# Curriculum Guide for Grade 11

## Mathematics: Algebra II

1) Many students begin high school level math in the middle grades, completing Algebra I and even Geometry before high school. By grade 11, a student may be taking a math course identified in the grade 12 typical course of study.

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.

• The complex number system
• Operations with complex numbers
• Exponents, including rational exponents
• Expressions in radical and exponent form
• Rewriting rational expressions in equivalent forms
• Arithmetic operations on polynomials
• Polynomial identities and equations
• Structure of expressions
• Expressions in equivalent forms to solve problems
• Equations and inequalities in one variable
• Reasoning and problem solving with equations and inequalities
• Graphic representations of equations and inequalities
• Number and type of solutions of a quadratic equation
• Systems of equations
• Graphic representations of systems of equations
• Concept of a function
• Function notation
• Inverse functions
• Interpreting and describing functions from models

• Building functions to show a relationship between two quantities
• Writing functions in different forms
• Comparing properties of two functions
• Rate of change of a function
• Inverse functions
• Linear functions
• Exponential functions
• Trigonometric functions
• Logarithmic functions
• Graphing functions
• Building new functions from existing functions
• Parameters of functions from a graph
• Modeling periodic phenomena with trigonometric functions
• Proving the trigonometric identities
• Translating between the geometric description and the equation for a conic section
• Modeling a bivariate data set with a function

## 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

## 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
• Compare and contrast treatments of the same topic in 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

## 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)

## 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

## 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

## Science: Chemistry

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

• Structure and properties of matter
• Physical and chemical properties of substances
• Atomic structure and formation
• Historical development of atomic theory
• Electrical forces within and between atoms
• Molecular structure
• Molecular behavior
• Periodic Table
• Properties of elements
• Physical properties of substances
• Physical changes
• Mixtures
• Solutions, solubility, and precipitation
• Acids, bases, and electrolytes
• Chemical properties of elements
• Chemical reactions and energy
• Changes during chemical reactions
• Describing and predicting chemical reactions
• Acid-base reactions
• Oxidation-reduction reactions
• Chemical kinetics
• Moles and stoichiometry
• Chemical equilibrium
• Chemical bonding
• Chemical formulas and equations
• Nuclear processes
• Carbon chemistry
• Organic compounds and reactions
• Safe practices during investigations

## Social Sciences: United States History

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

• Civilizations of indigenous nations in North America
• Explorations of the Americas
• European colonization of America
• Effects of colonization on indigenous people
• Mayflower Compact
• Independence movement
• American Revolution
• Founding documents
• Principles and values of the new democratic government
• Challenges of the new government
• Drafting and ratification of the Constitution
• Federalists and anti-federalists
• Economic expansion; agricultural and industrial growth (1792-1861)
• Conquest of indigenous people and Mexican territory
• Regional and ethnic divisions and reform movements
• Jeffersonian Era
• Louisiana Purchase
• Slavery and abolition
• Conflicts between the North and South
• Civil War and Reconstruction
• African-American struggle for rights
• Voting rights
• Industrialization (1870-1920)

• Growth as an industrial and global power
• Immigration
• Class and ethnic conflicts
• The Progressive Era
• Urbanization
• World War I: causes, events, and effects
• The Great Depression
• The New Deal
• World War II: causes, events, U.S. role, impacts
• Post World War II and the Cold War
• Vietnam War and protests
• Civil Rights movements
• Changes in policies about Native Americans
• Era of geopolitical dynamics and a global economy
• Impact of technological innovations on society
• U.S. identity, roles, and values in the world (1980-present)
• National security
• Current domestic and foreign policy
• Global interdependence and cooperation
• Current national and global issues (human rights, terrorism, environment, poverty, hunger, refugees, resource scarcity, genocide, etc.)

## 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 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
• Understand 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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