accounting tools to classify, record, and summarize financial data.

B3.4 Identify strategies financial institutions utilize to make decisions about profitability, such as savings and lending ratios.

B4.0 Interpret financial data, analyze results, and make sound business decisions to promote a financially healthy business.

B4.1 Apply differential analysis and present value concepts to make decisions.

B4.2 Interpret financial ratios and other metrics, such as cash flow and breakeven analysis, concentration risk, return on investment, leveraged debt, market share, and opportu-nity costs.

B4.3 Analyze an annual report and financial statement to predict profitability.

B4.4 Develop a working knowledge of individual income tax procedures and requirements to comply with tax laws and regulations.

B5.0 Evaluate the impact of federal, state, and local regulations on financial management decisions.

B5.1 Explain the role of the Federal Reserve System, Internal Revenue Service (IRS), and Consumer Protection Laws.

B5.2 Describe provisions of bankruptcy law.

B5.3 Compare state and federal regulatory compliance of financial institutions and related services.

B5.4 Calculate the impact of various taxes on financial decisions.

B6.0 Apply economic concepts as they relate to financial services.

B6.1 Define capital and explain how it is used to create wealth.

B6.2 Identify causes of stock price fluctuations and the relationship between bond prices and yields.

B6.3 Illustrate the business cycle elaborating on leading, coinciding, and lagging economic indicators.

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B6.4 Assess the ways in which financial markets influence interest rates, inflation, balance of trade, and unemployment and the impact on business decisions.

B6.5 Explain the role of investment banking in the primary marketplace.

B7.0 Explain the concepts, role, and importance of international finance and risk management.

B7.1 Compare the variety of ways in which funds are transferred in foreign trade.

B7.2 Analyze factors that affect currency and exchange rates.

B7.3 Formulate an insurance and risk management plan.

B7.4 Explain the importance of actuarial science in the insurance industry.

B7.5 Compare and contrast risk management methods of avoidance, reduction, assumption, and shifting.

B7.6 Analyze choices available to consumers for protection against risk and financial loss.

B7.7 Identify main operations and evaluate services provided by financial institutions.

B8.0 Evaluate the variety, nature, and diversity of investment vehicles and the elements that contribute to financial growth and success.

B8.1 Explain the time value of money.

B8.2 Describe the functions, responsibilities, and ethical considerations of a financial institution.

B8.3 Recognize the categories and characteristics of major investment vehicles, such as stocks, bonds, real estate, mutual funds, venture capital, retirement investment plans, and education savings plans.

B8.4 Describe reasons why investors buy and sell and the methods they use.

B8.5 Describe factors that affect the value of an asset, including industry trends, price to earnings ratio, cash flow, growth rate, timing, inflation, interest rate, opportunity cost, risk, and required return.

B8.6 Consult federal resources and independent rating companies for reports and research on investment vehicles and providers.

B8.7 Select sources to finance venture creation/start-up.

B8.8 Describe the role of the Securities and Exchange Commission (SEC) and the Financial Industry Regulation Authority (FINRA) and explain regulation of the industry, including legal and ethical considerations in all aspects of financial services.

B9.0 Evaluate financial services providers and explore the duties and activities of financial service careers.

B9.1 Identify electronic banking technologies.

B9.2 Identify licensure requirements for various professionals in the financial services industry.

12


B9.3 Demonstrate characteristics of professionalism in working relationships with customers and employees.

B9.4 Demonstrate techniques for managing human resources to maximize operational efficiencies and effectiveness.

B9.5 Discuss legal and ethical considerations in providing financial advice, buying or selling securities, insurance or real estate, and borrowing or lending money.

B9.6 Examine the environments in which securities and investments services are offered, including securities sales agents, securities and investment firms, and securities markets.

B9.7 Determine client needs and wants and develop and present a written investment ecommendation to the client using standard writing conventions.

B9.8 Scrutinize lending and borrowing practices.

13



C. International Business PathwayThe relative ease of travel and the use of electronic communication have seemingly diminished the size of the globe, yet the interdependence of countries for goods and services causes this market-place to grow, thrive, and become increasingly more competitive. Students focusing on the occupa-tional area of international trade develop an understanding of the global business environment and the interconnectedness of cultural, political, legal, historical, economic, and ethical systems.


International Shipping Specialist

Export Sales Representative

Customs Broker

Customs Inspector

International Market Researcher

C1.0 Describe the fundamental concepts of international business.

C1.1 Identify forms of business ownership and entrepreneurial opportunities available in international business.

C1.2 Conduct market research for a product or service traded internationally.

C1.3 Illustrate the process of buying, selling, and promoting products in a modern global trade.

C1.4 Analyze how domestic and international competition in a market economy affects goods and services produced and the quality, quantity, and price of those products.

C1.5 Construct and defend a business plan for a product or service traded internationally.

C2.0 Describe the interrelatedness of geographic, social, cultural, political, and legal factors and how they shape the global business environment.

C2.1 Interpret the effect of culture, customs, and politics on trade.

C2.2 Illustrate how geographic conditions affect trade.

C2.3 Apply communications strategies necessary and appropriate for effective and profitable international businesses relations.

C2.4 Analyze special challenges in human resources and strategic management in interna-tional business.

C3.0 Apply economic concepts as they relate to international business.

C3.1 Describe the laws of absolute and comparative advantage.

C3.2 Explain the importance of productivity and analyze how specialization, division of labor, investment in physical and human capital, and technological change affect productivity and global trade.

14


C3.3 Examine the role of trade, trade agreements, protectionism, and monetary markets in the global economy.

C3.4 Relate the balance of trade concepts to the import/export process.

C3.5 Examine the ways in which a country’s natural, financial, and human resources influence international business.

C3.6 Analyze the role of government in economic systems.

C4.0 Describe common financing sources and the payment methods used for international business transactions.

C4.1 Explain the concepts, role, and importance of international finance and risk management.

C4.2 Analyze factors that affect currency and exchange rates.

C4.3 Compare the variety of ways in which funds are transferred in foreign trade.

C4.4 Assess the ways in which financial markets influence interest rates, inflation, balance of trade, and unemployment and the impact on business decisions.

C4.5 Produce documentation for international trade, including letters of credit, import/export documents, permits, taxes, and duties.

C5.0 Recognize the role of information and communications technology in modern global trade.

C5.1 Identify hardware and software commonly used in international business operations.

C5.2 Integrate appropriate use of the Internet in business.

C5.3 Analyze security measures used to protect businesses and consumers engaging in international e-commerce.

C6.0 Analyze international markets and competition.

C6.1 Apply marketing concepts to international business situations.

C6.2 Differentiate between the types of market structures and their effect on the price and the quality of goods and services produced.

C6.3 Research measures used to evaluate the economic conditions of a country.

C6.4 Identify factors that determine balance of trade and research balance of trade for a developed nation, a developing nation, and an undeveloped nation.

C6.5 Develop strategies to adapt and respond to meeting the differences in culture, market, habits, experience, and laws.

C7.0 Assess the risks associated with various methods of entering the global marketplace.

C7.1 Calculate the effects of exchange rate fluctuation.

C7.2 Determine pricing for products and services traded internationally.

C7.3 Set inventory levels based upon location of customers, durability of products, and logistics.

15


C7.4 Analyze choices available to international businesses for protection against risk and financial loss.

C7.5 Determine exposure of doing business internationally and develop a recommendation for entering the international market.

C8.0 Reconstruct the logistics of importing and exporting products and services.

C8.1 Explain how private, nonprofit, and government agencies assist in global trade.

C8.2 Determine the effect of imports and exports on production and manufacturing.

C8.3 Distinguish between direct and indirect distribution channels.

C8.4 Compare how products are prepared for international versus domestic distribution.

C8.5 Contrast the four forms of international operations: working through a foreign inter-mediary, licensing agreement with the foreign business, forming a strategic alliance, or becoming a multinational corporation.

C8.6 Analyze special challenges in operations and strategic management in international business.

16


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

ENGL

ISH

LA

NGU

AGE

ART

S

Lang

uage

Sta

ndar

ds –

LS

(Sta

ndar

d A

rea,

Gra

de L

evel

, Sta

ndar

d #)

11.1

. Dem

onst

rate

com

man

d of

the

con

vent

ions

of s

tand

ard

Engl

ish

gram

mar

and

usa

ge w

hen

writ

ing

or

A1.0

, A3.

0, A

4.0,

C1

.0, C

3.0,

B1

.0, B

2.0,

B11

.0sp

eaki

ng.

A6.0

, A8.

0, A

9.0

C4.0

11.2

. Dem

onst

rate

com

man

d of

the

con

vent

ions

of s

tand

ard

Engl

ish

capi

taliz

atio

n, p

unct

uatio

n, a

nd s

pelli

ng

A1.0

, A3.

0, A

4.0,

B1

.0C1

.0, C

4.0

whe

n w

ritin

g.A6

.0, A

8.0,

A9.

