# Curriculum Guide for Grade 8

## Mathematics

Note about mathematics curriculum: 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.

## Algebra and Functions

• Work with radicals and integer exponents, including fractional exponents
• Read and write square root and cube root symbols to represent solutions to equations
• Interpret and write scientific notation to estimate very large or small quantities
• Perform operations with numbers expressed in scientific notation
• Analyze, solve, and graph linear equations in one variable with one solution, no solutions, or an infinite number of solutions
• Graph proportional relationships, interpreting the slope of a graph
• Analyze, graph, and solve pairs of simultaneous linear equations
• Write and solve real world problems leading to two linear equations
• Decide whether two quantities are in a proportional relationship from a graph
• Define slope as vertical change for each unit of horizontal change
• Graph a line, given its slope and a point on the line
• Find the slope of a line given its graph
• Define, evaluate, and compare functions
• Understand that a function assigns exactly one y-value (dependent variable) to each x-value (independent variable)
• Express functions algebraically, graphically, verbally, and numerically
• Know that the equation y = mx + b defines a linear function with a straight line graph
• Identify and give examples of functions that are not linear
• Use functions to model relationships between quantities
• Compare properties of two different functions

## The Number System

• Show the decimal expansion of a rational number
• Know that the decimal expansion of a rational number eventually repeats
• Know that there are numbers that are not rational
• Compare the size of irrational numbers with rational approximations
• Find approximate locations of irrational numbers on a number line
• Estimate the value of irrational number expressions
• Solve real world and mathematical problems with rational numbers using multiple operations

## Statistics and Probability

• Investigate patterns of association in bivariate data
• Construct and interpret scatter plots
• Examine and describe patterns of associations between quantities
• Use an equation of a linear model to solve bivariate measurement data problems
• Write and solve equations of linear relationships to make predictions involving bivariate measurement data
• Display frequencies and relative frequencies in a two-way table
• Represent probabilities of compound events with lists, tables, and diagrams
• Find probabilities of compound events using diagrams, tables, lists, or simulations
• Apply the multiplication counting principle to situations with a large number of outcomes

## Geometry

• Understand congruence and similarity of lines, line segments, angles, and figures
• Show properties of rotations, reflections, and translations of lines, line segments, angles, and parallel lines
• Describe effects of dilation, translations, rotations, and reflections of two-dimensional figures using coordinate plane
• Find sums of angles created when parallel lines are cut by a transversal
• Understand and apply the Pythagorean Theorem
• Explain a proof of the Pythagorean Theorem and its converse
• Apply the Pythagorean Theorem to determine unknown side lengths
• Solve real world and mathematical problems involving the Pythagorean Theorem
• Use the Pythagorean Theorem to find distances between points on a coordinate graph
• Know and use the formulas for the volume and surface area of cylinders, cones, spheres, and pyramids
• Solve real world and mathematical problems involving volume and surface area of solid figures

## English Language Skills

• Explain the functions of verbals in general and in specific sentences
• Form and use verbs in active and passive voice
• Form and use verbs in indicative, imperative, interrogative, conditional, and subjunctive moods
• Identify and correct inappropriate shifts in verb voice and mood
• Identify and use simple, compound, complex, and compound-complex sentences
• Use conventions of English correctly when writing (capitalization, punctuation, and spelling)
• Choose verb voice and mood to achieve specific effects
• Vary sentence patterns for meaning, interest, and style when writing; avoid passive constructions
• Maintain consistency in style and tone when writing
• Know the difference between formal and informal English and when to use each

## 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 to support analysis of primary and secondary sources
• Identify themes or central ideas in a text and analyze their development
• Summarize literary and informational or explanatory texts
• Analyze how incidents or specific dialogue moves a story along
• Analyze how a text makes connections between individuals, events, or ideas
• Identify key steps in a text’s description of a process related to history or social studies
• Describe how a text presents information
• Follow a multistep written procedure when performing science or technical tasks
• Determine meanings and effects of words, phrases, or symbols as used in a text
• Analyze the structure of a specific part of a text
• Compare and contrast the structure of two or more texts and how each structure contributes to meaning and style
• Analyze the effects of different points of view in a text
• Determine an author’s point of view and analyze how the author treats conflicting viewpoints
• Analyze the relationship between a primary and secondary source on the same topic
• Integrate quantitative or technical information presented in text form with information expressed visually
• Determine if a filmed or live production of a story is faithful to the text
• Evaluate the advantages and disadvantages of using different media to present an idea
• Trace and evaluate the argument and supporting reasons in a text
• Analyze whether an author supports a claim with sound reasoning and sufficient evidence
• Analyze two or more texts that provide conflicting information about the same topic
• 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 tools, including the Internet, to produce and publish writing
• Contribute to collaborative group writing projects
• Conduct short research tasks on a topic through investigation
• Gather information from various sources to answer a question
• Assess the credibility and accuracy of sources
• Quote or paraphrase data and conclusions while avoiding plagiarism
• Include evidence from literary or informational texts
• 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, find pronunciation or its part of speech
• Interpret and use figurative language in context
• Distinguish literal and nonliteral meanings of words in context
• Distinguish shades of meaning among related words
• Distinguish among connotations of words with similar denotations

