Click Study Flashcards above to open the flashcard hub — 308 ParaPathways cards you can flip, match, type, or quiz yourself on. The deck follows ETS’s four ParaPathways content categories across both subtests, so you study exactly what the test measures.[2] Pair it with our free practice test and study guide.
ParaPathways Flashcard Study Modes
Flip mode turns each card at your own pace, Match races you to pair terms with definitions, Type shows a definition and asks you to spell the term — a prompt about two consonants that make one sound should pull Consonant digraph out of you — and Quiz rebuilds all 308 cards into multiple-choice questions for a fast self-check.

What the ParaPathways Deck Covers
Reading is the largest category in the deck with 91 cards, matching its place as the biggest block on the test. Beyond comprehension terms such as Main idea, Inference, and Text structure, it covers the Science of Reading topics ETS added to ParaPathways: Phoneme, Syllable, Consonant blend, Vowel team, and the three fluency components — Accuracy, Reading rate, and Expression.
Writing follows with 83 cards. Conventions cards such as Subject-verb agreement, Comma splice, and Its vs. it’s sit beside the newer ParaPathways topics: Credible source, Peer-reviewed journal, In-text citation, Block quotation, Paraphrase, and Responsible AI use. Narrative elements — Setting, Theme, Conflict, and Climax — round it out.
Numbers and Operations has 63 cards, from Integer and Absolute value through Reciprocal, Percent increase, and Zero exponent to Order of operations and Solving a one-variable equation. Geometry, Measurement, and Data has 71 cards: Elapsed time and unit facts like Cups in a quart, shape terms like Trapezoid and Isosceles triangle, formulas like Area of a triangle and Circumference, the Coordinate plane, and the four statistics — Mean, Median, Mode, and Range.
Short, spaced sessions with these cards keep a wide test fresh.[2] Used with the practice test and study guide, they turn review time into a rising readiness score.
ParaPathways Flashcards by Category
The deck is organized by ETS’s four content categories. Question counts are ETS’s approximate numbers per test form:[2]
| Category | Subtest | Test questions | Cards |
|---|---|---|---|
| Reading | 5758 Reading and Writing | ≈30 | 91 |
| Writing | 5758 Reading and Writing | ≈21 | 83 |
| Numbers and Operations | 5759 Mathematics | ≈18 | 63 |
| Geometry, Measurement, & Data Analysis | 5759 Mathematics | ≈18 | 71 |
How to Get the Most Out of These Flashcards
- Start with Reading. At 91 cards and about 30 test questions it is the biggest category, and its phonics and fluency terms are new to many test-takers.
- Type-drill the look-alikes. Consonant digraph and Consonant blend, or Revising and Editing, are easy to swap in Quiz mode and hard to fake in Type mode.
- Use Match for the math facts. Unit conversions like Inches in a foot and Quarts in a gallon should become instant.
- Pair Writing cards with the practice test. Conventions stick best when you see them in real sentences.
- Rotate categories daily. A short mixed session across all four keeps both subtests ready.
ParaPathways Flashcards FAQ
Just over 300 free ParaPathways flashcards, organized by ETS's four content categories: Reading, Writing, Numbers and Operations, and Geometry, Measurement, and Data Analysis. Every card is free, with no account required.
The vocabulary and rules behind all 41 topics in ETS's ParaPathways Study Companion — from phonemes, digraphs, and reading fluency to credible sources, in-text citation, and the writing process, and from percents, exponents, and order of operations to unit conversions, the coordinate plane, and mean, median, mode, and range.
ParaPathways (ETS 5757). The ParaPro (1755) is a separate ETS test, and ParaPathways is not its replacement: ETS sells both in 2026–27, and your state or district decides which one it accepts. The reading, writing, and math vocabulary overlaps, but ParaPathways adds topics such as phonics, fluency, source credibility, and citation — check your state's requirement before you choose a deck.
Give Reading the most time — it is about 30 of the 87 questions — then Writing, then the two math categories. Flip to learn new cards, type to test recall, match for speed, and quiz yourself before a full practice test.
Yes — 100% free, all four study modes, no paywall.
Yes. ETS provides an on-screen four-function calculator on Mathematics (5759). It only adds, subtracts, multiplies, and divides, so cards on order of operations, fraction rules, exponents, and unit conversions still matter.
