§ 4.83. [Reserved].
The provisions of this § 4.83 reserved February 15, 2008, effective February 16, 2008, 38 Pa.B. 872. Immediately preceding text appears at serial page (286560).
APPENDIX A
Academic Standards for Reading, Writing,
Speaking and Listening
I. TABLE OF CONTENTS
Introduction … II.
THE ACADEMIC STANDARDS
| Learning to Read Independently … | 1.1. |
| Purposes for Reading Word Recognition Skills Vocabulary Development Comprehension and Interpretation Fluency | |
| Reading Critically in All Content Areas … | 1.2. |
| Detail Inferences Fact from opinion Comparison Analysis and Evaluation | |
| Reading, Analyzing and Interpreting Literature … | 1.3. |
| Literary Elements Literary Devices Poetry Drama | |
| Types of Writing … | 1.4. |
| Narrative Informational Persuasive | |
| Quality of Writing … | 1.5 |
| Focus Content Organization Style Conventions | |
| Speaking and Listening … | 1.6. |
| Listening Skills Speaking Skills Discussion Presentation | |
| Characteristics and Function of the English Language … | 1.7. |
| Word Origins Variations Application | |
| Research … | 1.8. |
| Selection Location of Information Organization | |
| Glossary … | III. |
II. INTRODUCTION
This document includes Reading, Writing, Speaking and Listening Standards:
• 1.1. Learning to Read Independently
• 1.2. Reading Critically in All Content Areas
• 1.3. Reading, Analyzing and Interpreting Literature
• 1.4. Types of Writing
• 1.5. Quality of Writing
• 1.6. Speaking and Listening
• 1.7. Characteristics and Function of the English Language
• 1.8. Research
The Reading, Writing, Speaking and Listening Standards describe what students should know and be able to do with the English Language at four grade levels (third, fifth, eighth and eleventh). The standards provide the targets for instruction and student learning essential for success in all academic areas, not just language arts classrooms. Although the standards are not a curriculum or a prescribed series of activities, school entities will use them to develop a local school curriculum that will meet local students’ needs.
The language arts—Reading, Writing, Speaking and Listening—are unique because they are processes that students use to learn and make sense of their world. Students do not read “reading”; they read about history, science, mathematics and other content areas as well as about topics for their interest and entertainment. Similarly, students do not write “writing”; they use written words to express their knowledge and ideas and to inform or entertain others.
Because of the unique nature of the language arts, all teachers in a school will use the Reading, Writing, Speaking and Listening Standards. The standards define the skills and strategies employed by effective readers and writers; therefore, all teachers will assist their students in learning them through multiple classroom situations in all the subject areas.
The Reading, Writing, Speaking and Listening standards also provide parents and community members with information about what students should know and be able to do as they progress through the educational program and at graduation. With a clearly defined target provided by the standards, parents, students, educators and community members become partners in learning success.
A glossary is included to assist the reader in understanding terminology contained in the standards.
| 1.1. Learning to Read Independently | |||||||
| 1.1.3. GRADE 3 | 1.1.5. GRADE 5 | 1.1.8. GRADE 8 | 1.1.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Identify the purposes and types of text (e.g., literature, information) before reading. | A. | Establish the purpose for reading a type of text (literature, information) before reading. | A. | Locate appropriate texts (literature, information, documents) for an assigned purpose before reading. | A. | Locate various texts, media and traditional resources for assigned and independent projects before reading. |
| B. | Preview the text formats (e.g., title, headings, chapters, and table of contents). | B. | Select texts for a particular purpose using the format of the text as a guide. | B. | Identify and use common organizational structures and graphic features to comprehend information. | B. | Analyze the structure of informational materials explaining how authors used these to achieve their purposes. |
| C. | Use knowledge of phonics, word analysis (e.g., root words, prefixes and suffixes), syllabication, picture and context clues to decode and understand new words during reading. | C. | Use knowledge of phonics, syllabication, prefixes, suffixes, the dictionary or context clues to decode and understand new words during reading. Use these words accurately in writing and speaking. | C. | Use knowledge of root words as well as context clues and glossaries to understand specialized vocabulary in the content areas during reading. Use these words accurately in speaking and writing. | C. | Use knowledge of root words and words from literary works to recognize and understand the meaning of new words during reading. Use these words accurately in speaking and writing. |
| D. | Read text using self-monitoring comprehen- sion strategies (e.g., predict, revise predictions, reread, use text organization headings, graphics, charts, and adjust reading rate). | D. | Identify the basic ideas and facts in text using strategies (e.g., prior knowledge, illustrations and headings) and information from other sources to make predictions about text. | D. | Identify basic facts and ideas in text using specific strategies (e.g., recall genre characteristics, set a purpose for reading, generate essential questions as aids to comprehension and clarify understanding through rereading and discussion). | D. | Identify, describe, evaluate and synthesize the essential ideas in text. Assess those reading strategies that were most effective in learning from a variety of texts. |
| E. | Acquire a reading vocab- ulary by identifying and correctly using words, (e.g. antonyms, synonyms, categories of words). Use a dictionary when appropriate. | E. | Acquire a reading vocabulary by correctly identifying and using words (e.g., synonyms, homophones and homographs and words with roots, suffixes, and/or prefixes). Use a dictionary or related reference. | E. | Expand a reading vocabulary by identifying and correctly using idioms and words with literal and figurative meanings. Use a dictionary or related reference. | E. | Establish a reading vocabulary by identifying and correctly using new words acquired through the study of their relationships to other words. Use a dictionary or related reference. |
| F. | Understand the meaning of and use correctly new vocabulary learned in various subject areas. | F. | Identify, understand the meaning of and use correctly key vocabulary from various subject areas. | F. | Understand the meaning of and apply key vocabulary across the various subject areas. | F. | Understand the meaning of and apply key vocabulary across the various subject areas. |
| G. | Demonstrate after reading understanding and interpretation of both fiction and nonfiction text. • Retell or summarize the major ideas, themes or procedures of the text. • Connect the new information or ideas in the text to known information. | G. | Demonstrate after reading understanding and interpretation of both fiction and nonfiction text, • Summarize the major ideas, themes or procedures of the text. • Relate new information or ideas from the text to that learned through additional reading and | G. | Demonstrate after reading understanding and interpretation of both fiction and nonfiction text, including public documents. • Make, and support with evidence, assertions about texts. • Compare and contrast texts using themes, | G. | Demonstrate after reading understanding and interpretation of both fiction and nonfiction text, including public documents. • Make, and support with evidence, assertions about texts. • Compare and contrast texts using themes, |
| • Clarify ideas and understandings through rereading and discussion. |
media (e.g., films, audiotapes). |
settings, characters and ideas. |
settings, characters and ideas. | ||||
| • Make responsible assertions about the text by citing evidence from the text. |
rereading and discussion. |
information. |
information. | ||||
| H. | Demonstrate fluency and comprehension in reading. • Read familiar materials aloud with accuracy. • Self-correct mistakes. • Use appropriate rhythm, flow, meter and pronunciation. • Read a variety of genres and types of text. • Demonstrate comprehension (Standard 1.1.3.G.). | H. | Demonstrate fluency and comprehension in reading. • Read familiar materials aloud with accuracy. • Self-correct mistakes. • Use appropriate rhythm, flow, meter and pronunciation. • Read a variety of genres and types of text. • Demonstrate comprehension (Standard 1.1.5.G.). | H. | Demonstrate fluency and comprehension in reading. • Read familiar materials aloud with accuracy. • Self-correct mistakes. • Use appropriate rhythm, flow, meter and pronunciation. • Read a variety of genres and types of text. • Demonstrate comprehension (Standard 1.1.8.G.). | H. | Demonstrate fluency and comprehension in reading. • Read familiar materials aloud with accuracy. • Self-correct mistakes. • Use appropriate rhythm, flow, meter and pronunciation. • Read a variety of genres and types of text. • Demonstrate comprehension (Standard 1.1.11.G.). |
| (Recommend: 25 books/year) | (Recommend: 25 books/year) | (Recommend: 25 books/year) | (Recommend: 25 books/year) | ||||
| 1.2. Reading Critically in All Content Areas | |||||||
| 1.2.3. GRADE 3 | 1.2.5. GRADE 5 | 1.2.8. GRADE 8 | 1.2.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Read and understand essential content of informational texts and documents in all academic areas. • Differentiate fact from opinion within text. • Distinguish between essential and nonessential information within a text. • Make inferences from text when studying a topic (e.g., science, social studies) and draw conclusions based on text. | A. | Read and understand essential content of informational texts and documents in all academic areas. • Differentiate fact from opinion across texts. • Distinguish between essential and nonessential information across a variety of texts, identifying stereotypes and exaggeration where present. • Make inferences about similar concepts in multiple texts and draw conclusions. | A. | Read and understand essential content of informational texts and documents in all academic areas. • Differentiate fact from opinion utilizing resources that go beyond traditional text (e.g., newspapers, magazines and periodicals) to electronic media. • Distinguish between essential and nonessential information across texts and going | A. | Read and understand essential content of informational texts and documents in all academic areas. • Differentiate fact from opinion across a variety of texts, by using complete and accurate information, coherent arguments and points of view. • Distinguish between essential and nonessential information across a variety of sources, identifying the |
| • Analyze text organization and content to derive meaning from text using established criteria. | • Evaluate text organization and content to determine the author’s purpose and effectiveness. |
beyond texts to a variety of media; identify bias and propaganda where present. |
use of proper references or authorities and propaganda techniques where present. | ||||
| B. | Use and understand a variety of media and evaluate the quality of material produced. • Use electronic media for research. • Identify techniques used in television and use the knowledge to distinguish between facts and misleading information. • Assess the quality of media project (e.g., script, play, audiotape) that has been developed for a targeted audience. | B. | Use and understand a variety of media and evaluate the quality of material produced. • Use a variety of media (e.g., computerized card catalogues, encyclopedias) for research. • Evaluate the role of media as a source of both entertainment and information. • Use established criteria to design and develop media project (e.g., script, play, audiotape) for a targeted audience. | B. | Use and understand a variety of media and evaluate the quality of material produced. • Compare and analyze how different media offer a unique perspective on the information presented. • Analyze the techniques of particular media messages and their effect on a targeted audience. • Use, design and develop a media project that expands understanding (e.g., authors and works from a particular historical period). | B. | Use and understand a variety of media and evaluate the quality of material produced. • Select appropriate electronic media for research and evaluate the quality of the information received. • Explain how the techniques used in electronic media modify traditional forms of discourse for different purposes. • Use, design and develop a media project to demonstrate understanding (e.g., a major writer or literary period or movement). |