0

11.3

. App

ly k

now

ledg

e of

lang

uage

to

unde

rsta

nd h

ow la

ngua

ge f

unct

ions

in d

iffe

rent

con

text

s, t

o m

ake

A3.0

B4.0

, B5.

0C2

.0, C

6.0

effe

ctiv

e ch

oice

s fo

r mea

ning

or s

tyle

, and

to

com

preh

end

mor

e fu

lly w

hen

read

ing

or li

sten

ing.

11.4

. Det

erm

ine

or c

larif

y th

e m

eani

ng o

f unk

now

n an

d m

ultip

le-m

eani

ng w

ords

and

phr

ases

bas

ed o

n A

2.0,

A3.

0B4

.0, B

5.0

C2.0

, C6.

0gr

ades

11–

12 re

adin

g an

d co

nten

t, ch

oosi

ng fl

exib

ly f

rom

a r

ange

of s

trat

egie

s.

11.5

. Dem

onst

rate

und

erst

andi

ng o

f figu

rativ

e la

ngua

ge, w

ord

rela

tions

hips

, and

nua

nces

in w

ord

mea

ning

s.A1

.0B4

.0, B

10.0

C2.0

, C6.

0

11.6

. Acq

uire

and

acc

urat

ely

use

gene

ral a

cade

mic

and

dom

ain-

spec

ific

wor

ds a

nd p

hras

es s

uffic

ient

for

re

adin

g, w

ritin

g, s

peak

ing,

and

list

enin

g at

the

col

lege

and

car

eer r

eadi

ness

leve

l; de

mon

stra

te in

depe

n-C1

.0, C

6.0,

A1

.0B2

.0, B

10.0

denc

e in

gat

herin

g vo

cabu

lary

kno

wle

dge

whe

n co

nsid

erin

g a

wor

d or

phr

ase

impo

rtan

t to

com

preh

ensi

on

C8.0

or e

xpre

ssio

n.

Read

ing

Stan

dard

s fo

r In

form

atio

nal T

ext

– RS

IT (

Stan

dard

Are

a, G

rade

Lev

el, S

tand

ard

#)

11.1

. Cite

str

ong

and

thor

ough

tex

tual

evi

denc

e to

sup

port

ana

lysi

s of

wha

t th

e te

xt s

ays

expl

icitl

y as

wel

l A4

.0B5

.0, B

6.0,

B8.

0C1

.0, C

8.0

as in

fere

nces

dra

wn

from

the

tex

t, in

clud

ing

dete

rmin

ing

whe

re t

he t

ext

leav

es m

atte

rs u

ncer

tain

.

11.2

. Det

erm

ine

two

or m

ore

cent

ral i

deas

of a

tex

t an

d an

alyz

e th

eir d

evel

opm

ent

over

the

cou

rse

of t

he

text

, inc

ludi

ng h

ow t

hey

inte

ract

and

bui

ld o

n on

e an

othe

r to

prov

ide

a co

mpl

ex a

naly

sis;

pro

vide

an

A3

.0, A

5.0

B5.0

obje

ctiv

e su

mm

ary

of t

he t

ext.

11.3

. Ana

lyze

a c

ompl

ex s

et o

f ide

as o

r seq

uenc

e of

eve

nts

and

expl

ain

how

spe

cific

indi

vidu

als,

idea

s, o

r B1

.0, B

2.0,

B3.

0,

C1.0

, C2.

0,

A1.0

, A2.

0, A

3.0,

ev

ents

inte

ract

and

dev

elop

ove

r the

cou

rse

of t

he t

ext.

B4.0

, B5.

0, B

6.0,

C3

.0, C

4.0,

A4

.0, A

5.0,

A6.

0,

B7.0

, B8.

0, B

9.0,

C5

.0, C

6.0,

A7

.0, A

8.0,

A9.

0B1

0, B

11C7

.0, C

8.0

11.4

. Det

erm

ine

the

mea

ning

of w

ords

and

phr

ases

as

they

are

use

d in

a t

ext,

incl

udin

g fig

urat

ive,

B1

.0, B

2.0,

B3.

0,

conn

otat

ive,

and

tec

hnic

al m

eani

ngs;

ana

lyze

how

an

auth

or u

ses

and

refin

es t

he m

eani

ng o

f a k

ey t

erm

or

A5.0

, A6.

0, A

7.0,

B4

.0, B

5.0,

B6.

0,

C1.0

, C8.

0te

rms

over

the

cou

rse

of a

tex

t (e

.g.,

how

Mad

ison

defi

nes

fact

ion

in F

eder

alis

t N

o. 1

0). (

See

grad

e 11

/12

A9.0

B7.0

, B8.

0, B

9.0,

La

ngua

ge s

tand

ards

4-6

on

page

46

for a

dditi

onal

exp

ecta

tions

.)B1

0

17


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

Read

ing

Stan

dard

s fo

r In

form

atio

nal T

ext

– RS

IT (

Stan

dard

Are

a, G

rade

Lev

el,

Stan

dard

#)

(con

tinue

d)11

.5. A

naly

ze a

nd e

valu

ate

the

effe

ctiv

enes

s of

the

str

uctu

re a

n au

thor

use

s in

his

or h

er e

xpos

ition

B1

.0, B

2.0,

B3.

0, B

6.0,

A4

.0, A

6.0,

A7.

0C5

.0, C

6.0,

C7.

0or

arg

umen

t, in

clud

ing

whe

ther

the

str

uctu

re m

akes

poi

nts

clea

r, co

nvin

cing

, and

eng

agin

g.B7

.0, B

8.0,

B10

.0

11.6

. Det

erm

ine

an a

utho

r’s p

oint

of v

iew

or p

urpo

se in

a te

xt in

whi

ch th

e rh

etor

ic is

par

ticul

arly

ef

fect

ive,

ana

lyzi

ng h

ow s

tyle

and

con

tent

con

trib

ute

to t

he p

ower

, per

suas

iven

ess,

or b

eaut

y of

the

B1

.0te

xt.

11.7

. Int

egra

te a

nd e

valu

ate

mul

tiple

sou

rces

of i

nfor

mat

ion

pres

ente

d in

dif

fere

nt m

edia

or f

orm

ats

A1.0

, A2.

0, A

3.0,

B1

.0, B

3.0,

B4.

0, B

5.0,

C1

.0, C

2.0,

C3.

0,

(e.g

., vi

sual

ly, q

uant

itativ

ely)

as

wel

l as

in w

ords

in o

rder

to

addr

ess

a qu

estio

n or

sol

ve a

pro

blem

.A4

.0, A

5.0,

A6.

0,

B6.0

, B7.

0, B

8.0,

B9.

0,

C4.0

, C5.

0, C

6.0,

A7

.0, A

8.0,

A9.

0B1

0, B

11.0

C7.0

, C8.

0

Writ

ing

Stan

dard

s –

WS

(Sta

ndar

d A

rea,

Gra

de L

evel

, Sta

ndar

d #)

11.1

. 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

val

id

A8.0

, A9.

0B1

.0, B

3.0,

B6.

0C3

.0re

ason

ing

and

rele

vant

and

suf

ficie

nt e

vide

nce.

11.2

. 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, a

nd

A1.0

, A2.

0, A

3.0,

B2

.0, B

4.0,

B5.

0, B

7.0,

C.

1.0,

C2.

0,

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

ana

lysi

s of

A4

.0, A

5.0,

A6.

0,

B8.0

, B9.

0, B

10.0

, C4

.0, C

5.0,

C6.

0,

cont

ent.

A7.0

B11.

0C7

.0, C

8.0

11.4

. Pro

duce

cle

ar a

nd c

oher

ent

writ

ing

in w

hich

the

dev

elop

men

t, or

gani

zatio

n, a

nd s

tyle

are

A1

.0, A

2.0,

A3.

0,

B1.0

, B2.

0, B

3.0,

B4.

0,

C1.0

, C2.

0, C

3.0,

ap

prop

riate

to

task

, pur

pose

, and

aud

ienc

e.A4

.0, A

5.0,

A6.

0,

B5.0

, B6.

0, B

7.0,

B8.

0,

C4.0

, C5.

0, C

6.0,

A7

.0, A

8.0,

A9.

0B9

.0, B

10.0

, B11

.0C7

.0, C

8.0

11.5

. Dev

elop

and

str

engt

hen

writ

ing

as n

eede

d by

pla

nnin

g, r

evis

ing,

edi

ting,

rew

ritin

g, o

r try

ing

a A1

.0, A

2.0,

A3.

0,

B1.0

, B2.

0, B

3.0,

B4.

0,

C1.0

, C2.

0, C

3.0,

ne

w a

ppro

ach,

foc

usin

g on

add

ress

ing

wha

t is

mos

t si

gnifi

cant

for

a s

peci

fic p

urpo

se a

nd a

udie

nce.