ParaPathways flashcard bank
All 308 cards, by topic
A reference copy of every card in this deck. Each answer stays hidden until you choose to show it. To study with Flip, Match, Type and Quiz modes and track what you have mastered, use Study Flashcards at the top of the page.
Reading (91)
- Main idea
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The central point of a passage — what the whole text is mostly about, which every paragraph helps develop.
- Supporting detail
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A fact, example, statistic, or reason that explains or proves the main idea.
- Summary
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A short restatement of a text's main idea and key points in your own words, leaving out minor details.
- Primary purpose
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The chief reason a text was written — usually to inform, persuade, or entertain.
- Topic sentence
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A sentence, often first in a paragraph, that states the paragraph's main point.
- Inference
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A conclusion a reader draws from clues in the text plus reasoning, when the author does not state it directly.
- Implication
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An idea a text suggests without saying it outright; the reader must work it out from the evidence.
- Drawing conclusions
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Combining several details in a text to reach a judgment the text supports but does not state.
- Explicit information
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Information the text states directly, in so many words.
- Implicit information
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Information the reader must infer because the text only suggests it.
- Context clues
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Nearby words, phrases, or sentences that help a reader work out the meaning of an unfamiliar word.
- Definition clue
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A context clue in which the sentence itself explains the unfamiliar word, often after a comma or 'which means'.
- Contrast clue
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A context clue signaled by words such as but, however, or unlike, showing the unknown word means the opposite of a nearby idea.
- Example clue
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A context clue in which examples (often after 'such as') reveal what an unfamiliar word means.
- Prefix
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A word part added to the beginning of a root that changes its meaning, such as un-, re-, pre-, or mis-.
- Suffix
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A word part added to the end of a root that changes its meaning or part of speech, such as -less, -ful, or -tion.
- Root word
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The core part of a word that carries its basic meaning, such as port (carry) in transport.
- Morpheme
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The smallest unit of meaning in a word; un-, break, and -able are the three morphemes in unbreakable.
- Denotation
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A word's literal, dictionary meaning.
- Connotation
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The feelings or associations a word carries beyond its literal meaning, such as thrifty (positive) versus stingy (negative).
- Multiple-meaning word
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A word with more than one definition, such as bank (a river's edge or a place that keeps money); context shows which applies.
- Glossary
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An alphabetical list of a book's key terms with short definitions, usually at the back.
- Online dictionary
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A digital reference tool that gives a word's definitions, pronunciation, part of speech, and often audio.
- Reading fluency
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The ability to read with accuracy, at an appropriate rate, and with expression — the three components ETS names.
- Accuracy (fluency)
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Reading the words correctly, without skipping, adding, or substituting words.
- Reading rate
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How quickly a student reads connected text; fluent rate is conversational, not as fast as possible.
- Expression (prosody)
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Reading with appropriate phrasing, pausing, stress, and intonation that match the meaning.
- Words correct per minute (WCPM)
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A fluency measure that counts words read correctly in one minute, combining accuracy and rate.
- Repeated reading
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A fluency practice in which a student rereads the same short passage several times to build speed and smoothness.
- Echo reading
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A fluency routine in which an adult reads a line aloud and the student immediately repeats it, copying the phrasing.
- Choral reading
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A group reads the same text aloud together, which supports less fluent readers with a model.
- Automaticity
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Recognizing words quickly and effortlessly, which frees attention for understanding.
- Tone
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The author's attitude toward the subject, shown through word choice (for example humorous, sad, angry, lighthearted).
- Mood
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The feeling a text creates in the reader.
- Word choice (diction)
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The specific words an author selects, which shape a text's meaning and tone.
- Figurative language
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Words used beyond their literal meaning to create an effect, such as similes, metaphors, and personification.
- Simile
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A comparison using like or as: 'The house groaned like an old man.'
- Metaphor
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A comparison that says one thing is another without like or as: 'The classroom was a zoo.'
- Personification
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Giving human qualities to something nonhuman: 'The wind whispered through the trees.'
- Sarcasm
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Saying the opposite of what one means, often to mock, such as 'Oh, wonderful' when something goes wrong.
