PEI EMA Grade 6 cheat sheet

Main idea = what the text is mostly about (state it in one sentence); theme = the underlying message about life or people and is always stated as a full sentence, not one word.

Inference = explicit text evidence + background knowledge. A valid inference must be traceable to at least one detail actually written in the text.

Common text structures and signal words: description (for example, such as), chronology (first, then, finally), compare–contrast (both, however, unlike), cause–effect (because, as a result, therefore), problem–solution (the issue, one way to solve).

Figurative language: simile uses like/as; metaphor makes a direct comparison without like/as; personification gives human traits to non-human things; hyperbole is deliberate exaggeration; idiom's meaning cannot be figured out from the individual words.

Point of view: first person uses I/we and is a character in the story; third-person limited follows one character's thoughts; third-person omniscient knows the thoughts of several characters.

Author's purpose is usually to persuade, inform, entertain, or explain/describe; the purpose determines whether the piece is mostly fact, mostly opinion, or story.

Context clue types for unknown words: definition (meaning stated directly), synonym/restatement, antonym/contrast, example, and general sense of the sentence.

Summarizing rule: keep the main idea plus key supporting details, drop minor examples, keep the author's order, and leave out personal opinion.

Fact vs opinion signals: facts can be checked and proven; opinion words include best, worst, should, always, never, and most beautiful.

Paragraph structure: topic sentence states the main idea, supporting sentences give details with evidence, closing sentence restates or links back to the main idea.

Six traits of writing: ideas, organization, voice, word choice, sentence fluency, conventions (presentation is often added as a seventh).

Transitions by job: addition (also, moreover), contrast (however, on the other hand), cause–effect (therefore, as a result), sequence (first, then, finally), example (for instance, such as).

Sentence types: simple = one independent clause; compound = two independent clauses joined by a comma plus a coordinating conjunction (for, and, nor, but, or, yet, so); complex = independent clause plus a dependent clause beginning with a subordinating conjunction (because, although, when, if, since).

Comma uses: items in a series, after an introductory phrase or clause, before a coordinating conjunction joining two independent clauses, in dates and addresses, in direct address, and around non-essential appositives.

Revising changes ideas, organization, word choice, and sentence variety; editing/proofreading fixes conventions (spelling, capitals, punctuation, grammar). They are separate steps, revision first.

Opinion/persuasive structure: state a clear claim, give reasons, support each reason with relevant evidence, acknowledge and answer a counterargument, end with a call to action.

Narrative plot: exposition, rising action, climax, falling action, resolution. 'Show, don't tell' means using sensory detail, action, and dialogue instead of naming an emotion.

Using a quotation: introduce who is speaking and where it comes from, copy the words exactly inside quotation marks, then explain how the quotation supports your point.

Active listening behaviours: face the speaker, make eye contact, take notes, hold questions until the speaker pauses, then paraphrase or ask a clarifying question.

Paraphrasing frames: 'So what you're saying is…', 'In other words…'. Paraphrasing checks understanding and does not mean agreeing with the speaker.

Accountable talk stems: 'I agree with ___ because…', 'I'd like to add…', 'Can you explain what you mean by…?'. Disagreement targets the idea, not the person.

Presentation structure: hook (question, statistic, short story), preview of main points, body with signposts ('first', 'in contrast', 'finally'), conclusion that restates the main point.

Delivery variables: volume projects to the back of the room, pace slows at key points, pauses replace filler sounds such as 'um' and 'like'.

Nonverbal message must match the spoken message: posture, gesture, and facial expression carry meaning; crossed arms or looking away can contradict friendly words.

Audience adaptation: choose vocabulary, examples, and length based on what listeners already know; define technical terms the first time they are used.

Evaluating a speaker or source: check credentials, check whether claims are supported by evidence, and check for bias or one-sided selection of facts.

Group discussion norms: one voice at a time, build on the previous speaker's idea, and record decisions so the group can report them accurately.

Order of operations (BEDMAS): brackets, exponents, multiplication and division left to right, addition and subtraction left to right.

Divisibility rules: 2 = last digit even; 3 = digit sum divisible by 3; 4 = last two digits divisible by 4; 5 = ends in 0 or 5; 6 = divisible by both 2 and 3; 9 = digit sum divisible by 9; 10 = ends in 0.

GCF = product of the prime factors the numbers share; LCM = product of the highest power of every prime that appears. For two numbers, GCF × LCM = a × b.

