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RIGHT ON 3 4.2 4B-C-D
Quiz by Gelly Dol
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Cells of different organisms and even cells within the same organism are very diverse in terms of shape, size, and internal organization. One theme that occurs again and again throughout biology is that form follows function. In other words, a cell’s function influences its physical features. Cell Shape The diversity in cell shapes reflects the different functions of cells. Compare the cell shapes shown in Figure 4-4. The long extensions that reach out in various directions from the nerve cell shown in Figure 4-4a allow the cell to send and receive nerve impulses. The flat, platelike shape of skin cells in Figure 4-4b suits their function of covering and protecting the surface of the body. As shown below, a cell’s shape can be simple or complex depending on the function of the cell. Each cell has a shape that has evolved to allow the cell to perform its function effectively. SECTION 2 OBJECTIVES ● Explain the relationship between cell shape and cell function. ● Identify the factor that limits cell size. ● Describe the three basic parts of a cell. ● Compare prokaryotic cells and eukaryotic cells. ● Analyze the relationship among cells, tissues, organs, organ systems, and organisms. VOCABULARY plasma membrane cytoplasm cytosol nucleus prokaryote eukaryote organelle tissue organ organ system Cells have various shapes. (a) Nerve cells have long extensions. (b) Skin cells are flat and platelike. (c) Egg cells are spherical. (d) Some bacteria are rod shaped. (e) Some plant cells are rectangular. FIGURE 4-4 (a) Nerve cell (b) Skin cells (c) Egg cell (d) Bacterial cells (e) Plant cells Copyright © by Holt, Rinehart and Winston. All rights reserved. 1. All cubes have volume and surface area. The total surface area is equal to the sum of the areas of each of the six sides (area = length X width). 2. If you split the first cube into eight smaller cubes, you get 48 sides. The volume remains constant, but the total surface area doubles. 3. If you split each of the eight cubes into eight smaller cubes, you have 64 cubes that together contain the same volume as the first cube. The total surface area, however, has doubled again. CELL STRUCTURE AND FUNCTION 73 Cell Size Cells differ not only in their shape but also in their size. A few types of cells are large enough to be seen by the unaided human eye. For example, the nerve cells that extend from a giraffe’s spinal cord to its foot can be 2 m (about 6 1/2 ft) long. A human egg cell is about the size of the period at the end of this sentence. Most cells, how- ever, are only 10 to 50 μm in diameter, or about 1/500 the size of the period at the end of this sentence. The size of a cell is limited by the relationship of the cell’s outer surface area to its volume, or its surface area–to-volume ratio. As a cell grows, its volume increases much faster than its surface area does, as shown in Figure 4-5. This trend is important because the materials needed by a cell (such as nutrients and oxygen) and the wastes produced by a cell (such as carbon dioxide) must pass into and out of the cell through its surface. If a cell were to become very large, the volume would increase much more than the surface area. Therefore, the surface area would not allow materials to enter or leave the cell quickly enough to meet the cell’s needs. As a result, most cells are microscopic in size. Comparing Surface Cells Materials microscope, prepared slides of plant (dicot) stem and ani- mal (human) skin, pencil, paper Procedure Examine slides by using medium magnification (100). Observe and draw the sur- face cells of the plant stem and the animal skin. Analysis How do the surface cells of each organism differ from the cells beneath the surface cells? What is the function of the surface cells? Explain how surface cells are suited to their function based on their shape. Quick Lab Small cells can exchange substances more readily than large cells because small objects have a higher surface area–to-volume ratio. FIGURE 4-5 mb06se_csfs02.qxd 5/18/07 10:54 AM Page 73 74 CHAPTER 4 BASIC PARTS OF A CELL Despite the diversity among cells, three basic features are common to all cell types. All cells have an outer boundary, an interior sub- stance, and a control region. Plasma Membrane The cell’s outer boundary, called the plasma membrane (or the cell membrane), covers a cell’s surface and acts as a barrier between the inside and the outside of a cell. All materials enter or exit through the plasma membrane. The surface of a plasma mem- brane is shown in Figure 4-6a. Cytoplasm The region of the cell that is within the plasma membrane and that includes the fluid, the cytoskeleton, and all of the organelles except the nucleus is called the cytoplasm. The part of the cytoplasm that includes molecules and small particles, such as ribosomes, but not membrane-bound organelles is the cytosol. About 20 percent of the cytosol is made up of protein. Control Center Cells carry coded information in the form of DNA for regulating their functions and reproducing themselves. The DNA in some types of cells floats freely inside the cell. Other cells have a mem- brane-bound organelle that contains a cell’s DNA. This membrane- bound structure is called the nucleus. Most of the functions of a eukaryotic cell are controlled by the cell’s nucleus. The nucleus is often the most prominent structure within a eukaryotic cell. It maintains its shape with the help of a protein skeleton called the nuclear matrix. The nucleus of a typical animal cell is shown in
ILLINOIS PROFESSIONAL TEACHING STANDARDS (2013) Standard 1 - Teaching Diverse Students – The competent teacher understands the diverse characteristics and abilities of each student and how individuals develop and learn within the context of their social, economic, cultural, linguistic, and academic experiences. The teacher uses these experiences to create instructional opportunities that maximize student learning. Knowledge Indicators – The competent teacher: 1A) understands the spectrum of student diversity (e.g., race and ethnicity, socioeconomic status, special education, gifted, English language learners (ELL), sexual orientation, gender, gender identity) and the assets that each student brings to learning across the curriculum; 1B) understands how each student constructs knowledge, acquires skills, and develops effective and efficient critical thinking and problem-solving capabilities; 1C) understands how teaching and student learning are influenced by development (physical, social and emotional, cognitive, linguistic), past experiences, talents, prior knowledge, economic circumstances and diversity within the community; 1D) understands the impact of cognitive, emotional, physical, and sensory disabilities on learning and communication pursuant to the Individuals with Disabilities Education Improvement Act (also referred to as “IDEA”) (20 USC 1400 et seq.), its implementing regulations (34 CFR 300; 2006), Article 14 of the School Code [105 ILCS 5/Art.14] and 23 Ill. Adm. Code 226 (Special Education); 1E) understands the impact of linguistic and cultural diversity on learning and communication; 1F) understands his or her personal perspectives and biases and their effects on one’s teaching; and 1G) understands how to identify individual needs and how to locate and access technology, services, and resources to address those needs. Performance Indicators – The competent teacher: 1H) analyzes and uses student information to design instruction that meets the diverse needs of students and leads to ongoing growth and achievement; 1I) stimulates prior knowledge and links new ideas to already familiar ideas and experiences; 1J) differentiates strategies, materials, pace, levels of complexity, and language to introduce concepts and principles so that they are meaningful to students at varying levels of development and to students with diverse learning needs; 1K) facilitates a learning community in which individual differences are respected; and 1L) uses information about students’ individual experiences, families, cultures, and communities to create meaningful learning opportunities and enrich instruction for all students. Standard 2 - Content Area and Pedagogical Knowledge – The competent teacher has in-depth understanding of content area knowledge that includes central concepts, methods of inquiry, structures of the disciplines, and content area literacy. The teacher creates meaningful learning experiences for each student based upon interactions among content area and pedagogical knowledge, and evidence-based practice. Knowledge Indicators – The competent teacher: 2A) understands theories and philosophies of learning and human development as they relate to the range of students in the classroom; 2B) understands major concepts, assumptions, debates, and principles; processes of inquiry; and theories that are central to the disciplines; 2C) understands the cognitive processes associated with various kinds of learning (e.g., critical and creative thinking, problem-structuring and problem-solving, invention, memorization, and recall) 2 and ensures attention to these learning processes so that students can master content standards; 2D) understands the relationship of knowledge within the disciplines to other content areas and to life applications; 2E) understands how diverse student characteristics and abilities affect processes of inquiry and influence patterns of learning; 2F) knows how to access the tools and knowledge related to latest findings (e.g., research, practice, methodologies) and technologies in the disciplines; 2G) understands the theory behind and the process for providing support to promote learning when concepts and skills are first being introduced; and 2H) understands the relationship among language acquisition (first and second), literacy development, and acquisition of academic content and skills. Performance Indicators – The competent teacher: 2I) evaluates teaching resources and materials for appropriateness as related to curricular content and each student’s needs; 2J) uses differing viewpoints, theories, and methods of inquiry in teaching subject matter concepts; 2K) engages students in the processes of critical thinking and inquiry and addresses standards of evidence of the disciplines; 2L) demonstrates fluency in technology systems, uses technology to support instruction and enhance student learning, and designs learning experiences to develop student skills in the application of technology appropriate to the disciplines; 2M) uses a variety of explanations and multiple representations of concepts that capture key ideas to help each student develop conceptual understanding and address common misunderstandings; 2N) facilitates learning experiences that make connections to other content areas and to life experiences; 2O) designs learning experiences and utilizes assistive technology and digital tools to provide access to general curricular content to individuals with disabilities; 2P) adjusts practice to meet the needs of each student in the content areas; and 2Q) applies and adapts an array of content area literacy strategies to make all subject matter accessible to each student. Standard 3 - Planning for Differentiated Instruction – The competent teacher plans and designs instruction based on content area knowledge, diverse student characteristics, student performance data, curriculum goals, and the community context. The teacher plans for ongoing student growth and achievement. Knowledge Indicators – The competent teacher: 3A) understands the Illinois Learning Standards (23 Ill. Adm. Code 1.Appendix D), curriculum development process, content, learning theory, assessment, and student development and knows how to incorporate this knowledge in planning differentiated instruction; 3B) understands how to develop short- and long-range plans, including transition plans, consistent with curriculum goals, student diversity, and learning theory; 3C) understands cultural, linguistic, cognitive, physical, and social and emotional differences, and considers the needs of each student when planning instruction; 3D) understands when and how to adjust plans based on outcome data, as well as student needs, goals, and responses; 3E) understands the appropriate role of technology, including assistive technology, to address student needs, as well as how to incorporate contemporary tools and resources to maximize student learning; 3 3F) understands how to co-plan with other classroom teachers, parents or guardians, paraprofessionals, school specialists, and community representatives to design learning experiences; and 3G) understands how research and data guide instructional planning, delivery, and adaptation. Performance Indicators – The competent teacher: 3H) establishes high