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Expressions & EquationsVocabulary, the properties, combining like terms and theโ€ฆ6th GradeANATOMY OF AN EXPRESSION7xยฒ + 3x โˆ’ 5coefficientvariableconstantThree terms, separated by + and โˆ’. A term is a number, a variable, or both multiplied.THE PROPERTIESCommutativeorder does not mattera + b = b + a ยท ab = baAssociativegrouping does not matter(a+b)+c = a+(b+c)Distributiveshare the multiplier outa(b + c) = ab + acIdentityleaves it unchangeda + 0 = a ยท a ร— 1 = aInverseundoes ita + (โˆ’a) = 0 ยท a ร— 1/a = 1COMBINING LIKE TERMS5x + 3y โˆ’ 2x + 7 + y = 3x + 4y + 7Like terms have the same variable to the same power. 3x and 3xยฒ are not alike.Add the coefficients only. The variable part never changes.EVALUATINGSubstitute first, then follow order of operations. If x = โˆ’3, then 2xยฒ = 2(9) = 18, not โˆ’18.Expressions & Equationslittleactivity.com

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Math ยท 6th Grade

Expressions & Equations

Vocabulary, the properties, combining like terms and the balance rule.

How to use it

Whatever you do to one side, do to the other. Everything else is arithmetic.

Free ยท print-ready PDF ยท US Letter and A4

Grade
6th Grade
Ages
11โ€“12
Subject
Math
Pages
1

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Integer RulesAdding, subtracting, multiplying and dividing negatives, withโ€ฆ6th Grade-6-5-4-3-2-10123456โ† smallerlarger โ†’ADD & SUBTRACT โ€” walk the lineSame signs โ†’ add and keep the sign.โˆ’7 + (โˆ’4) = โˆ’11Different signs โ†’ subtract, keep the bigger one's sign.โˆ’7 + 4 = โˆ’3 ยท 7 + (โˆ’4) = 3Subtracting is adding the opposite: 5 โˆ’ (โˆ’3) = 5 + 3 = 8.MULTIPLY & DIVIDE โ€” count the minus signs(+) ร— (+) = +6 ร— 3 = 18(โˆ’) ร— (โˆ’) = +(โˆ’6) ร— (โˆ’3) = 18(+) ร— (โˆ’) = โˆ’6 ร— (โˆ’3) = โˆ’18(โˆ’) ร— (+) = โˆ’(โˆ’6) ร— 3 = โˆ’18Even number of minus signs โ†’ positive. Odd number โ†’ negative. Same for รท.ABSOLUTE VALUE|โˆ’8| = 8 ยท |8| = 8distance from zero โ€” never negativeโˆ’8 is further from zero than 3, but โˆ’8 is still the smaller number.On the line, further left always means smaller.TEMPERATURE TESTIf โˆ’5ยฐC rises by 8ยฐ, it is 3ยฐC. Everything about integers behaves like a thermometer.Integer Ruleslittleactivity.com
Math

Integer Rules

Adding, subtracting, multiplying and dividing negatives, with a number line to check against.

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Ratios, Rates & PercentRatio, unit rate and percent as three views of the sameโ€ฆ6th GradeRATIO โ€” how many of one for each of the other3 : 5 ย  ยท ย  3 to 5 ย  ยท ย  3/5Three red for every five blue. Eight counters in total, not eight of each.part : part = 3 : 5 ย  part : whole = 3 : 8EQUIVALENT RATIOS & UNIT RATEkilometres36912minutes20406080Unit rate:3 km in 20 min= 9 km per hourMultiply both quantities by the same number and the relationship is unchanged.PERCENT = OUT OF 10035 shaded out of 100= 35% = 0.35 = 35/100 = 7/20To find a percent of a number, turn the percentinto a decimal and multiply: 35% of 60 = 0.35 ร— 60 = 21.BENCHMARKS WORTH KNOWING BY HEART10%รท 1025%รท 450%รท 275%half + a quarter1%รท 10020%รท 5Ratios, Rates & Percentlittleactivity.com
Math

Ratios, Rates & Percent

Ratio, unit rate and percent as three views of the same relationship.