| C. | Produce work in at least one literary genre that follows the conventions of the genre. | C. | Produce work in at least one literary genre that follows the conventions of the genre. | C. | Produce work in at least one literary genre that follows the conventions of the genre. | C. | Produce work in at least one literary genre that follows the conventions of the genre. |
| 1.3. Reading, Analyzing and Interpreting Literature | |||||||
| 1.3.3. GRADE 3 | 1.3.5. GRADE 5 | 1.3.8. GRADE 8 | 1.3.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Read and understand works of literature. | A. | Read and understand works of literature. | A. | Read and understand works of literature. | A. | Read and understand works of literature. |
| B. | Identify literary elements in stories describing characters, setting and plot. | B. | Compare the use of literary elements within and among texts, including characters, setting, plot, theme, and point of view. | B. | Analyze the use of literary elements by an author including characterization, setting, plot, theme, point of view, tone, and style. | B. | Analyze the relationships, uses and effectiveness of literary elements used by one or more authors in similar genres including characterization, setting, plot, theme, point of view, tone, and style. |
| C. | Identify literary devices in stories. (e.g., rhyme, rhythm, personification). | C. | Describe how the author uses literary devices to convey meaning. • Sound techniques (e.g., rhyme, rhythm, meter, alliteration) • Figurative language (e.g., personification, simile, metaphor, hyperbole). | C. | Analyze the effect of various literary devices. • Sound techniques (e.g., rhyme, rhythm, meter, alliteration) • Figurative language (e.g., personification, simile, metaphor, hyperbole, allusion). | C. | Analyze the effectiveness, in terms of literary quality, of the author’s use of literary devices. • Sound techniques (e.g., rhyme, rhythm, meter, alliteration) • Figurative language (e.g., personification, simile, metaphor, hyperbole, irony, satire) • Literary structures (e.g., foreshadowing, flashbacks, progressive and digressive time). |
| D. | Identify the structures in poetry (e.g., pattern books, predictable books nursery rhymes). | D. | Identify and respond to the effects of sound and structure in poetry (e.g., alliteration, rhyme, verse form). | D. | Identify poetic forms (e.g., ballad, sonnet, couplet). | D. | Analyze and evaluate in poetry the appropriateness of diction and figurative language (e.g., irony, understatement, overstatement, paradox). |
| E. | Identify the structures in drama (e.g., dialogue, story enactment, acts, scenes). | E. | Analyze drama as information source, entertainment, persuasion or transmitter of culture. | E. | Analyze drama to determine the reasons for a character’s actions taking into account the situation and basic motivation of the character. | E. | Analyze how a scriptwriter’s use of words creates tone and mood, and how choice of words advances the theme or purpose of the work. |
| F. | Read and respond to nonfiction and fiction including poetry and drama. | F. | Read and respond to nonfiction and fiction including poetry and drama. | F. | Read and respond to nonfiction and fiction including poetry and drama. | F. | Read and respond to nonfiction and fiction including poetry and drama. |
| 1.4. Types of Writing | |||||||
| 1.4.3. GRADE 3 | 1.4.5. GRADE 5 | 1.4.8. GRADE 8 | 1.4.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Write narrative pieces (e.g., stories, poems, plays). • Include detailed descriptions of people, places and things. • Use relevant illustrations. • Include literary elements (Standard 1.3.3.B.). | A. | Write poems, plays and multi-paragraph stories. • Include detailed descriptions of people, places and things. • Use relevant illustrations. • Utilize dialogue. • Apply literary conflict. • Include literary elements (Standard 1.3.5.B). • Use literary devices (Standard 1.3.5.C.). | A. | Write short stories, poems and plays. • Apply varying organizational methods. • Use relevant illustrations. • Utilize dialogue. • Apply literary conflict. • Include literary elements (Standard 1.3.8.B.). • Use literary devices (Standard 1.3.8.C.). | A. | Write short stories, poems and plays. • Apply varying organizational methods. • Use relevant illustrations. • Utilize dialogue. • Apply literary conflict. • Include varying characteristics (e.g., from limerick to epic, from whimsical to dramatic). • Include literary elements (Standard 1.3.11.B.). • Use literary devices (Standard 1.3.11.C.). |
| B. | Write informational pieces (e.g., descriptions, letters, reports, instructions) using illustrations when relevant. | B. | Write multi-paragraph informational pieces (e.g., essays, descriptions, letters, reports, instructions). • Include cause and effect. • Develop a problem and solution when appropriate to the topic. • Use relevant graphics (e.g., maps, charts, graphs, tables, illustrations, photographs). | B. | Write multi-paragraph informational pieces (e.g., letters, descriptions, reports, instructions, essays, articles, interviews). • Include cause and effect. • Develop a problem and solution when appropriate to the topic. • Use relevant graphics (e.g., maps, charts, graphs, tables, illustrations, photographs). • Use primary and secondary sources. | B. | Write complex informational pieces (e.g., research papers, analyses, evaluations, essays). • Include a variety of methods to develop the main idea. • Use precise language and specific detail. • Include cause and effect. • Use relevant graphics (e.g., maps, charts, graphs, tables, illustrations, photographs). • Use primary and secondary sources. |
| C. | Write an opinion and support it with facts. | C. | Write persuasive pieces with a clearly stated position or opinion and supporting detail, citing sources when needed. | C. | Write persuasive pieces. • Include a clearly stated position or opinion. • Include convincing, elaborated and properly cited evidence. • Develop reader interest. • Anticipate and counter reader concerns and arguments. | C. | Write persuasive pieces. • Include a clearly stated position or opinion. • Include convincing, elaborated and properly cited evidence. • Develop reader interest. • Anticipate and counter reader concerns and arguments. • Include a variety of methods to advance the argument or position. |
| D. | Maintain a written record of activities, course work, experience, honors and interests. | D. | Maintain a written record of activities, course work, experience, honors and interests. | ||||
| E. | Write a personal resum[eacute]. | ||||||
| 1.5. Quality of Writing | |||||||
| 1.5.3. GRADE 3 | 1.5.5. GRADE 5 | 1.5.8. GRADE 8 | 1.5.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Write with a sharp, distinct focus identifying topic, task and audience. | A. | Write with a sharp, distinct focus identifying topic, task and audience. | A. | Write with a sharp, distinct focus. • Identify topic, task and audience. • Establish a single point of view. | A. | Write with a sharp, distinct focus. • Identify topic, task and audience. • Establish and maintain a single point of view. |
| B. | Write using well-developed content appropriate for the topic. • Gather and organize information. • Write a series of related sentences or paragraphs with one central idea. • Incorporate details relevant and appropriate to the topic. | B. | Write using well-developed content appropriate for the topic. • Gather, organize and select the most effective information appropriate for the topic, task and audience. • Write paragraphs that have a topic sentence and supporting details. | B. | Write using well-developed content appropriate for the topic. • Gather, determine validity and reliability of and organize information. • Employ the most effective format for purpose and audience. • Write paragraphs that have details and information specific to the topic and relevant to the focus. | B. | Write using well-developed content appropriate for the topic. • Gather, determine validity and reliability of, analyze and organize information. • Employ the most effective format for purpose and audience. • Write fully developed paragraphs that have details and information specific to the topic and relevant to the focus. |
| C. | Write with controlled and/or subtle organization. • Sustain a logical order. • Include a recognizable beginning, middle and end. | C. | Write with controlled and/or subtle organization. • Sustain a logical order within sentences and between paragraphs using meaningful transitions. • Include an identifiable introduction, body and conclusion. | C. | Write with controlled and/or subtle organization. • Sustain a logical order within sentences and between paragraphs using meaningful transitions. • Establish topic and purpose in the introduction. • Reiterate the topic and purpose in the conclusion. | C. | Write with controlled and/or subtle organization. • Sustain a logical order throughout the piece. • Include an effective introduction and conclusion |
| D. | Write with an awareness of the stylistic aspects of composition. • Use sentences of differing lengths and complexities. | D. | Write with an understanding of the stylistic aspects of composition. • Use different types and lengths of sentences. | D. | Write with an understanding of the stylistic aspects of composition. • Use different types and lengths of sentences. | D. | Write with a command of the stylistic aspects of composition. • Use different types and lengths of sentences. • Use precise language. |
| • Use descriptive words and action verbs. | • Use precise language including adjectives, adverbs, action verbs and specific details that convey the writer’s meaning. • Develop and maintain a consistent voice. | • Use tone and voice through the use of precise language. | |||||
| E. | Revise writing to improve detail and order by identifying missing information and determining whether ideas follow logically. | E. | Revise writing to improve organization and word choice; check the logic, order of ideas and precision of vocabulary. | E. | Revise writing after rethinking logic of organization and rechecking central idea, content, paragraph development, level of detail, style, tone and word choice. | E. | Revise writing to improve style, word choice, sentence variety and subtlety of meaning after rethinking how questions of purpose, audience and genre have been addressed. |
| F. | Edit writing using the conventions of language. • Spell common, frequently used words correctly. • Use capital letters correctly (first word in sentences, proper nouns, pronoun “I”). • Punctuate correctly (periods, exclamation points, question marks, commas in a series). • Use nouns, pronouns, verbs, adjectives, adverbs and conjunctions properly. • Use complete sentences (simple, compound, | F. | Edit writing using the conventions of language. • Spell common, frequently used words correctly. • Use capital letters correctly • Punctuate correctly (periods, exclamation points, question marks, commas, quotation marks, apostrophes). • Use nouns, pronouns, verbs, adjectives, adverbs, conjunctions, prepositions and interjections properly. • Use complete sentences (simple, compound, | F. | Edit writing using the conventions of language. • Spell common, frequently used words correctly. • Use capital letters correctly. • Punctuate correctly (periods, exclamation points, question marks, commas, quotation marks, apostrophes, colons, semicolons, parentheses). • Use nouns, pronouns, verbs, adjectives, adverbs, conjunctions prepositions and interjections properly. | F. | Edit writing using the conventions of language. • Spell all words correctly. • Use capital letters correctly. • Punctuate correctly (periods, exclamation points, question marks, commas, quotation marks, apostrophes, colons, semicolons, parentheses, hyphens, brackets, ellipses). • Use nouns, pronouns, verbs, adjectives, adverbs, conjunctions, prepositions and interjections properly. |
