2025 Family and Consumer Sciences

Mississippi Administrative Code

Section: 7-77

Jurisdiction: MS

Bluebook Citation: 7 Miss. Admin. Code Pt. 77

Title 7: Education K-12 Part 77: 2025 Family and Consumer Sciences

2025 Family and Consumer Sciences Program CIP: 19.9999 – Family and Consumer Sciences Direct inquiries to: Project Manager Research and Curriculum Unit P.O. Drawer DX Mississippi State, MS 39762 662.325.2510 [email protected]

Program Supervisor Office of Career and Technical Education Mississippi Department of Education P.O. Box 771 Jackson, MS 39205 601.359.3974

Published by: Office of Career and Technical Education Mississippi Department of Education Jackson, MS 39205

Research and Curriculum Unit Mississippi State University Mississippi State, MS 39762

The Research and Curriculum Unit (RCU), located in Starkville, as part of Mississippi State University (MSU), was established to foster educational enhancements and innovations. In keeping with the land-grant mission of MSU, the RCU is dedicated to improving the quality of life for Mississippians. The RCU enhances intellectual and professional development of Mississippi students and educators while applying knowledge and educational research to the lives of the people of the state. The RCU works within the contexts of curriculum development and revision, research, assessment, professional development, and industrial training.

Table of Contents Acknowledgments .......................................................................................................................4 Standards ....................................................................................................................................5 Preface ........................................................................................................................................6 Mississippi Teacher Professional Resources ................................................................................7 Executive Summary ....................................................................................................................8 Course Outlines......................................................................................................................... 10 Career Pathway Outlook ........................................................................................................... 12 Professional Organizations ........................................................................................................ 16 Using This Document ............................................................................................................... 17 Family Dynamics ..................................................................................................................... 18 Unit 1: Orientation .................................................................................................................... 18 Unit 2: Discovering You ........................................................................................................... 19 Unit 3: Discovering Relationships ............................................................................................. 20 Unit 4: Discovering Family Growth .......................................................................................... 21 Unit 5: Careers Related to Family Dynamics ............................................................................. 22 Student Competency Profile: Family Dynamics ........................................................................ 23 Nutrition and Wellness ........................................................................................................... 24 Unit 1: Orientation and Lab Safety ............................................................................................ 24 Unit 2: Meal Planning and Preparation ...................................................................................... 25 Unit 3: Science of Food and Food Production ........................................................................... 26 Unit 4: Exercise and Diet .......................................................................................................... 27 Unit 5: Careers Related to Nutrition and Wellness ..................................................................... 28 Student Competency Profile: Nutrition and Wellness ................................................................ 29 Child Development .................................................................................................................. 31 Unit 1: Orientation .................................................................................................................... 31 Unit 2: Considerations for Parenthood ....................................................................................... 32 Unit 3: Child Growth and Development .................................................................................... 33 Unit 4: Behavior Guidance for Children .................................................................................... 34 Unit 5: Careers Related to Child Development .......................................................................... 35 Student Competency Profile: Child Development ...................................................................... 36 Resource Management ............................................................................................................ 37 Unit 1: Orientation .................................................................................................................... 37 2

Unit 2: Developing Decision-Making Skills .............................................................................. 38 Unit 3: Managing Personal Finances ......................................................................................... 39 Unit 4: Protecting the Role of the Consumer ............................................................................. 40 Unit 5: Careers Related to Resource Management ..................................................................... 41 Student Competency Profile: Resource Management................................................................. 42 Appendix A-1: Industry Standards: Family Dynamics ............................................................... 43 Appendix A-2: Industry Standards: Nutrition and Wellness ....................................................... 45 Appendix A-3: Industry Standards: Child Development ............................................................ 47 Appendix A-4: Industry Standards: Resource Management ....................................................... 49 Appendix B: 21st Century Skills ............................................................................................... 51 Appendix C: International Society for Technology in Education Standards (ISTE).................... 53 Appendix D: College and Career Ready Standards – English Language Arts............................. 55 Appendix E: College and Career Ready Standards – Mathematics ............................................. 69

Acknowledgments The Family and Consumer Sciences Curriculum was presented to the Mississippi Board of Education on January 16, 2025. The following persons were serving on the state board at the time: Dr. Lance Evans, State Superintendent of Education, Executive Secretary Mr. Glen East, Chair Mr. Matt Miller, Vice-Chair Dr. Ronnie McGehee Mr. Bill Jacobs Mr. Mike Pruitt Ms. Mary Werner Dr. Wendi Barrett Ms. Billye Jean Stroud Mr. Matt Mayo Ms. Kate Riddle, Student Representative Mr. Crosby Parker, Student Representative The following Mississippi Department of Education (MDE) and RCU managers and specialists assisted in the development of the family and consumer sciences curriculum: Brett Robinson, the associate state superintendent of the MDE Office of Career and Technical Education (CTE) and Workforce Development, supported the RCU and teachers throughout the development of the framework and supporting materials. Betsey Smith, the director of the RCU, supported RCU staff and teachers throughout the development of this framework and supporting materials. Susan Shedd, Family and Consumer Sciences program supervisor of the MDE office of CTE, supported the RCU and teachers throughout the development of this framework and supporting materials. Courtney McCubbins, the curriculum and assessment manager of the RCU, supported RCU staff and teachers throughout the development of this framework and supporting materials. Katherine Hancock, a project manager with the RCU, researched and co-authored this framework. Special thanks are extended to the educators who contributed to the development and revision of this framework and supporting materials: Demetria Brown, Long Beach High School, Long Beach Mandy Herrington, Pelahatchie High School, Pelahatchie Angel Fason, Human Development and Family Science, Mississippi State University Angel Pilcher, Center Hill High School, Olive Branch

Standards Standards and alignment crosswalks are referenced in the appendices. Depending on the curriculum, these crosswalks should identify alignment to the standards mentioned below, as well as possible related academic topics as required in the Subject Area Testing Program in Algebra I, Biology I, English II, and U.S. History from 1877, which could be integrated into the content of the units. Mississippi’s CTE Family and Consumer Sciences curriculum is aligned to the following standards: Family and Consumer Sciences Education National Standards (Copyright © 2018-2028) The Family and Consumer Sciences Education National were developed by the National Association of State Administrators of Family and Consumer Sciences (NASAFACS)— aafcs.org/credentialing-center/pre-pac/assessment-alignment. International Society for Technology in Education Standards (ISTE) Reprinted with permission from ISTE Standards for Students (2016). All rights reserved. Permission does not constitute an endorsement by ISTE (iste.org). College- and Career-Readiness Standards College- and career-readiness standards emphasize critical thinking, teamwork, and problemsolving skills. Students will learn the skills and abilities demanded by the workforce of today and the future. Mississippi adopted Mississippi College- and Career-Readiness Standards (MCCRS) to provide a consistent, clear understanding of what students are expected to learn and so teachers and parents know what they need to do to help them. mdek12.org/oae/college-and-career-readiness-standards Framework for 21st Century Learning In defining 21st-century learning, the Partnership for 21st Century Skills has embraced key themes and skill areas that represent the essential knowledge for the 21st century: global awareness; financial, economic, business, and entrepreneurial literacy; civic literacy; health literacy; environmental literacy; learning and innovation skills; information, media, and technology skills; and life and career skills. battelleforkids.org/networks/p21/frameworks-resources

Preface Secondary CTE programs in Mississippi face many challenges resulting from sweeping educational reforms at the national and state levels. Schools and teachers are increasingly being held accountable for providing applied learning activities to every student in the classroom. This accountability is measured through increased requirements for mastery and attainment of competency as documented through both formative and summative assessments. This document provides information, tools, and solutions that will aid students, teachers, and schools in creating and implementing applied, interactive, and innovative lessons. Through best practices, alignment with national standards and certifications, community partnerships, and a hands-on, studentcentered concept, educators will be able to truly engage students in meaningful and collaborative learning opportunities. The courses in this document reflect the statutory requirements as found in Section 37-3-49, Mississippi Code of 1972, as amended (Section 37-3-46). In addition, this curriculum reflects guidelines imposed by federal and state mandates (Laws, 1988, Ch. 487, §14; Laws, 1991, Ch. 423, §1; Laws, 1992, Ch. 519, §4 eff. from and after July 1, 1992; Strengthening Career and Technical Education for the 21st Century Act, 2019 [Perkins V]; and Every Student Succeeds Act, 2015).

Mississippi Teacher Professional Resources The following are resources for Mississippi teachers: Curriculum, Assessment, Professional Learning Program resources can be found at the RCU’s website, rcu.msstate.edu. Learning Management System: An Online Resource Learning management system information can be found at the RCU’s website, under Professional Learning. Should you need additional instructions, contact the RCU at 662.325.2510 or [email protected].

Executive Summary Pathway Description Family and Consumer Sciences (FCS) education in Mississippi consists of the CORE program and specific career and technical programs. The CORE program prepares students for living in the real world and helps them develop leadership, problem-solving, decision-making, criticalthinking, communication, computer, and mathematical skills. The specific career and technical programs focus on career exploration and gaining the skills in a specific profession for entrylevel employment or the continuation of education. FCS education enhances its students' leadership potential and essential life skills and encourages life-long learning. College, Career, and Certifications FCS Education National Standards Copyright © 2018-2028 developed by NASAFACS. aafcs.org/credentialing-center/pre-pac/assessment-alignment Grade Level and Class Size Recommendations It is recommended that students enter this program as a 9th or 10th grader. Exceptions to this are a district-level decision based on class size, enrollment numbers, student maturity, and CTE delivery method. This is a hands-on, lab- or shop-based course. Therefore, a maximum of 15 students is recommended per class with only one class with the teacher at a time. Student Prerequisites For students to experience success in the program, the following student prerequisites are suggested: 1. C or higher in English (the previous year) 2. C or higher in high school-level math (last course taken or the instructor can specify the level of math instruction needed) 3. Instructor approval and TABE reading score (eighth grade or higher) or 1. TABE reading and math score (eighth grade or higher) 2. Instructor approval or 1. Instructor approval Assessment The latest assessment blueprint for the curriculum can be found at: rcu.msstate.edu/curriculum. Applied Academic Credit The latest academic credit information can be found at: mdek12.org/ESE/Approved-Course-for-the-Secondary-Schools.

Teacher Licensure The latest teacher licensure information can be found at: mdek12.org/oel/apply-for-an-educator-license. Professional Learning If you have specific questions about the content of any of training sessions provided, please contact the RCU at 662.325.2510 or [email protected].

Course Outlines Option 1—Four half-Carnegie Unit Courses This curriculum consists of four half-credit courses that should be completed in the following sequence: 1. 2. 3. 4.

Family Dynamics—Course Code: 20.0121 Nutrition and Wellness—Course Code: 20.0130 Child Development—Course Code: 20.0122 Resource Management—Course Code: 20.0129

Course Description: Family Dynamics Family Dynamics is a course that focuses on developing skills related to personal, family, and social issues. It includes instruction in dimensions of adolescent development, family decisions and responsibilities, social decisions and responsibilities, and management of family systems today. (Grades 9–12, 1 Semester, 0.5 Carnegie Unit) Course Description: Nutrition and Wellness Nutrition and Wellness is a course designed to help develop skills related to proper nutrition and the concept of overall wellness. It includes instruction in nutrition, exercise and diet, healthy food choices, meal preparation, and components for a healthy lifestyle. (Grades 9–12, 1 Semester, 0.5 Carnegie Unit) Course Description: Child Development Child Development is a course centered on developing skills related to physical, social, intellectual, and emotional development of the child. It includes instruction on considerations for parenthood, prenatal care, child growth and development, behavior management, the needs of exceptional children, and career opportunities. (Grades 9–12, 1 Semester, 0.5 Carnegie Unit) Course Description: Resource Management Resource Management is a course that addresses the identification and management of personal resources and family finances to meet the needs and wants of individuals and families throughout the family life cycle, considering a broad range of economic, social, cultural, technological, environmental, and maintenance factors. (Grades 9–12, 1 Semester, 0.5 Carnegie Unit) Family Dynamics—Course Code: 20.0121 Unit Unit Name Number 1 Orientation 2 Discovering You 3 Discovering Relationships 4 Discovering Family Growth 5 Careers Related to Family Dynamics Total

Hours 1 22 20 20 7 70

Nutrition and Wellness—Course Code: 20.0130 Unit Unit Name Number 1 Orientation and Lab Safety 2 Meal Planning and Preparation 3 Science of Food and Food Production 4 Exercise and Diet 5 Careers Related to Nutrition and Wellness Total

Hours 15 30 12 8 5 70

Child Development—Course Code: 20.0122 Unit Unit Name Number 1 Orientation 2 Considerations for Parenthood 3 Child Growth and Development 4 Behavior Guidance for Children 5 Careers Related to Child Development Total

Hours 1 13 30 15 11 70

Resource Management—Course Code: 20.0129 Unit Unit Name Number 1 Orientation 2 Developing Decision-Making Skills 3 Managing Personal Finances 4 Protecting the Role of the Consumer 5 Careers Related to Resource Management Total

