Mississippi Secondary Curriculum Frameworks in Career and Technical Education,

Title 7: Education K-12 Part 118: Mississippi Secondary Curriculum Frameworks in Career and Technical Education, Agriculture, Food & Natural Resources Mississippi Secondary Curriculum Frameworks in Career and Technical Education, Agriculture, Food & Natural Resources 2 020 A gr icu ltu r e P ower an d Mach in er y Program CIP: 01.0204 – Agricultural Power Machinery Operation Direct inquiries to Instructional Design Specialist Program Coordinator Research and Curriculum Unit Office of Career and Technical Education P.O. Drawer DX Mississippi Department of Education Mississippi State, MS 39762 P.O. Box 771 662.325.2510 Jackson, MS 39205 601.359.3461 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 the 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 The agriculture power and machinery (APM) curriculum was presented to the Mississippi Board of Education on January 16, 2019. The following persons are serving on the State Board at this time: Dr. Carey M. Wright, state superintendent of education Dr. Jason S. Dean, chair Mr. Buddy Bailey, vice chair Ms. Rosemary G. Aultman Dr. Karen J. Elam Dr. John R. Kelly Ms. Nancy Collins Ms. Brittany Rye Mr. Sean Suggs Ms. Shelby Dean, Student Representative Mr. Omar G. Jamil, Student Representative Wendy Clemons, associate superintendent of education for the Office of Career and Technical Education at the Mississippi Department of Education (MDE), supported the RCU and the teachers throughout the development of the APM curriculum framework and supporting materials. Dr. Aimee Brown, bureau director for the Office of Career and Technical Education, supported the developmental and implementation process of the curriculum framework and supporting materials. Gayle Fortenberry, instructional design specialist for the RCU at MSU, researched and authored this framework. gayle.fortenberry@rcu.msstate.edu Also, special thanks are extended to the APM teachers who contributed teaching and assessment materials that are included in the framework and supporting materials. Members who contributed were as follows: Dennis Deaton, Alcorn County Career Technology Center, Corinth Nick Horne, Tishomingo County Career Technology Center, Tishomingo Paul Orr, Webster County Career Technology Center, Eupora Matt Powell, Pontotoc Ridge Career Technology Center, Pontotoc Jimmy Rushing, Winston-Louisville Career Technology Center, Louisville Dudley Vance, Choctaw County Career Technology Center, Ackerman Appreciation is expressed to the following professionals, who provided guidance and insight throughout the development process: Betsey Smith, director for the RCU at MSU Brad Skelton, curriculum manager for the RCU at MSU Standards Standards are superscripted in each unit and are referenced in the appendices. Standards in the APM curriculum framework and supporting materials are based on the following: National Agriculture, Food, and Natural Resources (AFNR) Career Cluster Content Standards The national AFNR Career Cluster Content Standards were developed by the National Council on Agricultural Education (NCAE) to serve as a guide for what students should know or be able to do through a study of agriculture in Grades 9-12 and two-year postsecondary programs. The standards were extensively researched and reviewed by leaders in the agricultural industry, secondary and postsecondary instructors, and university specialists. The standards consist of a pathway content standard for each of the eight career pathways. For each content standard, performance elements representing major topic areas with accompanying performance indicators were developed. Measurements of assessment of the performance elements and performance indicators were developed at the basic, intermediate, and advanced levels. A complete copy of the standards can be accessed at thecouncil.ffa.org/afnr/. The national AFNR Career Cluster Content Standards are copyrighted to the NCAE and are used by permission. College- and Career-Ready Standards College- and Career-Ready standards emphasize critical thinking, teamwork, and problem-solving skills. Students will learn the skills and abilities demanded by the workforce of today and the future. Mississippi adopted Mississippi College- and Career- Ready Standards (MS CCRS) 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 International Society for Technology in Education (ISTE) Standards Reprinted with permission from ISTE Standards for Students, © 2016, International Society for Technology in Education (ISTE), 800.336.5191 (US and Canada) or 541.302.3777 (international), iste@iste.org. All rights reserved. Permission does not constitute an endorsement by ISTE. iste.org 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. 21 Framework Definitions. Published 2015. p21.org/storage/documents/docs/P21_Framework_Definitions_New_Logo_2015.pdf Preface Secondary career and technical education (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 true 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. 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; Carl D. Perkins Vocational Education Act IV, 2007; 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, please call 662.325.2510. Executive Summary Pathway Description The APM pathway is a curriculum that provides an educational option for students who have successfully completed the agriculture technology and mechanical systems core (2 Carnegie credits). APM is a pathway designed to provide basic skills for students to become employed in the industry of agricultural power mechanics or to continue their education in postsecondary institutions. Skills taught in this pathway relate to the selection, operation, service, maintenance, and repair of a variety of agricultural power units and agricultural machinery and equipment. This pathway also includes instruction in diesel engines, advanced cutting and welding skills, hydraulics, pneumatics, and other advanced equipment and power systems. Students in the pathway will participate in active learning exercises including integral activities of the FFA organization and supervised experiences. Students who successfully complete the competencies in this pathway will possess fundamental knowledge and skills that can be used to secure entry-level employment or as a foundation for continuing their education. Industry standards are adapted from the publication Career Cluster Resources for Agriculture, Food, and Natural Resources, developed by the National Association of State Directors of Career and Technical Education. College, Career, and Certifications NCCER Learning Series—Core Standards Credential Grade Level and Class Size Recommendations It is recommended that students enter this program as a 10th grader. Exceptions to this are a district-level decision based on class size, enrollment numbers, and maturity of the student. The classroom and lab are designed to accommodate a maximum of 15 students. Student Prerequisites For students to be able to experience success in the ATMS program, the following student prerequisites are suggested: 1. C or higher in English (the previous year) 2. C or higher in math (last course taken or the instructor can specify the math) 3. Instructor approval and TABE reading score (eighth grade or higher) or 1. TABE reading 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/CurriculumDownload.aspx. If there are questions regarding assessment of this program, please contact the RCU at 662.325.2510. Applied Academic Credit The latest academic credit information can be found at mdek12.org/ESE/Approved-Course-for-the-Secondary-Schools. Once there, click on “Approved Courses for the Secondary Schools of Mississippi.” A PDF file will appear, and you will need to scroll down to the CTE section for the current applied academic credits for the current school year. Check this site often as it is updated frequently. Teacher Licensure The latest teacher licensure information can be found at mdek12.org/OTL/OEL. Professional Learning If you have specific questions about the content of each training session provided, please contact the RCU at 662.325.2510 and ask for a professional learning specialist. Course Outlines Option 1—Two 1-Carnegie Unit Courses This curriculum consists of two 1-credit courses, which should be completed in the following sequence: 1. APM: Diesel and Hydraulic Systems, and Advanced Cutting—Course Code: 991304 2. APM: Advanced Equipment Systems, Maintenance, and Repair—Course Code: 991305 Course Description: APM: Diesel and Hydraulic Systems and Advanced Cutting This course is designed to further develop student skills in metal cutting and welding, as well as broaden student knowledge of hydraulic and pneumatic systems and the operation, maintenance, and repair of diesel engines. An emphasis on following workplace safety guidelines is incorporated throughout the course, and workforce development skills and career options are emphasized. APM: Diesel and Hydraulic Systems and Advanced Cutting—Course Code: 991304 Unit Unit Name Hours Orientation, Safety, and Career Preparation Advanced Cutting and Welding Hydraulic and Pneumatic Systems Diesel Engines Total Course Description: APM: Advanced Equipment Systems, Maintenance, and Repair This course will offer students the opportunity to examine electrical and electronic systems found on modern agricultural equipment. Additionally, students will learn skills related to agricultural power equipment maintenance and operation. Students will also explore advanced and emerging technologies in the agricultural power and machinery industry. APM: Advanced Equipment Systems, Maintenance, and Repair—Course Code: 991305 Unit Unit Name Hours Electrical Systems in Agricultural Mechanics Agricultural Power Equipment Maintenance and Operation Advanced Technology in Agriculture Total Option 2—One 2-Carnegie Unit Course This curriculum consists of one 2-credit course as follows: 1. Agriculture Power and Machinery—Course Code: 991301 Course Description: Agriculture Power and Machinery This course is designed to further develop student skills in metal cutting and welding, as well as broaden student knowledge of hydraulic and pneumatic systems and the operation, maintenance, and repair of diesel engines. An emphasis on following workplace safety guidelines is incorporated throughout the course, and workforce development skills and career options are emphasized. This course will also offer students the opportunity to examine electrical and electronic systems found on modern agricultural equipment. Additionally, students will learn skills related to agricultural power equipment maintenance and operation. Students will also explore advanced and emerging technologies in the agriculture power and machinery industry. Agriculture Power and Machinery—Course Code: 991301 Unit Unit Name Hours Orientation, Safety, and Career Preparation Advanced Cutting and Welding Hydraulic and Pneumatic Systems Diesel Engines Electrical Systems in Agricultural Mechanics Agricultural Power Equipment Maintenance and Operation Advanced Technology in Agriculture Total Research Synopsis By implementing the agriculture power and machinery, students who