Curriculum Guide for Grade 12

Mathematics: Pre-Calculus or Statistics and Probability

Notes about mathematics curriculum:

1) Many students begin high school level math in the middle grades, completing Algebra I and even Geometry before high school.

2) Mathematics curriculum at any grade level or for any topic identifies what students should know and be able to do at a particular grade level or course. However, intricately connected to and supporting all mathematics content and curriculum are mathematical processes that are common to all strands and specific expectations. Students at all levels need experiences with and growing proficiency in these practices. Educators and parents keep these in mind and integrate them constantly into mathematics instruction. These processes describe ways that students need to engage with mathematical subject matter increasingly as they progress through the grades.

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

Source: National Council of Teachers of Mathematics process standards, National Research Council’s report on helping children learn mathematics, Adding It Up.

Pre-Calculus

• Exponents and scientific notation
• Radicals and rational exponents
• Polynomials
• Factoring polynomials
• Rational expressions
• Linear equations and inequalities
• Systems of equations
• Graphs of linear equations
• Lines and slopes
• Distance and midpoint formulas
• Vectors and operations on vectors
• Matrices and operations on matrices
• Applications of matrices
• Basic functions and properties of functions
• Interpreting and analyzing functions
• Combinations of functions
• Graphs of functions
• Transformations of functions
• Modeling with functions
• Complex number system
• Arithmetic operations with complex numbers
• Quadratic functions and applications
• Polynomials functions and graphs
• Zeros of polynomial functions
• Rational functions and graphs
• Polynomial and rational inequalities
• One-to-one functions
• Inverse functions
• Exponential functions
• Logarithmic functions
• Properties of logarithms
• Logarithmic and exponential equations
• Exponential growth and decay
• Logistic growth and decay
• Modeling with exponential and logarithmic functions
• Trigonometric functions
• Trigonometric equations
• The unit circle
• Angles and their measure
• Right triangle trigonometry
• Trigonometric identities and proof
• Trigonometric functions of any angle
• Law of Sines and Law of Cosines
• Graphs of sine, cosine, tangent, cotangent, cosecant, and secant functions
• Inverse trigonometric functions
• Applications of trigonometric functions
• Sum and difference formulas
• Double-angle and half-angle identities

Statistics and Probability

• Definition of statistics and data
• Statistical questions
• Summarizing and representing data, including with technology programs and models
• Interpreting models of data
• Definitions of mean, median, and mode
• Computation of mean, median, and mode from a data set
• Shape, center, and spread of data sets
• Extreme points in data
• Relative frequencies, possible associations, and trends
• Relationships between data items
• Variance and standard deviation
• Line of best fit to a given data distribution
• Mean and standard deviation to estimate population percentage
• Correlation coefficient of two variables
• Sampling distribution and population distribution
• Random sampling
• Evaluating random processes
• Margin of error for random sampling
• Uses of statistical data
• Making inferences from surveys, observations, and experiments
• Conditional probability
• Probabilities of compound events
• Probabilities of mutually exclusive and non-mutually exclusive events
• Probabilities for independent events
• Probabilities for dependent events
• Permutations and combinations
• Expected value of a random variable
• Interpreting results of probability experiments
• Odds in favor and odds against an occurrence
• Using probability to make decisions
• Using probability to solve real-world problems

Social Studies: United States Government; Economics

Note about social science curriculum: These ten themes of social studies serve as a background framework for the teaching of the social sciences at all grade levels. They weave through all content and are interrelated with one another. Students need exposure to and development of these themes throughout the grades.

Source: National Council for the Social Studies

Ten Themes of Social Studies

1. Culture
2. Time, continuity, and change
3. People, places, and environments
4. Individual development and identity
5. Individuals, groups, and institutions
6. Power, authority, and governance
7. Production, distribution, and consumption
8. Science, technology, and society
9. Global connections
10. Civic ideals and practices

In addition, there are social studies practices and habits and literacy skills that should be fostered and integrated with all social studies content. Students at all levels need grade-level appropriate experiences that develop and polish these practices.

1. Gathering, interpreting, and using evidence from various sources
2. Applying critical thinking skills to organize, use, and evaluate information
3. Problem solving and decision making processes
4. Chronological reasoning and understanding of causation
5. Comparing and understanding events and relationships in context
6. Comparing different ways of looking at an event or problem
7. Understanding how people might be affected by events, changes, settings, or problems
8. Communicating knowledge, research conclusions, and ideas in written, oral, and visual forms
9. Geographic reasoning and use of geographic tools
10. Describing and explaining economics and economic systems
11. Civic understanding and participation

United States Government (or national government of home country)