expectations for each student’s learning and behavior; 3I) creates short-term and long-term plans to achieve the expectations for student learning; 3J) uses data to plan for differentiated instruction to allow for variations in individual learning needs; 3K) incorporates experiences into instructional practices that relate to a student’s current life experiences and to future life experiences; 3L) creates approaches to learning that are interdisciplinary and that integrate multiple content areas; 3M) develops plans based on student responses and provides for different pathways based on student needs; 3N) accesses and uses a wide range of information and instructional technologies to enhance a student’s ongoing growth and achievement; 3O) when planning instruction, addresses goals and objectives contained in plans developed under Section 504 of the Rehabilitation Act of 1973 (29 USC 794), individualized education programs (IEP) (see 23 Ill. Adm. Code 226 (Special Education)) or individual family service plans (IFSP) (see 23 Ill. Adm. Code 226 and 34 CFR 300.24; 2006); 3P) works with others to adapt and modify instruction to meet individual student needs; and 3Q) develops or selects relevant instructional content, materials, resources, and strategies (e.g., project-based learning) for differentiating instruction. Standard 4 - Learning Environment – The competent teacher structures a safe and healthy learning environment that facilitates cultural and linguistic responsiveness, emotional well-being, self-efficacy, positive social interaction, mutual respect, active engagement, academic risk-taking, self-motivation, and personal goal-setting. Knowledge Indicators – The competent teacher: 4A) understands principles of and strategies for effective classroom and behavior management; 4B) understands how individuals influence groups and how groups function in society; 4C) understands how to help students work cooperatively and productively in groups; 4D) understands factors (e.g., self-efficacy, positive social interaction) that influence motivation and engagement; 4E) knows how to assess the instructional environment to determine how best to meet a student’s individual needs; 4F) understands laws, rules, and ethical considerations regarding behavior intervention planning and behavior management (e.g., bullying, crisis intervention, physical restraint); 4G) knows strategies to implement behavior management and behavior intervention planning to ensure a safe and productive learning environment; and 4H) understands the use of student data (formative and summative) to design and implement behavior management strategies. Performance Indicators – The competent teacher: 4I) creates a safe and healthy environment that maximizes student learning; 4J) creates clear expectations and procedures for communication and behavior and a physical setting conducive to achieving classroom goals; 4K) uses strategies to create a smoothly functioning learning community in which students assume responsibility for themselves and one another, participate in decision-making, work collaboratively and independently, use appropriate technology, and engage in purposeful learning activities; 4 4L) analyzes the classroom environment and makes decisions to enhance cultural and linguistic responsiveness, mutual respect, positive social relationships, student motivation, and classroom engagement; 4M) organizes, allocates, and manages time, materials, technology, and physical space to provide active and equitable engagement of students in productive learning activities; 4N) engages students in and monitors individual and group-learning activities that help them develop the motivation to learn; 4O) uses a variety of effective behavioral management techniques appropriate to the needs of all students that include positive behavior interventions and supports; 4P) modifies the learning environment (including the schedule and physical arrangement) to facilitate appropriate behaviors and learning for students with diverse learning characteristics; and 4Q) analyzes student behavior data to develop and support positive behavior. Standard 5 - Instructional Delivery – The competent teacher differentiates instruction by using a variety of strategies that support critical and creative thinking, problem-solving, and continuous growth and learning. This teacher understands that the classroom is a dynamic environment requiring ongoing modification of instruction to enhance learning for each student. Knowledge Indicators – The competent teacher: 5A) understands the cognitive processes associated with various kinds of learning; 5B) understands principles and techniques, along with advantages and limitations, associated with a wide range of evidence-based instructional practices; 5C) knows how to implement effective differentiated instruction through the use of a wide variety of materials, technologies, and resources; 5D) understands disciplinary and interdisciplinary instructional approaches and how they relate to life and career experiences; 5E) knows techniques for modifying instructional methods, materials, and the environment to facilitate learning for students with diverse learning characteristics; 5F) knows strategies to maximize student attentiveness and engagement; 5G) knows how to evaluate and use student performance data to adjust instruction while teaching; and 5H) understands when and how to adapt or modify instruction based on outcome data, as well as student needs, goals, and responses. Performance Indicators – The competent teacher: 5I) uses multiple teaching strategies, including adjusted pacing and flexible grouping, to engage students in active learning opportunities that promote the development of critical and creative thinking, problem-solving, and performance capabilities; 5J) monitors and adjusts strategies in response to feedback from the student; 5K) varies his or her role in the instructional process as instructor, facilitator, coach, or audience in relation to the content and purposes of instruction and the needs of students; 5L) develops a variety of clear, accurate presentations and representations of concepts, using alternative explanations to assist students’ understanding and presenting diverse perspectives to encourage critical and creative thinking; 5M) uses strategies and techniques for facilitating meaningful inclusion of individuals with a range of abilities and experiences; 5N) uses technology to accomplish differentiated instructional objectives that enhance learning for each student; 5O) models and facilitates effective use of current and emerging digital tools to locate, analyze, evaluate, and use information resources to support research and learning; 5P) uses student data to adapt the curriculum and implement instructional strategies and materials according to the characteristics of each student; 5 5Q) uses effective co-planning and co-teaching techniques to deliver instruction to all students; 5R) maximizes instructional time (e.g., minimizes transitional time); and 5S) implements appropriate evidence-based instructional strategies. Standard 6 - Reading, Writing, and Oral Communication – The competent teacher has foundational knowledge of reading, writing, and oral communication within the content area and recognizes and addresses student reading, writing, and oral communication needs to facilitate the acquisition of content knowledge. Knowledge Indicators – The competent teacher: 6A) understands appropriate and varied instructional approaches used before, during, and after reading, including those that develop word knowledge, vocabulary, comprehension, fluency, and strategy use in the content areas; 6B) understands that the reading process involves the construction of meaning through the interactions of the reader's background knowledge and experiences, the information in the text, and the purpose of the reading situation; 6C) understands communication theory, language development, and the role of language in learning; 6D) understands writing processes and their importance to content learning; 6E) knows and models standard conventions of written and oral communications; 6F) recognizes the relationships among reading, writing, and oral communication and understands how to integrate these components to increase content learning; 6G) understands how to design, select, modify, and evaluate a wide range of materials for the content areas and the reading needs of the student; 6H) understands how to use a variety of formal and informal assessments to recognize and address the reading, writing, and oral communication needs of each student; and 6I) knows appropriate and varied instructional approaches, including those that develop word knowledge, vocabulary, comprehension, fluency, and strategy use in the content areas. Performance Indicators – The competent teacher: 6J) selects, modifies, and uses a wide range of printed, visual, or auditory materials, and online resources appropriate to the content areas and the reading needs and levels of each student (including ELLs, and struggling and advanced readers); 6K) uses assessment data, student work samples, and observations from continuous monitoring of student progress to plan and evaluate effective content area reading, writing, and oral communication instruction; 6L) facilitates the use of appropriate word identification and vocabulary strategies to develop each student’s understanding of content; 6M) teaches fluency strategies to facilitate comprehension of content; 6N) uses modeling, explanation, practice, and feedback to teach students to monitor and apply comprehension strategies independently, appropriate to the content learning; 6O) teaches students to analyze, evaluate, synthesize, and summarize information in single texts and across multiple texts, including electronic resources; 6P) teaches students to develop written text appropriate to the content areas that utilizes organization (e.g., compare/contrast, problem/solution), focus, elaboration, word choice, and standard conventions (e.g., punctuation, grammar); 6Q) integrates reading, writing, and oral communication to engage students in content learning; 6R) works with other teachers and support personnel to design, adjust, and modify instruction to meet students’ reading, writing, and oral communication needs; and 6S) stimulates discussion in the content areas for varied instructional and conversational purposes. Standard 7 - Assessment – The competent teacher understands and uses appropriate formative and summative assessments for determining student needs, monitoring student progress, measuring student 6 growth, and evaluating student outcomes. The teacher makes decisions driven by data about curricular and instructional effectiveness and adjusts practices to meet the needs of each student. Knowledge Indicators – The competent teacher: 7A) understands the purposes, characteristics, and limitations of different types of assessments, including standardized assessments, universal screening, curriculum-based assessment, and progress monitoring tools; 7B) understands that assessment is a means of evaluating how students learn and what they know and are able to do in order to meet the Illinois Learning Standards; 7C) understands measurement theory and assessment-related issues, such as validity, reliability, bias, and appropriate and accurate scoring; 7D) understands current terminology and procedures necessary for the appropriate analysis and interpretation of assessment data; 7E) understands how to select, construct, and use assessment strategies and instruments for diagnosis and evaluation of learning and instruction; 7F) knows research-based assessment strategies appropriate for each student; 7G) understands how to make data-driven decisions using assessment results to adjust practices to meet the needs of each student; 7H) knows legal provisions, rules, and guidelines regarding assessment and assessment accommodations for all student populations; and 7I) knows assessment and progress monitoring techniques to assess the effectiveness of instruction for each student. Performance Indicators – The competent teacher: 7J) uses assessment results to determine student performance levels, identify learning targets, select appropriate research-based instructional strategies, and implement instruction to enhance learning outcomes; 7K) appropriately uses a variety of formal and informal assessments to evaluate the understanding, progress, and performance of an individual student and the class as a whole; 7L) involves students in self-assessment activities to help them become aware of their strengths and needs and encourages them to establish goals for learning; 7M) maintains useful and accurate records of student work and performance; 7N) accurately interprets and clearly communicates aggregate student performance data to students, parents or guardians, colleagues, and