|
declarative, interrogative, exclamatory and imperative). |
declarative, interrogative, exclamatory and imperative). | • Use complete sentences (simple, compound, complex, declarative, interrogative, exclamatory and imperative). | • Use complete sentences (simple, compound, complex, declarative, interrogative, exclamatory and imperative). | ||||
| G. | Present and/or defend written work for publication when appropriate. | G. | Present and/or defend written work for publication when appropriate. | G. | Present and/or defend written work for publication when appropriate. | G. | Present and/or defend written work for publication when appropriate. |
| 1.6. Speaking and Listening | |||||||
| 1.6.3. GRADE 3 | 1.6.5. GRADE 5 | 1.6.8. GRADE 8 | 1.6.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Listen to others. • Ask questions as an aid to understanding. • Distinguish fact from opinion. | A. | Listen to others. • Ask pertinent questions. • Distinguish relevant information, ideas and opinions from those that are irrelevant. • Take notes when prompted. | A. | Listen to others. • Ask probing questions. • Analyze information, ideas and opinions to determine relevancy. • Take notes when needed. | A. | Listen to others. • Ask clarifying questions. • Synthesize information, ideas and opinions to determine relevancy. • Take notes. |
| B. | Listen to a selection of literature (fiction and/or nonfiction). • Relate it to similar experiences. • Predict what will happen next. • Retell a story in chronological order. • Identify and define new words and concepts. | B. | Listen to a selection of literature (fiction and/or nonfiction). • Relate it to what is known. • Predict the result of the story actions. • Retell actions of the story in sequence, explain the theme and describe the characters and setting. | B. | Listen to selections of literature (fiction and/or nonfiction). • Relate them to previous knowledge. • Predict content/events. • Summarize events and identify the significant points. • Identify and define new words and concepts. • Analyze the selections. | B. | Listen to selections of literature (fiction and/or nonfiction). • Relate them to previous knowledge. • Predict solutions to identified problems. • Summarize and reflect on what has been heard. • Identify and define new words and concepts. • Analyze and synthesize |
| • Identify and define new words and concepts. • Summarize the selection. |
the selections relating them to other selections heard or read. | ||||||
| C. | Speak using skills appropriate to formal speech situations. • Use appropriate volume. • Pronounce most words accurately. • Pace speech so that is understandable. • Demonstrate an awareness of audience. | C. | Speak using skills appropriate to formal speech situations. • Use complete sentences. • Pronounce words correctly. • Use appropriate volume. • Pace speech so that it is understandable. • Adjust content for different audiences (e.g., fellow classmates, parents). • Speak with a purpose in mind. | C. | Speak using skills appropriate to formal speech situations. • Use complete sentences. • Pronounce words correctly. • Adjust volume to purpose and audience. • Adjust pace to convey meaning. • Add stress (emphasis) and inflection to enhance meaning. | C. | Speak using skills appropriate to formal speech situations. • Use a variety of sentence structures to add interest to a presentation. • Pace the presentation according to audience and purpose. • Adjust stress, volume, and inflection to provide emphasis to ideas or to influence the audience. |
| D. | Contribute to discussions. • Ask relevant questions. • Respond with appropriate information or opinions to questions asked. • Listen to and acknowledge the contributions of others. • Display appropriate turn-taking behaviors. | D. | Contribute to discussions. • Ask relevant questions. • Respond with relevant information or opinions to questions asked. • Listen to and acknowledge the contributions of others. • Adjust involvement to encourage equitable participation. • Give reasons for opinions. • Summarize, when prompted. | D. | Contribute to discussions. • Ask relevant, probing questions. • Respond with relevant information, ideas or reasons in support of opinions expressed. • Listen to and acknowledge the contributions of others. • Adjust tone and involvement to encourage equitable participation. • Clarify, illustrate or expand on a response when asked. • Present support for opinions. | D. | Contribute to discussions. • Ask relevant, clarifying questions. • Respond with relevant information or opinions to questions asked. • Listen to and acknowledge the contributions of others. • Adjust tone and involvement to encourage equitable participation. • Facilitate total group participation. • Introduce relevant, facilitating information, ideas and opinions to enrich the discussion. |
| • Paraphrase and summarize, when prompted. | • Paraphrase and summarize as needed. | ||||||
| E. | Participate in small and large group discussions and presentations. • Participate in everyday conversation. • Present oral readings. • Deliver short reports (e.g., Show-and-Tell, field trip summary). • Conduct short interviews. • Give simple directions and explanations. • Report an emergency. | E. | Participate in small and large group discussions and presentations. • Participate in everyday conversation. • Present an oral reading. • Deliver research reports. • Conduct interviews. • Plan and participate in group presentations. • Contribute to informal debates. | E. | Participate in small and large group discussions and presentations. • Initiate everyday conversation. • Select a topic and present an oral reading. • Conduct interviews as part of the research process. • Organize and participate in informal debates. | E. | Participate in small and large group discussions and presentations. • Initiate everyday conversation. • Select and present an oral reading on an assigned topic. • Conduct interviews. • Participate in a formal interview (e.g., for job, college). • Organize and participate in informal debate around a specific topic. |
| • Use evaluation guides (e.g., National Issues Forum, Toastmasters) to evaluate group discussion (e.g., of peers, on television). | |||||||
| F. | Use media for learning purposes. • Explain the importance of television, radio, film and Internet in the lives of people. • Explain how advertising sells products. • Show or explain what was learned (e.g., audiotape, computer download). | F. | Use media for learning purposes. • Compare information received on television with that received on radio or in newspapers. • Access information on Internet. • Discuss the reliability of information received on Internet sources. • Explain how film can | F. | Use media for learning purposes. • Describe how the media provides information that is sometimes accurate, sometimes biased based on a point of view or by the opinion or beliefs of the presenter. • Analyze the role of advertising in the media. | F. | Use media for learning purposes. • Use various forms of media to elicit information, to make a student presentation and to complete class assignments and projects. • Evaluate the role of media in focusing attention and forming |
|
represent either accurate versions or fictional versions of the same event. | • Create a multi-media (e.g., film, music, computer-graphic) presentation for display or transmission. |
opinions. | |||||
| 1.7. Characteristics and Functions of the English Language | |||||||
| 1.7.3. GRADE 3 | 1.7.5. GRADE 5 | 1.7.8. GRADE 8 | 1.7.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Identify words from other languages that are commonly used English words. | A. | Identify words from other languages that are commonly used English words. Use a dictionary to find the meanings and origins of these words. | A. | Describe the origins and meanings of common, learned and foreign words used frequently in English language (e.g., carte blanche, faux pas). | A. | Describe the influence of historical events on the English language. |
| B. | Identify variations in the dialogues of literary characters and relate them to differences in occupation or geographical location. | B. | Identify differences in formal and informal speech (e.g., dialect, slang, jargon). | B. | Analyze the role and place of standard American English in speech, writing and literature. | B. | Analyze when differences in language are a source of negative or positive stereotypes among groups. |
| C. | Identify word meanings that have changed over time (e.g., cool, mouse). | C. | Identify new words that have been added to the English language over time. | C. | Explain and evaluate the role and influence of the English language within and across countries. | ||
| 1.8. Research | |||||||
| 1.8.3. GRADE 3 | 1.8.5. GRADE 5 | 1.8.8. GRADE 8 | 1.8.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Select a topic for research. | A. | Select and refine a topic for research. | A. | Select and refine a topic for research. | A. | Select and refine a topic for research. |
| B. | Locate information using appropriate sources and strategies. • Locate resources for a particular task (e.g., newspapers, dictionary). • Select sources (e.g., dictionaries, encyclopedias, interviews to write a family history, observations, electronic media). • Use tables of contents, key words and guide words. | B. | Locate information using appropriate sources and strategies. • Evaluate the usefulness and qualities of the sources. • Select appropriate sources (e.g., dictionaries, encyclopedias, other reference materials, interviews, observations, computer databases). • Use tables of contents, indices, key words, cross-references and | B. | Locate information using appropriate sources and strategies. • Determine valid resources for researching the topic, including primary and secondary sources. • Evaluate the importance and quality of the sources. • Select essential sources (e.g., dictionaries, encyclopedias, other reference materials, interviews, | B. | Locate information using appropriate sources and strategies. • Determine valid resources for researching the topic, including primary and secondary sources. • Evaluate the importance and quality of the sources. • Select sources appropriate to the breadth and depth of the research (e.g., dictionaries, |
| • Use traditional and electronic search tools. |
appendices. |
observations, computer databases). |
thesauruses, other reference materials, interviews, observations, computer databases). | ||||
| C. | Organize and present the main ideas from research. • Take notes from sources using a structured format. • Summarize, orally or in writing, the main ideas. | C. | Organize and present the main ideas from research. • Take notes from sources using a structured format. • Present the topic using relevant information. • Credit sources using a structured format (e.g., author, title). | C. | Organize, summarize and present the main ideas from research. • Identify the steps necessary to carry out a research project. • Take relevant notes from sources. • Develop a thesis statement based on research. • Give precise, formal credit for others’ ideas, images or information using a standard method of documentation. • Use formatting techniques to create an understandable presentation for a designated audience. | C. | Organize, summarize and present the main ideas from research. • Take notes relevant to the research topic. • Develop a thesis statement based on research. • Anticipate readers’ problems or misunderstandings. • Give precise, formal credit for others’ ideas, images or information using a standard method of documentation. • Use formatting techniques (e.g., headings, graphics) to aid reader understanding. |
III. GLOSSARY
