ACT Standards of Transition and Pathways to Success in College
ACT Standards of Transition and Pathways to Success in College
| English Area of Transition | Score: 1-12 | Pathways for Improvement | Score: 13-15 | Pathways for Improvement | Score: 16-19 | Pathways for Improvement | Score: 20-23 | Pathways for Improvement | Score: 24-27 | Pathways for Improvement | Score: 28-32 | Pathways for Improvement | Score: 33-36 |
| Topic Development: Purpose and Focus | n/a | *read and discuss the work of favorite writers *regularly write informal responses to literature (fiction and nonfiction) in their journals *identify sentences that convey the main ideas in a variety of texts and then practice composing such sentences |
n/a | *read writers of various genres and imitate their work *discuss and practice common ways to organize straightforward texts *revise writing to ensure that every sentence is necessary to the purpose of the piece and that no important information has been left out |
Identify the basic purpose or role of a specified phrase or sentence Delete obviously irrelevant material from an essay |
*write longer and more complicated essays, stories, reviews, etc. *continue reading writers of various genres and imitating their work *state the main theme of or summarize essays they have written *revise essays by eliminating sentences or ideas that violate the essay's focus |
Identify the main theme or topic of a straightforward piece of writing Determine relevancy when presented with a variety of sentence-level details |
*continue reading the work of writers of various genres; begin experimenting with a variety of writing styles *revise fairly straightforward writing to sharpen focus and coherence of entire piece *write introductions that capture the reader's interest, write conclusions that provide a sense of closure, and describe the rhetorical effects that each creates |
Identify the focus of a simple essay, applying that knowledge to add a sentence that sharpens that focus or to determine if an essay has met a specified goal Delete material primarily because it disturbs the flow and development of the paragraph Add a sentence to introduce or summarize the essay and to accomplish a fairly straightforward purpose such as illustrating a given statement |
*develop awareness of ways that form and content can be changed as the audience for the writing changes *experiment with different ways of beginning and ending pieces; make sure piece is a coherent, organized whole *learn how meaning can be expressed through connotation |
Identify both the focus and purpose of a fairly involved essay, applying that knowledge to determine the rhetorical effect of a new or existing sentence, or the need to add supporting detail or delete plausible but irrelevant material Add a sentence to accomplish a subtle purpose such as emphasis and to express meaning through connotation |
*write essays that indicate a heightened awareness of the audience for those essays *recognize the role that specific sentences play in terms of the essay as a whole |
Determine whether a complex essay has accomplished a specific purpose Add a phrase or sentence to accomplish a complex purpose, often expressed in terms of the main focus of the essay |
| Organization, Unity and Coherance | n/a | *write short texts, in a variety of genres, illustrating simple organization use paragraphing as an organizational device |
Recognize blatantly illogical conjunctive adverbs | *write many simply organized short texts of various genres *revise writing to ensure that information is in the best order *revise writing to delete illogical conjunctive adverbs |
Select the most logical place to add a sentence in a paragraph | *recognize and experiment with more sophisticated organizational structures *discuss the purpose and the importance of the opening paragraph for directing the rest of the piece *discuss the most logical place to add specific information in a draft essay |
Use a conjunctive adverb or phrase to express a straightforward logical relationship, such as chronology Add a sentence that introduces a simple paragraph |
*experiment with using words and phrases that create clear transitions in writing *rearrange sentences in a paragraph in order to improve its coherence |
Use conjunctive adverbs or phrases to create subtle logical connections between sentences, such as cause-effect Rearrange the sentences in a fairly uncomplicated paragraph for the sake of logic Provide a transition between paragraphs when the essay is fairly straightforward |
*experiment with more subtle organizational structures *revise writing by refining introductions, conclusions, and transitions in complex paragraphs |
Make sophisticated distinctions concerning the logical use of conjunctive adverbs or phrases, particularly when signaling a shift between paragraphs Rearrange sentences to improve the logic and coherence of a complex paragraph Add a sentence to introduce or conclude a fairly complex paragraph |
*revise or add introductory sentences or transitions based on an understanding of the logic and rhetorical purpose of the paragraph and the essay as a whole | Consider the need for introductory sentences or transitions, basing decisions on a thorough understanding of both the logic and rhetorical effect of the paragraph and essay |
| Word Choice: Style, Clarity, Tone and Economy | n/a | *revise writing to clarify sentences containing too many phrases and clauses *check writing to make sure pronoun references are clear *revise writing to edit out empty words (e.g., really, very, big, kind of) |
Revise sentences to correct awkward and confusing arrangements of sentence elements Revise ambiguous pronouns that create obvious sense problems (e.g., meaning or logic) |
*identify and revise obviously wordy, redundant, or cluttered material *check writing to make sure they have chosen fresh, specific words |
Delete obviously synonymous and wordy material in a sentence Revise expressions that violate the essay's tone Revise phrases to provide the most specific detail |
*discuss and model tone and style *revise writing to make it more concise and precise |
Delete redundant material when information is repeated in different parts of speech (e.g., "alarmingly startled") Use the word or phrase most consistent with the style and tone of a fairly straightforward essay Determine the clearest and most logical conjunction to link clauses |