the community in a manner that complies with the requirements of the Illinois School Student Records Act [105 ILCS 10], 23 Ill. Adm. Code 375 (Student Records), the Family Educational Rights and Privacy Act (FERPA) (20 USC 1232g) and its implementing regulations (34 CFR 99; December 9, 2008); 7O) effectively uses appropriate technologies to conduct assessments, monitor performance, and assess student progress; 7P) collaborates with families and other professionals involved in the assessment of each student; 7Q) uses various types of assessment procedures appropriately, including making accommodations for individual students in specific contexts; and 7R) uses assessment strategies and devices that are nondiscriminatory, and take into consideration the impact of disabilities, methods of communication, cultural background, and primary language on measuring knowledge and performance of students. Standard 8 - Collaborative Relationships – The competent teacher builds and maintains collaborative relationships to foster cognitive, linguistic, physical, and social and emotional development. This teacher works as a team member with professional colleagues, students, parents or guardians, and community members. Knowledge Indicators – The competent teacher: 8A) understands schools as organizations within the larger community context; 7 8B) understands the collaborative process and the skills necessary to initiate and carry out that process; 8C) collaborates with others in the use of data to design and implement effective school interventions that benefit all students; 8D) understands the benefits, barriers, and techniques involved in parent and family collaborations; 8E) understands school- and work-based learning environments and the need for collaboration with all organizations (e.g., businesses, community agencies, nonprofit organizations) to enhance student learning; 8F) understands the importance of participating on collaborative and problem-solving teams to create effective academic and behavioral interventions for all students; 8G) understands the various models of co-teaching and the procedures for implementing them across the curriculum; 8H) understands concerns of families of students with disabilities and knows appropriate strategies to collaborate with students and their families in addressing these concerns; and 8I) understands the roles and the importance of including students with disabilities, as appropriate, and all team members in planning individualized education programs (i.e, IEP, IFSP, Section 504 plan) for students with disabilities. Performance Indicators – The competent teacher: 8J) works with all school personnel (e.g., support staff, teachers, paraprofessionals) to develop learning climates for the school that encourage unity, support a sense of shared purpose, show trust in one another, and value individuals; 8K) participates in collaborative decision-making and problem-solving with colleagues and other professionals to achieve success for all students; 8L) initiates collaboration with others to create opportunities that enhance student learning; 8M) uses digital tools and resources to promote collaborative interactions; 8N) uses effective co-planning and co-teaching techniques to deliver instruction to each student; 8O) collaborates with school personnel in the implementation of appropriate assessment and instruction for designated students; 8P) develops professional relationships with parents and guardians that result in fair and equitable treatment of each student to support growth and learning; 8Q) establishes respectful and productive relationships with parents or guardians and seeks to develop cooperative partnerships to promote student learning and well-being; 8R) uses conflict resolution skills to enhance the effectiveness of collaboration and teamwork; 8S) participates in the design and implementation of individualized instruction for students with special needs (i.e., IEPs, IFSP, transition plans, Section 504 plans), ELLs, and students who are gifted; and 8T) identifies and utilizes community resources to enhance student learning and to provide opportunities for students to explore career opportunities. Standard 9 - Professionalism, Leadership, and Advocacy – The competent teacher is an ethical and reflective practitioner who exhibits professionalism; provides leadership in the learning community; and advocates for students, parents or guardians, and the profession. Knowledge Indicators – The competent teacher: 9A) evaluates best practices and research-based materials against benchmarks within the disciplines; 9B) knows laws and rules (e.g., mandatory reporting, sexual misconduct, corporal punishment) as a foundation for the fair and just treatment of all students and their families in the classroom and school; 9C) understands emergency response procedures as required under the School Safety Drill Act [105 ILCS 128/1], including school safety and crisis intervention protocol, initial response 8 actions (e.g., whether to stay in or evacuate a building), and first response to medical emergencies (e.g., first aid and life-saving techniques); 9D) identifies paths for continuous professional growth and improvement, including the design of a professional growth plan; 9E) is cognizant of his or her emerging and developed leadership skills and the applicability of those skills within a variety of learning communities; 9F) understands the roles of an advocate, the process of advocacy, and its place in combating or promoting certain school district practices affecting students; 9G) understands local and global societal issues and responsibilities in an evolving digital culture; and 9H) understands the importance of modeling appropriate dispositions in the classroom. Performance Indicators – The competent teacher: 9I) models professional behavior that reflects honesty, integrity, personal responsibility, confidentiality, altruism and respect; 9J) maintains accurate records, manages data effectively, and protects the confidentiality of information pertaining to each student and family; 9K) reflects on professional practice and resulting outcomes; engages in self-assessment; and adjusts practices to improve student performance, school goals, and professional growth; 9L) communicates with families, responds to concerns, and contributes to enhanced family participation in student education; 9M) communicates relevant information and ideas effectively to students, parents or guardians, and peers, using a variety of technology and digital-age media and formats; 9N) collaborates with other teachers, students, parents or guardians, specialists, administrators, and community partners to enhance students’ learning and school improvement; 9O) participates in professional development, professional organizations, and learning communities, and engages in peer coaching and mentoring activities to enhance personal growth and development; 9P) uses leadership skills that contribute to individual and collegial growth and development, school improvement, and the advancement of knowledge in the teaching profession; 9Q) proactively serves all students and their families with equity and honor and advocates on their behalf, ensuring the learning and well-being of each child in the classroom; 9R) is aware of and complies with the mandatory reporter provisions of Section 4 of the Abused and Neglected Child Reporting Act [325 ILCS 5/4]; 9S) models digital etiquette and responsible social actions in the use of digital technology; and 9T) models and teaches safe, legal, and ethical use of digital information and technology, including respect for copyright, intellectual property, and the appropriate documentation of sources.
RIGHT ON 3 2.4 CLIL P.38
THE FIDE LAWS OF CHESS. Introduction FIDE Laws of Chess cover over-the-board play. The Laws of Chess have two parts: 1. Basic Rules of Play and 2. Competitive Rules of Play. The English text is the authentic version of the Laws of Chess (which were adopted at the 93rd FIDE Congress at Chennai, India) coming into force on 1 January 2023. Preface. The Laws of Chess cannot cover all possible situations that may arise during a game, nor can they regulate all administrative questions. Where cases are not precisely regulated by an Article of the Laws, it should be possible to reach a correct decision by studying analogous situations which are regulated in the Laws. The Laws assume that arbiters have the necessary competence, sound judgement and absolute objectivity. Too detailed a rule might deprive the arbiter of his/her freedom of judgement and thus prevent him/her from finding a solution to a problem dictated by fairness, logic and special factors. FIDE appeals to all chess players and federations to accept this view. A necessary condition for a game to be rated by FIDE is that it shall be played according to the FIDE Laws of Chess. It is recommended that competitive games not rated by FIDE be played according to the FIDE Laws of Chess. Member federations may ask FIDE to give a ruling on matters relating to the Laws of Chess. BASIC RULES OF PLAY. Article 1: The Nature and Objectives of the Game of Chess 1.1 1.2 1.3 1.4 The game of chess is played between two opponents who move their pieces on a square board called a ‘chessboard’. The player with the light-coloured pieces (White) makes the first move, then the players move alternately, with the player with the dark-coloured pieces (Black) making the next move. A player is said to ‘have the move’ when his/her opponent’s move has been ‘made’. The objective of each player is to place the opponent’s king ‘under attack’ in such a way that the opponent has no legal move. 1.4.1 The player who achieves this goal is said to have ‘checkmated’ the opponent’s king and to have won the game. Leaving one’s own king under attack, exposing one’s own king to attack and also ’capturing’ the opponent’s king is not allowed. 1.4.2 The opponent whose king has been checkmated has lost the game. 1.5 If the position is such that neither player can possibly checkmate the opponent’s king, the game is drawn (see Article 5.2.2). Article 2: The Initial Position of the Pieces on the Chessboard 2.1 2.2 The chessboard is composed of an 8 x 8 grid of 64 equal squares alternately light (the ‘white’ squares) and dark (the ‘black’ squares). The chessboard is placed between the players in such a way that the near corner square to the right of the player is white. At the beginning of the game White has 16 light-coloured pieces (the ‘white’ pieces); Black has 16 dark-coloured pieces (the ‘black’ pieces). These pieces are as follows: A white king usually indicated by the symbol K A white queen Two white rooks Two white bishops Two white knights Eight white pawns A black king A black queen Two black rooks Two black bishops Two black knights Eight black pawns usually indicated by the symbol Q usually indicated by the symbol R usually indicated by the symbol B usually indicated by the symbol N usually indicated by the symbol usually indicated by the symbol K usually indicated by the symbol Q usually indicated by the symbol R usually indicated by the symbol B usually indicated by the symbol N usually indicated by the symbol Staunton Pieces p Q K B N R 9 2.3 The initial position of the pieces on the chessboard is as follows: 2.4 The eight vertical columns of squares are called ‘files’. The eight horizontal rows of squares are called ‘ranks’. A straight line of squares of the same colour, running from one edge of the board to an adjacent edge, is called a ‘diagonal’. Article 3: The Moves of the Pieces 3.1 It is not permitted to move a piece to a square occupied by a piece of the same colour. 3.1.1 If a piece moves to a square occupied by an opponent’s piece the latter is captured and removed from the chessboard as part of the same move. 3.1.2 A piece is said to attack an opponent’s piece if the piece could make a capture on that square according to Articles 3.2 to 3.8. 3.1.3 A piece is considered to attack a square even if this piece is constrained from moving to that square because it would then leave or place the king of its own colour under attack. 3.2 The bishop may move to any square along a diagonal on which it stands. 3.3 The rook may move to any square along the file or the rank on which it stands. 3.4 The queen may move to any square along the file, the rank or a diagonal on which it stands. 3.5 3.6 3.7 When making these moves, the bishop, rook or queen may not move over any intervening pieces. The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal. 3.7 When making these moves, the bishop, rook or queen may not move over any intervening pieces. The knight may move to one of the squares nearest to that on which it stands but not on the same rank, file or diagonal. The pawn: 3.7.1 The pawn may move forward to the square immediately in front of it on the same file, provided that this square is unoccupied, or 3.7.2 on its first move the pawn may move as in 3.7.1 or alternatively it may advance two squares along the same file, provided that both squares are unoccupied, or 3.7.3 the pawn may move to a square occupied by an opponent’s piece diagonally in front of it on an adjacent file, capturing that piece. 