- Text structure
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The way an author organizes ideas: problem/solution, cause/effect, compare/contrast, sequence, or description.
- Problem and solution
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A text structure that presents an issue and then one or more ways to resolve it.
- Cause and effect
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A text structure that explains why something happened and what resulted; signal words include because and as a result.
- Compare and contrast
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A text structure that shows how two or more things are alike and different; signal words include similarly and however.
- Sequence (chronological order)
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A text structure that presents events or steps in time order; signal words include first, next, and finally.
- Description
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A text structure that presents the features or characteristics of a topic.
- Signal words
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Transition words that reveal a text's structure, such as because (cause/effect) or unlike (compare/contrast).
- Author's purpose
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The reason an author writes a text: to inform, to persuade, or to entertain.
- Author's perspective
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The author's background, beliefs, and viewpoint, which shape what the text includes and how it says it.
- Point of view (author's)
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The position or opinion an author takes on a topic.
- Bias
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A one-sided leaning that can lead an author to include only details that favor a view.
- Fact
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A statement that can be checked and proven true or false.
- Opinion
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A statement of belief, feeling, or judgment that cannot be proven true or false.
- Persuasive text
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Writing meant to convince readers to believe or do something, often with emotional appeals and loaded words.
- Informational text
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Nonfiction writing that explains facts about a topic.
- Graphic features
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Maps, tables, diagrams, charts, and graphs that present information visually alongside text.
- Map legend (key)
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The box on a map that explains what each symbol, line, or color stands for.
- Map scale
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The part of a map that shows how map distance relates to real distance, such as 1 inch = 5 miles.
- Axis label
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The words along a graph's axis that tell what quantity and unit the axis measures.
- Table
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Data arranged in rows and columns so values can be compared quickly.
- Diagram
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A labeled drawing that shows the parts of something or how a process works.
- Textual evidence
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Specific points, statistics, facts, direct quotations, or comparisons from a text that support a claim.
- Relevant evidence
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Evidence that directly relates to a claim and helps prove it.
- Claim
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A statement an author argues is true and supports with evidence.
- Valid argument
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An argument whose evidence is relevant and sufficient and logically supports its claim.
- Anecdote
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A brief personal story; as evidence it is weaker than data because it describes a single case.
- Phonological awareness
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Awareness that spoken language is made of units — words, syllables, onsets and rimes, and individual sounds.
- Phonemic awareness
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The ability to hear, identify, and manipulate the individual sounds (phonemes) in spoken words.
- Phoneme
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The smallest unit of sound in spoken language; /b/ and /p/ are the phonemes that make bat and pat different words.
- Syllable
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A word part with one vowel sound; dog has one syllable and apple has two.
- Phoneme blending
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Combining separate sounds into a word, such as /k/ /a/ /t/ → cat.
- Phoneme segmentation
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Breaking a spoken word into its separate sounds, such as sun → /s/ /u/ /n/.
- Phoneme substitution
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Changing one sound in a word to make a new word, such as mat → sat.
- Rhyme
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Words that share the same ending sound, such as cat, hat, and flat.
- Onset and rime
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The first consonant sound(s) of a syllable (onset) and the vowel and what follows (rime): in 'cat', c + at.
- Phonics
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Instruction in the relationships between letters (graphemes) and sounds (phonemes) used to decode words.
- Grapheme
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A letter or group of letters that represents one sound, such as sh or igh.
- Decoding
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Using letter-sound knowledge to read (sound out) a written word.
- Consonant digraph
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Two consonants that together make one sound, such as sh, ch, th, wh, and ph.
- Consonant blend
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Two or three consonants whose sounds are each heard, such as bl, st, and str.
- Vowel team
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Two or more letters that work together to make one vowel sound, such as ea, ai, oa, and ee.
- Silent e (VCe)
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A final e that is not pronounced and makes the earlier vowel say its name, as in kite and cake.
- R-controlled vowel
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A vowel followed by r that changes its sound, as in car, her, bird, and fork.
- Short vowel
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A vowel sound as in cat, bed, sit, hot, and cup, typical of closed CVC syllables.
- Long vowel
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A vowel that says its name, as in cake, feet, kite, boat, and cute.
- Sight word
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A common word students learn to recognize instantly, often because it does not follow regular patterns (the, of, said).