*continue to edit sentences for empty language, wordiness, redundancy *revise structurally complex sentences to correct vague or ambiguous pronoun references |
Revise a phrase that is redundant in terms of the meaning and logic of the entire sentence Use the word or phrase most appropriate in terms of the content of the sentence and tone of the essay |
*work toward developing awareness of how style and content interact *select and manipulate words, phrases, and clauses to convey shades of meaning and tone *avoid clutter and use vivid verbs and specific nouns |
Correct redundant material that involves sophisticated vocabulary and sounds acceptable as conversational English (e.g., "an aesthetic viewpoint" versus "the outlook of an aesthetic viewpoint") Correct vague and wordy or clumsy and confusing writing containing sophisticated language |
*revise writing to delete redundancies in terms of the paragraph as a whole | Delete redundant material that involves subtle concepts or that is redundant in terms of the paragraph as a whole |
| Sentence Structure/Formation | n/a | *check writing to make sure verb tenses are consistent *vary sentence length by combining simple sent |
Use conjunctions or punctuation to join simple clauses Revise shifts in verb tense between simple clauses in a sentence or between simple adjoining sentences |
*revise writing to make sure voice and verb tense are consistent throughout *check writing for pronoun-antecedent agreement *revise writing to correct glaring shifts in verb tense or voice |
Use punctuation or conjunctions to coordinate uncomplicated sentences and to avoid awkward-sounding fused sentences or sentence fragments Correct glaringly inappropriate shifts in verb tense or voice |
*experiment with writing more sophisticated sentences; check to ensure verbs agree with subjects and modifiers don't dangle | Recognize and correct marked disturbances of sentence flow and structure (e.g., participial phrase fragments, missing relative pronouns, dangling or misplaced modifiers) | *revise writing to correct faulty coordination and subordination of clauses *revise sentences to correct inconsistencies in verb tense and pronoun person |
Revise to avoid faulty placement of phrases and faulty coordination and subordination of clauses in sentences with subtle structural problems Maintain consistent verb tense and pronoun person on the basis of the preceding clause or sentence |
*use sentence-combining techniques to create more sophisticated sentences; check to avoid fragments, comma splices, and run-ons | Use sentence-combining techniques, effectively avoiding problematic comma splices, run-on sentences, and sentence fragments, especially in sentences containing compound subjects or verbs Maintain a consistent and logical use of verb tense and pronoun person on the basis of information in the paragraph or essay as a whole |
*maintain parallel structure between phrases and clauses in a complex sentence *employ a variety of sentence structures in their writing |
Work comfortably with long sentences and complex clausal relationships within sentences, avoiding weak conjunctions between independent clauses and maintaining parallel structure between clauses |
| Usage | n/a | *keep a personal spelling/vocabulary list *practice and understand correct usage of common homonyms |
Solve such basic usage problems as whether to use a comparative or a superlative adjective and which word to use in such pairs as past or passed | *revise writing to correct basic grammar and punctuation errors | Solve such basic grammatical problems as whether to use an adverb or an adjective form, how to form comparative and superlative adjectives, how to ensure straightforward subject-verb and pronoun-antecedent agreement, and when to use the contraction it's | *revise sentences to ensure that each verb agrees with its subject when there is some text between the two *recognize the past and past participle forms of irregular but commonly used verbs |
Identify the past and past participle forms of irregular but commonly used verbs and identify when prepositions are idiomatically appropriate to their context Ensure that a verb agrees with its subject when there is some text between the two |
*check to be sure pronouns agree with antecedents in increasingly complex sentences | Ensure that a pronoun agrees with its antecedent when the two occur in separate clauses or sentences Identify the correct past and past participle forms of irregular and infrequently used verbs and form present-perfect verbs by using have rather than of |
*recognize the difference between its and it's, your and you're, who and whom | Correctly use reflexive pronouns, the possessive pronouns its and your, and the relative pronoun who rather than whom Ensure that a verb agrees with its subject in unusual situations (e.g., when the subject-verb order is inverted or when the subject is an indefinite pronoun) |
*revise sentences to ensure agreement between verb and subject when a phrase between the two suggests a different number for the verb | Provide idiomatically and contextually appropriate prepositions following verbs in situations involving sophisticated language or ideas Ensure that a verb agrees with its subject when a phrase or clause between the two suggests a different number for the verb |
| Punctuation | n/a | *use commas between independent clauses joined by and, but, or *use commas to separate items in a series *learn to recognize when commas are overused |
Delete commas that create basic sense problems (e.g., between two parts of a compound noun, between verb and direct object) | *check for and correct unnecessary commas | Provide appropriate punctuation in straightforward situations (e.g., items in a series) Delete commas that disturb the sentence flow (e.g., between modifier and modified element) |
*use commas to set off parenthetical phrases | Use commas to set off simple parenthetical phrases Delete unnecessary commas when an incorrect reading of the sentence suggests a pause that should be punctuated (e.g., between verb and direct object clause) |
*use punctuation to set off complex parenthetical phrases *recognize inappropriate uses of apostrophes, semicolons, and colons |
Use punctuation to set off complex parenthetical phrases Recognize and delete unnecessary commas based on a careful reading of the entire sentence (e.g., between elements of a compound subject or a compound verb) Use apostrophes to indicate simple possessive nouns Recognize inappropriate uses of colons and semicolons |
