Homework

California State Homework Policy

Definition of Homework

Homework is the time students spend outside the classroom in assigned activities to practice, reinforce, or apply newly acquired skills and knowledge to learn necessary skills of independent study. Jocelyn A. Butler, School Improvement Research Series (SIRS)

Purpose of Homework

*to assist and improve a student's progress towards California State Standards
*to extend or make more meaningful concepts introduced at school
*to engage students in purposeful practice relevant to their learning
*to develop effective study habits

Recommended Nightly Minutes

Each school will establish homework expectations organized by grade level, course level, or department and follow the parameters established by district policy. Homework is to be reasonable in length, directly related to California State Standards and classroom work, well defined in advance by the teacher, understood by the students, and assessed and returned to the student in a reasonable time. Homework will vary according to the course description and the student's grade level.

Teachers and parents must recognize that students work and learn at different rates. Teachers are encouraged to make every effort not to exceed the recommended nightly minutes. In situations where the time it takes a student to complete expected homework assignments regularly exceeds the recommended amount of time listed in this policy, teachers and parents should confer to determine if adjustments are needed to fit within the following recommendations.

Homework includes all work assigned by teacher(s). These minutes and days are based on time estimated for an average student working at a focused pace in an uninterrupted environment. Long-term projects may require additional time to complete. The guidelines do not include minutes provided for school wide academic interventions. These minutes do not include daily independent reading, which is expected and encouraged. Homework times may vary occasionally.

The recommendations are as follows:

Kindergarten 10 minutes per night Monday -Thursday
1st Grade 15 minutes per night Monday -Thursday
2nd Grade 20 minutes per night Monday-Thursday
3rd Grade 30 minutes per night Monday-Thursday
4th Grade 40 minutes per night Monday-Thursday Return to Top
5th Grade 50 minutes per night Monday-Thursday
6th Grade 60 minutes per night Monday-Thursday
7th-8th Grades 90 minutes per night Monday-Friday
9th -12th Grades 120 minutes per night Monday-Friday

Certain classes/programs, such as college prep, honors, Advanced Placement (AP), college level and International Baccalaureate (IB) classes may have additional homework requirements.

Communication

*Homework is an important tool for home/school communication. Parents and students will be informed at the beginning of the school year of the homework policy through Back to School Night presentations, district and/or individual site handbooks, course expectations, and/or newsletters. Teachers and parents are encouraged to communicate frequently about how well homework is promoting student progress toward California State Standards.

Types of Homework

The five major homework types are as follows:

*Practice which is designed to reinforce skills and information covered in class;
*Preparation which is given to prepare students to benefit from subsequent lessons;
*Extension which is provided to determine if a student can extend the concept of skill learned in class to a new situation;
*Creative which is designed to require students to integrate many skills and
*Concepts in producing some project;
*Completion which is a continuation of assignments stared in class.

Responsibilities and Procedures

*Homework needs to reflect expectations for progressive student responsibility from kindergarten through twelfth grade. As capacity for self-direction increases, teaching and parenting roles change from more directive to more facilitative.

Teachers will:

*Assign homework that supports the California State Standards and is meaningful, useful, and appropriate to the individual child
provide a balance between long-range and short-term assignments

*Monitor long-term assignments in order to avoid last minute student efforts, whenever possible

*Give clear, concise directions; allow time for student questions; consider availability of materials and provide options when needed; provide legible, error free worksheets, whenever possible

*Ensure that students who have excused absences know how they may makeup homework and, at a minimum, are given the same number days of absent to complete work coordinate long term assignments with other department, whenever possible

*Ensure that if assignments are given on Friday, they will not exceed the
*Recommended Nightly Minutes as stated in the board policy

*Refrain from assigning homework the day prior to school break periods that would require completion of an assignment only during the school break whenever possible

*Refrain from using homework as a punishment and from exercising disciplinary action if homework is attempted for the full amount of Recommended Nightly Minutes as stated in the board policy ensure that individual students will not be penalized for other group
members not completing assigned tasks

*Agreement with the parent, whenever possible.

Students will:

record the directions for homework
ask questions when necessary to clarify the assignment
follow a schedule and keep materials orderly
hand in, on time, neat, accurate, and meaningful products
plan time for completion of long-term assignments
request and hand in homework which was assigned while absent
adhere to the guidelines of uninterrupted study time
speak with the teacher(s) immediately if home life conflicts with study time
speak with the teacher(s) immediately if homework exceeds recommended time.

Parents will:

provide a suitable place for study (well lit, free from distractions), whenever possible
assist students in obtaining make-up work due to absences
help students develop routine study habits (same time, same place)
assist and acknowledge errors but not do the actual homework
notify the teacher immediately

1. if child experiences extreme difficulty in the homework
2. if materials are unavailable
3. if the family's personal life conflicts with homework
4. if the child's uninterrupted time spent on homework regularly exceeds the policy guidelines
5. if he/she sees an absence of homework
6. if the student is participating in non-school sponsored academic intervention Homework and update status thereof assist child in making appropriate course and course level choices.

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Kindergarten
English-language Arts Content Standards

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students know about letters, words, and sounds. They apply this knowledge to read simple sentences.

Concepts About Print
1.1 Identify the front cover, back cover, and title page of a book.
1.2 Follow words from left to right and from top to bottom on the printed page.
1.3 Understand that printed materials provide information.
1.4 Recognize that sentences in print are made up of separate words.
1.5 Distinguish letters from words.
1.6 Recognize and name all uppercase and lowercase letters of the alphabet.

Phonemic Awareness
1.7 Track (move sequentially from sound to sound) and represent the number, sameness/difference, and order of two and three isolated phonemes (e.g., /f, s, th/, /j, d, j/ ).
1.8 Track (move sequentially from sound to sound) and represent changes in simple syllables and words with two and three sounds as one sound is added, substituted, omitted, shifted, or repeated (e.g., vowel-consonant, consonant-vowel, or consonant-vowel-consonant).
1.9 Blend vowel-consonant sounds orally to make words or syllables.
1.10 Identify and produce rhyming words in response to an oral prompt.
1.11 Distinguish orally stated one-syllable words and separate into beginning or ending sounds.
1.12 Track auditorily each word in a sentence and each syllable in a word.
1.13 Count the number of sounds in syllables and syllables in words.

Decoding and Word Recognition
1.14 Match all consonant and short-vowel sounds to appropriate letters.
1.15 Read simple one-syllable and high-frequency words (i.e., sight words).
1.16 Understand that as letters of words change, so do the sounds (i.e., the alphabetic principle).

Vocabulary and Concept Development
1.17 Identify and sort common words in basic categories (e.g., colors, shapes, foods).
1.18 Describe common objects and events in both general and specific language.

2.0 Reading Comprehension
Students identify the basic facts and ideas in what they have read, heard, or viewed. They use comprehension strategies (e.g., generating and responding to questions, comparing new information to what is already known). The selections in Recommended Literature, Kindergarten Through Grade Twelve (California Department of Education, 2002) illustrate the quality and complexity of the materials to be read by students.

Structural Features of Informational Materials
2.1 Locate the title, table of contents, name of author, and name of illustrator.

Comprehension and Analysis of Grade-Level-Appropriate Text
2.2 Use pictures and context to make predictions about story content.
2.3 Connect to life experiences the information and events in texts.
2.4 Retell familiar stories.
2.5 Ask and answer questions about essential elements of a text.

3.0 Literary Response and Analysis
Students listen and respond to stories based on well-known characters, themes, plots, and settings. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Narrative Analysis of Grade-Level-Appropriate Text
3.1 Distinguish fantasy from realistic text.
3.2 Identify types of everyday print materials (e.g., storybooks, poems, newspapers, signs, labels).
3.3 Identify characters, settings, and important events.

Writing
1.0 Writing Strategies
Students write words and brief sentences that are legible.

Organization and Focus
1.1 Use letters and phonetically spelled words to write about experiences, stories, people, objects, or events.
1.2 Write consonant-vowel-consonant words (i.e., demonstrate the alphabetic principle).
1.3 Write by moving from left to right and from top to bottom.

Penmanship
1.4 Write uppercase and lowercase letters of the alphabet independently, attending to the form and proper spacing of the letters.

Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions.

Sentence Structure
1.1 Recognize and use complete, coherent sentences when speaking.

Spelling
1.2 Spell independently by using pre-phonetic knowledge, sounds of the alphabet, and knowledge of letter names.

Listening and Speaking
1.0 Listening and Speaking Strategies
Students listen and respond to oral communication. They speak in clear and coherent sentences.

Comprehension
1.1 Understand and follow one-and two-step oral directions.
1.2 Share information and ideas, speaking audibly in complete, coherent sentences.

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver brief recitations and oral presentations about familiar experiences or interests, demonstrating command of the organization and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the listening and speaking strategies of kindergarten outlined in Listening and Speaking Standard 1.0, students:
2.1 Describe people, places, things (e.g., size, color, shape), locations, and actions.
2.2 Recite short poems, rhymes, and songs.
2.3 Relate an experience or creative story in a logical sequence.

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Grade One
English-language Arts Content Standards.

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students understand the basic features of reading. They select letter patterns and know how to translate them into spoken language by using phonics, syllabication, and word parts. They apply this knowledge to achieve fluent oral and silent reading.

Concepts About Print
1.1 Match oral words to printed words.
1.2 Identify the title and author of a reading selection.
1.3 Identify letters, words, and sentences.

Phonemic Awareness
1.4 Distinguish initial, medial, and final sounds in single-syllable words.
1.5 Distinguish long-and short-vowel sounds in orally stated single-syllable words (e.g., bit/bite).
1.6 Create and state a series of rhyming words, including consonant blends.
1.7 Add, delete, or change target sounds to change words (e.g., change cow to how; pan to an).
1.8 Blend two to four phonemes into recognizable words (e.g., /c/ a/ t/ = cat; /f/ l/ a/ t/ = flat).
1.9 Segment single-syllable words into their components (e.g., /c/ a/ t/ = cat; /s/ p/ l/ a/ t/ = splat; /r/ i/ ch/ = rich).

Decoding and Word Recognition
1.10 Generate the sounds from all the letters and letter patterns, including consonant blends and long-and short-vowel patterns (i.e., phonograms), and blend those sounds into recognizable words.
1.11 Read common, irregular sight words (e.g., the, have, said, come, give, of).
1.12 Use knowledge of vowel digraphs and r- controlled letter-sound associations to read words.
1.13 Read compound words and contractions.
1.14 Read inflectional forms (e.g., -s, -ed, -ing) and root words (e.g., look, looked, looking).
1.15 Read common word families (e.g., -ite, -ate).
1.16 Read aloud with fluency in a manner that sounds like natural speech.

Vocabulary and Concept Development
1.17 Classify grade-appropriate categories of words (e.g., concrete collections of animals, foods, toys).

2.0 Reading Comprehension
Students read and understand grade-level-appropriate material. They draw upon a variety of comprehension strategies as needed (e.g., generating and responding to essential questions, making predictions, comparing information from several sources). The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition to their regular school reading, by grade four, students read one-half million words annually, including a good representation of grade-level-appropriate narrative and expository text (e.g., classic and contemporary literature, magazines, newspapers, online information). In grade one, students begin to make progress toward this goal.

Structural Features of Informational Materials
2.1 Identify text that uses sequence or other logical order.

Comprehension and Analysis of Grade-Level-Appropriate Text
2.2 Respond to who, what, when, where, and how questions.
2.3 Follow one-step written instructions.
2.4 Use context to resolve ambiguities about word and sentence meanings.
2.5 Confirm predictions about what will happen next in a text by identifying key words (i.e., signpost words).
2.6 Relate prior knowledge to textual information.
2.7 Retell the central ideas of simple expository or narrative passages.

3.0 Literary Response and Analysis
Students read and respond to a wide variety of significant works of children's literature. They distinguish between the structural features of the text and the literary terms or elements (e.g., theme, plot, setting, characters). The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Narrative Analysis of Grade-Level-Appropriate Text
3.1 Identify and describe the elements of plot, setting, and character(s) in a story, as well as the story's beginning, middle, and ending.
3.2 Describe the roles of authors and illustrators and their contributions to print materials.
3.3 Recollect, talk, and write about books read during the school year.

Writing
1.0 Writing Strategies
Students write clear and coherent sentences and paragraphs that develop a central idea. Their writing shows they consider the audience and purpose. Students progress through the stages of the writing process (e.g., prewriting, drafting, revising, editing successive versions).

Organization and Focus
1.1 Select a focus when writing.
1.2 Use descriptive words when writing.

Penmanship
1.3 Print legibly and space letters, words, and sentences appropriately.

2.0 Writing Applications (Genres and Their Characteristics)
Students write compositions that describe and explain familiar objects, events, and experiences. Student writing demonstrates a command of standard American English and the drafting, research, and organizational strategies outlined in Writing Standard 1.0.

Using the writing strategies of grade one outlined in Writing Standard 1.0, students:
2.1 Write brief narratives (e.g., fictional, autobiographical) describing an experience.
2.2 Write brief expository descriptions of a real object, person, place, or event, using sensory details.

Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions appropriate to this grade level.

Sentence Structure
1.1 Write and speak in complete, coherent sentences.

Grammar
1.2 Identify and correctly use singular and plural nouns.
1.3 Identify and correctly use contractions (e.g., isn't, aren't, can't, won't) and singular possessive pronouns (e.g., my/ mine, his/ her, hers, your/s) in writing and speaking.

Punctuation
1.4 Distinguish between declarative, exclamatory, and interrogative sentences.
1.5 Use a period, exclamation point, or question mark at the end of sentences.
1.6 Use knowledge of the basic rules of punctuation and capitalization when writing.

Capitalization
1.7 Capitalize the first word of a sentence, names of people, and the pronoun I.

Spelling
1.8 Spell three-and four-letter short-vowel words and grade-level-appropriate sight words correctly.

Listening and Speaking
1.0 Listening and Speaking Strategies
Students listen critically and respond appropriately to oral communication. They speak in a manner that guides the listener to understand important ideas by using proper phrasing, pitch, and modulation.

Comprehension
1.1 Listen attentively.
1.2 Ask questions for clarification and understanding.
1.3 Give, restate, and follow simple two-step directions.

Organization and Delivery of Oral Communication
1.4 Stay on the topic when speaking.
1.5 Use descriptive words when speaking about people, places, things, and events.

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver brief recitations and oral presentations about familiar experiences or interests that are organized around a coherent thesis statement. Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the speaking strategies of grade one outlined in Listening and Speaking Standard 1.0, students:
2.1 Recite poems, rhymes, songs, and stories.
2.2 Retell stories using basic story grammar and relating the sequence of story events by answering who, what, when, where, why, and how questions.
2.3 Relate an important life event or personal experience in a simple sequence.
2.4 Provide descriptions with careful attention to sensory detail.

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Grade Two
English-language Arts Content Standards

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students understand the basic features of reading. They select letter patterns and know how to translate them into spoken language by using phonics, syllabication, and word parts. They apply this knowledge to achieve fluent oral and silent reading.

Decoding and Word Recognition
1.1 Recognize and use knowledge of spelling patterns (e.g., diphthongs, special vowel spellings) when reading.
1.2 Apply knowledge of basic syllabication rules when reading (e.g., vowel-consonant-vowel = su/ per; vowel-consonant/consonant-vowel = sup/ per).
1.3 Decode two-syllable nonsense words and regular multisyllable words.
1.4 Recognize common abbreviations (e.g., Jan., Sun., Mr., St.).
1.5 Identify and correctly use regular plurals (e.g., -s, -es, -ies) and irregular plurals (e.g., fly/ flies, wife/ wives).
1.6 Read aloud fluently and accurately and with appropriate intonation and expression.

Vocabulary and Concept Development
1.7 Understand and explain common antonyms and synonyms.
1.8 Use knowledge of individual words in unknown compound words to predict their meaning.
1.9 Know the meaning of simple prefixes and suffixes (e.g., over-, un-, -ing, -ly).
1.10 Identify simple multiple-meaning words.

2.0 Reading Comprehension
Students read and understand grade-level-appropriate material. They draw upon a variety of comprehension strategies as needed (e.g., generating and responding to essential questions, making predictions, comparing information from several sources). The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition to their regular school reading, by grade four, students read one-half million words annually, including a good representation of grade-level-appropriate narrative and expository text (e.g., classic and contemporary literature, magazines, newspapers, online information). In grade two, students continue to make progress toward this goal.

Structural Features of Informational Materials
2.1 Use titles, tables of contents, and chapter headings to locate information in expository text.

Comprehension and Analysis of Grade-Level-Appropriate Text
2.2 State the purpose in reading (i. e., tell what information is sought).
2.3 Use knowledge of the author's purpose( s) to comprehend informational text.
2.4 Ask clarifying questions about essential textual elements of exposition (e.g., why, what if, how).
2.5 Restate facts and details in the text to clarify and organize ideas.
2.6 Recognize cause-and-effect relationships in a text.
2.7 Interpret information from diagrams, charts, and graphs.
2.8 Follow two-step written instructions.

3.0. Literary Response and Analysis
Students read and respond to a wide variety of significant works of children's literature. They distinguish between the structural features of the text and the literary terms or elements (e.g., theme, plot, setting, characters). The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Narrative Analysis of Grade-Level-Appropriate Text
3.1 Compare and contrast plots, settings, and characters presented by different authors.
3.2 Generate alternative endings to plots and identify the reason or reasons for, and the impact of, the alternatives.
3.3 Compare and contrast different versions of the same stories that reflect different cultures.
3.4 Identify the use of rhythm, rhyme, and alliteration in poetry.

Writing
1.0 Writing Strategies
Students write clear and coherent sentences and paragraphs that develop a central idea. Their writing shows they consider the audience and purpose. Students progress through the stages of the writing process (e.g., prewriting, drafting, revising, editing successive versions).

Organization and Focus
1.1 Group related ideas and maintain a consistent focus.

Penmanship
1.2 Create readable documents with legible handwriting.

Research
1.3 Understand the purposes of various reference materials (e.g., dictionary, thesaurus, atlas).

Evaluation and Revision
1.4 Revise original drafts to improve sequence and provide more descriptive detail.

2.0 Writing Applications (Genres and Their Characteristics)
Students write compositions that describe and explain familiar objects, events, and experiences. Student writing demonstrates a command of standard American English and the drafting, research, and organizational strategies outlined in Writing Standard 1.0.

Using the writing strategies of grade two outlined in Writing Standard 1.0, students:

2.1 Write brief narratives based on their experiences:

Move through a logical sequence of events.
Describe the setting, characters, objects, and events in detail.
2.2 Write a friendly letter complete with the date, salutation, body, closing, and signature.

Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions appropriate to this grade level.

Sentence Structure
1.1 Distinguish between complete and incomplete sentences.
1.2 Recognize and use the correct word order in written sentences.

Grammar
1.3 Identify and correctly use various parts of speech, including nouns and verbs, in writing and speaking.

Punctuation
1.4 Use commas in the greeting and closure of a letter and with dates and items in a series.
1.5 Use quotation marks correctly.

Capitalization
1.6 Capitalize all proper nouns, words at the beginning of sentences and greetings, months and days of the week, and titles and initials of people.

Spelling
1.7 Spell frequently used, irregular words correctly (e.g., was, were, says, said, who, what, why).
1.8 Spell basic short-vowel, long-vowel, r- controlled, and consonant-blend patterns correctly.

Listening and Speaking
1.0 Listening and Speaking Strategies
Students listen critically and respond appropriately to oral communication. They speak in a manner that guides the listener to understand important ideas by using proper phrasing, pitch, and modulation.

Comprehension
1.1 Determine the purpose or purposes of listening (e.g., to obtain information, to solve problems, for enjoyment).
1.2 Ask for clarification and explanation of stories and ideas.
1.3 Paraphrase information that has been shared orally by others.
1.4 Give and follow three-and four-step oral directions.

Organization and Delivery of Oral Communication
1.5 Organize presentations to maintain a clear focus.
1.6 Speak clearly and at an appropriate pace for the type of communication (e.g., informal discussion, report to class).
1.7 Recount experiences in a logical sequence.
1.8 Retell stories, including characters, setting, and plot.
1.9 Report on a topic with supportive facts and details.

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver brief recitations and oral presentations about familiar experiences or interests that are organized around a coherent thesis statement. Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the speaking strategies of grade two outlined in Listening and Speaking Standard 1.0, students:

2.1 Recount experiences or present stories:

Move through a logical sequence of events.
Describe story elements (e.g., characters, plot, setting).
2.2 Report on a topic with facts and details, drawing from several sources of information.

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Grade Three
English-language Arts Content Standards

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students understand the basic features of reading. They select letter patterns and know how to translate them into spoken language by using phonics, syllabication, and word parts. They apply this knowledge to achieve fluent oral and silent reading.