• Foundations of the U.S. government
• Major traditions informing the founding of the U.S.
• Characteristics of and political ideas behind a constitutional government
• Contributions of key individuals to the founding political philosophies
• Federalism
• U.S Constitution, the Bill of Rights, and other significant documents
• Amendments to the Constitution; the amendment process
• Structure of the U.S. government
• Powers of the federal and state governments, and shared powers
• Historical conflicts over the roles of state and federal governments
• Executive branch: structure, powers, functions, agencies, and cabinet
• Legislative branch: structure, powers, functions, committees
• Judicial branch: structure, powers, functions
• Limits on the powers of government and on each branch
• Checks and balances; separation of powers
• How laws are made
• The U.S. Supreme Court; key court decisions
• State and local governments
• Other governmental agencies and organizations
• Voting, campaigns, and elections; voting rights
• Electoral college and electoral processes
• Political parties and the political process
• Government finances and taxes
• Policy making process
• Fiscal policy
• Social and domestic policy
• Foreign and defense policy
• Economic policy
• Environmental policy
• Influence of political parties, interest groups, public, and media on public policy
• Civil rights and civil liberties
• Equality and due process
• Personal liberties and social responsibility
• Personal liberty and safety
• Responsibilities of citizens
• Freedom of the press
• National security
• Military service
• Social welfare
• Impact of science and technology on government and society
• Key issues facing the government
• Compare political systems with other countries
• International relationships and interconnectedness

Economics

• Market economy; free enterprise system
• Characteristics of the United States economy
• Kinds of resources; scarcity of resources
• Economic decision making
• Costs and benefits
• Allocation of goods and services
• Incentives
• International trade and exchange rates
• Specialization
• Markets and prices; role of prices
• Supply and demand
• Profits and losses
• Competition and market structure
• Economic institutions
• Other institutions that influence economics
• Jobs, employer and employee issues, rights of workers
• Human productivity
• Moral, ethical, and legal business issues
• Money and inflation
• Interest, credit, and debt
• Income
• Investment
• Entrepreneurship
• Economic growth; measuring economic performance
• Economic role of government in a market economy
• Government failure
• Economic fluctuations and economic indicators
• Unemployment and inflation
• Fiscal and monetary policy
• Global economic dependence
• Effects of technology on economies and economic practices
• World financial issues
• Comparison of economic systems
• Personal financial literacy

Reading Literature and Informational Text History/Social Studies, Science, and Technical Subjects

• Cite evidence from text to support analysis of both explicit and implicit messages within the text
• Cite evidence from text to support analysis of primary and secondary sources
• Identify the theme or central idea of a text and analyze its development
• Identify in detail a series of events described and the relationships among them
• Summarize literary and informational or explanatory texts
• Follow a multistep procedure when performing science or technical tasks
• Compare and contrast treatments of the same topic from several sources
• Analyze how the author’s choices effect the development of a story
• Analyze how a text makes connections among individuals, events, or ideas
• Analyze how a complex primary source is structured
• Determine meanings and effects of words, phrases, or symbols as used in a text
• Evaluate the effectiveness of the structure of a work in furthering the key ideas or argument
• Analyze how the structure of parts of a text contribute to the overall meaning
• Analyze a work that uses satire, sarcasm, irony, or understatement
• Determine author’s purpose or point of view and how rhetoric is used to advance that purpose or point of view
• Analyze multiple interpretations of a story, drama, or poem
• Compare the point of view or claims of two or more authors on similar topics
• Show knowledge of 18th-, 19th-, and 20th-century foundational works of American (or home country) literature
• Integrate and evaluate multiple sources of information in different formats
• Integrate information from diverse primary and secondary sources
• Analyze whether an author supports a claim with sound reasoning and sufficient evidence
• Analyze and evaluate 17th-, 18th-, and 19th-century foundational U.S. literary and historical documents (or similar documents from appropriate periods for home country)
• Evaluate the hypotheses, data, analysis, and conclusions of a science or technical text
• By the end of the academic year, read and understand grade-level literary and informational texts (including history/social studies, science, and technical subjects) independently and with proficiency

Speaking and Listening

• Participate in collaborative discussions on a variety of grade-level topics
• Express ideas clearly and respectfully in group discussions
• Follow agreed-upon rules and preparation procedures for discussions
• Ask questions and respond to others, building on others’ ideas
• Integrate into speech preparation diverse sources of information in a variety of formats
• Evaluate a speaker’s point of view, reasoning, and use of rhetoric and evidence
• Identify an argument, claims; evaluate the soundness of reasoning and evidence
• Present claims or information in logical sequence, communicating a clear perspective, supported with sound reasoning and relevant facts and details
• Use clear pronunciation and appropriate eye contact and volume when speaking
• Add digital media and other visual components to clarify ideas in presentations
• Adapt speech to a variety of tasks, showing command of formal English