*use semicolons to indicate relationships between independent clauses *use commas to set off nonessential appositives or clauses |
Use commas to set off a nonessential/ nonrestrictive appositive or clause Deal with multiple punctuation problems (e.g., compound sentences containing unnecessary commas and phrases that may or may not be parenthetical) Use an apostrophe to show possession, especially with irregular plural nouns Use a semicolon to indicate a relationship between closely related independent clauses |
*use the colon to introduce an example or an elaboration | Use a colon to introduce an example or an elaboration |
| Reading Area of Transition | Score: 1-12 | Pathways for Improvement | Score: 13-15 | Pathways for Improvement | Score: 16-19 | Pathways for Improvement | Score: 20-23 | Pathways for Improvement | Score: 24-27 | Pathways for Improvement | Score: 28-32 | Pathways for Improvement | Score: 33-36 |
| Main Ideas | n/a | *make predictions about characters and events presented in a literary text, verifying or rejecting those predictions and making new ones as they read *establish connections (relationships) between details or outcomes in a text to better understand what is happening and why |
Draw simple conclusions about people and events in uncomplicated literary narratives | *work with peers to formulate a concise statement about the central idea(s) suggested in written or nonprint sources (e.g., films, artwork) *draw reasonable conclusions about people and situations using evidence presented in a text |
Draw simple conclusions about the main points and people in uncomplicated passages | *identify details in a challenging text that confirm or disprove conclusions drawn by the author or narrator and by the students themselves or their peers *make reasoned judgments about ideas and events based on evidence from written or nonprint sources |
Draw simple conclusions using details that support the main points of more challenging passages | *analyze specific parts of a text, drawing accurate conclusions *determine how an inference might change based on the inclusion of additional information *synthesize information from challenging texts to clarify understanding of important concepts and ideas *distinguish between key concepts and subordinate ideas in a text and write a concise summary |
Identify a clear main idea in any paragraph or paragraphs in uncomplicated passages Infer the main idea of some paragraphs in more challenging passages Summarize basic events and ideas in more challenging passages |
*use two different mediums (e.g., sculpture, photography, music) to present a synopsis of the main idea(s) of a text, thereby expanding understanding of the text's meaning *develop a reasonable interpretation of the central theme(s) or main point(s) of a challenging text *divide challenging texts into sections, determining what the key points are for each section |
Infer the main idea of a passage, paragraph, or paragraphs in more challenging passages Summarize events and ideas in virtually any passage |
*identify and analyze ideas embedded in a complex text and write a reasoned synopsis of the text | Identify main ideas of passages and paragraphs in complex passages |
| Significant Details | n/a | *write, exchange, and answer a series of questions that examine significant details presented in a text *locate and discuss details presented in a text (e.g., who, what, where) |
Locate specific facts (e.g., names, dates, events) clearly stated in a passage | *determine which details in a text are essential to understanding the author's or narrator's intended message *scan a text in order to locate specific details (e.g., dates, specialized terms, facts) |
Locate simple details at the sentence and paragraph level in uncomplicated passages | *explain in their own words the significance of specific information in written or nonprint sources *distinguish between what is most and least important in a text |
Locate important details in uncomplicated passages | *gather and interpret details presented in a text, determining the contribution of each to the author's or narrator's intended message *identify details that clearly support the key point(s) of written or nonprint sources *check inferences against information provided in a text, identifying what is and is not sufficiently supported by the text |
Locate and interpret minor or subtly stated details in uncomplicated passages Discern which details, though they may appear in different sections throughout a passage, support important points in more challenging passages |
*recognize and study the evolution of an author's argument(s) as presented in a complex informational text *interpret and integrate details in a text in order to verify or contradict a specific point or claim made by the author or narrator *enumerate aspects or characteristics of people, objects, events, or ideas |
Locate and interpret minor or subtly stated details in more challenging passages Use details from different sections of some complex informational passages to support a specific point or argument |
*identify facts embedded in complex informational texts *identify and analyze subtly stated or complex evidence presented by the author or narrator to defend his or her premise(s) |
Locate and interpret minor or subtly stated details in complex passages Locate and interpret important details and facts that support any idea or argument in complex passages |
| Sequence of Events | n/a | *discuss an issue of interest, determining how past events affected the present *use various strategies (e.g., timelines, event chains, discussion) to determine whether an event occurred and, if so, when it occurred |
Determine when (e.g., first, last, before, after) or if an event occurred in uncomplicated passages | n/a | n/a | *place events from a literary text in chronological order by locating substantial evidence from the text | Order simple sequences of events in uncomplicated literary narratives | *analyze the sequence of events in written or nonprint sources *map sequences of events in texts or films or from everyday occurrences, defending their reasoning |
Order sequences of events in uncomplicated passages | *read texts containing challenging sequences (e.g., flashback, flash-forward), discussing how the order of events affects understanding of the text *explain how altering a series of events would likely change the outcome of a situation or the actions of the characters |