A4.0

, A5.

0, A

6.0,

B5

.0, B

6.0,

B7.

0, B

8.0,

C4

.0, C

5.0,

C6.

0,

A7.0

, A8.

0, A

9.0

B9.0

, B10

.0, B

11.0

C7.0

, C8.

0

11.6

. Use

tec

hnol

ogy,

incl

udin

g th

e In

tern

et, t

o pr

oduc

e, p

ublis

h, a

nd u

pdat

e in

divi

dual

or s

hare

d

A1.0

, A2.

0, A

3.0,

B1

.0, B

2.0,

B3.

0, B

4.0,

C1

.0, C

2.0,

C3.

0,

writ

ing

prod

ucts

in r

espo

nse

to o

ngoi

ng f

eedb

ack,

incl

udin

g ne

w a

rgum

ents

or i

nfor

mat

ion.

A4.0

, A5.

0, A

6.0,

B5

.0, B

6.0,

B7.

0, B

8.0,

C4

.0, C

5.0,

C6.

0,

A7.0

, A8.

0, A

9.0

B9.0

, B10

.0, B

11.0

C7.0

, C8.

0

11.7

. Con

duct

sho

rt a

s w

ell a

s m

ore

sust

aine

d re

sear

ch p

roje

cts

to a

nsw

er a

que

stio

n (in

clud

ing

a A1

.0, A

2.0,

A3.

0,

B1.0

, B2.

0, B

3.0,

B4.

0,

C1.0

, C2.

0, C

3.0,

se

lf-ge

nera

ted

ques

tion)

or s

olve

a p

robl

em; n

arro

w o

r bro

aden

the

inqu

iry

whe

n ap

prop

riate

; A4

.0, A

5.0,

A6.

0,

B5.0

, B6.

0, B

7.0,

B8.

0,

C4.0

, C5.

0, C

6.0,

sy

nthe

size

mul

tiple

sou

rces

on

the

subj

ect,

dem

onst

ratin

g un

ders

tand

ing

of t

he s

ubje

ct u

nder

A7

.0, A

8.0,

A9.

0B9

.0, B

10.0

, B11

.0C7

.0, C

8.0

inve

stig

atio

n.

18


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

Writ

ing

Stan

dard

s –

WS

(Sta

ndar

d A

rea,

Gra

de L

evel

, Sta

ndar

d #)

(con

tinue

d)

11.8

. Gat

her r

elev

ant

info

rmat

ion

from

mul

tiple

aut

horit

ativ

e pr

int

and

digi

tal s

ourc

es, u

sing

ad

vanc

ed s

earc

hes

effe

ctiv

ely;

ass

ess

the

stre

ngth

s an

d lim

itatio

ns o

f eac

h so

urce

in t

erm

s of

the

A1

.0, A

2.0,

A3.

0,

B1.0

, B2.

0, B

3.0,

B4.

0,

C1.0

, C2.

0, C

3.0,

ta

sk, p

urpo

se, a

nd a

udie

nce;

inte

grat

e in

form

atio

n in

to t

he t

ext

sele

ctiv

ely

to m

aint

ain

the

flow

of

A4.0

, A5.

0, A

6.0,

B5

.0, B

6.0,

B7.

0, B

8.0,

C4

.0, C

5.0,

C6.

0,

idea

s, a

void

ing

plag

iaris

m a

nd o

verr

elia

nce

on a

ny o

ne s

ourc

e an

d fo

llow

ing

a st

anda

rd f

orm

at f

or

A7.0

, A8.

0, A

9.0

B9.0

, B10

.0, B

11.0

C7.0

, C8.

0ci

tatio

n in

clud

ing

foot

note

s an

d en

dnot

es.

11.9

. Dra

w e

vide

nce

from

lite

rary

or i

nfor

mat

iona

l tex

ts t

o su

ppor

t an

alys

is, r

eflec

tion,

and

res

earc

h.A1

.0, A

2.0,

A3.

0,

B1.0

, B2.

0, B

3.0,

B4.

0,

C1.0

, C2.

0, C

3.0,

A4

.0, A

5.0,

A6.

0,

B5.0

, B6.

0, B

7.0,

B8.

0,

C4.0

, C5.

0, C

6.0,

A7

.0, A

8.0,

A9.

0B9

.0, B

10.0

, B11

.0C7

.0, C

8.0

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.

B2.0

, B3.

0, B

4.0,

B5.

0,

C3.0

, C4.

0, C

6.0,

b.

Inte

rpre

t co

mpl

icat

ed e

xpre

ssio

ns b

y vi

ewin

g on

e or

mor

e of

the

ir pa

rts

as a

sin

gle

entit

y. F

or

B6.0

, B7.

0, B

8.0,

B10

.0C7

.0, C

8.0

exam

ple,

inte

rpre

t P(1

+r)’

as th

e pr

oduc

t of P

and

a fa

ctor

not

dep

endi

ng o

n 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 – y

4 as

(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 )(x2 +

y2 ).

a. U

se t

he d

istr

ibut

ive

prop

erty

to

expr

ess

a su

m o

f ter

ms

with

a c

omm

on f

acto

r as

a m

ultip

le o

f 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).

(Com

mon

Cor

e B2

.0, B

3.0,

B4.

0, B

5.0,

C3

.0, C

4.0,

C6.

0,

Stan

dard

A-S

SE-2

a)B6

.0, B

7.0,

B8.

0, B

10.0

C7.0

, C8.

0b.

Use

the

prop

ertie

s of o

pera

tions

to e

xpre

ss a

pro

duct

of a

sum

of t

erm

s as a

sum

of p

rodu

cts.

For

ex

ampl

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 + c

x -

2x +

5c

+ 15

. (C

omm

on C

ore

Stan

dard

A-S

SE-2

b)

19


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

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

solv

e pr

oble

ms

in a

nd o

ut o

f con

text

, inc

ludi

ng e

quat

ions

aris

ing

from

line

ar f

unct

ions

.B1

.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

xpon

ents

, and

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 e

quat

ions

on

B1.0

coor

dina

te a

xes

with

labe

ls a

nd s

cale

s.

3. R

epre

sent

con

stra

ints

by

equa

tions

or i

nequ

aliti

es, a

nd b

y sy

stem

s of

equ

atio

ns a

nd/o

r ine

qual

ities

, and

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 in

equa

litie

s B1

.0de

scrib

ing

nutr

ition

al a

nd c

ost

cons

trai

nts

on c

ombi

natio

ns o

f dif

fere

nt f

oods

.

4. R

earr

ange

for

mul

as t

o hi

ghlig

ht a

qua

ntit

y of

inte

rest

, usi

ng t

he s

ame

reas

onin

g as

in s

olvi

ng e

quat

ions

. For

B1

.0ex

ampl

e, r

earr

ange

Ohm

’s la

w V

= IR

to

high

light

res

ista

nce

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 a

sser

ted

at t

he

B1.0

, B3.

0, B

4.0,

C3

.0, C

4.0,

pr

evio

us s

tep,

sta

rtin

g fr

om t

he a

ssum

ptio

n th

at t

he o

rigin

al e

quat

ion

has

a so

lutio

n. C

onst

ruct

a v

iabl

e

B5.0

, B6.

0, B

7.0,

C6

.0, C

7.0,

ar

gum

ent

to ju

stif

y a

solu

tion

met

hod.

B8.0

, B10

.0C8

.0

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

ext

rane

ous

B1

.0, B

3.0,

B4.

0,

C3.0

, C4.

0,

solu

tions

may

aris

e.B5

.0, B

6.0,

B7.

0,

C6.0

, C7.

0,

B8.0

, B10

.0C8

.0

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 r

epre

sent

ed b

y le

tter

s.B1

.0, B

3.0,

B4.

0,

C3.0

, C4.

0,

B5.0

, B6.

0, B

7.0,

C6

.0, C

7.0,

3.

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

Stan

dard

B8

.0, B

10.0

C8.0

Alge

bra

II -

1.0)

20


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

e-Se

rvic

esBu

sine

ssm

ent

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) a

ssig

ns t

o ea

ch

A4.0

, A5.

0,

elem

ent

of t

he d

omai

n ex

actly

one

ele

men

t of

the

ran

ge. I

f f is

a f

unct

ion

and

x is

an

elem

ent

of it

s do

mai

n, t

hen

A6.0

, A7.

0,

f(x)

den

otes

the

out

put

of f

corr

espo

ndin

g to

the

inpu

t x.

The

gra

ph o

f f is

the

gra

ph o

f the

equ

atio

n y

= f(

x).

A8.0

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

atem

ents

tha

t us

e

A4.0

, A5.

0,

func

tion

nota

tion

in t

erm

s of

a c

onte

xt.

A6.0

, A7.

0,

A8.0

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

sub

set

of t

he in

te-

A4.0

, A5.