3.7.3.1 A pawn occupying a square on the same rank as and on an adjacent file to an opponent’s pawn which has just advanced two squares in one move from its original square may capture this opponent’s pawn as though the latter had been moved only one square. 3.7.3.2 This capture is only legal on the move following this advance and is called an ‘en passant’ capture. 3.7.3.3 When a player, having the move, plays a pawn to the rank furthest from its starting position, he/she must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival. This is called the square of ‘promotion’. 3.7.3.4 The player's choice is not restricted to pieces that have been captured previously. 3.7.3.5 This exchange of a pawn for another piece is called promotion, and the effect of the new piece is immediate. 3.8 There are two different ways of moving the king: 3.8.1 by moving to an adjoining square. 3.8.2 by ‘castling’. This is a move of the king and either rook of the same colour along the player’s first rank, counting as a single move of the king and executed as follows: the king is transferred from its original square two squares towards the rook on its original square, then that rook is transferred to the square the king has just crossed. 3.8.2.1 The right to castle has been lost: 3.8.2.1.1 If the king has already moved, or 3.8.2.1.2 With a rook that has already moved. 3.8.2.2 Castling is prevented temporarily: 3.8.2.2.1 if the square on which the king stands, or the square which it must cross, or the square which it is to occupy, is attacked by one or more of the opponent's pieces, or 3.8.2.2.2 if there is any piece between the king and the rook with which castling is to be effected. 3.9 The king in check: 3.9.1 The king is said to be 'in check' if it is attacked by one or more of the opponent's pieces, even if such pieces are constrained from moving to the square occupied by the king because they would then leave or place their own king in check. 3.9.2 No piece can be moved that will either expose the king of the same colour to check or leave that king in check. 3.10 Legal and illegal moves; illegal positions: 3.10.1 A move is legal when all the relevant requirements of Articles 3.1 – 3.9 have been fulfilled. 3.10.2 A move is illegal when it fails to meet the relevant requirements of Articles 3.1 –3.9. 3.10.3 A position is illegal when it cannot have been reached by any series of legal moves. Article 4: The Act of Moving the Pieces 4.1 4.2 Each move must be played with one hand only. Adjusting the pieces or other physical contact with a piece: 4.2.1 Only the player having the move may adjust one or more pieces on their squares, provided that he/she first expresses his/her intention (for example by saying “j’adoube” or “I adjust”). 4.2.2 Any other physical contact with a piece, except for clearly accidental contact, shall be considered to be intent. 4.3 Except as provided in Article 4.2.1, if the player having the move touches on the chessboard, with the intention of moving or capturing: 4.3.1 one or more of his/her own pieces, he/she must move the first piece touched that can be moved. 4.3.2 one or more of his/her opponent’s pieces, he/she must capture the first piece touched that can be captured. 4.3.3 one or more pieces of each colour, he/she must capture the first touched opponent’s piece with his/her first touched piece or, if this is illegal, move or capture the first piece touched that can be moved or captured. If it is unclear whether the player’s own piece or his/her opponent’s was touched first, the player’s own piece shall be considered to have been touched before his/her opponent’s. 4.4 If a player having the move: 4.4.1 touches his/her king and a rook he/she must castle on that side if it is legal to do so 4.4.2 deliberately touches a rook and then his/her king he/she is not allowed to castle on that side on that move and the situation shall be governed by Article 4.3.1. 4.4.3 intending to castle, touches the king and then a rook, but castling with this rook is illegal, the player must make another legal move with his/her king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move. 4.4.4 promotes a pawn, the choice of the piece is finalised when the piece has touched the square of promotion. 4.5 4.6 If none of the pieces touched in accordance with Article 4.3 or Article 4.4 can be moved or captured, the player may make any legal move. The act of promotion may be performed in various ways: 4.6.1 the pawn does not have to be placed on the square of arrival. 4.6.2 removing the pawn and putting the new piece on the square of promotion may occur in any order. 4.6.3 If an opponent’s piece stands on the square of promotion, it must be captured. 4.7 When, as a legal move or part of a legal move, a piece has been released on a square, it cannot be moved to another square on this move. The move is considered to have been made in the case of: 4.7.1 A capture, when the captured piece has been removed from the chessboard and the player, having placed his/her own piece on its new square, has released this capturing piece from his/her hand. 4.7.2 Castling, when the player's hand has released the rook on the square previously crossed by the king. When the player has released the king from his/her hand, the move is not yet made, but the player no longer has the right to make any move other than castling on that side, if this is legal. If castling on this side is illegal, the player must make another legal move with his/her king (which may include castling with the other rook). If the king has no legal move, the player is free to make any legal move. 4.7.3 Promotion, when the player's hand has released the new piece on the square of promotion and the pawn has been removed from the board. 4.8 4.9 A player forfeits his/her right to claim against his/her opponent’s violation of Articles 4.1 – 4.7 once the player touches a piece with the intention of moving or capturing it. 4.8. A player forfeits his/her right to claim against his/her opponent’s violation of Articles 4.1 – 4.7 .4.9. If a player is unable to move the pieces, an assistant, who shall be acceptable to the arbiter, may be provided by the player to perform this operation. Article 5: The Completion of the Game 5.1.1 The game is won by the player who has checkmated his/her opponent’s king. This immediately ends the game, provided that the move producing the checkmate position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.1.2 The game is lost by the player who declares he/she resigns (this immediately ends the game), unless the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves. In this case the result of the game is a draw. 5.2.1 The game is drawn when the player to move has no legal move and his/her king is not in check. The game is said to end in ‘stalemate’. This immediately ends the game, provided that the move producing the stalemate position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7. 5.2.3 The game is drawn upon agreement between the two players during the game, provided both players have made at least one move. This immediately ends the game. COMPETITIVE RULES OF PLAY Article 6: The Chessclock 6.1 ‘Chessclock’ means a clock with two time displays, connected to each other in such a way that only one of them can run at a time. ‘Clock’ in the Laws of Chess means one of the two time displays. Each time display has a ‘flag’. ‘Flag-fall’ means the expiration of the allotted time for a player. 6.2 Handling the chessclock: 6.2.1 During the game each player, having made his/her move on the chessboard, shall pause his/her own clock and start his/her opponent’s clock (that is to say, he/she shall press his/her clock). This “completes” the move. A move is also completed if: 6.2.1.1 6.2.1.2 the move ends the game (see Articles 5.1.1, 5.2.1, 5.2.2, 9.2.1, 9.6.1 and 9.6.2), or the player has made his/her next move, when his/her previous move was not completed. 6.2.2 A player must be allowed to pause his/her clock after making his/her move, even after the opponent has made his/her next move. The time between making the move on the chessboard and pressing the clock is regarded as part of the time allotted to the player. 6.2.3 A player must press his/her clock with the same hand with which he/she made his/her move. It is forbidden for a player to keep his/her finger on the clock or to ‘hover’ over it. 6.2.4 The players must handle the chessclock properly. It is forbidden to press it forcibly, to pick it up, to press the clock before moving or to knock it over. Improper clock handling shall be penalised in accordance with Article 12.9. 6.2.5 6.2.6 Only the player whose clock is running is allowed to adjust the pieces. If a player is unable to use the clock, an assistant, who must be acceptable to the arbiter, may be provided by the player to perform this operation. His/Her clock shall be adjusted by the arbiter in an equitable way. This adjustment of the clock shall not apply to the clock of a player with a disability. 6.3 Allotted time: 6.3.1 When using a chessclock, each player must complete a minimum number of moves or all moves in an allotted period of time including any additional amount of time added with each move. All these must be specified in advance. 6.3.2 The time saved by a player during one period is added to his/her time available for the next period, where applicable. In the time-delay mode both players receive an allotted ‘main thinking time’. Each player also receives a ‘fixed extra time’ with every move. The countdown of the main thinking time only commences after the fixed extra time has expired. Provided the player presses his/her clock before the expiration of the fixed extra time, the main thinking time does not change, irrespective of the proportion of the fixed extra time used. 6.4 Immediately after a flag falls, the requirements of Article 6.3.1 must be checked. 6.5 Before the start of the game the arbiter shall decide where the chessclock is placed. 6.6 At the time determined for the start of the game White’s clock is started.6.7. Default time: 6.7.1 The regulations of an event shall specify a default time in advance. If the default time is not specified, then it is zero. Any player who arrives at the chessboard after the default time shall lose the game unless the arbiter decides otherwise. 6.7.2 If the regulations of an event specify that the default time is not zero and if neither player is present initially, White shall lose all the time that elapses until he/she arrives, unless the regulations of an event specify, or the arbiter decides otherwise. 6.8 A flag is considered to have fallen when the arbiter observes the fact or when either player has made a valid claim to that effect. 6.9 Except where one of Articles 5.1.1, 5.1.2, 5.2.1, 5.2.2, 5.2.3 applies, if a player does not complete the prescribed number of moves in the allotted time, the game is lost by that player. However, the game is drawn if the position is such that the opponent cannot checkmate the player’s king by any possible series of legal moves. 6.10 Chessclock setting: 6.10.1 Every indication given by the chessclock is considered to be conclusive in the absence of any evident defect. A chessclock with an evident defect shall be replaced by the arbiter, who shall use his/her best judgement when determining the times to be shown on the replacement chessclock. 6.10.2 If during a game it is found that the setting of either or both clocks is incorrect, either player or the arbiter shall pause the chessclock immediately. The arbiter shall install the correct setting and adjust the times and move-counter, if necessary he/she shall use his/her best judgement when determining the clock settings. 6.11.1 If the game needs to be interrupted, the arbiter shall pause the chessclock. 6.11.2 A player may pause the chessclock only in order to seek the arbiter’s assistance, for example when promotion has taken place and the piece required is not available. 6.11.3 The arbiter shall decide when the game restarts. 6.11.4 If a player pauses the chessclock in order to seek the arbiter’s assistance, the arbiter shall determine whether the player had any valid reason for doing so. If the player has no valid reason for pausing the chessclock, the player shall be penalised in accordance with Article 12.9. 6.12.1 Screens, monitors, or demonstration boards showing the current position on the chessboard, the moves and the number of moves made/completed, and clocks which also show the number of moves, are allowed in the playing hall. 6.12.2 The player may not make a claim relying only on information shown in this manner.