Order sequences of events as they occur in more challenging passages | *determine the chronological sequence of events and the spatial relationships in complex texts (e.g., Dickens, García Marquez, Morrison, Tolstoy) | Order sequences of events in complex passages |
| Comparative Relationships | n/a | n/a | n/a | *analyze how an author or narrator uses description, dialogue, and action to suggest relationships between characters in written or nonprint sources *select phrases or statements from a literary text that illustrate how a specific character feels toward others in the text |
Identify relationships between principal characters in uncomplicated literary narratives | *identify similarities and differences between people, objects, events, or ideas, drawing accurate conclusions *identify interrelationships between and among people, objects, events, or ideas in written or nonprint sources |
Identify comparative relationships between ideas and people in uncomplicated passages | *evaluate the extent to which comparisons made by the author or narrator help clarify specific textual relationships | Have a sound grasp of relationships between people and ideas in uncomplicated passages Identify clearly established relationships between characters and ideas in more challenging literary narratives |
*develop an in-depth understanding of the fine distinctions between literary characters in a challenging text by closely examining the language used by the author or narrator *identify relationships between ideas and/or people in a challenging text and how those relationships develop over the course of the text |
Reveal an understanding of the dynamics between people and ideas in more challenging passages | *analyze subtle relationships between and among people, objects, events, and ideas in complex texts or films, forming accurate inferences | Make comparisons, conclusions, and generalizations that reveal a feeling for the subtleties in relationships between people and ideas in virtually any passage |
| Cause-Effect Relationships | n/a | *locate evidence in a text that explicitly states why an event or a series of events occurred *search for patterns or clues (e.g., signal words) that indicate cause-effect relationships |
Recognize cause-effect relationships explicitly described within a single sentence in a passage | *read portions of a literary text, predicting how a person's actions or words would likely impact a specific situation *use various strategies (e.g., questioning, role-playing) to determine plausible cause-effect relationships |
Recognize clearly stated cause-effect relationships within a single paragraph in uncomplicated literary narratives | *determine factors that have clearly influenced the outcome of a situation *identify statements in texts that clearly state the cause(s) and effect(s) of specific events |
Identify clearly stated cause-effect relationships in uncomplicated passages | *search for clues embedded in a text that suggest cause-effect relationships *examine events in written or nonprint sources to determine the precipitating cause(s) and final outcome(s) |
Identify subtly stated cause-effect relationships in uncomplicated passages Identify clearly stated cause-effect relationships in more challenging passages |
*identify clues in a challenging text that suggest possible motives for and effects of a person's actions or words *read conflicting viewpoints of an event and use textual evidence to identify which one has the most reasonable explanations of causes and effects |
Identify implied or subtly stated cause-effect relationships in more challenging passages | *identify implications and possible consequences of actions in complex texts | Identify implied, subtle, or complex cause-effect relationships in virtually any passage |
| Word Meaning | n/a | *use various resources (e.g., dictionary, thesaurus) to explore connotations of familiar words or descriptive language | Understand the implication of a familiar word and of simple descriptive language | *examine specific language in a text and propose plausible interpretations based in part on their own viewpoints and experiences | Use context clues to understand basic figurative language | *clarify the meanings of words or descriptive phrases by searching for clues in the text (e.g., sentence structure, context, prefixes/suffixes, spelling patterns) | Use context clues to define some words and interpret some figurative language in uncomplicated passages | *investigate the meanings of words and their possible effect(s) on the perceptions and behavior of people *research words and phrases from different sources, identifying their shades of meaning in various contexts or situations |
Use context clues to determine the appropriate meaning of multiple-meaning words or phrases in uncomplicated passages | *develop and use strategies for deciphering the meanings of words or phrases embedded in richly figurative or technical contexts *analyze figurative and technical language in the media, relating some instances to a personal experience |
Determine the appropriate meanings of words, phrases, or statements from figurative or somewhat technical contexts | *employ strategies for defining a difficult concept, such as identifying its characteristics or providing examples of what it is and is not like | Determine, even in situations where the language is richly figurative and the vocabulary is difficult, the meanings of context-dependent words, phrases, or statements in virtually any passage |
| Generalizations | n/a | *recognize generalizations about the main character in a literary text *combine several pieces of information to make a reasonable generalization about a specific character |
Make simple generalizations about the main character in uncomplicated literary narratives | *analyze the reasonableness of generalizations by reviewing information presented in the text and from other sources *compose generalizations that include qualifying language (e.g., a few, sometimes) when limited evidence is presented by the author or narrator *determine what a literary narrative is generally about, organizing the text's information into general statements that are supported by details from the text |
Make simple generalizations about the main points and characters in uncomplicated literary narratives | *make accurate generalizations about people and events based on evidence presented in the text *identify inaccurate generalizations (e.g., stereotypes) in written or nonprint sources |