0,

gers

. For

exa

mpl

e, t

he F

ibon

acci

seq

uenc

e is

defi

ned

recu

rsiv

ely

by f(

0) =

f(1)

= 1

, f(n

+1) =

f(n)

+f(

n-1)

for n

1

.A6

.0, A

7.0,

A8

.0

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 g

raph

s an

d ta

bles

A4

.0, A

5.0,

in

ter

ms

of t

he q

uant

ities

, and

ske

tch

grap

hs s

how

ing

key

feat

ures

giv

en a

ver

bal d

escr

iptio

n of

the

rel

atio

nshi

p.

A6.0

, A7.

0,

B3.0

, B4.

0Ke

y fe

atur

es in

clud

e: in

terc

epts

; int

erva

ls w

here

the

fun

ctio

n is

incr

easi

ng, d

ecre

asin

g, p

ositi

ve, o

r neg

ativ

e;

A8.0

rela

tive

max

imum

s an

d m

inim

ums;

sym

met

ries;

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

tions

hip

it A4

.0, A

5.0,

de

scrib

es. F

or e

xam

ple,

if t

he f

unct

ion

h(n)

giv

es t

he n

umbe

r of p

erso

n-ho

urs

it ta

kes

to a

ssem

ble

n en

gine

s in

a

A6.0

, A7.

0,

fact

ory,

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.A8

.0

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 a

tabl

e) o

ver a

A4

.0, A

5.0,

B3

.0, B

4.0,

B5.

0,

C3.0

, C6.

0,

spec

ified

inte

rval

. Est

imat

e th

e ra

te o

f cha

nge

from

a g

raph

.A6

.0, A

7.0,

B6

.0, B

7.0,

B8.

0C7

.0, C

8.0

A8.0

21


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

Func

tion

s –

F-IF

– In

terp

retin

g Fu

ncti

ons

(con

tinue

d)

Anal

yze

func

tions

usi

ng d

iffer

ent r

epre

sent

atio

ns

7. G

raph

fun

ctio

ns e

xpre

ssed

sym

bolic

ally

and

sho

w k

ey f

eatu

res

of t

he g

raph

, by

hand

in s

impl

e ca

ses

and

usin

g te

chno

logy

for

mor

e co

mpl

icat

ed c

ases

.

a. G

raph

line

ar a

nd q

uadr

atic

fun

ctio

ns a

nd s

how

inte

rcep

ts, m

axim

a, a

nd m

inim

a.

b. G

raph

squ

are

root

, cub

e ro

ot, a

nd p

iece

wis

e-de

fined

fun

ctio

ns, i

nclu

ding

ste

p fu

nctio

ns a

nd a

bsol

ute

valu

e fu

nctio

ns.

A4.0

, A5.

0, A

6.0,

c.

Gra

ph p

olyn

omia

l fun

ctio

ns, i

dent

ifyi

ng z

eros

whe

n su

itabl

e fa

ctor

izat

ions

are

ava

ilabl

e, a

nd s

how

ing

B3.0

A7.0

, A8.

0en

d be

havi

or.

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 a

re a

vail-

able

, and

sho

win

g en

d be

havi

or.

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

fu

nctio

ns, s

how

ing

perio

d, m

idlin

e, a

nd a

mpl

itude

.

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

exp

lain

dif

fere

nt

prop

ertie

s of

the

fun

ctio

n.

a. U

se t

he p

roce

ss o

f fac

torin

g an

d co

mpl

etin

g th

e sq

uare

in a

qua

drat

ic f

unct

ion

to s

how

zer

os, e

xtre

me

A4.0

, A5.

0, A

6.0,

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

.A7

.0, A

8.0

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 e

xam

ple,

iden

-tif

y pe

rcen

t ra

te o

f cha

nge

in f

unct

ions

suc

h as

y =

(1.0

2)t,

y =

(0.9

7)t,

y =

(1.0

1)12

t, y

= (1

.2)t

/10,

and

cl

assi

fy t

hem

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

, gra

phic

ally

, A4

.0, A

5.0,

A6.

0,

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

qua

drat

ic f

unct

ion

and

an

A7.0

, A8.

0al

gebr

aic

expr

essi

on f

or a

noth

er, s

ay w

hich

has

the

larg

er m

axim

um.

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 t

hem

. (CA

A4

.0, A

5.0,

A6.

0,

Stan

dard

Mat

h An

alys

is -

7.0

)A7

.0, A

8.0

22


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

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

text

.

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

nctio

n th

at m

odel

s th

e 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 ex

pone

ntia

l, an

d re

late

thes

e A9

.0fu

nctio

ns to

the

mod

el.

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

ctio

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

lo

catio

n of

the

wea

ther

bal

loon

as

a fu

nctio

n of

tim

e.

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

the

m t

o m

odel

A9

.0si

tuat

ions

, and

tra

nsla

te b

etw

een

the

two

form

s.

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 v

alue

s of

k

(bot

h po

sitiv

e an

d ne

gativ

e); fi

nd t

he v

alue

of k

giv

en t

he g

raph

s. E

xper

imen

t w

ith c

ases

and

illu

stra

te a

n ex

plan

atio

n of

the

eff

ects

on

the

grap

h us

ing

tech

nolo

gy. I

nclu

de r

ecog

nizi

ng e

ven

and

odd

func

tions

fro

m

A9.0

thei

r gra

phs

and

alge

brai

c ex

pres

sion

s fo

r 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

tion

and

perf

orm

ing

arith

met

ic o

pera

tions

on

func

tions

. (CA

Sta

ndar

d Al

gebr

a II

- 24

.0)

4. F

ind

inve

rse

func

tions

.

a. S

olve

an

equa

tion

of t

he f

orm

f(x

) = c

for

a s

impl

e fu

nctio

n f t

hat

has

an in

vers

e an

d w

rite

an e

xpre

ssio

n fo

r the

inve

rse.

For

exa

mpl

e, f

(x) =

2 x3

or f

(x) =

(x+1

)/(x

-1) f

or x

1

.A9

.0b.

(+) V

erif

y by

com

posi

tion

that

one

fun

ctio

n is

the

inve

rse

of a

noth

er.

c. (+

) Rea

d va

lues

of a

n in

vers

e fu

nctio

n fr

om a

gra

ph o

r a t

able

, giv

en t

hat

the

func

tion

has

an in

vers

e.

d. (+

) Pro

duce

an

inve

rtib

le f

unct

ion

from

a n

on-i

nver

tible

fun

ctio

n by

res

tric

ting

the

dom

ain.

5. (+

) Und

erst

and

the

inve

rse

rela

tions

hip

betw

een

expo

nent

s an

d lo

garit

hms

and

use

this

rel

atio

nshi

p to

sol

ve

A9.0

prob

lem

s in

volv

ing

loga

rithm

s an

d ex

pone

nts.

23


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

Geom

etry

– G

-CO

– C

ongr

uenc

e

Mak

e ge

omet

ric c

onst

ruct

ions

12. M

ake

form

al g

eom

etric

con

stru

ctio

ns w

ith a

var

iety

of t

ools

and

met

hods

(com

pass

and

str

aigh

t-ed

ge, s

trin

g, r

eflec

tive

devi

ces,

pap

er f

oldi

ng, d

ynam

ic g

eom

etric

sof

twar

e, e

tc.).

Cop

ying

a s

egm

ent;

B3

.0, B

4.0,

B5.

0, B

6.0,

C3

.0, C

4.0,

co

pyin

g an

ang

le; b

isec

ting

a se

gmen

t; b

isec

ting

an a

ngle

; con

stru

ctin

g pe

rpen

dicu

lar l

ines

, inc

ludi

ng

B7.0

, B8.

0, B

10.0

C6.0

, C7.

0, C

8.0

the

perp

endi

cula

r bis

ecto

r of a

line

seg

men

t; a

nd c

onst

ruct

ing

a lin

e pa

ralle

l to

a gi

ven

line

thro

ugh

a po

int

not

on t

he li

ne.

Geom

etry

– G

-MG

– M

odel

ing

wit

h Ge

omet

ry

Appl

y ge

omet

ric c

once

pts i

n m

odel

ing

situa

tions

1. U

se g

eom

etric

sha

pes,

the

ir m

easu

res,

and

the

ir pr

oper

ties

to d

escr

ibe

obje

cts

(e.g

., m

odel

ing

a tr

ee

B3.0

, B4.

0, B

5.0,

B6.

0,

C3.0

, C4.

0,

trun

k or

a h

uman

tor

so a

s a

cylin

der.

B7.0

, B8.

0, B

10.0

C6.0

, C7.

0, C

8.0

2. A

pply

con

cept

s of

den

sity

bas

ed o

n ar

ea a

nd v

olum

e in

mod

elin

g si

tuat

ions

(e.g

., pe

rson

s pe

r squ

are

B3.0

, B4.

0, B

5.0,

B6.

0,

C3.0

, C4.