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Area, Surface Area & VolumeNets, surface area and volume formulas for the solids they'llโ€ฆ6th GradeVOLUME โ€” how much fits insideRectangular prismV = l ร— w ร— hor V = B ร— h, B = base areaCubeV = sยณevery edge the sameTriangular prismV = ยฝbh ร— lengthbase area ร— lengthCylinderV = ฯ€rยฒhcircle area ร— heightSURFACE AREA โ€” the wrapping paperRectangular prismSA = 2lw + 2lh + 2whsix faces, three pairsCubeSA = 6sยฒsix identical squaresCylinderSA = 2ฯ€rยฒ + 2ฯ€rhtwo circles + the labelNETS โ€” unfold it and countA net is the solid flattened out. Surface area isjust the area of every piece of the net, added up.A cube net always has six squares โ€” count them before you calculate.UNITSSurface area is squared (cmยฒ). Volume is cubed (cmยณ).Area, Surface Area & Volumelittleactivity.com
Math

Area, Surface Area & Volume

Nets, surface area and volume formulas for the solids they'll be tested on.

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Figurative LanguageSimile, metaphor, personification and friends โ€” with anโ€ฆ6th GradeSimileCompares using like or asHer smile was like sunrise.MetaphorSays one thing IS anotherThe classroom was a zoo.PersonificationGives human traits to a thingThe wind whispered.HyperboleWild exaggeration for effectI've told you a million times.OnomatopoeiaA word that sounds like its noisebuzz, splash, crackAlliterationSame starting sound, close togethersilly Sally sang.IdiomMeans something other than the wordsIt's raining cats and dogs.ImageryLanguage that hits the five sensesWarm bread, crackling crust.REMEMBERNaming it earns half the mark. Saying what it does to the reader earns the rest.Figurative Languagelittleactivity.com
Literacy

Figurative Language

Simile, metaphor, personification and friends โ€” with an example line each.

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Comma & Punctuation RulesThe eight comma rules, semicolons, colons and apostrophes โ€”โ€ฆ6th GradeNearly every comma mistake is one of these eight rules used, or missed.Comma 1Between items in a listWe bought bread, cheese and figs.Comma 2Before and / but / so joining two full sentencesIt rained, so we stayed in.Comma 3After an introductory word or phraseAfter the film, we walked home.Comma 4Around extra, removable informationMy aunt, a pilot, called.Comma 5Between two adjectives of the same kinda cold, grey morningComma 6Before a direct quotationShe said, โ€œWait here.โ€Comma 7Around the name of the person spoken toThanks, Ravi, for helping.Comma 8In dates and addressesMarch 4, 2026, in LeedsSemicolon ;Joins two closely linked full sentencesIt rained; we stayed in.Colon :Introduces a list, quote or explanationBring three things: map, torch, water.Apostrophe 'Contraction, or possession (s' after a plural)don't ยท the dog's lead ยท the dogs' leadsDash โ€”Sets off a sharp break or a strong asideHe left โ€” without a word โ€” at dawn.If both halves could stand alone, you need ; or a comma + joining word.Comma & Punctuation Ruleslittleactivity.com
Literacy

Comma & Punctuation Rules

The eight comma rules, semicolons, colons and apostrophes โ€” each with an example.

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Plant & Animal CellsBoth cells labelled side by side, with what each organelleโ€ฆ6th GradeANIMAL CELLPLANT CELLWHAT IS INSIDE, AND WHAT IT DOESNucleusControl centre โ€” holds the DNA.Cell membraneDecides what gets in and out.CytoplasmJelly where the reactions happen.MitochondriaReleases energy from sugar.RibosomesBuild proteins.Endoplasmic reticulumTransport network for proteins and fats.Golgi bodyPackages and ships what the cell makes.VacuoleStorage. Large and permanent in plants.Cell wallRigid outer layer โ€” gives shape and strength.plant onlyChloroplastMakes food using sunlight (photosynthesis).plant onlyThe three plant-only parts โ€” cell wall, chloroplasts, one large vacuole โ€” are the exam question.Plant & Animal Cellslittleactivity.com
Science

Plant & Animal Cells

Both cells labelled side by side, with what each organelle does.

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The Scientific MethodThe six steps plus the variable vocabulary that trips peopleโ€ฆ6th Grade1ASK A QUESTIONSomething testable. โ€œWhich paper towel absorbs most?โ€ not โ€œAre towels good?โ€2RESEARCHFind out what is already known before you design anything.3HYPOTHESISIf I change โ€ฆ, then โ€ฆ will happen, because โ€ฆ4EXPERIMENTChange one thing only. Keep everything else the same.5ANALYSE DATARecord, table, graph. Look for the pattern, not the answer you wanted.6CONCLUDE & SHAREWas the hypothesis supported? What next?VARIABLES โ€” the bit everyone loses marks onIndependentthe ONE thing you changeamount of lightDependentthe thing you measureheight of the plantControlledeverything kept the samepot, soil, water, seedChange two things at once and you cannot tell which one caused the result.The Scientific Methodlittleactivity.com
Science

The Scientific Method

The six steps plus the variable vocabulary that trips people up.

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