successfully master the core should have the skills required to earn the NCCER Learning Series—Core Standards Credential and will be eligible to enter the second-year pathway. These skills are based on industry-validated performance indicators. The pathway will include applied instruction designed to articulate with programs offered in Mississippi’s community and junior colleges. Needs of the Future Workforce Data for this synopsis were compiled from the Mississippi Department of Employment Security (2016). Employment opportunities for each of the occupations listed below are: Table 1.1: Current and Projected Occupation Report Occupation Employment Projected Growth 2016-2026 Average Wage Current (2016) Projected (2026) Number Percent Weekly Annual Agricultural Equipment Operators 6.3 $747 $38,818 Outdoor Power Equipment and Other Small Engine Mechanics 10.5 $550 $28,600 Maintenance Workers, Machinery 1,480 1,660 12.2 $957 $49,743 Maintenance and Repair Workers, General 12,960 13,820 6.6 $957 $49,743 Career and Technical Education Teachers 1,220 1,310 7.4 $33,254 Logging Equipment Operators 1,680 1,740 3.6 $705 $36,662 Farm Equipment Mechanics and Service Technicians 1,030 1,100 6.8 $849 $44,123 Support Activities for Agriculture and Forestry 4,780 4,980 4.2 $747 $38,818 Primary Metal Manufacturing 3,370 3,490 3.6 $923 $47,980 Source: Mississippi Department of Employment Security; mdes.ms.gov (accessed May 7, 2019). Perkins IV Requirements The agriculture power and machinery curriculum meets Perkins IV requirements of exposing students to these skills/occupations to prepare them for the workforce. It also offers students a program of study including secondary, postsecondary, and IHL courses that will prepare them for occupations in these fields. Additionally, the agriculture technology and mechanical systems curriculum is integrated with academic Mississippi’s College- and Career-Readiness Standards. Lastly, the agriculture technology and mechanical systems curriculum focuses on ongoing and meaningful professional development for teachers as well as relationships with industry. Curriculum Content Summary of Standards  Opportunities to enter careers in agriculture power and machinery on a full-scale commercial enterprise basis exist and are expected to increase as agriculture machinery manufacturers continue to locate their production facilities in our state. Career opportunities are also expected to increase for specialized technicians who can maintain and repair the equipment.  There was general agreement among all interviewed that students need to better develop soft skills related to leadership, teamwork, communication, work ethic, habits, and values. All respondents also indicated that a basic knowledge of economics, recordkeeping, budgeting, and business decision-making skills are essential in today’s competitive environment.  Opportunities are growing for high school graduates who possess a specialization of skills in agriculture power and machinery and want to pursue further specialized skill development, especially training offered by the manufacturer of the equipment. The availability of basic entry-level positions is determined by geographic location and the predominant type of agricultural enterprises in the area. More abundant opportunities exist for students who have received advanced training at the community college or university level. Academic Infusion The APM curriculum is tied to the Mississippi College- and Career-Ready Standards. The curriculum provides multiple opportunities to enhance and reinforce academic skills. Because students will be required to communicate effectively in the classroom and in the workforce, there is a considerable amount of reading and writing in this curriculum. Overall, the APM curriculum requires students to make presentations, read technical manuals, and use strategic and critical- thinking skills to solve real-world problems. The location of the College- and Career-Ready standards for each unit is located in Appendices D-F. Transition to Postsecondary Education The latest articulation information for secondary to postsecondary can be found at the Mississippi Community College Board (MCCB) website, mccb.edu/. Best Practices The premise of the success of all school-based, agricultural-education programs is focused on the implementation of the three-circle model, which depicts the three major components of the program interlocked and working together as one. The three components are classroom and laboratory instruction, experiential learning through supervised agricultural experience (SAE) programs for individual students, and participation in the CTE student organization for agriculture education, the National FFA Organization. Classroom and Laboratory Instruction The classroom and laboratory component of the school-based, agricultural-education three-circle model is the foundation for the success of the other two components, SAE and FFA. Through contextual learning, students in agricultural education can learn the science, business, and technology of modern agriculture through innovative instructional technologies, differentiated instruction, and cooperative learning. Innovative Instructional Technologies Recognizing that today’s students are digital learners, the classroom should be equipped with tools that will teach them in the way they need to learn. The APM curriculum teacher’s goal should be to include teaching strategies that incorporate current technology. It is suggested each classroom house a set of smart tablets and one teacher laptop. The classroom teacher is encouraged to make use of the latest online communication tools, such as wikis, blogs, and podcasts, through the use of a learning management system that introduces students to teaching and learning strategies in an online environment and places the responsibility of learning on the student. Differentiated Instruction All students are unique and possess individualized learning styles. Differentiated instruction is an approach to teaching that addresses the differences in learning styles by providing alternative teaching and assessment methods that reach across the spectrum of student needs in the classroom. By differentiating instruction in APM, teachers can more effectively reach students and address their strengths and weaknesses, therefore increasing student success. The implementation of various forms of technology; the use of alternative assessments, such as rubrics and problem-based assessment; and utilizing hands-on and work-based learning opportunities in the program of instruction truly enhance the quality of the curriculum presentation. Cooperative Learning Cooperative learning can help students understand topics when independent learning cannot. Therefore, you will see several opportunities in the APM 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 APM curriculum provides opportunities for students to work together and help each other complete complex tasks. Experiential Learning The experiential learning, or SAE, component has long been an integral part of the school-based, agricultural-education three-component model. Students are encouraged to explore their career interests and plan an experiential, service, and/or work-based learning program to guide them to their career goals. This SAE program guides the students as they maintain a record-keeping system of time and money invested, and the skills gained from their experiences. The experiential learning projects can be used in a variety of situations to reinforce and complement classroom theory and content. The experiential learning project consists of entrepreneurship, placement, research/experimentation, and exploratory discovery, and the project spans the duration of program enrollment. CTE Student Organizations As the third part of the school-based, agricultural-education model, the FFA component is the showcase of leadership, growth, and development for students. The FFA is the student organization for the APM curriculum. It offers many opportunities for student success, such as leadership development, career development events, degrees of attainment, awards and scholarships, and community service. The organization provides students with growth opportunities and competitive events. It also opens the doors to the world of agriculture and scholarship opportunities. Conclusion The APM curriculum is designed to prepare students for the agriculture power machinery workforce. It is a systematic program of instruction, and students who complete this program are well equipped for a variety of careers and have the basic skills in agricultural mechanics that will serve as a catalyst to further develop according to specific industry skill standards. Instructors are urged to encourage APM students to pursue postsecondary educational opportunities at community colleges and universities in Mississippi. Professional Organizations Agricultural Education Division of the Association for Career and Technical Education acteonline.org/ American Association for Agricultural Education aaaeonline.org/ Mississippi ACTE mississippiacte.com/ Mississippi Association of Vocational Agriculture Teachers (MAVAT) mississippiffa.org National Association of Agricultural Educators naae.org/ National Association of Supervisors of Agricultural Education ffa.org/thecouncil/nasae/ National FFA Alumni Association ffa.org/getinvolved/alumni/ National FFA Foundation, Inc. ffa.org/support/foundation/ National Farm and Ranch Business Management Education Association nfrbmea.org/ National Postsecondary Agricultural Student Organization nationalpas.org/ National Young Farmer Educational Association nyfea.org Using This Document Suggested Time on Task An estimated number of clock hours of instruction that should be required to teach the competencies and objectives of the unit. A minimum of 140 hours of instruction is required for each Carnegie unit credit. The curriculum framework should account for approximately 75–80% of the time in the course. 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. Integrated Academic Topics, 21st Century Skills and Information and Communication Technology Literacy Standards, ACT College Readiness Standards, and Technology Standards for Students This section identifies related academic topics as required in the Subject Area Testing Program (SATP) in Algebra I, Biology I, English II, and U.S. History from 1877, which are integrated into the content of the unit. Research-based teaching strategies also incorporate ACT College Readiness Standards. This section also identifies the 21st Century Skills and Information and Communication Technology Literacy skills. In addition, national technology standards for students associated with the competencies and suggested objectives for the unit are also identified. References A list of suggested references is provided for each unit. The list includes some of the primary instructional resources that may be used to teach the competencies and suggested objectives. Again, these resources are suggested, and the list may be modified or enhanced based on the needs and abilities of students and on available resources. The teacher resource document can be downloaded at rcu.msstate.edu/Curriculum/CurriculumDownload.aspx. Unit 1: Orientation, Safety, and Career Preparation Competencies and Suggested Objectives 1. Review the local school rules and regulations. DOK1 a. Describe the local school rules found in the student handbook. b. Describe attendance policies. c. Describe the laboratories and facilities associated with the program. 