0,

mile

, BTU

s pe

r cub

ic f

oot)

.B7

.0, B

8.0,

B10

.0C6

.0, C

7.0,

C8.

0

3. A

pply

geo

met

ric m

etho

ds t

o so

lve

desi

gn p

robl

ems

(e.g

., de

sign

ing

an o

bjec

t or

str

uctu

re t

o sa

tisfy

B3

.0, B

4.0,

B5.

0, B

6.0,

C3

.0, C

4.0,

ph

ysic

al c

onst

rain

ts o

r min

imiz

e co

st; w

orki

ng w

ith t

ypog

raph

ic g

rid s

yste

ms

base

d on

rat

ios)

B7.0

, B8.

0, B

10.0

C6.0

, C7.

0, C

8.0

Num

ber

and

Qua

ntit

y –

N-R

N –

The

Rea

l Num

ber

Syst

em

Exte

nd th

e pr

oper

ties o

f exp

onen

ts to

ratio

nal e

xpon

ents

1. E

xpla

in h

ow t

he d

efini

tion

of t

he m

eani

ng o

f rat

iona

l exp

onen

ts f

ollo

ws

from

ext

endi

ng t

he

prop

ertie

s of

inte

ger e

xpon

ents

to

thos

e va

lues

, allo

win

g fo

r a n

otat

ion

for r

adic

als

in t

erm

s of

rat

iona

l B1

.0, B

3.0,

B4.

0, B

5.0,

C3

.0, C

4.0,

ex

pone

nts.

For

exa

mpl

e, w

e de

fine

51/3 t

o be

the

cub

e ro

ot o

f 5 b

ecau

se w

e w

ant

(51/

3 )3 =

5(1/

3 )3 t

o ho

ld,

B6.0

, B7.

0, B

8.0,

B10

.0C6

.0, C

7.0,

C8.

0so

(51/

3 )3 m

ust

equa

l 5.

2. R

ewrit

e ex

pres

sion

s in

volv

ing

radi

cals

and

rat

iona

l exp

onen

ts u

sing

the

pro

pert

ies

of e

xpon

ents

. B1

.0, B

3.0,

B4.

0, B

5.0,

C3

.0, C

4.0,

B6

.0, B

7.0,

B8.

0, B

10.0

C6.0

, C7.

0, C

8.0

Use

prop

ertie

s of r

atio

nal a

nd ir

ratio

nal n

umbe

r

3. E

xpla

in w

hy t

he s

um o

r pro

duct

of t

wo

ratio

nal n

umbe

rs is

rat

iona

l; th

at t

he s

um o

f a r

atio

nal

B1.0

, B3.

0, B

4.0,

B5.

0,

C3.0

, C4.

0,

num

ber a

nd a

n irr

atio

nal n

umbe

r is

irrat

iona

l; an

d th

at t

he p

rodu

ct o

f a n

onze

ro r

atio

nal n

umbe

r and

B6

.0, B

7.0,

B8.

0, B

10.0

C6.0

, C7.

0, C

8.0

an ir

ratio

nal n

umbe

r is

irrat

iona

l.

24


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

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

rel

a-B1

.0tio

nshi

ps in

a n

etw

ork.

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

B1

.0ga

me

are

doub

led.

8. (+

) Add

, sub

trac

t, an

d m

ultip

ly m

atric

es o

f app

ropr

iate

dim

ensi

ons.

B1.0

9. (+

) Und

erst

and

that

, unl

ike

mul

tiplic

atio

n of

num

bers

, mat

rix m

ultip

licat

ion

for s

quar

e m

atric

es

B1.0

is n

ot a

com

mut

ativ

e op

erat

ion,

but

stil

l sat

isfie

s th

e as

soci

ativ

e an

d di

strib

utiv

e pr

oper

ties.

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

B1

.0no

nzer

o if

and

only

if t

he m

atrix

has

a m

ultip

licat

ive

inve

rse.

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-

B1.0

sion

s to

pro

duce

ano

ther

vec

tor.

Wor

k w

ith m

atric

es a

s tr

ansf

orm

atio

ns o

f vec

tors

.

12. (

+) W

ork

with

2 x

2 m

atric

es a

s tr

ansf

orm

atio

ns o

f the

pla

ne, a

nd in

terp

ret

the

abso

lute

val

ue

B1.0

of t

he d

eter

min

ant

in t

erm

s of

are

a.

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

B1.0

, B3.

0, B

4.0,

B5.

0,

C1.0

, C2.

0, C

3.0,

A4

.0, A

5.0,

1.

Und

erst

and

stat

istic

s as

a p

roce

ss f

or m

akin

g in

fere

nces

abo

ut p

opul

atio

n pa

ram

eter

s ba

sed

on

B6.0

, B7.

0, B

8.0,

B9.

0,

C4.0

, C6.

0, C

7.0,

A6

.0, A

7.0,

A8.

0a

rand

om s

ampl

e fr

om t

hat

popu

latio

n.B1

0.0,

B11

.0C8

.0

2. D

ecid

e if

a sp

ecifi

ed m

odel

is c

onsi

sten

t w

ith r

esul

ts f

rom

a g

iven

dat

a-ge

nera

ting

proc

ess,

e.g

., B1

.0, B

3.0,

B4.

0, B

5.0,

C1

.0, C

2.0,

C3.

0,

A4.0

, A5.

0,

usin

g si

mul

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

0.5.

B6

.0, B

7.0,

B8.

0, B

10.0

, C4

.0, C

6.0,

C7.

0,

A6.0

, A7.

0, A

8.0

Wou

ld a

res

ult

of 5

tai

ls in

a r

ow c

ause

you

to

ques

tion

the

mod

el?

B11.

0C8

.0

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 stu

dies

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,

B1

.0, B

3.0,

B4.

0, B

5.0,

C1

.0, C

2.0,

C3.

0,

tiona

l stu

dies

; exp

lain

how

ran

dom

izat

ion

rela

tes

to e

ach.

A4.0

, A5.

0,

B6.0

, B7.

0, B

8.0,

B9.

0,

C4.0

, C6.

0, C

7.0,

A6

.0, A

7.0,

A8.

0B1

0.0,

B11

.0C8

.0

25


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

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)B1

.0, B

3.0,

B4.

0,

C1.0

, C2.

0,

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

deci

de if

A3

.0, A

4.0,

A5.

0,

B5.0

, B6.

0, B

7.0,

C3

.0, C

4.0,

di

ffer

ence

s be

twee

n pa

ram

eter

s ar

e si

gnifi

cant

.A6

.0, A

7.0,

A8.

0B8

.0, B

9.0,

B10

.0C6

.0, C

7.0,

C8.

0

6. E

valu

ate

repo

rts

base

d on

dat

a.B1

.0, B

3.0,

B4.

0,

A1.0

, A2.

0, A

3.0,

C1

.0, C

2.0,

B5

.0, B

6.0,

A4

.0, A

5.0,

A6.

0,

C3.0

, C4.

0,

B7.0

, B8.

0, B

9.0,

A7

.0, A

8.0,

A9.

0C6

.0, C

7.0,

C8.

0B1

0.0,

B11

.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

).B4

.0, B

5.0,

B6.

0,

C3.0

, C4.

0,

B7.0

, B8.

0, B

10.0

C6.0

, C7.

0, C

8.0

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, m

ean)

and

B4

.0, B

5.0,

B6.

0,

C3.0

, C4.

0,

spre

ad (i

nter

quar

tile

rang

e, s

tand

ard

devi

atio

n) o

f tw

o or

mor

e di

ffer

ent

data

set

s.B7

.0, B

8.0,

B10

.0C6

.0, C

7.0,

C8.

0

3. In

terp

ret

diff

eren

ces

in s

hape

, cen

ter,

and

spre

ad in

the

con

text

of t

he d

ata

sets

, acc

ount

ing

for p

ossi

ble

B4.0

, B5.

0, B

6.0,

C3

.0, C

4.0,

ef

fect

s of

ext

rem

e da

ta p

oint

s (o

utlie

rs).

B7.0

, B8.

0, B

10.0

C6.0

, C7.

0, C

8.0

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

est

imat

e

B4.0

, B5.

0, B

6.0,

C3

.0, C

4.0,

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 is

not

app

ropr

iate

. B7

.0, B

8.0,

B10

.0C6

.0, C

7.0,

C8.

0U

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 c

urve

.

Sum

mar

ize,

repr

esen

t, an

d in

terp

ret d

ata

on tw

o ca

tego

rical

and

qua

ntita

tive

varia

bles

5. S

umm

ariz

e ca

tego

rical

dat

a fo

r tw

o ca

tego

ries

in t

wo-

way

fre

quen

cy t

able

s. In

terp

ret

rela

tive

freq

uen-

B4.0

, B5.

0, B

6.0,

C3

.0, C

4.0,

ci

es 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 fr

eque

ncie

s). R

ecog

nize

B7

.0, B

8.0,

B10

.0C6

.0, C

7.0,

C8.