- Compound word
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A word made of two smaller words, such as sunflower; splitting it helps a student decode it.
- Text-based discussion
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A conversation in which students talk about a text and support their ideas with evidence from it.
- Citing textual evidence (discussion)
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Pointing to the specific line or detail in a text that supports what a student says.
- Open-ended question
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A question with more than one reasonable answer that invites students to explain their thinking.
- Sentence starter
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A prompt such as 'I agree with ___, and I would add...' that helps students join a discussion.
Writing (83)
- Standard English conventions
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The accepted rules of usage, grammar, punctuation, capitalization, and spelling in formal writing.
- Subject-verb agreement
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A singular subject takes a singular verb and a plural subject takes a plural verb; ignore phrases between them.
- Indefinite pronoun
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A pronoun such as each, everyone, nobody, or either that does not refer to a specific person; most are singular.
- Pronoun-antecedent agreement
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A pronoun must match the noun it replaces (its antecedent) in number and gender.
- Antecedent
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The noun a pronoun refers back to.
- Pronoun case
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The form a pronoun takes for its job: subjective (I, he, who), objective (me, him, whom), or possessive (my, his, whose).
- Who vs. whom
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Who is a subject (Who called?); whom is an object, often after a preposition (To whom?).
- Reflexive pronoun
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A pronoun ending in -self or -selves used when the subject acts on itself: 'I taught myself.'
- Vague pronoun reference
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A pronoun that could refer to more than one noun, making the sentence unclear.
- Verb tense consistency
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Keeping verbs in the same time frame unless the meaning requires a change.
- Sentence fragment
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A group of words punctuated as a sentence but missing a subject, a verb, or a complete thought.
- Run-on sentence
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Two or more independent clauses joined with no punctuation or conjunction.
- Comma splice
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Two independent clauses joined by only a comma.
- Independent clause
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A group of words with a subject and a verb that can stand alone as a sentence.
- Dependent clause
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A clause that has a subject and verb but cannot stand alone, often starting with because, although, or when.
- Coordinating conjunctions (FANBOYS)
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For, and, nor, but, or, yet, so — with a comma, they join two independent clauses.
- Conjunctive adverb
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A transition such as however, therefore, or moreover; between two clauses it takes a semicolon before and a comma after.
- Semicolon
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Punctuation that joins two closely related independent clauses without a conjunction.
- Colon
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Punctuation that follows a complete clause to introduce a list, an explanation, or a quotation.
- Serial (Oxford) comma
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The comma before and or or in a list of three or more items: red, white, and blue.
- Introductory comma
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A comma that follows an introductory word, phrase, or clause: 'After the assembly, we returned.'
- Apostrophe
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Punctuation that shows possession (the teacher's desk) or a contraction (don't) — never a simple plural.
- Plural possessive
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For a plural noun ending in s, add only an apostrophe: the teachers' lounge.
- Quotation marks
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Punctuation that encloses a speaker's or author's exact words; in American usage commas and periods go inside.
- Proper noun
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The name of a specific person, place, or thing, which is capitalized (Grand Canyon National Park).
- Its vs. it's
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Its shows possession (the dog wagged its tail); it's means it is or it has.
- Their / there / they're
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Their shows ownership, there names a place, and they're means they are.
- Affect vs. effect
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Affect is usually a verb (to influence); effect is usually a noun (a result).
- Then vs. than
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Then refers to time; than is used in comparisons (bigger than).
- Fewer vs. less
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Fewer is for things you can count (fewer students); less is for amounts you cannot count (less water).
- To / too / two
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To shows direction, too means also or excessively, and two is the number 2.
- Double negative
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Two negative words in one clause (don't have no), which standard English avoids.
- Parallel structure
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Using the same grammatical form for items in a series or comparison: hiking, swimming, and biking.
- Misplaced modifier
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A describing word or phrase placed so it seems to modify the wrong word.
- Dangling modifier
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An opening phrase with no clear word to describe: 'Running to the bus, my backpack fell open.'
- Coherent writing
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Writing whose ideas are logically ordered and clearly connected, so it reads as one unified piece.
- Unity
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Every sentence in a paragraph relates to the paragraph's main idea; off-topic sentences break unity.