Decoding and Word Recognition
1.1 Know and use complex word families when reading (e.g., -ight) to decode unfamiliar words.
1.2 Decode regular multisyllabic words.
1.3 Read aloud narrative and expository text fluently and accurately and with appropriate pacing, intonation, and expression.

Vocabulary and Concept Development
1.4 Use knowledge of antonyms, synonyms, homophones, and homographs to determine the meanings of words.
1.5 Demonstrate knowledge of levels of specificity among grade-appropriate words and explain the importance of these relations (e.g., dog/ mammal/ animal/ living things).
1.6 Use sentence and word context to find the meaning of unknown words.
1.7 Use a dictionary to learn the meaning and other features of unknown words.
1.8 Use knowledge of prefixes (e.g., un-, re-, pre-, bi-, mis-, dis-) and suffixes (e.g., -er, -est, -ful) to determine the meaning of words.

2.0 Reading Comprehension
Students read and understand grade-level-appropriate material. They draw upon a variety of comprehension strategies as needed (e.g., generating and responding to essential questions, making predictions, comparing information from several sources). The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition to their regular school reading, by grade four, students read one-half million words annually, including a good representation of grade-level-appropriate narrative and expository text (e.g., classic and contemporary literature, magazines, newspapers, online information). In grade three, students make substantial progress toward this goal.

Structural Features of Informational Materials
2.1 Use titles, tables of contents, chapter headings, glossaries, and indexes to locate information in text.

Comprehension and Analysis of Grade-Level-Appropriate Text
2.2 Ask questions and support answers by connecting prior knowledge with literal information found in, and inferred from, the text.
2.3 Demonstrate comprehension by identifying answers in the text.
2.4 Recall major points in the text and make and modify predictions about forthcoming information.
2.5 Distinguish the main idea and supporting details in expository text.
2.6 Extract appropriate and significant information from the text, including problems and solutions.
2.7 Follow simple multiple-step written instructions (e.g., how to assemble a product or play a board game).

3.0 Literary Response and Analysis
Students read and respond to a wide variety of significant works of children's literature.
They distinguish between the structural features of the text and literary terms or elements (e.g., theme, plot, setting, characters). The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Structural Features of Literature
3.1 Distinguish common forms of literature (e.g., poetry, drama, fiction, nonfiction).

Narrative Analysis of Grade-Level-Appropriate Text
3.2 Comprehend basic plots of classic fairy tales, myths, folktales, legends, and fables from around the world.
3.3 Determine what characters are like by what they say or do and by how the author or illustrator portrays them.
3.4 Determine the underlying theme or author's message in fiction and nonfiction text.
3.5 Recognize the similarities of sounds in words and rhythmic patterns (e.g., alliteration, onomatopoeia) in a selection.
3.6 Identify the speaker or narrator in a selection.

Writing
1.0 Writing Strategies
Students write clear and coherent sentences and paragraphs that develop a central idea. Their writing shows they consider the audience and purpose. Students progress through the stages of the writing process (e.g., prewriting, drafting, revising, editing successive versions).

Organization and Focus
1.1 Create a single paragraph:

Develop a topic sentence.
Include simple supporting facts and details.
Penmanship
1.2 Write legibly in cursive or joined italic, allowing margins and correct spacing between letters in a word and words in a sentence.

Research
1.3 Understand the structure and organization of various reference materials (e.g., dictionary, thesaurus, atlas, encyclopedia).

Evaluation and Revision
1.4 Revise drafts to improve the coherence and logical progression of ideas by using an established rubric.

2.0 Writing Applications (Genres and Their Characteristics)
Students write compositions that describe and explain familiar objects, events, and experiences. Student writing demonstrates a command of standard American English and the drafting, research, and organizational strategies outlined in Writing Standard 1.0.

Using the writing strategies of grade three outlined in Writing Standard 1.0, students:

2.1 Write narratives:

Provide a context within which an action takes place.
Include well-chosen details to develop the plot.
Provide insight into why the selected incident is memorable.
2.2 Write descriptions that use concrete sensory details to present and support unified impressions of people, places, things, or experiences.

2.3 Write personal and formal letters, thank-you notes, and invitations:

Show awareness of the knowledge and interests of the audience and establish a purpose and context.
Include the date, proper salutation, body, closing, and signature.
Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions appropriate to this grade level.

Sentence Structure
1.1 Understand and be able to use complete and correct declarative, interrogative, imperative, and exclamatory sentences in writing and speaking.

Grammar
1.2 Identify subjects and verbs that are in agreement and identify and use pronouns, adjectives, compound words, and articles correctly in writing and speaking.
1.3 Identify and use past, present, and future verb tenses properly in writing and speaking.
1.4 Identify and use subjects and verbs correctly in speaking and writing simple sentences.

Punctuation
1.5 Punctuate dates, city and state, and titles of books correctly.
1.6 Use commas in dates, locations, and addresses and for items in a series.

Capitalization
1.7 Capitalize geographical names, holidays, historical periods, and special events correctly.

Spelling
1.8 Spell correctly one-syllable words that have blends, contractions, compounds, orthographic patterns (e.g., qu, consonant doubling, changing the ending of a word from -y to -ies when forming the plural), and common homophones (e.g., hair-hare). 1.9 Arrange words in alphabetic order.

Listening and Speaking
1.0 Listening and Speaking Strategies
Students listen critically and respond appropriately to oral communication. They speak in a manner that guides the listener to understand important ideas by using proper phrasing, pitch, and modulation.

Comprehension
1.1 Retell, paraphrase, and explain what has been said by a speaker.
1.2 Connect and relate prior experiences, insights, and ideas to those of a speaker.
1.3 Respond to questions with appropriate elaboration.
1.4 Identify the musical elements of literary language (e.g., rhymes, repeated sounds, instances of onomatopoeia).

Organization and Delivery of Oral Communication
1.5 Organize ideas chronologically or around major points of information.
1.6 Provide a beginning, a middle, and an end, including concrete details that develop a central idea.
1.7 Use clear and specific vocabulary to communicate ideas and establish the tone.
1.8 Clarify and enhance oral presentations through the use of appropriate props (e.g., objects, pictures, charts).
1.9 Read prose and poetry aloud with fluency, rhythm, and pace, using appropriate intonation and vocal patterns to emphasize important passages of the text being read.

Analysis and Evaluation of Oral and Media Communications
1.10 Compare ideas and points of view expressed in broadcast and print media.
1.11 Distinguish between the speaker's opinions and verifiable facts.

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver brief recitations and oral presentations about familiar experiences or interests that are organized around a coherent thesis statement. Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the speaking strategies of grade three outlined in Listening and Speaking Standard 1.0, students:

2.1 Make brief narrative presentations:

Provide a context for an incident that is the subject of the presentation.
Provide insight into why the selected incident is memorable.
Include well-chosen details to develop character, setting, and plot.
2.2 Plan and present dramatic interpretations of experiences, stories, poems, or plays with clear diction, pitch, tempo, and tone.

2.3 Make descriptive presentations that use concrete sensory details to set forth and support unified impressions of people, places, things, or experiences.

____________________________________________________________________________________________________

Grade Four
English-language Arts Content Standards

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students understand the basic features of reading. They select letter patterns and know how to translate them into spoken language by using phonics, syllabication, and word parts. They apply this knowledge to achieve fluent oral and silent reading.

Word Recognition
1.1 Read narrative and expository text aloud with grade-appropriate fluency and accuracy and with appropriate pacing, intonation, and expression.

Vocabulary and Concept Development
1.2 Apply knowledge of word origins, derivations, synonyms, antonyms, and idioms to determine the meaning of words and phrases.
1.3 Use knowledge of root words to determine the meaning of unknown words within a passage.
1.4 Know common roots and affixes derived from Greek and Latin and use this knowledge to analyze the meaning of complex words (e.g., international).
1.5 Use a thesaurus to determine related words and concepts.
1.6 Distinguish and interpret words with multiple meanings.

2.0 Reading Comprehension
Students read and understand grade-level-appropriate material. They draw upon a variety of comprehension strategies as needed (e.g., generating and responding to essential questions, making predictions, comparing information from several sources). The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition to their regular school reading, students read one-half million words annually, including a good representation of grade-level-appropriate narrative and expository text (e.g., classic and contemporary literature, magazines, newspapers, online information).

Structural Features of Informational Materials
2.1 Identify structural patterns found in informational text (e.g., compare and contrast, cause and effect, sequential or chronological order, proposition and support) to strengthen comprehension.

Comprehension and Analysis of Grade-Level-Appropriate Text
2.2 Use appropriate strategies when reading for different purposes (e.g., full comprehension, location of information, personal enjoyment).
2.3 Make and confirm predictions about text by using prior knowledge and ideas presented in the text itself, including illustrations, titles, topic sentences, important words, and foreshadowing clues.
2.4 Evaluate new information and hypotheses by testing them against known information and ideas.
2.5 Compare and contrast information on the same topic after reading several passages or articles.
2.6 Distinguish between cause and effect and between fact and opinion in expository text.
2.7 Follow multiple-step instructions in a basic technical manual (e.g., how to use computer commands or video games).

3.0 Literary Response and Analysis
Students read and respond to a wide variety of significant works of children's literature. They distinguish between the structural features of the text and the literary terms or elements (e.g., theme, plot, setting, characters). The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Structural Features of Literature
3.1 Describe the structural differences of various imaginative forms of literature, including fantasies, fables, myths, legends, and fairy tales.

Narrative Analysis of Grade-Level-Appropriate Text
3.2 Identify the main events of the plot, their causes, and the influence of each event on future actions.
3.3 Use knowledge of the situation and setting and of a character's traits and motivations to determine the causes for that character's actions.
3.4 Compare and contrast tales from different cultures by tracing the exploits of one character type and develop theories to account for similar tales in diverse cultures (e.g., trickster tales).
3.5 Define figurative language (e.g., simile, metaphor, hyperbole, personification) and identify its use in literary works.

Writing
1.0 Writing Strategies
Students write clear, coherent sentences and paragraphs that develop a central idea. Their writing shows they consider the audience and purpose. Students progress through the stages of the writing process (e.g., prewriting, drafting, revising, editing successive versions).

Organization and Focus
1.1 Select a focus, an organizational structure, and a point of view based upon purpose, audience, length, and format requirements.

1.2 Create multiple-paragraph compositions:

Provide an introductory paragraph.
Establish and support a central idea with a topic sentence at or near the beginning of the first paragraph.
Include supporting paragraphs with simple facts, details, and explanations.
Conclude with a paragraph that summarizes the points.
Use correct indention.

1.3 Use traditional structures for conveying information (e.g., chronological order, cause and effect, similarity and difference, posing and answering a question).

Penmanship
1.4 Write fluidly and legibly in cursive or joined italic.

Research and Technology
1.5 Quote or paraphrase information sources, citing them appropriately.
1.6 Locate information in reference texts by using organizational features (e.g., prefaces, appendixes).
1.7 Use various reference materials (e.g., dictionary, thesaurus, card catalog, encyclopedia, online information) as an aid to writing.
1.8 Understand the organization of almanacs, newspapers, and periodicals and how to use those print materials.
1.9 Demonstrate basic keyboarding skills and familiarity with computer terminology (e.g., cursor, software, memory, disk drive, hard drive).

Evaluation and Revision
1.10 Edit and revise selected drafts to improve coherence and progression by adding, deleting, consolidating, and rearranging text.

2.0 Writing Applications (Genres and Their Characteristics)
Students write compositions that describe and explain familiar objects, events, and experiences. Student writing demonstrates a command of standard American English and the drafting, research, and organizational strategies outlined in Writing Standard 1.0.

Using the writing strategies of grade four outlined in Writing Standard 1.0, students:

2.1 Write narratives:

Relate ideas, observations, or recollections of an event or experience.
Provide a context to enable the reader to imagine the world of the event or experience.
Use concrete sensory details.
Provide insight into why the selected event or experience is memorable.
2.2 Write responses to literature:

Demonstrate an understanding of the literary work.
Support judgments through references to both the text and prior knowledge.
2.3 Write information reports:

Frame a central question about an issue or situation.
Include facts and details for focus.
Draw from more than one source of information (e.g., speakers, books, newspapers, other media sources).
2.4 Write summaries that contain the main ideas of the reading selection and the most significant details.

Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions appropriate to this grade level.

Sentence Structure
1.1 Use simple and compound sentences in writing and speaking.
1.2 Combine short, related sentences with appositives, participial phrases, adjectives, ad-verbs, and prepositional phrases.

Grammar
1.3 Identify and use regular and irregular verbs, adverbs, prepositions, and coordinating conjunctions in writing and speaking.

Punctuation
1.4 Use parentheses, commas in direct quotations, and apostrophes in the possessive case of nouns and in contractions.
1.5 Use underlining, quotation marks, or italics to identify titles of documents.

Capitalization
1.6 Capitalize names of magazines, newspapers, works of art, musical compositions, organizations, and the first word in quotations when appropriate.

Spelling
1.7 Spell correctly roots, inflections, suffixes and prefixes, and syllable constructions.

Listening and Speaking
1.0 Listening and Speaking Strategies
Students listen critically and respond appropriately to oral communication. They speak in a manner that guides the listener to understand important ideas by using proper phrasing, pitch, and modulation.

Comprehension
1.1 Ask thoughtful questions and respond to relevant questions with appropriate elaboration in oral settings.
1.2 Summarize major ideas and supporting evidence presented in spoken messages and formal presentations.
1.3 Identify how language usages (e.g., sayings, expressions) reflect regions and cultures.
1.4 Give precise directions and instructions.

Organization and Delivery of Oral Communication
1.5 Present effective introductions and conclusions that guide and inform the listener's understanding of important ideas and evidence.
1.6 Use traditional structures for conveying information (e.g., cause and effect, similarity and difference, posing and answering a question).
1.7 Emphasize points in ways that help the listener or viewer to follow important ideas and concepts.
1.8 Use details, examples, anecdotes, or experiences to explain or clarify information.
1.9 Use volume, pitch, phrasing, pace, modulation, and gestures appropriately to enhance meaning.

Analysis and Evaluation of Oral Media Communication
1.10 Evaluate the role of the media in focusing attention on events and in forming opinions on issues.

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver brief recitations and oral presentations about familiar experiences or interests that are organized around a coherent thesis statement. Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the speaking strategies of grade four outlined in Listening and Speaking Standard 1.0, students:

2.1 Make narrative presentations:

Relate ideas, observations, or recollections about an event or experience.
Provide a context that enables the listener to imagine the circumstances of the event or experience.
Provide insight into why the selected event or experience is memorable.
2.2 Make informational presentations:

Frame a key question.
Include facts and details that help listeners to focus.
Incorporate more than one source of information (e.g., speakers, books, newspapers, television or radio reports).
2.3 Deliver oral summaries of articles and books that contain the main ideas of the event or article and the most significant details.

2.4 Recite brief poems (i.e., two or three stanzas), soliloquies, or dramatic dialogues, using clear diction, tempo, volume, and phrasing.

____________________________________________________________________________________________________

Grade Five
English-language Arts Content Standards

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students use their knowledge of word origins and word relationships, as well as historical and literary context clues, to determine the meaning of specialized vocabulary and to understand the precise meaning of grade-level-appropriate words.

Word Recognition
1.1 Read aloud narrative and expository text fluently and accurately and with appropriate pacing, intonation, and expression.

Vocabulary and Concept Development
1.2 Use word origins to determine the meaning of unknown words.
1.3 Understand and explain frequently used synonyms, antonyms, and homographs.
1.4 Know abstract, derived roots and affixes from Greek and Latin and use this knowledge to analyze the meaning of complex words (e.g., controversial).
1.5 Understand and explain the figurative and metaphorical use of words in context.

2.0 Reading Comprehension (Focus on Informational Materials)
Students read and understand grade-level-appropriate material. They describe and connect the essential ideas, arguments, and perspectives of the text by using their knowledge of text structure, organization, and purpose. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition, by grade eight, students read one million words annually on their own, including a good representation of grade-level-appropriate narrative and expository text (e.g., classic and contemporary literature, magazines, newspapers, online information). In grade five, students make progress toward this goal.

Structural Features of Informational Materials
2.1 Understand how text features (e.g., format, graphics, sequence, diagrams, illustrations, charts, maps) make information accessible and usable.
2.2 Analyze text that is organized in sequential or chronological order.

Comprehension and Analysis of Grade-Level-Appropriate Text
2.3 Discern main ideas and concepts presented in texts, identifying and assessing evidence that supports those ideas.
2.4 Draw inferences, conclusions, or generalizations about text and support them with textual evidence and prior knowledge.

Expository Critique
2.5 Distinguish facts, supported inferences, and opinions in text.

3.0 Literary Response and Analysis
Students read and respond to historically or culturally significant works of literature. They begin to find ways to clarify the ideas and make connections between literary works. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Structural Features of Literature
3.1 Identify and analyze the characteristics of poetry, drama, fiction, and nonfiction and explain the appropriateness of the literary forms chosen by an author for a specific purpose.

Narrative Analysis of Grade-Level-Appropriate Text
3.2 Identify the main problem or conflict of the plot and explain how it is resolved.
3.3 Contrast the actions, motives (e.g., loyalty, selfishness, conscientiousness), and appearances of characters in a work of fiction and discuss the importance of the contrasts to the plot or theme.
3.4 Understand that theme refers to the meaning or moral of a selection and recognize themes (whether implied or stated directly) in sample works.
3.5 Describe the function and effect of common literary devices (e.g., imagery, metaphor, symbolism).

Literary Criticism
3.6 Evaluate the meaning of archetypal patterns and symbols that are found in myth and tradition by using literature from different eras and cultures.
3.7 Evaluate the author's use of various techniques (e.g., appeal of characters in a picture book, logic and credibility of plots and settings, use of figurative language) to influence readers' perspectives.

Writing
1.0 Writing Strategies
Students write clear, coherent, and focused essays. The writing exhibits the students' awareness of the audience and purpose. Essays contain formal introductions, supporting evidence, and conclusions. Students progress through the stages of the writing process as needed.

Organization and Focus
1.1 Create multiple-paragraph narrative compositions:

Establish and develop a situation or plot.
Describe the setting.
Present an ending.
1.2 Create multiple-paragraph expository compositions:

Establish a topic, important ideas, or events in sequence or chronological order.
Provide details and transitional expressions that link one paragraph to another in a clear line of thought.
Offer a concluding paragraph that summarizes important ideas and details.
Research and Technology
1.3 Use organizational features of printed text (e.g., citations, end notes, bibliographic references) to locate relevant information.
1.4 Create simple documents by using electronic media and employing organizational features (e.g., passwords, entry and pull-down menus, word searches, a thesaurus, spell checks).
1.5 Use a thesaurus to identify alternative word choices and meanings.

Evaluation and Revision
1.6 Edit and revise manuscripts to improve the meaning and focus of writing by adding, deleting, consolidating, clarifying, and rearranging words and sentences.

2.0 Writing Applications (Genres and Their Characteristics)
Students write narrative, expository, persuasive, and descriptive texts of at least 500 to 700 words in each genre. Student writing demonstrates a command of standard American English and the research, organizational, and drafting strategies outlined in Writing Standard 1.0.

Using the writing strategies of grade five outlined in Writing Standard 1.0, students:

2.1 Write narratives:

Establish a plot, point of view, setting, and conflict.
Show, rather than tell, the events of the story.
2.2 Write responses to literature:

Demonstrate an understanding of a literary work.
Support judgments through references to the text and to prior knowledge.
Develop interpretations that exhibit careful reading and understanding.
2.3 Write research reports about important ideas, issues, or events by using the following guidelines:

Frame questions that direct the investigation.
Establish a controlling idea or topic.
Develop the topic with simple facts, details, examples, and explanations.
2.4 Write persuasive letters or compositions:

State a clear position in support of a proposal.
Support a position with relevant evidence.
Follow a simple organizational pattern.
Address reader concerns.
Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions appropriate to this grade level.

Sentence Structure
1.1 Identify and correctly use prepositional phrases, appositives, and independent and dependent clauses; use transitions and conjunctions to connect ideas.

Grammar
1.2 Identify and correctly use verbs that are often misused (e.g., lie/ lay, sit/ set, rise/ raise), modifiers, and pronouns.

Punctuation
1.3 Use a colon to separate hours and minutes and to introduce a list; use quotation marks around the exact words of a speaker and titles of poems, songs, short stories, and so forth.

Capitalization
1.4 Use correct capitalization.

Spelling
1.5 Spell roots, suffixes, prefixes, contractions, and syllable constructions correctly.

Listening and Speaking
1.0 Listening and Speaking Strategies
Students deliver focused, coherent presentations that convey ideas clearly and relate to the background and interests of the audience. They evaluate the content of oral communication.

Comprehension
1.1 Ask questions that seek information not already discussed.
1.2 Interpret a speaker's verbal and nonverbal messages, purposes, and perspectives.
1.3 Make inferences or draw conclusions based on an oral report.