0po

ssib

le a

ssoc

iatio

ns a

nd t

rend

s in

the

dat

a.

6. R

epre

sent

dat

a on

tw

o qu

antit

ativ

e va

riabl

es o

n a

scat

ter p

lot,

and

desc

ribe

how

the

varia

bles

are

rela

ted.

a. F

it a

func

tion

to t

he d

ata;

use

fun

ctio

ns fi

tted

to

data

to

solv

e pr

oble

ms

in t

he c

onte

xt o

f 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

B4.0

, B5.

0, B

6.0,

C3

.0, C

4.0,

ex

pone

ntia

l mod

els.

B7.0

, B8.

0, B

10.0

C6.0

, C7.

0, C

8.0

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.

26


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

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

(c

ontin

ued)

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

of

A5.0

, A6.

0, A

7.0,

B4

.0, B

5.0,

B6.

0,

C3.0

, C4.

0,

the

data

.A8

.0B7

.0, B

8.0,

B10

.0C6

.0, C

7.0,

C8.

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.B4

.0, B

5.0,

B6.

0,

C3.0

, C4.

0,

B7.0

, B8.

0, B

10.0

C6.0

, C7.

0, C

8.0

9. D

istin

guis

h be

twee

n co

rrel

atio

n an

d ca

usat

ion.

B4.0

, B5.

0, B

6.0,

C3

.0, C

4.0,

B7

.0, B

8.0,

B10

.0C6

.0, C

7.0,

C8.

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

yUn

ders

tand

inde

pend

ence

and

con

ditio

nal p

roba

bilit

y an

d us

e th

em to

inte

rpre

t dat

a

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

egor

ies)

B3

.0, B

4.0,

B5.

0,

A4.0

, A5.

0, A

6.0,

C3

.0, C

4.0,

of

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”)

.B6

.0, B

7.0,

B8.

0,

A7.0

C6.0

, C7.

0, C

8.0

B10.

0

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 is

B3

.0, B

4.0,

B5.

0,

A4.0

, A5.

0, A

6.0,

C3

.0, C

4.0,

th

e pr

oduc

t of

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.

B6.0

, B7.

0, B

8.0,

A7

.0C6

.0, C

7.0,

C8.

0B1

0.0

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 B3

.0, B

4.0,

B5.

0,

A4.0

, A5.

0, A

6.0,

C3

.0, C

4.0,

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

the

B6

.0, B

7.0,

B8.

0,

A7.0

C6.0

, C7.

0, C

8.0

cond

ition

al p

roba

bilit

y of

B g

iven

A is

the

sam

e as

the

pro

babi

lity

of B

.B1

0.0

4. C

onst

ruct

and

inte

rpre

t tw

o-w

ay f

requ

ency

tab

les

of d

ata

whe

n tw

o ca

tego

ries

are

asso

ciat

ed w

ith

each

obj

ect

bein

g cl

assi

fied.

Use

the

tw

o-w

ay t

able

as

a sa

mpl

e sp

ace

to d

ecid

e if

even

ts a

re in

depe

nden

t B3

.0, B

4.0,

B5.

0,

and

to a

ppro

xim

ate

cond

ition

al p

roba

bilit

ies.

For

exa

mpl

e, c

olle

ct d

ata

from

a r

ando

m s

ampl

e of

stu

dent

s A4

.0, A

5.0,

A6.

0,

C3.0

, C4.

0,

B6.0

, B7.

0, B

8.0,

in

you

r sch

ool o

n th

eir f

avor

ite s

ubje

ct a

mon

g m

ath,

sci

ence

, and

Eng

lish.

Est

imat

e th

e pr

obab

ility

tha

t a

A7.0

C6.0

, C7.

0, C

8.0

B10.

0ra

ndom

ly s

elec

ted

stud

ent

from

you

r sch

ool w

ill f

avor

sci

ence

giv

en t

hat

the

stud

ent

is in

ten

th g

rade

. Do

the

sam

e fo

r oth

er s

ubje

cts

and

com

pare

the

res

ults

.

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

A4.0

, A5.

0, A

6.0,

in

terp

ret

the

answ

er in

ter

ms

of t

he m

odel

.A7

.0

27


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

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 (c

ontin

ued)

A4.0

, A5.

0,

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

mod

el.

A6.0

, A7.

0

8. (+

) App

ly t

he g

ener

al M

ultip

licat

ion

Rule

in a

uni

form

pro

babi

lity

mod

el, P

(A a

nd B

) = P

(A)P

(BIA

) = P

(B)P

(AIB

), A4

.0, A

5.0,

an

d in

terp

ret

the

answ

er in

ter

ms

of t

he m

odel

.A6

.0, A

7.0

9. (+

) Use

per

mut

atio

ns a

nd c

ombi

natio

ns t

o co

mpu

te p

roba

bilit

ies

of c

ompo

und

even

ts a

nd s

olve

pro

blem

s.A4

.0, A

5.0,

A6

.0, A

7.0

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

B1.0

, B3.

0,

A4.0

, A5.

0,

C1.0

, C2.

0, C

3.0,

1.

(+) D

efine

a r

ando

m v

aria

ble

for a

qua

ntit

y of

inte

rest

by

assi

gnin

g a

num

eric

al v

alue

to

each

eve

nt in

a s

ampl

e B4

.0, B

5.0,

A6

.0, A

7.0,

C4

.0, C

6.0,

C7.

0,

spac

e; g

raph

the

cor

resp

ondi

ng p

roba

bilit

y di

strib

utio

n us

ing

the

sam

e gr

aphi

cal d

ispl

ays

as f

or d

ata

dist

ribut

ions

.B6

.0, B

7.0,

A8

.0, A

9.0

C8.0

B8.0

, B10

.0

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 di

strib

utio

n.A4

.0, A

5.0,

C1

.0, C

2.0,

C3.

0,

A6.0

, A7.

0,

C4.0

, C6.

0, C

7.0,

A8

.0, A

9.0

C8.0

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 t

heor

etic

al

B1.0

, B3.

0,

A4.0

, A5.

0,

C1.0

, C2.

0, C

3.0,

pr

obab

ilitie

s ca

n be

cal

cula

ted,

find

the

exp

ecte

d va

lue.

For

exa

mpl

e, fi

nd t

he t

heor

etic

al p

roba

bilit

y di

strib

utio

n B4

.0, B

5.0,

A6

.0, A

7.0,

C4

.0, C

6.0,

C7.

0,

for t

he n

umbe

r of c

orre

ct a

nsw

ers

obta

ined

by

gues

sing

on

all fi

ve q

uest

ions

of a

mul

tiple

-cho

ice

test

whe

re e

ach

B6.0

, B7.

0,

A8.0

, A9.

0C8

.0qu

estio

n ha

s fo

ur c

hoic

es, a

nd fi

nd t

he e

xpec

ted

grad

e un

der v

ario

us g

radi

ng s

chem

es.

B8.0

, B10

.0

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

roba

bilit

ies

B1.0

, B3.

0,

A4.0

, A5.

0,

C1.0

, C2.

0, C

3.0,

ar

e as

sign

ed e

mpi

rical

ly; fi

nd t

he e

xpec

ted

valu

e. F

or e

xam

ple,

find

a c

urre

nt d

ata

dist

ribut

ion

on t

he n

umbe

r of

B4.0

, B5.

0,

A6.0

, A7.

0,

C4.0

, C6.

0, C

7.0,

TV

set

s pe

r hou

seho

ld in

the

Uni

ted

Stat

es, a

nd c

alcu

late

the

exp

ecte

d nu

mbe

r of s

ets

per h

ouse

hold

. How

man

y B6

.0, B

7.0,

A8

.0, A

9.0

C8.0

TV s

ets

wou

ld y

ou e

xpec

t to

find

in 1

00 r

ando

mly

sel

ecte

d ho

useh

olds

?B8

.0, B

10.0

28


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

Stat

isti

cs a

nd P

roba

bilit

y –

S-M

D –

Usin

g Pr

obab

ility

to

Mak

e De

cisi

ons

(con

tinue

d)Us

e pr

obab

ility

to e

valu

ate

outc

omes

of d

ecisi

ons

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

sta

te

A2.

0, A

4.0,

B1

.0, B

3.0,

B4.

0,

C1.0

, C2.

0, C

3.0,

lo

tter

y tic

ket

or a

gam

e at

a f

ast-

food

res

taur

ant.

A5.0

, A6.

0,

B5.0

, B6.

0, B

7.0,

C4

.0, C

6.0,

C7.

0,

B8.0

, B10

.0C8

.0b.

Eva

luat

e an

d co

mpa

re s

trat

egie

s on

the

bas

is o

f exp

ecte

d va

lues

. For

exa

mpl

e, c

ompa

re a

hig

h de

duct

-A7

.0, A

8.0,

ib

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 h

avin

g a

A9.0

min

or o

r a m

ajor

acc

iden

t.