- Transition words
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Words such as first, however, furthermore, and as a result that show how ideas connect.
- Concise writing
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Writing that says what it means without unnecessary words, such as 'because' instead of 'due to the fact that'.
- Formal style
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Writing that uses complete sentences, precise words, and no slang — appropriate for letters to a principal.
- Audience
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The readers a piece of writing is meant for, which shapes its style and word choice.
- Writing process
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The stages of producing writing: planning (prewriting), drafting, revising, editing, and publishing.
- Prewriting (planning)
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The writing stage for generating and organizing ideas with lists, webs, or outlines before drafting.
- Drafting
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The writing stage for turning planned ideas into sentences and paragraphs without worrying about perfection.
- Revising
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Improving a draft's ideas, organization, and clarity — adding, removing, moving, or substituting content.
- Editing
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Correcting a draft's conventions: capitalization, usage, punctuation, and spelling.
- Publishing
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Sharing a finished piece of writing with an audience.
- Outline
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A planning tool that arranges main ideas and supporting details in order before drafting.
- Peer review
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Classmates reading each other's drafts and giving feedback, usually to guide revision.
- Credible source
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A trustworthy source such as a peer-reviewed journal article, an .edu site, or a .gov site, with a named author and date.
- Noncredible source
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An unreliable source such as a social media post, an anonymous blog, or a tabloid.
- Peer-reviewed journal
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A publication whose articles are checked by experts in the field before they are published.
- .gov website
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A U.S. government website; generally a credible source for official data and laws.
- .edu website
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A website of an educational institution such as a university; generally more credible than a personal blog.
- Primary source
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An original, firsthand record such as a diary, a speech, a photograph, or the text of a law.
- Secondary source
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A work that interprets or summarizes primary sources, such as a textbook or an encyclopedia article.
- In-text citation
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A brief note in the text, such as (Garcia, 2021, p. 14), showing where a quotation or idea came from.
- Direct quotation
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A source's exact words, placed in quotation marks and cited.
- Block quotation
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A long quotation (typically more than about four lines) set off as an indented block without quotation marks.
- Paraphrase
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Restating a source's idea in your own words and sentence structure — it still needs a citation.
- Ellipsis (…)
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Three dots showing that words have been left out of a quotation.
- Plagiarism
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Presenting someone else's words or ideas as your own without credit.
- Counterclaim
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An opposing view that a strong argument acknowledges and answers.
- Reasoning
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The explanation that connects evidence to a claim, showing why the evidence proves the point.
- Expert testimony
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Evidence from a person with professional knowledge of the topic, such as a pediatrician on child health.
- Statistic
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A numerical fact from data, such as 'nearly 70 percent of students surveyed'.
- Heading
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A title for a section of an informational text that previews the topic of that section.
- Caption
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A short explanation under a photo or graphic telling what it shows.
- Bold print
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Dark type that signals a key term, often defined in the text or a glossary.
- Index
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An alphabetical list of topics at the back of a book with the pages where each appears.
- Plot
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The sequence of events in a story: exposition, rising action, climax, falling action, and resolution.
- Setting
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The time and place in which a story happens.
- Character
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A person, animal, or figure who takes part in a story's events.
- Character motivation
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The reason behind a character's actions.
- Theme
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The central message or lesson about life that a story conveys.
- Conflict
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The problem or struggle the main character faces.
- Climax
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The turning point of a story, when tension is highest.
- Resolution
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The part of a story, after the climax, where the conflict is settled.
- First-person point of view
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A story told by a character in the story, using I and me.
- Third-person point of view
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A story told by a narrator outside the story, using he, she, and they.
- Digital citizenship
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Using technology safely, respectfully, and responsibly, including protecting privacy and crediting sources.
- Responsible AI use
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Using AI tools only as the teacher allows, saying how they were used, and checking their output against credible sources.
- Shared document
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An online file several people can edit; responsible collaboration uses comments and suggestions instead of deleting others' work.
Numbers and Operations (63)
- Integer
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A whole number or its opposite, including zero: …, −2, −1, 0, 1, 2, …
- Absolute value
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A number's distance from zero on the number line; |−7| = 7.
- Adding integers with different signs
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Subtract the absolute values and keep the sign of the number with the larger absolute value: −8 + 15 = 7.