Alliteration: The repetition of initial consonant sounds in neighboring words. Allusion: An implied or indirect reference in literature to a familiar person, place or event. Analysis: The process or result of identifying the parts of a whole and their relationships to one another. Antonym: A word that is the opposite of another word. Characterization: The method an author uses to reveal characters and their various personalities. Compare: Place together characters, situations or ideas to show common or differing features in literary selections. Context clues: Information from the reading that identifies a word or group of words. Conventions of Language: Mechanics, usage and sentence completeness. Evaluate: Examine and judge carefully. Figurative language: Language that cannot be taken literally since it was written to create a special effect or feeling. Fluency: The clear, easy, written or spoken expression of ideas. Freedom from word-identification problems which might hinder comprehension in silent reading or the expression of ideas in oral reading. Focus: The center of interest or attention. Genre: A category used to classify literary works, usually by form, technique or content (e.g., prose, poetry). Graphic organizer: A diagram or pictorial device that shows relationships. Homophone: One of two or more words pronounced alike, but different in spelling or meaning (e.g., hair/hare, scale (fish)/scale (musical)). Hyperbole: An exaggeration or overstatement (e.g., I was so embarrassed I could have died.). Idiomatic language: An expression peculiar to itself grammatically or that cannot be understood if taken literally (e.g., Let’s get on the ball.). Irony: The use of a word or phrase to mean the exact opposite of its literal or usual meaning; incongruity between the actual result of a sequence of events and the expected result. Literary conflict: The struggle that grows out of the interplay of the two opposing forces in a plot. Literary elements: The essential techniques used in literature (e.g., characterization, setting, plot, theme). Literary devices: Tools used by the author to enliven and provide voice to the writing (e.g., dialogue, alliteration). Literary
structures: The author’s method of organizing text, (e.g., foreshadowing and flashbacks). Metaphor: The comparison of two unlike things in which no words of comparison (like or as) are used (e.g., That new kid in class is really a squirrel.). Meter: The repetition of stressed and unstressed syllables in a line of poetry. Narrative: A story, actual or fictional, expressed orally or in writing. Paraphrase: Restate text or passage in other words, often to clarify meaning or show understanding. Pattern book: A book with a predictable plot structure and often written with predictable text; also known as predictable book. Personification: An object or abstract idea given human qualities or human form (e.g., Flowers danced about the lawn.). Phonics: The relationship between letters and sounds fundamental in beginning reading. Point of view: The way in which an author reveals characters, events and ideas in telling a story; the vantage point from which the story is told. Public document: A document that focuses on civic issues or matters of public policy at the community level and beyond. Reading critically: Reading in which a questioning attitude, logical analysis and inference are used to judge the worth of text; evaluating relevancy and adequacy of what is read; the judgment of validity or worth of what is read, based on sound criteria. Reading rate: The speed at which a person reads, usually silently. Research: A systematic inquiry into a subject or problem in order to discover, verify or revise relevant facts or principles having to do with that subject or problem. Satire: A literary tone used to ridicule or make fun of human vice or weakness. Self-monitor: Know when what one is reading or writing is not making sense; adjust strategies for comprehension. Semantics: The study of meaning in language. Simile: A comparison of two unlike things in which a word of comparison (like or as) is used (e.g., She eats like a bird.). Sources: Primary: Text and/or artifacts that tell or show a first-hand account of an event; original works used when researching. Secondary: Text and/or artifacts used when researching that are derived from something original. Subject area: An organized body of knowledge; a discipline; a content area. Style: How an author writes; an author’s use of language, its effects and appropriateness to the author’s intent and theme. Synonym: One of two or more words in a language that have highly similar meanings (e.g., sorrow, grief, sadness). Syntax: The pattern or structure of word order in sentences, clauses and phrases. Theme: A topic of discussion or writing; a major idea broad enough to cover the entire scope of a literary 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. Tone: The attitude of the author toward the audience and characters (e.g., serious or humorous). Voice: The fluency, rhythm and liveliness in writing that makes it unique to the writer.
| Alliteration: | The repetition of initial consonant sounds in neighboring words. |
| Allusion: | An implied or indirect reference in literature to a familiar person, place or event. |
| Analysis: | The process or result of identifying the parts of a whole and their relationships to one another. |
| Antonym: | A word that is the opposite of another word. |
| Characterization: | The method an author uses to reveal characters and their various personalities. |
| Compare: | Place together characters, situations or ideas to show common or differing features in literary selections. |
| Context clues: | Information from the reading that identifies a word or group of words. |
| Conventions of Language: | Mechanics, usage and sentence completeness. |
| Evaluate: | Examine and judge carefully. |
| Figurative language: | Language that cannot be taken literally since it was written to create a special effect or feeling. |
| Fluency: | The clear, easy, written or spoken expression of ideas. Freedom from word-identification problems which might hinder comprehension in silent reading or the expression of ideas in oral reading. |
| Focus: | The center of interest or attention. |
| Genre: | A category used to classify literary works, usually by form, technique or content (e.g., prose, poetry). |
| Graphic organizer: | A diagram or pictorial device that shows relationships. |
| Homophone: | One of two or more words pronounced alike, but different in spelling or meaning (e.g., hair/hare, scale (fish)/scale (musical)). |
| Hyperbole: | An exaggeration or overstatement (e.g., I was so embarrassed I could have died.). |
| Idiomatic language: | An expression peculiar to itself grammatically or that cannot be understood if taken literally (e.g., Let’s get on the ball.). |
| Irony: | The use of a word or phrase to mean the exact opposite of its literal or usual meaning; incongruity between the actual result of a sequence of events and the expected result. |
| Literary conflict: | The struggle that grows out of the interplay of the two opposing forces in a plot. |
| Literary elements: | The essential techniques used in literature (e.g., characterization, setting, plot, theme). |
| Literary devices: | Tools used by the author to enliven and provide voice to the writing (e.g., dialogue, alliteration). |
| Literary structures: | The author’s method of organizing text, (e.g., foreshadowing and flashbacks). |
| Metaphor: | The comparison of two unlike things in which no words of comparison (like or as) are used (e.g., That new kid in class is really a squirrel.). |
| Meter: | The repetition of stressed and unstressed syllables in a line of poetry. |
| Narrative: | A story, actual or fictional, expressed orally or in writing. |
| Paraphrase: | Restate text or passage in other words, often to clarify meaning or show understanding. |
| Pattern book: | A book with a predictable plot structure and often written with predictable text; also known as predictable book. |
| Personification: | An object or abstract idea given human qualities or human form (e.g., Flowers danced about the lawn.). |
| Phonics: | The relationship between letters and sounds fundamental in beginning reading. |
| Point of view: | The way in which an author reveals characters, events and ideas in telling a story; the vantage point from which the story is told. |
| Public document: | A document that focuses on civic issues or matters of public policy at the community level and beyond. |
| Reading critically: | Reading in which a questioning attitude, logical analysis and inference are used to judge the worth of text; evaluating relevancy and adequacy of what is read; the judgment of validity or worth of what is read, based on sound criteria. |
| Reading rate: | The speed at which a person reads, usually silently. |
| Research: | A systematic inquiry into a subject or problem in order to discover, verify or revise relevant facts or principles having to do with that subject or problem. |
| Satire: | A literary tone used to ridicule or make fun of human vice or weakness. |
| Self-monitor: | Know when what one is reading or writing is not making sense; adjust strategies for comprehension. |
| Semantics: | The study of meaning in language. |
| Simile: | A comparison of two unlike things in which a word of comparison (like or as) is used (e.g., She eats like a bird.). |
| Sources: | |
| Primary: | Text and/or artifacts that tell or show a first-hand account of an event; original works used when researching. |
| Secondary: | Text and/or artifacts used when researching that are derived from something original. |
| Subject area: | An organized body of knowledge; a discipline; a content area. |
| Style: | How an author writes; an author’s use of language, its effects and appropriateness to the author’s intent and theme. |
| Synonym: | One of two or more words in a language that have highly similar meanings (e.g., sorrow, grief, sadness). |
| Syntax: | The pattern or structure of word order in sentences, clauses and phrases. |
| Theme: | A topic of discussion or writing; a major idea broad enough to cover the entire scope of a literary 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. |
| Tone: | The attitude of the author toward the audience and characters (e.g., serious or humorous). |
| Voice: | The fluency, rhythm and liveliness in writing that makes it unique to the writer. |
Academic Standards for Mathematics
IV. TABLE OF CONTENTS
Introduction … V.
THE ACADEMIC STANDARDS
| Numbers, Number Systems and Number Relationships… | 2.1. |
| Types of numbers (e.g., whole, prime, irrational, complex) Equivalent forms (e.g. fractions, decimals, percents) | |
| Computation and Estimation… | 2.2. |
| Basic functions (+, -, x, ÷) Reasonableness of answers Calculators | |
| Measurement and Estimation… | 2.3. |
| Types of measurement (e.g., length, time) Units and tools of measurement Computing and comparing measurements | |
| Mathematical Reasoning and Connections… | 2.4. |
| Using inductive and deductive reasoning Validating arguments (e.g., if . . . then statements, proofs) | |
| Mathematical Problem Solving and Communication… | 2.5. |
| Problem solving strategies Representing problems in various ways Interpreting results | |
| Statistics and Data Analysis… | 2.6. |
| Collecting and reporting data (e.g., charts, graphs) Analyzing data | |
| Probability and Predictions… | 2.7. |
| Validity of data Calculating probability to make predictions | |
| Algebra and Functions… | 2.8. |
| Equations Patterns and functions | |
| Geometry… | 2.9. |
| Shapes and their properties Using geometric principles to solve problems | |
| Trigonometry… | 2.10. |
| Right angles Measuring and computing with triangles Using graphing calculators | |
| Concepts of Calculus… | 2.11. |
| Comparing quantities and values Graphing rates of change Continuing patterns infinitely | |
| Glossary… | VI. |
V. INTRODUCTION
This document includes Mathematics Standards:
• 2.1. Numbers, Number Systems and Number Relationships
• 2.2. Computation and Estimation
• 2.3. Measurement and Estimation
• 2.4. Mathematical Reasoning and Connections
• 2.5. Mathematical Problem Solving and Communication
• 2.6. Statistics and Data Analysis
• 2.7. Probability and Predictions
• 2.8. Algebra and Functions
• 2.9. Geometry
• 2.10. Trigonometry
• 2.11. Concepts of Calculus
The Mathematics Standards describe what students should know and be able to do at four grade levels (third, fifth, eighth and eleventh). They reflect the increasing complexity and sophistication that students are expected to achieve as they progress through school.