Make more specific generalizations about people and ideas in uncomplicated passages | *defend or challenge the author's or narrator's assertions by locating several key pieces of information in a challenging text *make accurate generalizations based on implicit information in the text |
Make subtle generalizations about characters in uncomplicated literary narratives Make generalizations about people and situations in more challenging passages |
*synthesize information in challenging texts, making valid generalizations about people and situations *confirm or disprove generalizations suggested in texts by providing examples or counterexamples from other sources |
Use information from different sections of more challenging passages to make generalizations about people and situations | *evaluate the impact of literary devices (e.g., figurative language) on the meaning of a literary narrative *examine information from multiple sources and perspectives (including the author's or narrator's) in order to make reasonable generalizations about people, objects, ideas, and situations |
Make complex or subtle generalizations about people, ideas, and situations, often by synthesizing information from different portions of the passage Understand and generalize about portions of a complex literary narrative that use a range of literary devices |
| Author's Voice/Method | n/a | *locate details in a literary text that suggest the author's or narrator's intent *speculate about an author's or narrator's beliefs, motives, or thinki |
Recognize a clear intent by an author or narrator in uncomplicated literary narratives | *identify details in a text that reveal relationships between and among portions of the text and the text as a whole *infer the author's or narrator's reasons for including specific pieces of information in the text |
Recognize clear relationships between a part of a passage and the whole passage or another part in uncomplicated passages | *analyze techniques used by the author of an informational text to reveal or conceal his or her point of view *characterize the author's or narrator's feelings toward his or her subject by locating relevant phrases or sentences in the text |
Make generalizations about the author's or narrator's attitude toward his or her subject in uncomplicated passages Understand the overall approach taken by an author or narrator, including point of view, in uncomplicated informational passages |
*search for clues that suggest the viewpoint from which a literary text is written or told and determine whether the author's or narrator's point of view is valid or biased *analyze the relationship between an author's or narrator's intended message and the rhetorical devices used to convey that message (e.g., language used, evidence provided) |
Understand the overall approach taken by an author or narrator, including point of view, in uncomplicated literary narratives | *identify subtle evidence that conveys the author's or narrator's point of view in challenging texts *change the wording of a text in order to convey a different tone or attitude (e.g., persuasive, serious) |
Understand how one part of a passage functions in relation to the whole passage or another part in uncomplicated passages Understand the overall approach taken by an author or narrator, including point of view, in virtually any passage |
*determine the author's or narrator's position toward a specific topic, issue, or idea by noting key facts, claims, and details from the text | Understand how one part of a passage functions in relation to the whole passage or another part when the relationship is subtle or complex Identify and then generalize about an author's or narrator's attitude or point of view toward his or her subject in virtually any passage |
| Mathematics Area of Transition | Score: 1-12 | Pathways for Improvement | Score: 13-15 | Pathways for Improvement | Score: 16-19 | Pathways for Improvement | Score: 20-23 | Pathways for Improvement | Score: 24-27 | Pathways for Improvement | Score: 28-32 | Pathways for Improvement | Score: 33-36 |
| Basic Operations/Applications | n/a | *practice and apply estimation and computation using whole numbers and decimals *choose the appropriate method of computation to solve multistep problems (e.g., calculator, mental, or pencil and paper) *practice selecting appropriate units of measure (e.g., inches or feet, hours or minutes, centimeters or meters) and converting between units *model and connect physical, verbal, and symbolic representations of money |
Perform one-operation computation with whole numbers and decimals Perform common conversions (e.g., inches to feet or hours to minutes) Find equivalent values of coins |
*investigate and build understanding of the concept of percentage as a comparison of a part to a whole *use multiple operations to solve multistep arithmetic problems |
Solve routine one-step arithmetic problems (using whole numbers, fractions, and decimals) such as single-step percent and calculate a simple average of whole numbers Solve some routine two-step arithmetic problems |
*solve routine arithmetic problems that involve rates, proportions, and percents *do multistep computations with rational numbers |
Solve routine two-step or three-step arithmetic problems involving concepts such as rate and proportion, tax added, percentage off, computing an average with negative integers, and computing with a given average | *apply and use number properties to model and solve problems that involve reasoning with proportions *select and use appropriate units when solving problems that involve one or more units of measure |
Solve multistep arithmetic problems that involve planning or converting units of measure (e.g., feet per second to miles per hour) | *model and solve real-world problems that involve a combination of rates, proportions, and/or percents |
Solve word problems containing several rates, proportions, or percentages | *solve problems that require combining multiple concepts | Solve complex arithmetic problems involving percent of increase or decrease and problems requiring integration of several concepts from pre-algebra and/or pre-geometry (e.g., comparing percentages or averages, using several ratios, and finding ratios in geometry settings) |
| Probability, Statistics and Data Analysis | n/a | *interpret data from a variety of displays and use it in computation (e.g., mean, median, mode, range) *organize, display, and analyze data in a variety of ways |