- Subtracting a negative
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Subtracting a negative number is the same as adding its opposite: 6 − (−9) = 6 + 9 = 15.
- Multiplying or dividing signed numbers
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Same signs give a positive result; different signs give a negative result.
- Opposite (additive inverse)
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The number the same distance from zero on the other side; the opposite of 4 is −4, and they sum to 0.
- Numerator
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The top number of a fraction; it counts how many equal parts are taken.
- Denominator
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The bottom number of a fraction; it tells how many equal parts make one whole.
- Equivalent fractions
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Fractions that name the same amount, such as 2/5 and 4/10.
- Simplest form
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A fraction whose numerator and denominator share no common factor other than 1, such as 3/4.
- Common denominator
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A shared denominator needed before adding or subtracting fractions: 2/3 + 1/4 = 8/12 + 3/12.
- Least common denominator
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The smallest number both denominators divide into evenly; for 1/4 and 1/6 it is 12.
- Multiplying fractions
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Multiply the numerators and multiply the denominators: 3/4 × 2/5 = 6/20 = 3/10.
- Dividing fractions (keep, change, flip)
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Keep the first fraction, change ÷ to ×, and flip the second: 2/3 ÷ 4/9 = 2/3 × 9/4 = 3/2.
- Reciprocal
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The number you multiply by to get 1; the reciprocal of 4/9 is 9/4.
- Mixed number
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A whole number plus a fraction, such as 2 1/2.
- Improper fraction
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A fraction whose numerator is greater than or equal to its denominator, such as 5/4 = 1 1/4.
- Place value
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The value of a digit based on its position; in 4,862.37 the 3 is in the tenths place (0.3).
- Tenths place
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The first digit to the right of the decimal point.
- Hundredths place
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The second digit to the right of the decimal point.
- Adding decimals
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Line up the decimal points, then add as with whole numbers: 4.50 + 2.75 = 7.25.
- Multiplying decimals
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Multiply as whole numbers, then give the product as many decimal places as the factors have in total: 0.6 × 0.4 = 0.24.
- Dividing by a decimal
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Move the decimal point in the divisor and dividend the same number of places to make the divisor whole: 7.2 ÷ 0.3 = 72 ÷ 3.
- Rounding
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Look at the digit to the right of the place you are rounding to; 5 or more rounds up, 4 or less rounds down.
- Percent
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A ratio out of 100; 25% means 25 per 100, or 0.25.
- Percent of a number
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Change the percent to a decimal and multiply: 15% of 80 = 0.15 × 80 = 12.
- Finding the percent
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Divide the part by the whole and multiply by 100: 18 ÷ 72 = 0.25 = 25%.
- Percent increase
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(new − old) ÷ old × 100; from 2,000 to 2,300 is a 15% increase.
- Percent decrease
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(old − new) ÷ old × 100; always divide by the original amount.
- Discount
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The amount taken off a price; a 25% discount on $40 is $10, so the sale price is $30.
- Decimal to percent
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Multiply by 100 and add a percent sign: 0.08 = 8%.
- Fraction to decimal
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Divide the numerator by the denominator: 3/8 = 3 ÷ 8 = 0.375.
- Benchmark equivalents
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1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/10 = 0.1 = 10%.
- Number line
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A line on which numbers are placed in order; values increase to the right.
- Comparing decimals
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Compare digit by digit from the left: 0.7 > 0.699 because 7 tenths is more than 6 tenths.
- Expanded form
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A number written as the sum of its digits' values: 5,307.09 = 5,000 + 300 + 7 + 0.09.
- Sum
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The result of addition.
- Difference
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The result of subtraction.
- Product
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The result of multiplication.
- Quotient
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The result of division; the quotient of 48 and 6 is 8.
- Factor
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A number that divides another number with no remainder; 4 is a factor of 12.
- Multiple
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The result of multiplying a number by a whole number; 12 is a multiple of 4.
- Not-equal symbol (≠)
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The symbol meaning 'is not equal to', as in 3 ≠ 4.
- Inequality symbols (< and >)
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< means is less than and > means is greater than; the open side faces the larger number.
- Exponent
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A small raised number telling how many times the base is used as a factor: 2⁵ = 2 × 2 × 2 × 2 × 2 = 32.