This document avoids repetition of learned skills, making an obvious progression across grade levels less explicit. Teachers shall expect that students know and can apply the concepts and skills expressed at the preceding level. Consequently, previous learning is reinforced but not retaught.
Students who achieve these mathematical standards will be able to communicate mathematically. Although it is an interesting and enjoyable study for its own sake, mathematics is most appropriately used as a tool to help organize and understand information from other academic disciplines. Because our capacity to deal with all things mathematical is changing rapidly, students must be able to bring the most modern and effective technology to bear on their learning of mathematical concepts and skills.
A glossary is included to assist the reader in understanding terminology contained in the standards.
| 2.1. Numbers, Number Systems and Number Relationships | |||||||
| 2.1.3. GRADE 3 | 2.1.5. GRADE 5 | 2.1.8. GRADE 8 | 2.1.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Count using whole numbers (to 10,000) and by 2’s, 3’s, 5’s, 10’s, 25’s and 100’s. | A. | Use expanded notation to represent whole numbers or decimals. | A. | Represent and use numbers in equivalent forms (e.g., integers, fractions, decimals, percents, exponents, scientific notation, square roots). | A. | Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms). |
| B. | Use whole numbers and fractions to represent quantities. | B. | Apply number theory concepts to rename a number quantity (e.g., six, 6, 12/2, 3 x 2, 10 - 4). | B. | Simplify numerical expressions involving exponents, scientific notation and using order of operations. | ||
| C. | Represent equivalent forms of the same number through the use of concrete objects, drawings, word names and symbols. | C. | Demonstrate that mathematical operations can represent a variety of problem situations. | C. | Distinguish between and order rational and irrational numbers. | ||
| D. | Use drawings, diagrams or models to show the concept of fraction as part of a whole. | D. | Use models to represent fractions and decimals. | D. | Apply ratio and proportion to mathematical problem situations involving distance, rate, time and similar triangles. | ||
| E. | Count, compare and make change using a collection of coins and one-dollar bills. | E. | Explain the concepts of prime and composite numbers. | E. | Simplify and expand algebraic expressions using exponential forms. | ||
| F. | Apply number patterns (even and odd) and compare values of numbers on the hundred board. | F. | Use simple concepts of negative numbers (e.g., on a number line, in counting and in temperature). | F. | Use the number line model to demonstrate integers and their applications. | ||
| G. | Use concrete objects to count, order and group. | G. | Develop and apply number theory concepts (e.g., primes, factors, multiples, composites) to represent numbers in various ways. | G. | Use the inverse relationships between addition, subtraction, multiplication, division, exponentiation and root extraction to determine unknown quantities in equations. | ||
| H. | Demonstrate understanding of one-to-one correspondence. | ||||||
| I. | Apply place-value concepts and numeration to counting, ordering and grouping. | ||||||
| J. | Estimate, approximate, round or use exact numbers as appropriate. | ||||||
| K. | Describe the inverse relationship between addition and subtraction. | ||||||
| L. | Demonstrate knowledge of basic facts in four basic operations. | ||||||
| 2.2. Computation and Estimation | |||||||
| 2.2.3. GRADE 3 | 2.2.5. GRADE 5 | 2.2.8. GRADE 8 | 2.2.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Apply addition and subtraction in everyday situations using concrete objects. | A. | Create and solve word problems involving addition, subtraction, multiplication and division of whole numbers. | A. | Complete calculations by applying the order of operations. | A. | Develop and use computation concepts, operations and procedures on real numbers in problem solving situations. |
| B. | Solve single- and double-digit addition and subtraction problems with regrouping in vertical form. | B. | Develop and apply algorithms to solve word problems that involve addition, subtraction, and/or multiplication with decimals with and without regrouping. | B. | Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions. | B. | Use estimation to solve problems for which exact answer is not needed. |
| C. | Demonstrate the concept of multiplication as repeated addition and arrays. | C. | Develop and apply algorithms to solve word problems that involve addition, subtraction, and/or multiplication with fractions and mixed numbers that include like and unlike denominators. | C. | Estimate the value of irrational numbers. | C. | Construct and apply mathematical models, including lines and curves of best fit, to estimate values of related quantities. |
| D. | Demonstrate the concept of division as repeated subtraction and as sharing. | D. | Demonstrate the ability to round numbers. | D. | Estimate amount of tips and discounts using ratios, proportions and percents. | D. | Describe and explain the amount of error that may exist in a computation using estimates. |
| E. | Use estimation skills to arrive at conclusions. | E. | Determine through estimations the reasonableness of answers to problems involving addition, subtraction, multiplication and division of whole numbers. | E. | Determine the appropriateness of overestimating or underestimating in computation. | E. | Recognize that the degree of precision needed in calculating a number depends on how the results will be used and the instruments used to generate the measure. |
| F. | Determine the reasonableness of calculated answers. | F. | Demonstrate skills for using fraction calculators to verify conjectures, confirm computations and explore complex problem-solving situations. | F. | Identify the difference between exact value and approximation and determine which is appropriate for a given situation. | F. | Demonstrate skills for using computer spreadsheets and scientific and graphing calculators. |
| G. | Explain addition and subtraction algorithms with regrouping. | G. | Apply estimation strategies to a variety of problems including time and money. | ||||
| H. | Explain multiplication and division algorithms. | ||||||
| I. | Select a method for computation and explain why it is appropriate. | ||||||
| 2.3. Measurement and Estimation | |||||||
| 2.3.3. GRADE 3 | 2.3.5. GRADE 5 | 2.3.8. GRADE 8 | 2.3.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills to: | |||||||
| A. | Compare measurable characteristics of different objects on the same dimensions (e.g., time, temperature, area, length, weight, capacity, perimeter). | A. | Select and use appropriate instruments and units for measuring quantities (e.g., perimeter, volume, area, weight, time, temperature). | A. | Develop formulas and procedures for determining measurements (e.g., area, volume, distance). | A. | Select and use appropriate units and tools to measure to the degree of accuracy required in particular measurement situations. |
| B. | Determine the measurement of objects with nonstandard and standard units (e.g., US customary and metric). | B. | Select and use standard tools to measure the size of figures with specified accuracy, including length, width, perimeter and area. | B. | Solve rate problems (e.g., rate x time = distance, principal x interest rate = interest). | B. | Measure and compare angles in degrees and radians. |
| C. | Determine and compare elapsed times. | C. | Estimate, refine and verify specified measurements of objects. | C. | Measure angles in degrees and determine relations of angles. | C. | Demonstrate the ability to produce measures with specified levels of precision. |
| D. | Tell time (analog and digital) to the minute. | D. | Convert linear measurements within the same system. | D. | Estimate, use and describe measures of distance, rate, perimeter, area, volume, weight, mass and angles. | ||
| E. | Determine appropriate unit of measure. | E. | Add and subtract measurements. | E. | Describe how a change in linear dimension of an object affects its perimeter, area and volume. | ||
| F. | Use concrete objects to determine area and perimeter. | F. | Use scale measurements to interpret maps or drawings. | ||||
| G. | Estimate and verify measurements. | G. | Create and use scale models. | ||||
| Demonstrate that a single object has different attributes that can be measured in different ways (e.g. length, mass, weight, time, area, temperature, capacity, perimeter). | |||||||
| 2.4. Mathematical Reasoning and Connections | |||||||
| 2.4.3. GRADE 3 | 2.4.5. GRADE 5 | 2.4.8. GRADE 8 | 2.4.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills to: | |||||||
| A. | Make, check and verify predictions about the quantity, size and shape of objects and groups of objects. | A. | Compare quantities and magnitudes of numbers. | A. | Make conjectures based on logical reasoning and test conjectures by using counter-examples. | A. | Use direct proofs, indirect proofs or proof by contradiction to validate conjectures. |
| B. | Use measurements in everyday situations (e.g., determine the geography of the school building). | B. | Use models, number facts, properties and relationships to check and verify predictions and explain reasoning. | B. | Combine numeric relationships to arrive at a conclusion. | B. | Construct valid arguments from stated facts. |
| C. | Draw inductive and deductive conclusions within mathematical contexts. | C. | Use if . . . then statements to construct simple valid arguments. | C. | Determine the validity of an argument. | ||
| D. | Distinguish between relevant and irrelevant information in a mathematical problem. | D. | Construct, use and explain algorithmic procedures for computing and estimating with whole numbers, fractions, decimals and integers. | D. | Use truth tables to reveal the logic of mathematical statements. | ||
| E. | Interpret statements made with precise language of logic (e.g., ‘‘all,’’ ‘‘or,’’ ‘‘every,’’ ‘‘none,’’ ‘‘some,’’ ‘‘or,’’ ‘‘many’’). | E. | Distinguish between inductive and deductive reasoning. | E. | Demonstrate mathematical solutions to problems (e.g., in the physical sciences). | ||
| F. | Use statistics to quantify issues (e.g., in social studies, in science). | F. | Use measurements and statistics to quantify issues (e.g., in family and consumer science situations). | ||||
| 2.5. Mathematical Problem Solving and Communication | |||||||
| 2.5.3. GRADE 3 | 2.5.5. GRADE 5 | 2.5.8. GRADE 8 | 2.5.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills to: | |||||||
| A. | Use appropriate problem-solving strategies (e.g., guess and check, working backwards). | A. | Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense and explain how the problem was solved. | A. | Invent, select, use and justify the appropriate methods, materials and strategies used to solve problems. | A. | Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems. |
| B. | Determine when sufficient information is present to solve a problem and explain how to solve a problem. | B. | Use appropriate mathematical terms, vocabulary, language symbols and graphs to clearly and logically explain solutions to problems. | B. | Verify and interpret results using precise mathematical language, notation and representations, including numerical tables and equations, simple algebraic equations and formulas, charts, graphs and diagrams. | B. | Use symbols, mathematical terminology, standard notation, mathematical rules, graphing and other types of mathematical representations to communicate observations, predictions, concepts, procedures, generalizations, ideas and results. |