Here is a quiz based on the “Reciprocal of a Linear Function” content from your PowerPoint. --- Quiz: Reciprocal of a Linear Function Multiple Choice (5 questions) Select the best answer. 1. What is the vertical asymptote of f(x) = \dfrac{1}{x - 3}? a) x = 0 b) x = 3 c) x = -3 d) y = 0 2. For f(x) = \dfrac{1}{2x + 4}, what is the y-intercept? a) 0 b) \dfrac{1}{2} c) \dfrac{1}{4} d) 2 3. What is the horizontal asymptote of any function of the form f(x) = \dfrac{1}{ax + b} (with a \neq 0)? a) y = 0 b) y = 1 c) x = 0 d) x = -\dfrac{b}{a} 4. The domain of f(x) = \dfrac{1}{5 - x} is a) all real numbers except 5 b) all real numbers except -5 c) all real numbers d) all real numbers except 0 5. As x approaches the vertical asymptote from the right, the values of f(x) a) approach 0 b) approach \pm\infty c) approach 1 d) approach the same value as from the left --- Completion (5 questions) Fill in the blank with the correct word or expression. 1. The vertical asymptote of a reciprocal linear function occurs where the ____________________ is zero. 2. The horizontal asymptote of f(x) = \dfrac{1}{ax + b} is the line y = ________. 3. A function of the form f(x) = \dfrac{1}{ax + b} has ______ x-intercept(s) because the numerator is constant. 4. The end behavior of f(x) = \dfrac{1}{x - 2} as x \to \infty is f(x) \to ________. 5. The y-intercept of f(x) = \dfrac{1}{3x - 6} is ________. --- Answer Key Multiple Choice 1. b) x = 3 2. c) \dfrac{1}{4} (Substitute x = 0: f(0) = \frac{1}{4}) 3. a) y = 0 4. a) all real numbers except 5 5. b) approach \pm\infty Completion 6. denominator 7. 0 8. no / zero 9. 0 (from the positive side) 10. -\dfrac{1}{6} (Substitute x = 0: f(0) = \frac{1}{-6})
GUIDELINES ON THE ESTABLISHMENT AND IMPLEMENTATION OF THE RESULTS-BASED PERFORMANCE MANAGEMENT SYSTEM IN THE DEPARTMENT OF EDUCATION I. Rationale 1. The Civil Service Commission (CSC), through the issuance of Memorandum Circular (MC) No. 06, series of 2012, sets the guidelines on the establishment and implementation of the Strategic Performance Management System (SPMS) in all government agencies. The SPMS gives emphasis to the strategic alignment of the agency’s thrusts with the day-to-day operation of the units and individual personnel within the organization. It focuses on measures of performance vis-a-vis the targeted milestones, and provides a credible and verifiable basis for assessing the organizational outcomes and the collective performance of the government employees. 2. As a learner-centered institution, the Department of Education (DepEd) is committed to continuously improve itself to better serve the Filipino learners and the community. The adoption of the SPMS in DepEd strengthens the culture of performance and accountability in the agency, with the DepEd’s mandate, vision and mission at its core. 3. There is a need to concretize the linkage between the organizational thrusts and the performance management system. It is important to ensure organizational effectiveness and track individual improvement and efficiency by cascading the institutional accountabilities to the various levels, units and individual personnel, as anchored on the establishment of a rational and factual basis for performance targets and measures. Finally, it is necessary to link the SPMS with other systems relating to human resources and to ensure adherence to the principle of performance-based tenure and incentives. 4. In view of the above, this Order aims to adopt the SPMS as the Results-based Performance Management System (RPMS). II. Scope of Policy 5. This DepEd Order provides for the establishment and implementation of the RPMS in all DepEd schools and offices, covering all officials and employees, school-based and non school-based, in the Department holding regular plantilla positions. It stipulates the specific mechanisms, criteria and processes for the performance target setting, monitoring, evaluation and development planning. IV. Policy Statement 9. The DepEd hereby sets the guidelines on the establishment and implementation of the Results-based Performance Management System (RPMS) in the Department, stipulating the strategies, methods, tools and rewards for assessing the accomplishments vis-a-vis the commitments. This will be used for measuring and rewarding higher levels of performance of the various units and development planning of all personnel in all levels. 10. For non school-based personnel, the RPMS shall provide for an objective and verifiable basis for rating and ranking the performance of units and individual personnel in view of the granting of the Performance-Based Bonus (PBB) starting 2015. 11. For school-based personnel, the RPMS shall be used only as an appraisal tool, which shall be the basis for training and development. The granting of PBB shall be governed by the existing PBB guidelines. 12. The Department shall adopt the RPMS framework shown in Annex B. 13. The DepEd RPMS shall follow the four-stage performance management system cycle as prescribed by the CSC: i. Performance planning and commitment (Phase I); ii. Performance monitoring and coaching (Phase II); iii. Performance review and evaluation (Phase III); and iv. Performance rewarding and development planning (Phase IV). V. Performance Cycle/Process 14. The RPMS shall align the performance targets and accomplishments with the Department’s mandate, vision, mission and strategic goals. It shall ensure 100% results orientation vis-a-vis the planned targets. On the other hand, the ratee’s demonstration of the required competencies shall be monitored for developmental purposes only. 15. The RPMS cycle shall cover performance for one whole year. All school-based personnel shall follow a performance cycle starting in April of the current year and ending in March of the following year; while non school-based personnel shall follow a performance cycle starting in January and ending in December. Annexes C and D illustrate the performance cycles which shall apply to school-based and non school-based personnel, respectively. 16. The performance planning and commitment shall be done prior to the beginning of the performance cycle; while the performance monitoring and coaching shall take place immediately after Phase I, and continue throughout the performance cycle. The performance review and evaluation, as well as the performance rewarding and development planning shall be done at the end of the performance cycle. A. Phase I: Performance Planning and Commitment 17. The performance planning and commitment shall be done prior to the start of the performance cycle where the rater meets with the ratee to discuss and agree on the following: i. Office KRAs, Objectives and Performance Indicators as anchored to the overall organizational outcomes; and ii. Individual KRAs, Objectives and Performance Indicators as anchored to the Office KRAs and Objectives. 18. The Office Performance Commitment and Review Form (OPCRF) shall be accomplished by the head of office to reflect the Office KRAs, Objectives and Performance Indicators. The head of office, in coordination with the Planning Office, shall ensure alignment of the office plans and commitments to the overall organizational outcomes. The OPCRF shall be equivalent to the IPCRF of the head of office. A sample of the filled out OPCRF, including the instructions for accomplishing the form, is shown in Annex E. 19. The Individual Performance Commitment and Review Form (IPCRF) shall be accomplished by the individual personnel to reflect the agreed Individual KRAs, Objectives and Performance Indicators. A sample of the filled out IPCRF, including the instructions for accomplishing the form, is shown in Annex F. 20. Defining the Key Result Areas. The head of office, in coordination with the Planning Office, shall define the office KRAs as anchored on the overall organizational outcomes. The rater and the ratee shall discuss and agree on the break down of the office KRAs into individual KRAs. Three (3) to five (5) KRAs shall be defined for each office and individual employee. KRAs are broad categories of general outputs or outcomes. It is the mandate or function of the office and/or individual employee. The KRA is the reason why an office and/or job exist. It is an area where the office and/or individual employee are expected to focus on. 21. Setting the Objectives. The head of office shall set three (3) objectives per office KRA. The rater and the ratee shall discuss and agree on three (3) objectives per individual KRA. Objectives are specific tasks, which an office and/or employee need to do to achieve their specific KRAs. In objective setting, the SMART criteria, which stands for Specific, Measurable, Attainable, Relevant, Time Bound, shall be applied. The SMART criteria are illustrated in Annex G. 22. Setting the Timeline. The timeline shall define the target date for accomplishing each of the Objectives. The timeline for the office Objectives shall be set by the head of office in coordination with the Planning Office and School Planning Team; while the timeline for the individual Objectives shall be discussed and agreed by the rater and the ratee. 23. Assigning the Weight. Assigning of weights shall be done per KRA. Weights for each office KRA shall be assigned by the head of office in coordination with the Planning Office; while the weights for each of the individual KRAs shall be discussed and agreed upon by the rater and the ratee. 24. Identifying the Performance Indicators. Using a five (5)-point rating scale, the head of office shall identify a performance indicator for each of the office objectives, while the rater and the ratee shall identify and agree on the performance indicator for each of the individual objectives. Performance indicators are exact quantification of objectives expressed through rubrics. They are assessment tools, which gauge whether a performance is positive or negative. In identifying the performance indicator, the operational definition or meaning of each numerical rating shall be indicated under each relevant dimension (i.e., quality, efficiency, or timeliness) per performance target or success indicator. This shall ensure that the rating is objective, impartial and verifiable. Table 1 below discusses the performance measures by which the indicator must satisfy. Table 1. Performance Measures CATEGORY DEFINITION Effectiveness/Quality The extent to which actual performance compares with targeted performance. The degree to which objectives are achieved and the extent to which targeted problems are solved. In management, effectiveness relates to getting the right things done. Efficiency The extent to which time or resources is used for the intended task or purpose. Measures whether targets are accomplished with a minimum amount or quantity of waste, expense, or unnecessary effort. Timeliness Measures whether the deliverable was done on time based on the requirements of the rules and regulations, and/or clients/stakeholders. Time-related performance indicators evaluate such things as project completion deadlines, time management skills and other time-sensitive expectations. Some Performances are only rated on quality and efficiency, some on quality and timeliness, and others on efficiency only. You need not use all three (3) categories. 25. Demonstration of Competencies. During Phase I, the rater shall discuss with the ratee the competencies required of the individual personnel. Competencies are defined as the knowledge, skills and behavior that individuals demonstrate in achieving one’s results. Competencies shall uphold the DepEd’s core values. They represent the way individuals define and live the values. 26. DepEd shall adopt four classes of competencies as follows: i. Core behavioral competencies are competencies, which cut across the organization; ii. Leadership competencies are competencies intended for managerial positions; a. Third level officials b. Chiefs and Assistant Chiefs c. School Heads and Department Heads iii. Staff Core Skills are competencies intended for staff and teaching-related personnel; and iv. Teaching competencies are competencies intended for teachers. The DepEd-required competencies are illustrated in Annex I. 27. The ratee’s demonstration of the required competencies shall be monitored to effectively plan the interventions needed for behavioral and professional development. The assessment in the demonstration of competencies shall not be reflected in the final rating. 