2. Review the general laboratory safety requirements for APM. DOK1 a. Review the personal safety rules for working in the laboratory and/or APM industry, including the eye safety law. b. Review general workplace safety rules and/or other safety organizations standards. c. Review accident reporting procedures. d. Review procedures for applying fire safety in the agricultural mechanics shop. e. Review the location of firefighting equipment. f. Review the classes of fires and the associated equipment for each class. g. Review exit locations in case of emergency. 3. Investigate and develop the skills necessary for pursuing a career in the APM industry. DOK3 a. Compare the careers available in the APM industry. b. Build a personal résumé and cover letter for the purpose of applying for jobs. c. Perform a mock interview utilizing a personal résumé and cover letter. 4. Develop an individual FFA activity plan. DOK2 a. Identify FFA activities and programs that contribute to career advancement and individual achievement. b. Select and document FFA activities and programs that contribute to personal development. 5. Develop and present a 3- to 5-minute multimedia presentation on an APM-related topic. DOK3 a. Discuss the guidelines for preparing a successful presentation, including preparation, resource development, writing skills, and presentation skills. 6. Maintain SAE records. DOK2 a. Maintain records as they relate to SAE activities. 7. Develop an understanding of personal financial management. DOK2 a. Explain how wages, salaries, and benefits work when you become employed. b. Describe the differences in wages and salary payment options (monthly, weekly, bi- weekly, overtime, salary vs. hourly wage, flat rate, etc.). c. Describe how to open and maintain personal financial bank accounts. d. Describe employment benefits (insurance, vacation/personal/medical leave, retirement, etc.). e. Calculate the amount of income and other taxes that are to be deducted from your paycheck. f. Understand the cost of living associated with where you work and live. g. Develop an individual cost of living budget. Unit 2: Advanced Cutting and Welding Competencies and Suggested Objectives 1. Perform advanced Shielded Metal Arc Welding (SMAW).DOK2 a. Perform vertical and horizontal butt welds in mild steel. b. Perform fillet and lap welds in vertical and horizontal positions. 2. Perform Gas Metal Arc Welding (GMAW). DOK2 a. Demonstrate the safety procedures for GMAW. b. Identify and describe the use of different supplies and accessories associated with GMAW. c. Discuss the welding equipment setup associated with metal thicknesses and types. d. Set up GMAW welding equipment. e. Weld mild steel with GMAW welding equipment in the flat, vertical, horizontal, and overhead positions. 3. Perform Gas Tungsten Arc Welding (GTAW) welding. DOK2 a. Demonstrate the safety procedures for GTAW welding. b. Identify the accessories and supplies used in GTAW welding and describe their use. c. Discuss the welding equipment setup associated with metal thicknesses and types. d. Set up GTAW welding equipment. e. Weld with GTAW welding equipment. 4. Perform Plasma Arc Cutting (PAC). DOK2 a. Demonstrate the safety procedures for PAC. b. Discuss the plasma arc cutting process. c. Discuss the components of a plasma arc cutter. d. Set up PAC equipment. e. Cut mild steel with PAC equipment. f. Discuss the use of computer-controlled machinery in metal fabrication. g. Design and construct a metal project with computer-controlled machinery. 5. Fabricate metal components from a blueprint. DOK4 a. Interpret the basic elements of a blueprint. b. Interpret welding symbol information. c. Apply the design of a blueprint to the construction of a metal project using a variety of fittings and welding skills that are used in a local or regional industrial manufacturing facility. Unit 3: Hydraulic and Pneumatic Systems Competencies and Suggested Objectives 1. Explain the physical laws of hydraulics and pneumatics. DOK1 a. Define kinetic energy. b. Define potential energy. 2. Identify the types of hydraulic pumps. DOK1 a. Identify a constant displacement pump. b. Identify a variable displacement pump. 3. Identify and describe the functions of hydraulic and pneumatic control valves. DOK2 a. Describe the types of hydraulic and pneumatic valves.  Spool valve  Check valve  Relief valve b. Explain the functions of hydraulic and pneumatic valves. 4. Identify and describe the functions of hydraulic and pneumatic actuators. DOK2 a. Distinguish among the types of hydraulic and pneumatic actuators.  Manual  Solenoid b. Explain the functions of hydraulic and pneumatic actuators. 5. Explain the functions of hydraulic and pneumatic systems. DOK2 a. Describe the function of an open center hydraulic and pneumatic system. b. Describe the function of a closed center hydraulic and pneumatic system. c. Read and interpret basic hydraulic and pneumatic schematics symbols.  Pump  Valve (relief and spool)  Reservoir  Motor  Filter  Actuator (cylinder) 6. Demonstrate the maintenance of hydraulic and pneumatic systems per the manufacturer’s specifications. DOK2 a. Check the fluid levels and condition. b. Service the filter system. c. Change hydraulic fluids. d. Inspect the system for external leaks and correct where necessary. 7. Demonstrate and explain how hydraulic and pneumatic systems operate. DOK3 Unit 4: Diesel Engines Competencies and Suggested Objectives 1. Describe the basic operating principles of diesel engines. DOK1 a. Identify the differences between a diesel engine and a gasoline engine. b. Describe the sequence of events in each stroke of a four-cycle diesel engine. 2. Describe the components of the diesel engine. DOK1 a. Identify the components of the basic engine block assembly.  Engine block  Cylinder head  Pistons  Connecting rods  Crankshaft and bearings  Camshaft and bearings  Cylinder liners  Turbocharger b. Explain the functions of each component of the diesel engine. 3. Describe the components of the lubrication system. DOK1 a. Identify the components of the lubrication system.  Oil pump  Oil cooler  Filter  Relief valve b. Describe the functions of each component of the lubrication system. 4. Describe the components of the cooling system. DOK1 a. Identify the components of the cooling system.  Radiator  Thermostat  Water pump  Radiator cap  Radiator hoses  Belts and pulleys  Coolant and shroud  Mechanical fan clutch b. Describe the functions of each component of the cooling system. 5. Describe the components of the fuel system. DOK1 a. Identify the components of the fuel system.  Reservoir  Transfer pump  Injector pump  Injectors  Filter  Valves  Lines and hoses  Fuel b. Describe the functions of each component of the fuel system. 6. Describe the components of the intake and exhaust system. DOK2 a. Label the components of the intake and exhaust system.  DPF (diesel particulate filter)  DEF (diesel exhaust fluid)  EGR valve (exhaust gas recirculation) b. Describe the functions of the intake and exhaust system. 7. Perform basic maintenance and troubleshoot problems regarding the operation of a diesel engine. a. Set up a preventative maintenance plan for diesel engine-operated equipment or machinery. b. Perform primary engine checks on diesel equipment or machinery. c. Perform basic diesel engine preventative maintenance. d. Outline the general procedure for troubleshooting diesel engines. e. Use troubleshooting charts and engine service information to pinpoint the source of problems in a diesel engine. Unit 5: Electrical Systems in Agricultural Mechanics Competencies and Suggested Objectives 1. Explain the functions of the components of the cranking and charging systems. DOK1 a. Describe the function of the cranking system.  Starter  Solenoid  Relay  Battery b. Describe the function of the charging system. 2. Demonstrate the troubleshooting and repair procedures for the electrical system. DOK2 a. Demonstrate the ability to use a digital multimeter to troubleshoot amps, ohms, and volts. b. Use service sources to check manufacturers’ specifications on the electrical systems. c. Read and interpret electrical symbols and schematics.  Open/close switch  Fuse  Fuse link  Conductor  Breaker  Power source  Relay  Solenoid  Light bulb  Electric motor d. Make the necessary wire and terminal repairs using the soldering method and wire connectors. 3. Investigate the electronics systems used on tractors, implements, stationary systems, and recreational vehicles. DOK2 a. Discuss the use of electronic sensors on tractors and implements. b. Research emerging technology for or in electronics and electrical systems in the agriculture power and machinery industry. Unit 6: Agricultural Power Equipment Maintenance and Operation Competencies and Suggested Objectives 1. Review the basic concepts of how power is generated and transferred through the use of agricultural equipment. DOK2 a. Describe the terms of power including work, force, and torque. b. Explain the differences in PTO, drawbar, and brake horsepower. c. Identify the different types and uses of clutches (centrifugal, mechanical, and hydraulic). d. Identify the parts associated with differential and axle systems. e. Explore hydraulic and air brake systems. 2. Review manufacturers’ manuals for periodic maintenance of agricultural power equipment. DOK1 a. Read and interpret manufacturers’ manuals to obtain specifications for periodic maintenance. b. Perform periodic maintenance according to manufacturers’ specifications. 3. Review manufacturers’ manuals for seasonal maintenance of agricultural power equipment. DOK1 a. Read and interpret manufacturers’ manuals to obtain specifications for seasonal maintenance. b. Perform seasonal maintenance according to manufacturers’ specifications. 4. Review the operator's manuals to determine the procedures for safe operation of agricultural power equipment. DOK1 a. Identify equipment controls and describe their functions. b. Identify instruments and indicators and describe their functions. c. Identify safety equipment including safety switches, rollover protection, and seat belts. d. Apply safety rules when operating agricultural power equipment. 5. Operate agricultural power equipment safely. DOK1 a. Conduct an inspection prior to operation. b. Operate the tractor safely including starting, warm-up, clutch engagement, and brake controls. c. Attach, set up, and adjust an implement on a tractor. d. Demonstrate operation under field conditions. 6. Perform basic maintenance regarding the operation of agricultural equipment. a. Set up a preventative maintenance plan for a specific piece of agricultural equipment. b. Perform primary preoperational checks on agricultural equipment. c. Perform basic preventative maintenance on equipment. d. Use troubleshooting charts and engine service information to pinpoint the source of problems in a diesel engine. 