Organization and Delivery of Oral Communication
1.4 Select a focus, organizational structure, and point of view for an oral presentation.
1.5 Clarify and support spoken ideas with evidence and examples.
1.6 Engage the audience with appropriate verbal cues, facial expressions, and gestures.

Analysis and Evaluation of Oral and Media Communications
1.7 Identify, analyze, and critique persuasive techniques (e.g., promises, dares, flattery, glittering generalities); identify logical fallacies used in oral presentations and media messages.
1.8 Analyze media as sources for information, entertainment, persuasion, interpretation of events, and transmission of culture.

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver well-organized formal presentations employing traditional rhetorical strategies (e.g., narration, exposition, persuasion, description). Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the speaking strategies of grade five outlined in Listening and Speaking Standard 1.0, students:

2.1 Deliver narrative presentations:

Establish a situation, plot, point of view, and setting with descriptive words and phrases.
Show, rather than tell, the listener what happens.
2.2 Deliver informative presentations about an important idea, issue, or event by the following means:

Frame questions to direct the investigation.
Establish a controlling idea or topic.
Develop the topic with simple facts, details, examples, and explanations.
2.3 Deliver oral responses to literature:

Summarize significant events and details.
Articulate an understanding of several ideas or images communicated by the literary work.
Use examples or textual evidence from the work to support conclusions.

_____________________________________________________________________________________________________
Grade Six
English-language Arts Content Standards

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students use their knowledge of word origins and word relationships, as well as historical and literary context clues, to determine the meaning of specialized vocabulary and to understand the precise meaning of grade-level-appropriate words.

Word Recognition
1.1 Read aloud narrative and expository text fluently and accurately and with appropriate pacing, intonation, and expression.

Vocabulary and Concept Development
1.2 Identify and interpret figurative language and words with multiple meanings.
1.3 Recognize the origins and meanings of frequently used foreign words in English and use these words accurately in speaking and writing.
1.4 Monitor expository text for unknown words or words with novel meanings by using word, sentence, and paragraph clues to determine meaning.
1.5 Understand and explain "shades of meaning" in related words (e.g., softly and quietly).

2.0 Reading Comprehension (Focus on Informational Materials)
Students read and understand grade-level-appropriate material. They describe and connect the essential ideas, arguments, and perspectives of the text by using their knowledge of text structure, organization, and purpose. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition, by grade eight, students read one million words annually on their own, including a good representation of grade-level-appropriate narrative and expository text (e.g., classic and contemporary literature, magazines, newspapers, online information). In grade six, students continue to make progress toward this goal.

Structural Features of Informational Materials
2.1 Identify the structural features of popular media (e.g., newspapers, magazines, online information) and use the features to obtain information.
2.2 Analyze text that uses the compare-and-contrast organizational pattern.

Comprehension and Analysis of Grade-Level-Appropriate Text
2.3 Connect and clarify main ideas by identifying their relationships to other sources and related topics.
2.4 Clarify an understanding of texts by creating outlines, logical notes, summaries, or reports.
2.5 Follow multiple-step instructions for preparing applications (e.g., for a public library card, bank savings account, sports club, league membership).

Expository Critique
2.6 Determine the adequacy and appropriateness of the evidence for an author's conclusions.
2.7 Make reasonable assertions about a text through accurate, supporting citations.
2.8 Note instances of unsupported inferences, fallacious reasoning, persuasion, and propaganda in text.

3.0 Literary Response and Analysis
Students read and respond to historically or culturally significant works of literature that reflect and enhance their studies of history and social science. They clarify the ideas and connect them to other literary works. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Structural Features of Literature
3.1 Identify the forms of fiction and describe the major characteristics of each form.

Narrative Analysis of Grade-Level-Appropriate Text
3.2 Analyze the effect of the qualities of the character (e.g., courage or cowardice, ambition or laziness) on the plot and the resolution of the conflict.
3.3 Analyze the influence of setting on the problem and its resolution.
3.4 Define how tone or meaning is conveyed in poetry through word choice, figurative language, sentence structure, line length, punctuation, rhythm, repetition, and rhyme.
3.5 Identify the speaker and recognize the difference between first-and third-person narration (e.g., autobiography compared with biography).
3.6 Identify and analyze features of themes conveyed through characters, actions, and images.
3.7 Explain the effects of common literary devices (e.g., symbolism, imagery, metaphor) in a variety of fictional and nonfictional texts.

Literary Criticism
3.8 Critique the credibility of characterization and the degree to which a plot is contrived or realistic (e.g., compare use of fact and fantasy in historical fiction).

Writing
1.0 Writing Strategies
Students write clear, coherent, and focused essays. The writing exhibits students' awareness of the audience and purpose. Essays contain formal introductions, supporting evidence, and conclusions. Students progress through the stages of the writing process as needed.

Organization and Focus
1.1 Choose the form of writing (e.g., personal letter, letter to the editor, review, poem, report, narrative) that best suits the intended purpose.

1.2 Create multiple-paragraph expository compositions:

Engage the interest of the reader and state a clear purpose.
Develop the topic with supporting details and precise verbs, nouns, and adjectives to paint a visual image in the mind of the reader.
Conclude with a detailed summary linked to the purpose of the composition.
1.3 Use a variety of effective and coherent organizational patterns, including comparison and contrast; organization by categories; and arrangement by spatial order, order of importance, or climactic order.

Research and Technology
1.4 Use organizational features of electronic text (e.g., bulletin boards, databases, keyword searches, e-mail addresses) to locate information.
1.5 Compose documents with appropriate formatting by using word-processing skills and principles of design (e.g., margins, tabs, spacing, columns, page orientation).

Evaluation and Revision
1.6 Revise writing to improve the organization and consistency of ideas within and between paragraphs.

2.0 Writing Applications (Genres and Their Characteristics)
Students write narrative, expository, persuasive, and descriptive texts of at least 500 to 700 words in each genre. Student writing demonstrates a command of standard American English and the research, organizational, and drafting strategies outlined in Writing Standard 1.0.

Using the writing strategies of grade six outlined in Writing Standard 1.0, students:

2.1 Write narratives:

Establish and develop a plot and setting and present a point of view that is appropriate to the stories.
Include sensory details and concrete language to develop plot and character.
Use a range of narrative devices (e.g., dialogue, suspense).
2.2 Write expository compositions (e.g., description, explanation, comparison and contrast, problem and solution):

State the thesis or purpose.
Explain the situation.
Follow an organizational pattern appropriate to the type of composition.
Offer persuasive evidence to validate arguments and conclusions as needed.
2.3 Write research reports:

Pose relevant questions with a scope narrow enough to be thoroughly covered.
Support the main idea or ideas with facts, details, examples, and explanations from multiple authoritative sources (e.g., speakers, periodicals, online information searches).
Include a bibliography.
2.4 Write responses to literature:

Develop an interpretation exhibiting careful reading, understanding, and insight.
Organize the interpretation around several clear ideas, premises, or images.
Develop and justify the interpretation through sustained use of examples and textual evidence.
2.5 Write persuasive compositions:

State a clear position on a proposition or proposal.
Support the position with organized and relevant evidence.
Anticipate and address reader concerns and counterarguments.
Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions appropriate to this grade level.

Sentence Structure
1.1 Use simple, compound, and compound-complex sentences; use effective coordination and subordination of ideas to express complete thoughts.

Grammar
1.2 Identify and properly use indefinite pronouns and present perfect, past perfect, and future perfect verb tenses; ensure that verbs agree with compound subjects.

Punctuation
1.3 Use colons after the salutation in business letters, semicolons to connect independent clauses, and commas when linking two clauses with a conjunction in compound sentences.

Capitalization
1.4 Use correct capitalization.

Spelling
1.5 Spell frequently misspelled words correctly (e.g., their, they're, there).

Listening and Speaking
1.0 Listening and Speaking Strategies
Students deliver focused, coherent presentations that convey ideas clearly and relate to the background and interests of the audience. They evaluate the content of oral communication.

Comprehension
1.1 Relate the speaker's verbal communication (e.g., word choice, pitch, feeling, tone) to the nonverbal message (e.g., posture, gesture).
1.2 Identify the tone, mood, and emotion conveyed in the oral communication.
1.3 Restate and execute multiple-step oral instructions and directions.

Organization and Delivery of Oral Communication
1.4 Select a focus, an organizational structure, and a point of view, matching the purpose, message, occasion, and vocal modulation to the audience.
1.5 Emphasize salient points to assist the listener in following the main ideas and concepts.
1.6 Support opinions with detailed evidence and with visual or media displays that use appropriate technology.
1.7 Use effective rate, volume, pitch, and tone and align nonverbal elements to sustain audience interest and attention.

Analysis and Evaluation of Oral and Media Communications
1.8 Analyze the use of rhetorical devices (e.g., cadence, repetitive patterns, use of onomatopoeia) for intent and effect.
1.9 Identify persuasive and propaganda techniques used in television and identify false and misleading information.

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver well-organized formal presentations employing traditional rhetorical strategies (e.g., narration, exposition, persuasion, description). Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the speaking strategies of grade six outlined in Listening and Speaking Standard 1.0, students:

2.1 Deliver narrative presentations:

Establish a context, plot, and point of view.
Include sensory details and concrete language to develop the plot and character.
Use a range of narrative devices (e.g., dialogue, tension, or suspense).
2.2 Deliver informative presentations:

Pose relevant questions sufficiently limited in scope to be completely and thoroughly answered.
Develop the topic with facts, details, examples, and explanations from multiple authoritative sources (e.g., speakers, periodicals, online information).
2.3 Deliver oral responses to literature:

Develop an interpretation exhibiting careful reading, understanding, and insight.
Organize the selected interpretation around several clear ideas, premises, or images.
Develop and justify the selected interpretation through sustained use of examples and textual evidence.
2.4 Deliver persuasive presentations:

Provide a clear statement of the position.
Include relevant evidence.
Offer a logical sequence of information.
Engage the listener and foster acceptance of the proposition or proposal.
2.5 Deliver presentations on problems and solutions:

Theorize on the causes and effects of each problem and establish connections between the defined problem and at least one solution.
Offer persuasive evidence to validate the definition of the problem and the proposed solutions
______________________________________________________________________________________________________

Grade Seven
English-language Arts Content Standards

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students use their knowledge of word origins and word relationships, as well as historical and literary context clues, to determine the meaning of specialized vocabulary and to understand the precise meaning of grade-level-appropriate words.

Vocabulary and Concept Development
1.1 Identify idioms, analogies, metaphors, and similes in prose and poetry.
1.2 Use knowledge of Greek, Latin, and Anglo-Saxon roots and affixes to understand content-area vocabulary.
1.3 Clarify word meanings through the use of definition, example, restatement, or contrast.

2.0 Reading Comprehension (Focus on Informational Materials)
Students read and understand grade-level-appropriate material. They describe and connect the essential ideas, arguments, and perspectives of the text by using their knowledge of text structure, organization, and purpose. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition, by grade eight, students read one million words annually on their own, including a good representation of grade-level-appropriate narrative and expository text (e.g., classic and contemporary literature, magazines, newspapers, online information). In grade seven, students make substantial progress toward this goal.

Structural Features of Informational Materials
2.1 Understand and analyze the differences in structure and purpose between various categories of informational materials (e.g., textbooks, newspapers, instructional manuals, signs).
2.2 Locate information by using a variety of consumer, workplace, and public documents.
2.3 Analyze text that uses the cause-and-effect organizational pattern.

Comprehension and Analysis of Grade-Level-Appropriate Text
2.4 Identify and trace the development of an author's argument, point of view, or perspective in text.
2.5 Understand and explain the use of a simple mechanical device by following technical directions.

Expository Critique
2.6 Assess the adequacy, accuracy, and appropriateness of the author's evidence to support claims and assertions, noting instances of bias and stereotyping.

3.0 Literary Response and Analysis
Students read and respond to historically or culturally significant works of literature that reflect and enhance their studies of history and social science. They clarify the ideas and connect them to other literary works. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Structural Features of Literature
3.1 Articulate the expressed purposes and characteristics of different forms of prose (e.g., short story, novel, novella, essay).

Narrative Analysis of Grade-Level-Appropriate Text
3.2 Identify events that advance the plot and determine how each event explains past or present action(s) or foreshadows future action(s).
3.3 Analyze characterization as delineated through a character's thoughts, words, speech patterns, and actions; the narrator's description; and the thoughts, words, and actions of other characters.
3.4 Identify and analyze recurring themes across works (e.g., the value of bravery, loyalty, and friendship; the effects of loneliness).
3.5 Contrast points of view (e.g., first and third person, limited and omniscient, subjective and objective) in narrative text and explain how they affect the overall theme of the work.

Literary Criticism
3.6 Analyze a range of responses to a literary work and determine the extent to which the literary elements in the work shaped those responses.

Writing
1.0 Writing Strategies
Students write clear, coherent, and focused essays. The writing exhibits students' awareness of the audience and purpose. Essays contain formal introductions, supporting evidence, and conclusions. Students progress through the stages of the writing process as needed.

Organization and Focus
1.1 Create an organizational structure that balances all aspects of the composition and uses effective transitions between sentences to unify important ideas.
1.2 Support all statements and claims with anecdotes, descriptions, facts and statistics, and specific examples.
1.3 Use strategies of note taking, outlining, and summarizing to impose structure on composition drafts.

Research and Technology
1.4 Identify topics; ask and evaluate questions; and develop ideas leading to inquiry, investigation, and research.
1.5 Give credit for both quoted and paraphrased information in a bibliography by using a consistent and sanctioned format and methodology for citations.
1.6 Create documents by using word-processing skills and publishing programs; develop simple databases and spreadsheets to manage information and prepare reports.

Evaluation and Revision
1.7 Revise writing to improve organization and word choice after checking the logic of the ideas and the precision of the vocabulary.

2.0 Writing Applications (Genres and Their Characteristics)
Students write narrative, expository, persuasive, and descriptive texts of at least 500 to 700 words in each genre. The writing demonstrates a command of standard American English and the research, organizational, and drafting strategies outlined in Writing Standard 1.0.

Using the writing strategies of grade seven outlined in Writing Standard 1.0, students:

2.1 Write fictional or autobiographical narratives:

Develop a standard plot line (having a beginning, conflict, rising action, climax, and denouement) and point of view.
Develop complex major and minor characters and a definite setting.
Use a range of appropriate strategies (e.g., dialogue; suspense; naming of specific narrative action, including movement, gestures, and expressions).
2.2 Write responses to literature:
a. Develop interpretations exhibiting careful reading, understanding, and insight.
b. Organize interpretations around several clear ideas, premises, or images from the literary work.
c. Justify interpretations through sustained use of examples and textual evidence.

2.3 Write research reports:
a. Pose relevant and tightly drawn questions about the topic.
b. Convey clear and accurate perspectives on the subject.
c. Include evidence compiled through the formal research process (e.g., use of a card catalog, Reader's Guide to Periodical Literature, a computer catalog, magazines, newspapers, dictionaries).
d. Document reference sources by means of footnotes and a bibliography.

2.4 Write persuasive compositions:
a. State a clear position or perspective in support of a proposition or proposal.
b. Describe the points in support of the proposition, employing well-articulated evidence.
c. Anticipate and address reader concerns and counterarguments.

2.5 Write summaries of reading materials:
a. Include the main ideas and most significant details.
b. Use the student's own words, except for quotations.
c. Reflect underlying meaning, not just the superficial details.

Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions appropriate to the grade level.

Sentence Structure
1.1 Place modifiers properly and use the active voice.

Grammar
1.2 Identify and use infinitives and participles and make clear references between pronouns and antecedents.
1.3 Identify all parts of speech and types and structure of sentences.
1.4 Demonstrate the mechanics of writing (e.g., quotation marks, commas at end of dependent clauses) and appropriate English usage (e.g., pronoun reference).

Punctuation
1.5 Identify hyphens, dashes, brackets, and semicolons and use them correctly.

Capitalization
1.6 Use correct capitalization.

Spelling
1.7 Spell derivatives correctly by applying the spellings of bases and affixes.

Listening and Speaking
1.0 Listening and Speaking Strategies
Deliver focused, coherent presentations that convey ideas clearly and relate to the background and interests of the audience. Students evaluate the content of oral communication.

Comprehension
1.1 Ask probing questions to elicit information, including evidence to support the speaker's claims and conclusions.
1.2 Determine the speaker's attitude toward the subject.
1.3 Respond to persuasive messages with questions, challenges, or affirmations.

Organization and Delivery of Oral Communication
1.4 Organize information to achieve particular purposes and to appeal to the background and interests of the audience.
1.5 Arrange supporting details, reasons, descriptions, and examples effectively and persuasively in relation to the audience.
1.6 Use speaking techniques, including voice modulation, inflection, tempo, enunciation, and eye contact, for effective presentations.

Analysis and Evaluation of Oral and Media Communications
1.7 Provide constructive feedback to speakers concerning the coherence and logic of a speech's content and delivery and its overall impact upon the listener.
1.8 Analyze the effect on the viewer of images, text, and sound in electronic journalism; identify the techniques used to achieve the effects in each instance studied.

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver well-organized formal presentations employing traditional rhetorical strategies (e.g., narration, exposition, persuasion, description). Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the speaking strategies of grade seven outlined in Listening and Speaking Standard 1.0, students:

2.1 Deliver narrative presentations:
a. Establish a context, standard plot line (having a beginning, conflict, rising action, climax, and denouement), and point of view.
b. Describe complex major and minor characters and a definite setting.
c. Use a range of appropriate strategies, including dialogue, suspense, and naming of specific narrative action (e.g., movement, gestures, expressions).

2.2 Deliver oral summaries of articles and books:
a. Include the main ideas of the event or article and the most significant details.
b. Use the student's own words, except for material quoted from sources.
c. Convey a comprehensive understanding of sources, not just superficial details.

2.3 Deliver research presentations:
a. Pose relevant and concise questions about the topic.
b. Convey clear and accurate perspectives on the subject.
c. Include evidence generated through the formal research process (e.g., use of a card catalog, Reader's Guide to Periodical Literature, computer databases, magazines, newspapers, dictionaries).
d. Cite reference sources appropriately.

2.4 Deliver persuasive presentations:
a. State a clear position or perspective in support of an argument or proposal.
b. Describe the points in support of the argument and employ well-articulated evidence.

_______________________________________________________________________________________________________

Grade Eight
English-language Arts Content Standards

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students use their knowledge of word origins and word relationships, as well as historical and literary context clues, to determine the meaning of specialized vocabulary and to understand the precise meaning of grade-level-appropriate words.

Vocabulary and Concept Development
1.1 Analyze idioms, analogies, metaphors, and similes to infer the literal and figurative meanings of phrases.
1.2 Understand the most important points in the history of English language and use common word origins to determine the historical influences on English word meanings.
1.3 Use word meanings within the appropriate context and show ability to verify those meanings by definition, restatement, example, comparison, or contrast.

2.0 Reading Comprehension (Focus on Informational Materials)
Students read and understand grade-level-appropriate material. They describe and connect the essential ideas, arguments, and perspectives of the text by using their knowledge of text structure, organization, and purpose. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition, students read one million words annually on their own, including a good representation of narrative and expository text (e.g., classic and contemporary literature, magazines, newspapers, online information).

Structural Features of Informational Materials
2.1 Compare and contrast the features and elements of consumer materials to gain meaning from documents (e.g., warranties, contracts, product information, instruction manuals).
2.2 Analyze text that uses proposition and support patterns.

Comprehension and Analysis of Grade-Level-Appropriate Text
2.3 Find similarities and differences between texts in the treatment, scope, or organization of ideas.
2.4 Compare the original text to a summary to determine whether the summary accurately captures the main ideas, includes critical details, and conveys the underlying meaning.
2.5 Understand and explain the use of a complex mechanical device by following technical directions.
2.6 Use information from a variety of consumer, workplace, and public documents to explain a situation or decision and to solve a problem.

Expository Critique
2.7 Evaluate the unity, coherence, logic, internal consistency, and structural patterns of text.

3.0 Literary Response and Analysis
Students read and respond to historically or culturally significant works of literature that reflect and enhance their studies of history and social science. They clarify the ideas and connect them to other literary works. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Structural Features of Literature
3.1 Determine and articulate the relationship between the purposes and characteristics of different forms of poetry (e.g., ballad, lyric, couplet, epic, elegy, ode, sonnet).

Narrative Analysis of Grade-Level-Appropriate Text
3.2 Evaluate the structural elements of the plot (e.g., subplots, parallel episodes, climax), the plot's development, and the way in which conflicts are (or are not) addressed and resolved.
3.3 Compare and contrast motivations and reactions of literary characters from different historical eras confronting similar situations or conflicts.
3.4 Analyze the relevance of the setting (e.g., place, time, customs) to the mood, tone, and meaning of the text.
3.5 Identify and analyze recurring themes (e.g., good versus evil) across traditional and contemporary works.
3.6 Identify significant literary devices (e.g., metaphor, symbolism, dialect, irony) that define a writer's style and use those elements to interpret the work.