Hours 1 12 46 7 4 70

Career Pathway Outlook Overview The Family and Consumer Sciences program presents careers related to family dynamics, nutrition and wellness, child development, and resource management. Students enrolled in this course will develop essential employability and leadership skills. Upon completion of this course, they will develop a professional resume and will have honed their interviewing skills. It prioritizes professional development, punctuality, and workplace behavioral etiquette. Some topics include pregnancy and childbirth, toddler development, meeting an exceptional child’s needs, and developing strategic plans for misbehavior, family crises, and stress. Other topics explored are relationships and personal growth, basic first aid, safe work habits, nutritional quality, food safety, preparation and preservation, personal fitness, and physical and mental wellness. It teaches students how to implement intervention skills and enact preventive measures when supporting individuals who may be at risk of certain crises, such as child mistreatment, domestic violence, and housing or food instability. The course examines financial management, including budgeting, expenses, improving credit rating, and taxes. Also, ethical discussions involving identity protection and consumer rights are highlighted. Workplaces that family and consumer science professionals may occupy include colleges and universities, government agencies, hospitals and healthcare settings, offices, private research groups, product manufacturers (conducting product testing or development), restaurants, schools, and community and social service agencies. A childcare professional, for example, may even care for children in a converted segment of their own home. Most careers related to this program require at least a high school diploma, although careers with the highest earning potential—family and consumer sciences educators, registered dietitians, financial planners, marriage and family therapists, human development specialists, postsecondary teachers, and social workers, for example—require advanced degrees. Particularly, social workers develop critical thinking skills when utilizing math and general statistics in their careers. They will encounter topics including correlation, causation, sample sizes, selecting test groups, accuracy, and precision as they advance toward a college degree. Needs of the Future Workforce The U.S. Bureau of Labor and Statistics stated in 2021 that nearly 67% of workers with a family and consumer sciences (FCS) degree were employed in educational instruction and library occupations, management occupations, office and administrative support occupations, community and social service occupations, and business and financial operations occupations. Nationally, through 2032, some of the top twenty fastest-growing careers are nurse practitioners (45%), medical and health services managers (28%), physical therapist assistants (26%), occupational therapy assistants (24%), home health and personal care aides (22%), and personal care and service workers (21%). Also, in terms of growth rate, the top four FCS-specific occupational fields are: social workers (7%), registered nurses (6%), post-secondary teachers (4%), and managers (3%). Concerning job growth specific to social work, these consecutive fields involve child, family, and school social workers (49%), healthcare social workers (26%), mental health and substance abuse social workers (16%), and all other social workers (9%). The largest employers of social workers are individual and family services, ambulatory healthcare 12

services, local or state government, and state, local or private hospitals. These professionals maintain case history records and prepare reports. They also interview clients both individually and in groups to assess their situational or capability needs. The patterns of job growth shown below in Table 1.1 are connected to a relevant range of occupations. Table 1.1: Current and Projected Occupation Report Description Jobs, Projected Change Change Average Hourly 2020 Jobs, 2030 (Number) (Percent) Earnings, 2023 Accountants and 6,490 6,880 390 6% $32.71 Auditors Bakers 830 1,020 190 22.9% $12.69 Budget Analysts 460 480 20 4.3% $34.68 Chefs and Head Cooks 320 390 70 21.9% $19.37 Child, Family, and 3,350 3,600 250 7.5% $18.58 School Social Workers Early Childhood 7,160 7,900 740 10.3% $10.30 Professionals Community and Social 780 910 130 16.7% $18.45 Service Specialists, All Other Court, Municipal, and 2,350 2,570 220 9.4% $17.40 License Clerks Diagnostic Medical 680 800 120 17.6% $31.94 Sonographers Dietitians and 730 850 120 16.4% $24.59 Nutritionists Education, Training, and 240 250 10 4.2% $23.15 Library Workers Educational, Guidance, 2,370 2,690 320 13.5% $24.45 School, and Vocational Counselors Emergency Management 140 150 10 7.1% $24.48 Directors Family Medicine 940 1,100 160 17% $110.84 Physicians Farm and Home 90 100 10 11.1% $35.72 Management Advisors First-Line Supervisors of 1,810 2,150 340 18.8% $17.65 Housekeeping and Janitorial Workers Fitness Trainers and 1,400 1,620 220 15.7% $19.18 Aerobics Instructors Hairdressers, 1,950 1,950 0 0% $14.27 Hairstylists, and Cosmetologists Health Educators 770 880 110 14.3% $22.31 13

Healthcare Social 1,670 2,030 360 21.6% Workers Home Health and 19,130 25,200 6,070 31.7% Personal Care Aides Legal Occupations 6,440 6,870 430 6.7% Maids and 8,650 9,770 1,120 12.9% Housekeeping Cleaners Marriage and Family 130 150 20 15.4% Therapists Personal Care and 25,420 29,160 3,740 14.7% Service Occupations Personal Financial 870 920 50 5.7% Advisors Pharmacy Technicians 3,600 4,200 600 16.7% Physical Therapist 850 1,090 240 28.2% Assistants Preschool Teachers 2,490 2,960 470 18.9% Recreational Therapists 210 220 10 4.8% Registered Nurses 29,270 33,220 3,950 13.5% Rehabilitation 570 620 50 8.8% Counselors Social Workers 580 600 20 3.4% Speech-Language 1,410 1,810 400 28.4% Pathologists Substance Abuse, 1,960 2,300 340 17.3% Behavioral Disorder, and Mental Health Counselors Tailors, Dressmakers, 240 240 0 0% and Custom Sewers Source: Mississippi Department of Employment Security; mdes.ms.gov (2023).

$26.33 $11.13 $37.35 $10.82 $18.64 $14.42 $44.65 $16.79 $29.46 $13.23 $18.59 $32.66 $18.52 $29.95 $35.93 $22.00

$13.59

Perkins V Requirements and Academic Infusion The FCS curriculum meets Perkins V requirements of introducing students to and preparing them for high-skill, high-wage occupations in FCS fields. It also offers students a program of study, including secondary, postsecondary, and institutions of higher learning courses, that will further prepare them for careers in Family and Consumer Science. Additionally, this curriculum is integrated with academic college- and career-readiness standards. Lastly, it focuses on ongoing and meaningful professional development for teachers as well as relationships with industry. Transition to Postsecondary Education The latest articulation information for secondary to postsecondary can be found at the Mississippi Community College Board website, mccb.edu.

Best Practices Innovative Instructional Technologies Classrooms should be equipped with tools that will teach today’s digital learners through applicable and modern practices. The FCS educator’s goal should be to include teaching strategies that incorporate current technology. To make use of the latest online communication tools—wikis, blogs, podcasts, and social media platforms, for example—the classroom teacher is encouraged to use a learning management system that introduces students to education in an online environment and places more of the responsibility of learning on the student. Differentiated Instruction Students learn in a variety of ways, and numerous factors—students’ background, emotional health, and circumstances, for example—create unique learners. By providing various teaching and assessment strategies, students with various learning preferences can have more opportunities to succeed. CTE Student Organizations Teachers should investigate opportunities to sponsor a student organization. Family, Career, and Community Leaders of America (FCCLA) is the recommended student organization with many outlets for FCS. Student organizations provide participants and members with growth opportunities and competitive events. They also open the doors to the world of family and consumer science careers and scholarship opportunities. Cooperative Learning Cooperative learning can help students understand topics when independent learning cannot. Therefore, you will see several opportunities in the FCS curriculum for group work. To function in today’s workforce, students need to be able to work collaboratively with others and solve problems without excessive conflict. The FCS curriculum provides opportunities for students to work together and help each other complete complex tasks. There are many field experiences within the FCS curriculum that will allow and encourage collaboration with professionals currently in the family and consumer science field.

Title 7: Education K-12 Part 77: 2025 Family and Consumer Sciences

Professional Organizations American Culinary Federation acfchefs.org Association of Career and Technical Education acteonline.org American Association of Family and Consumer Sciences aafcs.org/ Family, Career and Community Leaders of America (FCCLA) National Headquarters fcclainc.org International Society for Technology in Education iste.org Mississippi FCCLA mdek12.org/cte/so/fccla Mississippi HOSA mdek12.org/cte/so/hosa National Association for the Education of Young Children naeyc.org

Using This Document Competencies and Suggested Objectives A competency represents a general concept or performance that students are expected to master as a requirement for satisfactorily completing a unit. Students will be expected to receive instruction on all competencies. The suggested objectives represent the enabling and supporting knowledge and performances that will indicate mastery of the competency at the course level. Teacher Resources All teachers should request to be added to the Canvas Resource Guide for their course. For questions or to be added to the guide, send a Help Desk ticket to the RCU by emailing [email protected]. Perkins V Quality Indicators and Enrichment Material Some of the units may include an enrichment section at the end. This material will greatly enhance the learning experiences of students. If the FCS program is using a national certification, work-based learning, or another measure of accountability that aligns with Perkins V as a quality indicator, this material could very well be assessed on that quality indicator. It is the responsibility of the teacher to ensure all competencies for the selected quality indicator are covered throughout the year.

Family Dynamics Unit 1: Orientation Competencies and Suggested Objectives 1. Describe local high school or career and technical center policies and procedures, including dress code, attendance, academic requirements, discipline, and transportation regulations. DOK1

a. Introduce students to the course, discussing its importance and how it relates to the other courses in the curriculum. b. Students take the safety test for this course, with 100% mastery required for all students. 2. Explore the leadership skills and personal development opportunities provided to students by student organizations, including Family, Career, and Community Leaders of America (FCCLA). DOK1. a. Demonstrate effective team building and leadership skills. b. Identify the motto, creed, and pledge, and discuss their meanings. Note: This unit will be ongoing throughout the year. Time allotted for this unit will be distributed over the entire year.

Unit 2: Discovering You Competencies and Suggested Objectives 1. Explore personality development in relation to oneself and others. DOK2 a. Identify forces that shape personality development, including personality traits, heredity, and environment. b. Explain how self-concept influences a person’s behavior and relationships with others. c. Create a list of ways to improve self-esteem. 2. Identify personal traits that build character. DOK2 a. Describe positive character traits such as honesty, self-discipline, responsibility, compassion, motivation, and perseverance. b. Explain how a person’s character is revealed by his or her behavior. c. Create a list of responsibilities that help teenagers to become responsible adults. 3. Describe the role of decision-making in setting and attaining goals. DOK3 a. Recognize the importance of setting and attaining goals. b. Define short and long-range goals. c. List the steps in the decision-making process. d. Design the goals and strategies for reaching one’s potential. 4. Demonstrate the ability to achieve an appropriate balance between self-expression and the practical use of the physical and aesthetic components related to basic human needs (e.g., self-care, clothing, etc.). DOK3 a. Distinguish between appropriate clothing fitting to certain occasions and/or weather (e.g., pants worn during winter, tie worn to interviews). b. Discover the practical skills that contribute to self-care (e.g. tying a tie, sewing a button, basic ironing).

Unit 3: Discovering Relationships Competencies and Suggested Objectives 1. Compare and contrast communication techniques. DOK3 a. Explore communication with sensitivity to anti-biases such as gender, equity, age, culture, and ethnicity. b. Discuss social etiquette/netiquette and the dangers and consequences of technology usage, addressing unrealistic expectations for a mate furthered by the influence of social media (e.g., TikTok, Instagram, Snapchat). c. Identify the types of communication (e.g., verbal, nonverbal, etc.). d. Demonstrate positive approaches to communication (e.g., “I” messages vs. “You” messages). 2. Identify types of peer relationships and expectations. DOK2 a. Describe the qualities of friendship. b. Identify ways to maintain and improve friendships. c. Evaluate techniques for effectively dealing with peer pressure. d. Analyze ways to build peer relationships. 3. Recognize the functions of dating. DOK2 a. Identify patterns in a dating relationship. b. Discuss challenges associated with dating. c. Practice interpersonal skills related to dating. d. Explore the advantages of delayed dating. 4. Explore the concepts of love and commitment. DOK2 a. Discuss misconceptions regarding love and commitment. b. Identify factors to consider in selecting a partner. c. Describe issues that should be discussed before commitment. d. Specify factors that contribute to a successful marriage. e. Practice decision-making skills needed in a marital relationship related to topics such as budget, recreation, housing, other friends, and children. f. Explore patterns of adjustment (e.g., interpersonal, social, and financial). Note: Check to see if your district chose abstinence-only or abstinence-plus (Mississippi Code §37-13-171-).

Unit 4: Discovering Family Growth Competencies and Suggested Objectives 1. Examine the criteria for creating a family. DOK3 a. Identify issues that should be discussed before starting a family, including physical, social, emotional, financial, and legal responsibilities. b. Explain the impact of parenting on a person’s life goals. c. Create a sample budget for a given family size. 2. Evaluate the dynamics involved in preserving the family as a unit. DOK2. a. Describe all stages of the family system. b. Explain the functions of a family, including nurturing, economic, social, and intellectual support. c. Analyze factors that make strong families, including commitment, communication, and decision-making. d. Describe a successful family support system and its value. 3. Develop coping techniques for individuals dealing with crises in the family. DOK3 a. Define the types of crises that families face. b. Locate resources that assist individuals and families in crisis situations. c. Identify appropriate solutions for individuals in family crises. d. Develop a family and individual crisis stress management plan. 4. Examine factors for balancing work and family. DOK2 a. Explain how attitudes about who does the work in a family have changed over the years. b. Summarize ways in which jobs affect family life and vice versa. c. Practice prioritizing self-care amidst work, school, and family life. 5. Explore the aspects of domestic/intimate partner violence. DOK1 a. Identify types of domestic/intimate partner violence. b. Discuss warning signs of violence. c. Identify preventive measures and intervention skills.