Perform a single computation using information from a table or chart | *interpret data from a variety of displays (e.g., box-and-whisker plot) and use it along with additional information to solve real-world problems *conduct simple probability experiments and represent results using different formats |
Read tables and graphs Use the relationship between the probability of an event and the probability of its complement |
*solve real-world problems that involve measures of central tendency (e.g., mean, median, mode) *gather, organize, display, and analyze data in a variety of ways to use in problem solving *conduct simple probability experiments, use a variety of counting techniques (e.g., Venn diagrams, Fundamental Counting Principle, organized lists), and represent results from data using different formats |
Translate from one representation of data to another (e.g., a bar graph to a circle graph) Determine the probability of a simple event Exhibit knowledge of simple counting techniques* |
*interpret data and use appropriate measures of central tendency to find unknown values *find the probability of a simple event in a variety of settings *construct and analyze Venn diagrams to help determine simple probabilities |
Manipulate data from tables and graphs Use Venn diagrams in counting* Compute straightforward probabilities for common situations |
*find the probability of simple events, disjoint events, compound events, and independent events in a variety of settings using a variety of counting techniques | Interpret and use information from figures, tables, and graphs, including graphs in the coordinate plane Apply counting techniques Compute a probability when the event and/or sample space are not given or obvious |
*design and conduct probability investigations (e.g., how the margin of error is determined) and then determine, analyze, and communicate the results | Analyze and draw conclusions based on information from figures, tables, and graphs, including graphs in the coordinate plane Exhibit knowledge of conditional and joint probability |
| Numbers: Concepts and Properties | n/a | n/a | n/a | *recognize and apply place value, rounding, and elementary number theory concepts | Recognize one-digit factors of a number Identify a digit's place value |
*apply elementary number concepts, including identifying patterns pictorially and numerically (e.g., triangular numbers, arithmetic and geometric sequences), ordering numbers, and factoring *recognize, identify, and apply field axioms (e.g., commutative) |
Exhibit knowledge of elementary number concepts including rounding, the ordering of decimals, pattern identification, absolute value, primes, and greatest common factor | *use the inverse relationships for the four basic operations, exponentiation, and root extractions to determine unknown quantities *perform basic operations with complex numbers† |
Work problems involving [positive integer exponents*], scientific notation, ordering fractions, numerical factors, least common multiple, square roots, [and cube roots*] Determine when an expression is undefined* Square numbers [and expressions*] Exhibit some knowledge of the complex numbers† |
*apply and use elementary number concepts and number properties to model and solve nonroutine problems that involve new ideas | Apply the rules of exponents and number properties—often in a new context—to solve problems that involve even/odd numbers, positive/negative integers, factors/multiples, and prime factorizations Multiply two complex numbers† |
*explain, solve, and/or draw conclusions for complex problems using relationships and elementary number concepts | Draw conclusions based on number concepts, algebraic properties, and/or relationships between expressions and numbers Exhibit knowledge of logarithms and geometric sequences Apply properties of complex numbers |
| Algebric Expressions | n/a | *model a variety of problem situations with expressions and/or equations | Exhibit knowledge of basic expressions (e.g., identify an expression for a total as b + g) | *use mathematical symbols and variables to express a relationship between quantities (e.g., list the whole number values of x such that x < 5 and x > 1 + 2) |
Combine like terms (e.g., 2x + 5x)* Substitute whole numbers for unknown quantities to evaluate expressions |
*create expressions that model mathematical situations using combinations of symbols and numbers | Manipulate basic algebraic expressions (e.g., substitute integers for unknown quantities, add and subtract simple algebraic expressions, [multiply two binomials*], and perform straightforward word-to-symbol translations) | *identify, interpret, and generate symbolic representations that model the context of a problem *factor and perform the basic operations on polynomials |
Factor simple quadratics (e.g., the difference of squares and perfect square trinomials)* Add, subtract, and multiply polynomials* Write expressions with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions) |
*manipulate radical expressions (e.g., rationalize denominators) | Manipulate expressions Write expressions for common algebra settings |
*formulate expressions that require planning to accurately model real-world problems | Write expressions that require planning and/or manipulating to accurately model a situation |
| Equations and Inequalities | n/a | *use the inverse relationships for the basic operations of addition and subtraction to determine unknown quantities | Solve equations in the form x + a = b,where a and b are whole numbers or decimals | *evaluate algebraic expressions and solve simple equations using integers | Solve one-step equations having integer or decimal answers | *evaluate algebraic expressions and solve multistep first-degree equations | Solve routine first-degree equations | *create and solve linear equations and inequalities that model real-world situations *solve literal equations for any variable |
Solve real-world problems using first-degree equations Solve first-degree inequalities that do not require reversing the inequality sign* Identify solutions to simple quadratic equations Write equations and inequalities with a single variable for common pre-algebra settings (e.g., rate and distance problems and problems that can be solved by using proportions) |
*create and use basic families of functions (which include linear, absolute value, and quadratic) to model and solve problems in common settings *explore and use different methods to solve systems of equations |