Literary Criticism
3.7 Analyze a work of literature, showing how it reflects the heritage, traditions, attitudes, and beliefs of its author. (Biographical approach)

Writing
1.0 Writing Strategies
Students write clear, coherent, and focused essays. The writing exhibits students' awareness of audience and purpose. Essays contain formal introductions, supporting evidence, and conclusions. Students progress through the stages of the writing process as needed.

Organization and Focus
1.1 Create compositions that establish a controlling impression, have a coherent thesis, and end with a clear and well-supported conclusion.
1.2 Establish coherence within and among paragraphs through effective transitions, parallel structures, and similar writing techniques.
1.3 Support theses or conclusions with analogies, paraphrases, quotations, opinions from authorities, comparisons, and similar devices.

Research and Technology
1.4 Plan and conduct multiple-step information searches by using computer networks and modems.
1.5 Achieve an effective balance between researched information and original ideas.

Evaluation and Revision
1.6 Revise writing for word choice; appropriate organization; consistent point of view; and transitions between paragraphs, passages, and ideas.

2.0 Writing Applications (Genres and Their Characteristics)
Students write narrative, expository, persuasive, and descriptive essays of at least 500 to 700 words in each genre. Student writing demonstrates a command of standard American English and the research, organizational, and drafting strategies outlined in Writing Standard 1.0.

Using the writing strategies of grade eight outlined in Writing Standard 1.0, students:

2.1 Write biographies, autobiographies, short stories, or narratives:
a. Relate a clear, coherent incident, event, or situation by using well-chosen details.
b. Reveal the significance of, or the writer's attitude about, the subject.
c. Employ narrative and descriptive strategies (e.g., relevant dialogue, specific action, physical description, background description, comparison or contrast of characters).

2.2 Write responses to literature:
a. Exhibit careful reading and insight in their interpretations.
b. Connect the student's own responses to the writer's techniques and to specific textual references.
c. Draw supported inferences about the effects of a literary work on its audience.
d. Support judgments through references to the text, other works, other authors, or to personal knowledge.

2.3 Write research reports:
a. Define a thesis.
b. Record important ideas, concepts, and direct quotations from significant information sources and paraphrase and summarize all perspectives on the topic, as appropriate.
c. Use a variety of primary and secondary sources and distinguish the nature and value of each.
d. Organize and display information on charts, maps, and graphs.

2.4 Write persuasive compositions:
a. Include a well-defined thesis (i.e., one that makes a clear and knowledgeable judgment).
b. Present detailed evidence, examples, and reasoning to support arguments, differentiating between facts and opinion.
c. Provide details, reasons, and examples, arranging them effectively by anticipating and answering reader concerns and counterarguments.

2.5 Write documents related to career development, including simple business letters and job applications:
a. Present information purposefully and succinctly and meet the needs of the intended audience.
b. Follow the conventional format for the type of document (e.g., letter of inquiry, memorandum).

2.6 Write technical documents:
a. Identify the sequence of activities needed to design a system, operate a tool, or explain the bylaws of an organization.
b. Include all the factors and variables that need to be considered.
c. Use formatting techniques (e.g., headings, differing fonts) to aid comprehension.

Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions appropriate to this grade level.

Sentence Structure
1.1 Use correct and varied sentence types and sentence openings to present a lively and effective personal style.
1.2 Identify and use parallelism, including similar grammatical forms, in all written discourse to present items in a series and items juxtaposed for emphasis.
1.3 Use subordination, coordination, apposition, and other devices to indicate clearly the relationship between ideas.

Grammar
1.4 Edit written manuscripts to ensure that correct grammar is used.

Punctuation and Capitalization
1.5 Use correct punctuation and capitalization.

Spelling
1.6 Use correct spelling conventions.

Listening and Speaking
1.0 Listening and Speaking Strategies
Students deliver focused, coherent presentations that convey ideas clearly and relate to the background and interests of the audience. They evaluate the content of oral communication.

Comprehension
1.1 Analyze oral interpretations of literature, including language choice and delivery, and the effect of the interpretations on the listener.
1.2 Paraphrase a speaker's purpose and point of view and ask relevant questions concerning the speaker's content, delivery, and purpose.

Organization and Delivery of Oral Communication
1.3 Organize information to achieve particular purposes by matching the message, vocabulary, voice modulation, expression, and tone to the audience and purpose.
1.4 Prepare a speech outline based upon a chosen pattern of organization, which generally includes an introduction; transitions, previews, and summaries; a logically developed body; and an effective conclusion.
1.5 Use precise language, action verbs, sensory details, appropriate and colorful modifiers, and the active rather than the passive voice in ways that enliven oral presentations.
1.6 Use appropriate grammar, word choice, enunciation, and pace during formal presentations.
1.7 Use audience feedback (e.g., verbal and nonverbal cues):
a. Reconsider and modify the organizational structure or plan.
b. Rearrange words and sentences to clarify the meaning.

Analysis and Evaluation of Oral and Media Communications
1.8 Evaluate the credibility of a speaker (e.g., hidden agendas, slanted or biased material).
1.9 Interpret and evaluate the various ways in which visual image makers (e.g., graphic artists, illustrators, news photographers) communicate information and affect impressions and opinions.

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver well-organized formal presentations employing traditional rhetorical strategies (e.g., narration, exposition, persuasion, description). Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the speaking strategies of grade eight outlined in Listening and Speaking Standard 1.0, students:

2.1 Deliver narrative presentations (e.g., biographical, autobiographical):
a. Relate a clear, coherent incident, event, or situation by using well-chosen details.
b. Reveal the significance of, and the subject's attitude about, the incident, event, or situation.
c. Employ narrative and descriptive strategies (e.g., relevant dialogue, specific action, physical description, background description, comparison or contrast of characters).

2.2 Deliver oral responses to literature:
a. Interpret a reading and provide insight.
b. Connect the students' own responses to the writer's techniques and to specific textual references.
c. Draw supported inferences about the effects of a literary work on its audience.
d. Support judgments through references to the text, other works, other authors, or personal knowledge.

2.3 Deliver research presentations:
a. Define a thesis.
b. Record important ideas, concepts, and direct quotations from significant information sources and paraphrase and summarize all relevant perspectives on the topic, as appropriate.
c. Use a variety of primary and secondary sources and distinguish the nature and value of each.
d. Organize and record information on charts, maps, and graphs.

2.4 Deliver persuasive presentations:
a. Include a well-defined thesis (i.e., one that makes a clear and knowledgeable judgment).
b. Differentiate fact from opinion and support arguments with detailed evidence, examples, and reasoning.
c. Anticipate and answer listener concerns and counterarguments effectively through the inclusion and arrangement of details, reasons, examples, and other elements.
d. Maintain a reasonable tone.

2.5 Recite poems (of four to six stanzas), sections of speeches, or dramatic soliloquies, using voice modulation, tone, and gestures expressively to enhance the meaning.

________________________________________________________________________________________________________

Grades Nine & Ten
English-language Arts Content Standards

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students apply their knowledge of word origins to determine the meaning of new words encountered in reading materials and use those words accurately.

Vocabulary and Concept Development
1.1 Identify and use the literal and figurative meanings of words and understand word derivations.
1.2. Distinguish between the denotative and connotative meanings of words and interpret the connotative power of words.
1.3 Identify Greek, Roman, and Norse mythology and use the knowledge to understand the origin and meaning of new words (e.g., the word narcissistic drawn from the myth of Narcissus and Echo).

2.0 Reading Comprehension (Focus on Informational Materials)
Students read and understand grade-level-appropriate material. They analyze the organizational patterns, arguments, and positions advanced. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition, by grade twelve, students read two million words annually on their own, including a wide variety of classic and contemporary literature, magazines, newspapers, and online information. In grades nine and ten, students make substantial progress toward this goal.

Structural Features of Informational Materials
2.1 Analyze the structure and format of functional workplace documents, including the graphics and headers, and explain how authors use the features to achieve their purposes.
2.2 Prepare a bibliography of reference materials for a report using a variety of consumer, workplace, and public documents. Comprehension and Analysis of Grade-Level-Appropriate Text
2.3 Generate relevant questions about readings on issues that can be researched.
2.4 Synthesize the content from several sources or works by a single author dealing with a single issue; paraphrase the ideas and connect them to other sources and related topics to demonstrate comprehension.
2.5 Extend ideas presented in primary or secondary sources through original analysis, evaluation, and elaboration.
2.6 Demonstrate use of sophisticated learning tools by following technical directions (e.g., those found with graphic calculators and specialized software programs and in access guides to World Wide Web sites on the Internet).

Expository Critique
2.7 Critique the logic of functional documents by examining the sequence of information and procedures in anticipation of possible reader misunderstandings.
2.8 Evaluate the credibility of an author's argument or defense of a claim by critiquing the relationship between generalizations and evidence, the comprehensiveness of evidence, and the way in which the author's intent affects the structure and tone of the text (e.g., in professional journals, editorials, political speeches, primary source material).

3.0 Literary Response and Analysis
Students read and respond to historically or culturally significant works of literature that reflect and enhance their studies of history and social science. They conduct in-depth analyses of recurrent patterns and themes. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Structural Features of Literature
3.1 Articulate the relationship between the expressed purposes and the characteristics of different forms of dramatic literature (e.g., comedy, tragedy, drama, dramatic monologue).
3.2 Compare and contrast the presentation of a similar theme or topic across genres to explain how the selection of genre shapes the theme or topic.

Narrative Analysis of Grade-Level-Appropriate Text
3.3 Analyze interactions between main and subordinate characters in a literary text (e.g., internal and external conflicts, motivations, relationships, influences) and explain the way those interactions affect the plot.
3.4 Determine characters' traits by what the characters say about themselves in narration, dialogue, dramatic monologue, and soliloquy.
3.5 Compare works that express a universal theme and provide evidence to support the ideas expressed in each work.
3.6 Analyze and trace an author's development of time and sequence, including the use of complex literary devices (e.g., foreshadowing, flashbacks).
3.7 Recognize and understand the significance of various literary devices, including figurative language, imagery, allegory, and symbolism, and explain their appeal.
3.8 Interpret and evaluate the impact of ambiguities, subtleties, contradictions, ironies, and incongruities in a text.
3.9 Explain how voice, persona, and the choice of a narrator affect characterization and the tone, plot, and credibility of a text.
3.10 Identify and describe the function of dialogue, scene designs, soliloquies, asides, and character foils in dramatic literature.

Literary Criticism
3.11 Evaluate the aesthetic qualities of style, including the impact of diction and figurative language on tone, mood, and theme, using the terminology of literary criticism. (Aesthetic approach)
3.12 Analyze the way in which a work of literature is related to the themes and issues of its historical period. (Historical approach)

Writing
1.0 Writing Strategies
Students write coherent and focused essays that convey a well-defined perspective and tightly reasoned argument. The writing demonstrates students' awareness of the audience and purpose. Students progress through the stages of the writing process as needed.

Organization and Focus
1.1 Establish a controlling impression or coherent thesis that conveys a clear and distinctive perspective on the subject and maintain a consistent tone and focus throughout the piece of writing.
1.2 Use precise language, action verbs, sensory details, appropriate modifiers, and the active rather than the passive voice.

Research and Technology
1.3 Use clear research questions and suitable research methods (e.g., library, electronic media, personal interview) to elicit and present evidence from primary and secondary sources.
1.4 Develop the main ideas within the body of the composition through supporting evidence (e.g., scenarios, commonly held beliefs, hypotheses, definitions).
1.5 Synthesize information from multiple sources and identify complexities and discrepancies in the information and the different perspectives found in each medium (e.g., almanacs, microfiche, news sources, in-depth field studies, speeches, journals, technical documents).
1.6 Integrate quotations and citations into a written text while maintaining the flow of ideas.
1.7 Use appropriate conventions for documentation in the text, notes, and bibliographies by adhering to those in style manuals (e.g., Modern Language Association Handbook, The Chicago Manual of Style).
1.8 Design and publish documents by using advanced publishing software and graphic programs.

Evaluation and Revision
1.9 Revise writing to improve the logic and coherence of the organization and controlling perspective, the precision of word choice, and the tone by taking into consideration the audience, purpose, and formality of the context.

2.0 Writing Applications (Genres and Their Characteristics)
Students combine the rhetorical strategies of narration, exposition, persuasion, and description to produce texts of at least 1,500 words each. Student writing demonstrates a command of standard American English and the research, organizational, and drafting strategies outlined in Writing Standard 1.0.

Using the writing strategies of grades nine and ten outlined in Writing Standard 1.0, students:

2.1 Write biographical or autobiographical narratives or short stories:
a. Relate a sequence of events and communicate the significance of the events to the audience.
b. Locate scenes and incidents in specific places.
c. Describe with concrete sensory details the sights, sounds, and smells of a scene and the specific actions, movements, gestures, and feelings of the characters; use interior monologue to depict the characters' feelings.
d. Pace the presentation of actions to accommodate changes in time and mood.
e. Make effective use of descriptions of appearance, images, shifting perspectives, and sensory details.

2.2 Write responses to literature:
a. Demonstrate a comprehensive grasp of the significant ideas of literary works.
b. Support important ideas and viewpoints through accurate and detailed references to the text or to other works.
c. Demonstrate awareness of the author's use of stylistic devices and an appreciation of the effects created.
d. Identify and assess the impact of perceived ambiguities, nuances, and complexities within the text.

2.3 Write expository compositions, including analytical essays and research reports:
a. Marshal evidence in support of a thesis and related claims, including information on all relevant perspectives.
b. Convey information and ideas from primary and secondary sources accurately and coherently.
c. Make distinctions between the relative value and significance of specific data, facts, and ideas.
d. Include visual aids by employing appropriate technology to organize and record information on charts, maps, and graphs.
e. Anticipate and address readers' potential misunderstandings, biases, and expectations.
f. Use technical terms and notations accurately.

2.4 Write persuasive compositions:
a. Structure ideas and arguments in a sustained and logical fashion.
b. Use specific rhetorical devices to support assertions (e.g., appeal to logic through reasoning; appeal to emotion or ethical belief; relate a personal anecdote, case study, or analogy).
c. Clarify and defend positions with precise and relevant evidence, including facts, expert opinions, quotations, and expressions of commonly accepted beliefs and logical reasoning.
d. Address readers' concerns, counterclaims, biases, and expectations.

2.5 Write business letters:
a. Provide clear and purposeful information and address the intended audience appropriately.
b. Use appropriate vocabulary, tone, and style to take into account the nature of the relationship with, and the knowledge and interests of, the recipients.
c. Highlight central ideas or images.
d. Follow a conventional style with page formats, fonts, and spacing that contribute to the documents' readability and impact.

2.6 Write technical documents (e.g., a manual on rules of behavior for conflict resolution, procedures for conducting a meeting, minutes of a meeting):
a. Report information and convey ideas logically and correctly.
b. Offer detailed and accurate specifications.
c. Include scenarios, definitions, and examples to aid comprehension (e.g., troubleshooting guide).
d. Anticipate readers' problems, mistakes, and misunderstandings.

Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions.

Grammar and Mechanics of Writing
1.1 Identify and correctly use clauses (e.g., main and subordinate), phrases (e.g., gerund, infinitive, and participial), and mechanics of punctuation (e.g., semicolons, colons, ellipses, hyphens).
1.2 Understand sentence construction (e.g., parallel structure, subordination, proper placement of modifiers) and proper English usage (e.g., consistency of verb tenses).
1.3 Demonstrate an understanding of proper English usage and control of grammar, paragraph and sentence structure, diction, and syntax.

Manuscript Form
1.4 Produce legible work that shows accurate spelling and correct use of the conventions of punctuation and capitalization.
1.5 Reflect appropriate manuscript requirements, including title page presentation, pagination, spacing and margins, and integration of source and support material (e.g., in-text citation, use of direct quotations, paraphrasing) with appropriate citations.

Listening and Speaking
1.0 Listening and Speaking Strategies
Students formulate adroit judgments about oral communication. They deliver focused and coherent presentations of their own that convey clear and distinct perspectives and solid reasoning. They use gestures, tone, and vocabulary tailored to the audience and purpose.

Comprehension
1.1 Formulate judgments about the ideas under discussion and support those judgments with convincing evidence.
1.2 Compare and contrast the ways in which media genres (e.g., televised news, news magazines, documentaries, online information) cover the same event.

Organization and Delivery of Oral Communication
1.3 Choose logical patterns of organization (e.g., chronological, topical, cause and effect) to inform and to persuade, by soliciting agreement or action, or to unite audiences behind a common belief or cause.
1.4 Choose appropriate techniques for developing the introduction and conclusion (e.g., by using literary quotations, anecdotes, references to authoritative sources).
1.5 Recognize and use elements of classical speech forms (e.g., introduction, first and second transitions, body, conclusion) in formulating rational arguments and applying the art of persuasion and debate.
1.6 Present and advance a clear thesis statement and choose appropriate types of proof (e.g., statistics, testimony, specific instances) that meet standard tests for evidence, including credibility, validity, and relevance.
1.7 Use props, visual aids, graphs, and electronic media to enhance the appeal and accuracy of presentations.
1.8 Produce concise notes for extemporaneous delivery.
1.9 Analyze the occasion and the interests of the audience and choose effective verbal and nonverbal techniques (e.g., voice, gestures, eye contact) for presentations.

Analysis and Evaluation of Oral and Media Communications
1.10 Analyze historically significant speeches (e.g., Abraham Lincoln's "Gettysburg Address," Martin Luther King, Jr.'s "I Have a Dream") to find the rhetorical devices and features that make them memorable.
1.11 Assess how language and delivery affect the mood and tone of the oral communication and make an impact on the audience.
1.12 Evaluate the clarity, quality, effectiveness, and general coherence of a speaker's important points, arguments, evidence, organization of ideas, delivery, diction, and syntax.
1.13 Analyze the types of arguments used by the speaker, including argument by causation, analogy, authority, emotion, and logic.
1.14 Identify the aesthetic effects of a media presentation and evaluate the techniques used to create them (e.g., compare Shakespeare's Henry V with Kenneth Branagh's 1990 film version).

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver polished formal and extemporaneous presentations that combine the traditional rhetorical strategies of narration, exposition, persuasion, and description. Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the speaking strategies of grades nine and ten outlined in Listening and Speaking Standard 1.0, students:

2.1 Deliver narrative presentations:
a. Narrate a sequence of events and communicate their significance to the audience.
b. Locate scenes and incidents in specific places.
c. Describe with concrete sensory details the sights, sounds, and smells of a scene and the specific actions, movements, gestures, and feelings of characters.
d. Pace the presentation of actions to accommodate time or mood changes.

2.2 Deliver expository presentations:
a. Marshal evidence in support of a thesis and related claims, including information on all relevant perspectives.
b. Convey information and ideas from primary and secondary sources accurately and coherently.
c. Make distinctions between the relative value and significance of specific data, facts, and ideas.
d. Include visual aids by employing appropriate technology to organize and display information on charts, maps, and graphs.
e. Anticipate and address the listener's potential misunderstandings, biases, and expectations.
f. Use technical terms and notations accurately.

2.3 Apply appropriate interviewing techniques:
a. Prepare and ask relevant questions.
b. Make notes of responses.
c. Use language that conveys maturity, sensitivity, and respect.
d. Respond correctly and effectively to questions.
e. Demonstrate knowledge of the subject or organization.
f. Compile and report responses.
g. Evaluate the effectiveness of the interview.

2.4 Deliver oral responses to literature:
a. Advance a judgment demonstrating a comprehensive grasp of the significant ideas of works or passages (i.e., make and support warranted assertions about the text).
b. Support important ideas and viewpoints through accurate and detailed references to the text or to other works.
c. Demonstrate awareness of the author's use of stylistic devices and an appreciation of the effects created.
d. Identify and assess the impact of perceived ambiguities, nuances, and complexities within the text.

2.5 Deliver persuasive arguments (including evaluation and analysis of problems and solutions and causes and effects):
a. Structure ideas and arguments in a coherent, logical fashion.
b. Use rhetorical devices to support assertions (e.g., by appeal to logic through reasoning; by appeal to emotion or ethical belief; by use of personal anecdote, case study, or analogy).
c. Clarify and defend positions with precise and relevant evidence, including facts, expert opinions, quotations, expressions of commonly accepted beliefs, and logical reasoning.
d. Anticipate and address the listener's concerns and counterarguments.

2.6 Deliver descriptive presentations:
a. Establish clearly the speaker's point of view on the subject of the presentation.
b. Establish clearly the speaker's relationship with that subject (e.g., dispassionate observation, personal involvement).
c. Use effective, factual descriptions of appearance, concrete images, shifting perspectives and vantage points, and sensory details.