7. Apply troubleshooting methods for resolving mechanical issues with agricultural equipment. DOK2 a. Explain the meaning and importance of troubleshooting. b. Describe the processes and tools used in agricultural equipment troubleshooting. c. Use computer-aided diagnostic equipment to troubleshoot agricultural power equipment. d. Apply troubleshooting procedures in solving a problem on a piece of agricultural power equipment. Unit 7: Advanced Technology in Agriculture Competencies and Suggested Objectives 1. Research how advanced technology is being utilized in agriculture. DOK3 a. Discuss areas of new technology applications in APM. b. Observe applications of new technology in the agriculture power and machinery industry. c. Conduct investigations to observe and record applications of advanced technology in agriculture.  Remanufacturing equipment  3-D metal fabrication  Development of electrical sensors and applications for APM  The use of robotics in manufacturing APM 2. Discuss the concepts and operating principles of precision agriculture technology. DOK2 a. Identify and describe the components of a precision agriculture technology system. b. Describe the use of global positioning systems in precision agriculture. c. Describe the use of spatial imagery in precision agriculture. d. Describe the use of geographic information system software in precision agriculture. e. Describe the use of variable-rate application in precision agriculture. f. Describe the use of yield monitoring in precision agriculture. Student Competency Profile 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, record the date on which the student mastered the competency. Unit 1: Orientation, Safety, and Career Preparation 1. Review the local school rules and regulations. 2. Review the general laboratory safety requirements for APM. 3. Investigate and develop the skills necessary for pursuing a career in the APM industry. 4. Develop an individual FFA activity plan. 5. Develop and present a 3- to 5-minute multimedia presentation on an APM-related topic. 6. Maintain SAE records. 7. Develop an understanding of personal financial management. Unit 2: Advanced Cutting and Welding 1. Perform advanced SMAW. 2. Perform GMAW. 3. Perform GTAW. 4. Perform Plasma Arc Cutting (PAC). 5. Fabricate metal components from a blueprint. 6. Perform advanced SMAW. Unit 3: Hydraulic and Pneumatic Systems 1. Explain the physical laws of hydraulics and pneumatics. 2. Identify the types of hydraulic pumps. 3. Identify and describe the functions of hydraulic and pneumatic control valves. 4. Identify and describe the functions of hydraulic and pneumatic actuators. 5. Explain the functions of hydraulic and pneumatic systems. 6. Demonstrate the maintenance of hydraulic and pneumatic systems per manufacturers’ specifications. 7. Demonstrate and explain how hydraulic and pneumatic systems operate. Unit 4: Diesel Engines 1. Describe the basic operating principles of diesel engines. 2. Describe the components of the diesel engine. 3. Describe the components of the lubrication system. 4. Describe the components of the cooling system. 5. Describe the components of the fuel system. 6. Describe the components of an intake and exhaust system. 7. Perform basic maintenance and troubleshoot problems regarding the operation of a diesel engine. Unit 5: Electrical Systems in Agricultural Mechanics 1. Explain the functions of the components of the cranking and charging systems. 2. Demonstrate the troubleshooting and repair procedures for the electrical system. 3. Investigate the electronics systems used on tractors, implements, stationary systems, and recreational vehicles. Unit 6: Agricultural Power Equipment Maintenance and Operation 1. Review the basic concepts of how power is generated and transferred through the use of agricultural equipment. 2. Review the manufacturers’ manuals for periodic maintenance of agricultural power equipment. 3. Review the manufacturers’ manuals for seasonal maintenance of agricultural power equipment. 4. Review the operator's manuals to determine the procedures for the safe operation of agricultural power equipment. 5. Operate agricultural power equipment safely. 6. Perform basic maintenance regarding the operation of agricultural equipment. 7. Apply troubleshooting methods for resolving mechanical issues with agricultural equipment. Unit 7: Advanced Technology in Agriculture 1. Research how advanced technology is being utilized in agriculture. 2. Discuss the concepts and operating principles of precision agriculture technology. Source: Miss. Code Ann. §§ 37-1-3 and 37-31-103 Appendix A: Industry Standards AGRICULTURE, FOOD, AND NATURAL RESOURCES (AFNR) PATHWAY CONTENT STANDARDS AND PERFORMANCE ELEMENTS Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 AFNR ABS -AGRIBUSINESS SYSTEMS AS -ANIMAL SYSTEMS BS -BIOTECHNOLOGY CRP - CAREER READY PRACTICES X X CS – AGRICULTURE, FOOD, AND NATURAL RESOURCES CLUSTER SKILL X X ES -ENVIRONMENTAL SERVICE SYSTEMS FPP- FOOD PRODUCTS AND PROCESSING SYSTEMS NRS -NATURAL RESOURCE SYSTEMS PS -PLANT SYSTEMS PST -POWER, STRUCTURAL, AND TECHNICAL SYSTEMS X X X X X ABS AGRIBUSINESS SYSTEMS AS ANIMAL SYSTEMS BS BIOTECHNOLOGY CRP CAREER READY PRACTICES CS AGRICULTURE, FOOD, AND NATURAL RESOURCES CLUSTER SKILL ES ENVIRONMENTAL SERVICE SYSTEMS FPP FOOD PRODUCTS AND PROCESSING SYSTEMS NRS NATURAL RESOURCE SYSTEMS PS PLANT SYSTEMS PST POWER, STRUCTURAL, AND TECHNICAL SYSTEMS The AFNR pathway content standards and performance elements are adapted from the National Agriculture, Food, and Natural Resources (AFNR) Career Cluster Content Standards. Reprinted with permission from the National Council for Agricultural Education, 1410 King Street, Suite 400, Alexandria, VA 22314, 800.772.0939. Copyright © 2015 A complete copy of the National Standards can be downloaded from the FFA website at ffa.org/thecouncil. Agribusiness Systems Career Pathway Content Standards The Agribusiness Systems (ABS) Career Pathway encompasses the study of agribusinesses and their management including, but not limited to, record keeping, budget management (cash and credit), and business planning, and sales and marketing. Students completing a program of study in this pathway will demonstrate competence in the application of principles and techniques for the planning, development, application and management of agribusiness systems in AFNR settings. Within each pathway, the standards are organized as follows:  Common Career Technical Core (CCTC) Standards – These are the standards for Agribusiness Systems (AG-ABS) from the 2012 version of the Common Career and Technical Core Standards, which are owned by the National Association of State Directors of Career and Technical Education/National Career Technical Education Foundation and are used here with permission. These statements define what students should know and be able to do after completing instruction in a program of study for this pathway.  Performance Indicators – These statements distill each CCTC Standard into more discrete indicators of the knowledge and skills students should attain through a program of study in this pathway. Attainment of the knowledge and skills outlined in the performance indicators is intended to demonstrate an acceptable level of proficiency with the related CCTC Standard at the conclusion of a program of study in this area. ABS.01. CCTC Standard: Apply management planning principles in AFNR businesses. ABS.01.01. Performance Indicator: Apply micro- and macroeconomic principles to plan and manage inputs and outputs in an AFNR business. ABS.01.02. Performance Indicator: Read, interpret, evaluate and write statements of purpose to guide business goals, objectives and resource allocation. ABS.01.03. Performance Indicator: Devise and apply management skills to organize and run an AFNR business in an efficient, legal and ethical manner. ABS.01.04. Performance Indicator: Evaluate, develop and implement procedures used to recruit, train and retain productive human resources for AFNR businesses. ABS.02. CCTC Standard: Use record keeping to accomplish AFNR business objectives, manage budgets and comply with laws and regulations. ABS.02.01. Performance Indicator: Apply fundamental accounting principles, systems, tools and applicable laws and regulations to record, track and audit AFNR business transactions (e.g., accounts, debits, credits, assets, liabilities, equity, etc.). ABS.02.02. Performance Indicator: Assemble, interpret and analyze financial information and reports to monitor AFNR business performance and support decision-making (e.g., income statements, balance sheets, cash-flow analysis, inventory reports, break-even analysis, return on investment, taxes, etc.). ABS.03. CCTC Standard: Manage cash budgets, credit budgets and credit for an AFNR business using generally accepted accounting principles. ABS.03.01. Performance Indicator: Develop, assess and manage cash budgets to achieve AFNR business goals. ABS.03.02. Performance Indicator: Analyze credit needs and manage credit budgets to achieve AFNR business goals. ABS.04. CCTC Standard: Develop a business plan for an AFNR business. ABS.04.01. Performance Indicator: Analyze characteristics and planning requirements associated with developing business plans for different types of AFNR businesses. ABS.04.02. Performance Indicator: Develop production and operational plans for an AFNR business. ABS.04.03. Performance Indicator: Identify and apply strategies to manage or mitigate risk. ABS.05. CCTC Standard: Use sales and marketing principles to accomplish AFNR business objectives. ABS.05.01. Performance Indicator: Analyze the role of markets, trade, competition and price in relation to an AFNR business sales and marketing plans. ABS.05.02. Performance Indicator: Assess and apply sales principles and skills to accomplish AFNR business objectives. ABS.05.03. Performance Indicator: Assess marketing principles and develop marketing plans to accomplish AFNR business objectives. Animal Systems Career Pathway Content Standards The Animal Systems (AS) Career Pathway encompasses the study of animal systems, including content areas such as life processes, health, nutrition, genetics, and management and processing, as applied to small animals, aquaculture, exotic animals, livestock, dairy, horses and/or poultry. Students completing a program of study in this pathway will demonstrate competence in the application of principles and techniques for the development, application and management of animal systems in AFNR settings. Within each pathway, the standards are organized as follows:  Common Career Technical Core (CCTC) Standards – These are the standards for Animal Systems (AG-AS) from the 2012 version of the Common Career and Technical Core Standards, which are owned by the National Association of State Directors of Career and Technical Education/National Career Technical Education Foundation and are used here with permission. These statements define what students should know and be able to do after completing instruction in a program of study for this pathway.  