## 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
• Analyze the purpose and motives of information presented in many media and formats
• 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
• Show command of formal English language when speaking for a variety of tasks

## Science

Note about science curriculum: 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

## Life Science

• Plant development and reproduction
• Animal development and reproduction
• Cell division and growth
• Structure and function of genes
• Changes (mutations) to genes
• Genetic diseases
• Genetic engineering
• Variations and adaptations in organisms
• Natural selection
• Existence, diversity, extinction, and change of life forms in Earth's history
• Fossils and the fossil record
• Similarities and differences between organisms today and organisms in the fossil record
• Evolutionary history of life on Earth

## Physical Science

• Types of forces and force interaction
• Force and motion
• Energy and motion
• Newton’s laws of motion
• Electric and electromagnetic forces
• Gravitational force
• Gravitational forces between objects in the solar system
• Waves (light, heat, sound), their properties, and transmission
• Magnetic fields; Earth’s magnetic fields
• Transmission of digital signals as wave pulses

## Earth and Space Science

• The universe and its stars
• Observation of the universe
• Classification of celestial objects
• Milky Way and other galaxies
• The structure of Earth’s solar system
• Sun, Earth, and moon relationships
• Motions of bodies in the solar system
• Patterns of apparent motion of the sun, moon, and stars
• The tilt of Earth’s axis and its effects
• Moon phases
• Tides
• History of planet Earth
• Geologic time scale, interpreted from rock strata and the fossil record
• Renewable and nonrenewable energy sources
• Environmental concerns and conservation

## Social Science -  United States History through Reconstruction

1. 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

2. 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 contex
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 History through Reconstruction

• The First Americans
• Exploring the Americas
• European colonization of America
• Colonial life
• The Mayflower Compact
• Moves toward independence
• Founding documents
• The American Revolution
• Challenges of the new government
• Representative government
• Drafting of the Constitution
• Federalist Era
• Jeffersonian Era
• Louisiana Purchase
• War of 1812
• Conflicts between the North and South
• Slavery
• Missouri Compromise
• Monroe Doctrine
• Age of Jackson
• Westward expansion
• Conflicts with Native Americans
• Indian Removal Act
• Manifest Destiny
• U.S.-Mexican War
• Gold Rush
• Compromise of 1850
• Civil War
• Reconstruction

## Health and Safety

• Health choices and long-term consequences of choices
• Benefits of, practices for, and personal responsibility for health (including healthy eating, personal hygiene, exercise, stress-management, adequate sleep, social and emotional health, disease prevention, avoidance of accidents and dangers)
• Interrelationships of physical, mental, and social health
• Impacts of social pressures on physical, emotional, and social health
• 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
• Possible physical, social, and emotional impacts of decisions regarding sexual behavior
• Strategies to resist pressures to become sexually active
• Characteristics of healthy relationships and dating behaviors
• Lifelong strategies for identifying and preventing depression and anxiety
• Importance of regular medical assessment
• Myths and facts related to disease transmission and prevention
• Ways the body defends itself against germs
• Communicable, noncommunicable, and hereditary diseases
• Evaluation of health products
• 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 substances
• Relationship between tobacco, alcohol, and drugs and unsafe situations
• 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
• Understand 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
• How and where to get help in making health decisions

## Arts

Note about middle school arts curriculum: Middle-level curriculum often includes and offers 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
•  Mosaics
•  Sculpture
•  Metal Sculpture
•  Textile and fiber art

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

•  Skills of 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 form
•  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
•  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

## Technology

General goal for middle-level 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
• Use of a variety of common applications and productivity tools
• Creation of products combining text, images, sound, music, and video
• 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 collaborative forums
• Gathering weather information and predictions
• Use of online databases or simulation software to interpret and predict trends
• Use of digital collaboration tools
• Increasing knowledge about many cultures through digital content
• Use of online interactive tools to communicate with learners from other cultures
• Communicating with multiple audiences through a variety of formats and media
• Increasing understanding of a local or global issue
• Choosing appropriate digital resources to plan a project or solve a problem
• Choosing appropriate search engines or directories
• Selecting and using appropriate online applications for various purposes
• 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
• Following fair use rules
• Use of bibliography tools to cite sources from digital sources
• Reporting and sharing of results or solutions
• Exploring ways to receive feedback from multiple, appropriate audiences
• Recognition and avoidance of potential online dangers
• Safe and legal use of online sites and information
• Understanding of privacy issues
• Understanding how data are kept and available publicly
• Demonstrating safe use of sharing personal information online
• Practicing ethical and respectful behavior
• Careful, responsible use and maintenance of digital equipment
• Demonstrating openness to learning new technologies and procedures

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