Fraction operations: add/subtract after rewriting with a common denominator; multiply numerator × numerator over denominator × denominator; divide by multiplying by the reciprocal of the divisor.

Decimals: multiply by ignoring decimal points, then place the decimal so the product has the same total number of decimal places as the factors; to divide, move the divisor's decimal point to make a whole number and move the dividend's point the same number of places.

Percent: percent = part ÷ whole × 100; to find a percent of a number, multiply by the decimal form (15% of 60 = 0.15 × 60); to find the whole when part and percent are known, divide the part by the decimal percent.

Ratios: part-to-part compares two parts, part-to-whole compares a part with the total; equivalent ratios are made by multiplying or dividing both terms by the same number; unit rate = first quantity ÷ second quantity.

Integers: subtracting a negative is the same as adding a positive (5 − (−3) = 8); adding two negatives gives a negative; use a number line to model direction and distance.

Estimation strategies for checking reasonableness: rounding to friendly numbers, front-end estimation, and compatible numbers (e.g., 48 × 21 ≈ 50 × 20 = 1000).

Recursive rule describes the step between terms ('add 4 each time'); an explicit (functional) rule gives any term directly from its position, such as 4n + 1.

Variables are letters or symbols standing for unknown or changing values; an expression has no equals sign (3n + 5) while an equation states two expressions are equal (3n + 5 = 20).

Translating words to symbols: '5 more than triple a number' = 3n + 5; '4 less than a number' = n − 4; 'the product of 6 and a number' = 6n.

Substitution: replace the variable with the given value, then apply order of operations (e.g., 2n + 7 when n = 5 gives 2 × 5 + 7 = 17).

Solving one-step equations uses inverse operations: undo addition with subtraction, undo multiplication with division; whatever is done to one side must be done to the other to keep the balance.

Input–output tables: find the rule by testing one operation on two different pairs, then verify the rule on a third pair before using it to extend the table.

Linear patterns change by a constant amount, so their graphs are straight lines and equal steps in the table produce equal steps in the output.

The same pattern can be represented four ways: concrete materials, a table of values, a graph, and a symbolic rule - each representation should agree with the others.

Area formulas: rectangle A = l × w; triangle A = ½ × b × h; parallelogram A = b × h; trapezoid A = ½ × (a + b) × h. Height must be perpendicular to the base.

Perimeter is the distance around a figure (add all side lengths); area is measured in square units and perimeter in linear units.

Circle: circumference C = π × d or C = 2 × π × r; area A = π × r²; use π ≈ 3.14.

Volume of a prism = area of the base × height; rectangular prism V = l × w × h. 1 cm³ = 1 mL, and 1 000 cm³ = 1 L.

Surface area of a rectangular prism = 2(lw + lh + wh); a net shows all faces and is a reliable way to count them.

Angle facts: complementary angles total 90°, supplementary angles total 180°, angles on a straight line total 180°, angles around a point total 360°, vertically opposite angles are equal.

Triangle interior angles total 180°; quadrilateral interior angles total 360°.

Transformations: translation slides, rotation turns about a point, reflection flips over a line; all three keep the figure congruent (same size and shape).

Coordinate plane: ordered pair (x, y) - x is horizontal, y is vertical; the origin is (0, 0); quadrants are numbered I to IV counterclockwise from the top right.

Measures of centre: mean = sum of values ÷ number of values; median = middle value of an ordered list (mean of the two middle values if the count is even); mode = most frequent value.

Range = greatest value − smallest value and measures spread, not centre; an outlier strongly affects the mean but barely affects the median.

Data types: categorical (names or categories) vs numerical; numerical data can be discrete (counted) or continuous (measured).

Graph choice: bar graph for comparing categories, line graph for change over time, circle graph for parts of a whole, histogram for numerical intervals, scatter plot for a relationship between two variables.

Misleading graph checks: truncated y-axis that does not start at zero, uneven or changing intervals, missing labels or units, and 3-D effects that exaggerate differences.

Probability of an event = number of favourable outcomes ÷ total number of equally likely outcomes; the value lies between 0 (impossible) and 1 (certain) and can be written as a fraction, decimal, or percent.

Complement rule: P(not A) = 1 − P(A); the probabilities of all outcomes in the sample space add to 1.

Theoretical probability comes from counting outcomes; experimental probability comes from actually performing trials, and results get closer to the theoretical value as the number of trials increases.

Graph literacy: read the title, axis labels, units, and scale before interpreting the data, and note the sample size to judge whether a conclusion is reasonable.