Performance Indicators – These statements distill each CCTC Standard into more discrete indicators of the knowledge and skills students should attain through a program of study in this pathway. Attainment of the knowledge and skills outlined in the performance indicators is intended to demonstrate an acceptable level of proficiency with the related CCTC Standard at the conclusion of a program of study in this area. AS.01. CCTC Standard: Analyze historic and current trends impacting the animal systems industry. AS.01.01. Performance Indicator: Evaluate the development and implications of animal origin, domestication and distribution on production practices and the environment. AS.01.02. Performance Indicator: Assess and select animal production methods for use in animal systems based upon their effectiveness and impacts. AS.01.03. Performance Indicator: Analyze and apply laws and sustainable practices to animal agriculture from a global perspective. AS.02. CCTC Standard: Utilize best-practice protocols based upon animal behaviors for animal husbandry and welfare. AS.02.01. Performance Indicator: Demonstrate management techniques that ensure animal welfare. AS.02.02. Performance Indicator: Analyze procedures to ensure that animal products are safe for consumption (e.g., use in food system, etc.). AS.03. CCTC Standard: Design and provide proper animal nutrition to achieve desired outcomes for performance, development, reproduction and/or economic production. AS.03.01. Performance Indicator: Analyze the nutritional needs of animals. AS.03.02 Performance Indicator: Analyze feed rations and assess if they meet the nutritional needs of animals. AS.03.03 Performance Indicator: Utilize industry tools to make animal nutrition decisions. AS.04. CCTC Standard: Apply principles of animal reproduction to achieve desired outcomes for performance, development and/or economic production. AS.04.01. Performance Indicator: Evaluate animals for breeding readiness and soundness. AS.04.02. Performance Indicator: Apply scientific principles to select and care for breeding animals. AS.04.03 Performance Indicator: Apply scientific principles to breed animals. AS.05. CCTC Standard: Evaluate environmental factors affecting animal performance and implement procedures for enhancing performance and animal health. AS.05.01. Performance Indicator: Design animal housing, equipment and handling facilities for the major systems of animal production. AS.05.02. Performance Indicator: Comply with government regulations and safety standards for facilities used in animal production. AS.06. CCTC Standard: Classify, evaluate and select animals based on anatomical and physiological characteristics. AS.06.01. Performance Indicator: Classify animals according to taxonomic classification systems and use (e.g. agricultural, companion, etc.). AS.06.02. Performance Indicator: Apply principles of comparative anatomy and physiology to uses within various animal systems. AS.06.03. Performance Indicator: Select and train animals for specific purposes and maximum performance based on anatomy and physiology. AS.07. CCTC Standard: Apply principles of effective animal health care. AS.07.01. Performance Indicator: Design programs to prevent animal diseases, parasites and other disorders and ensure animal welfare. AS.07.02. Performance Indicator: Analyze biosecurity measures utilized to protect the welfare of animals on a local, state, national, and global level. AS.08. CCTC Standard: Analyze environmental factors associated with animal production. AS.08.01. Performance Indicator: Design and implement methods to reduce the effects of animal production on the environment. AS.08.02. Performance Indicator: Evaluate the effects of environmental conditions on animals and create plans to ensure favorable environments for animals. Common Career Technical Core Career Ready Practices Content Standards The CCTC CRPs encompass fundamental skills and practices that all students should acquire to be career ready such as: responsibility, productivity, healthy choices, maintaining personal finances, communication, decision-making, creativity and innovation, critical-thinking, problem solving, integrity, ethical leadership, management, career planning, technology use and cultural/global competency. Students completing a program of study in any AFNR career pathway will demonstrate the knowledge, skills and behaviors that are important to career ready through experiences in a variety of settings (e.g., classroom, CTSO, work-based learning, community etc.). DEFINITIONS: Within each pathway, the standards are organized as follows:  Common Career Technical Core (CCTC) Standards – These are the standards for CRPs from the 2012 version of the Common Career and Technical Core Standards, which are owned by the National Association of State Directors of Career and Technical Education/National Career Technical Education Foundation and are used here with permission. These statements define what students should know and be able to do after completing instruction in a program of study for this pathway.  Performance Indicators –These statements distill each CCTC Standard into more discrete indicators of the knowledge and skills students should attain through a program of study in this pathway. Attainment of the knowledge and skills outlined in the performance indicators is intended to demonstrate an acceptable level of proficiency with the related CCTC Standard at the conclusion of a CTE program of study. CRP.01. CCTC Standard: Act as a responsible and contributing citizen and employee. CRP.01.01. Performance Indicator: Model personal responsibility in the workplace and community. CRP.01.02 Performance Indicator: Evaluate and consider the near-term and long-term impacts of personal and professional decisions on employers and community before taking action. CRP.01.03. Performance Indicator: Identify and act upon opportunities for professional and civic service at work and in the community. CRP.02. CCTC Standard: Apply appropriate academic and technical skills. CRP.02.01. Performance Indicator: Use strategic thinking to connect and apply academic learning, knowledge and skills to solve problems in the workplace and community. CRP.02.02. Performance Indicator: Use strategic thinking to connect and apply technical concepts to solve problems in the workplace and community. CRP.03. CCTC Standard: Attend to personal health and financial well-being. CRP.03.01. Performance Indicator: Design and implement a personal wellness plan. CRP.03.02. Performance Indicator: Design and implement a personal financial management plan. CRP.04. CCTC Standard: Communicate clearly, effectively and with reason. CRP.04.01. Performance Indicator: Speak using strategies that ensure clarity, logic, purpose and professionalism in formal and informal settings. CRP.04.02. Performance Indicator: Produce clear, reasoned and coherent written and visual communication in formal and informal settings. CRP.04.03. Performance Indicator: Model active listening strategies when interacting with others in formal and informal settings. CRP.05. CCTC Standard: Consider the environmental, social and economic impacts of decisions. CRP.05.01. Performance Indicator: Assess, identify and synthesize the information and resources needed to make decisions that positively impact the workplace and community. CRP.05.02. Performance Indicator: Make, defend and evaluate decisions at work and in the community using information about the potential environmental, social and economic impacts. CRP.06. CCTC Standard: Demonstrate creativity and innovation. CRP.06.01. Performance Indicator: Synthesize information, knowledge and experience to generate original ideas and challenge assumptions in the workplace and community. CRP.06.02. Performance Indicator: Assess a variety of workplace and community situations to identify ways to add value and improve the efficiency of processes and procedures. CRP.06.03. Performance Indicator: Create and execute a plan of action to act upon new ideas and introduce innovations to workplace and community organizations. CRP.07. CCTC Standard: Employ valid and reliable research strategies. CRP.07.01. Performance Indicator: Select and implement reliable research processes and methods to generate data for decision-making in the workplace and community. CRP.07.02. Performance Indicator: Evaluate the validity of sources and data used when considering the adoption of new technologies, practices and ideas in the workplace and community. CRP.08. CCTC Standard: Utilize critical thinking to make sense of problems and persevere in solving them. CRP.08.01. Performance Indicator: Apply reason and logic to evaluate workplace and community situations from multiple perspectives. CRP.08.02. Performance Indicator: Investigate, prioritize and select solutions to solve problems in the workplace and community. CRP.08.03. Performance Indicator: Establish plans to solve workplace and community problems and execute them with resiliency. CRP.09. CCTC Standard: Model integrity, ethical leadership and effective management. CRP.09.01. Performance Indicator: Model characteristics of ethical and effective leaders in the workplace and community (e.g. integrity, self-awareness, self- regulation, etc.). CRP.09.02. Performance Indicator: Implement personal management skills to function effectively and efficiently in the workplace (e.g., time management, planning, prioritizing, etc.). CRP.09.03. Performance Indicator: Demonstrate behaviors that contribute to a positive morale and culture in the workplace and community (e.g., positively influencing others, effectively communicating, etc.). CRP.10. CCTC Standard: Plan education and career path aligned to personal goals. CRP.10.01. Performance Indicator: Identify career opportunities within a career cluster that match personal interests, talents, goals and preferences. CRP.10.02. Performance Indicator: Examine career advancement requirements (e.g., education, certification, training, etc.) and create goals for continuous growth in a chosen career. CRP.10.03. Performance Indicator: Develop relationships with and assimilate input and/or advice from experts (e.g., counselors, mentors, etc.) to plan career and personal goals in a chosen career area. CRP.10.04. Performance Indicator: Identify, prepare, update and improve the tools and skills necessary to pursue a chosen career path. CRP.11. CCTC Standard: Use technology to enhance productivity. CRP.11.01. Performance Indicator: Research, select and use new technologies, tools and applications to maximize productivity in the workplace and community. CRP.11.02. Performance Indicator: Evaluate personal and organizational risks of technology use and take actions to prevent or minimize risks in the workplace and community. CRP.12. CCTC Standard: Work productively in teams while using cultural/global competence. CRP.12.01. Performance Indicator: Contribute to team-oriented projects and builds consensus to accomplish results using cultural global competence in the workplace and community. CRP.12.02. Performance Indicator: Create and implement strategies to engage team members to work toward team and organizational goals in a variety of workplace and community situations (e.g., meetings, presentations, etc.). Agriculture, Food, and Natural Resources Cluster Skill Content Standards The AFNR Cluster Skills (CS) encompasses the study of fundamental knowledge and skills related to all AFNR professions. Students completing a program of study in any AFNR career pathway will demonstrate fundamental knowledge of the nature, scope and relationships of AFNR systems and the skills necessary for analysis of current and historical issues and trends; application of technologies; safety, health and environmental practices; stewardship of natural resources; and exploration of career opportunities. Within each pathway, the standards are organized as follows:  Common Career Technical Core (CCTC) Standards – These are the standards for Agriculture, Food and Natural Resources Career Cluster® (AG) from the 2012 version of the Common Career and Technical Core Standards, which are owned by the National Association of State Directors of Career and Technical Education/National Career Technical Education Foundation and are used here with permission. These statements define what students should know and be able to do after completing instruction in a program of study for this pathway.  