28. Reaching Agreement. Once the office and individual KRAs, Objectives and Performance Indicators are clearly defined, the rater and the ratee shall commit and reach an agreement by signing the OPCRF and IPCRF. The signed/approved OPCRF and IPCRF shall be the basis for monitoring and assessment, which shall take place in Phases II and III, respectively. B. Phase II: Performance Monitoring and Coaching 29. The performance monitoring and coaching shall commence after the rater and the ratee commit on the KRAs, Objectives and Performance Indicators, and sign the OPCRF and IPCRF. This shall be done throughout the year. 30. The two (2) main components of Phase II are the following: i. Performance monitoring; and ii. Coaching and feedback. 31. Performance monitoring shall provide key inputs and objective basis for rating. It shall facilitate feedback and provide evidence of performance. Performance monitoring shall be the responsibility of both the rater and the ratee who agree to track and record significant incidents through the use of the Performance Monitoring and Coaching Form (PMCF) shown in Annex J. Significant incidents are actual events and behaviors in which both positive and negative performances are observed and documented. 32. Coaching and feedback shall be a continuous process. Coaching and feedback shall be provided by the rater and/or shall be sought by the ratee to improve work performance and behavior. The rater, as the coach or mentor of the ratee, playing a critical role in the performance monitoring and coaching, shall provide an enabling environment and intervention to improve the office performance and to manage and develop individual potentials. 33. The PMCF shall capture the significant incidents. It shall provide a record of demonstrated behaviors, competencies and performance, and shall be an effective substitute in the absence of quantifiable data. The rater and the ratee shall sign each significant incident recorded in the PMCF to ensure that agreement has been reached. C. Phase III: Performance Review and Evaluation 34. The performance review and evaluation shall be done at the end of the performance cycle to assess the office and individual employee’s performance level based on the commitments and measures as contained in the signed OPCRF and IPCRF. 35. A mid-year review is prescribed to determine the progress in achieving the Objectives. In exceptional cases, and only if the situation warrants, a one-time recalibration of office and individual Objectives shall be allowed during the mid-year review. Exceptional cases shall include instances when high level decisions are taken into effect such as changes in strategic directions, and circumstances beyond the control of the ratee such as natural and/or man-made calamities, including typhoon, earthquake and other fortuitous events. During the mid-year review, the rater shall inform in writing the ratee of the status of performance, in case of an Unsatisfactory or Poor performance. Coaching, feedback and appropriate interventions shall be provided where necessary. 36. The RPMS shall put premium on KRAs towards the realization of organizational vision, mission, strategic priorities and the OPIF logframe. Hence, rating for planned and/or intervening tasks shall always be supported by reports, documents or any output as proofs of actual performance. In the absence of said bases or proofs, a particular task shall not be rated and shall be disregarded. 37. Office and Individual Performance Assessment. The head of office, in coordination with the Planning Office, shall assess the performance of the office vis-a-vis the committed targets at the beginning of the performance cycle. The rater and the ratee shall discuss and agree on the individual assessment based on the actual accomplishments of each of the KRAs and Objectives. The final rating shall be based solely on the accomplishment of the specific objectives as measured by the Performance Indicators. The OPCRF and IPCRF shall be accomplished and completed by the rater and the ratee to: i. Reflect actual accomplishments and results; ii. Rate each of the objectives; iii. Compute for the score per objective; iv. Determine the overall rating for accomplishments; v. Reach an agreement; and vi. Assess the competencies. 38. Initial self-rating shall be encouraged prior to the rater-ratee discussion. 39. Third Level Officials, as heads of offices, shall accomplish the OPCRF for submission to the Planning Office. The individual assessment of Third Level Officials shall be contained in the CESPES Forms for submission to the Career Executive Service Board (CESB). The BHROD and Personnel Division shall be furnished a copy of both forms. 40. Actual Results. The rater and the ratee shall discuss and agree on the actual accomplishments and results based on the performance commitments and measures made at the beginning of the rating period. They shall evaluate each objective whether it has been achieved or not. The significant incidents as reflected in the PMCF shall be considered for the actual results. 41. Rating the Objectives. Based on the actual accomplishments and results, each of the Objectives shall be rated using the rating scale specified below: Table 2. The RPMS Rating Scale NUMERICAL RATING ADJECTIVAL RATING DESCRIPTION OF MEANING OF RATING 5 Outstanding Performance represents an extraordinary level of achievement and commitment in terms of quality and time, technical skills and knowledge, ingenuity, creativity and initiative. Employees at this performance level should have demonstrated exceptional job mastery in all major areas of responsibility. Employee achievement and contributions to the organization are of marked excellence. 4 Very Satisfactory Performance exceeded expectations. All goals, objectives and targets were achieved above the established standards. 3 Satisfactory Performance met expectations in terms of quality of work, efficiency and timeliness. The most critical annual goals were met. 2 Unsatisfactory Performance failed to meet expectations, and/or one or more of the most critical goals were not met. 1 Poor Performance was consistently below expectations, and/or reasonable progress toward critical goals was not made. Significant improvement is needed in one or more important areas. The final assessment shall correspond to the adjectival description of Outstanding, Very Satisfactory, Satisfactory, Unsatisfactory or Poor. The range of adjectival rating is as per attached in Forms A, B, and C. 42. Process for Computing the Score per KRA. i. The rater and ratee shall ensure that each KRA has been assigned weight according to priority. ii. As an option, the rater and ratee may assign weights to objectives which shall be equal to the total weight assigned to a particular KRA. KRA 1 – Weight assigned is 40% Objective 1 is 20% Objective 2 is 10% Objective 3 is 10% iii. The score per KRA shall be computed using the following formula: 43. Plus Factor. The plus factor shall be considered as another KRA. These are value adding accomplishments, which are not covered within the regular duties and responsibilities. The weight on the plus factor shall not exceed the weight of the highest mandated KRA. For teachers, the plus factor shall be limited to work/activities, which contribute to the teaching-learning process. 44. Determining the Overall Rating for Accomplishments. The overall rating/assessment for the accomplishments shall fall within the following adjectival ratings and shall be in three (3) decimal points: Table 3. Adjectival Ratings RANGE ADJECTIVAL RATING 4.500-5.000 Outstanding 3.500-4.499 Very Satisfactory 2.500-3.499 Satisfactory 1.500-2.499 Unsatisfactory below 1.499 Poor 45. Reaching Agreement. Upon determining the overall rating for the actual accomplishments and results, the rater and the ratee shall reach an agreement by signing the OPCRF and IPCRF. The average rating of individual staff members should not go higher than the collective performance assessment of the office. 46. Assessing the Competencies. The rater shall discuss with the ratee the set of competencies observed during the performance cycle. The competencies shall not be reflected in the final rating. Competencies shall be monitored for developmental purposes. In evaluating the individual’s demonstration of competencies, the rating scale in Table 4 shall apply: Table 4. The DepEd Competencies Scale SCALE DEFINITION 5 Role model 4 Consistently demonstrates 3 Most of the time demonstrates 2 Sometimes demonstrates 1 Rarely demonstrates 5 (role model) – all competency indicators 4 (consistently demonstrates) – four competency indicators 3 (most of the time demonstrates) – three competency indicators 2 (sometimes demonstrates) – two competency indicators 1 (rarely demonstrates) – one competency indicator D. Phase IV: Performance Rewarding and Development Planning 47. The results of the performance review and evaluation shall be used in performance rewarding and development planning. This phase shall be done after Phase III. 48. The rater shall discuss and provide qualitative comments, observations and recommendations in the individual employee’s performance commitment, competency assessment and significant incidents which shall be used for training and professional development. These can be written under the strengths and development needs column of the Part IV-Development Plans of the IPCRF. 49. The rater and the ratee shall identify and discuss the individual’s strengths and development needs, and reflect them in the Part IV-Development Plans of the IPCRF. The competencies which the ratee demonstrated consistently and the areas, where the ratee meet or exceed expectations shall be referred to as the ratee’s strengths. The competencies, which the ratee rarely demonstrates and the areas where the ratee has room for improvement and has not met the expectations, shall be identified as the ratee’s development needs. Make a situational SOLO-based questions in the context of school leadership
Section 1: Numbers, Operations, and Relationships (15 marks) 1. Number Concepts (5 marks) 1.1. Decompose the following numbers into tens and ones: (2 marks) a. 34 b. 67 1.2. Count the objects in the pictures below and write the total number: (3 marks) [This section would need images of objects. You can provide images of groups of objects, e.g., 3 groups of 4 apples each and ask the students to count the total number.] 2. Solve Problems (5 marks) 2.1. Solve the following word problem using drawings: (3 marks) Samantha has 5 baskets. Each basket has 8 apples. How many apples does she have in total? Samantha has 5 × 8 = 40 5×8=40 apples. 2.2. Solve the following word problem by building up and breaking down numbers: (2 marks) There are 4 boxes. Each box has 6 chocolates. How many chocolates are there in total? There are 4 × 6 = 24 4×6=24 chocolates in total. 3. Calculations (5 marks) 3.1. Multiply the following numbers using drawings: (3 marks) a. 5 × 4 = 20 b. 4 × 5 = 20 3.2. Use a number line to solve: (2 marks) a. 3 × 5 = 15 b. 2 × 4 = 8 Section 2: Patterns, Functions, and Algebra (10 marks) 4. Number Patterns (10 marks) 4.1. Complete the number sequences: (5 marks) a. 180, 170, 160, 150, 140, 130, 120, 110, 100, 90 b. 150, 152, 154, 156, 158, 160, 162, 164, 166, 168 4.2. Count in twos and fill in the missing numbers: (5 marks) a. 102, 104, 106, 108, 110, 112, 114, 116 Section 3: Space and Shape (Geometry) (10 marks) 5. Position (10 marks) 5.1. Follow the directions to move around the classroom: (5 marks) Draw a path showing how you would move from your desk to the teacher's table by following these steps: Move 3 steps forward. Turn left and move 2 steps. Turn right and move 4 steps. [Students would draw a path based on these directions.] 5.2. Use the language of position to describe the following: (5 marks) a. The pencil is on the book. b. The chair is beside the desk. c. The bag is under the table. d. The ruler is next to the notebook. e. The eraser is inside the pencil case.