Manipulate equations Write equations and inequalities for common algebra settings Solve absolute value and quadratic equations Solve linear inequalities that require reversing the inequality sign Find solutions to systems of linear equations |
*formulate equations and inequalities that require planning to accurately model real-world problems (e.g., direct and inverse variation) | Solve simple absolute value inequalities Write equations and inequalities that require planning, manipulating, and/or solving |
| Graphic Representations | n/a | *locate and describe points in terms of their position on the number line | Identify the location of a point with a positive coordinate on the number line | *locate and describe objects in terms of their position on the number line and on a grid | Locate points on the number line and in the first quadrant | *sketch and identify line segments, midpoints, intersections, and vertical and horizontal lines | Comprehend the concept of length on the number line* Locate points in the coordinate plane Exhibit knowledge of vertical and horizontal lines and of their point of intersection Exhibit knowledge of slope* |
*represent and interpret relationships defined by equations and formulas; translate between representations as ordered pairs, graphs, and equations; and investigate symmetry and transformations (e.g., reflections, translations, rotations) | Identify the graph of a linear inequality on the number line* Determine the slope of a line from points or equations* Match linear graphs with their equations* Find the midpoint of a line segment* |
*graph linear equations and inequalities, determine slopes of lines, identify parallel and perpendicular lines, and find distances *identify characteristics of figures from a general equation |
Match number line graphs with solution sets of linear inequalities Use the distance formula Use properties of parallel and perpendicular lines to determine an equation of a line or coordinates of a point Recognize special characteristics of parabolas and circles (e.g., the vertex of a parabola and the center or radius of a circle)† |
*solve and graph quadratic inequalities | Match number line graphs with solution sets of simple quadratic inequalities Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax2 + c Solve problems integrating multiple algebraic and/or geometric concepts |
| Properties of Plane Figures | n/a | n/a | n/a | *describe, compare, and contrast plane and solid figures using their attributes | n/a | *describe angles and triangles using mathematical terminology and apply their properties | Exhibit knowledge of basic angle properties and special sums of angle measures (e.g., 90°, 180°, and 360°) | *recognize what geometric properties and relationships for parallel lines to apply to find unknown angle measures *recognize when to apply geometric properties and relationships of triangles to find unknown angle measures |
Use properties of isosceles triangles* Recognize Pythagorean triples* Use several angle properties to find an unknown angle measure |
*apply special right-triangle properties and the Pythagorean theorem to solve congruent and similar shape problems | Apply properties of 30°-60°-90°, 45°-45°-90°, similar, and congruent triangles Use the Pythagorean theorem |
*make generalizations, arrive at conclusions based on conditional statements, and offer solutions for new situations that involve connecting mathematics with other content areas *investigate angle and arc relationships for circles |
Draw conclusions based on a set of conditions Solve multistep geometry problems that involve integrating concepts, planning, visualization, and/or making connections with other content areas Use relationships among angles, arcs, and distances in a circle |
| Measurement | n/a | *identify line segments in geometric figures and estimate or calculate their measure | Estimate or calculate the length of a line segment based on other lengths given on a geometric figure | *distinguish between area and perimeter, and find the area or perimeter when all relevant dimensions are given | Compute the perimeter of polygons when all side lengths are given Compute the area of rectangles when whole number dimensions are given |
*find area and perimeter of a variety of polygons by substituting given values into standard geometric formulas | Compute the area and perimeter of triangles and rectangles in simple problems Use geometric formulas when all necessary information is given |
*apply a variety of strategies to determine the circumference or perimeter and the area for circles, triangles, rectangles, and composite geometric figures | Compute areas and circumferences of circles after identifying necessary information Compute areas of rectangles and triangles when one or more additional simple steps are required Compute the perimeter of simple composite geometric figures with unknown side lengths* |
*apply a variety of strategies using relationships between perimeter, area, and volume to calculate desired measures | Use relationships involving area, perimeter, and volume of geometric figures to compute another measure | *examine and compare a variety of methods to find areas of composite figures and construct scale drawings | Use scale factors to determine the magnitude of a size change Compute the area of composite geometric figures when planning or visualization is required |
| Functions | n/a | n/a | n/a | *recognize functions as mappings of an independent variable into a dependent variable† | Work with function notation in evaluating simple quadratic functions at integer values† | *evaluate polynomial functions that use function notation† *distinguish between range and domain† |
Work with function notation in evaluating simple quadratic functions at integer values† | *identify the basic trigonometric ratios† | Work with function notation in evaluating polynomial functions at integer values† Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths† |
*write an expression for and evaluate composite functions† *use basic trigonometric ratios to solve problems involving indirect measurement† |
Evaluate composite functions at integer values† Apply basic trigonometric ratios to solve right-triangle problems† |
*explore geometric models where unit circle trigonometry and basic identities can be used to solve problems† | Write an expression for the composite of two simple functions† Use trigonometric concepts and basic identities to solve problems† Exhibit knowledge of unit circle trigonometry† Match graphs of basic trigonometric functions with their equations† |