- Base (exponents)
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The number being multiplied repeatedly in a power; in 3⁴ the base is 3.
- Zero exponent
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Any nonzero number raised to the zero power equals 1: 7⁰ = 1.
- Product of powers
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When multiplying powers with the same base, add the exponents: 4² × 4³ = 4⁵.
- Perfect square
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A number that is a whole number times itself, such as 49 = 7².
- Order of operations (PEMDAS)
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Parentheses, exponents, multiplication and division left to right, then addition and subtraction left to right.
- Left-to-right rule
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Multiplication and division have equal rank, as do addition and subtraction — work each pair left to right: 12 ÷ 3 × 2 = 8.
- Variable
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A letter that stands for an unknown number, such as n in n + 12 = 30.
- Expression
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A math phrase with numbers, variables, and operations but no equals sign, such as 25 + 5g.
- Equation
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A math sentence with an equals sign stating that two expressions have the same value.
- Coefficient
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The number multiplied by a variable; in 7t the coefficient is 7.
- 'Less than' in word problems
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Reverses the order: '5 less than a number n' is n − 5, not 5 − n.
- Rate
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A comparison of two quantities with different units, such as 55 miles per hour.
- Distance formula (d = rt)
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Distance equals rate times time: 55 mph for 3.5 hours is 192.5 miles.
- Proportion
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Two equal ratios; 3 eggs per 2 cups of flour means 12 eggs for 8 cups.
- Inverse operations
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Operations that undo each other: addition and subtraction, multiplication and division.
- Solving a one-variable equation
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Use inverse operations on both sides to isolate the variable: 3x + 7 = 22 → 3x = 15 → x = 5.
- Distributive property
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a(b + c) = ab + ac; 2(m + 3) = 2m + 6.
- Checking a solution
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Substitute the answer back into the original equation to see whether both sides are equal.
Geometry, Measurement & Data (71)
- Elapsed time
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The amount of time that passes between a start and an end time; count to the next hour first (9:45 to 11:10 is 1 h 25 min).
- Minutes in an hour
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60 minutes = 1 hour; 2.5 hours = 150 minutes.
- Reading an analog clock
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The minute hand counts by fives from 12 (pointing to 8 means 40 minutes); the hour hand shows the hour.
- Liquid volume
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The amount of space a liquid takes up, measured in units such as cups, quarts, gallons, milliliters, or liters.
- Mass
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How much matter an object contains, measured in grams and kilograms.
- Weight
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How heavy an object is, measured in ounces, pounds, and tons in U.S. customary units.
- Estimation (measurement)
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A reasonable approximate measurement, such as a door about 2 meters tall or a paper clip about 1 inch long.
- Benchmark: 1 meter
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About the height of a doorknob from the floor, or a little more than a yard.
- Benchmark: 1 gram
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About the mass of a paper clip.
- Benchmark: 1 liter
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About the capacity of a large water bottle.
- Inches in a foot
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12 inches = 1 foot.
- Feet in a yard
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3 feet = 1 yard.
- Feet in a mile
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5,280 feet = 1 mile.
- Ounces in a pound
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16 ounces = 1 pound.
- Pounds in a ton
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2,000 pounds = 1 ton.
- Cups in a quart
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4 cups = 1 quart (2 cups = 1 pint, 2 pints = 1 quart).
- Quarts in a gallon
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4 quarts = 1 gallon.
- Metric prefixes
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Kilo- = 1,000, centi- = 1/100, milli- = 1/1,000; each metric step is a power of 10.
- Meters in a kilometer
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1,000 meters = 1 kilometer.
- Centimeters in a meter
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100 centimeters = 1 meter; 1 centimeter = 10 millimeters.
- Grams in a kilogram
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1,000 grams = 1 kilogram.
- Milliliters in a liter
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1,000 milliliters = 1 liter.
- Converting to a smaller unit
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Multiply — a smaller unit takes more of them: 4 feet × 12 = 48 inches.
- Converting to a larger unit
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Divide — a larger unit takes fewer of them: 72 inches ÷ 12 = 6 feet.
- Polygon
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A closed flat figure made of straight sides.
- Regular polygon
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A polygon whose sides are all equal and whose angles are all equal.