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Grades Eleven & Twelve
English-language Arts Content Standards

Reading
1.0 Word Analysis, Fluency, and Systematic Vocabulary Development
Students apply their knowledge of word origins to determine the meaning of new words encountered in reading materials and use those words accurately.

Vocabulary and Concept Development
1.1 Trace the etymology of significant terms used in political science and history.
1.2 Apply knowledge of Greek, Latin, and Anglo-Saxon roots and affixes to draw inferences concerning the meaning of scientific and mathematical terminology.
1.3 Discern the meaning of analogies encountered, analyzing specific comparisons as well as relationships and inferences.

2.0 Reading Comprehension (Focus on Informational Materials)
Students read and understand grade-level-appropriate material. They analyze the organizational patterns, arguments, and positions advanced. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students. In addition, by grade twelve, students read two million words annually on their own, including a wide variety of classic and contemporary literature, magazines, newspapers, and online information.

Structural Features of Informational Materials
2.1 Analyze both the features and the rhetorical devices of different types of public documents (e.g., policy statements, speeches, debates, platforms) and the way in which authors use those features and devices.

Comprehension and Analysis of Grade-Level-Appropriate Text
2.2 Analyze the way in which clarity of meaning is affected by the patterns of organization, hierarchical structures, repetition of the main ideas, syntax, and word choice in the text.
2.3 Verify and clarify facts presented in other types of expository texts by using a variety of consumer, workplace, and public documents.
2.4 Make warranted and reasonable assertions about the author's arguments by using elements of the text to defend and clarify interpretations.
2.5 Analyze an author's implicit and explicit philosophical assumptions and beliefs about a subject.

Expository Critique
2.6 Critique the power, validity, and truthfulness of arguments set forth in public documents; their appeal to both friendly and hostile audiences; and the extent to which the arguments anticipate and address reader concerns and counterclaims (e.g., appeal to reason, to authority, to pathos and emotion).

3.0 Literary Response and Analysis
Students read and respond to historically or culturally significant works of literature that reflect and enhance their studies of history and social science. They conduct in-depth analyses of recurrent themes. The selections in Recommended Literature, Kindergarten Through Grade Twelve illustrate the quality and complexity of the materials to be read by students.

Structural Features of Literature
3.1 Analyze characteristics of subgenres (e.g., satire, parody, allegory, pastoral) that are used in poetry, prose, plays, novels, short stories, essays, and other basic genres.

Narrative Analysis of Grade-Level-Appropriate Text
3.2 Analyze the way in which the theme or meaning of a selection represents a view or comment on life, using textual evidence to support the claim.

3.3 Analyze the ways in which irony, tone, mood, the author's style, and the "sound" of language achieve specific rhetorical or aesthetic purposes or both.

3.4 Analyze ways in which poets use imagery, personification, figures of speech, and sounds to evoke readers' emotions.

3.5 Analyze recognized works of American literature representing a variety of genres and traditions:
a. Trace the development of American literature from the colonial period forward.
b. Contrast the major periods, themes, styles, and trends and describe how works by members of different cultures relate to one another in each period.
c. Evaluate the philosophical, political, religious, ethical, and social influences of the historical period that shaped the characters, plots, and settings.

3.6 Analyze the way in which authors through the centuries have used archetypes drawn from myth and tradition in literature, film, political speeches, and religious writings (e.g., how the archetypes of banishment from an ideal world may be used to interpret Shakespeare's tragedy Macbeth).

3.7 Analyze recognized works of world literature from a variety of authors:
a. Contrast the major literary forms, techniques, and characteristics of the major literary periods (e.g., Homeric Greece, medieval, romantic, neoclassic, modern).
b. Relate literary works and authors to the major themes and issues of their eras.
c. Evaluate the philosophical, political, religious, ethical, and social influences of the historical period that shaped the characters, plots, and settings.

Literary Criticism
3.8 Analyze the clarity and consistency of political assumptions in a selection of literary works or essays on a topic (e.g., suffrage, women's role in organized labor). (Political approach)
3.9 Analyze the philosophical arguments presented in literary works to determine whether the authors' positions have contributed to the quality of each work and the credibility of the characters. (Philosophical approach)

Writing
1.0 Writing Strategies
Students write coherent and focused texts that convey a well-defined perspective and tightly reasoned argument. The writing demonstrates students' awareness of the audience and purpose and progression through the stages of the writing process.

Organization and Focus
1.1 Demonstrate an understanding of the elements of discourse (e.g., purpose, speaker, audience, form) when completing narrative, expository, persuasive, or descriptive writing assignments.
1.2 Use point of view, characterization, style (e.g., use of irony), and related elements for specific rhetorical and aesthetic purposes.
1.3 Structure ideas and arguments in a sustained, persuasive, and sophisticated way and support them with precise and relevant examples.
1.4 Enhance meaning by employing rhetorical devices, including the extended use of parallelism, repetition, and analogy; the incorporation of visual aids (e.g., graphs, tables, pictures); and the issuance of a call for action.
1.5 Use language in natural, fresh, and vivid ways to establish a specific tone.

Research and Technology
1.6 Develop presentations by using clear research questions and creative and critical research strategies (e.g., field studies, oral histories, interviews, experiments, electronic sources).
1.7 Use systematic strategies to organize and record information (e.g., anecdotal scripting, annotated bibliographies).
1.8 Integrate databases, graphics, and spreadsheets into word-processed documents.

Evaluation and Revision
1.9 Revise text to highlight the individual voice, improve sentence variety and style, and enhance subtlety of meaning and tone in ways that are consistent with the purpose, audience, and genre.

2.0 Writing Applications (Genres and Their Characteristics)
Students combine the rhetorical strategies of narration, exposition, persuasion, and description to produce texts of at least 1,500 words each. Student writing demonstrates a command of standard American English and the research, organizational, and drafting strategies outlined in Writing Standard 1.0.

Using the writing strategies of grades eleven and twelve outlined in Writing Standard 1.0, students:

2.1 Write fictional, autobiographical, or biographical narratives:
a. Narrate a sequence of events and communicate their significance to the audience.
b. Locate scenes and incidents in specific places.
c. Describe with concrete sensory details the sights, sounds, and smells of a scene and the specific actions, movements, gestures, and feelings of the characters; use interior monologue to depict the characters' feelings.
d. Pace the presentation of actions to accommodate temporal, spatial, and dramatic mood changes.
e. Make effective use of descriptions of appearance, images, shifting perspectives, and sensory details.

2.2 Write responses to literature:
a. Demonstrate a comprehensive understanding of the significant ideas in works or passages.
b. Analyze the use of imagery, language, universal themes, and unique aspects of the text.
c. Support important ideas and viewpoints through accurate and detailed references to the text and to other works.
d. Demonstrate an understanding of the author's use of stylistic devices and an appreciation of the effects created.
e. Identify and assess the impact of perceived ambiguities, nuances, and complexities within the text.

2.3 Write reflective compositions:
a. Explore the significance of personal experiences, events, conditions, or concerns by using rhetorical strategies (e.g., narration, description, exposition, persuasion).
b. Draw comparisons between specific incidents and broader themes that illustrate the writer's important beliefs or generalizations about life.
c. Maintain a balance in describing individual incidents and relate those incidents to more general and abstract ideas.

2.4 Write historical investigation reports:
a. Use exposition, narration, description, argumentation, or some combination of rhetorical strategies to support the main proposition.
b. Analyze several historical records of a single event, examining critical relationships between elements of the research topic.
c. Explain the perceived reason or reasons for the similarities and differences in historical records with information derived from primary and secondary sources to support or enhance the presentation.
d. Include information from all relevant perspectives and take into consideration the validity and reliability of sources.
e. Include a formal bibliography.

2.5 Write job applications and résumés:
a. Provide clear and purposeful information and address the intended audience appropriately.
b. Use varied levels, patterns, and types of language to achieve intended effects and aid comprehension.
c. Modify the tone to fit the purpose and audience.
d. Follow the conventional style for that type of document (e.g., résumé, memorandum) and use page formats, fonts, and spacing that contribute to the readability and impact of the document.

2.6 Deliver multimedia presentations:
a. Combine text, images, and sound and draw information from many sources (e.g., television broadcasts, videos, films, newspapers, magazines, CD-ROMs, the Internet, electronic media-generated images).
b. Select an appropriate medium for each element of the presentation.
c. Use the selected media skillfully, editing appropriately and monitoring for quality.
d. Test the audience's response and revise the presentation accordingly.

Written and Oral English Language Conventions
The standards for written and oral English language conventions have been placed between those for writing and for listening and speaking because these conventions are essential to both sets of skills.

1.0 Written and Oral English Language Conventions
Students write and speak with a command of standard English conventions.

1.1 Demonstrate control of grammar, diction, and paragraph and sentence structure and an understanding of English usage.
1.2 Produce legible work that shows accurate spelling and correct punctuation and capitalization.
1.3 Reflect appropriate manuscript requirements in writing.

Listening and Speaking
1.0 Listening and Speaking Strategies
Students formulate adroit judgments about oral communication. They deliver focused and coherent presentations that convey clear and distinct perspectives and demonstrate solid reasoning. They use gestures, tone, and vocabulary tailored to the audience and purpose.

Comprehension
1.1 Recognize strategies used by the media to inform, persuade, entertain, and transmit culture (e.g., advertisements; perpetuation of stereotypes; use of visual representations, special effects, language).
1.2 Analyze the impact of the media on the democratic process (e.g., exerting influence on elections, creating images of leaders, shaping attitudes) at the local, state, and national levels.
1.3 Interpret and evaluate the various ways in which events are presented and information is communicated by visual image makers (e.g., graphic artists, documentary filmmakers, illustrators, news photographers).

Organization and Delivery of Oral Communication
1.4 Use rhetorical questions, parallel structure, concrete images, figurative language, characterization, irony, and dialogue to achieve clarity, force, and aesthetic effect.

1.5 Distinguish between and use various forms of classical and contemporary logical arguments, including:
a. Inductive and deductive reasoning
b. Syllogisms and analogies

1.6 Use logical, ethical, and emotional appeals that enhance a specific tone and purpose.

1.7 Use appropriate rehearsal strategies to pay attention to performance details, achieve command of the text, and create skillful artistic staging.

1.8 Use effective and interesting language, including:
a. Informal expressions for effect
b. Standard American English for clarity
c. Technical language for specificity

1.9 Use research and analysis to justify strategies for gesture, movement, and vocalization, including dialect, pronunciation, and enunciation.

1.10 Evaluate when to use different kinds of effects (e.g., visual, music, sound, graphics) to create effective productions.

Analysis and Evaluation of Oral and Media Communications
1.11 Critique a speaker's diction and syntax in relation to the purpose of an oral communication and the impact the words may have on the audience.
1.12 Identify logical fallacies used in oral addresses (e.g., attack ad hominem, false causality, red herring, overgeneralization, bandwagon effect).
1.13 Analyze the four basic types of persuasive speech (i.e., propositions of fact, value, problem, or policy) and understand the similarities and differences in their patterns of organization and the use of persuasive language, reasoning, and proof.
1.14 Analyze the techniques used in media messages for a particular audience and evaluate their effectiveness (e.g., Orson Welles' radio broadcast "War of the Worlds").

2.0 Speaking Applications (Genres and Their Characteristics)
Students deliver polished formal and extemporaneous presentations that combine traditional rhetorical strategies of narration, exposition, persuasion, and description. Student speaking demonstrates a command of standard American English and the organizational and delivery strategies outlined in Listening and Speaking Standard 1.0.

Using the speaking strategies of grades eleven and twelve outlined in Listening and Speaking Standard 1.0, students:

2.1 Deliver reflective presentations:
a. Explore the significance of personal experiences, events, conditions, or concerns, using appropriate rhetorical strategies (e.g., narration, description, exposition, persuasion).
b. Draw comparisons between the specific incident and broader themes that illustrate the speaker's beliefs or generalizations about life.
c. Maintain a balance between describing the incident and relating it to more general, abstract ideas.

2.2 Deliver oral reports on historical investigations:
a. Use exposition, narration, description, persuasion, or some combination of those to support the thesis.
b. Analyze several historical records of a single event, examining critical relationships between elements of the research topic.
c. Explain the perceived reason or reasons for the similarities and differences by using information derived from primary and secondary sources to support or enhance the presentation.
d. Include information on all relevant perspectives and consider the validity and reliability of sources.

2.3 Deliver oral responses to literature:
a. Demonstrate a comprehensive understanding of the significant ideas of literary works (e.g., make assertions about the text that are reasonable and supportable).
b. Analyze the imagery, language, universal themes, and unique aspects of the text through the use of rhetorical strategies (e.g., narration, description, persuasion, exposition, a combination of those strategies).
c. Support important ideas and viewpoints through accurate and detailed references to the text or to other works.
d. Demonstrate an awareness of the author's use of stylistic devices and an appreciation of the effects created.
e. Identify and assess the impact of perceived ambiguities, nuances, and complexities within the text.

2.4 Deliver multimedia presentations:
a. Combine text, images, and sound by incorporating information from a wide range of media, including films, newspapers, magazines, CD-ROMs, online information, television, videos, and electronic media-generated images.
b. Select an appropriate medium for each element of the presentation.
c. Use the selected media skillfully, editing appropriately and monitoring for quality.
d. Test the audience's response and revise the presentation accordingly.

2.5 Recite poems, selections from speeches, or dramatic soliloquies with attention to performance details to achieve clarity, force, and aesthetic effect and to demonstrate an understanding of the meaning (e.g., Hamlet's soliloquy "To Be or Not to Be").

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Glossary
English-language Arts Content Standards.

active voice. A verb form in which the subject of the verb carries out some action. Example: He hit the ball.

affix. A bound (nonword) morpheme that changes the meaning or function of a root or stem to which it is attached, such as the prefix ad- and the suffix -ing in adjoining.

alliteration. The repetition of the same sound, usually of a consonant, at the beginning of two or more words immediately succeeding each other or at short intervals. Example: The repetition of f and g in fields ever fresh, groves ever green

alphabetic principle. The assumption underlying alphabetic writing systems that each speech sound or phoneme of a language should have its own distinctive graphic representation.

analogy. A resemblance in some particulars between things otherwise unlike.

anecdotal scripting. The systematic recording of behavioral incidents cited in a literary work for purposes of organization and clarity.

annotated bibliography. The inclusion of additional comments in the works listed in the standard bibliography.

antecedent. A word, phrase, or clause to which a following pronoun refers. Example: Iris tried, but she couldn't find the book. Iris is the antecedent of she.

appeal to reason. A call upon the reader's faculty to think in a rational way to persuade his or her thoughts.

appeal to authority. A call upon an individual or other source as an expert to strengthen an argument made by the author of a work.

appeal to emotion. The ad populum approach is a common fallacy in arguments. Instead of presenting evidence in an argument, it relies on expressive language and other devices calculated to incite enthusiasm, excitement, anger, or hatred.

appeal to pathos (pity). A common fallacy in arguments, the ad misericordiam approach is a special case of the appeal to emotion in which the altruism and mercy of the audience are the special emotions to which the speaker appeals.

appositive. A word or phrase that restates or modifies an immediately preceding noun. Note: An appositive is often useful as a context clue for determining or refining the meaning of the word or words to which it refers. Example: My son Enrico (appositive) is twelve years old.

archetypal criticism. The study of apparent perennial images, themes, symbols, stories, and myths in literature, including narratives that unite the seasons with literary genres.

archetype. The original pattern or model of which all things of the same type are representations or copies; a perfect example.

attack. ad hominem. An attack "against the man"; a fallacious attack in which the thrust is directed, not at the conclusion one wishes to deny, but at the person who asserts or defends it.

bandwagon. A popular party, faction, or cause that attracts growing support; a current or fashionable trend.

base word. A word to which affixes may be added to create related words. Example: Teach in reteach or teaching.

blend. A combination of sounds represented by letters to pronounce a word; sounding out the joining of the sounds represented by two or more letters with minimal change in those sounds, such as the consonant cluster in /gr/ in grow, /spl/ in splash.

boundary. A division between units of a language, such as between words, word parts, or syllables.

climax. The point of highest dramatic tension or a major turning point in the action (such as in a play, story, or other literary composition).

clustering. A content field technique or strategy to help students freely associate ideas in their experience with a keyword proposed by the teacher, thus forming a group of related concepts; a teaching process of relating a target word to a set of synonyms and other word associations. Note: Clustering may be used to stimulate the recall of related ideas in reading and writing, especially in prewriting.

complement. The word (or words) that completes the action in the predicate of a sentence; to complete a grammatical construction in this way. Example: Tom is a policeman (complement).

compound sentence. A sentence consisting of two or more coordinate independent clauses. Example: George talked and Harry listened.

concrete image. A literal representation of a sensory experience or of an object that can be known by more than one of the senses; representation that involves no necessary change or extension in the obvious meaning of the words; the words call up a sensory representation of the literal object or sensation.

consonant doubling. The addition of a consonant in the formation of some gerunds and participles. Example: Running.

context clues. The information from the immediate textual setting that helps identify a word for decoding (sounding out) and words being read for the first time. The reader's speaking vocabulary is a back-up strategy and is primarily useful to resolve ambiguity (is bread pronounced bred or breed?) and to confirm the accuracy of decoding (does it make sense and does it sound right?). The context helps resolve which shade of meaning is intended (prog-ress or pro-gress) and is used for learning the meaning of new words that can be decoded or pronounced but are not yet in the reader's speaking vocabulary; it is a primary strategy.

decoding. The ability and willingness to sound out words by generating all the sounds into a recognizable word (technically called phonological recoding). The ability to get the meaning of a word quickly, effortlessly, and unconsciously after a brief visual scan, such as in automaticity with individual words (which is the product of initial phonological decoding, followed by the reading of that word successfully several times, preferably in text, until the neural connections among the letters, the sounds, and the meaning of the word are fully established).

denouement. The final outcome of the main dramatic event in a literary work.

description. One of the four traditional forms of composition in speech and writing, it is meant to give a verbal picture of the character and event, including the setting.

digraphs. Two letters that represent one speech sound, such as ch for /ch/ in chin or ea for /e/ in bread.

discourse. A conversation; the act or result of making a formal written or spoken presentation on a subject; in linguistics, any form of oral or written communication more extensive than a sentence.

etymology. The history of words; the study of the history of words.

exposition. One of the four traditional forms of composition in speech and writing, it is intended to set forth or explain. Note: Good exposition is clear in conception, well organized, and understandable. It may include limited amounts of argumentation, description, and narration to achieve that purpose.

expressive writing. Highly personal writing, such as in diaries, personal letters, and autobiographies.

false causality. Any reasoning that relies upon treating as the cause of a thing that which is not really its cause (e. g., the error of concluding that an event is caused by another simply because it follows that other).

fluency. The clear, easy, written or spoken expression of ideas; freedom from word-identification problems that might hinder comprehension in silent reading or the expression of ideas in oral reading; automaticity; the ability to execute motor movements smoothly, easily, and readily.

high-frequency words. A word that appears many more times than most other words in spoken or written language. Note: Basic word lists generally provide words ranked in order of their frequency of occurrence as calculated from a sample of written or spoken text suitable for the level of intended use.

historical investigation.
(reports). The techniques used by historians to reconstruct and interpret the past. Note: The data for historical research are the spoken, written, and printed sources or other material originating from those who participated in or witnessed the events studied; the historian must evaluate these data for authenticity, bias, and generalizability and draw conclusions from them.

homograph. A word with the same spelling as another word but having a different meaning or sometimes a different pronunciation. Example: Bow, as in bow and arrow compared to bow of a ship.

homophone. A word with a different origin and meaning but having the same pronunciation as another word whether or not spelled alike. Example: Hair and hare; scale, as in scale of a fish compared to scale a ladder. Also two or more graphemes that represent the same sound. Example: The /k/ sound in /c/ andy, k/ ing, and s/ ch/ ool.

idiom. A use of words peculiar to a particular language.

initial consonants
. (initial blends). The joining of two or more consonant sounds, represented by letters, that begin a word without losing the identity of the sounds, such as /bl/ in black, /skr/ in scramble; the joining of the first consonant and vowel sounds in a word, such as /b/ and /a/ in baby. Note: This process is regarded by some to be a crucial step in learning phonics.

irregularity. An exception to a linguistic pattern or rule. Example: Good, better, and best are exceptions to the usual -er, -est pattern of comparatives and superlatives in English.

literary analysis. The study of a literary work by a critic, student, or scholar; a careful, detailed reading and report thereof.

literary criticism. The analysis and judgment of works of literature. The body of principles by which the work of writers is judged. Note: The principles used in judging a literary work vary from the highly personal and subjective to the relatively objective; they may involve but are not limited to specific consideration of moral values, historical accuracy, and literary form and type; they may be different from one literary period to another.