Performance Indicators –These statements distill each CCTC Standard into more discrete indicators of the knowledge and skills students should attain through a program of study in this pathway. Attainment of the knowledge and skills outlined in the performance indicators is intended to demonstrate an acceptable level of proficiency with the related CCTC Standard at the conclusion of a program of study in this area. CS.01. CCTC Standard: Analyze how issues, trends, technologies and public policies impact systems in the Agriculture, Food & Natural Resources Career Cluster. CS.01.01. Performance Indicator: Research, examine and discuss issues and trends that impact AFNR systems on local, state, national and global levels. CS.01.02. Performance Indicator: Examine technologies and analyze their impact on AFNR systems. CS.01.03. Performance Indicator: Identify public policies and examine their impact on AFNR systems. CS.02. CCTC Standard: Evaluate the nature and scope of the Agriculture, Food & Natural Resources Career Cluster and the role of agriculture, food and natural resources (AFNR) in society and the economy. CS.02.01. Performance Indicator: Research and use geographic and economic data to solve problems in AFNR systems. CS.02.02. Performance Indicator: Examine the components of the AFNR systems and assess their impact on the local, state, national and global society and economy. CS.03. CCTC Standard: Examine and summarize the importance of health, safety and environmental management systems in AFNR workplaces. CS.03.01. Performance Indicator: Identify and explain the implications of required regulations to maintain and improve safety, health and environmental management systems. CS.03.02. Performance Indicator: Develop and implement a plan to maintain and improve health, safety and environmental compliance and performance. CS.03.03. Performance Indicator: Apply health and safety practices to AFNR workplaces. CS.03.04. Performance Indicator: Use appropriate protective equipment and demonstrate safe and proper use of AFNR tools and equipment. CS.04. CCTC Standard: Demonstrate stewardship of natural resources in AFNR activities. CS.04.01. Performance Indicator: Identify and implement practices to steward natural resources in different AFNR systems. CS.04.02. Performance Indicator: Assess and explain the natural resource related trends, technologies and policies that impact AFNR systems. CS.05. CCTC Standard: Describe career opportunities and means to achieve those opportunities in each of the Agriculture, Food & Natural Resources career pathways. CS.05.01. Performance Indicator: Evaluate and implement the steps and requirements to pursue a career opportunity in each of the AFNR career pathways (e.g., goals, degrees, certifications, resumes, cover letter, portfolios, interviews, etc.). CS.06. CCTC Standard: Analyze the interaction among AFNR systems in the production, processing and management of food, fiber and fuel and the sustainable use of natural resources. CS.06.01. Performance Indicator: Examine and explain foundational cycles and systems of AFNR. CS.06.02. Performance Indicator: Analyze and explain the connection and relationships between different AFNR systems on a national and global level. Biotechnology Systems Career Pathway Content Standards The Biotechnology Systems (BS) Career Pathway encompasses the study of using data and scientific techniques to solve problems concerning living organisms with an emphasis on applications to agriculture, food and natural resource systems. Students completing a program of study in this pathway will demonstrate competence in the application of principles and techniques for the development, application and management of biotechnology in the context of AFNR. Within each pathway, the standards are organized as follows:  National Council for Agricultural Education (NCAE) Standard* – These are the standards set forth by the National Council for Agricultural Education for Biotechnology Systems. They define what students should know and be able to do after completing instruction in a program of study focused on applying biotechnology to AFNR systems.  Performance Indicators – These statements distill each performance element into more discrete indicators of the knowledge and skills students should attain through a program of study in this pathway. Attainment of the knowledge and skills outlined in the performance indicators is intended to demonstrate an acceptable level of proficiency with the related performance element at the conclusion of a program of study in this area. BS.01. NCAE Standard: Assess factors that have influenced the evolution of biotechnology in agriculture (e.g., historical events, societal trends, ethical and legal implications, etc.). BS.01.01. Performance Indicator: Investigate and explain the relationship between past, current and emerging applications of biotechnology in agriculture (e.g., major innovators, historical developments, potential applications of biotechnology, etc.). BS.01.02. Performance Indicator: Evaluate the scope and implications of regulatory agencies on applications of biotechnology in agriculture and protection of public interests (e.g., health, safety, environmental issues, etc.). BS.01.03. Performance Indicator: Analyze the relationship and implications of bioethics, laws and public perceptions on applications of biotechnology in agriculture (e.g., ethical, legal, social, cultural issues). BS.02. NCAE Standard: Demonstrate proficiency by safely applying appropriate laboratory skills to complete tasks in a biotechnology research and development environment (e.g., standard operating procedures, record keeping, aseptic technique, equipment maintenance, etc.). BS.02.01. Performance Indicator: Read, document, evaluate and secure accurate laboratory records of experimental protocols, observations and results. BS.02.02. Performance Indicator: Implement standard operating procedures for the proper maintenance, use and sterilization of equipment in a laboratory. BS.02.03. Performance Indicator: Apply standard operating procedures for the safe handling of biological and chemical materials in a laboratory. BS.02.04. Performance Indicator: Safely manage and dispose of biological materials, chemicals and wastes according to standard operating procedures. BS.02.05. Performance Indicator: Examine and perform scientific procedures using microbes, DNA, RNA and proteins in a laboratory. BS.03. NCAE Standard: Demonstrate the application of biotechnology to solve problems in Agriculture, Food and Natural Resources (AFNR) systems (e.g., bioengineering, food processing, waste management, horticulture, forestry, livestock, crops, etc.). BS.03.01. Performance Indicator: Apply biotechnology principles, techniques and processes to create transgenic species through genetic engineering. BS.03.02. Performance Indicator: Apply biotechnology principles, techniques and processes to enhance the production of food through the use of microorganisms and enzymes. BS.03.03. Performance Indicator: Apply biotechnology principles, techniques and processes to protect the environment and maximize use of natural resources (e.g., biomass, bioprospecting, industrial biotechnology, etc.). BS.03.04. Performance Indicator: Apply biotechnology principles, techniques and processes to enhance plant and animal care and production (e.g., selective breeding, pharmaceuticals, biodiversity, etc.). BS.03.05. Performance Indicator: Apply biotechnology principles, techniques and processes to produce biofuels (e.g., fermentation, transesterification, methanogenesis, etc.). BS.03.06. Performance Indicator: Apply biotechnology principles, techniques and processes to improve waste management (e.g., genetically modified organisms, bioremediation, etc.). Environmental Service Systems Career Pathway Content Standards The Environmental Service Systems (ESS) Career Pathway encompasses the study of systems, instruments and technology used to monitor and minimize the impact of human activity on environmental systems. Students completing a program of study in this pathway will demonstrate competence in the application of principles and techniques for the development, application and management of environmental service systems in AFNR settings. Within each pathway, the standards are organized as follows:  Common Career Technical Core (CCTC) Standards – These are the standards for Environmental Service Systems (AG-ESS) from the 2012 version of the Common Career and Technical Core Standards, which are owned by the National Association of State Directors of Career and Technical Education/National Career Technical Education Foundation and are used here with permission. These statements define what students should know and be able to do after completing instruction in a program of study for this pathway.  