Unit 5: Careers Related to Family Dynamics Competencies and Suggested Objectives 1. Describe employment opportunities and responsibilities related to Family Dynamics. DOK1 a. Analyze potential earnings, employee benefits, job availabilities, working conditions, educational requirements, required technology skills, and continuing education/training for careers, including teacher, family counselor, or youth director. b. Discuss résumé development. c. Demonstrate interview skills (e.g., dress, professionalism, punctuality, etc.). d. Describe how proper etiquette and social skills improve employability. e. Specify basic employee responsibilities and appropriate work ethics. f. Define effective relationship skills and workplace issues, including, but not limited to, sexual harassment, bullying, stress, and substance abuse. g. Demonstrate 21st-century skills such as critical thinking, problem-solving, collaboration, flexibility, and other professional skills related to a career in Family Dynamics.

Student Competency Profile : Family Dynamics Student’s Name: ___________________________________________ This record is intended to serve as a method of noting student achievement of the competencies in each unit. It can be duplicated for each student, and it can serve as a cumulative record of competencies achieved in the course. In the blank before each competency, place the date on which the student mastered the competency. Unit 1: Orientation 1. Describe local high school or career and technical center policies and procedures, including dress code, attendance, academic requirements, discipline, and transportation regulations. 2. Explore leadership skills and personal development opportunities provided to students by student organizations, including Family, Career, and Community Leaders of America (FCCLA). Unit 2: Discovering You 1. Explore personality development in relation to oneself and others. 2. Identify personal traits that build character. 3. Describe the role of decision-making in setting and attaining goals. 4. Demonstrate the ability to achieve an appropriate balance between self-expression and the practical use of the physical and aesthetic components related to basic human needs (e.g., self-care and clothing). Unit 3: Discovering Relationships 1. Compare and contrast communication techniques. 2. Identify types of peer relationships and expectations. 3. Recognize the functions of dating. 4. Explore the concepts of love and commitment. Unit 4: Discovering Family Growth 1. Examine the criteria for creating a family. 2. Evaluate the dynamics involved in preserving the family as a unit. 3. Develop coping techniques for individuals dealing with crises in the family. 4. Examine factors for balancing work and family. 5. Explore the aspects of domestic/intimate partner violence. Unit 5: Careers Related to Family Dynamics 1. Describe employment opportunities and responsibilities related to Family Dynamics.

Nutrition and Wellness Unit 1: Orientation and Lab Safety Competencies and Suggested Objectives 1. Describe local high school or career and technical center policies and procedures, including dress code, attendance, academic requirements, discipline, lab rules and regulations, and transportation regulations. DOK1 a. Introduce students to the course, discussing its importance and how it relates to the other courses in the curriculum. 2. Explore leadership skills and personal development opportunities provided to students by student organizations, including FCCLA. DOK1 a. Demonstrate effective team building and leadership skills. b. Practice appropriate work ethic. c. Identify the motto, creed, and pledge, and discuss their meanings. 3. Explain emergency techniques and procedures in the lab. DOK2 a. Describe and demonstrate basic first aid concepts and procedures for choking, cuts, burns, falls, strains, electrical shocks, and heart attacks. 4. Implement safe work habits to prevent injuries (ongoing throughout the course). DOK2 a. Identify the location and purpose of accident reports. b. List ways to use protective clothing and equipment to prevent injuries. c. Classify fire hazards that contribute to accidental fires and the extinguishers used for each type of fire. d. List hazards that contribute to injury due to slips, trips, or falls. e. Demonstrate the proper use of ladders, stepstools, etc. f. Demonstrate proper lifting and carrying procedures to avoid injury. g. Demonstrate the correct and safe use of knives, including handling, walking, passing, washing, and storing. h. Explain the safe use and care of kitchen equipment. i. Students take safety test for this course, with 100% mastery required for all students. 5. Evaluate procedures that preserve nutritional quality, sanitation, and safety during food preparation (ongoing throughout the course). DOK2 a. Identify major bacteria, viruses, and molds that cause food-borne illnesses. b. Describe how bacteria, viruses, and molds make food unsafe. c. Discuss steps to follow in handling and storing foods to protect nutritional quality, and food safety. d. Utilize sanitation rules and guidelines. e. Define cross-contamination and demonstrate methods that prevent food-borne illnesses. f. Identify the temperature danger zone. Note: Safety is to be taught as an ongoing part of the program. Students are required to complete a written safety test with 100% accuracy before entering the shop for lab simulations and projects. This test should be documented in each student’s file. Note: This unit will be ongoing throughout the year. Time allotted for this unit will be distributed over the entire year. 24

Unit 2: Meal Planning and Preparation Competencies and Suggested Objectives 1. Identify food preparation tools and equipment and their use. DOK1 a. Describe food preparation tools and equipment. b. Demonstrate the use of food preparation tools and equipment. 2. Demonstrate the proper procedures for measuring liquid and dry ingredients. DOK2 a. Apply proper procedures for measuring liquid and dry ingredients. b. Apply basic math skills to calculate conversions of measurements to equivalents. 3. Plan menus for individuals and groups. DOK3 a. Utilize current federal nutrition guidelines to identify appropriate portion sizes. b. Analyze existing menus for nutrition and acceptability. c. Considering various factors, develop menus for individuals and groups. 4. Apply acceptable food purchasing guidelines. DOK3 a. Identify the steps to follow when purchasing food. b. Compare costs, services, and other factors among different types of food stores, including grocery stores, convenience stores, food cooperatives, warehouses, specialty stores, and government distribution agencies (e.g., Supplemental Nutrition Assistance Program, Special Supplemental Nutrition Program for Women, Infants, and Children). c. Apply basic math skills to compute the cost of food per serving. d. Compare the costs and acceptability of commercially prepared foods versus homeprepared foods. 5. Prepare and critique food products. DOK4 a. Interpret recipe terminology and the importance of preparation. b. Prepare/critique food products using regular and low-fat recipes, two or more cooking methods, and compare convenience versus scratch methods. 6. Select and prepare a sampling of various ethnic foods. DOK3 a. Explain how religion, education, and family values affect food choices. b. Demonstrate food preparation techniques that are unique to certain regions. c. Discuss cooking methods from various regions of the world. 7. Describe the common forms of food preservation. DOK1 a. Explain the different methods of freezing food. b. Demonstrate the various methods of home canning. c. Discuss ways to dehydrate foods. d. Identify methods of commercial food preservation. 8. Demonstrate proper social etiquette. DOK2 a. Discuss table service, including formal and informal service. b. Demonstrate basic table-setting techniques. c. Demonstrate proper table manners.

Unit 3: Science of Food and Food Production Competencies and Suggested Scenarios 1. Explain the connection between nutrition and wellness. DOK2 a. Differentiate between nutrition and wellness. b. Discover how healthy food choices influence wellness. 2. Describe the classes and respective functions of nutrients. DOK3 a. Identify the six major classes of nutrients, their respective functions, and examples of each. b. Distinguish between organic and inorganic nutrients. c. Distinguish between fat-soluble and water-soluble vitamins. d. Describe the proper use of nonfood sources of nutrients. e. Distinguish between saturated and unsaturated fatty acids. f. Examine and interpret food labels for nutritional content. 3. Explain the processes of digestion, absorption, and metabolism. DOK2 a. Identify the organs involved in digestion. b. Describe the stages of digestion. c. Explain the process of absorption. 4. Discover the processes involved in food production. DOK2 a. Discuss the government agencies responsible for assuring the safety of the food supply (e.g., U.S. Department of Agriculture, Food and Drug Administration). b. Identify and contrast the roles of the USDA and the FDA. c. Identify factors that affect the food supply chain. d. Discuss current topics related to food access (e.g., food insecurity, food deserts).

Unit 4: Exercise and Diet Competencies and Suggested Objectives 1. Understand the role of energy in well-being and performance. DOK1 a. Determine the energy needs necessary to maintain optimal health. b. Explain the factors that increase or decrease body energy usage. 2. Describe the effects of body weight on overall wellness. DOK2 a. Define terms related to body weight, including ideal body weight, overweight, obesity, underweight, and body types. b. Analyze factors that affect body weight. • Physical (e.g., malnutrition, illness, exercise, etc.) • Emotional/psychological (e.g., eating disorders) • Hereditary factors (e.g., thyroid issues, obesity, fat disposition, etc.) c. Analyze the effects of social media on self-image and self-perception (e.g., body dysmorphia). d. Analyze factors that affect body weight. e. Describe the use of body composition evaluations, including a height/weight chart, body circumference, skinfold, and medical/laboratory methods. 3. Evaluate methods of weight control. DOK3 a. Discuss the roles of diet and physical activity as keys to weight control. b. Evaluate whether a weight loss or weight gain program is nutritionally sound and effective (e.g., fad diets). c. Discuss the effectiveness of various medications in weight control. 4. Describe the relationship between personal fitness and various health risk factors. DOK2 a. Explain terms related to personal fitness, including health, wellness, functional health, physically active lifestyle, and sedentary lifestyle. b. Differentiate between exercise and physical fitness. c. Identify health risk factors, including age, heredity, gender, smoking, hypertension, high cholesterol, diabetes, stress, and obesity, and evaluate their effect on diseases such as cardiovascular disease, hypertension, cancer, and diabetes.

Unit 5: Careers Related to Nutrition and Wellness Competencies and Suggested Objectives 1. Describe the role of decision-making in setting and attaining goals related to nutrition and wellness. DOK1 a. Recognize the importance of setting and attaining goals. b. Define short and long-range goals. c. List the steps in the decision-making process. d. Develop strategies for reaching one’s goals. 2. Describe employment opportunities and responsibilities related to Nutrition and Wellness. DOK1

a. Analyze potential earnings, employee benefits, job availability, working conditions, educational requirements, required technology skills, and continuing education/training for careers including culinary teacher, chef/sous chef, nutritionist, food sciences researcher, and agricultural careers. b. Discuss résumé development. c. Demonstrate interview skills (e.g., dress, professionalism, punctuality, etc.). d. Describe how proper etiquette and social skills improve employability. e. Specify basic employee responsibilities and appropriate work ethics. f. Define effective relationship skills. g. Examine workplace issues, including, but not limited to, sexual harassment, bullying, stress, and substance abuse. h. Demonstrate 21st-century skills such as critical thinking, problem-solving, collaboration, flexibility, and other professional skills related to a career in Nutrition and Wellness.

Student Competency Profile : Nutrition and Wellness Student’s Name: ___________________________________________ This record is intended to serve as a method of noting student achievement of the competencies in each unit. It can be duplicated for each student, and it can serve as a cumulative record of competencies achieved in the course. In the blank before each competency, place the date on which the student mastered the competency. Unit 1: Orientation and Lab Safety 1. Describe local high school or career and technical center policies and procedures, including dress code, attendance, academic requirements, discipline, lab rules and regulations, and transportation regulations. 2. Explore leadership skills and personal development opportunities provided to students by student organizations, including FCCLA. 3. Explain emergency techniques and procedures in the lab. 4.

Implement safe work habits to prevent injuries (ongoing throughout the course).

Evaluate procedures that preserve nutritional quality, sanitation, and safety during food preparation (ongoing throughout the course).

Unit 2: Meal Planning and Preparation 1. Identify food preparation tools and equipment and their use. 2.

Demonstrate the proper procedures for measuring liquid and dry ingredients.

Plan menus for individuals and groups.

Apply acceptable food purchasing guidelines.

Prepare and critique food products.

Select and prepare a sampling of various ethnic foods.

Describe the common forms of food preservation.

Demonstrate proper social etiquette.

Unit 3: Science of Food and Food Production 1. Explain the connection between nutrition and wellness. 2.

Describe the classes and respective functions of nutrients.

Explain the processes of digestion, absorption, and metabolism.

Discover the processes involved in food production.

Unit 4: Exercise and Diet 1. Understand the role of energy in well-being and performance. 2.

Describe the effects of body weight on overall wellness.

Evaluate methods of weight control. 29

Describe the relationship between personal fitness and various health risk factors.

Unit 5: Careers Related to Nutrition and Wellness 1. Describe the role of decision-making in setting and attaining goals related to nutrition and wellness. 2. Describe employment opportunities and responsibilities related to Nutrition and Wellness.

Child Development Unit 1: Orientation Competencies and Suggested Objectives 1. Describe local high school or career and technical center policies and procedures, including dress code, attendance, academic requirements, discipline, and transportation regulations. DOK1.

a. Introduce students to the course, discussing its importance and how it relates to the other courses in the curriculum. b. Students take safety test for this course, with 100% mastery required for all students. 2. Explore leadership skills and personal development opportunities provided to students by student organizations, including FCCLA. DOK1 a. Demonstrate effective team building and leadership skills. b. Practice appropriate work ethic. c. Identify the motto, creed, and pledge, and discuss their meanings. Note: This unit will be ongoing throughout the year. Time allotted for this unit will be distributed over the entire year.

Unit 2: Considerations for Parenthood Competencies and Suggested Objectives 1. Evaluate the choices and consequences of decisions regarding parenthood. DOK2 a. Define abstinence. b. Summarize the symptoms, diagnosis, and treatment of sexually transmitted infections (STIs). c. List options for parenthood (e.g., adoption, fostering, in vitro fertilization, guardianship). 2. Discuss considerations before parenting. DOK1 a. Identify issues that should be discussed before starting a family, including physical, social, emotional, financial, and legal responsibilities. b. Explain the impact of parenting on a person’s life goals. 3. Analyze the importance of good parenting. DOK2 a. Determine reasons to plan before parenthood. b. Describe the importance of responsible parenthood. Note: Check to see if your district chose abstinence-only or abstinence-plus (Mississippi Code §37-13-171-).

