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Proportions & Percent ChangeCross-multiplication, the percent proportion, andโ€ฆ7th GradePROPORTION โ€” two equal ratiosa / b = c / d โ†’ a ร— d = b ร— c3 / 4 = x / 20 โ†’ 3 ร— 20 = 4x โ†’ 60 = 4x โ†’ x = 15Set it up with the same quantity on top of both fractions. Units keep you honest.THE PERCENT PROPORTIONpart / whole = % / 100"What is 15% of 80?" โ†’ x / 80 = 15 / 100 โ†’ x = 12"12 is what percent of 80?" โ†’ 12 / 80 = p / 100 โ†’ p = 15PERCENT CHANGEchange รท original ร— 100ยฃ40 โ†’ ยฃ52: change is 12, so 12 รท 40 ร— 100 = 30% increase.Shortcut: multiply by (1 ยฑ rate)+30% โ†’ ร— 1.30 ยท โˆ’25% โ†’ ร— 0.75 ยท 8% tax โ†’ ร— 1.08THE FOUR YOU WILL BE ASKEDTipbill ร— rateยฃ46 ร— 0.18 = ยฃ8.28Discountprice ร— (1 โˆ’ rate)ยฃ60 ร— 0.75 = ยฃ45Taxprice ร— (1 + rate)ยฃ25 ร— 1.07 = ยฃ26.75Simple interestI = P ร— r ร— tยฃ500 ร— 0.04 ร— 3 = ยฃ60Proportions & Percent Changelittleactivity.com

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Math ยท 7th Grade

Proportions & Percent Change

Cross-multiplication, the percent proportion, and increase/decrease/interest formulas.

How to use it

Tax, tip and discount are all the same formula wearing different clothes.

Free ยท print-ready PDF ยท US Letter and A4

Grade
7th Grade
Ages
12โ€“13
Subject
Math
Pages
1

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Operations with Rational Numbers

The rest of the 7th Grade wall

7 more posters, all free to print.

Operations with Rational NumbersNegative fractions and decimals โ€” the sign rules plusโ€ฆ7th GradeONE FORM AT A TIMEBefore you apply a sign rule, put both numbers in the same form.Fraction โ†’ decimal: divide top by bottom. 3/8 = 0.375Decimal โ†’ fraction: say it, write it. 0.35 = 35/100 = 7/20MULTIPLY & 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.ADD & SUBTRACTSame signs โ†’ add the sizes, keep the sign.โˆ’3.4 + (โˆ’1.2) = โˆ’4.6Different signs โ†’ subtract, keep the bigger sign.โˆ’5/6 + 1/3 = โˆ’5/6 + 2/6 = โˆ’3/6 = โˆ’1/2Subtracting is adding the opposite: a โˆ’ b = a + (โˆ’b).FRACTION ยท DECIMAL ยท PERCENT1/2= 0.5= 50%1/4= 0.25= 25%1/3= 0.333โ€ฆ= 33โ…“%2/5= 0.4= 40%3/8= 0.375= 37.5%5/6= 0.8333โ€ฆ= 83โ…“%Operations with Rational Numberslittleactivity.com
Math

Operations with Rational Numbers

Negative fractions and decimals โ€” the sign rules plus conversion between forms.

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Solving EquationsOne-step to multi-step equations and inequalities, solved inโ€ฆ7th GradeTHE BALANCE RULEWhatever you do to one side, do to the other.Undo in reverse order of operations: + and โˆ’ first, then ร— and รท.ONE STEPx + 7 = 12x = 12 โˆ’ 7 = 5subtract 7 from both sidesTWO STEP3x โˆ’ 4 = 113x = 15 โ†’ x = 5add 4, then divide by 3VARIABLES BOTH SIDES5x + 2 = 3x + 102x = 8 โ†’ x = 4collect variables on one sideDISTRIBUTIVE2(x + 3) = 142x + 6 = 14 โ†’ x = 4expand the bracket firstFRACTIONSx/4 + 1 = 6x/4 = 5 โ†’ x = 20multiply everything by the denominatorINEQUALITIESMultiply or divide by a negative โ†’ flip the sign.โˆ’2x > 8 โ†’ x < โˆ’4. Everything else works exactly like an equation.ALWAYS CHECKPut your answer back into the original equation. Both sides must match.Solving Equationslittleactivity.com
Math

Solving Equations

One-step to multi-step equations and inequalities, solved in order on the sheet.