main idea. The gist of a passage; central thought; the chief topic of a passage expressed or implied in a word or phrase; the topic sentence of a paragraph; a statement that gives the explicit or implied major topic of a passage and the specific way in which the passage is limited in content or reference.

media sources. The means of communication, especially of mass communication, such as books, newspapers, magazines, radio, television, motion pictures, recordings.

metaphor. A figure of speech in which a word or phrase literally denoting one kind of object or idea is used in place of another to suggest a likeness between them. Example: He was drowning in money.

narration. One of the four traditional forms of composition in speech and writing, it tells a story or gives an account of something dealing with sequences of events and experiences, though not necessarily in strict order.

nonverbal. A nonlanguage communication, such as a noise, gesture, or facial expression.

nonsense syllable. A pronounceable combination of graphic characters, usually trigrams, that do not make a word, such as kak, vor, mek, pronounced in English as spellings. Note: Nonsense syllables are sometimes used in reading to test phonics knowledge; they are sometimes used in spelling to test for desired syllabic patterns while avoiding known words.

onomatopoeia. The term used to describe words whose pronunciations suggest their meaning (e. g., meow, buzz).

oral histories. The stories and histories kept alive by the spoken word rather than the written word. Note: Although an oral tradition is characteristic of an oral culture, it may coexist in a writing culture.

orthography. The study of the nature and use of symbols in a writing system; correct or standardized spelling according to established usage in a given language.

parallelism. The phrasing of language so as to balance ideas of equal importance. Note: Parallelism may apply to phrases, sentences, paragraphs, longer passages, or whole selections.

passive voice. A verb form in which the subject of the verb is the receiver of some action or state indicated by the verb. Example: He was hit by the ball.

persuasion. One of the four traditional forms of composition in speech and writing, it is meant to move the reader by argument or entreaty to a belief or position.

phoneme. A minimal sound unit of speech that, when contrasted with another phoneme, affects the naming of words in a language, such as /b/ in book contrasts with /t/ in took, /k/ in cook, /h/ in hook. Note: The phoneme is an abstract concept manifested in actual speech as a phonetic variant, such as the allophones of the phoneme /t/ in top, stop, pot.

phonemic awareness. The awareness of the sounds (phonemes) that make up spoken words. Such awareness does not appear when young children learn to talk; the ability is not necessary for speaking and understanding spoken language; however, phonemic awareness is important for learning to read. In alphabetic languages, letters (and letter clusters) represent phonemes; to learn the correspondences between letters and sounds, one must have some understanding of the notion that words are made up of phonemes.

phonics. A system of teaching reading and spelling that stresses basic symbol-sound relationships and their application in decoding words; a system used especially in beginning instruction.

phonogram. A graphic character or symbol that may represent a phonetic sound, phoneme, or word; in word recognition, a graphic sequence composed of a vowel grapheme and an ending consonant grapheme, such as -ed in red, bed, fed.

prewriting. The initial creative stage of writing, prior to drafting, in which the writer formulates ideas, gathers information, and considers ways in which to organize the information; planning.

principal parts of verbs. The principal parts; the set of inflected forms of a grammatical class, such as sing, sang, sung.

prior knowledge. The knowledge that stems from previous experience. Note: Prior knowledge is a major component of schema theories of reading comprehension in spite of the redundancy inherent in the term.

r-. controlled sound. The modified sound of a vowel immediately preceding /r/ in the same syllable, such as in care, never, sir, or curse.

red herring. A distractor that draws attention away from the real issue.

rhetorical strategies. The traditional forms of composition in speech and writing: exposition, narration, persuasion, and description (each is defined in this glossary).

root word. The meaningful base form of a complex word after all affixes are removed. Note: A root may be independent or free, such as read in unreadable, or may be dependent, or bound, such as -liter- (from the Greek for letter) in illiterate.

sentences:
declarative. A sentence that makes a statement.
exclamatory. A sentence that makes a vehement statement or conveys strong or sudden emotion.
imperative. A sentence that expresses a command or request.
interrogative. A sentence that asks a question or makes an inquiry.

sight word. A word that is immediately recognized as a whole and does not require word analysis for identification.

standard American English. The language in which most educational texts and government and media publications are written in the United States. Note: Standard American English, a relative concept, varies widely in pronunciation and in idiomatic use but maintains a fairly uniform grammatical structure.

syllabication. The division of words into syllables (the minimal units of sequential speech sounds composed of a vowel sound or a vowel-consonant combination, such as /a/, /ba/, /ab/, /bab/).

theme. A topic of discussion or writing; a major idea or proposition broad enough to cover the entire scope of a literary or other work of art. Note: A theme may be stated or implicit, but clues to it may be found in the ideas that are given special prominence or tend to recur in a work.

thesis. The basic argument advanced by a speaker or writer who then attempts to prove it; the subject or major argument of a speech or composition.

topic. The general category or class of ideas, often stated in a word or phrase, to which the ideas of a passage as a whole belong.

topic sentence. A sentence intended to express the main idea in a paragraph or passage.

transitive verb. A verb that takes a direct object. Example: Francesca read (transitive verb) the book.

voice. A syntactic pattern that indicates the verb-subject relationship; the principal voices in English and many other languages are active and passive.

word recognition. The process of determining the pronunciation and some degree of meaning of a word in written or printed form; the quick and easy identification of the form, pronunciation, and appropriate meaning of a word previously encountered in print or writing.

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Kindergarten
Mathematics Content Standards

By the end of kindergarten, students understand small numbers, quantities, and simple shapes in their everyday environment. They count, compare, describe and sort objects, and develop a sense of properties and patterns.

Number Sense
1.0 Students understand the relationship between numbers and quantities (i.e., that a set of objects has the same number of objects in different situations regardless of its position or arrangement):

1.1 Compare two or more sets of objects (up to ten objects in each group) and identify which set is equal to, more than, or less than the other.

1.2 Count, recognize, represent, name, and order a number of objects (up to 30).

1.3 Know that the larger numbers describe sets with more objects in them than the smaller numbers have.

2.0 Students understand and describe simple additions and subtractions:

2.1 Use concrete objects to determine the answers to addition and subtraction problems (for two numbers that are each less than 10).

3.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones and tens places:

3.1 Recognize when an estimate is reasonable.

Algebra and Functions
1.0 Students sort and classify objects:

1.1 Identify, sort, and classify objects by attribute and identify objects that do not belong to a particular group (e.g., all these balls are green, those are red).

Measurement and Geometry
1.0 Students understand the concept of time and units to measure it; they understand that objects have properties, such as length, weight, and capacity, and that comparisons may be made by referring to those properties:

1.1 Compare the length, weight, and capacity of objects by making direct comparisons with reference objects (e.g., note which object is shorter, longer, taller, lighter, heavier, or holds more).

1.2 Demonstrate an understanding of concepts of time (e.g., morning, afternoon, evening, today, yesterday, tomorrow, week, year) and tools that measure time (e.g., clock, calendar).

1.3 Name the days of the week.

1.4 Identify the time (to the nearest hour) of everyday events (e.g., lunch time is 12 o'clock; bedtime is 8 o'clock at night).

2.0 Students identify common objects in their environment and describe the geometric features:

2.1 Identify and describe common geometric objects (e.g., circle, triangle, square, rectangle, cube, sphere, cone).

2.2 Compare familiar plane and solid objects by common attributes (e.g., position, shape, size, roundness, number of corners).

Statistics, Data Analysis, and Probability
1.0 Students collect information about objects and events in their environment:

1.1 Pose information questions; collect data; and record the results using objects, pictures, and picture graphs.

1.2 Identify, describe, and extend simple patterns (such as circles or triangles) by referring to their shapes, sizes, or colors.

Mathematical Reasoning
1.0 Students make decisions about how to set up a problem:

1.1 Determine the approach, materials, and strategies to be used.

1.2 Use tools and strategies, such as manipulatives or sketches, to model problems.

2.0 Students solve problems in reasonable ways and justify their reasoning:

2.1 Explain the reasoning used with concrete objects and/ or pictorial representations.

2.2 Make precise calculations and check the validity of the results in the context of the problem.

___________________________________________________________________________________________________

Grade One
Mathematics Content Standards

By the end of grade one, students understand and use the concept of ones and tens in the place value number system. Students add and subtract small numbers with ease. They measure with simple units and locate objects in space. They describe data and analyze and solve simple problems.

Number Sense
1.0 Students understand and use numbers up to 100:

1.1 Count, read, and write whole numbers to 100.

1.2 Compare and order whole numbers to 100 by using the symbols for less than, equal to, or greater than (<, =, >).

1.3 Represent equivalent forms of the same number through the use of physical models, diagrams, and number expressions (to 20) (e.g., 8 may be represented as 4 + 4, 5 + 3, 2 + 2 + 2 + 2, 10 -2, 11 -3).

1.4 Count and group object in ones and tens (e.g., three groups of 10 and 4 equals 34, or 30 + 4).

1.5 Identify and know the value of coins and show different combinations of coins that equal the same value.

2.0 Students demonstrate the meaning of addition and subtraction and use these operations to solve problems:

2.1 Know the addition facts (sums to 20) and the corresponding subtraction facts and commit them to memory.

2.2 Use the inverse relationship between addition and subtraction to solve problems.

2.3 Identify one more than, one less than, 10 more than, and 10 less than a given number.

2.4 Count by 2s, 5s, and 10s to 100.

2.5 Show the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, finding the difference).

2.6 Solve addition and subtraction problems with one-and two-digit numbers (e.g., 5 + 58 = __).

2.7 Find the sum of three one-digit numbers.

3.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, and hundreds places:

3.1 Make reasonable estimates when comparing larger or smaller numbers.

Algebra and Functions
1.0 Students use number sentences with operational symbols and expressions to solve problems:

1.1 Write and solve number sentences from problem situations that express relationships involving addition and subtraction.

1.2 Understand the meaning of the symbols +, -, =.

1.3 Create problem situations that might lead to given number sentences involving addition and subtraction.

Measurement and Geometry
1.0 Students use direct comparison and nonstandard units to describe the measurements of objects:

1.1 Compare the length, weight, and volume of two or more objects by using direct comparison or a nonstandard unit.

1.2 Tell time to the nearest half hour and relate time to events (e.g., before/after, shorter/longer).

2.0 Students identify common geometric figures, classify them by common attributes, and describe their relative position or their location in space:

2.1 Identify, describe, and compare triangles, rectangles, squares, and circles, including the faces of three-dimensional objects.

2.2 Classify familiar plane and solid objects by common attributes, such as color, position, shape, size, roundness, or number of corners, and explain which attributes are being used for classification.

2.3 Give and follow directions about location.

2.4 Arrange and describe objects in space by proximity, position, and direction (e.g., near, far, below, above, up, down, behind, in front of, next to, left or right of).

Statistics, Data Analysis, and Probability
1.0 Students organize, represent, and compare data by category on simple graphs and charts:

1.1 Sort objects and data by common attributes and describe the categories.

1.2 Represent and compare data (e.g., largest, smallest, most often, least often) by using pictures, bar graphs, tally charts, and picture graphs.

2.0 Students sort objects and create and describe patterns by numbers, shapes, sizes, rhythms, or colors:

2.1 Describe, extend, and explain ways to get to a next element in simple repeating patterns (e.g., rhythmic, numeric, color, and shape).

Mathematical Reasoning
1.0 Students make decisions about how to set up a problem:

1.1 Determine the approach, materials, and strategies to be used.

1.2 Use tools, such as manipulatives or sketches, to model problems.

2.0 Students solve problems and justify their reasoning:

2.1 Explain the reasoning used and justify the procedures selected.

2.2 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students note connections between one problem and another.
_______________________________________________________________________________________________________

Grade Two
Mathematics Content Standards

By the end of grade two, students understand place value and number relationships in addition and subtraction, and they use simple concepts of multiplication. They measure quantities with appropriate units. They classify shapes and see relationships among them by paying attention to their geometric attributes. They collect and analyze data and verify the answers.

Number Sense
1.0 Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000:
1.1 Count, read, and write whole numbers to 1,000 and identify the place value for each digit.

1.2 Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000).

1.3 Order and compare whole numbers to 1,000 by using the symbols <, =, >.

2.0 Students estimate, calculate, and solve problems involving addition and subtraction of two-and three-digit numbers:
2.1 Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 14 is 14 - 6 = 8) to solve problems and check solutions.

2.2 Find the sum or difference of two whole numbers up to three digits long.

2.3 Use mental arithmetic to find the sum or difference of two two-digit numbers.

3.0 Students model and solve simple problems involving multiplication and division:
3.1 Use repeated addition, arrays, and counting by multiples to do multiplication.

3.2 Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division.

3.3 Know the multiplication tables of 2s, 5s, and 10s (to "times 10") and commit them to memory.

4.0 Students understand that fractions and decimals may refer to parts of a set and parts of a whole:
4.1 Recognize, name, and compare unit fractions from 1/12 to 1/2.

4.2 Recognize fractions of a whole and parts of a group (e.g., one-fourth of a pie, two-thirds of 15 balls).

4.3 Know that when all fractional parts are included, such as four-fourths, the result is equal to the whole and to one.

5.0 Students model and solve problems by representing, adding, and subtracting amounts of money:
5.1 Solve problems using combinations of coins and bills.

5.2 Know and use the decimal notation and the dollar and cent symbols for money.

6.0 Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places:
6.1 Recognize when an estimate is reasonable in measurements (e.g., closest inch).

Algebra and Functions
1.0 Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction:
1.1 Use the commutative and associative rules to simplify mental calculations and to check results.

1.2 Relate problem situations to number sentences involving addition and subtraction.

1.3 Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences.

Measurement and Geometry
1.0 Students understand that measurement is accomplished by identifying a unit of measure, iterating (repeating) that unit, and comparing it to the item to be measured:
1.1 Measure the length of objects by iterating (repeating) a nonstandard or standard unit.

1.2 Use different units to measure the same object and predict whether the measure will be greater or smaller when a different unit is used.

1.3 Measure the length of an object to the nearest inch and/ or centimeter.

1.4 Tell time to the nearest quarter hour and know relationships of time (e.g., minutes in an hour, days in a month, weeks in a year).

1.5 Determine the duration of intervals of time in hours (e.g., 11:00 a.m. to 4:00 p.m.).

2.0 Students identify and describe the attributes of common figures in the plane and of common objects in space:
2.1 Describe and classify plane and solid geometric shapes (e.g., circle, triangle, square, rectangle, sphere, pyramid, cube, rectangular prism) according to the number and shape of faces, edges, and vertices.

2.2 Put shapes together and take them apart to form other shapes (e.g., two congruent right triangles can be arranged to form a rectangle).

Statistics, Data Analysis, and Probability
1.0 Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations:
1.1 Record numerical data in systematic ways, keeping track of what has been counted.

1.2 Represent the same data set in more than one way (e.g., bar graphs and charts with tallies).

1.3 Identify features of data sets (range and mode).

1.4 Ask and answer simple questions related to data representations.

2.0 Students demonstrate an understanding of patterns and how patterns grow and describe them in general ways:
2.1 Recognize, describe, and extend patterns and determine a next term in linear patterns (e.g., 4, 8, 12 ...; the number of ears on one horse, two horses, three horses, four horses).

2.2 Solve problems involving simple number patterns.

Mathematical Reasoning
1.0 Students make decisions about how to set up a problem:
1.1 Determine the approach, materials, and strategies to be used.

1.2 Use tools, such as manipulatives or sketches, to model problems.

2.0 Students solve problems and justify their reasoning:
2.1 Defend the reasoning used and justify the procedures selected.

2.2 Make precise calculations and check the validity of the results in the context of the problem.

3.0 Students note connections between one problem and another.

_____________________________________________________________________________________________________

Grade Three
Mathematics Content Standards

By the end of grade three, students deepen their understanding of place value and their understanding of and skill with addition, subtraction, multiplication, and division of whole numbers. Students estimate, measure, and describe objects in space. They use patterns to help solve problems. They represent number relationships and conduct simple probability experiments.

Number Sense
1.0 Students understand the place value of whole numbers:
1.1 Count, read, and write whole numbers to 10,000.

1.2 Compare and order whole numbers to 10,000.

1.3 Identify the place value for each digit in numbers to 10,000.

1.4 Round off numbers to 10,000 to the nearest ten, hundred, and thousand.

1.5 Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).

2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.1 Find the sum or difference of two whole numbers between 0 and 10,000.

2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10.

2.3 Use the inverse relationship of multiplication and division to compute and check results.

2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers (3,671 x 3 = __).

2.5 Solve division problems in which a multidigit number is evenly divided by a one-digit number (135 ÷ 5 = __).

2.6 Understand the special properties of 0 and 1 in multiplication and division.

2.7 Determine the unit cost when given the total cost and number of units.

2.8 Solve problems that require two or more of the skills mentioned above.

3.0 Students understand the relationship between whole numbers, simple fractions, and decimals:
3.1 Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than 1/4).

3.2 Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2).

3.3 Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amounts in decimal notation by using whole-number multipliers and divisors.

3.4 Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is 3/4 of a dollar).

Algebra and Functions
1.0 Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships:
1.1 Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities.

1.2 Solve problems involving numeric equations or inequalities.

1.3 Select appropriate operational and relational symbols to make an expression true
(e.g., if 4 __ 3 = 12, what operational symbol goes in the blank?).

1.4 Express simple unit conversions in symbolic form
(e.g., __ inches = __ feet x 12).

1.5 Recognize and use the commutative and associative properties of multiplication
(e.g., if 5 x 7 = 35, then what is 7 x 5? and if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?).

2.0 Students represent simple functional relationships:
2.1 Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit).

2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4).

Measurement and Geometry
1.0 Students choose and use appropriate units and measurement tools to quantify the properties of objects:
1.1 Choose the appropriate tools and units (metric and U.S.) and estimate and measure the length, liquid volume, and weight/mass of given objects.

1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them.

1.3 Find the perimeter of a polygon with integer sides.

1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes).

2.0 Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems:
2.1 Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).

2.2 Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle).

2.3 Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square).

2.4 Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle.

2.5 Identify, describe, and classify common three-dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).

2.6 Identify common solid objects that are the components needed to make a more complex solid object.

Statistics, Data Analysis, and Probability
1.0 Students conduct simple probability experiments by determining the number of possible outcomes and make simple predictions:
1.1 Identify whether common events are certain, likely, unlikely, or improbable.

1.2 Record the possible outcomes for a simple event (e.g., tossing a coin) and systematically keep track of the outcomes when the event is repeated many times.

1.3 Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot).

1.4 Use the results of probability experiments to predict future events (e.g., use a line plot to predict the temperature forecast for the next day).

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

1.2 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.

2.2 Apply strategies and results from simpler problems to more complex problems.

2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.6 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.

3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

3.3 Develop generalizations of the results obtained and apply them in other circumstances.

_______________________________________________________________________________________________________
Grade Four
Mathematics Content Standards

By the end of grade four, students understand large numbers and addition, subtraction, multiplication, and division of whole numbers. They describe and compare simple fractions and decimals. They understand the properties of, and the relationships between, plane geometric figures. They collect, represent, and analyze data to answer questions.

Number Sense
1.0 Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers and decimals relate to simple fractions. Students use the concepts of negative numbers:
1.1 Read and write whole numbers in the millions.

1.2 Order and compare whole numbers and decimals to two decimal places.

1.3 Round whole numbers through the millions to the nearest ten, hundred, thousand, ten thousand, or hundred thousand.

1.4 Decide when a rounded solution is called for and explain why such a solution may be appropriate.

1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions (see Standard 4.0).

1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or .50; 7/4 = 1 3/4 = 1.75).

1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.

1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in "owing").

1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.

2.0 Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals:
2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two places.

2.2 Round two-place decimals to one decimal or the nearest whole number and judge the reasonableness of the rounded answer.

3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and understand the relationships among the operations:
3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition and subtraction of multidigit numbers.

3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a multidigit number by a two-digit number and for dividing a multidigit number by a one-digit number; use relationships between them to simplify computations and to check results.

3.3 Solve problems involving multiplication of multidigit numbers by two-digit numbers.

3.4 Solve problems involving division of multidigit numbers by one-digit numbers.

4.0 Students know how to factor small whole numbers:
4.1 Understand that many whole numbers break down in different ways (e.g., 12 = 4 x 3 = 2 x 6 = 2 x 2 x 3).

4.2 Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers are called prime numbers.

Algebra and Functions
1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences:
1.1 Use letters, boxes, or other symbols to stand for any number in simple expressions or equations (e.g., demonstrate an understanding and the use of the concept of a variable).

1.2 Interpret and evaluate mathematical expressions that now use parentheses.

1.3 Use parentheses to indicate which operation to perform first when writing expressions containing more than two terms and different operations.

1.4 Use and interpret formulas (e.g., area = length x width or A = lw) to answer questions about quantities and their relationships.

1.5 Understand that an equation such as y = 3 x + 5 is a prescription for determining a second number when a first number is given.