Unit 3: Child Growth and Development Competencies and Suggested Objectives 1. Explain the stages of pregnancy and childbirth. DOK1 a. Explain conception. b. Identify signs of pregnancy. c. Discuss prenatal development. d. Identify the physical changes that occur for the mother during pregnancy (i.e., first, second, and third trimesters). e. Explain potential complications of pregnancy. f. Analyze the importance of good prenatal care for the mother and unborn child. g. Discuss the various types of childbirth and the options available to the mother. 2. Prepare for the care and development of infants. DOK2 a. Demonstrate basic care of infants. b. Discuss developmental milestones (i.e., physical, emotional, social, and intellectual). c. Explore how parents and caregivers meet needs, including nutrition, play, and self-help skills. 3. Prepare for the care and development of a toddler. DOK2 a. Describe basic care of toddlers. b. Discuss developmental milestones (i.e., physical, emotional, social, and intellectual). c. Explore how parents and caregivers meet needs, including nutrition, play, and self-help skills. 4. Prepare for the care and development of a preschooler. DOK2 a. Discuss developmental milestones (i.e., physical, emotional, social, and intellectual). b. Explore how parents and caregivers meet needs, including nutrition, play and, self-help skills. 5. Determine ways to meet the needs of an exceptional child. DOK2 a. Define the exceptional child. b. Describe the needs of exceptional children (e.g., children with special needs or gifted children). c. Explain how parents and other caregivers can assist, encourage, and advocate for exceptional children. d. Discover the resources available for parents of exceptional children (e.g., early intervention services, special education services).

Unit 4: Behavior Guidance for Children Competencies and Suggested Objectives 1. Analyze strategies for managing behavior. DOK2 a. Identify types of parenting styles. b. Define and differentiate guidance terms and strategies for managing behavior. c. Illustrate appropriate methods for guiding children’s behavior. 2. Demonstrate effective ways of dealing with misbehavior. DOK2 a. Discuss reasons for misbehavior in children. b. Demonstrate how to handle common child misbehavior such as temper tantrums, separation anxiety, sibling conflicts, and aggression/bullying. 3. Analyze methods of dealing with crises affecting parent-child relationships such as divorce, remarriage, stepparents, moving, death, and family crises. DOK2 4. Examine types of child abuse. DOK2 a. Identify types of child abuse and neglect. b. Summarize risk factors for child abuse and prevention strategies. c. Discuss child abuse intervention procedures. Enrichment Explore and identify the risks, protective factors, and prevention strategies for individuals with Adverse Childhood Experiences (ACEs). Students utilize various resources to identify their own potential ACEs and how they impact their overall health. DOK2

Unit 5: Careers Related to Child Development Competencies and Suggested Objectives 1. Discuss professional organization credentialing and state licensure for the various types of early childhood facilities. DOK1 a. Identify professional organizations in the early childhood industry. b. Discuss credentials required for positions in the early childhood industry. c. Identify licensure requirements for the state of Mississippi. 2. Explore career and job opportunities in the field of Child Development. DOK1 a. Identify competencies needed by caregiver personnel, including positive work habits and attitudes, good management skills, good communication skills, leadership skills, ethical behavior, and emotional maturity. b. Research careers in the early childhood field, including early childhood professionals, teachers, social workers, early interventionists, and child advocates. c. Demonstrate 21st-century skills such as critical thinking, problem-solving, collaboration, flexibility, and other professional skills related to a career in Child Development.

Student Competency Profile : Child Development Student’s Name: ___________________________________________ This record is intended to serve as a method of noting student achievement of the competencies in each unit. It can be duplicated for each student, and it can serve as a cumulative record of competencies achieved in the course. In the blank before each competency, place the date on which the student mastered the competency. Unit 1: Orientation 1. Describe local high school or career and technical center policies and procedures, including dress code, attendance, academic requirements, discipline, and transportation regulations. 2. Explore leadership skills and personal development opportunities provided for students by student organizations, including FCCLA. Unit 2: Considerations for Parenthood 1. Evaluate the choices and consequences of decisions regarding parenthood 2. Discuss considerations before parenting. 3. Analyze the importance of good parenting. Unit 3: Child Growth and Development 1. Explain the stages of pregnancy and childbirth. 2. Prepare for the care and development of infants. 3. Prepare for the care and development of a toddler. 4. Prepare for the care and development of a preschooler. 5. Determine ways to meet the needs of an exceptional child. Unit 4: Behavior Guidance for Children 1. Analyze strategies for managing behavior. 2. Demonstrate effective ways of dealing with misbehavior. 3. Analyze methods of dealing with crises affecting parent-child relationships, such as divorce, remarriage, stepparents, moving, death, and family crises. 4. Examine the types of child abuse. Unit 5: Career Related to Child Development 1. Discuss professional organization credentialing and state licensure for the various types of early childhood facilities. 2. Explore career and job opportunities related to Child Development.

Resource Management Unit 1: Orientation Competencies and Suggested Objectives 1. Describe local high school or career and technical center policies and procedures, including dress code, attendance, academic requirements, discipline, and transportation regulations. DOK1

a. Introduce students to the course, discussing its importance and how it relates to the other courses in the curriculum. b. Students take the safety test for this course, with 100% mastery required for all students. 2. Explore leadership skills and personal development opportunities provided for students by student organizations, including FCCLA. DOK1 a. Demonstrate effective team building and leadership skills. b. Practice appropriate work ethic. c. Identify the motto, creed, and/or pledge and discuss their meanings. Note: This unit will be ongoing throughout the year. Time allotted for this unit will be distributed over the entire year

Unit 2: Developing Decision -Making Skills Competencies and Suggested Objectives 1. Apply the decision-making process to personal financial decisions. DOK2 2. Evaluate and utilize available resources. DOK2 a. Define the difference between a human resource (i.e. skills, knowledge, and competencies of personnel) and a non-human resource (i.e. equipment and tools). b. Differentiate between renewable and non-renewable resources. c. Apply decision-making skills and goal planning to financial management and quality of life. d. Discuss educational opportunities and their financial obligations, including financial aid and student loans.

Unit 3: Managing Personal Finances Competencies and Suggested Objectives 1. Discover the different banking services. DOK2 a. Identify the types of financial institutions (e.g., banks, credit unions, loan companies, Payday lending). b. Describe the types of services offered by financial institutions. c. Simulate banking procedures (e.g., checking/debit, savings, online, etc.). d. Find and evaluate financial information from a variety of sources. 2. Employ a budget process to manage income and expenses. DOK4 a. List different sources of income. b. Interpret a paycheck and explain deductions. c. Recognize categories of fixed and variable expenses. d. Prepare, evaluate, and modify a budget. 3. Analyze the effective use of credit. DOK2 a. Distinguish among various types of credit, identifying costs and benefits. b. Evaluate different sources of credit and interest rates. c. Identify procedures for establishing and maintaining a good credit rating, including debt management and credit report review. d. Develop security precautions to protect personal information. 4. Analyze effective saving and investment practices. DOK2 a. Discuss how saving contributes to financial well-being. b. Compare and contrast various methods of saving and investing. c. Explain how investing builds wealth and helps meet financial goals. d. Evaluate investment alternatives and describe how to buy and sell investments. 5. Analyze the need and use of various types of insurance. DOK2 a. Distinguish among the types of life insurance. b. List health insurance coverage plans. c. Identify the basic types of automobile insurance coverage. d. Identify the types of property insurance. e. Discuss the procedures for filing insurance claims. 6. Distinguish among local, state, and federal tax assessments. DOK3 a. Discuss and compute local tax assessments. b. Compute state and federal income taxes.

Unit 4: Protecting the Role of the Consumer Competencies and Suggested Objectives 1. Identify a consumer’s rights and responsibilities and evaluate consumer information. DOK2 a. Simulate the role of the consumer in the marketplace. b. Discuss consumer choice, rights, and responsibilities. c. Summarize major consumer protection laws. d. Identify procedures for filing a consumer complaint, including contesting an incorrect billing statement. e. Interpret product labels, guarantees, and warranties. f. Describe the impact of advertising and evaluate advertising for truthfulness. g. Identify the impact of consumer decisions on the environment (e.g., buying local, fairtrade/ethically sourced). 2. Identify the different types and impact of identity theft. DOK2 a. Discover ways to safeguard against identity theft. b. Explain ways that the government can aid in consumer protection (e.g., Federal Trade Commission).

Unit 5: Careers Related to Resource Management Competencies and Suggested Objectives 1. Describe employment opportunities and responsibilities related to Resource Management. DOK1

a. Analyze potential earnings, employee benefits, job availability, working conditions, educational requirements, required technology skills, and continuing education/training for careers including bank tellers, loan officers, insurance agents, insurance adjusters, financial planners, entrepreneurs, and human resource managers. b. Discuss résumé development. c. Demonstrate interview skills (e.g., dress, professionalism, punctuality, etc.). d. Describe how proper etiquette and social skills improve employability. e. Specify basic employee responsibilities and appropriate work ethic. f. Define effective relationship skills and workplace issues including, but not limited to, sexual harassment, bullying, stress, and substance abuse. g. Demonstrate 21st-century skills such as critical thinking, problem-solving, collaboration, flexibility, and other professional skills related to Resource Management

Student Competency Profile : Resource Management Student’s Name: ___________________________________________ This record is intended to serve as a method of noting student achievement of the competencies in each unit. It can be duplicated for each student, and it can serve as a cumulative record of competencies achieved in the course. In the blank before each competency, place the date on which the student mastered the competency. Unit 1: Orientation 1. Describe local high school or career and technical center policies and procedures, including dress code, attendance, academic requirements, discipline, and transportation regulations. 2. Explore leadership skills and personal development opportunities provided for students by student organizations, including FCCLA. Unit 2: Developing Decision-Making Skills 1. Apply the decision-making process to personal financial decisions. 2. Evaluate and utilize available resources. Unit 3: Managing Personal Finances 1. Discover the different banking services. 2. Employ a budget process to manage income and expenses. 3. Analyze the effective use of credit. 4. Analyze effective saving and investment practices. 5. Analyze the need and use of various types of insurance. 6. Distinguish among local, state, and federal tax assessments. Unit 4: Protecting the Role of the Consumer 1. Identify a consumer’s rights and responsibilities and evaluate consumer information. 2. Identify the different types and impact of identity theft. Unit 5: Careers Related to Resource Management 1. Describe employment opportunities and responsibilities related to Resource Management.

Appendix A-1: Industry Standards : Family Dynamics Units

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

FCS 1 FCS2

X X

FCS3

FCS4

FCS5

X X

FCS6

FCS7

FCS8

X X

FCS9

FCS10

FCS11

FCS12 FCS13

FCS14

FCS3 FCS4 FCS5 FCS6 FCS7 FCS8 FCS9 FCS10 FCS11 FCS12 FCS13 FCS14 FCS15

X X

FCS16

FCS2

X X

FCS15

FCS1

CAREER, COMMUNITY, AND FAMILY CONNECTIONS Integrate multiple life roles and responsibilities in family, work, and community settings. CONSUMER AND FAMILY RESOURCES Evaluate management practices related to the human, economic, and environmental resources. CONSUMER SERVICES Integrate knowledge, skills, and practices required for careers in consumer services. EARLY CHILDHOOD, EDUCATION, AND SERVICES Integrate knowledge, skills, and practices required for careers in early childhood, education, and services. FACILITIES MANAGEMENT AND MAINTENANCE Integrate knowledge, skills, and practices required for careers in facilities management and maintenance. FAMILY Evaluate the significance of family and its impact on the well-being of individuals and society. FAMILY AND COMMUNITY SERVICES Integrate knowledge, skills, and practices required for careers in family and community services. FOOD PRODUCTION AND SERVICES Integrate knowledge, skills, and practices required for careers in food production and services. FOOD SCIENCE, DIETETICS, AND NUTRITION Integrate knowledge, skills, and practices required for careers in food science, dietetics, and nutrition. HOSPITALITY, TOURISM, AND RECREATION Integrate knowledge, skills, and practices required for careers in hospitality, tourism, and recreation. HOUSING, INTERIORS, AND FURNISHINGS Integrate knowledge, skills, and practices required for careers in housing, interiors, and furnishings. HUMAN DEVELOPMENT Analyze factors that impact human growth and development. INTERPERSONAL RELATIONSHIPS Demonstrate respectful and caring relationships in the family, workplace, and community. NUTRITION AND WELLNESS Demonstrate nutrition and wellness practices that enhance individual and family well-being. PARENTING

Evaluate the impact of parenting roles and responsibilities on strengthening the well-being of individuals and families. FCS16 TEXTILES AND APPAREL Integrate knowledge, skills, and practices required for careers in textiles and apparel.

Appendix A-2: Industry Standards: Nutrition and Wellness Units

Unit 1

Unit 2

Unit 3

Unit 4

Unit FCS2 FCS3

X X

X X X

FCS4 FCS5

X X

X X X

X X

FCS6 FCS7 FCS8 FCS9 FCS10 FCS11 FCS12 FCS13 FCS14 FCS15 FCS16

FCS1 FCS2 FCS3 FCS4 FCS5 FCS6 FCS7 FCS8 FCS9 FCS10 FCS11 FCS12 FCS13 FCS14 FCS15

X X

X X X X

X X

Appendix A-3: Industry Standards: Child Development Units

Unit 1

Unit 2

Unit 3

Unit 4

Unit FCS2

X X

FCS3

FCS4

FCS5

X X

X X X

FCS6 FCS7

X X

FCS8

FCS9

FCS10 FCS11 FCS12 FCS13

FCS14

FCS15 FCS16

FCS1 FCS2 FCS3 FCS4 FCS5 FCS6 FCS7 FCS8 FCS9 FCS10 FCS11 FCS12 FCS13 FCS14

Demonstrate nutrition and wellness practices that enhance individual and family well-being. FCS15 PARENTING Evaluate the impact of parenting roles and responsibilities on strengthening the well-being of individuals and families. FCS16 TEXTILES AND APPAREL Integrate knowledge, skills, and practices required for careers in textiles and apparel.