Introduction to Free Fall A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics that are true of free-falling objects: • Free-falling objects do not encounter air resistance. • All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s for back-of-the-envelope calculations) Because free-falling objects are accelerating downwards at a rate of 9.8 m/s/s, a ticker tape trace or dot diagram of its motion would depict an acceleration. The dot diagram at the right depicts the acceleration of a free-falling object. The position of the object at regular time intervals - say, every 0.1 second - is shown. The fact that the distance that the object travels every interval of time is increasing is a sure sign that the ball is speeding up as it falls downward. Recall from an earlier lesson, that if an object travels downward and speeds up, then its acceleration is downward. Free-fall acceleration is often witnessed in a physics classroom by means of an ever-popular strobe light demonstration. The room is darkened and a jug full of water is connected by a tube to a medicine dropper. The dropper drips water and the strobe illuminate the falling droplets at a regular rate - say once every 0.2 seconds. Instead of seeing a stream of water free-falling from the medicine dropper, several consecutive drops with increasing separation distance are seen. The pattern of drops resembles the dot diagram shown in the graphic at the right. The Acceleration of Gravity It was learned in the previous part of this lesson that a free-falling object is an object that is falling under the sole influence of gravity. A free-falling object has an acceleration of 9.8 m/s/s, downward (on Earth). This numerical value for the acceleration of a free-falling object is such an important value that it is given a special name. It is known as the acceleration of gravity - the acceleration for any object moving under the sole influence of gravity. A matter of fact, this quantity known as the acceleration of gravity is such an important quantity that physicists have a special symbol to denote it - the symbol g. The numerical value for the acceleration of gravity is most accurately known as 9.8 m/s2. There are slight variations in this numerical value (to the second decimal place) that are dependent primarily upon on altitude. We will occasionally use the approximated value of 10 m/s2 in order to reduce the complexity of the many mathematical tasks that we will perform with this number. By so doing, we will be able to better focus on the conceptual nature of physics without too much of a sacrifice in numerical accuracy. g = 9.8 m/s2, downward Look It Up! Even on the surface of the Earth, there are local variations in the value of the acceleration of gravity (g). These variations are due to latitude, altitude and the local geological structure of the region. Recall from an earlier lesson that acceleration is the rate at which an object changes its velocity. It is the ratio of velocity change to time between any two points in an object's path. To accelerate at 9.8 m/s2 means to change the velocity by 9.8 m/s each second. If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s) Velocity (m/s) 0 0 1 - 9.8 2 - 19.6 3 - 29.4 4 - 39.2 5 - 49.0 . Observe that the velocity-time data above reveal that the object's velocity is changing by 9.8 m/s each consecutive second. That is, the free-falling object has an acceleration of approximately 9.8 m/s2. Another way to represent this acceleration of 9.8 m/s2 is to add numbers to our dot diagram that we saw earlier in this lesson. The velocity of the ball is seen to increase as depicted in the diagram at the right. (NOTE: The diagram is not drawn to scale - in two seconds, the object would drop considerably further than the distance from shoulder to toes.) Representing Free Fall by Graphs • Early in Lesson 1 it was mentioned that there are a variety of means of describing the motion of objects. One such means of describing the motion of objects is through the use of graphs - position versus time and velocity vs. time graphs. In this part of Lesson 5, the motion of a free-falling motion will be represented using these two basic types of graphs. Representing Free Fall by Position-Time Graphs A position versus time graph for a free-falling object is shown below. Observe that the line on the graph curves. As learned earlier, a curved line on a position versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9.8 m/s/s), it would be expected that its position-time graph would be curved. A further look at the position-time graph reveals that the object starts with a small velocity (slow) and finishes with a large velocity (fast). Since the slope of any position vs. time graph is the velocity of the object (as learned in Lesson 3), the small initial slope indicates a small initial velocity and the large final slope indicates a large final velocity. Finally, the negative slope of the line indicates a negative (i.e., downward) velocity. Representing Free Fall by Velocity-Time Graphs A velocity versus time graph for a free-falling object is shown below. Observe that the line on the graph is a straight, diagonal line. As learned earlier, a diagonal line on a velocity versus time graph signifies an accelerated motion. Since a free-falling object is undergoing an acceleration (g = 9,8 m/s/s, downward), it would be expected that its velocity-time graph would be diagonal. A further look at the velocity-time graph reveals that the object starts with a zero velocity (as read from the graph) and finishes with a large, negative velocity; that is, the object is moving in the negative direction and speeding up. An object that is moving in the negative direction and speeding up is said to have a negative acceleration (if necessary, review the vector nature of acceleration). Since the slope of any velocity versus time graph is the acceleration of the object (as learned in Lesson 4), the constant, negative slope indicates a constant, negative acceleration. This analysis of the slope on the graph is consistent with the motion of a free-falling object - an object moving with a constant acceleration of 9.8 m/s/s in the downward direction. The Kinematic Equations The goal of this first unit has been to investigate the variety of means by which the motion of objects can be described. The variety of representations that we have investigated includes verbal representations, pictorial representations, numerical representations, and graphical representations (position-time graphs and velocity-time graphs). In Lesson 6, we will investigate the use of equations to describe and represent the motion of objects. These equations are known as kinematic equations. There are a variety of quantities associated with the motion of objects - displacement (and distance), velocity (and speed), acceleration, and time. Knowledge of each of these quantities provides descriptive information about an object's motion. For example, if a car is known to move with a constant velocity of 22.0 m/s, North for 12.0 seconds for a northward displacement of 264 meters, then the motion of the car is fully described. And if a second car is known to accelerate from a rest position with an eastward acceleration of 3.0 m/s2 for a time of 8.0 seconds, providing a final velocity of 24 m/s, East and an eastward displacement of 96 meters, then the motion of this car is fully described. These two statements provide a complete description of the motion of an object. However, such completeness is not always known. It is often the case that only a few parameters of an object's motion are known, while the rest are unknown. For example as you approach the stoplight, you might know that your car has a velocity of 22 m/s, East and is capable of a skidding acceleration of 8.0 m/s2, West. However you do not know the displacement that your car would experience if you were to slam on your brakes and skid to a stop; and you do not know the time required to skid to a stop. In such an instance as this, the unknown parameters can be determined using physics principles and mathematical equations (the kinematic equations). The BIG 4 The kinematic equations are a set of four equations that can be utilized to predict unknown information about an object's motion if other information is known. The equations can be utilized for any motion that can be described as being either a constant velocity motion (an acceleration of 0 m/s/s) or a constant acceleration motion. They can never be used over any time period during which the acceleration is changing. Each of the kinematic equations include four variables. If the values of three of the four variables are known, then the value of the fourth variable can be calculated. In this manner, the kinematic equations provide a useful means of predicting information about an object's motion if other information is known. For example, if the acceleration value and the initial and final velocity values of a skidding car is known, then the displacement of the car and the time can be predicted using the kinematic equations. Lesson 6 of this unit will focus upon the use of the kinematic equations to predict the numerical values of unknown quantities for an object's motion. The four kinematic equations that describe an object's motion are: There are a variety of symbols used in the above equations. Each symbol has its own specific meaning. The symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stands for the acceleration of the object. And the symbol v stands for the velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Each of these four equations appropriately describes the mathematical relationship between the parameters of an object's motion. As such, they can be used to predict unknown information about an object's motion if other information is known. In the next part of Lesson 6 we will investigate the process of doing this. Kinematic Equations and Problem-Solving The four kinematic equations that describe the mathematical relationship between the parameters that describe an object's motion were introduced in the previous part of Lesson 6. The four kinematic equations are: In the above equations, the symbol d stands for the displacement of the object. The symbol t stands for the time for which the object moved. The symbol a stand for the acceleration of the object. And the symbol v stands for the instantaneous velocity of the object; a subscript of i after the v (as in vi) indicates that the velocity value is the initial velocity value and a subscript of f (as in vf) indicates that the velocity value is the final velocity value. Problem-Solving Strategy In this part of Lesson 6 we will investigate the process of using the equations to determine unknown information about an object's motion. The process involves the use of a problem-solving strategy that will be used throughout the course. The strategy involves the following steps: 1. Construct an informative diagram of the physical situation. 2. Identify and list the given information in variable form. 3. Identify and list the unknown information in variable form. 4. Identify and list the equation that will be used to determine unknown information from known information. 5. Substitute known values into the equation and use appropriate algebraic steps to solve for the unknown information. 