| C. | Select and use an appropriate method, materials and strategy to solve problems, including mental mathematics, paper and pencil and concrete objects. | C. | Show ideas in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams and models. | C. | Justify strategies and defend approaches used and conclusions reached. | C. | Present mathematical procedures and results clearly, systematically, succinctly and correctly. |
| D. | Connect, extend and generalize problem solutions to other concepts, problems and circumstances in mathematics. | D. | Determine pertinent information in problem situations and whether any further information is needed for solution. | D. | Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid. | ||
| E. | Select, use and justify the methods, materials and strategies used to solve problems. | ||||||
| F. | Use appropriate problem-solving strategies (e.g., solving a simpler problem, drawing a picture or diagram. | ||||||
| 2.6. Statistics and Data Analysis | |||||||
| 2.6.3. GRADE 3 | 2.6.5. GRADE 5 | 2.6.8. GRADE 8 | 2.6.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills to: | |||||||
| A. | Gather, organize and display data using pictures, tallies, charts, bar graphs and pictographs. | A. | Organize and display data using pictures, tallies, tables, charts, bar graphs and circle graphs. | A. | Compare and contrast different plots of data using values of mean, median, mode, quartiles and range. | A. | Design and conduct an experiment using random sampling. Describe the data as an example of a distribution using statistical measures of center and spread. Organize and represent the results with graphs. (Use standard deviation, variance and t-tests). |
| B. | Formulate and answer questions based on data shown on graphs. | B. | Describe data sets using mean, median, mode and range. | B. | Explain effects of sampling procedures and missing or incorrect information on reliability. | B. | Use appropriate technology to organize and analyze data taken from the local community. |
| C. | Predict the likely number of times a condition will occur based on the analyzed data. | C. | Sort data using Venn diagrams. | C. | Fit a line to the scatter plot of two quantities and describe any correlation of the variables. | C. | Determine the regression equation of best fit (e.g., linear, quadratic and exponential). |
| D. | Form and justify an opinion on whether a given statement is reasonable based on a comparison to data. | D. | Predict the likely number of times a condition will occur based on analyzed data. | D. | Design and carry out a random sampling procedure. | D. | Make predictions using interpolation, extrapolation, regression and estimation using technology to verify them. |
| E. | Construct and defend simple conclusions based on data. | E. | Analyze and display data in stem-and-leaf and box-and-whisker plots. | E. | Determine the validity of the sampling method described in a given study. | ||
| F. | Use scientific and graphing calculators and computer spreadsheets to organize and analyze data. | F. | Determine the degree of dependence of two quantities specified by a two-way table. | ||||
| G. | Determine the validity of the sampling method described in studies published in local or National newspapers. | G. | Describe questions of experimental design, control groups, treatment groups, cluster sampling and reliability. | ||||
| H. | Use sampling techniques to draw inferences about large populations. | ||||||
| I. | Describe the normal curve and use its properties to answer questions about sets of data that are assumed to be normally distributed. | ||||||
| 2.7. Probability and Predictions | |||||||
| 2.7.3. GRADE 3 | 2.7.5. GRADE 5 | 2.7.8. GRADE 8 | 2.7.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills needed to: | |||||||
| A. | Predict and measure the likelihood of events and recognize that the results of an experiment may not match predicted outcomes. | A. | Perform simulations with concrete devices (e.g., dice, spinner) to predict the chance of an event occurring. | A. | Determine the number of combinations and permutations for an event. | A. | Compare odds and probability. |
| B. | Design a fair and an unfair spinner. | B. | Determine the fairness of the design of a spinner. | B. | Present the results of an experiment using visual representations (e.g., tables, charts, graphs). | B. | Apply probability and statistics to perform an experiment involving a sample and generalize its results to the entire population. |
| C. | List or graph the possible results of an experiment. | C. | Express probabilities as fractions and decimals. | C. | Analyze predictions (e.g., election polls). | C. | Draw and justify a conclusion regarding the validity of a probability or statistical argument. |
| D. | Analyze data using the concepts of largest, smallest, most often, least often and middle. | D. | Compare predictions based on theoretical probability and experimental results. | D. | Compare and contrast results from observations and mathematical models. | D. | Use experimental and theoretical probability distributions to make judgments about the likelihood of various outcomes in uncertain situations. |
| E. | Calculate the probability of a simple event. | E. | Make valid inferences, predictions and arguments based on probability. | E. | Solve problems involving independent simple and compound events. | ||
| F. | Determine patterns generated as a result of an experiment. | ||||||
| G. | Determine the probability of an event involving ‘‘and,’’ ‘‘or’’ or ‘‘not.’’ | ||||||
| H. | Predict and determine why some outcomes are certain, more likely, less likely, equally likely or impossible. | ||||||
| I. | Find all possible combinations and arrangements involving a limited number of variables. | ||||||
| J. | Develop a tree diagram and list the elements. | ||||||
| 2.8. Algebra and Functions | |||||||
| 2.8.3. GRADE 3 | 2.8.5. GRADE 5 | 2.8.8. GRADE 8 | 2.8.11. GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills to: | |||||||
| A. | Recognize, describe, extend, create and replicate a variety of patterns including attribute, activity, number and geometric patterns. | A. | Recognize, reproduce, extend, create and describe patterns, sequences and relationships verbally, numerically, symbolically and graphically, using a variety of materials. | A. | Apply simple algebraic patterns to basic number theory and to spatial relations. | A. | Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically. |
| B. | Use concrete objects and trial and error to solve number sentences and check if solutions are sensible and accurate. | B. | Connect patterns to geometric relations and basic number skills. | B. | Discover, describe and generalize patterns, including linear, exponential and simple quadratic relationships. | B. | Give examples of patterns that occur in data from other disciplines. |
| C. | Substitute a missing addend in a number sentence. | C. | Form rules based on patterns (e.g., an equation that relates pairs in a sequence). | C. | Create and interpret expressions, equations or inequalities that model problem situations. | C. | Use patterns, sequences and series to solve routine and nonroutine problems. |
| D. | Create a story to match a given combination of symbols and numbers. | D. | Use concrete objects and combinations of symbols and numbers to create expressions that model mathematical situations. | D. | Use concrete objects to model algebraic concepts. | D. | Formulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and nonroutine problem situations. |
| E. | Use concrete objects and symbols to model the concepts of variables, expressions, equations and inequalities. | E. | Explain the use of combinations of symbols and numbers in expressions, equations and inequalities. | E. | Select and use a strategy to solve an equation or inequality, explain the solution and check the solution for accuracy. | E. | Use equations to represent curves (e.g., lines, circles, ellipses, parabolas, hyperbolas). |
| F. | Explain the meaning of solutions and symbols. | F. | Describe a realistic situation using information given in equations, inequalities, tables or graphs. | F. | Solve and graph equations and inequalities using scientific and graphing calculators and computer spreadsheets. | F. | Identify whether systems of equations and inequalities are consistent or inconsistent. |
| G. | Use a table or a chart to display information. | G. | Select and use appropriate strategies, including concrete materials, to solve number sentences and explain the method of solution. | G. | Represent relationships with tables or graphs in the coordinate plane and verbal or symbolic rules. | G. | Analyze and explain systems of equations, systems of inequalities and matrices. |
| H. | Describe and interpret the data shown in tables and charts. | H. | Locate and identify points on a coordinate system. | H. | Graph a linear function from a rule or table. | H. | Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets and other software. |
| I. | Demonstrate simple function rules. | I. | Generate functions from tables of data and relate data to corresponding graphs and functions. | I. | Generate a table or graph from a function and use graphing calculators and computer spreadsheets to graph and analyze functions. | I. | Use matrices to organize and manipulate data, including matrix addition, subtraction, multiplication and scalar multiplication. |
| J. | Analyze simple functions and relationships and locate points on a simple grid. | J. | Show that an equality relationship between two quantities remains the same as long as the same change is made to both quantities; explain how a change in one quantity determines another quantity in a functional relationship. | J. | Demonstrate the connection between algebraic equations and inequalities and the geometry of relations in the coordinate plane. | ||
| K. | Select, justify and apply an appropriate technique to graph a linear function in two variables, including slope-intercept, x- and y-intercepts, graphing by transformations and the use of a graphing calculator. | ||||||
| L. | Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a point on the line. | ||||||
| M. | Given a set of data points, write an equation for a line of best fit. | ||||||
| N. | Solve linear, quadratic and exponential equations both symbolically and graphically. | ||||||
| O. | Determine the domain and range of a relation, given a graph or set of ordered pairs. | ||||||
| P. | Analyze a relation to determine whether a direct or inverse variation exists and represent it algebraically and graphically. | ||||||
| Q. | Represent functional relationships in tables, charts and graphs. | ||||||
| R. | Create and interpret functional models. | ||||||
| S. | Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). | ||||||
| T. | Analyze and categorize functions by their characteristics. | ||||||
| 2.9. Geometry | |||||||
| 2.9.3 GRADE 3 | 2.9.5. GRADE 5 | 2.9.8 GRADE 8 | 2.9.11 GRADE 11 | ||||
| Pennsylvania’s public school shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills to: | |||||||
| A. | Name and label geometric shapes in two and three dimensions (e.g., circle/sphere, square/cube, triangle/pyramid, rectangle/prism). | A. | Give formal definitions of geometric figures. | A. | Construct figures incorporating perpendicular and parallel lines, the perpendicular bisector of a line segment and an angle bisector using computer software. | A. | Construct geometric figures using dynamic geometry tools (e.g., Geometer’s Sketchpad, Cabri Geometre). |
| B. | Build geometric shapes using concrete objects (e.g., manipulatives). | B. | Classify and compare triangles and quadri- laterals according to sides or angles. | B. | Draw, label, measure and list the properties of complementary, supplementary and vertical angles. | B. | Prove two triangles or two polygons are congruent or similar using algebraic, coordinate and deductive proofs. |