2.0 Students know how to manipulate equations:
2.1 Know and understand that equals added to equals are equal.

2.2 Know and understand that equals multiplied by equals are equal.

Measurement and Geometry
1.0 Students understand perimeter and area:
1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square kilometer (km2), square inch (in2), square yard (yd2), or square mile (mi2).

1.2 Recognize that rectangles that have the same area can have different perimeters.

1.3 Understand that rectangles that have the same perimeter can have different areas.

1.4 Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.

2.0 Students use two-dimensional coordinate grids to represent points and graph lines and simple figures:
2.1 Draw the points corresponding to linear relationships on graph paper (e.g., draw 10 points on the graph of the equation y = 3 x and connect them by using a straight line).

2.2 Understand that the length of a horizontal line segment equals the difference of the x- coordinates.

2.3 Understand that the length of a vertical line segment equals the difference of the y- coordinates.

3.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems:
3.1 Identify lines that are parallel and perpendicular.

3.2 Identify the radius and diameter of a circle.

3.3 Identify congruent figures.

3.4 Identify figures that have bilateral and rotational symmetry.

3.5 Know the definitions of a right angle, an acute angle, and an obtuse angle. Understand that 90°, 180°, 270°, and 360° are associated, respectively, with 1/4, 1/2, 3/4, and full turns.

3.6 Visualize, describe, and make models of geometric solids (e.g., prisms, pyramids) in terms of the number and shape of faces, edges, and vertices; interpret two-dimensional representations of three-dimensional objects; and draw patterns (of faces) for a solid that, when cut and folded, will make a model of the solid.

3.7 Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes.

3.8 Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).

Statistics, Data Analysis, and Probability
1.0 Students organize, represent, and interpret numerical and categorical data and clearly communicate their findings:
1.1 Formulate survey questions; systematically collect and represent data on a number line; and coordinate graphs, tables, and charts.

1.2 Identify the mode(s) for sets of categorical data and the mode(s), median, and any apparent outliers for numerical data sets.

1.3 Interpret one-and two-variable data graphs to answer questions about a situation.

2.0 Students make predictions for simple probability situations:
2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).

2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; 3 /4).

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

1.2 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.

2.2 Apply strategies and results from simpler problems to more complex problems.

2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.6 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.

3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

3.3 Develop generalizations of the results obtained and apply them in other circumstances.

_______________________________________________________________________________________________________

Grade Five
Mathematics Content Standards

By the end of grade five, students increase their facility with the four basic arithmetic operations applied to fractions, decimals, and positive and negative numbers. They know and use common measuring units to determine length and area and know and use formulas to determine the volume of simple geometric figures. Students know the concept of angle measurement and use a protractor and compass to solve problems. They use grids, tables, graphs, and charts to record and analyze data.

Number Sense
1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers:
1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths) numbers.

1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.

1.3 Understand and compute positive integer powers of nonnegative integers; compute examples as repeated multiplication.

1.4 Determine the prime factors of all numbers through 50 and write the numbers as the product of their prime factors by using exponents to show multiples of a factor (e.g., 24 = 2 x 2 x 2 x 3 = 23 x 3).

1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers.

2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals:
2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results.

2.2 Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.

2.3 Solve simple problems, including ones arising in concrete situations, involving the addition and subtraction of fractions and mixed numbers (like and unlike denominators of 20 or less), and express answers in the simplest form.

2.4 Understand the concept of multiplication and division of fractions.

2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems.

Algebra and Functions
1.0 Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results:
1.1 Use information taken from a graph or equation to answer questions about a problem situation.

1.2 Use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution.

1.3 Know and use the distributive property in equations and expressions with variables.

1.4 Identify and graph ordered pairs in the four quadrants of the coordinate plane.

1.5 Solve problems involving linear functions with integer values; write the equation; and graph the resulting ordered pairs of integers on a grid.

Measurement and Geometry
1.0 Students understand and compute the volumes and areas of simple objects:
1.1 Derive and use the formula for the area of a triangle and of a parallelogram by comparing it with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by cutting and pasting a right triangle on the parallelogram).

1.2 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area for these objects.

1.3 Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm3], cubic meter [m3], cubic inch [in3], cubic yard [yd3]) to compute the volume of rectangular solids.

1.4 Differentiate between, and use appropriate units of measures for, two-and three-dimensional objects (i.e., find the perimeter, area, volume).

2.0 Students identify, describe, and classify the properties of, and the relationships between, plane and solid geometric figures:
2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor, drawing software).

2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems.

2.3 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular solids.

Statistics, Data Analysis, and Probability
1.0 Students display, analyze, compare, and interpret different data sets, including data sets of different sizes:
1.1 Know the concepts of mean, median, and mode; compute and compare simple examples to show that they may differ.

1.2 Organize and display single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets.

1.3 Use fractions and percentages to compare data sets of different sizes.

1.4 Identify ordered pairs of data from a graph and interpret the meaning of the data in terms of the situation depicted by the graph.

1.5 Know how to write ordered pairs correctly; for example, ( x, y ).

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

1.2 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.

2.2 Apply strategies and results from simpler problems to more complex problems.

2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

2.4 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

2.5 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.6 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.

3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

3.3 Develop generalizations of the results obtained and apply them in other circumstances.

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Grade Six
Mathematics Content Standards

By the end of grade six, students have mastered the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative integers; they accurately compute and solve problems. They apply their knowledge to statistics and probability. Students understand the concepts of mean, median, and mode of data sets and how to calculate the range. They analyze data and sampling processes for possible bias and misleading conclusions; they use addition and multiplication of fractions routinely to calculate the probabilities for compound events. Students conceptually understand and work with ratios and proportions; they compute percentages (e.g., tax, tips, interest). Students know about pi and the formulas for the circumference and area of a circle. They use letters for numbers in formulas involving geometric shapes and in ratios to represent an unknown part of an expression. They solve one-step linear equations.

Number Sense
1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve problems involving fractions, ratios, proportions, and percentages:
1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line.

1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative sizes of two quantities, using appropriate notations ( a/b, a to b, a:b ).

1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/ 21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse.

1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips.

2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation.

2.2 Explain the meaning of multiplication and division of positive fractions and perform the calculations (e.g., 5/8 ÷ 15/16 = 5/8 x 16/15 = 2/3).

2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations.

2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction).

Algebra and Functions
1.0 Students write verbal expressions and sentences as algebraic expressions and equations; they evaluate algebraic expressions, solve simple linear equations, and graph and interpret their results:
1.1 Write and solve one-step linear equations in one variable.

1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables.

1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.

1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator.

2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions:
2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches).

2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity.

2.3 Solve problems involving rates, average speed, distance, and time.

3.0 Students investigate geometric patterns and describe them algebraically:
3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = 1/2bh, C = pd - the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively).

3.2 Express in symbolic form simple relationships arising from geometry.

Measurement and Geometry
1.0 Students deepen their understanding of the measurement of plane and solid shapes and use this understanding to solve problems:
1.1 Understand the concept of a constant such as p; know the formulas for the circumference and area of a circle.

1.2 Know common estimates of p (3.14; 22/7) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements.

1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base x height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid.

2.0 Students identify and describe the properties of two-dimensional figures:
2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.

2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).

Statistics, Data Analysis, and Probability
1.0 Students compute and analyze statistical measurements for data sets:
1.1 Compute the range, mean, median, and mode of data sets.

1.2 Understand how additional data added to data sets may affect these computations of measures of central tendency.

1.3 Understand how the inclusion or exclusion of outliers affects measures of central tendency.

1.4 Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given context.

2.0 Students use data samples of a population and describe the characteristics and limitations of the samples:
2.1 Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample.

2.2 Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling) and which method makes a sample more representative for a population.

2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.

2.4 Identify data that represent sampling errors and explain why the sample (and the display) might be biased.

2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.

3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events:
3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree diagrams) and express the theoretical probability of each outcome.

3.2 Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven).

3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1- P is the probability of an event not occurring.

3.4 Understand that the probability of either of two disjoint events occurring is the sum of the two individual probabilities and that the probability of one event following another, in independent trials, is the product of the two probabilities.

3.5 Understand the difference between independent and dependent events.

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.

1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.

1.3 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.

2.2 Apply strategies and results from simpler problems to more complex problems.

2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.

2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

2.5 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

2.6 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.7 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.

3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

3.3 Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.

___________________________________________________________________________________________________

Grade Seven
Mathematics Content Standards

By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use factoring of numerators and denominators and properties of exponents. They know the Pythagorean theorem and solve problems in which they compute the length of an unknown side. Students know how to compute the surface area and volume of basic three-dimensional objects and understand how area and volume change with a change in scale. Students make conversions between different units of measurement. They know and use different representations of fractional numbers (fractions, decimals, and percents) and are proficient at changing from one to another. They increase their facility with ratio and proportion, compute percents of increase and decrease, and compute simple and compound interest. They graph linear functions and understand the idea of slope and its relation to ratio.

Number Sense
1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms:
1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10) with approximate numbers using scientific notation.

1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers.

1.3 Convert fractions to decimals and percents and use these representations in estimations, computations, and applications.

1.4 Differentiate between rational and irrational numbers.

1.5 Know that every rational number is either a terminating or repeating decimal and be able to convert terminating decimals into reduced fractions.

1.6 Calculate the percentage of increases and decreases of a quantity.

1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest.

2.0 Students use exponents, powers, and roots and use exponents in working with fractions:
2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.

2.2 Add and subtract fractions by using factoring to find common denominators.

2.3 Multiply, divide, and simplify rational numbers by using exponent rules.

2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square integer; for an integer that is not square, determine without a calculator the two integers between which its square root lies and explain why.

2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers.

Algebra and Functions
1.0 Students express quantitative relationships by using algebraic terminology, expressions, equations, inequalities, and graphs:
1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).

1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x + 5)2.

1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, commutative) and justify the process used.

1.4 Use algebraic terminology (e.g., variable, equation, term, coefficient, inequality, expression, constant) correctly.

1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph in the situation represented by the graph.

2.0 Students interpret and evaluate expressions involving integer powers and simple roots:
2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.

2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials when the latter results in a monomial with an integer exponent.

3.0 Students graph and interpret linear and some nonlinear functions:
3.1 Graph functions of the form y = nx2 and y = nx3 and use in solving problems.

3.2 Plot the values from the volumes of three-dimensional shapes for various values of the edge lengths (e.g., cubes with varying edge lengths or a triangle prism with a fixed height and an equilateral triangle base of varying lengths).

3.3 Graph linear functions, noting that the vertical change (change in y- value) per unit of horizontal change (change in x- value) is always the same and know that the ratio ("rise over run") is called the slope of a graph.

3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.

4.0 Students solve simple linear equations and inequalities over the rational numbers:
4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.

4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.

Measurement and Geometry
1.0 Students choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems:
1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).

1.2 Construct and read drawings and models made to scale.

1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer.

2.0 Students compute the perimeter, area, and volume of common geometric objects and use the results to find measures of less common objects. They know how perimeter, area, and volume are affected by changes of scale:
2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

2.2 Estimate and compute the area of more complex or irregular two-and three-dimensional figures by breaking the figures down into more basic geometric objects.

2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a three-dimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor.

2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1 square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately 16.38 cubic centimeters or [1 in3] = [16.38 cm3]).

3.0 Students know the Pythagorean theorem and deepen their understanding of plane and solid geometric shapes by constructing figures that meet given conditions and by identifying attributes of figures:
3.1 Identify and construct basic elements of geometric figures (e.g., altitudes, mid-points, diagonals, angle bisectors, and perpendicular bisectors; central angles, radii, diameters, and chords of circles) by using a compass and straightedge.

3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.

3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement.

3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationships between the sides and angles of the two figures.

3.5 Construct two-dimensional patterns for three-dimensional models, such as cylinders, prisms, and cones.

3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangular solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).

Statistics, Data Analysis, and Probability
1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program:
1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot; use the forms to display a single set of data or to compare two sets of data.

1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level).

1.3 Understand the meaning of, and be able to compute, the minimum, the lower quartile, the median, the upper quartile, and the maximum of a data set.

Mathematical Reasoning
1.0 Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.

1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.

1.3 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.

2.2 Apply strategies and results from simpler problems to more complex problems.

2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.

2.4 Make and test conjectures by using both inductive and deductive reasoning.

2.5 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.

2.6 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.

2.7 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

2.8 Make precise calculations and check the validity of the results from the context of the problem.

3.0 Students determine a solution is complete and move beyond a particular problem by generalizing to other situations:
3.1 Evaluate the reasonableness of the solution in the context of the original situation.

3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.

3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem situations.

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Grades Eight Through Twelve Introduction
Mathematics Content Standards

The standards for grades eight through twelve are organized differently from those for kindergarten through grade seven. In this section strands are not used for organizational purposes as they are in the elementary grades because the mathematics studied in grades eight through twelve falls naturally under discipline headings: algebra, geometry, and so forth. Many schools teach this material in traditional courses; others teach it in an integrated fashion. To allow local educational agencies and teachers flexibility in teaching the material, the standards for grades eight through twelve do not mandate that a particular discipline be initiated and completed in a single grade. The core content of these subjects must be covered; students are expected to achieve the standards however these subjects are sequenced.

Standards are provided for algebra I, geometry, algebra II, trigonometry, mathematical analysis, linear algebra, probability and statistics, Advanced Placement probability and statistics, and calculus. Many of the more advanced subjects are not taught in every middle school or high school. Moreover, schools and districts have different ways of combining the subject matter in these various disciplines. For example, many schools combine some trigonometry, mathematical analysis, and linear algebra to form a precalculus course. Some districts prefer offering trigonometry content with algebra II.

Table 1, "Mathematics Disciplines, by Grade Level," reflects typical grade-level groupings of these disciplines in both integrated and traditional curricula. The lightly shaded region reflects the minimum requirement for mastery by all students. The dark shaded region depicts content that is typically considered elective but that should also be mastered by students who complete the other disciplines in the lower grade levels and continue the study of mathematics.

Table 1

Mathematics Disciplines, by Grade Level
(see above paragraph for explanation of table below)

Discipline	Grade Eight	Grade Nine	Grade Ten	Grade Eleven	Grade Twelve
Algebra I	Required	Required	Required	Required	Required
Geometry	Required	Required	Required	Required	Required
Algebra II	Required	Required	Required	Required	Required
Probability and Statistics	Required	Required	Required	Required	Required
Trigonometry	n/a	n/a	Elective	Elective	Elective
Linear Algebra	n/a	n/a	Elective	Elective	Elective
Mathematical Analysis	n/a	n/a	Elective	Elective	Elective
Advanced Placement Probability and Statistics	n/a	n/a	n/a	Elective	Elective
Calculus	n/a	n/a	n/a	Elective	Elective

Many other combinations of these advanced subjects into courses are possible. What is described in this section are standards for the academic content by discipline; this document does not endorse a particular choice of structure for courses or a particular method of teaching the mathematical content.

When students delve deeply into mathematics, they gain not only conceptual understanding of mathematical principles but also knowledge of, and experience with, pure reasoning. One of the most important goals of mathematics is to teach students logical reasoning. The logical reasoning inherent in the study of mathematics allows for applications to a broad range of situations in which answers to practical problems can be found with accuracy.

By grade eight, students' mathematical sensitivity should be sharpened. Students need to start perceiving logical subtleties and appreciate the need for sound mathematical arguments before making conclusions. As students progress in the study of mathematics, they learn to distinguish between inductive and deductive reasoning; understand the meaning of logical implication; test general assertions; realize that one counterexample is enough to show that a general assertion is false; understand conceptually that although a general assertion is true in a few cases, it is not true in all cases; distinguish between something being proven and a mere plausibility argument; and identify logical errors in chains of reasoning.

Mathematical reasoning and conceptual understanding are not separate from content; they are intrinsic to the mathematical discipline students master at more advanced levels.

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Algebra I
Grades Eight Through Twelve - Mathematics Content Standards

Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences. In addition, algebraic skills and concepts are developed and used in a wide variety of problem-solving situations.
1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable:

1.1 Students use properties of numbers to demonstrate whether assertions are true or false.

2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.

3.0 Students solve equations and inequalities involving absolute values.

4.0 Students simplify expressions before solving linear equations and inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.

5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

6.0 Students graph a linear equation and compute the x- and y- intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).

7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using the point-slope formula.

8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are able to find the equation of a line perpendicular to a given line that passes through a given point.

9.0 Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets.

10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.

11.0 Students apply basic factoring techniques to second-and simple third-degree polynomials. These techniques include finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials.

12.0 Students simplify fractions with polynomials in the numerator and denominator by factoring both and reducing them to the lowest terms.

13.0 Students add, subtract, multiply, and divide rational expressions and functions. Students solve both computationally and conceptually challenging problems by using these techniques.

14.0 Students solve a quadratic equation by factoring or completing the square.

15.0 Students apply algebraic techniques to solve rate problems, work problems, and percent mixture problems.

16.0 Students understand the concepts of a relation and a function, determine whether a given relation defines a function, and give pertinent information about given relations and functions.

17.0 Students determine the domain of independent variables and the range of dependent variables defined by a graph, a set of ordered pairs, or a symbolic expression.

18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion.

19.0 Students know the quadratic formula and are familiar with its proof by completing the square.

20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.

21.0 Students graph quadratic functions and know that their roots are the x- intercepts.

22.0 Students use the quadratic formula or factoring techniques or both to determine whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.

23.0 Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.

24.0 Students use and know simple aspects of a logical argument:

24.1 Students explain the difference between inductive and deductive reasoning and identify and provide examples of each.

24.2 Students identify the hypothesis and conclusion in logical deduction. 24.3 Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion.

25.0 Students use properties of the number system to judge the validity of results, to justify each step of a procedure, and to prove or disprove statements:

25.1 Students use properties of numbers to construct simple, valid arguments (direct and indirect) for, or formulate counterexamples to, claimed assertions.

25.2 Students judge the validity of an argument according to whether the properties of the real number system and the order of operations have been applied correctly at each step.

25.3 Given a specific algebraic statement involving linear, quadratic, or absolute value expressions or equations or inequalities, students determine whether the statement is true sometimes, always, or never.

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Geometry
Grades Eight Through Twelve - Mathematics Content Standards

The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings and problems.

1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning.

2.0 Students write geometric proofs, including proofs by contradiction.

3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.

4.0 Students prove basic theorems involving congruence and similarity.

5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles.

6.0 Students know and are able to use the triangle inequality theorem.

7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.

8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures.

9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders.

10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.

11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids.

12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems.

13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles.

14.0 Students prove the Pythagorean theorem.

15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.

16.0 Students perform basic constructions with a straightedge and compass, such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line.

17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles.

18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan( x ) = sin( x )/cos( x ), (sin( x )) 2 + (cos( x )) 2 = 1.

19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.

20.0 Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.

21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.

22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections.

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Algebra II
Grades Eight Through Twelve - Mathematics Content Standards

This discipline complements and expands the mathematical content and concepts of algebra I and geometry. Students who master algebra II will gain experience with algebraic solutions of problems in various content areas, including the solution of systems of quadratic equations, logarithmic and exponential functions, the binomial theorem, and the complex number system.

1.0 Students solve equations and inequalities involving absolute value.

2.0 Students solve systems of linear equations and inequalities (in two or three variables) by substitution, with graphs, or with matrices.

3.0 Students are adept at operations on polynomials, including long division.

4.0 Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes.

5.0 Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically. In particular, they can plot complex numbers as points in the plane.

6.0 Students add, subtract, multiply, and divide complex numbers.

7.0 Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator.

8.0 Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula. Students apply these techniques in solving word problems. They also solve quadratic equations in the complex number system.

9.0 Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y = a(x-b)2 + c.

10.0 Students graph quadratic functions and determine the maxima, minima, and zeros of the function.

11.0 Students prove simple laws of logarithms.

11.1 Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

11.2 Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step.

12.0 Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay.

13.0 Students use the definition of logarithms to translate between logarithms in any base.

14.0 Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values.

15.0 Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true.

16.0 Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it.

17.0 Given a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola. Students can then graph the equation.

18.0 Students use fundamental counting principles to compute combinations and permutations.

19.0 Students use combinations and permutations to compute probabilities.

20.0 Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers.

21.0 Students apply the method of mathematical induction to prove general statements about the positive integers.

22.0 Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series.

23.0 Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series.

24.0 Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions.

25.0 Students use properties from number systems to justify steps in combining and simplifying functions.

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Trigonometry
Grades Eight Though Twelve - Mathematics Content Standards

Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric functions studied are defined geometrically rather than in terms of algebraic equations. Facility with these functions as well as the ability to prove basic identities regarding them is especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college.
1.0 Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians.

2.0 Students know the definition of sine and cosine as y- and x- coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.