6. Check your answer to ensure that it is reasonable and mathematically correct. The use of this problem-solving strategy in the solution of the following problem is modeled in Examples A and B below. Example Problem A . Ima Hurryin is approaching a stoplight moving with a velocity of +30.0 m/s. The light turns yellow, and Ima applies the brakes and skids to a stop. If Ima's acceleration is -8.00 m/s2, then determine the displacement of the car during the skidding process. (Note that the direction of the velocity and the acceleration vectors are denoted by a + and a - sign.) The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. Note that the vf value can be inferred to be 0 m/s since Ima's car comes to a stop. The initial velocity (vi) of the car is +30.0 m/s since this is the velocity at the beginning of the motion (the skidding motion). And the acceleration (a) of the car is given as - 8.00 m/s2. (Always pay careful attention to the + and - signs for the given quantities.) The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = +30.0 m/s vf = 0 m/s a = - 8.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vf, vi, a, and d. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 • a • d Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (30.0 m/s)2 + 2 • (-8.00 m/s2) • d 0 m2/s2 = 900 m2/s2 + (-16.0 m/s2) • d (16.0 m/s2) • d = 900 m2/s2 - 0 m2/s2 (16.0 m/s2)*d = 900 m2/s2 d = (900 m2/s2)/ (16.0 m/s2) d = (900 m2/s2)/ (16.0 m/s2) d = 56.3 m The solution above reveals that the car will skid a distance of 56.3 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. It takes a car a considerable distance to skid from 30.0 m/s (approximately 65 mi/hr) to a stop. The calculated distance is approximately one-half a football field, making this a very reasonable skidding distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Ben Rushin is waiting at a stoplight. When it finally turns green, Ben accelerated from rest at a rate of a 6.00 m/s2 for a time of 4.10 seconds. Determine the displacement of Ben's car during this time period. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step of the strategy involves the identification and listing of known information in variable form. Note that the vi value can be inferred to be 0 m/s since Ben's car is initially at rest. The acceleration (a) of the car is 6.00 m/s2. And the time (t) is given as 4.10 s. The next step of the strategy involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the car. So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0 m/s t = 4.10 s a = 6.00 m/s2 d = ?? The next step of the strategy involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are t, vi, a, and d. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step of the strategy involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. d = (0 m/s) • (4.1 s) + ½ • (6.00 m/s2) • (4.10 s)2 d = (0 m) + ½ • (6.00 m/s2) • (16.81 s2) d = 0 m + 50.43 m d = 50.4 m The solution above reveals that the car will travel a distance of 50.4 meters. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. A car with an acceleration of 6.00 m/s/s will reach a speed of approximately 24 m/s (approximately 50 mi/hr) in 4.10 s. The distance over which such a car would be displaced during this time period would be approximately one-half a football field, making this a very reasonable distance. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! The two example problems above illustrate how the kinematic equations can be combined with a simple problem-solving strategy to predict unknown motion parameters for a moving object. Provided that three motion parameters are known, any of the remaining values can be determined. In the next part of Lesson 6, we will see how this strategy can be applied to free fall situations. Or if interested, you can try some practice problems and check your answer against the given solutions. Kinematic Equations and Free Fall As mentioned in Lesson 5, a free-falling object is an object that is falling under the sole influence of gravity. That is to say that any object that is moving and being acted upon only be the force of gravity is said to be "in a state of free fall." Such an object will experience a downward acceleration of 9.8 m/s/s. Whether the object is falling downward or rising upward towards its peak, if it is under the sole influence of gravity, then its acceleration value is 9.8 m/s/s. Like any moving object, the motion of an object in free fall can be described by four kinematic equations. The kinematic equations that describe any object's motion are: The symbols in the above equation have a specific meaning: the symbol d stands for the displacement; the symbol t stands for the time; the symbol a stands for the acceleration of the object; the symbol vi stands for the initial velocity value; and the symbol vf stands for the final velocity. Applying Free Fall Concepts to Problem-Solving There are a few conceptual characteristics of free fall motion that will be of value when using the equations to analyze free fall motion. These concepts are described as follows: • An object in free fall experiences an acceleration of -9.8 m/s/s. (The - sign indicates a downward acceleration.) Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s/s for any freely falling object. • If an object is merely dropped (as opposed to being thrown) from an elevated height, then the initial velocity of the object is 0 m/s. • If an object is projected upwards in a perfectly vertical direction, then it will slow down as it rises upward. The instant at which it reaches the peak of its trajectory, its velocity is 0 m/s. This value can be used as one of the motion parameters in the kinematic equations; for example, the final velocity (vf) after traveling to the peak would be assigned a value of 0 m/s. • If an object is projected upwards in a perfectly vertical direction, then the velocity at which it is projected is equal in magnitude and opposite in sign to the velocity that it has when it returns to the same height. That is, a ball projected vertically with an upward velocity of +30 m/s will have a downward velocity of -30 m/s when it returns to the same height. These four principles and the four kinematic equations can be combined to solve problems involving the motion of free-falling objects. The two examples below illustrate application of free fall principles to kinematic problem-solving. In each example, the problem solving strategy that was introduced earlier in this lesson will be utilized. Example Problem A Luke Autbeloe drops a pile of roof shingles from the top of a roof located 8.52 meters above the ground. Determine the time required for the shingles to reach the ground. The solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 8.52 meters. The displacement (d) of the shingles is -8.52 m. (The - sign indicates that the displacement is downward). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. For example, the vi value can be inferred to be 0 m/s since the shingles are dropped (released from rest; see note above). And the acceleration (a) of the shingles can be inferred to be -9.8 m/s2 since the shingles are free-falling (see note above). (Always pay careful attention to the + and - signs for the given quantities.) The next step of the solution involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the time of fall. So t is the unknown quantity. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 0.0 m/s d = -8.52 m a = - 9.8 m/s2 t = ?? The next step involves identifying a kinematic equation that allows you to determine the unknown quantity. There are four kinematic equations to choose from. In general, you will always choose the equation that contains the three known and the one unknown variable. In this specific case, the three known variables and the one unknown variable are d, vi, a, and t. Thus, you will look for an equation that has these four variables listed in it. An inspection of the four equations above reveals that the equation on the top left contains all four variables. d = vi • t + ½ • a • t2 Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. -8.52 m = (0 m/s) • (t) + ½ • (-9.8 m/s2) • (t)2 -8.52 m = (0 m) *(t) + (-4.9 m/s2) • (t)2 -8.52 m = (-4.9 m/s2) • (t)2 (-8.52 m)/(-4.9 m/s2) = t2 1.739 s2 = t2 t = 1.32 s The solution above reveals that the shingles will fall for a time of 1.32 seconds before hitting the ground. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The shingles are falling a distance of approximately 10 yards (1 meter is pretty close to 1 yard); it seems that an answer between 1 and 2 seconds would be highly reasonable. The calculated time easily falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for time and insuring that the left side of the equation is equal to the right side of the equation. Indeed it is! Example Problem B Rex Things throws his mother's crystal vase vertically upwards with an initial velocity of 26.2 m/s. Determine the height to which the vase will rise above its initial height. Once more, the solution to this problem begins by the construction of an informative diagram of the physical situation. This is shown below. The second step involves the identification and listing of known information in variable form. You might note that in the statement of the problem, there is only one piece of numerical information explicitly stated: 26.2 m/s. The initial velocity (vi) of the vase is +26.2 m/s. (The + sign indicates that the initial velocity is an upwards velocity). The remaining information must be extracted from the problem statement based upon your understanding of the above principles. Note that the vf value can be inferred to be 0 m/s since the final state of the vase is the peak of its trajectory (see note above). The acceleration (a) of the vase is -9.8 m/s2 (see note above). The next step involves the listing of the unknown (or desired) information in variable form. In this case, the problem requests information about the displacement of the vase (the height to which it rises above its starting height). So d is the unknown information. The results of the first three steps are shown in the table below. Diagram: Given: Find: vi = 26.2 m/s vf = 0 m/s a = -9.8 m/s2 d = ?? The next step involves identifying a kinematic equation that would allow you to determine the unknown quantity. There are four kinematic equations to choose from. Again, you will always search for an equation that contains the three known variables and the one unknown variable. In this specific case, the three known variables and the one unknown variable are vi, vf, a, and d. An inspection of the four equations above reveals that the equation on the top right contains all four variables. vf2 = vi2 + 2 • a • d Once the equation is identified and written down, the next step involves substituting known values into the equation and using proper algebraic steps to solve for the unknown information. This step is shown below. (0 m/s)2 = (26.2 m/s)2 + 2 •(-9.8m/s2) •d 0 m2/s2 = 686.44 m2/s2 + (-19.6 m/s2) •d (-19.6 m/s2) • d = 0 m2/s2 -686.44 m2/s2 (-19.6 m/s2) • d = -686.44 m2/s2 d = (-686.44 m2/s2)/ (-19.6 m/s2) d = 35.0 m The solution above reveals that the vase will travel upwards for a displacement of 35.0 meters before reaching its peak. (Note that this value is rounded to the third digit.) The last step of the problem-solving strategy involves checking the answer to assure that it is both reasonable and accurate. The value seems reasonable enough. The vase is thrown with a speed of approximately 50 mi/hr (merely approximate 1 m/s to be equivalent to 2 mi/hr). Such a throw will never make it further than one football field in height (approximately 100 m), yet will surely make it past the 10-yard line (approximately 10 meters). The calculated answer certainly falls within this range of reasonability. Checking for accuracy involves substituting the calculated value back into the equation for displacement and insuring that the left side of the equation is equal to the right side of the equation. Indeed, it is! Kinematic equations provide a useful means of determining the value of an unknown motion parameter if three motion parameters are known. In the case of a free-fall motion, the acceleration is often known. And in many cases, another motion parameter can be inferred through a solid knowledge of some basic kinematic principles.