Appendix A-4: Industry Standards: Resource Management Units

Unit 1

Unit 2

Unit 3

Unit 4

Unit FCS2

X X

FCS3

FCS4 FCS5 FCS6 FCS7

X X

FCS8 FCS9 FCS10 FCS11 FCS12 FCS13

FCS14 FCS15 FCS16

FCS1 FCS2 FCS3 FCS4 FCS5 FCS6 FCS7 FCS8 FCS9 FCS10 FCS11 FCS12 FCS13 FCS14

Appendix B: 21st Century Skills 1 21st Century Crosswalk for Family and Consumer Sciences Units

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Standards

CS1 CS2 CS3 CS4 CS5 CS6 CS7 CS8 CS9 CS10 CS11 CS12 CS13 CS14 CS15 CS16

X X X X X X

X X X X X X X

X X X X X X X X X X X X X X X

X X X X X

X X X X X X X X X X X X X X X X

X X X X X X X X X X X X X X X

CSS1-21st Century Themes CS1 Global Awareness 1. Using 21st century skills to understand and address global issues 2. Learning from and working collaboratively with individuals representing diverse cultures, religions, and lifestyles in a spirit of mutual respect and open dialogue in personal, work, and community contexts 3. Understanding other nations and cultures, including the use of non-English languages CS2 Financial, Economic, Business, and Entrepreneurial Literacy 1. Knowing how to make appropriate personal economic choices 2. Understanding the role of the economy in society 3. Using entrepreneurial skills to enhance workplace productivity and career options CS3 Civic Literacy 1. Participating effectively in civic life through knowing how to stay informed and understanding governmental processes 2. Exercising the rights and obligations of citizenship at local, state, national, and global levels 3. Understanding the local and global implications of civic decisions CS4 Health Literacy 1. Obtaining, interpreting, and understanding basic health information and services and using such information and services in ways that enhance health 2. Understanding preventive physical and mental health measures, including proper diet, nutrition, exercise, risk avoidance, and stress reduction 3. Using available information to make appropriate health-related decisions 4. Establishing and monitoring personal and family health goals 5. Understanding national and international public health and safety issues CS5 Environmental Literacy

21st century skills. (n.d.). Washington, DC: Partnership for 21st Century Skills.

2. 3. 4.

Demonstrate knowledge and understanding of the environment and the circumstances and conditions affecting it, particularly as relates to air, climate, land, food, energy, water, and ecosystems. Demonstrate knowledge and understanding of society’s impact on the natural world (e.g., population growth, population development, resource consumption rate, etc.). Investigate and analyze environmental issues, and make accurate conclusions about effective solutions. Take individual and collective action toward addressing environmental challenges (e.g., participating in global actions, designing solutions that inspire action on environmental issues).

CSS2-Learning and Innovation Skills CS6 Creativity and Innovation 1. Think Creatively 2. Work Creatively with Others 3. Implement Innovations CS7 Critical Thinking and Problem Solving 1. Reason Effectively 2. Use Systems Thinking 3. Make Judgments and Decisions 4. Solve Problems CS8 Communication and Collaboration 1. Communicate Clearly 2. Collaborate with Others CSS3-Information, Media and Technology Skills CS9 Information Literacy 1. Access and Evaluate Information 2. Use and Manage Information CS10 Media Literacy 1. Analyze Media 2. Create Media Products CS11 ICT Literacy 1. Apply Technology Effectively CSS4-Life and Career Skills CS12 Flexibility and Adaptability 1. Adapt to change 2. Be Flexible CS13 Initiative and Self-Direction 1. Manage Goals and Time 2. Work Independently 3. Be Self-directed Learners CS14 Social and Cross-Cultural Skills 1. Interact Effectively with others 2. Work Effectively in Diverse Teams CS15 Productivity and Accountability 1. Manage Projects 2. Produce Results CS16 Leadership and Responsibility 1. Guide and Lead Others 2. Be Responsible to Others

Appendix C: International Society for Technology in Education Standards (ISTE) Family and Consumer Sciences

Units

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

X X X X X X X

X X X X

X X X

X X X X

X X X X X X X

Standards T1 T2 T3 T4 T5 T6 T7

X X X

X X

T1 T2 T3 T4 T5 T6 T7

Empowered Learner Digital Citizen Knowledge Constructor Innovative Designer Computational Thinker Creative Communicator Global Collaborator

Empowered Learner Students leverage technology to take an active role in choosing, achieving, and demonstrating competency in their learning goals, informed by the learning sciences. Students: a. Articulate and set personal learning goals, develop strategies leveraging technology to achieve them and reflect on the learning process itself to improve learning outcomes. b. Build networks and customize their learning environments in ways that support the learning process. c. Use technology to seek feedback that informs and improves their practice and to demonstrate their learning in a variety of ways. d. Understand the fundamental concepts of technology operations, demonstrate the ability to choose, use and troubleshoot current technologies and are able to transfer their knowledge to explore emerging technologies.

Digital Citizen Students recognize the rights, responsibilities, and opportunities of living, learning and working in an interconnected digital world, and they act and model in ways that are safe, legal and ethical. Students: a. Cultivate and manage their digital identity and reputation and are aware of the permanence of their actions in the digital world. b. Engage in positive, safe, legal and ethical behavior when using technology, including social interactions online or when using networked devices. c. Demonstrate an understanding of and respect for the rights and obligations of using and sharing intellectual property. d. Manage their personal data to maintain digital privacy and security and are aware of data-collection technology used to track their navigation online.

Knowledge Constructor Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others. Students: a. Plan and employ effective research strategies to locate information and other resources for their intellectual or creative pursuits. b. Evaluate the accuracy, perspective, credibility and relevance of information, media, data or other resources.

c. d.

Curate information from digital resources using a variety of tools and methods to create collections of artifacts that demonstrate meaningful connections or conclusions. Build knowledge by actively exploring real-world issues and problems, developing ideas and theories and pursuing answers and solutions.

Innovative Designer Students use a variety of technologies within a design process to identify and solve problems by creating new, useful, or imaginative solutions. Students: a. Know and use a deliberate design process for generating ideas, testing theories, creating innovative artifacts, or solving authentic problems. b. Select and use digital tools to plan and manage a design process that considers design constraints and calculated risks. c. Develop, test and refine prototypes as part of a cyclical design process. d. Exhibit a tolerance for ambiguity, perseverance, and the capacity to work with open-ended problems.

Computational Thinker Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions. Students: a. Formulate problem definitions suited for technology-assisted methods such as data analysis, abstract models, and algorithmic thinking in exploring and finding solutions. b. Collect data or identify relevant data sets, use digital tools to analyze them, and represent data in various ways to facilitate problem-solving and decision-making. c. Break problems into component parts, extract key information, and develop descriptive models to understand complex systems or facilitate problem-solving. d. Understand how automation works and use algorithmic thinking to develop a sequence of steps to create and test automated solutions.

Creative Communicator Students communicate clearly and express themselves creatively for a variety of purposes using the platforms, tools, styles, formats, and digital media appropriate to their goals. Students: a. Choose the appropriate platforms and tools for meeting the desired objectives of their creation or communication. b. Create original works or responsibly repurpose or remix digital resources into new creations. c. Communicate complex ideas clearly and effectively by creating or using a variety of digital objects such as visualizations, models, or simulations. d. Publish or present content that customizes the message and medium for their intended audiences.

Global Collaborator Students use digital tools to broaden their perspectives and enrich their learning by collaborating with others and working effectively in teams locally and globally. Students: a. Use digital tools to connect with learners from a variety of backgrounds and cultures, engaging with them in ways that broaden mutual understanding and learning. b. Use collaborative technologies to work with others, including peers, experts, or community members, to examine issues and problems from multiple viewpoints. c. Contribute constructively to project teams, assuming various roles and responsibilities to work effectively toward a common goal. d. Explore local and global issues and use collaborative technologies to work with others to investigate solutions.

Appendix D: College and Career Ready Standards – English Language Arts Family and Consumer Sciences

Units

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

X X

X X X X X X X X X X X X X X X X X X X X X X

X X

Standards

RL.9.1 RL.9.2 RL.9.3 RL.9.4 RL.9.5 RL.9.6 RL.9.7 RL.9.8 RL.9.9 RL.9.10 RI.9.3 RI.9.5 RI.9.6 RI.9.7 RI.9.8 RI.9.9 W.9.1 W.9.2 W.9.3 W.9.4 W.9.5 W.9.6 W.9.7 W.9.8 W.9.9 W.9.10 SL.9.1 SL.9.2 SL.9.3 SL.9.4 SL.9.5 SL.9.6 L.9.1 L.9.2 L.9.3 L.9.4 L.9.5 L.9.6 RL.10.10 RH.9-10.1 RH.9-10.2 RH.9-10.3 RH.9-10.4 RH.9-10.5 RH.9-10.6 RH.9-10.7 RH.9-10.8 RH.9-10.9 RH.9-10.10 RST.9-10.1 RST.9-10.2 RST.9-10.3 RST.9-10.4 RST.9-10.5 RST.9-10.6

RST.9-10.7 RST.9-10.8 RST.9-10.9 RST.9-10.10 WHST.9-10.1 WHST.9-10.2 WHST.9-10.3 WHST.9-10.4 WHST.9-10.5 WHST.9-10.6 WHST.9-10.7 WHST.9-10.8 WHST.9-10.9 WHST.9-10.10 RL.11.1 RL.11.2 RL.11.3 RL.11.4 RL.11.5 RL.11.6 RL.11.7 RL.11.8 RL.11.9 RL.11.10 RI.11.3 RI.11.4 RI.11.5 RI.11.6 RI.11.7 RI.11.8 RI.11.9 RI.11.10 W.11.1 W.11.2 W.11.3 W.11.4 W.11.5 W.11.6 W.11.7 W.11.8 W.11.9 W.11.10 SL.11.1 SL.11.2 SL.11.3 SL.11.4 SL.11.5 SL.11.6 L.11.1 L.11.2 L.11.3 L.11.4 RL.12.10 RH.11-12.1 RH.11-12.2 RH.11-12.3 RH.11-12.4 RH.11-12.5 RH.11-12.6 RH.11-12.7 RH.11-12.8 RH.11-12.9 RH.11-12.10 RST.11-12.1 RST.11-12.2

X X X X X X X X X X X X

X X

X X X X X X X X X X X X X

X X X X

X X

RST.11-12.3 RST.11-12.4 RST.11-12.5 RST.11-12.6 RST.11-12.7 RST.11-12.8 RST.11-12.9 RST.11-12.10 WHST.11-12.1 WHST.11-12.2 WHST.11-12.6 WHST.11-12.8

X X X X X X X X X X

College and Career Ready English I Reading Literature Key Ideas and Details RL.9.1 Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text. RL.9.2 Determine a theme or central idea of a text and analyze in detail its development over the course of the text, including how it emerges and is shaped and refined by specific details; provide an objective summary of the text. RL.9.3 Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme. Craft and Structure RL.9.4 Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the cumulative impact of specific word choices on meaning and tone (e.g., how the language evokes a sense of time and place; how it sets a formal or informal tone). RL.9.5 Analyze how an author’s choices concerning how to structure a text, order events within it (e.g., parallel plots), and manipulate time (e.g., pacing, flashbacks) create such effects as mystery, tension, or surprise. RL.9.6 Analyze a particular point of view or cultural experience reflected in a work of literature from outside the United States, drawing on a wide reading of world literature. Integration of Knowledge and Ideas RL.9.7 Analyze the representation of a subject or a key scene in two different artistic mediums, including what is emphasized or absent in each treatment (e.g., Auden’s “Musée des Beaux Arts” and Breughel’s Landscape with the Fall of Icarus). RL.9.8 Not applicable to literature. College and Career Ready English I RL.9.9 Analyze how an author draws on and transforms source material in a specific work (e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare). Range of Reading and Level of Text Complexity RL.9.10 By the end of grade 9, read and comprehend literature, including stories, dramas, and poems, in the grades 9-10 text complexity band proficiently, with scaffolding as needed at the high end of the range. College and Career Ready English I Reading Informational Text Key Ideas and Details RI.9.3 Analyze how the author unfolds an analysis or series of ideas or events, including the order in which the points are made, how they are introduced and developed, and the connections that are drawn between them.