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 g

ener

ator

).A

2.0,

A4.

0,

B1.0

, B3.

0, B

4.0,

C1

.0, C

2.0,

C3.

0,

A5.0

, A6.

0,

B5.0

, B6.

0, B

7.0,

C4

.0, C

6.0,

C7.

0,

A7.0

, A8.

0,

B8.0

, B10

.0C8

.0A9

.0

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 t

estin

g,

B1.0

, B3.

0, B

4.0,

C1

.0, C

2.0,

C3.

0,

A2.

0, A

8.0,

pu

lling

a h

ocke

y go

alie

at

the

end

of a

gam

e).

B5.0

, B6.

0, B

7.0,

C4

.0, C

6.0,

C7.

0,

A9.0

B8.0

, B10

.0C8

.0

Stat

isti

cs a

nd P

roba

bilit

y –

APP

S –

Adva

nced

Pla

cem

ent

Prob

abili

ty a

nd S

tati

stic

s7.

0 St

uden

ts d

emon

stra

te a

n un

ders

tand

ing

of th

e st

anda

rd d

istr

ibut

ions

(nor

mal

, bin

omia

l, an

d ex

pone

ntia

l) A4

.0, A

5.0,

C3

.0, C

4.0,

an

d ca

n us

e th

e di

strib

utio

ns to

sol

ve fo

r eve

nts

in p

robl

ems

in w

hich

the

dist

ribut

ion

belo

ngs

to th

ose

fam

ilies

.A6

.0, A

7.0

C6.0

, C7.

0, C

8.0

10.0

Stu

dent

s kn

ow t

he d

efini

tions

of t

he m

ean,

med

ian

and

mod

e of

dis

trib

utio

n of

dat

a an

d ca

n co

mpu

te

A4.0

, A5.

0,

C3.0

, C4.

0,

each

of t

hem

in p

artic

ular

situ

atio

ns.

A6.0

, A7.

0C6

.0, C

7.0,

C8.

0

15.0

Stu

dent

s ar

e fa

mili

ar w

ith t

he n

otio

ns o

f a s

tatis

tic o

f a d

istr

ibut

ion

of v

alue

s, o

f the

sam

plin

g di

strib

u-A4

.0, A

5.0,

C3

.0, C

4.0,

tio

n of

a s

tatis

tic. A

nd o

f the

var

iabi

lity

of a

sta

tistic

.A6

.0, A

7.0

C6.0

, C7.

0, C

8.0

16.0

Stu

dent

s kn

ow b

asic

fac

ts c

once

rnin

g th

e re

latio

n be

twee

n th

e m

ean

and

the

stan

dard

dev

iatio

n of

a

A4.0

, A5.

0,

C3.0

, C4.

0,

sam

plin

g di

strib

utio

n an

d th

e m

ean

and

the

stan

dard

dev

iatio

n of

the

pop

ulat

ion

dist

ribut

ion.

A6.0

, A7.

0C6

.0, C

7.0,

C8.

0

Calc

ulus

– C

11.0

Stu

dent

s us

e di

ffer

entia

tion

to s

olve

opt

imiz

atio

n (m

axim

um-m

inim

um p

robl

ems)

in a

var

iety

of p

ure

A4.0

, A5.

0,

C3.0

, C4.

0,

and

appl

ied

cont

exts

.A6

.0, A

7.0

C6.0

, C7.

0, C

8.0

29


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

HIS

TORY

/SO

CIAL

SCI

ENCE

Prin

cipl

es o

f A

mer

ican

Dem

ocra

cy a

nd E

cono

mic

s –

AD12

.7 S

tude

nts

anal

yze

and

com

pare

the

pow

ers

and

proc

edur

es o

f the

nat

iona

l, st

ate,

trib

al, a

nd lo

cal

gove

rnm

ents

.

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

nmen

ts.

B8.0

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

impl

emen

-B8

.0ta

tion

of it

thr

ough

reg

ulat

ions

and

exe

cutiv

e or

ders

.

Prin

cipl

es o

f Ec

onom

ics

– PE

12.1

Stu

dent

s un

ders

tand

com

mon

eco

nom

ic t

erm

s an

d co

ncep

ts a

nd e

cono

mic

rea

soni

ng.

A1.0

, A2.

0B1

.0, B

8.0

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

.A1

.0, A

2.0,

A4.

0,

B1.0

, B6.

0, B

8.0

A7.0

, A8.

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.A1

.0, A

2.0,

A4.

0,

B1.0

, B2.

0, B

4.0,

C1

.0, C

3.0,

C4.

0,

A7.0

B6.0

, B8.

0C6

.0, C

8.0

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 c

hang

es in

B1

.0, B

11.0

ince

ntiv

es c

ause

cha

nges

in b

ehav

ior.

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

A3

.0, A

4.0,

A6.

0,

B1.0

, B4.

0re

sour

ces,

incl

udin

g re

new

able

and

non

rene

wab

le n

atur

al r

esou

rces

.A9

.0

12.1

.5. A

naly

ze t

he r

ole

of a

mar

ket

econ

omy

in e

stab

lishi

ng a

nd p

rese

rvin

g po

litic

al a

nd p

erso

nal

A4.0

liber

ty (e

.g.,

thro

ugh

the

wor

ks o

f Ada

m S

mith

).

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.B1

.0, B

3.0,

B4.

0,

A1.0

, A3.

0, A

4.0

C2.0

, C6.

0B8

.0, B

10.0

, B11

.0

12.2

.1. U

nder

stan

d th

e re

latio

nshi

p of

the

con

cept

of i

ncen

tives

to

the

law

of s

uppl

y an

d th

e re

latio

n-C1

.0, C

2.0,

C3.

0,

A4.0

, A8.

0sh

ip o

f the

con

cept

of i

ncen

tives

and

sub

stitu

tes

to t

he la

w o

f dem

and.

C6.0

, C7.

0, C

8.0

12.2

.2. D

iscu

ss t

he e

ffec

ts o

f cha

nges

in s

uppl

y an

d! o

r dem

and

on t

he r

elat

ive

scar

city

, pric

e, a

nd

C1.0

, C2.

0, C

3.0,

A4

.0, A

8.0

B1.0

, B4.

0qu

antit

y of

par

ticul

ar p

rodu

cts.

C6.0

, C7.

0, C

8.0

12.2

.3. E

xpla

in t

he r

oles

of p

rope

rty

right

s, c

ompe

titio

n, a

nd p

rofit

in a

mar

ket

econ

omy.

A3.0

, A4.

0, A

8.0,

C1

.0, C

2.0,

C3.

0,

A9.0

C6.0

, C7.

0, C

8.0

30


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

Prin

cipl

es o

f Ec

onom

ics

– PE

(con

tinue

d)12

.2.4

. Exp

lain

how

pric

es r

eflec

t th

e re

lativ

e sc

arci

ty o

f goo

ds a

nd s

ervi

ces

and

perf

orm

the

allo

cativ

e A4

.0, A

8.0

func

tion

in a

mar

ket

econ

omy.

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

A4.0

B1.0

, B4.

0, B

6.0

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

.A3

.0, A

4.0

12.2

.7. A

naly

ze h

ow d

omes

tic a

nd in

tern

atio

nal c

ompe

titio

n in

a m

arke

t ec

onom

y af

fect

s go

ods

and

A7.0

, A4.

0B6

.0se

rvic

es p

rodu

ced

and

the

qual

ity,

qua

ntit

y, a

nd p

rice

of t

hose

pro

duct

s.

12.2

.8. E

xpla

in t

he r

ole

of p

rofit

as

the

ince

ntiv

e to

ent

repr

eneu

rs in

a m

arke

t ec

onom

y.A1

.0, A

3.0,

A4.

0,

B6.0

, B8.

0A9

.0

12.2

.9. D

escr

ibe

the

func

tions

of t

he fi

nanc

ial m

arke

ts.

B3.0

, B4.

0, B

6.0

A5.0

B8.0

, B10

.0, B

11.0

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

dust

ry

A1.0

, A4.

0an

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.A3

.0, A

4.0,

A5.

0,

B1.0

, B2.

0, B

4.0,

A6

.0, A

8.0,

A9.

0B5

.0, B

6.0,

B10

.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 f

or

B1.0

, B2.

0, B

3.0,

C2

.0, C

3.0,

na

tiona

l def

ense

, add

ress

ing

envi

ronm

enta

l con

cern

s, d

efini

ng a

nd e

nfor

cing

pro

pert

y rig

hts,

att

empt

ing

A3.0

, A4.

0, A

9.0

B5.0

C7.0

, C8.

0to

mak

e m

arke

ts m

ore

com

petit

ive,

and

pro

tect

ing

cons

umer

s’ rig

hts.

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

.C2

.0, C

3.0,

A3

.0, A

4.0

B1.0

, B4.