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Circles, Angles & VolumeCircumference, area of a circle, angle-pair rules and prismโ€ฆ7th GradeCIRCLES โ€” do not mix these two uprd = 2rC = 2ฯ€r = ฯ€dcircumference โ€” the distance aroundA = ฯ€rยฒarea โ€” the space inside. Square the radius, never the diameter.ฯ€ โ‰ˆ 3.14 โ‰ˆ 22/7ANGLE PAIRSComplementaryadd to 90ยฐtwo angles making a right angleSupplementaryadd to 180ยฐtwo angles on a straight lineVerticalequalopposite angles where two lines crossAdjacentshare a sidenext to each other, no overlapCorrespondingequalsame position at each parallel lineAlternate interiorequalthe Z shape between parallel linesTRIANGLES & PRISMSAngles in a triangle add to 180ยฐ.In a quadrilateral, 360ยฐ.Prism volume = area of the base ร— the length. Cylinder: V = ฯ€rยฒh.Circles, Angles & Volumelittleactivity.com
Math

Circles, Angles & Volume

Circumference, area of a circle, angle-pair rules and prism volume.

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Literary DevicesSixteen devices grouped by what they do โ€” sound, meaning,โ€ฆ7th GradeSOUNDAlliterationRepeated opening consonant.SOUNDAssonanceRepeated vowel sound inside words.SOUNDConsonanceRepeated consonant sound anywhere.SOUNDOnomatopoeiaThe word imitates the noise.SOUNDRhyme / rhythmMatched endings, measured beat.MEANINGSimileComparison using like or as.MEANINGMetaphorDirect comparison โ€” one thing is another.MEANINGPersonificationHuman qualities given to non-human things.MEANINGHyperboleDeliberate overstatement.MEANINGSymbolismAn object standing in for an idea.MEANINGImagerySensory detail the reader can picture.MEANINGIdiomFixed phrase with a figurative sense.STRUCTUREForeshadowingAn early hint at what is coming.STRUCTUREFlashbackA jump backwards in time.STRUCTUREIronyThe opposite of what is expected.STRUCTUREMood / toneMood = reader's feeling. Tone = writer's attitude.Sound devices work on the ear. Meaning devices work on the picture. Structure works on the plot.Literary Deviceslittleactivity.com
Literacy

Literary Devices

Sixteen devices grouped by what they do โ€” sound, meaning, structure.

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Argument Essay FrameClaim, evidence, reasoning, counterclaim, rebuttal โ€” withโ€ฆ7th GradeMarks live in the counterclaim. An essay that never argues with itself scores in the middle.1CLAIMThe position you are arguing.โ€œSchools should start later becauseโ€ฆโ€2EVIDENCEFacts, data or quotations that support it.โ€œAccording to a 2024 study,โ€ฆโ€3REASONINGWhy the evidence proves the claim.โ€œThis matters becauseโ€ฆโ€4COUNTERCLAIMThe strongest objection, stated fairly.โ€œSome argue thatโ€ฆโ€5REBUTTALWhy the objection does not defeat you.โ€œHowever, this overlooksโ€ฆโ€6CONCLUSIONRestate the claim and its stakes.โ€œThe evidence makes clear thatโ€ฆโ€Claim โ†’ Evidence โ†’ Reasoning. Every body paragraph, every time.Argument Essay Framelittleactivity.com
Literacy

Argument Essay Frame

Claim, evidence, reasoning, counterclaim, rebuttal โ€” with sentence stems.

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SI Units & ConversionsThe seven base units, the metric prefixes and the decimal-moveโ€ฆ7th GradeTHE SEVEN SI BASE UNITSLengthmetremMasskilogramkgTimesecondsTemperaturekelvinKAmountmolemolCurrentampereALuminous intensitycandelacdTHE PREFIX LADDERkilo-kร— 1 000hecto-hร— 100deca-daร— 10BASEm ยท g ยท Lร— 1deci-dรท 10centi-cรท 100milli-mรท 1 000each step right = move the decimal point one place rightWORKED3.6 km โ†’ m: three steps right โ†’ 3600 m450 mg โ†’ g: three steps left โ†’ 0.45 gSI Units & Conversionslittleactivity.com
Science

SI Units & Conversions

The seven base units, the metric prefixes and the decimal-move shortcut.

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Reading the Periodic TableWhat a box tells you, and how groups and periods areโ€ฆ7th GradeHOW TO READ ONE SQUARE6CCarbon12.01Atomic numberprotons โ€” this is what makes it carbonSymbolone or two letters, first one a capitalNamethe full element nameAtomic massprotons + neutrons, averagedHOW THE TABLE IS ORGANISEDGROUPSthe columns. Same number of outer electrons โ†’ they behave alike.PERIODSthe rows. Reading left to right, each element has one more proton.Metals sit on the left, non-metals on the right, with a staircase of metalloids between.THE FIRST TWENTY1HHydrogen2HeHelium3LiLithium4BeBeryllium5BBoron6CCarbon7NNitrogen8OOxygen9FFluorine10NeNeon11NaSodium12MgMagnesium13AlAluminium14SiSilicon15PPhosphorus16SSulfur17ClChlorine18ArArgon19KPotassium20CaCalciumChange the number of protons and you have a different element entirely.Reading the Periodic Tablelittleactivity.com
Science

Reading the Periodic Table

What a box tells you, and how groups and periods are organised.

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