Craft and Structure

RI.9.5 Analyze in detail how an author’s ideas or claims are developed and refined by particular sentences, paragraphs, or larger portions of a text (e.g., a section or chapter). RI.9.6 Determine an author’s point of view or purpose in a text and analyze how an author uses rhetoric to advance that point of view or purpose. Integration of Knowledge and Ideas RI.9.7 Analyze various accounts of a subject told in different mediums (e.g., a person’s life story in both print and multimedia), determining which details are emphasized in each account. RI.9.8 Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning. RI.9.9 Analyze seminal U.S. documents of historical and literary significance (e.g., Washington’s Farewell Address, the Gettysburg Address, Roosevelt’s Four Freedoms speech, King’s “Letter from Birmingham Jail”), including how they address related themes and concepts. College and Career Ready English I Writing Text Types and Purposes W.9.1 Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence. W.9.1a Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among claim(s), counterclaims, reasons, and evidence. W.9.1b Develop claim(s) and counterclaims fairly, supplying evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level and concerns. W.9.1c Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. W.9.1d Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. W.9.1e Provide a concluding statement or section that follows from and supports the argument presented. W.9.2 Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. W.9.2a Introduce a topic; organize complex ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. W.9.2b Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. W.9.2c Use appropriate and varied transitions to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts. College and Career Ready English I W.9.2d Use precise language and domain-specific vocabulary to manage the complexity of the topic. W.9.2e Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. W.9.2f Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic). W.9.3 Write narratives to develop real or imagined experiences or events using effective technique, wellchosen details, and well-structured event sequences. W.9.3a Engage and orient the reader by setting out a problem, situation, or observation, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events. W.9.3b Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters. W.9.3c Use a variety of techniques to sequence events so that they build on one another to create a coherent whole. W.9.3d Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters.

W.9.3e Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative. Production and Distribution of Writing W.9.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) W.9.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grades 9–10.) W.9.6 Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically. Research to Build and Present Knowledge W.9.7 Conduct short as well as more sustained research projects to answer a question (including a selfgenerated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. College and Career Ready English I W.9.8 Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation. W.9.9 Draw evidence from literary or informational texts to support analysis, reflection, and research. W.9.9a Apply grades 9–10 Reading standards to literature (e.g., “Analyze how an author draws on and transforms source material in a specific work [e.g., how Shakespeare treats a theme or topic from Ovid or the Bible or how a later author draws on a play by Shakespeare]”). W.9.9b Apply grades 9–10 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the argument and specific claims in a text, assessing whether the reasoning is valid and the evidence is relevant and sufficient; identify false statements and fallacious reasoning”). Range of Writing W.9.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audience. College and Career Ready English I SL.9.1 Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9– 10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. SL.9.1a Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas. SL.9.1b Work with peers to set rules for collegial discussions and decision making (e.g., informal consensus, taking votes on key issues, presentation of alternate views), clear goals and deadlines, and individual roles as needed. SL.9.1c Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate others into the discussion; and clarify, verify, or challenge ideas and conclusions. SL.9.1d Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own views and understanding and make new connections in light of the evidence and reasoning presented. SL.9.2 Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source. SL.9.3 Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence.

Presentation of Knowledge and Ideas SL.9.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. College and Career Ready English I SL.9.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest. SL.9.6 Adapt speech to a variety of contexts and tasks, demonstrating command of formal English when indicated or appropriate. (See grades 9–10 Language standards 1 and 3 for specific expectations.) College and Career Ready English I Language Conventions of Standard English L.9.1 Demonstrate command of the conventions of standard English grammar and usage when writing or speaking. L.9.1a Use parallel structure.* L.9.1b Use various types of phrases (noun, verb, adjectival, adverbial, participial, prepositional, absolute) and clauses (independent, dependent; noun, relative, adverbial) to convey specific meanings and add variety and interest to writing or presentations. L.9.2 Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing. L.9.2a Use a semicolon (and perhaps a conjunctive adverb) to link two or more closely related independent clauses. L.9.2b Use a colon to introduce a list or quotation. L.9.2c Spell correctly Knowledge of Language L.9.3 Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening L.9.3a Write and edit work so that it conforms to the guidelines in a style manual (e.g., MLA Handbook, Turabian’s Manual for Writers) appropriate for the discipline and writing type. Vocabulary Acquisition and Use L.9.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 9–10 reading and content, choosing flexibly from a range of strategies. L.9.4a Use context (e.g., the overall meaning of a sentence, paragraph, or text; a word’s position or function in a sentence) as a clue to the meaning of a word or phrase. L.9.4b Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., analyze, analysis, analytical; advocate, advocacy). College and Career Ready English I L.9.4c Consult general and specialized reference materials (e.g., dictionaries, glossaries, thesauruses), both print and digital, to find the pronunciation of a word or determine or clarify its precise meaning, its part of speech, or its etymology. L.9.4d Verify the preliminary determination of the meaning of a word or phrase (e.g., by checking the inferred meaning in context or in a dictionary). L.9.5 Demonstrate understanding of figurative language, word relationships, and nuances in word meanings. L.9.5a Interpret figures of speech (e.g., euphemism, oxymoron) in context and analyze their role in the text. L.9.5b Analyze nuances in the meaning of words with similar denotations. L.9.6 Acquire and use accurately general academic and domain-specific words and phrases, sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when considering a word or phrase important to comprehension or expression.

College and Career Ready English II Range of Reading and Level of Text Complexity RL.10.10 By the end of grade 10, read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 9-10 text complexity band independently and proficiently. Grades 9-10: Literacy in History/SS Reading in History/Social Studies Key Ideas and Details RH.9-10.1 Cite specific textual evidence to support analysis of primary and secondary sources, attending to such features as the date and origin of the information. RH.9-10.2 Determine the central ideas or information of a primary or secondary source; provide an accurate summary of how key events or ideas develop over the course of the text. RH.9-10.3 Analyze in detail a series of events described in a text; determine whether earlier events caused later ones or simply preceded them. Craft and Structure RH.9-10.4 Determine the meaning of words and phrases as they are used in a text, including vocabulary describing political, social, or economic aspects of history/social science. RH.9-10.5 Analyze how a text uses structure to emphasize key points or advance an explanation or analysis. RH.9-10.6 Compare the point of view of two or more authors for how they treat the same or similar topics, including which details they include and emphasize in their respective accounts. Integration of Knowledge and Ideas RH.9-10.7 Integrate quantitative or technical analysis (e.g., charts, research data) with qualitative analysis in print or digital text. RH.9-10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claims. RH.9-10.9 Compare and contrast treatments of the same topic in several primary and secondary sources. Range of Reading and Level of Text Complexity RH.9-10.10 By the end of grade 10, read and comprehend history/social studies texts in the grades 9–10 text complexity band independently and proficiently. Grades 9-10: Literacy in Science and Technical Subjects Reading in Science and Technical Subjects Key Ideas and Details RST.9-10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions. RST.9-10.2 Determine the central ideas or conclusions of a text; trace the text’s explanation or depiction of a complex process, phenomenon, or concept; provide an accurate summary of the text. RST.9-10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text. Craft and Structure RST.9-10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. RST.9-10.5 Analyze the structure of the relationships among concepts in a text, including relationships among key terms (e.g., force, friction, reaction force, energy). RST.9-10.6 Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, defining the question the author seeks to address. Integration of Knowledge and Ideas RST.9-10.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. RST.9-10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a recommendation for solving a scientific or technical problem.

RST.9-10.9 Compare and contrast findings presented in a text to those from other sources (including their own experiments), noting when the findings support or contradict previous explanations or accounts Range of Reading and Level of Text Complexity RST.9-10.10 By the end of grade 10, read and comprehend science/technical texts in the grades 9–10 text complexity band independently and proficiently. Grades 9-10: Writing in History/SS, Science, and Technical Subjects Writing Text Types and Purposes WHST.9-10.1 Write arguments focused on discipline-specific content. WHST.9-10.1a Introduce precise claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that establishes clear relationships among the claim(s), counterclaims, reasons, and evidence. WHST.9-10.1b Develop claim(s) and counterclaims fairly, supplying data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form and in a manner that anticipates the audience’s knowledge level and concerns. WHST.9-10.1c Use words, phrases, and clauses to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. WHST.9-10.1d Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. WHST.9-10.1e Provide a concluding statement or section that follows from or supports the argument presented. WHST.9-10.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes. WHST.9-10.2a Introduce a topic and organize ideas, concepts, and information to make important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. WHST.9-10.2b Develop the topic with well-chosen, relevant, and sufficient facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. Grades 9-10 Writing in History/SS, Science, and Technical Subjects WHST.9-10.2c Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and concepts. WHST.9-10.2d Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers. WHST.9-10.2e Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. WHST.9-10.2f Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic). WHST.9-10.3 Not Applicable Production and Distribution of Writing WHST.9-10.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. WHST.9-10.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. WHST.9-10.6 Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically. Research to Build and Present Knowledge

WHST.9-10.7 Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. WHST.9-10.8 Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation. WHST.9-10.9 Draw evidence from informational texts to support analysis, reflection, and research. Grades 9-10 Writing in History/SS, Science, and Technical Subjects Range of Writing WHST.9-10.10 Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences. English III Reading Literature Key Ideas and Details RL.11.1 Cite strong and thorough textual evidence to support analysis of what the text says explicitly as well as inferences drawn from the text, including determining where the text leaves matters uncertain. RL.11.2 Determine two or more themes or central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to produce a complex account; provide an objective summary of the text. RL.11.3 Analyze the impact of the author’s choices regarding how to develop and relate elements of a story or drama (e.g., where a story is set, how the action is ordered, how the characters are introduced and developed). Craft and Structure RL.11.4 Determine the meaning of words and phrases as they are used in the text, including figurative and connotative meanings; analyze the impact of specific word choices on meaning and tone, including words with multiple meanings or language that is particularly fresh, engaging, or beautiful. (Include Shakespeare as well as other authors.) RL.11.5 Analyze how an author’s choices concerning how to structure specific parts of a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its overall structure and meaning as well as its aesthetic impact. RL.11.6 Analyze a case in which grasping a point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement). Integration of Knowledge and Ideas RL.11.7 Analyze multiple interpretations of a story, drama, or poem (e.g., recorded or live production of a play or recorded novel or poetry), evaluating how each version interprets the source text. (Include at least one play by Shakespeare and one play by an American dramatist.) RL.11.8 Not applicable to literature. RL.11.9 Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics. Range of Reading and Level of Text Complexity RL.11.10 By the end of grade 11, read and comprehend literature, including stories, dramas, and poems, in the grades 11-CCR text complexity band proficiently, with scaffolding as needed at the high end of the range. English III Reading Informational Text Key Ideas and Details

Rl.11.3 Analyze a complex set of ideas or sequence of events and explain how specific individuals, ideas, or events interact and develop over the course of the text. Craft and Structure Rl.11.4 Determine the meaning of words and phrases as they are used in a text, including figurative, connotative, and technical meanings; analyze how an author uses and refines the meaning of a key term or terms over the course of a text (e.g., how Madison defines faction in Federalist No. 10). Rl.11.5 Analyze and evaluate the effectiveness of the structure an author uses in his or her exposition or argument, including whether the structure makes points clear, convincing, and engaging. Rl.11.6 Determine an author’s point of view or purpose in a text in which the rhetoric is particularly effective, analyzing how style and content contribute to the power, persuasiveness or beauty of the text. Integration of Knowledge and Ideas Rl.11.7 Integrate and evaluate multiple sources of information presented in different media or formats (e.g., visually, quantitatively) as well as in words in order to address a question or solve a problem. Rl.11.8 Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning (e.g., in U.S. Supreme Court majority opinions and dissents) and the premises, purposes, and arguments in works of public advocacy (e.g., The Federalist, presidential addresses). Rl.11.9 Analyze seventeenth-, eighteenth-, and nineteenth-century foundational U.S. documents of historical and literary significance (including Them Declaration of Independence, the Preamble to the Constitution, the Bill of Rights, and Lincoln’s Second Inaugural Address) for their themes, purposes, and rhetorical features. Range of Reading and Level of Text Complexity Rl.11.10 By the end of grade 11, read and comprehend literary nonfiction in the grades 11-CCR text complexity band proficiently, with scaffolding as needed at the high end of the range. English III Writing W.11.1 Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence. W.11.1a Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences claim(s), counterclaims, reasons, and evidence. W.11.1b Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant evidence for each while pointing out the strengths and limitations of both in a manner that anticipates the audience’s knowledge level, concerns, values, and possible biases. W.11.1c Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. W.11.1d Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. W.11.1e Provide a concluding statement or section that follows from and supports the argument presented. W.11.2 Write informative/explanatory texts to examine and convey complex ideas, concepts, and information clearly and accurately through the effective selection, organization, and analysis of content. W.11.2a Introduce a topic; organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. English III W.11.2b Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other information and examples appropriate to the audience’s knowledge of the topic. W.11.2c Use appropriate and varied transitions and syntax to link the major sections of the text, create cohesion, and clarify the relationships among complex ideas and concepts.