Performance Indicators – These statements distill each CCTC Standard into more discrete indicators of the knowledge and skills students should attain through a program of study in this pathway. Attainment of the knowledge and skills outlined in the performance indicators is intended to demonstrate an acceptable level of proficiency with the related CCTC Standard at the conclusion of a program of study in this area. ESS.01. CCTC Standard: Use analytical procedures and instruments to manage environmental service systems. ESS.01.01. Performance Indicator: Analyze and interpret laboratory and field samples in environmental service systems. ESS.01.02. Performance Indicator: Properly utilize scientific instruments in environmental monitoring situations (e.g., laboratory equipment, environmental monitoring instruments, etc.). ESS.02. CCTC Standard: Evaluate the impact of public policies and regulations on environmental service system operations. ESS.02.01. Performance Indicator: Interpret and evaluate the impact of laws, agencies, policies and practices affecting environmental service systems. ESS.02.02. Performance Indicator: Compare and contrast the impact of current trends on regulation of environmental service systems (e.g., climate change, population growth, international trade, etc.). ESS.02.03. Performance Indicator: Examine and summarize the impact of public perceptions and social movements on the regulation of environmental service systems. ESS.03. CCTC Standard: Develop proposed solutions to environmental issues, problems and applications using scientific principles of meteorology, soil science, hydrology, microbiology, chemistry and ecology. ESS.03.01. Performance Indicator: Apply meteorology principles to environmental service systems. ESS.03.02. Performance Indicator: Apply soil science and hydrology principles to environmental service systems. ESS.03.03. Performance Indicator: Apply chemistry principles to environmental service systems. ESS.03.04. Performance Indicator: Apply microbiology principles to environmental service systems. ESS.03.05. Performance Indicator: Apply ecology principles to environmental service systems. ESS.04. CCTC Standard: Demonstrate the operation of environmental service systems (e.g., pollution control, water treatment, wastewater treatment, solid waste management and energy conservation). ESS.04.01. Performance Indicator: Use pollution control measures to maintain a safe facility and environment. ESS.04.02. Performance Indicator: Manage safe disposal of all categories of solid waste in environmental service systems. ESS.04.03. Performance Indicator: Apply techniques to ensure a safe supply of drinking water and adequate treatment of wastewater according to applicable rules and regulations. ESS.04.04. Performance Indicator: Compare and contrast the impact of conventional and alternative energy sources on the environment and operation of environmental service systems. ESS.05. CCTC Standard: Use tools, equipment, machinery and technology common to tasks in environmental service systems. ESS.05.01. Performance Indicator: Use technological and mathematical tools to map land, facilities and infrastructure for environmental service systems. ESS.05.02. Performance Indicator: Perform assessments of environmental conditions using equipment, machinery and technology. Food Products and Processing Systems Career Pathway Content Standards The Food Products and Processing Systems (FPP) Career Pathway encompasses the study of food safety and sanitation; nutrition, biology, microbiology, chemistry and human behavior in local and global food systems; food selection and processing for storage, distribution and consumption; and the historical and current development of the food industry. Students completing a program of study in this pathway will demonstrate competence in the application of principles and techniques for the development, application and management of food products and processing systems in AFNR settings. Within each pathway, the standards are organized as follows:  Common Career Technical Core (CCTC) Standards – These are the standards for Food Products and Processing Systems (AG-FPP) from the 2012 version of the Common Career and Technical Core Standards, which are owned by the National Association of State Directors of Career and Technical Education/National Career Technical Education Foundation and are used here with permission. These statements define what students should know and be able to do after completing instruction in a program of study for this pathway.  Performance Indicators – These statements distill each CCTC Standard into more discrete indicators of the knowledge and skills students should attain through a program of study in this pathway. Attainment of the knowledge and skills outlined in the performance indicators is intended to demonstrate an acceptable level of proficiency with the related CCTC Standard at the conclusion of a program of study in this area. FPP.01. CCTC Standard: Develop and implement procedures to ensure safety, sanitation and quality in food product and processing facilities. FPP.01.01. Performance Indicator: Analyze and manage operational and safety procedures in food products and processing facilities. FPP.01.02. Performance Indicator: Apply food safety and sanitation procedures in the handling and processing of food products to ensure food quality. FPP.01.03. Performance Indicator: Apply food safety procedures when storing food products to ensure food quality. FPP.02. CCTC Standard: Apply principles of nutrition, biology, microbiology, chemistry and human behavior to the development of food products. FPP.02.01. Performance Indicator: Apply principles of nutrition and biology to develop food products that provide a safe, wholesome and nutritious food supply for local and global food systems. FPP.02.02. Performance Indicator: Apply principles of microbiology and chemistry to develop food products to provide a safe, wholesome and nutritious food supply for local and global food systems. FPP.02.03. Performance Indicator: Apply principles of human behavior to develop food products to provide a safe, wholesome and nutritious food supply for local and global food systems. FPP.03. CCTC Standard: Select and process food products for storage, distribution and consumption. FPP.03.01. Performance Indicator: Implement selection, evaluation and inspection techniques to ensure safe and quality food products. FPP.03.02. Performance Indicator: Design and apply techniques of food processing, preservation, packaging and presentation for distribution and consumption of food products. FPP.03.03. Performance Indicator: Create food distribution plans and procedures to ensure safe delivery of food products. FPP.04. CCTC Standard: Explain the scope of the food industry and the historical and current developments of food product and processing. FPP.04.01. Performance Indicator: Examine the scope of the food industry by evaluating local and global policies, trends and customs for food production. FPP.04.02. Performance Indicator: Evaluate the significance and implications of changes and trends in the food products and processing industry in the local and global food systems. FPP.04.03. Performance Indicator: Identify and explain the purpose of industry organizations, groups and regulatory agencies that influence the local and global food systems. Natural Resource Systems Career Pathway Content Standards The Natural Resource Systems (NRS) Career Pathway encompasses the study of the management, protection, enhancement and improvement of soil, water, wildlife, forests and air as natural resources. Students completing a program of study in this pathway will demonstrate competence in the application of principles and techniques for the development, application and management of natural resource systems in AFNR settings. Within each pathway, the standards are organized as follows:  Common Career Technical Core (CCTC) Standards – These are the standards for Natural Resource Systems (AG-NRS) from the 2012 version of the Common Career and Technical Core Standards, which are owned by the National Association of State Directors of Career and Technical Education/National Career Technical Education Foundation and are used here with permission. These statements define what students should know and be able to do after completing instruction in a program of study for this pathway.  Performance Indicators – These statements distill each CCTC Standard into more discrete indicators of the knowledge and skills students should attain through a program of study in this pathway. Attainment of the knowledge and skills outlined in the performance indicators is intended to demonstrate an acceptable level of proficiency with the related CCTC Standard at the conclusion of a program of study in this area. NRS.01. CCTC Standard: Plan and conduct natural resource management activities that apply logical, reasoned and scientifically based solutions to natural resource issues and goals. NRS.01.01. Performance Indicator: Apply methods of classification to examine natural resource availability and ecosystem function in a particular region. NRS.01.02. Performance Indicator: Classify different types of natural resources in order to enable protection, conservation, enhancement and management in a particular geographical region. NRS.01.03. Performance Indicator: Apply ecological concepts and principles to atmospheric natural resource systems. NRS.01.04. Performance Indicator: Apply ecological concepts and principles to aquatic natural resource systems. NRS.01.05. Performance Indicator: Apply ecological concepts and principles to terrestrial natural resource systems. NRS.01.06. Performance Indicator: Apply ecological concepts and principles to living organisms in natural resource systems. NRS.02. CCTC Standard: Analyze the interrelationships between natural resources and humans. NRS.02.01. Performance Indicator: Examine and interpret the purpose, enforcement, impact and effectiveness of laws and agencies related to natural resource management, protection, enhancement and improvement (e.g., water regulations, game laws, historic preservation laws, environmental policy, etc.). NRS.02.02. Performance Indicator: Assess the impact of human activities on the availability of natural resources. NRS.02.03. Performance Indicator: Analyze how modern perceptions of natural resource management, protection, enhancement and improvement change and develop over time. NRS.02.04. Performance Indicator: Examine and explain how economics affects the use of natural resources. NRS.02.05. Performance Indicator: Communicate information to the public regarding topics related to the management, protection, enhancement, and improvement of natural resources. NRS.03. CCTC Standard: Develop plans to ensure sustainable production and processing of natural resources. NRS.03.01. Performance Indicator: Sustainably produce, harvest, process and use natural resource products (e.g., forest products, wildlife, minerals, fossil fuels, shale oil, alternative energy, recreation, aquatic species, etc.). NRS.03.02. Performance Indicator: Demonstrate cartographic skills, tools and technologies to aid in developing, implementing and evaluating natural resource management plans. NRS.04. CCTC Standard: Demonstrate responsible management procedures and techniques to protect, maintain, enhance, and improve natural resources. NRS.04.01. Performance Indicator: Demonstrate natural resource protection, maintenance, enhancement and improvement techniques. NRS.04.02. Performance Indicator: Diagnose plant and wildlife diseases and follow protocols to prevent their spread. NRS.04.03. Performance Indicator: Prevent or manage introduction of ecologically harmful species in a particular region. NRS.04.04. Performance Indicator: Manage fires in natural resource systems. Plant Science Systems Career Pathway Content Standards The Plant Systems (PS) Career Pathway encompasses the study of plant life cycles, classifications, functions, structures, reproduction, media and nutrients, as wells as growth and cultural practices through the study of crops, turf grass, trees, shrubs and/or ornamental plants. Students completing a program of study in this pathway will demonstrate competence in the application of principles and techniques for the development, application and management of plant systems in AFNR settings. Within each pathway, the standards are organized as follows:  Common Career Technical Core (CCTC) Standards – These are the standards for Plant Systems (AG-PS) from the 2012 version of the Common Career and Technical Core Standards, which are owned by the National Association of State Directors of Career and Technical Education/National Career Technical Education Foundation and are used here with permission. These statements define what students should know and be able to do after completing instruction in a program of study for this pathway.  