| Science Area of Transition | Score: 1-12 | Pathways for Improvement | Score: 13-15 | Pathways for Improvement | Score: 16-19 | Pathways for Improvement | Score: 20-23 | Pathways for Improvement | Score: 24-27 | Pathways for Improvement | Score: 28-32 | Pathways for Improvement | Score: 33-36 |
| Data Interpretation | n/a | *locate data in simple tables and graphs *become familiar with units of measurement commonly used in science *become familiar with different types of graphs (e.g., line graphs, pie charts, bar graphs) |
Select a single piece of textual (nonnumerical) information from a table Select the highest/lowest value from a specified column or row in a table Select a single data point from a simple table, graph, or diagram |
*locate several data points in a simple table or graph and make comparisons between them
*create basic tables and graphs from sets of scientific data *become familiar with common terms used in science (e.g., star, force, mineral) *describe trends and relationships in data displayed in simple graphs and tables |
Select data from a simple table, graph, or diagram (e.g., a table or graph with two or three variables; a food web) Understand basic scientific terminology Find basic information in a brief body of text Identify a direct relationship between variables in a simple table, graph, or diagram |
*examine line graphs to determine if they show a direct or inverse relationship between variables *display data gathered in laboratory exercises in a variety of formats (e.g., line graphs, bar graphs, pie charts) |
Compare data from a simple table, graph, or diagram Identify an inverse relationship between variables in a simple table, graph, or diagram Translate information (data or text) into graphic form Select data from a complex table, graph, or diagram (e.g., a table or graph with more than three variables) |
*determine a simple mathematical relationship between two variables *integrate scientific information from popular sources (e.g., newspapers, magazines, the Internet) with that found in textbooks *become familiar with multidimensional graphs such as scatterplots |
Compare data from a complex table, graph, or diagram Identify or use a simple mathematical relationship that exists between data Identify a direct or inverse relationship between variables in a complex table, graph, or diagram Compare or combine data from two simple data sets Combine new, simple information (data or text) with given information (data or text) |
*relate scientific information contained in written text to numerical scientific information *manipulate algebraic equations that represent scientific relationships |
Identify or use a complex mathematical relationship that exists between data Compare or combine given text with data from tables, graphs, or diagrams |
examine two related sets of data and then combine those data in ways that are useful | Compare or combine data from two complex data sets Combine new, complex information (data or text) with given information (data or text) |
| Scientific Investigation | n/a | *observe experiments being performed and discuss what was done and why | n/a | *conduct a simple experiment and collect data | *conduct a simple experiment that makes use of a control group *perform simple laboratory activities designed to teach familiarity with a number of commonly used tools (e.g., thermometers, balances, glassware) |
Understand simple lab procedures Identify the control in an experiment |
*perform experiments that require more than one step | Understand moderately complex lab procedures
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*determine the hypothesis behind an experiment that requires more than one step *determine alternate methods of testing a hypothesis *perform several repetitions of an experiment to determine the reliability of results |
Understand complex lab procedures Understand moderately complex experimental designs Identify an alternate method for testing a hypothesis |
*carry out scientific investigations in which the importance of accuracy and precision is stressed *consider how changing an experimental procedure will affect the results of their scientific investigations *design and carry out additional scientific inquiries to answer specific questions |
Understand precision and accuracy issues Identify new information that could be collected from a new experiment or by modifying an existing experiment |
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| Evaluation of Experiments, Models and Assertions | n/a | *discuss what hypotheses and conclusions are and how they are different from each other | n/a | *read articles of an appropriate level from newspapers and science newsmagazines and identify any hypotheses or conclusions made by the author(s) | n/a | *read descriptions of actual experiments (e.g., completed science fair research, simple experiments from science education journals) and discuss whether the conclusions that were made support or contradict the hypotheses | n/a | *formulate hypthoses, predictions, or conclusions based on the results of an experiment *compare and contrast two different viewpoints about a scientific phenomenon |
Select a simple hypothesis, prediction, or conclusion that is supported by one or more data sets or viewpoints Identify similarities and differences in two or more viewpoints Identify key issues or assumptions in an argument or viewpoint Determine whether new information supports or weakens a viewpoint or hypothesis |
*evaluate whether the data produced by an experiement adequately support a given conclusion *communicate findings of an experiment and compare conclusions with those of peers |
Select a complex hypothesis, prediction, or conclusion that is supported by a data set or viewpoint Select a set of data or a viewpoint that supports or contradicts a hypothesis, prediction, or conclusion Predict the most likely or least likely result based on a given viewpoint |
*seek out new information that enhances or challenges their existing knowledge *formulate hypotheses, predictions, or conclusions by comparing and contrasting several different sets of data from different experiments *evaluate the merits of a conclusion based on the analysis of several sets of dat |
Select a complex hypothesis, prediction, or conclusion that is supported by two or more data sets or viewpoints Determine why given information (data or text) supports or contradicts a hypothesis or conclusion |