NYSTCE Multi-Subject 5-9 cheat sheet

Five essential components of reading: phonemic awareness, phonics, fluency, vocabulary, and comprehension; instruction that omits any one component leaves a gap in skilled reading.

Phonological awareness is the umbrella skill (syllables, rhymes, onset-rime); phonemic awareness is the narrower ability to isolate and manipulate individual phonemes and is the strongest early predictor of decoding success.

Ehri's phases of word reading: pre-alphabetic, partial alphabetic, full alphabetic, consolidated alphabetic; sight-word recognition grows as grapheme-phoneme mappings become automatic.

The Simple View of Reading: comprehension = decoding x language comprehension; a deficit in either factor alone depresses reading comprehension, so a struggling reader needs assessment of both.

Fluency has three measurable dimensions: accuracy, rate (correct words per minute), and prosody; repeated reading with feedback and modeling improves all three.

Text complexity for grades 5-9 is judged on three axes: qualitative (levels of meaning, structure, knowledge demands), quantitative (readability, word frequency, sentence length), and reader-task considerations.

The writing process is recursive, not linear: planning, drafting, revising, editing, and publishing, with revision focused on ideas and organization and editing focused on conventions.

Narrative vs. informational text structure: narratives use character, setting, plot, and conflict; informational texts use description, sequence, compare-contrast, cause-effect, and problem-solution, and teaching these structures improves recall.

Academic language has three tiers: Tier 1 everyday words, Tier 2 cross-content academic words (e.g., analyze, contrast), Tier 3 domain-specific terms; Tier 2 words yield the highest instructional payoff for middle-grade readers.

Order of operations: grouping symbols, exponents, multiplication and division left to right, addition and subtraction left to right.

Fraction division rule: a/b divided by c/d equals a/b times d/c; a complex fraction can be simplified by multiplying numerator and denominator by the least common denominator.

Percent change = (new - old) / old x 100; percent increase and decrease are not symmetric (a 20% rise then a 20% fall returns to 96% of the original).

Proportional relationships: y = kx, constant of proportionality k = y/x, graph passes through the origin; a linear relationship is proportional only if its y-intercept is zero.

Slope = (y2 - y1)/(x2 - x1); slope-intercept form y = mx + b; parallel lines share slope, perpendicular slopes are negative reciprocals whose product is -1.

Area formulas: triangle (1/2)bh, parallelogram bh, trapezoid (1/2)(b1 + b2)h, circle pi r^2; volume of prism or cylinder = area of base x height, pyramid or cone = (1/3) base area x height.

Mean, median, mode, and range describe center and spread; the mean is pulled toward outliers while the median resists them, and mean absolute deviation measures typical distance from the mean.

Probability of a compound independent event = product of individual probabilities; theoretical probability = favorable outcomes / total equally likely outcomes, and larger samples bring experimental results closer to theoretical.

Integer rules: subtracting a negative adds its absolute value; product or quotient of two negatives is positive, of one negative is negative; any nonzero base to the zero power equals 1.

Earth's layers: crust, mantle, outer core (liquid), inner core (solid); plate tectonics explains earthquakes, volcanoes, and mountain belts along convergent, divergent, and transform boundaries.

Water cycle terms: evaporation, transpiration, condensation, precipitation, runoff, infiltration; the sun is the energy source driving the cycle.

Photosynthesis converts carbon dioxide and water into glucose and oxygen using light energy in chloroplasts; cellular respiration reverses the equation to release energy in mitochondria.

Food webs: producers capture energy, consumers transfer it, decomposers recycle nutrients; roughly 10% of energy passes to the next trophic level, so food chains rarely exceed four or five links.

Newton's laws: inertia (no net force means no change in motion), F = ma, and equal-and-opposite action-reaction pairs acting on different objects.

American government: separation of powers among legislative, executive, and judicial branches; checks and balances (veto, override, judicial review); federalism divides power between national and state governments.

Early U.S. history sequence: colonial settlement, Declaration of Independence (1776), Constitution (1787), Bill of Rights (1791), westward expansion, Civil War and Reconstruction (1861-1877).

Ancient river-valley civilizations: Mesopotamia between the Tigris and Euphrates, Egypt along the Nile, Indus along the Indus, China along the Yellow River; each depended on irrigation and surplus agriculture.

Elements of visual art: line, shape, form, color, value, texture, space; principles of design include balance, contrast, emphasis, movement, pattern, rhythm, and unity.

IDEA guarantees students with disabilities a free appropriate public education in the least restrictive environment, delivered through an individualized education program (IEP).

Section 504 covers students with a physical or mental impairment that substantially limits a major life activity and provides accommodations, not specialized instruction.

Response to Intervention uses tiered supports: Tier 1 universal instruction, Tier 2 targeted small-group intervention, Tier 3 intensive individualized intervention, with progress monitoring to inform movement between tiers.

English language learners: New York uses stand-alone and integrated English as a New Language plus bilingual education programs; students exit English language learner status by meeting state proficiency criteria.

WIDA English language development levels run 1 Entering, 2 Emerging, 3 Developing, 4 Expanding, 5 Bridging, 6 Reaching; instruction should scaffold content at the student's current level.

Disproportionality refers to overrepresentation of a racial, ethnic, or linguistic group in special education; referral decisions must rely on multiple data sources and not on cultural or linguistic difference alone.

Culturally responsive teaching connects curriculum to students' backgrounds, uses varied participation structures, and avoids deficit assumptions about families and communities.

Restorative practices respond to conflict by repairing harm through dialogue and community circles rather than exclusionary discipline, which research links to higher dropout risk.

Confidentiality: student records are protected under FERPA; parents have the right to inspect records, and personally identifiable information may not be disclosed without consent except under specified exceptions.