Performance Indicators – These statements distill each CCTC Standard into more discrete indicators of the knowledge and skills students should attain through a program of study in this pathway. Attainment of the knowledge and skills outlined in the performance indicators is intended to demonstrate an acceptable level of proficiency with the related CCTC Standard at the conclusion of a program of study in this area. PS.01. CCTC Standard: Develop and implement a crop management plan for a given production goal that accounts for environmental factors. PS.01.01. Performance Indicator: Determine the influence of environmental factors on plant growth. PS.01.02. Performance Indicator: Prepare and manage growing media for use in plant systems. PS.01.03. Performance Indicator: Develop and implement a fertilization plan for specific plants or crops. PS.02. CCTC Standard: Apply principles of classification, plant anatomy, and plant physiology to plant production and management. PS.02.01. Performance Indicator: Classify plants according to taxonomic systems. PS.02.02. Performance Indicator: Apply knowledge of plant anatomy and the functions of plant structures to activities associated with plant systems. PS.02.03. Performance Indicator: Apply knowledge of plant physiology and energy conversion to plant systems. PS.03. CCTC Standard: Propagate, culture and harvest plants and plant products based on current industry standards. PS.03.01. Performance Indicator: Demonstrate plant propagation techniques in plant system activities. PS.03.02. Performance Indicator: Develop and implement a management plan for plant production. PS.03.03. Performance Indicator: Develop and implement a plan for integrated pest management for plant production. PS.03.04. Performance Indicator: Apply principles and practices of sustainable agriculture to plant production. PS.03.05. Performance Indicator: Harvest, handle and store crops according to current industry standards. PS.04. CCTC Standard: Apply principles of design in plant systems to enhance an environment (e.g. floral, forest landscape, and farm). PS.04.01. Performance Indicator: Evaluating, identifying and preparing plants to enhance an environment. PS.04.02. Performance Indicator: Create designs using plants. Power, Structural and Technical Systems Career Pathway Content Standards The Power, Structural and Technical Systems (PST) Career Pathway encompasses the study of agricultural equipment, power systems, alternative fuel sources and precision technology, as well as woodworking, metalworking, welding and project planning for agricultural structures. Students completing a program of study in this pathway will demonstrate competence in the application of principles and techniques for the development, application and management of power, structural and technical systems in AFNR settings. Within each pathway, the standards are organized as follows:  Common Career Technical Core (CCTC) Standards – These are the standards for Power, Structural and Technical Systems (AG-PST) from the 2012 version of the Common Career and Technical Core Standards, which are owned by the National Association of State Directors of Career and Technical Education/National Career Technical Education Foundation and are used here with permission. These statements define what students should know and be able to do after completing instruction in a program of study for this pathway.  Performance Indicators – These statements distill each CCTC Standard into more discrete indicators of the knowledge and skills students should attain through a program of study in this pathway. Attainment of the knowledge and skills outlined in the performance indicators is intended to demonstrate an acceptable level of proficiency with the related CCTC Standard at the conclusion of a program of study in this area. PST.01. CCTC Standard: Apply physical science principles and engineering applications to solve problems and improve performance in AFNR power, structural and technical systems. PST.01.01. Performance Indicator: Apply physical science and engineering principles to assess and select energy sources for AFNR power, structural and technical systems. PST.01.02. Performance Indicator: Apply physical science and engineering principles to design, implement and improve safe and efficient mechanical systems in AFNR situations. PST.01.03. Performance Indicator: Apply physical science principles to metal fabrication using a variety of welding and cutting processes (e.g., SMAW, GMAW, GTAW, fuel-oxygen and plasma arc torch, etc.). PST.02. CCTC Standard: Operate and maintain AFNR mechanical equipment and power systems. PST.02.01. Performance Indicator: Perform preventative maintenance and scheduled service to maintain equipment, machinery and power units used in AFNR settings. PST.02.02. Performance Indicator: Operate machinery and equipment while observing all safety precautions in AFNR settings. PST.03. CCTC Standard: Service and repair AFNR mechanical equipment and power systems. PST.03.01. Performance Indicator: Troubleshoot, service and repair components of internal combustion engines using manufacturers’ guidelines. PST.03.02. Performance Indicator: Service electrical systems and components of mechanical equipment and power systems using a variety of troubleshooting and/or diagnostic methods. PST.03.03. Performance Indicator: Utilize manufacturers’ guidelines to diagnose and troubleshoot malfunctions in machinery, equipment and power source systems (e.g., hydraulic, pneumatic, transmission, steering, suspension, etc.). PST.04. CCTC Standard: Plan, build and maintain AFNR structures. PST.04.01. Performance Indicator: Create sketches and plans for AFNR structures. PST.04.02. Performance Indicator: Determine structural requirements, specifications and estimate costs for AFNR structures PST.04.03. Performance Indicator: Follow architectural and mechanical plans to construct, maintain and/or repair AFNR structures (e.g., material selection, site preparation and/or layout, plumbing, concrete/masonry, etc.). PST.04.04. Performance Indicator: Apply electrical wiring principles in AFNR structures. PST.05. CCTC Standard: Use control, monitoring, geospatial and other technologies in AFNR power, structural and technical systems. PST.05.01. Performance Indicator: Apply computer and other technologies (e.g., robotics, CNC, UAS, etc.) to solve problems and increase the efficiency of AFNR systems. PST.05.02. Performance Indicator: Prepare and/or use electrical drawings to design, install and troubleshoot electronic control systems in AFNR settings. PST.05.03. Performance Indicator: Apply geospatial technologies to solve problems and increase the efficiency of AFNR systems. Appendix B: 21st Century Skills 1 21st Century Crosswalk for Agriculture Power and Machinery 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 1 21st century skills. (n.d.). Washington, DC: Partnership for 21st Century Skills. Units Standards CS1 CS2 X CS3 CS4 X CS5 CS6 X X X X X X CS7 X X X X X X X CS8 X X X X X X CS9 X CS10 X CS11 X CS12 X X X X X X X CS13 X X X X X X X CS14 X X X X X X X CS15 X X X X X X CS16 X X X X X X X 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 1. 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. 2. Demonstrate knowledge and understanding of society’s impact on the natural world (e.g., population growth, population development, resource consumption rate, etc.). 3. Investigate and analyze environmental issues, and make accurate conclusions about effective solutions. 4. 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) T1 Empowered Learner T2 Digital Citizen T3 Knowledge Constructor T4 Innovative Designer T5 Computational Thinker T6 Creative Communicator T7 Global Collaborator T1 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. T2 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. Units Standards T1 X X X T2 X X T3 X X X X X X T4 X X X X T5 X X X X T6 X x X T7 X X d. Manage their personal data to maintain digital privacy and security and are aware of data-collection technology used to track their navigation online. T3 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. Curate information from digital resources using a variety of tools and methods to create collections of artifacts that demonstrate meaningful connections or conclusions. d. Build knowledge by actively exploring real-world issues and problems, developing ideas and theories and pursuing answers and solutions. T4 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. T5 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. T6 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. T7 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 Units 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 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 X W.9.5 W.9.6 W.9.7 X W.9.8 W.9.9 W.9.10 X SL.9.1 X X SL.9.2 SL.9.3 SL.9.4 SL.9.5 SL.9.6 X L.9.1 L.9.2 L.9.3 X X X X X X L.9.4 X X X X X X L.9.5 X X X X X X L.9.6 RL.10.10 RH.9-10.1 RH.9-10.2 RH.9-10.3 RH.9-10.4 X X X X X X RH.9-10.5 X X X X X X RH.9-10.6 X X X X X X RH.9-10.7 X X X X X X RH.9-10.8 X X X X X X RH.9-10.9 X X X X X X 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 X 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 X X X X X X 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 X X X X X X RST.11-12.2 X X X X X X RST.11-12.3 X X X X X X RST.11-12.4 X X X X X X RST.11-12.5 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. RST.11-12.6 X X X X X X RST.11-12.7 X X X X X X RST.11-12.8 X X X X X X RST.11-12.9 X X X X X X RST.11-12.10 X X X X X X WHST.11-12.1 WHST.11-12.2 WHST.11-12.6 WHST.11-12.8 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, well- chosen 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 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. 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, well- chosen 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 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. 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 Units Standards N-Q.1 X X X X X X X N-Q.2 X X X X X X X N-Q.3 X X X X X X X 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.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 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 X X X X X X G-MG.2 X X X X X X G-MG.3 X X X X X X N-CN.1 N-CN.2 N-CN.3 N-CN.4 N-CN.5 N-CN.6 Mathematics Standards Number and Quantity Reason quantitatively and use unites 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 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. 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 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 high- deductible 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).*