English Language Skills

• Show a command of conventions of standard English grammar and usage when writing or speaking
• Use conventions of English correctly when writing (capitalization, punctuation, and spelling)
• Make effective choices of language for meaning and style when writing or speaking
• Know the difference between formal and informal English and when to use each

Vocabulary

• Use context clues to determine word and phrase meanings
• Use word structure clues to determine meanings of unknown words
• Use relationships between words to better understand each word’s meaning
• Use references (print and digital) to determine or verify a word’s meanings, or to find its pronunciation or part of speech
• Interpret, analyze, and use figurative language in context
• Analyze nuances in the meaning of words with similar denotations
• Distinguish shades of meaning among related words
• Distinguish among connotations of words with similar denotations
• Learn and use grade-level general academic vocabulary

Writing

• Write arguments supported with clear reasons and relevant evidence, including arguments in history, social studies, science, and technical topics
• Write informative or explanatory pieces developed with relevant details, including arguments in history, social studies, science, and technical topics
• Write narrations that include details, put events in order, and provide a conclusion
• Produce writing appropriate to the task, purpose, and audience
• Strengthen writing by getting feedback, revising, editing, and rewriting
• Add dialogue and descriptions to develop characters and events
• Use technology, including the Internet, to produce and publish writing
• Contribute to collaborative group writing projects
• Conduct short and sustained research projects on a topic through investigation
• Draw and cite evidence from a variety of texts to support analysis
• Assess the credibility and accuracy of sources
• Quote or paraphrase data and conclusions while avoiding plagiarism
• Include evidence from literary or informational texts to support analysis
• Regularly produce clear writing for a variety of tasks, purposes, and audiences (including writing in history/social studies, science, and technical subjects)

Science: Physics

Notes about science curriculum:

1. In the high school grades, there is significant variation in science courses offered or required in the sequence of science courses. In addition to courses in biology or life science, earth science, chemistry, and physics that may be the standard courses, students may be offered such options as basic physical science, environmental science, ecology, principles of technology, urban ecology, botany, geology, astronomy, basic physical science, anatomy and physiology, and biochemistry.

2. The Next Generation Science and Engineering Standards (developed in 2013 in a joint collaboration among the American Association for the Advancement of Science, the National Research Council, the National Science Teachers Association, and Achieve) describe scientific practices that scientists use as they investigate the natural world and engineering practices that engineers use as they design and build models and systems. In addition, they present seven crosscutting concepts that apply across all the topics and fields of science. The teaching of science topics and the corresponding standards at all grade levels K-12 are intricately interwoven with these practices and crosscutting concepts. Students need consistent experience and connection with these two dimensions of science education (practices and cross-cutting concepts) as they work with the third dimension (core science content topics).

Science and Engineering Practices

1. Asking questions (science) and defining problems (engineering)
2. Developing and using models
3. Designing and carrying out investigations
4. Organizing and interpreting data
5. Using mathematics and computational thinking
6. Constructing explanations (science) and designing solutions (engineering)
7. Engaging in argument from evidence
8. Obtaining, evaluating, and communication information

Crosscutting Concepts

1. Patterns
2. Cause and effect
3. Scale, proportion, and quantity
4. Systems and system models
5. Energy and matter: Flows, cycles, and conservation
6. Structure and function
7. Stability and change

• Force
• Laws of conservation of energy
• Energy transfer
• Energy in chemical processes
• Measurement and mathematics for physics
• Force and calculations of force
• Force fields
• Kinematics
• Statics and dynamics
• Motion; Laws of Motion
• Concepts of distance, displacement, speed, average velocity, instantaneous  velocity, and acceleration
• Relative motion
• Relationships between force and motion
• Gravitation
• Friction
• Momentum
• Definitions of energy and forms of energy
• Work and energy

• Thermal energy transfer processes
• Laws of thermodynamics
• Electric fields, currents, and circuits
• Magnetism
• Wave properties and behaviors
• Real-world applications of wave behaviors
• Light
• Wave-particle duality
• Electromagnetic spectrum
• Nuclear structure and processes
• Atomic and nuclear phenomena
• Real-world atomic and nuclear applications
• Quantum phenomena
• Particle physics
• Safe practices during investigations

Technology

General goal for high school students: Use technology within all content areas to collaborate, communicate, generate innovative ideas, create original works, and investigate and solve problems.