| C. | Draw two- and three-dimensional geometric shapes and construct rectangles, squares and triangles on the geoboard and on graph paper satisfying specific criteria. | C. | Identify and measure circles, their diameters and radii. | C. | Classify familiar polygons as regular or irregular up to a decagon. | C. | Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles and diagonals using deductive proofs. |
| D. | Find and describe geometric figures in real life. | D. | Describe in words how geometric shapes are constructed. | D. | Identify, name, draw and list all properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms and cylinders. | D. | Identify corresponding parts in congruent triangles to solve problems. |
| E. | Identify and draw lines of symmetry in geometric figures. | E. | Construct two- and three-dimensional shapes and figures using manipulatives, geoboards and computer software. | E. | Construct parallel lines, draw a transversal and measure and compare angles formed (e.g., alternate interior and exterior angles). | E. | Solve problems involving inscribed and circumscribed polygons. |
| F. | Identify symmetry in nature. | F. | Find familiar solids in the environment and describe them. | F. | Distinguish between similar and congruent polygons. | F. | Use the properties of angles, arcs, chords, tangents and secants to solve problems involving circles. |
| G. | Fold paper to demonstrate the reflections about a line. | G. | Create an original tessellation. | G. | Approximate the value of [pgr ] (pi) through experimentation. | G. | Solve problems using analytic geometry. |
| H. | Show relationships between and among figures using reflections. | H. | Describe the relationship between the perimeter and area of triangles, quadrilaterals and circles. | H. | Use simple geometric figures (e.g., triangles and squares) to create, through rotation, transformational figures in three dimensions. | H. | Construct a geometric figure and its image using various transformations. |
| I. | Predict how shapes can be changed by combining or dividing them. | I. | Represent and use the concepts of line, point and plane. | I. | Generate transformations using computer software. | I. | Model situations geometrically to formulate and solve problems. |
| J. | Define the basic properties of squares, pyramids, parallelograms, quadrilaterials, trapezoids, polygons, rectangles, rhombi, circles, triangles, cubes, prisms, spheres and cylinders. | J. | Analyze geometric patterns (e.g., tessellations and sequences of shapes) and develop descriptions of the patterns. | J. | Analyze figures in terms of the kinds of symmetries they have. | ||
| K. | Analyze simple transformations of geometric figures and rotations of line segments. | K. | Analyze objects to determine if they illustrate tessellations, symmetry, congruence, similarity and scale. | ||||
| L. | Identify properties of geometric figures (e.g., parallel, perpendicular, similar, congruent, symmetrical). | ||||||
| 2.10. Trigonometry | |||||||
| 2.10.3 GRADE 3 | 2.10.5. GRADE 5 | 2.10.8 GRADE 8 | 2.10.11 GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills to: | |||||||
| A. | Identify right angles in the environment. | A. | Identify and compare parts of right triangles including right angles, acute angles, hypotenuses and legs. | A. | Compute measures of sides and angles using proportions, the Pythagorean Theorem and right triangle relationships. | A. | Use graphing calculators to display periodic and circular functions; describe properties of the graphs. |
| B. | Model right angles and right triangles using concrete objects. | B. | Create right triangles on a geoboard. | B. | Solve problems requiring indirect measurement for lengths of sides of triangles. | B. | Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. |
| 2.11. Concepts of Calculus | |||||||
| 2.11.3 GRADE 3 | 2.11.5. GRADE 5 | 2.11.8 GRADE 8 | 2.11.11 GRADE 11 | ||||
| Pennsylvania’s public schools shall teach, challenge and support every student to realize the student’s maximum potential and to acquire the knowledge and skills to: | |||||||
| A. | Identify whole number quantities and measurements from least to most and greatest value. | A. | Make comparisons of numbers (e.g., more, less, same, least, most, greater than, less than). | A. | Analyze graphs of related quantities for minimum and maximum values and justify the findings. | A. | Determine maximum and minimum values of a function over a specified interval. |
| B. | Identify least and greatest values represented in bar graphs and pictographs. | B. | Identify least and greatest values represented in bar and circle graphs. | B. | Describe the concept of unit rate, ratio, and slope in context of rate of change. | B. | Interpret maximum and minimum values in problem situations. |
| C. | Categorize rates of change as faster and slower. | C. | Identify maximum and minimum. | C. | Continue a pattern of numbers or objects that could be extended infinitely. | C. | Graph and interpret rates of growth/decay. |
| D. | Continue a pattern of numbers or objects that could be extended infinitely. | D. | Describe the relationship between rates of change and time. | D. | Determine sums of finite sequences of numbers and infinite geometric series. | ||
| E. | Estimate areas and volumes as the sums of areas of tiles and volumes of cubes. | E. | Estimate areas under curves using sequences of areas. | ||||
| F. | Describe the relationship between the size of the unit of measurement and the estimate of the areas and volumes. | ||||||
VI. GLOSSARY
| Absolute value: | A number’s distance from zero on a number line. The absolute value of 2 is equal to the absolute value of -2. |
| Algorithm: | A method of performing an arithmetic operation. |
| Analog time: | Time displayed on a timepiece having hour and minute hands. |
| Array: | Arrangement of a series of items according to the values of the items, e.g., largest to smallest. |
| Box-and-whisker plot: | A graphic method for showing a summary of data using median, quartiles and extremes of data. |
| Combination: | A subset of the elements in a given set, without regard to the order in which those elements are arranged. |
| Composite number: | Any positive integer exactly divisible by one or more positive integers other than itself and 1. |
| Congruent: | Having the same shape and the same size. |
| Conjecture: | A statement believed to be true but not proved. |
| Coordinate system: | A method of locating points in the plane or in space by means of numbers. A point in the plane is located by its distances from both a horizontal and a vertical line called the axes. The horizontal line is called the x-axis. The vertical line is called the y-axis. The pairs of numbers are called ordered pairs. The first number, called the x-coordinate, designates the distance along the horizontal axis. The second number, called the y-coordinate, designates the distance along the vertical axis. The point at which the two axes intersect has the coordinates (0,0) and is called the origin. |
| Correlation: | A measure of the mutual relationship between two variables. |
| Customary system: | A system of weights and measures frequently used in the United States. The basic unit of weight is the pound; the basic unit of capacity is the quart. |
| Deductive reasoning: | The process of reasoning from statements accepted as true to reach a conclusion. |
| Direct variation: | Two variables are so related that their ratio remains constant. |
| Domain: | The set of all possible values for the unknown in an open sentence. |
| Equation: | A statement of equality between two mathematical expressions (e.g., X + 5 = Y - 2). |
| Equivalent forms: | Different forms of numbers that name the same number (e.g., fraction, decimal, percent as 1/2, .5, 50%). |
| Expanded notation: | Involves writing the number in expanded form to show the value of each digit (e.g., 15,629 = 10,000 + 5,000 + 600 + 20 + 9). |
| Exponential function: | A function whose general equation is y = a x bx or y = a x bkx, where a, b and k stand for constants. |
| Exponent: | A numeral used to tell how many times a number or variable is used as a factor (e.g., a2, 2n, yx). |
| Expression: | A mathematical phrase that can include operations, numerals and variables. In algebraic terms: 2l + 3x; in numeric terms: 13.4 - 4.7. |
| Factor: | The number or variable multiplied in a multiplication expression. |
| Factorial: | The expression n! (n factorial) is the product of all the numbers from 1 to n for any positive integer n. |
| Function: | A relation in which each value of an independent variable is associated with a unique value of the dependent value. |
| Geoboard: | A board with pegs aligned in grid fashion that permits rubber bands to be wrapped around pegs to form geometric figures. |
| Graphing calculator: | A calculator that will store and draw the graphs of several functions at once. |
| Independent events: | Events such that the outcome of the first event has no effect on the probabilities of the outcome of the second event (e.g., two tosses of the same coin are independent events). |
| Inductive reasoning: | Generalizations made from particular observations in a common occurrence. |
| Inequality: | A mathematical sentence that contains a symbol, (e.g., ›, ‹, ›=, ‹= or µ') in which the terms on either side of the symbol are unequal (e.g., x ‹ y, 7 › 3, n ›= 4). |
| Infinite: | Has no end or goes on forever. |
| Integer: | A number that is a positive whole number, a negative whole number or zero. |
| Inverse: | A new conditional formed by negating both the antecedent and the consequent of a conditional. |
| Inverse operations: | Operations that undo each other (e.g., addition and subtraction are inverse operations; multiplication and division are inverse operations). |
| Inverse variation: | When the ratio of one variable to the reciprocal of the other is constant, one of them is said to vary inversely as the other. |
| Irrational number: | A number that cannot be written as a simple fraction. It is an infinite and nonrepeating decimal. |
| Limit: | A number to which the terms of a sequence get closer so that beyond a certain term all terms are as close as desired to that number. |
| Line of best fit: | The line that fits a set of data points with the smallest value for the sum of the squares of the errors (vertical distances) from the data points to the line; the regression line. |
| Linear function: | A function whose general equation is y = mx + b, where m and b stand for constants and m µ' 0. |
| Linear measurement: | Measurement in a straight line. |
| Logarithm: | The exponent indicating the power to which a fixed number, the base, must be raised to produce a given number. For example, if nx = a, the logarithm of a, with n as the base, is x; symbolically, logna = x. If the base is 10, the log of 100 is 2. |
| Manipulatives: | Materials that allow students to explore mathematical concepts in a concrete mode. |
| Mathematical model: | A representation in the mathematical world of some phenomenon in the real world. It frequently consists of a function or relation specifying how two variables are related. |
| Matrix: | A rectangular array of numbers representing such things as the coefficients in a system of equations arranged in rows and columns. |
| Maximum: | The greatest number in a set of data. |
| Mean: | The sum of the set of numbers divided by n, the number of numbers in the set. |
| Median: | The number that lies in the middle when a set of numbers is arranged in order. If there are two middle values, the median is the mean of these values. |
| Metric system: | A system of measurement used throughout the world based on factors of 10. It includes measures of length, weight and capacity. |
| Minimum: | The least number in a set of data. |
