# Curriculum Guide for Grade 10

## Mathematics - Geometry

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. See mathematics category in grades 11-12 for typical course of study information for higher-level math courses.

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.

• Similarity
• Pythagorean Theorem and its converse
• Trigonometric ratios in right triangles
• Solving problems with trigonometric ratios in right triangles
• Trigonometry in general triangles
• Similarity of circles
• Elements of circles and relationships between them
• Constructing inscribed and circumscribed circles of a triangle
• Constructing tangents
• Arc lengths and areas of circle sectors
• Applying theorems about circles
• Deriving equations of parabola, ellipse, hyperbola, and center
• Proving theorems algebraically using coordinates
• Using coordinates to prove simple geometric theorems algebraically
• Proving slope criteria for parallel and perpendicular lines
• Finding the bisecting point on a line segment
• Computing perimeters and areas
• Explaining and using formulas for circumference, circle area, and volume of a cylinder, sphere, cone, and pyramid
• Cavalieri’s principle
• Shapes of two-dimensional slices of three-dimensional objects
• Geometric concepts in describing objects, modeling situations, and solving design problems
• Solving real world problems with geometric concepts and formulas

## Reading Literature and Informational Text and Literacy in 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
• Identify key steps in a text’s description of a process related to history or social studies
• Summarize literary and informational or explanatory texts
• Follow a multistep written procedure when performing science or technical tasks
• Compare and contrast treatments of the same topic in several sources
• Analyze how characters develop and how this advances the theme or plot
• Analyze how a text unfolds a series of events and the connections among them
• Determine meanings and effects of words, phrases, or symbols as used in a text
• Analyze how the author’s structural choices, order of events, and use of time create effects, such as tension or surprise
• Analyze a particular point of view or experience reflected in a work of world literature
• Analyze how an author transforms source material from an earlier work by a previous author
• Determine author’s purpose or point of view and how rhetoric is used to advance that purpose or point of view
• Integrate quantitative or technical information presented in text form with information expressed visually
• Explain how visual and multimedia elements help to contribute to the meaning or tone of a text
• Compare the point of view or claims of two or more authors on similar topics
• Identify and evaluate the argument, reasoning, and evidence in a text
• Analyze and compare various accounts of a subject told in different media
• Analyze significant U.S. (or home country) historical and literary documents
• 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 supported with relevant facts and details
• Use clear pronunciation and appropriate eye contact and volume when speaking
• Add multimedia and visual components to clarify ideas in presentations
• Adapt speech to a variety of tasks, showing command of formal English

## 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 and use figurative language in context
• Distinguish shades of meaning among related words
• Distinguish among connotations of words with similar denotations
• Learn and use grade-level general academic vocabulary

## 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

## 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 - Earth Science

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 content 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 communicating 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

• The universe and its stars
• The sun and its chemical processes
• Stars, their light, brightness, and movement
• Structure of and forces in the solar system
• Movements of objects in the solar system
• Patterns of apparent motion of the sun, moon, and stars
• Sun, Earth, and moon relationships
• Moon phases and tides
• Theories of Earth’s origin
• Earth’s history
• Geologic time, rock strata and the fossil record
• Earth systems and their interactions
• Plate tectonics and large-scale interactions
• Structure and properties of Earth
• Minerals, rocks, and soil
• Changes in Earth’s surface
• Role of water in Earth changes
• Ocean features and movement
• Earth’s atmosphere
• Weather and climate
• Changes in climate
• Earth’s natural resources and resource use
• Renewable and nonrenewable energy sources
• Human impact on Earth systems
• Environmental concerns and conservation

## Social Science   World History: The Modern World

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. Geographical reasoning and use of geographical tools
10. Describing and explaining economics and economic systems
11. Civic understanding and participation

• Influences on the development of western political thought
• Glorious Revolution of England
• American Revolution
• French Revolution
• Influences of the revolutions of 1688-1799 on government and individual liberty
• The Industrial Revolution in Europe and the United States
• Emergence of Romanticism
• Global changes brought about by European imperialism
• Causes and course of World War I
• Effects of World War I
• Russian Revolution
• Totalitarian governments after World War I
• German, Italian, and Japanese drives for empire in the 1930s
• United States isolationism prior to World War II
• Rise of the Nazi party in Germany
• The Holocaust
• Causes and course of World War II

• Consequences of World War II
• International developments after World War II
• Causes, course, and effects of the Cold War
• The Truman Doctrine and the Marshall Plan
• The Chinese Civil War and upheavals in China
• Nationalism in the Middle East
• Establishment of Israel
• Collapse of the Soviet Union and end of the Cold War
• Work of the UN, SEATO, NATO, and the OAS
• Globalization and the spread of capitalism
• Effects of information, technological, and communications revolutions
• Connectedness and cooperation of countries in the world economy
• Current conflicts in the modern world
• Global issues in the modern world

## 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
• 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
• Basic safety rules for daily and recreational activities
• 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
• Preventing the use of tobacco, alcohol, and illegal drugs
• 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
• Appropriate ways to express emotions
• Positive social interactions with peers, in home, and in the community
• Bullying, alternative behaviors to bullying, and appropriate responses to bullying
• Strategies for resolving conflicts with peers and others
• Getting personal support from family

## 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 these:

• 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

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## Typical Course of Study

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