• Demonstrating proficient keyboarding skills
• Understanding of operating system tools, applications, and storage devices
• Use of a variety of common applications and productivity tools
• Creating products combining text, images, sound, music, and video
• Creating and publishing stories, games, animations, problems, and solutions
• Creating Web pages
• Use of spreadsheet and concept-mapping software
• Use of interactive tools to design polls or surveys to gather data
• Making contributions to blogs, wikis, and other digital collaborative forums
• Use of online databases or simulation software to interpret and predict trends
• Increasing knowledge about many cultures through digital content
• Communicating with multiple audiences through a variety of formats and media
• Increasing understanding of a local or global issue
• Researching and using information fluently
• Choosing appropriate search engines, directories, and online applications
• Selecting appropriate, relevant sources for a purpose or audience
•  Analysis and synthesis of information to make decisions or develop solutions
• Assessing the credibility and validity of online sources
• Use of bibliography tools to cite sources from digital sources
• Reporting and sharing results or solutions
• Exploring ways to receive feedback from multiple, appropriate audiences
• Demonstrate understanding and avoidance of potential online dangers
• Understanding health hazards of frequent technology use
• Demonstrating safe and legal use of online sites and information
• Use of passwords, virus prevention, and other protective procedures
• Understanding risks of social networking sites; safe sharing of personal information online
• Understanding privacy issues and how data are kept and available publicly
• Practicing ethical and respectful behavior online
• Careful, responsible use and maintenance of digital equipment
• Demonstrating openness to learning new technologies and procedures

Arts

Note about high school arts curriculum: High school curriculum generally requires some sort of study and credit in the arts. Most schools offer experiences and study in a variety of areas in the arts. Some examples are:

• Animation
• Architecture
• Casting
• Ceramics
• Choral music
• Computer graphics and applications
• Construction
• Dance or other creative movement
• Digital arts
• Drama (including mime, storytelling, and technical aspects of theater)
• Drawing
• Film
• Graphic design
• Improvisational music
• Instrumental music
• Jewelry-making
• Metal Sculpture
• Mosaics
• Painting
• Photography
• Printmaking
• Sculpture
• Textiles and fiber art

In the study and practice of any of the performance or visual arts, students encounter such topics and sharpen such skills as:

• Watching, listening, and responding to works of art
• Background and elements of particular art form
• Understanding of the processes and techniques of particular forms
• Principles of design
• Vocabulary of particular art forms
• Interpretation, analysis, and evaluation of works of art
• Reflecting on own experiences and creations or performances
• Art history
• Well-known artists and works of visual or performing art forms
• Cultural contexts and expressions of art
• Style, materials, and techniques used in a work of art
• Generating questions about a work of art
• Considering messages and purposes of a particular work of art
• Responding orally, in writing, or some other way to works of art
• Reflecting on the contributions of artists to society
• Careers in art
• Discipline and mindset for improving and developing skills in art
• Fostering of creativity and self-expression
• Development of artistic awareness, imagination, perception, skill
• Experimenting with a variety of media, forms, and techniques
• Solving design problems
• Use of digital media and tools for producing, viewing, or responding to art
• Polishing and furthering personal skills in a chosen area of art
• Participation in collaborative discussions about works of art
• Participation in collaborative creation of works of art
• Proper safety procedures for activities in the specific arts

Health and Safety

• Gaining, analyzing, and applying health information
• Knowledge about and use of available health services
• Health choices and long-term consequences of choices
• Benefits of, practices for, and personal responsibility for health
• Personal health profile and plan
• Interrelationships of physical, mental, and social health
• Impacts of social pressures on physical, emotional, and social health
• Marketing and advertising effects on health behavior
• Structure, functions, and interdependence of major body systems
• Causes and effects of poor body image
• Eating disorders and their prevention and treatment
• Changes in anatomy during puberty
• Role of hormones in growth, development, and personal health
• Reproductive processes; healthy development of fetus
• Consequences of sexual activity
• Strategies to resist pressures to become sexually active
• Characteristics of healthy relationships and dating behaviors
• Lifelong strategies for identifying and preventing depression and anxiety
• Avoidance of risky or self-destructive behaviors
• Health risks and effects of technology use
• Environmental conditions and factors harmful to health
• Myths and facts related to disease transmission and prevention
• Laws relating to tobacco, alcohol, drugs, and other controlled substances
• Treatment options for drug and other addictions
• Understanding of first-aid procedures and emergency response
• Use, abuse, and effects of medications, tobacco, alcohol, and other controlled substances
• Relationship between tobacco, alcohol, or illegal drugs and such unsafe situations as date rape, sexually-transmitted disease, and drinking and driving
• Prevention of and response to deliberate and accidental injuries
• Reasons and ways to avoid violence, gangs, weapons, and illegal drugs
• Skills to identify, avoid, report, and cope with potentially dangerous situations
• Positive and negative characteristics of social groups, gangs, clubs, cliques
• Development of self-confidence, self-esteem, and self-control
• Understanding appropriate ways to express emotions
• Skills for building and maintaining healthy relationships
• Bullying, alternative behaviors to bullying, and appropriate responses to bullying
• Strategies for resolving conflicts with peers and others

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Typical Course of Study

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