W.11.2d Use precise language, domain-specific vocabulary, and techniques such as metaphor, simile, and analogy to manage the complexity of the topic. W.11.2e Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. W.11.2f Provide a concluding statement or section that follows from and supports the information or explanation presented (e.g., articulating implications or the significance of the topic). W.11.3 Write narratives to develop real or imagined experiences or events using effective technique, wellchosen details, and well-structured event sequences. W.11.3a Engage and orient the reader by setting out a problem, situation, or observation and its significance, establishing one or multiple point(s) of view, and introducing a narrator and/or characters; create a smooth progression of experiences or events. W.11.3b Use narrative techniques, such as dialogue, pacing, description, reflection, and multiple plot lines, to develop experiences, events, and/or characters. W.11.3c Use a variety of techniques to sequence events so that they build on one another to create a coherent whole and build toward a particular tone and outcome (e.g., a sense of mystery, suspense, growth, or resolution). W.11.3d Use precise words and phrases, telling details, and sensory language to convey a vivid picture of the experiences, events, setting, and/or characters. W.11.3e Provide a conclusion that follows from and reflects on what is experienced, observed, or resolved over the course of the narrative. Production and Distribution of Writing W.11.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1–3 above.) English III W.11.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience. (Editing for conventions should demonstrate command of Language standards 1–3 up to and including grades 11–12.) W.11.6 Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information. Research to Build and Present Knowledge W.11.7 Conduct short as well as more sustained research projects to answer a question (including a selfgenerated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. W.11.8 Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation. W.11.9 Draw evidence from literary or informational texts to support analysis, reflection, and research. W.11.9a Apply grades 11–12 Reading standards to literature (e.g., “Demonstrate knowledge of eighteenth-, nineteenth- and early-twentieth-century foundational works of American literature, including how two or more texts from the same period treat similar themes or topics”). W.11.9b Apply grades 11–12 Reading standards to literary nonfiction (e.g., “Delineate and evaluate the reasoning in seminal U.S. texts, including the application of constitutional principles and use of legal reasoning [e.g., in U.S. Supreme Court Case majority opinions and dissents] and the premises, purposes, and arguments in works of public advocacy [e.g., The Federalist, presidential addresses]”). Range of Writing W.11.10 Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences. English III Speaking and Listening

Comprehension and Collaboration SL.11.1 Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 11–12 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. SL11.1a Come to discussions prepared, having read and researched material under study; explicitly draw on that preparation by referring to evidence from texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas. SL.11.1b Work with peers to promote civil, democratic discussions and decision making, set clear goals and deadlines, and establish individual roles as needed. SL.11.1c Propel conversations by posing and responding to questions that probe reasoning and evidence; ensure a hearing for a full range of positions on a topic or issue; clarify, verify, or challenge ideas and conclusions; and promote divergent and creative perspectives. SL.11.1d Respond thoughtfully to diverse perspectives; synthesize comments, claims, and evidence made on all sides of an issue; resolve contradictions when possible; and determine what additional information or research is required to deepen the investigation or complete the task. SL.11.2 Integrate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, orally) in order to make informed decisions and solve problems, evaluating the credibility and accuracy of each source and noting any discrepancies among the data. SL.11.3 Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, assessing the stance, premises, links among ideas, word choice, points of emphasis, and tone used. Presentation of Knowledge and Ideas SL.11.4 Present information, findings, and supporting evidence, conveying a clear and distinct perspective, such that listeners can follow the line of reasoning, alternative or opposing perspectives are addressed, and the organization, development, substance, and style are appropriate to purpose, audience, and a range of formal and informal tasks. English III SL11.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest. SL.11.6 Adapt speech to a variety of contexts and tasks, demonstrating a command of formal English when indicated or appropriate. (See grades 11–12 Language standards 1 and 3 for specific expectations.) English III Language Conventions of Standard English L.11.1a Apply the understanding that usage is a matter of convention, can change over time, and is sometimes contested. L.11.1b Resolve issues of complex or contested usage, consulting references (e.g., Merriam-Webster’s Dictionary of English Usage, Garner’s Modern American Usage) as needed. L.11.2a Observe hyphenation conventions. L.11.3a Vary syntax for effect, consulting references (e.g., Tufte’s Artful Sentences) for guidance as needed; apply an understanding of syntax to the study of complex texts when reading. Vocabulary Acquisition and Use L.11.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases based on grades 11–12 reading and content, choosing flexibly from a range of strategies. L.11.4b Identify and correctly use patterns of word changes that indicate different meanings or parts of speech (e.g., conceive, conception, conceivable). English IV Range of Reading and Level of Text Complexity RL.12.10 By the end of grade 12, read and comprehend literature, including stories, dramas, and poems, at the high end of the grades 11–CCR text complexity band independently and proficiently. Grades 11-12: Literacy in History/SS

Reading in History/Social Studies Key Ideas and Details RH.11-12.1 Cite specific textual evidence to support analysis of primary and secondary sources, connecting insights gained from specific details to an understanding of the text as a whole. RH.11-12.2 Determine the central ideas or information of a primary or secondary source; provide an accurate summary that makes clear the relationships among the key details and ideas. RH.11-12.3 Evaluate various explanations for actions or events and determine which explanation best accords with textual evidence, acknowledging where the text leaves matters uncertain. Craft and Structure RH.11-12.4 Determine the meaning of words and phrases as they are used in a text, including analyzing how an author uses and refines the meaning of a key term over the course of a text (e.g., how Madison defines faction in Federalist No. 10). RH.11-12.5 Analyze in detail how a complex primary source is structured, including how key sentences, paragraphs, and larger portions of the text contribute to the whole. RH.11-12.6 Evaluate authors’ differing points of view on the same historical event or issue by assessing the authors’ claims, reasoning, and evidence. Integration of Knowledge and Ideas Rh.11-12.7 Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., visually, quantitatively, as well as in words) in order to address a question or solve a problem. RH.11-12.8 Evaluate an author’s premises, claims, and evidence by corroborating or challenging them with other information. RH.11-12.9 Integrate information from diverse sources, both primary and secondary, into a coherent understanding of an idea or event, noting discrepancies among sources. Range of Reading and Level of Text Complexity RH.11-12.10 By the end of grade 12, read and comprehend history/social studies texts in the grades 11– CCR text complexity band independently and proficiently. Grades 11-12: Literacy in Science and Technical Subjects Reading in Science and Technical Subjects Key Ideas and Details RST. 11-12.1 Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. RST.11-12.2 Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms. RST.11-12.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text. Craft and Structure RST.11-12.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11–12 texts and topics. RST.11-12.5 Analyze how the text structures information or ideas into categories or hierarchies, demonstrating understanding of the information or ideas. RST.11-12.6 Analyze the author’s purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, identifying important issues that remain unresolved. RST.11-12.7 Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. RST.11-12.8 Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information. RST.11-12.9 Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible. Range of Reading and Level of Text Complexity RST.11-12.10 Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible. Grades 11-12: Writing I History/SS, Science and Technical Subjects Writing Text Types and Purposes

WHST.11-12.1a Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and create an organization that logically sequences the claim(s), counterclaims, reasons, and evidence. WHST.11-12.1b Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant data and evidence for each while pointing out the strengths and limitations of both claim(s) and counterclaims in a discipline-appropriate form that anticipates the audience’s knowledge level, concerns, values, and possible biases. WHST.11-12.1c Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims. WHST.11-12.2a Introduce a topic and organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. Grades 11-12: Writing I History/SS, Science and Technical Subjects WHST.11-12.2d Use precise language, domain-specific vocabulary and techniques such as metaphor, simile, and analogy to manage the complexity of the topic; convey a knowledgeable stance in a style that responds to the discipline and context as well as to the expertise of likely readers. Production and Distribution of Writing WHST.11-12.6 Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information. WHST.11-12.8 Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the strengths and limitations of each source in terms of the specific task, purpose, and audience; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and overreliance on any one source and following a standard format for citation.

Appendix E: College and Career Ready Standards – Mathematics Family and Consumer Sciences

Units

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Standards

N-Q.1 N-Q.2 N-Q.3 8.EE.8 A-SSE.1 A-SSE.2 A-SSE.3 A-SSE.4 A-CED.1 A-CED.2 A-CED.3 A-CED.4 A-REI.1 A-REI.2 A-REI.3 A-REI.4 A-REI.5 A-REI.6 A-REI.7 A-REI.8 A-REI.9 A-REI.10 A-REI.11 A-REI.12 8.F.1 8.F.2 8.F.3 8.F.4 8.F.5 F-IF.1 F-IF.2 F-IF.3 F-IF.4 F-IF.5 F-IF.6 F-IF.7 F-IF.8 F-IF.9 F-BF.1 F-BF.2 F-BF.3 F-BF.4 F-BF.5 F-LE.1 F-LE.2 F-LE.3 F-LE.4 F-LE.5 8.G.6 8.G.7 8.G.8 G-CO.1 G-CO.2 G-CO.3 G-CO.4

X X X

X X X X

G-CO.5 G-CO.6 G-CO.7 G-CO.8 G-CO.9 G-CO.10 G-CO.11 G-CO.12 G-CO.13 8.SP.1 8.SP.2 8.SP.3 8.SP.4 S-ID.1 S-ID.2 S-ID.3 S-ID.4 S-ID.5 S-ID.6 S-ID.7 S-ID.8 S-ID.9 N-RN.1 N-RN.2 N-RN.3 A-APR. A-APR.2 A-APR.3 A-APR.4 A-APR.5 A-APR.6 A-APR.7 G-SRT.1 G-SRT.2 G-SRT.3 G-SRT.4 G-SRT.5 G-SRT.6 G-SRT.7 G-SRT.8 G-SRT.9 G-SRT.10 G-SRT.11 G-C.1 G-C.2 G-C.3 G-C.4 G-C.5 G-GPE.1 G-GPE.2 G-GPE.3 G-GPE.4 G-GPE.5 G-GPE.6 G-GPE.7 G-GMD.1 G-GMD.2 G-GMD.3 G-GMD.4 G-MG.1 G-MG.2 G-MG.3 N-CN.1 N-CN.2 N-CN.3

X X X

X X

N-CN.4 N-CN.5 N-CN.6 N-CN.7 N-CN.8 N-CN.9 F-TF.1 F-TF.2 F-TF.3 F-TF.4 F-TF.5 F-TF.6 F-TF.7 F-TF.8 F-TF.9 S-IC.1 S-IC.2 S-IC.3 S-IC.4 S-IC.5 S-IC.6 S-CP.1 S-CP.2 S-CP.3 S-CP.4 S-CP.5 S-CP.6 S-CP.7 S-CP.8 S-CP.9 N-VM.1 N-VM.2 N-VM.3 N-VM.4 N-VM.5 N-VM.6 N-VM.7 N-VM.8 N-VM.9 N-VM.10 N-VM.11 N-VM.12 S-MD.1 S-MD.2 S-MD.3 S-MD.4 S-MD.5 S-MD.6 S-MD.7

X X

Mathematics Standards Number and Quantity Reason quantitatively and use unites to solve problems N-Q.1 Use units to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.* N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.* N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.* Algebra Analyze and solve linear equations and pairs of simultaneous linear equations

8.EE.8 Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Interpret the structure of expressions A-SSE.1 Interpret expressions that represent a quantity in terms of its context.* a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as [1.151/12] 12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Creating equations that describe numbers or relationships A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.* A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.* Solve equations and inequalities in one variable A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Solve systems of equations A-REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Represent and solve equations and inequalities graphically A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Functions Define, evaluate, and compare functions 8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. 1

8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. Use functions to model relationships between quantities 8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. Understand the concept of a function and use function notation F-IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. Interpret functions that arise in applications in terms of the context F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* Analyze functions using different representations Supporting F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* a. Graph linear and quadratic functions and show intercepts, maxima, and minima. F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Build a function that models a relationship between two quantities F-BF.1 Write a function that describes a relationship between two quantities.* a. Determine an explicit expression, a recursive process, or steps for calculation from a context. F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* Construct and compare linear, quadratic, and exponential models and solve problems F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.*

a. Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).* F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.* Interpret expressions for functions in terms of the situation they model Supporting F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.* Geometry Understand and apply the Pythagorean Theorem 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G-CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G-CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G-CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Understand congruence in terms of rigid motions G-CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G-CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G-CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Prove geometric theorems G-CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. G-CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. G-CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Statistics and Probability

Investigate patterns of association in bivariate data 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. 8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. 8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Summarize, represent, and interpret data on a single count or measurement variable S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).* S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.* S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* Summarize, represent, and interpret data on two categorical and quantitative variables S-ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.* S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. c. Fit a linear function for a scatter plot that suggests a linear association. Interpret linear models S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.* S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.* S-ID.9 Distinguish between correlation and causation.* Algebra I Number and Quantity Use properties of rational and irrational numbers N-RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Reason quantitatively and use units to solve problems N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.* N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.* N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.*

Algebra Interpret the structure of expressions A-SSE.1 Interpret expressions that represent a quantity in terms of its context.* a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y 4 as (x2 ) 2 – (y2 ) 2 thus recognizing it as a difference of squares that can be factored as (x2 – y 2 ) (x2 + y2 ). Write expressions in equivalent forms to solve problems A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as [1.151/12] 12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Algebra I Perform arithmetic operations on polynomials A-APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Understand the relationship between zeros and factors of polynomials A-APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Create equations that describe numbers or relationships A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.* A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.* Understand solving equations as a process of reasoning and explain the reasoning A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve equations and inequalities in one variable A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A-REI.4 Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p) 2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Algebra I Solve systems of equations A-REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Represent and solve equations and inequalities graphically A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Functions Understand the concept of a function and use function notation F-IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1 Interpret functions that arise in applications in terms of the context F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* Algebra I Analyze functions using different representations F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. B Build a function that models a relationship between two quantities F-BF.1 Write a function that describes a relationship between two quantities.* a. Determine an explicit expression, a recursive process, or steps for calculation from a context. Build new functions from existing functions F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them Construct and compare linear, quadratic, and exponential models and solve problems F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.* a. Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).* F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.* Algebra I Interpret expressions for functions in terms of the situation they model F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.* Statistics and Probability * Summarize, represent, and interpret data on a single count or measurement variable S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).* S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.* S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* Summarize, represent, and interpret data on two categorical and quantitative variables S-ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.* S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association. Interpret linear models S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.* S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.* S-ID.9 Distinguish between correlation and causation.*

Geometry Course Geometry Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G-CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G-CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G-CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Understand congruence in terms of rigid motions G-CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G-CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G-CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Prove geometric theorems G-CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. G-CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. G-CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Geometry Course Make geometric constructions G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. G-CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Understand similarity in terms of similarity transformations G-SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