3.0 Students know the identity cos2 (x) + sin2 (x) = 1:

3.1 Students prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, conversely, they can prove the Pythagorean theorem as a consequence of this identity).

3.2 Students prove other trigonometric identities and simplify others by using the identity cos2 (x) + sin2 (x) = 1. For example, students use this identity to prove that sec2 (x) = tan2 (x) + 1.

4.0 Students graph functions of the form f(t) = A sin ( Bt + C ) or f(t) = A cos ( Bt + C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.

5.0 Students know the definitions of the tangent and cotangent functions and can graph them.

6.0 Students know the definitions of the secant and cosecant functions and can graph them.

7.0 Students know that the tangent of the angle that a line makes with the x- axis is equal to the slope of the line.

8.0 Students know the definitions of the inverse trigonometric functions and can graph the functions.

9.0 Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points.

10.0 Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs and can use those formulas to prove and/ or simplify other trigonometric identities.

11.0 Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines and can use those formulas to prove and/ or simplify other trigonometric identities.

12.0 Students use trigonometry to determine unknown sides or angles in right triangles.

13.0 Students know the law of sines and the law of cosines and apply those laws to solve problems.

14.0 Students determine the area of a triangle, given one angle and the two adjacent sides.

15.0 Students are familiar with polar coordinates. In particular, they can determine polar coordinates of a point given in rectangular coordinates and vice versa.

16.0 Students represent equations given in rectangular coordinates in terms of polar coordinates.

17.0 Students are familiar with complex numbers. They can represent a complex number in polar form and know how to multiply complex numbers in their polar form.

18.0 Students know DeMoivre's theorem and can give n th roots of a complex number given in polar form.

19.0 Students are adept at using trigonometry in a variety of applications and word problems.

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Mathematical Analysis
Grades Eight Through Twelve - Mathematics Content Standards

This discipline combines many of the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus and strengthens their conceptual understanding of problems and mathematical reasoning in solving problems. These standards take a functional point of view toward those topics. The most significant new concept is that of limits. Mathematical analysis is often combined with a course in trigonometry or perhaps with one in linear algebra to make a year-long precalculus course.

1.0 Students are familiar with, and can apply, polar coordinates and vectors in the plane. In particular, they can translate between polar and rectangular coordinates and can interpret polar coordinates and vectors graphically.

2.0 Students are adept at the arithmetic of complex numbers. They can use the trigonometric form of complex numbers and understand that a function of a complex variable can be viewed as a function of two real variables. They know the proof of DeMoivre's theorem.

3.0 Students can give proofs of various formulas by using the technique of mathematical induction.

4.0 Students know the statement of, and can apply, the fundamental theorem of algebra.

5.0 Students are familiar with conic sections, both analytically and geometrically:

5.1 Students can take a quadratic equation in two variables; put it in standard form by completing the square and using rotations and translations, if necessary; determine what type of conic section the equation represents; and determine its geometric components (foci, asymptotes, and so forth).

5.2 Students can take a geometric description of a conic section - for example, the locus of points whose sum of its distances from (1, 0) and (-1, 0) is 6 - and derive a quadratic equation representing it.

6.0 Students find the roots and poles of a rational function and can graph the function and locate its asymptotes.

7.0 Students demonstrate an understanding of functions and equations defined parametrically and can graph them.

8.0 Students are familiar with the notion of the limit of a sequence and the limit of a function as the independent variable approaches a number or infinity. They determine whether certain sequences converge or diverge.

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Linear Algebra
Grades Eight Through Twelve - Mathematics Content Standards

The general goal in this discipline is for students to learn the techniques of matrix manipulation so that they can solve systems of linear equations in any number of variables. Linear algebra is most often combined with another subject, such as trigonometry, mathematical analysis, or precalculus.
1.0 Students solve linear equations in any number of variables by using Gauss-Jordan elimination.

2.0 Students interpret linear systems as coefficient matrices and the Gauss-Jordan method as row operations on the coefficient matrix.

3.0 Students reduce rectangular matrices to row echelon form.

4.0 Students perform addition on matrices and vectors.

5.0 Students perform matrix multiplication and multiply vectors by matrices and by scalars.

6.0 Students demonstrate an understanding that linear systems are inconsistent (have no solutions), have exactly one solution, or have infinitely many solutions.

7.0 Students demonstrate an understanding of the geometric interpretation of vectors and vector addition (by means of parallelograms) in the plane and in three-dimensional space.

8.0 Students interpret geometrically the solution sets of systems of equations. For example, the solution set of a single linear equation in two variables is interpreted as a line in the plane, and the solution set of a two-by-two system is interpreted as the intersection of a pair of lines in the plane.

9.0 Students demonstrate an understanding of the notion of the inverse to a square matrix and apply that concept to solve systems of linear equations.

10.0 Students compute the determinants of 2 x 2 and 3 x 3 matrices and are familiar with their geometric interpretations as the area and volume of the parallelepipeds spanned by the images under the matrices of the standard basis vectors in two-dimensional and three-dimensional spaces.

11.0 Students know that a square matrix is invertible if, and only if, its determinant is nonzero. They can compute the inverse to 2 x 2 and 3 x 3 matrices using row reduction methods or Cramer's rule.

12.0 Students compute the scalar (dot) product of two vectors in n- dimensional space and know that perpendicular vectors have zero dot product.

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Probability and Statistics
Grades Eight Through Twelve - Mathematics Content Standards

This discipline is an introduction to the study of probability, interpretation of data, and fundamental statistical problem solving. Mastery of this academic content will provide students with a solid foundation in probability and facility in processing statistical information.
1.0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.

2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.

3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.

4.0 Students are familiar with the standard distributions (normal, binomial, and exponential) and can use them to solve for events in problems in which the distribution belongs to those families.

5.0 Students determine the mean and the standard deviation of a normally distributed random variable.

6.0 Students know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations.

7.0 Students compute the variance and the standard deviation of a distribution of data.

8.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.

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Advanced Placement Probability and Statistics
Grades Eight Through Twelve - Mathematics Content Standards

This discipline is a technical and in-depth extension of probability and statistics. In particular, mastery of academic content for advanced placement gives students the background to succeed in the Advanced Placement examination in the subject.

1.0 Students solve probability problems with finite sample spaces by using the rules for addition, multiplication, and complementation for probability distributions and understand the simplifications that arise with independent events.

2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.

3.0 Students demonstrate an understanding of the notion of discrete random variables by using this concept to solve for the probabilities of outcomes, such as the probability of the occurrence of five or fewer heads in 14 coin tosses.

4.0 Students understand the notion of a continuous random variable and can interpret the probability of an outcome as the area of a region under the graph of the probability density function associated with the random variable.

5.0 Students know the definition of the mean of a discrete random variable and can determine the mean for a particular discrete random variable.

6.0 Students know the definition of the variance of a discrete random variable and can determine the variance for a particular discrete random variable.

7.0 Students demonstrate an understanding of the standard distributions (normal, binomial, and exponential) and can use the distributions to solve for events in problems in which the distribution belongs to those families.

8.0 Students determine the mean and the standard deviation of a normally distributed random variable.

9.0 Students know the central limit theorem and can use it to obtain approximations for probabilities in problems of finite sample spaces in which the probabilities are distributed binomially.

10.0 Students know the definitions of the mean, median, and mode of distribution of data and can compute each of them in particular situations.

11.0 Students compute the variance and the standard deviation of a distribution of data.

12.0 Students find the line of best fit to a given distribution of data by using least squares regression.

13.0 Students know what the correlation coefficient of two variables means and are familiar with the coefficient's properties.

14.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.

15.0 Students are familiar with the notions of a statistic of a distribution of values, of the sampling distribution of a statistic, and of the variability of a statistic.

16.0 Students know basic facts concerning the relation between the mean and the standard deviation of a sampling distribution and the mean and the standard deviation of the population distribution.

17.0 Students determine confidence intervals for a simple random sample from a normal distribution of data and determine the sample size required for a desired margin of error.

18.0 Students determine the P- value for a statistic for a simple random sample from a normal distribution.

19.0 Students are familiar with the chi- square distribution and chi- square test and understand their uses.

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Calculus
Grades Eight Through Twelve - Mathematics Content Standards

When taught in high school, calculus should be presented with the same level of depth and rigor as are entry-level college and university calculus courses. These standards outline a complete college curriculum in one variable calculus. Many high school programs may have insufficient time to cover all of the following content in a typical academic year. For example, some districts may treat differential equations lightly and spend substantial time on infinite sequences and series. Others may do the opposite. Consideration of the College Board syllabi for the Calculus AB and Calculus BC sections of the Advanced Placement Examination in Mathematics may be helpful in making curricular decisions. Calculus is a widely applied area of mathematics and involves a beautiful intrinsic theory. Students mastering this content will be exposed to both aspects of the subject.

1.0 Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions. This knowledge includes one-sided limits, infinite limits, and limits at infinity. Students know the definition of convergence and divergence of a function as the domain variable approaches either a number or infinity:

1.1 Students prove and use theorems evaluating the limits of sums, products, quotients, and composition of functions.

1.2 Students use graphical calculators to verify and estimate limits.

1.3 Students prove and use special limits, such as the limits of (sin(x))/x and (1-cos(x))/x as x tends to 0.

2.0 Students demonstrate knowledge of both the formal definition and the graphical interpretation of continuity of a function.

3.0 Students demonstrate an understanding and the application of the intermediate value theorem and the extreme value theorem.

4.0 Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability:

4.1 Students demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph of the function.

4.2 Students demonstrate an understanding of the interpretation of the derivative as an instantaneous rate of change. Students can use derivatives to solve a variety of problems from physics, chemistry, economics, and so forth that involve the rate of change of a function.

4.3 Students understand the relation between differentiability and continuity.

4.4 Students derive derivative formulas and use them to find the derivatives of algebraic, trigonometric, inverse trigonometric, exponential, and logarithmic functions.

5.0 Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite functions.

6.0 Students find the derivatives of parametrically defined functions and use implicit differentiation in a wide variety of problems in physics, chemistry, economics, and so forth.

7.0 Students compute derivatives of higher orders.

8.0 Students know and can apply Rolle's theorem, the mean value theorem, and L'Hôpital's rule.

9.0 Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.

10.0 Students know Newton's method for approximating the zeros of a function.

11.0 Students use differentiation to solve optimization (maximum-minimum problems) in a variety of pure and applied contexts.

12.0 Students use differentiation to solve related rate problems in a variety of pure and applied contexts.

13.0 Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals.

14.0 Students apply the definition of the integral to model problems in physics, economics, and so forth, obtaining results in terms of integrals.

15.0 Students demonstrate knowledge and proof of the fundamental theorem of calculus and use it to interpret integrals as antiderivatives.

16.0 Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.

17.0 Students compute, by hand, the integrals of a wide variety of functions by using techniques of integration, such as substitution, integration by parts, and trigonometric substitution. They can also combine these techniques when appropriate.

18.0 Students know the definitions and properties of inverse trigonometric functions and the expression of these functions as indefinite integrals.

19.0 Students compute, by hand, the integrals of rational functions by combining the techniques in standard 17.0 with the algebraic techniques of partial fractions and completing the square.

20.0 Students compute the integrals of trigonometric functions by using the techniques noted above.

21.0 Students understand the algorithms involved in Simpson's rule and Newton's method. They use calculators or computers or both to approximate integrals numerically.

22.0 Students understand improper integrals as limits of definite integrals.

23.0 Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges.

24.0 Students understand and can compute the radius (interval) of the convergence of power series.

25.0 Students differentiate and integrate the terms of a power series in order to form new series from known ones.

26.0 Students calculate Taylor polynomials and Taylor series of basic functions, including the remainder term.

27.0 Students know the techniques of solution of selected elementary differential equations and their applications to a wide variety of situations, including growth-and-decay problems.

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Glossary
Grades Eight Through Twelve - Mathematics Content Standards

absolute value. A number's distance from zero on the number line. The absolute value of -4 is 4; the absolute value of 4 is 4.

algorithm. An organized procedure for performing a given type of calculation or solving a given type of problem. An example is long division.

arithmetic sequence. A sequence of elements, a1 , a2 , a3 , . . ., such that the difference of successive terms is a constant ai+1 - ai = k ; for example, the sequence {2, 5, 8, 11, 14, . . .} where the common difference is 3.

asymptotes. Straight lines that have the property of becoming and staying arbitrarily close to the curve as the distance from the origin increases to infinity. For example, the x- axis is the only asymptote to the graph of sin( x)/x.

axiom. A basic assumption about a mathematical system from which theorems can be deduced. For example, the system could be the points and lines in the plane. Then an axiom would be that given any two distinct points in the plane, there is a unique line through them.

binomial. In algebra, an expression consisting of the sum or difference of two monomials (see the definition of monomial), such as 4a-8b.

binomial distribution. In probability, a binomial distribution gives the probabilities of k outcomes A (or n-k outcomes B) in n independent trials for a two-outcome experiment in which the possible outcomes are denoted A and B.

binomial theorem. In mathematics, a theorem that specifies the complete expansion of a binomial raised to any positive integer power.

box-and-whisker plot. A graphical method for showing the median, quartiles, and extremes of data. A box plot shows where the data are spread out and where they are concentrated.

complex numbers. Numbers that have the form a + bi where a and b are real numbers and i satisfies the equation i2 = -1. Multiplication is denoted by ( a + bi )( c + di ) = ( ac - bd ) + ( ad + bc ) i , and addition is denoted by ( a + bi ) + ( c + di ) = ( a + c ) + ( b + d ) i .

congruent. Two shapes in the plane or in space are congruent if there is a rigid motion that identifies one with the other (see the definition of rigid motion).

conjecture. An educated guess.

coordinate system. A rule of correspondence by which two or more quantities locate points unambiguously and which satisfies the further property that points unambiguously determine the quantities; for example, the usual Cartesian coordinates x, y in the plane.

cosine. Cos(q) is the x- coordinate of the point on the unit circle so that the ray connecting the point with the origin makes an angle of q with the positive x- axis. When q is an angle of a right triangle, then cos(q) is the ratio of the adjacent side with the hypotenuse.

dilation. In geometry, a transformation D of the plane or space is a dilation at a point P if it takes P to itself, preserves angles, multiplies distances from P by a positive real number r, and takes every ray through P onto itself. In case P is the origin for a Cartesian coordinate system in the plane, then the dilation D maps the point ( x, y ) to the point ( rx, ry ).

dimensional analysis. A method of manipulating unit measures algebraically to determine the proper units for a quantity computed algebraically. For example, velocity has units of the form length over time (e.g., meters per second [ m/sec ]), and acceleration has units of velocity over time; so it follows that acceleration has units ( m/sec)/sec = m/(sec2).

expanded form. The expanded form of an algebraic expression is the equivalent expression without parentheses. For example, the expanded form of ( a + b )2 is a2 + 2ab + b2 .

exponent. The power to which a number or variable is raised (the exponent may be any real number).

exponential function. A function commonly used to study growth and decay. It has the form y = ax with a positive.

factors. Any of two or more quantities that are multiplied together. In the expression 3.712 x 11.315, the factors are 3.712 and 11.315.

function. A correspondence in which values of one variable determine the values of another.

geometric sequence. A sequence in which there is a common ratio between successive terms. Each successive term of a geometric sequence is found by multiplying the preceding term by the common ratio. For example, in the sequence {1, 3, 9, 27, 81, . . .} the common ratio is 3.

histogram. A vertical block graph with no spaces between the blocks. It is used to represent frequency data in statistics.

inequality. A relationship between two quantities indicating that one is strictly less than or less than or equal to the other.

integers. The set consisting of the positive and negative whole numbers and zero; for example, {. . . -2, -1, 0, 1, 2 . . .}.

irrational number. A number that cannot be represented as an exact ratio of two integers. For example, the square root of 2 or p .

linear expression. An expression of the form ax+b where x is variable and a and b are constants; or in more variables, an expression of the form ax + by + c, ax + by + cz + d, etc.

linear equation. An equation containing linear expressions.

logarithm. The inverse of exponentiation; for example, alogax = x.

mean. In statistics, the average obtained by dividing the sum of two or more quantities by the number of these quantities.

median. In statistics, the quantity designating the middle value in a set of numbers.

mode. In statistics, the value that occurs most frequently in a given series of numbers.

monomial. In the variables x, y, z, a monomial is an expression of the form axm yn zk , in which m, n, and k are nonnegative integers and a is a constant (e.g., 5x2 , 3x2 y or 7x3yz2 ).

nonstandard unit. Unit of measurement expressed in terms of objects (such as paper clips, sticks of gum, shoes, etc.).

parallel. Given distinct lines in the plane that are infinite in both directions, the lines are parallel if they never meet. Two distinct lines in the coordinate plane are parallel if and only if they have the same slope.

permutation. A permutation of the set of numbers {1, 2, . . . , n } is a reordering of these numbers.

polar coordinates. The coordinate system for the plane based on r , q , the distance from the origin and q , and the angle between the positive x- axis and the ray from the origin to the point.

polar equation. Any relation between the polar coordinates (r, q ) of a set of points (e.g., r = 2cosq is the polar equation of a circle).

polynomial. In algebra, a sum of monomials; for example, x2 + 2xy + y2 .

prime. A natural number p greater than 1 is prime if and only if the only positive integer factors of p are 1 and p. The first seven primes are 2, 3, 5, 7, 11, 13, 17.

quadratic function. A function given by a polynomial of degree 2.

random variable. A function on a probability space.

range. In statistics, the difference between the greatest and smallest values in a data set. In mathematics, the image of a function.

ratio. A comparison expressed as a fraction. For example, there is a ratio of three boys to two girls in a class (3/2, 3:2).

rational numbers. Numbers that can be expressed as the quotient of two integers; for example, 7/3, 5/11, -5/13, 7 = 7/1.

real numbers. All rational and irrational numbers.

reflection. The reflection through a line in the plane or a plane in space is the transformation that takes each point in the plane to its mirror image with respect to the line or its mirror image with respect to the plane in space. It produces a mirror image of a geometric figure.

rigid motion. A transformation of the plane or space, which preserves distance and angles.

root extraction. Finding a number that can be used as a factor a given number of times to produce the original number; for example, the fifth root of 32 = 2 because 2 x 2 x 2 x 2 x 2 = 32).

rotation. A rotation in the plane through an angle q and about a point P is a rigid motion T fixing P so that if Q is distinct from P, then the angle between the lines PQ and PT(Q) is always q . A rotation through an angle q in space is a rigid motion T fixing the points of a line l so that it is a rotation through q in the plane perpendicular to l through some point on l.

scalar matrix. A matrix whose diagonal elements are all equal while the nondiagonal elements are all 0. The identity matrix is an example.

scatterplot. A graph of the points representing a collection of data.

scientific notation. A shorthand way of writing very large or very small numbers. A number expressed in scientific notation is expressed as a decimal number between 1 and 10 multiplied by a power of 10 (e.g., 7000 = 7 x 103 or 0.0000019 = 1.9 x 10-6 ).

similarity. In geometry, two shapes R and S are similar if there is a dilation D (see the definition of dilation) that takes S to a shape congruent to R. It follows that R and S are similar if they are congruent after one of them is expanded or shrunk.

sine. Sin(q) is the y- coordinate of the point on the unit circle so that the ray connecting the point with the origin makes an angle of q with the positive x- axis. When q is an angle of a right triangle, then sin(q) is the ratio of the opposite side with the hypotenuse.

square root. The square roots of n are all the numbers m so that m2 = n. The square roots of 16 are 4 and -4. The square roots of -16 are 4 i and -4 i .

standard deviation. A statistic that measures the dispersion of a sample.

symmetry. A symmetry of a shape S in the plane or space is a rigid motion T that takes S onto itself (T(S) = S). For example, reflection through a diagonal and a rotation through a right angle about the center are both symmetries of the square.

system of linear equations. Set of equations of the first degree (e.g., x + y = 7 and x - y = 1 ). A solution of a set of linear equations is a set of numbers a, b, c, . . . so that when the variables are replaced by the numbers all the equations are satisfied. For example, in the equations above, x = 4 and y = 3 is a solution.

translation. A rigid motion of the plane or space of the form X goes to X + V for a fixed vector V.

transversal. In geometry, given two or more lines in the plane a transversal is a line distinct from the original lines and intersects each of the given lines in a single point.

unit fraction. A fraction whose numerator is 1 (e.g., 1/ p , 1/3, 1/x). Every nonzero number may be written as a unit fraction since, for n not equal to 0, n = 1/(1/ n ).

variable. A placeholder in algebraic expressions; for example, in 3x + y = 23, x and y are variables.

vector. Quantity that has magnitude (length) and direction. It may be represented as a directed line segment.

zeros of a function. The points at which the value of a function is zero.

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Table 1

Mathematics Disciplines, by Grade Level (see above paragraph for explanation of table below)

Mathematics Disciplines, by Grade Level
(see above paragraph for explanation of table below)