| Missing addend: | A member of an addition number sentence in which that term is missing (e.g., 5 +
= 8). |
| Mode: | The number(s) that occurs most often in a set of numbers (e.g., in the set 1, 2, 3, 3, 5, 8; the mode is 3). |
| Multiple: | A number that is the product of a given integer and another integer (e.g., 6 and 9 are multiples of 3). |
| Normal curve: | A graphical plot of a mathematical function (frequency distribution) which is unimodal and symmetrical. |
| One-to-one correspondence: | When one and only one element of a second set is assigned to an element of a first set, all elements of the second set are assigned, and every element of the first set has an assignment, the mapping is called one-to-one (e.g., in the set Bill Clinton, George Bush, Ronald Reagan, Jimmy Carter, Hillary Clinton, Barbara Bush, Nancy Reagan and Rosalynn Carter, there is a one-to-one correspondence between the pairs.) |
| Open sentence: | A statement that contains at least one unknown. It becomes true or false when a quantity is substituted for the unknown (e.g., x + 5 = 9, y - 2 = 7). |
| Order of operations: | Rules for evaluating an expression: work first within parentheses; then calculate all powers, from left to right; then do multiplications or divisions, from left to right; then do additions and subtractions, from left to right. |
| Patterns: | Regularities in situations such as those in nature, events, shapes, designs and sets of numbers (e.g., spirals on pineapples, geometric designs in quilts, the number sequence 3, 6, 9, 12, . . ). |
| Permutation: | An arrangement of a given number of objects from a given set in which the order of the objects is significant. |
| Perpendicular lines: | Two lines that intersect to form right angles. (e.g.,  ,  |, |- ). |
| Plotting points: | Locating points by means of coordinates, or a curve by plotted points, representing an equation by means of a curve so constructed. |
| Polygon: | A union of segments connected end to end, so that each segment intersects exactly two others at its endpoints. |
| Powers: | A number expressed using an exponent. The number 53 is read five to the third power or five cubed. |
| Prime: | An integer greater than one whose only positive factors are 1 and itself (e.g., 2, 3, 5, 7, 11, 13, 17 and 19). |
| Probability: | A number from 0 to 1 that indicates how likely something is to happen. |
| Problem solving: | Finding ways to reach a goal when no routine path is apparent. |
| Proof by contradiction: | A proof in which, if s is to be proven, one reasons from not-s until a contradiction is deduced; from this it is concluded that not-s is false, which means that s is true. |
| Proportion: | An equation of the form a/b = c/d that states that the two ratios are equivalent. |
| Quadrilateral: | A four-sided polygon. |
| Quartiles: | The three values that divide an ordered set into four subsets of approximately equal size. The second quartile is the median. |
| Radian: | A unit of angular measure equal to 1/2[pgr ] of a complete revolution. |
| Range (1): | The difference between the greatest number and the least number in a set of data. |
| Range (2): | The set of output values for a function. |
| Rate of change: | The limit of the ratio of an increment of the function value at the point to that of the independent variable as the increment of the variable approaches zero. |
| Ratio: | A comparison of two numbers by division. |
| Rational numbers: | Any number that can be written in the form a/b where a is any interger and b is any integer except zero. |
| Real numbers: | The set consisting of all rational numbers and all irrational numbers. |
| Reasonableness: | Quality of a solution so that it is not extreme or excessive. |
| Reciprocal: | The fractional number that results from dividing one by the number. |
| Rectangular prism: | A three-dimensional figure whose sides are all rectangles; a box. |
| Reflection: | A transformation that produces the mirror image of a geometric figure. |
| Regression: | The line that represents the least deviation from the points in a scatter plot of data. |
| Regular polygon: | A polygon in which all sides have the same measure and all angles have the same measure. |
| Relation: | A set of ordered pairs. |
| Reliability: | The extent to which a measuring procedure yields the same results on repeated trials. |
| Repeated addition: | A model for multiplication (e.g., 2 + 2 + 2 = 3 x 2). |
| Rotation: | A transformation that maps every point in the plane to its image by rotating the plane around a fixed point or line. |
| Scientific calculator: | A calculator that represents very large or very small numbers in scientific notation and with the powering, factorial, square root, negative and reciprocal keys. |
| Scientific notation: | A way of writing a number of terms of an integer power of 10 multiplied by a number greater than or equal to 1 and less than 10. |
| Sequence: | A set of ordered quantities (e.g., positive integers). |
| Series: | The indicated sum of the terms of a sequence. |
| Similarity: | Having the same shape but not necessarily the same size. |
| Simple event: | An event whose probability can be obtained from consideration of a single occurrence (e.g., the tossing of a coin is a simple event). |
| Simulation: | Modeling a real event without actually observing the event. |
| Slope: | The slope of a line is the ratio of the change in y to the corresponding change in x; the constant m in the linear function equation; rise/run. |
| Standard deviation: | The square root of the variance. |
| Stem-and-leaf plot: | A frequency distribution made by arranging data (e.g., student scores on a test were 98, 96, 85, 93, 83, 87, 85, 87, 93, 75, 77 and 83. This data are displayed in a stem-and-leaf plot below. 9 8, 6, 3, 3 8 7, 7, 5, 5, 3, 3 7 7, 5 |
| Systems of equations: | Two or more equations that are conditions imposed simultaneously on all the variables, but may or may not have common solutions (e.g., x + y = 2, and 3x + 2y = 5). |
| Symmetry: | A line of symmetry separates a figure into two congruent halves, each of which is a reflection of the other (e.g., [odot ]u, the line through the center of the circle divides it into congruent halves). |
| t-test: | A statistical test done to test the difference of means of two samples. |
| Tessellation: | A repetitive pattern of polygons that covers an area with no holes and no overlaps, like floor tiles. |
| Transformation: | An operation on a geometric figure by which each point gives rise to a unique image. |
| Translation: | A transformation that moves a geometric figure by sliding each of the points the same distance in the same direction. |
| Tree diagram: | A diagram used to show the total number of possible outcomes in a probability experiment. |
| Trigonometric functions: | A function (e.g., sine, cosine, tangent, cotangent, secant, cosecant) whose independent variable is an angle measure, usually in degrees or radians. |
| Valid argument: | An argument with the property no matter what statements are substituted in the premises, the truth value of the form is true. If the premises are true, then the conclusion is true. |
| Variable: | A symbol used to stand for any one of a given set of numbers or other objects (e.g., in the equation y = x + 5, y and x are variables). |
| Variance: | In a data set, the sum of the squared deviations divided by one less than the number of elements in the set (sample variance s2) or by the number of elements in the set (population variance  2). |
| Vector: | A quantity that has both magnitude and direction (e.g., physical quantities such as velocity and force). |
| Venn diagram: | A display that pictures unions and intersections of sets. |
| Volume: | The amount of space enclosed in a space (3-dimensional) figure, measured in cubic units. |
| Y-intercept: | The y-intercept of a line is the y-coordinate of the point at which the graph of an equation crosses the y-axis. |
| [pgr ]: | pi, the ratio of the circumference of a circle to its diameter: about 3.1415926535. |
APPENDIX B
Academic Standards for Science and Technology and Environment and Ecology
The provisions of this Appendix B adopted January 4, 2002, effective January 5, 2002, 32 Pa.B. 17, unless otherwise noted
VII. TABLE OF CONTENTS
Introduction… VIII.
THE ACADEMIC STANDARDS
| Unifying Themes… | 3.1. |
| A. Systems | |
| B. Models | |
| C. Patterns | |
| D. Scale | |
| E. Change | |
| Inquiry and Design… | 3.2. |
| A. Nature of Scientific Knowledge | |
| B. Process Knowledge | |
| C. Scientific Method | |
| D. Problem Solving in Technology | |
| Biological Sciences… | 3.3. |
| A. Living Forms | |
| B. Structure and Function | |
| C. Inheritance | |
| D. Evolution | |
| Physical Science, Chemistry and Physics… | 3.4. |
| A. Matter | |
| B. Energy | |
| C. Forces and Motion | |
| D. Astronomy | |
| Earth Sciences… | 3.5. |
| A. Land Forms and Processes | |
| B. Resources | |
| C. Meteorology | |
| D. Hydrology and Oceanography | |
| Technology Education… | 3.6. |
| A. Biotechnology | |
| B. Information Technology | |
| C. Physical Technologies | |
| (Construction, Manufacturing, and Transportation) | |
| Technological Devices… | 3.7. |
| A. Tools | |
| B. Instruments | |
| C. Computer Operations | |
| D. Computer Software | |
| E. Computer Communication Systems | |
| Science, Technology and Human Endeavors… | 3.8. |
| A. Constraints | |
| B. Meeting Human Needs | |
| C. Consequences and Impacts | |
| Glossary… | IX. |
VIII. INTRODUCTION
This document describes what students should know and be able to do in the following eight areas:
• 3.1. Unifying Themes of Science
• 3.2. Inquiry and Design
• 3.3. Biological Sciences
• 3.4. Physical Science, Chemistry and Physics
• 3.5. Earth Sciences
• 3.6. Technology Education
• 3.7. Technological Devices
• 3.8. Science, Technology and Human Endeavors
These standards describe what students should know and be able to do by the end of fourth, seventh, tenth and twelfth grade. In addition, these standards reflect the increasing complexity and sophistication that students are expected to achieve as they progress through school.
This document avoids repetition, making an obvious progression across grade levels less explicit. Teachers shall expect that students know and can apply the concepts and skills expressed at the preceding level. Consequently, previous learning is reinforced but not retaught.
Standards are arranged by categories, for example, 3.5 Earth Science. Under each category are standard statements that are preceded by a capital letter; for example, in 3.1 Unifying Themes, grade 10.B, ‘‘Describe concepts of models as a way to predict and understand science and technology.’’ Following the standard statements are bulleted standard descriptors, which explain the nature and scope of the standard. Descriptors specify the nature of the standard and the level of complexity needed in meeting that standard in a proficient manner. Descriptors serve to benchmark the standard statement. Curriculum, instruction and assessment should focus on meeting the standard statement. Technology education, computer applications and science are separate curricular areas. Meeting standards should be approached as a collaborative effort among all curricular areas.
The following descriptors explain the intent of each standard category:
| 3.1. Unifying Themes | Unifying themes of science and technology provide big ideas that integrate with significant concepts. There are only a few fundamental concepts and processes that form the framework upon which science and technology knowledges are organized—motion and forces, energy, structure of matter, change over time and machines. These themes create the context through which the content of the disciplines can be taught and are emphasized in each standard. |
| 3.2. Inquiry and Design | The nature of science and technol |