G-SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Prove theorems involving similarity G-SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. G-SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Define trigonometric ratios and solve problems involving right triangles G-SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* Understand and apply theorems about circles G-C.1 Prove that all circles are similar G-C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. G-C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Find arc lengths and areas of sectors of circles G-C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Translate between the geometric description and the equation for a conic section A G-GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Use coordinates to prove simple geometric theorems algebraically G-GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). G-GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). G-GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* Explain volume formulas and use them to solve problems G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* Visualize relationships between two-dimensional and three-dimensional objects G-GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Apply geometric concepts in modeling situations

G-MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* G-MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* G-MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).* Algebra II Number and Quantity Extend the properties of exponents to rational exponents N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want [51/3] 3 = 5(1/3) 3 to hold, so [51/3] 3 must equal 5. N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Reason quantitatively and use units to solve problems N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.* Perform arithmetic operations with complex numbers N-CN.1 Know there is a complex number i such that i 2 = −1, and every complex number has the form a + bi with a and b real. N-CN.2 Use the relation i 2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Use complex numbers in polynomial identities and equations N-CN.7 Solve quadratic equations with real coefficients that have complex solutions. Algebra Interpret the structure of expressions A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y 4 as (x2) 2 – (y2) 2, thus recognizing it as a difference of squares that can be factored as (x2 – y 2) (x2 + y2). Write expressions in equivalent forms to solve problems A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as [1.151/12] 12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Algebra II A-SSE.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.* Understand the relationship between zeros and factors of polynomials A-APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). A-APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Use polynomial identities to solve problems A-APR.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2) 2 = (x2 – y 2) 2 + (2xy) 2 can be used to generate Pythagorean triples. Rewrite rational expressions A-APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Create equations that describe numbers or relationships A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* Understand solving equations as a process of reasoning and explain the reasoning A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A-REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Solve equations and inequalities in one variable A-REI.4 Solve quadratic equations in one variable. b. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Algebra II Solve systems of equations A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A-REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2 + y2 = 3. Represent and solve equations and inequalities graphically A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* Functions Understand the concept of a function and use function notation F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. Interpret functions that arise in applications in terms of the context F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* Analyze functions using different representations F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. Algebra II

F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t , y = (0.97)t , y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth and decay. F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Build a function that models a relationship between two quantities F-BF.1 Write a function that describes a relationship between two quantities.* a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* Build new functions from existing functions F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. F-BF.4 Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x 3 or f(x) = (x+1)/(x-1) for x ≠ 1. Construct and compare linear, quadratic, and exponential models and solve problems F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).* F-LE.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.* Interpret expressions for functions in terms of the situation they model F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.* Algebra II Extend the domain of trigonometric functions using the unit circle F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Model periodic phenomena with trigonometric functions F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* Prove and apply trigonometric identities F-TF.8 Prove the Pythagorean identity sin (Θ)2 + cos (Θ)2 = 1 and use it to find sin (Θ), cos (Θ), or tan (Θ), given sin (Θ), cos (Θ), or tan (Θ) and the quadrant of the angle. Geometry Translate between the geometric description and the equation for a conic section G-GPE.2 Derive the equation of a parabola given a focus and directrix. Statistics and Probability

Summarize, represent, and interpret data on a single count or measurement variable S-ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.* Summarize, represent, and interpret data on two categorical and quantitative variables S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. Algebra II Understand and evaluate random processes underlying statistical experiments S-IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.* S-IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?* Make inferences and justify conclusions from sample surveys, experiments, and observational studies S-IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.* S-IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.* S-IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.* S-IC.6 Evaluate reports based on data.* Understand independence and conditional probability and use them to interpret data S-CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).* S-CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.* S-CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.* S-CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.* S-CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.* Use the rules of probability to compute probabilities of compound events in a uniform probability model S-CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.* S-CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.* Integrated Mathematics

Number and Quantity Reason quantitatively and use units to solve problems N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.* N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.* N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.* Algebra Interpret the structure of expressions A-SSE.1 Interpret expressions that represent a quantity in terms of its context.* a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. Write expressions in equivalent forms to solve problems A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as [1.151/12] 12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. Create equations that describe numbers or relationships A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.* A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.* Integrated Mathematics I Solve equations and inequalities in one variable A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Solve systems of equations A-REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. Represent and solve equations and inequalities graphically A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. Functions

Understand the concept of a function and use function notation F-IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. Interpret functions that arise in applications in terms of the context F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* Integrated Mathematics I F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* Analyze functions using different representations F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* a. Graph linear and quadratic functions and show intercepts, maxima, and minima. F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Build a function that models a relationship between two quantities F-BF.1 Write a function that describes a relationship between two quantities.* a. Determine an explicit expression, a recursive process, or steps for calculation from a context. F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.* Construct and compare linear, quadratic, and exponential models and solve problems F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.* a. Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).* F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.* Interpret expressions for functions in terms of the situation they model F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.* Integrated Mathematics I Geometry

Experiment with transformations in the plane G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G-CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G-CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G-CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Understand congruence in terms of rigid motions G-CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G-CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G-CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. Prove geometric theorems G-CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. G-CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. G-CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Integrated Mathematics I Statistics and Probability Summarize, represent, and interpret data on a single count or measurement variable S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).* S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.* S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).* Summarize, represent, and interpret data on two categorical and quantitative variables S-ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.* S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. c. Fit a linear function for a scatter plot that suggests a linear association.

Interpret linear models S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.* S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.* S-ID.9 Distinguish between correlation and causation.* Integrated Mathematics I Number and Quantity Extend the properties of exponents to rational exponents N-RN.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want [51/3] 3 = 5(1/3) 3 to hold, so [51/3] 3 must equal 5. N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Use properties of rational and irrational numbers N-RN.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. Reason quantitatively and use units to solve problems N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.* Perform arithmetic operations with complex numbers N-CN.1 Know there is a complex number i such that i 2 = −1, and every complex number has the form a + bi with a and b real. N-CN.2 Use the relation i 2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers. Use complex numbers in polynomial identities and equations N-CN.7 Solve quadratic equations with real coefficients that have complex solutions. Algebra Interpret the structure of expressions A-SSE.1 Interpret expressions that represent a quantity in terms of its context.* b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. Integrated Mathematics II A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y 4 as (x2 ) 2 – (y2 ) 2, thus recognizing it as a difference of squares that can be factored as (x2 – y 2 ) (x2 + y2 ). Write expressions in equivalent forms to solve problems A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. Perform arithmetic operations on polynomials A-APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Create equations that describe numbers or relationships A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.*

A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.* Understand solving equations as a process of reasoning and explain the reasoning M A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Solve equations and inequalities in one variable A-REI.4 Solve quadratic equations in one variable. a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p) 2 = q that has the same solutions. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x 2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b. Solve systems of equations A-REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = -3x and the circle x2 + y2 = 3. Functions Interpret functions that arise in applications in terms of the context M F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* Analyze functions using different representations F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t , y = (0.97)t , y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth and decay. F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Integrated Mathematics II Build a function that models a relationship between two quantities

F-BF.1 Write a function that describes a relationship between two quantities.* a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. Build new functions from existing functions F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Geometry Understand similarity in terms of similarity transformations G-SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. G-SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G-SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. Prove theorems using similarity G-SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. G-SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Define trigonometric ratios and solve problems involving right triangles G-SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Integrated Mathematics II G-SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.* Explain volume formulas and use them to solve problems G-GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. G-GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.* Statistics and Probability* Summarize, represent, and interpret data on two categorical and quantitative variables S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. Understand independence and conditional probability and use them to interpret data

S-CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).* S-CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.* S-CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.* S-CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.* S-CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. Integrated Mathematics II Use the rules of probability to compute probabilities of compound events in a uniform probability model S-CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.* S-CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.* Integrated Mathematics III Number and Quantity Reason quantitatively and use units to solve problems N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.* Algebra Interpret the structure of expressions A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y 4 as (x2 ) 2 – (y2 ) 2 , thus recognizing it as a difference of squares that can be factored as (x2 – y 2 )(x2 + y2 ). Write expressions in equivalent forms to solve problems A-SSE.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments.* Understand the relationship between zeros and factors of polynomials A-APR.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). A-APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Use polynomial identities to solve problems A-APR.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2 ) 2 = (x2 – y 2 ) 2 + (2xy)2 can be used to generate Pythagorean triples. Rewrite rational expressions A-APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Integrated Mathematics III Create equations that describe numbers or relationships A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.* A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* Understand solving equations as a process of reasoning and explain the reasoning A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A-REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Represent and solve equations and inequalities graphically A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.* Interpret functions that arise in applications in terms of the context F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* Analyze functions using different representations F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Build new functions from existing functions F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. F-BF.4 Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x3 or f(x) = (x+1)/(x-1) for x ≠ 1. Construct and compare linear, quadratic, and exponential models and solve problems F-LE.4 For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.* Extend the domain of trigonometric functions using the unit circle F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Model periodic phenomena with trigonometric functions F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* Prove and apply trigonometric identities F-TF.8 Prove the Pythagorean identity sin (Θ)2 + cos (Θ)2 = 1 and use it to find sin (Θ), cos (Θ), or tan (Θ), given sin (Θ), cos (Θ), or tan (Θ) and the quadrant of the angle. Integrated Mathematics III Geometry Make geometric constructions G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. G-CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Understand and apply theorems about circles G-C.1 Prove that all circles are similar. G-C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. G-C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Find arc lengths and areas of sectors of circles G-C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Translate between the geometric description and the equation for a conic section G-GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. G-GPE.2 Derive the equation of a parabola given a focus and directrix. Use coordinates to prove simple geometric theorems algebraically G-GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). G-GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Integrated Mathematics III G-GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.* Visualize relationships between two-dimensional and three-dimensional objects

G-GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Apply geometric concepts in modeling situations G-MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).* G-MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).* G-MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).* Statistics and Probability* Summarize, represent, and interpret data on a single count or measurement variable S S-ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.* Summarize, represent, and interpret data on two categorical and quantitative variables S-ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.* a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. b. Informally assess the fit of a function by plotting and analyzing residuals. Understand and evaluate random processes underlying statistical experiments S-IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Integrated Mathematics III S-IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?* Make inferences and justify conclusions from sample surveys, experiments, and observational studies S-IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.* S-IC.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.* S-IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.* S-IC.6 Evaluate reports based on data.* Advanced Mathematics Plus Number and Quantity Perform arithmetic operations with complex numbers N-CN.3 Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers. Represent complex numbers and their operations on the complex plane N-CN.4 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number. N-CN.5 Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example, (–1 + √3 i)3 = 8 because (–1 + √3 i) has modulus 2 and argument 120°.

N-CN.6 Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints. Use complex numbers in polynomial identities and equations N-CN.8 Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i). N-CN.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials Represent and model with vector quantities N-VM.1 Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v). N-VM.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. N-VM.3 Solve problems involving velocity and other quantities that can be represented by vectors. Advanced Mathematics Plus Perform operations on vectors N-VM.4 Add and subtract vectors. a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum. c. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise. N-VM.5 Multiply a vector by a scalar. a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy). b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v 0, the direction of cv is either along v (for c > 0) or against v (for c < 0). Perform operations on matrices and use matrices in applications N-VM.6 Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network. N-VM.7 Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled. N-VM.8 Add, subtract, and multiply matrices of appropriate dimensions. N-VM.9 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties. N-VM.10 Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse. N-VM.11 Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors. N-VM.12 Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area. Algebra Use polynomial identities to solve problems A-APR.5 Know and apply the Binomial Theorem for the expansion of (x + y) n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. Advanced Mathematics Plus Rewrite rational expressions

A-APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions. Solve systems of equations A-REI.8 Represent a system of linear equations as a single matrix equation in a vector variable. A-REI.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater). Functions Analyze functions using different representations F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. Build a function that models a relationship between two quantities F-BF.1 Write a function that describes a relationship between two quantities. * c. Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t is the temperature at the location of the weather balloon as a function of time. Build new functions from existing functions F-BF.4 Find inverse functions. b. Verify by composition that one function is the inverse of another. c. Read values of an inverse function from a graph or a table, given that the function has an inverse. d. Produce an invertible function from a non-invertible function by restricting the domain. F-BF.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. Advanced Mathematics Plus Extend the domain of trigonometric functions using the unit circle F-TF.3 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number. F-TF.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. Model periodic phenomena with trigonometric functions F-TF.6 Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed. F-TF.7 Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context. * Prove and apply trigonometric identities F-TF.9 Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. Geometry Apply trigonometry to general triangles G-SRT.9 Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. G-SRT.10 Prove the Laws of Sines and Cosines and use them to solve problems. G-SRT.11 Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). Understand and apply theorems about circles

G-C.4 Construct a tangent line from a point outside a given circle to the circle. Translate between the geometric description and the equation for a conic section Advanced Mathematics Plus G-GPE.3 Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant. Explain volume formulas and use them to solve problems G-GMD.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures. Statistics and Probability* Use the rules of probability to compute probabilities of compound events in a uniform probability model S-CP.8 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.* S-CP.9 Use permutations and combinations to compute probabilities of compound events and solve problems.* Calculate expected values and use them to solve problems S-MD.1 Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.* S-MD.2 Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.* S-MD.3 Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.* S-MD.4 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?* Advanced Mathematics Plus Use probability to evaluate outcomes of decisions S-MD.5 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. * a. Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant. b. Evaluate and compare strategies on the basis of expected values. For example, compare a highdeductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.* S-MD.6 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).* S-MD.7 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).*

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