0, B

6.0

C7.0

, 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

-B1

.0, B

3.0,

B4.

0,

C2.0

, C3.

0,

A5.0

, A6.

0, A

8.0

ence

on

prod

uctio

n, e

mpl

oym

ent,

and

pric

e le

vels

.B5

.0, B

6.0

C7.0

, C8.

0

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

(e.g

., B2

.0, B

3.0,

B5.

0,

C2.0

, C3.

0,

A5.0

, A8.

0th

e Fe

dera

l Res

erve

).B6

.0, B

10.0

C7.0

, C8.

0

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.

A3.0

, A4.

0, A

5.0,

A7

.0

12.4

.1. U

nder

stan

d th

e op

erat

ions

of t

he la

bor m

arke

t, in

clud

ing

the

circ

umst

ance

s su

rrou

ndin

g th

e C1

.0, C

2.0,

es

tabl

ishm

ent

of p

rinci

pal A

mer

ican

labo

r uni

ons,

pro

cedu

res

that

uni

ons

use

to g

ain

bene

fits

for t

heir

A4.0

B7.0

, B8.

0C3

.0, C

6.0,

m

embe

rs, t

he e

ffec

ts o

f uni

oniz

atio

n, t

he m

ini-

mum

wag

e, a

nd u

nem

ploy

men

t in

sura

nce.

C7.0

, C8.

0

31


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

Prin

cipl

es o

f Ec

onom

ics

– PE

(con

tinue

d)12

.4.2

. Des

crib

e th

e cu

rren

t ec

onom

y an

d la

bor m

arke

t, in

clud

ing

the

type

s of

goo

ds a

nd s

ervi

ces

A3.0

, A4.

0, A

5.0,

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 o

f B7

.0, B

8.0

A7.0

inte

rnat

iona

l com

petit

ion.

12.4

.3. D

iscu

ss w

age

diff

eren

ces

amon

g jo

bs a

nd p

rofe

ssio

ns, u

sing

the

law

s of

dem

and

and

supp

ly a

nd

A6.0

, A7.

0th

e co

ncep

t of

pro

duct

ivit

y.

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.C1

.0, C

2.0,

C3.

0,

A7.0

C4.0

, C5.

0,

C6.0

, C7.

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.

A4.0

, A5.

0

12.5

.1. D

istin

guis

h be

twee

n no

min

al a

nd r

eal d

ata.

A4.0

B1.0

, B5.

0, B

11.0

12.5

.2. D

efine

, cal

cula

te, a

nd e

xpla

in t

he s

igni

fican

ce o

f an

unem

ploy

men

t ra

te, t

he n

umbe

r of n

ew

A4.0

, A5.

0B5

.0, B

6.0

C6.0

jobs

cre

ated

mon

thly

, infl

atio

n or

defl

atio

n ra

te, a

nd a

rat

e of

eco

nom

ic g

row

th.

12.5

.3. D

istin

guis

h be

twee

n sh

ort-

term

and

long

-ter

m in

tere

st r

ates

and

exp

lain

the

ir re

lativ

e si

gnifi

-B3

.0, B

4.0,

B6.

0,

A5.0

canc

e.B8

.0, B

10.0

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

C1

.0, C

3.0,

C4.

0,

A4.0

, A5.

0, A

7.0

affe

cted

by,

eco

nom

ic f

orce

s be

yond

the

Uni

ted

Stat

es’ b

orde

rs.

C6.0

, C7.

0, C

8.0

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 C1

.0, C

2.0,

C3.

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

B7.0

C6.0

, C7.

0, C

8.0

Wes

tern

Hem

isph

ere.

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

-C1

.0, C

2.0,

C3.

0,

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 fre

e B7

.0C6

.0, C

7.0,

C8.

0tr

ade

on t

he e

cono

mic

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

C1

.0, C

2.0,

C3.

0,

glob

al e

cono

my.

B7.0

C4.0

, C6.

0, C

7.0,

C8

.0

12.6

.4. E

xpla

in f

orei

gn e

xcha

nge,

the

man

ner i

n w

hich

exc

hang

e ra

tes

are

dete

rmin

ed, a

nd t

he e

ffec

ts

C1.0

, C2.

0, C

3.0,

of

the

dol

lar’s

gai

ning

(or l

osin

g) v

alue

rel

ativ

e to

oth

er c

urre

ncie

s.A4

.0, A

5.0,

A7.

0B7

.0C4

.0, C

6.0,

C7.

0,

C8.0

32


Acad

emic

Alig

nmen

t M

atrix

PATH

WAY

S

A.

B.

C.

BU

SIN

ES

S A

ND

FIN

AN

CE

Busi

ness

Fi

nanc

ial

Inte

rnat

iona

l M

anag

emen

tSe

rvic

esBu

sine

ss

U.S.

His

tory

and

Geo

grap

hy –

US

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

-B1

.0, B

5.0

men

tally

cha

nged

the

rol

e of

the

fed

eral

gov

ernm

ent.

11.6

.5. T

race

the

adv

ance

s an

d re

trea

ts o

f org

aniz

ed la

bor,

from

the

cre

atio

n of

the

Am

eric

an F

eder

a-tio

n of

Lab

or a

nd t

he C

ongr

ess

of In

dust

rial O

rgan

izat

ions

to

curr

ent

issu

es o

f a p

ostin

dust

rial,

mul

ti-A3

.0na

tiona

l eco

nom

y, in

clud

ing

the

Uni

ted

Farm

Wor

kers

in C

alifo

rnia

.

11.9

Stu

dent

s an

alyz

e U

.S. f

orei

gn p

olic

y si

nce

Wor

ld W

ar II

.B5

.0

11.11

Stu

dent

s an

alyz

e th

e m

ajor

soc

ial p

robl

ems

and

dom

estic

pol

icy

issu

es in

con

tem

pora

ry A

mer

ican

C1

.0, C

2.0,

C6.

0so

ciet

y.

11.11

.1. D

iscu

ss t

he r

easo

ns f

or t

he n

atio

n’s

chan

ging

imm

igra

tion

polic

y, w

ith e

mph

asis

on

how

the

A3

.0Im

mig

ratio

n Ac

t of

196

5 an

d su

cces

sor a

cts

have

tra

nsfo

rmed

Am

eric

an s

ocie

ty.

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

.1. A

naly

ze w

hy E

ngla

nd w

as t

he fi

rst

coun

try

to in

dust

rializ

e.A1

.0, A

7.0

10.3

.5. U

nder

stan

d th

e co

nnec

tions

am

ong

natu

ral r

esou

rces

, ent

repr

eneu

rshi

p, la

bor,

and

capi

tal i

n an

A1

.0in

dust

rial e

cono

my.

10.3

.6. A

naly

ze t

he e

mer

genc

e of

cap

italis

m a

s a

dom

inan

t ec

onom

ic p

atte

rn a

nd t

he r

espo

nses

to

it,

A1.0

incl

udin

g U

topi

anis

m, S

ocia

l Dem

ocra

cy, S

ocia

lism

, and

Com

mun

ism

.

33

Contributors

Business and Finance

Lloyd McCabe, Administrator, California Department of Education

Kay Ferrier, Education Consultant, California Department of Education

Mindi Yates, Education Consultant, California Department of Education

Standards Review TeamPatricia Biagi, Curriculum Specialist, Sonoma County Office of Education

Joe Gaestel, Instructor, Merced High School

Tena Lozano, Director, CU Development, California and Nevada Credit Union Leagues

Tony Tyler, Instructor, Corona–Norco Unified School District

Sarah Vielma, Business Occupations Consultant, Los Angeles County Office of Education

Standards Writing TeamPatricia Biagi, Curriculum Specialist, Sonoma County Office of Education

Adam Connors, Director, CK Cooper and Company

Steven Devan, President and CEO, Grossmont Schools Federal Credit Unions

Bruce Kajiwara, CPA

Panda Morgan, Director, Northeastern California Small Business Development Center (SBDC)

Patrick Rogan, CPA, California Society of Certified Public Accountants (CalCPA)

Sheryl Ryder, Coordinator, California Business Education Leadership Project, Napa County Office of Education

Ellen Tower, Instructor, San Diego Unified School District

Virginia Wade, SVP Employee Services, SAFE Credit Union

Kevin Zimmer, Vice President, Relationship Management and Business Development, LPL Financial

Common Core Alignment TeamSusan Beckenham, Instructor, Providence High School, Burbank

John Fleming, Instructor, Sacramento City Unified School District

Yvette Fraga, Instructor, Los Angeles Unified School District

Robert Guernsey, Instructor, Sacramento City Unified School District

Kamilah Jackson, Instructor, Los Angeles Unified School District

Linh Tran, Instructor, Sacramento City Unified School District

BF | California Career Technical Education Model Curriculum Standards34


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35

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36

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37Published January 2017

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Documents

CTE Model Curr Stds: Business and Finance - Standards and