- Quadrilateral
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A four-sided polygon; its angles add up to 360°.
- Parallelogram
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A quadrilateral with two pairs of parallel sides.
- Rectangle
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A parallelogram with four right angles.
- Square
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A rectangle with four equal sides — it is also a rhombus.
- Rhombus
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A parallelogram with four equal sides; its angles need not be right angles.
- Trapezoid
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A quadrilateral with exactly one pair of parallel sides (the definition most U.S. elementary programs use).
- Pentagon / hexagon / octagon
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Polygons with 5, 6, and 8 sides.
- Triangle angle sum
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The three angles of any triangle add up to 180°.
- Equilateral triangle
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A triangle with three equal sides and three 60° angles.
- Isosceles triangle
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A triangle with at least two equal sides.
- Scalene triangle
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A triangle with no equal sides.
- Right triangle
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A triangle with one 90° angle.
- Acute / obtuse angle
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An acute angle is less than 90°; an obtuse angle is greater than 90° but less than 180°.
- Perimeter
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The distance around a figure — add all the side lengths (rectangle: 2l + 2w).
- Area
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The amount of surface a flat figure covers, in square units.
- Area of a rectangle
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A = length × width.
- Area of a triangle
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A = ½ × base × height.
- Area of a square
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A = side × side = s².
- Volume
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The amount of space a solid figure takes up, in cubic units.
- Volume of a rectangular prism
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V = length × width × height.
- Surface area
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The total area of all the faces of a solid; a rectangular prism's is 2(lw + lh + wh).
- Circumference
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The distance around a circle: C = 2πr = πd.
- Area of a circle
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A = πr².
- Square units vs. cubic units
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Area is measured in square units (m²) and volume in cubic units (m³); a length alone uses plain units (m).
- Coordinate plane
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A grid formed by a horizontal x-axis and a vertical y-axis that locate points with ordered pairs.
- Ordered pair (x, y)
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Two numbers giving a point's location: move across by x first, then up or down by y.
- Origin
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The point (0, 0) where the x-axis and y-axis cross.
- x-axis
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The horizontal number line on the coordinate plane.
- y-axis
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The vertical number line on the coordinate plane; every point on it has x = 0.
- Quadrants
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The four regions of the coordinate plane: I (+, +), II (−, +), III (−, −), IV (+, −).
- Data set
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A collection of values, such as test scores or daily temperatures.
- One-variable data
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Data that describes a single quantity, such as a list of heights.
- Two-variable data
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Data that relates two quantities, such as temperature by hour, often shown on a line or bar graph.
- Mean
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The average: the sum of the values divided by how many values there are.
- Median
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The middle value of an ordered data set; with an even count, the mean of the two middle values.
- Mode
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The value that occurs most often in a data set; a set can have no mode or more than one.
- Range
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The spread of a data set: greatest value minus least value.
- Outlier
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A value far from the rest of the data; it pulls the mean toward it much more than the median.
- Frequency table
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A table that shows how many times each value or category occurs.
- Bar graph
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A graph that compares amounts across categories with bars of different lengths.
- Line graph
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A graph that shows how a quantity changes over time, with points connected by line segments.
- Circle graph
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A graph that shows parts of a whole as slices; the whole circle is 100% (360°).
- Pictograph
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A graph that uses symbols to show counts; the key tells what one symbol represents.
- Double bar graph
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A bar graph that compares two groups side by side for each category, with a legend telling which color is which.
- Graph scale
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The value between gridlines on a graph's axis; each gridline may stand for 1, 5, 20, or another amount.
References
- 1.Educational Testing Service (ETS). “ParaPathways Assessment (5757; subtests 5758 and 5759).” parapro.ets.org. ↑
- 2.Educational Testing Service (ETS). “The ParaPathways Study Companion — 5757.” ETS, via the Rhode Island Department of Education. ↑
- 3.Educational Testing Service (ETS). “2026–27 ParaPro Assessment Information Bulletin (covers the ParaPro 1755 and ParaPathways 5757 Assessments; effective August 1, 2026 – July 31, 2027).” ets.org. ↑
- 4.Educational Testing Service (ETS). “ParaPathways and ParaPro — State Requirements.” parapro.ets.org. ↑

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