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Area & PerimeterFormulas for every shape they meet this year, with a labelled…5th GradeAREA — the space insideRectanglelwA = l × wSquaresA = s²TrianglebhA = ½ × b × hParallelogrambhA = b × hTrapezoidb₁b₂A = ½(b₁+b₂)hCirclerA = πr²PERIMETER — the distance aroundAny shapeadd every sideRectangleP = 2l + 2wSquareP = 4sCircle (circumference)C = 2πr = πdUNITSPerimeter is measured in cm. Area is measured in cm² — always squared.Perimeter is the fence around the field. Area is the grass inside it.Area & Perimeterlittleactivity.com

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Math · 5th Grade

Area & Perimeter

Formulas for every shape they meet this year, with a labelled diagram each.

How to use it

Perimeter is the fence, area is the grass. Then use the formulas.

Free · print-ready PDF · US Letter and A4

Grade
5th Grade
Ages
10–11
Subject
Math
Pages
1

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Greek & Latin Roots

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Order of OperationsPEMDAS with the two rules everyone gets wrong, worked out step…5th GradePParenthesesWork inside brackets first — innermost outwards.EExponentsPowers and roots next.MDMultiply & DivideSame rank — left to right, whichever comes first.ASAdd & SubtractSame rank — left to right, whichever comes first.WORKED — 4 + 3 × (8 − 5)² ÷ 91. Brackets8 − 5 = 34 + 3 × 3² ÷ 92. Exponent3² = 94 + 3 × 9 ÷ 93. × then ÷ (left to right)3 × 9 = 27, 27 ÷ 9 = 34 + 34. Add4 + 3 = 77THE TWO TRAPS8 ÷ 2 × 4 is 16, not 1.Multiply and divide have equal rank — go left to right.10 − 3 + 2 is 9, not 5.So do add and subtract.Order of Operationslittleactivity.com
Math

Order of Operations

PEMDAS with the two rules everyone gets wrong, worked out step by step.

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Decimals & RoundingPlace value to thousandths plus a rounding rule with a…5th GradeTENS310ONES61.TENTHS40.1HUNDREDTHS00.01THOUSANDTHS70.001SEE IT0.4 = four tenths = 4/100.40 = 0.4 — extra zeros never change the value0.407 is 407 thousandths — read all three places.Line up the decimal points before adding or comparing.ROUNDING — which one is it nearer?3.63.653.73.673.67 is past themidpoint, so itrounds to 3.7RULELook at the digit to the right. 5 or more rounds up; 4 or less leaves it alone.Decimals & Roundinglittleactivity.com
Math

Decimals & Rounding

Place value to thousandths plus a rounding rule with a number-line picture.

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Fraction RulesAdd, subtract, multiply and divide fractions — one worked…5th GradeADD & SUBTRACT — denominators must matchSame bottom: 3/8 + 2/8 = 5/8Add the tops only. The bottom names the pieces — it does not change.Different: 1/2 + 1/3 → 3/6 + 2/6 = 5/6Find a common denominator first — the smallest number both bottoms divide into.MULTIPLY — straight across2/3 × 4/5 = 8/15tops × tops, bottoms × bottoms"Of" means multiply: half of 1/3 is 1/2 × 1/3 = 1/6.Multiplying by a fraction less than 1 makes the answer smaller.DIVIDE — keep, change, flip3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 ⅞Keep the first fraction. Change ÷ to ×. Flip the second one over.Dividing by a fraction less than 1 makes the answer bigger — you are asking"how many of these fit inside that?"MIXED NUMBERS2 ⅓ → (2 × 3) + 1 = 7 → 7/3Convert to improper fractions before multiplying or dividing. Convert back at the end.11/4 → 4 goes into 11 twice with 3 left → 2 ¾SIMPLIFY LASTDivide top and bottom by the same number until nothing else goes into both.Fraction Ruleslittleactivity.com
Math

Fraction Rules

Add, subtract, multiply and divide fractions — one worked example each.

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Greek & Latin RootsTwenty-four roots with meanings and two example words each.5th GradeOne root unlocks a dozen words. Learn the root, then collect the family.audhearaudience, audiblebiolifebiology, biographychrontimechronicle, synchronisedictsaydictate, predictducleadconduct, educategeoearthgeography, geologygraphwrite, drawautograph, graphicjectthroweject, projectmetermeasurethermometer, perimeterphonsoundtelephone, symphonyportcarrytransport, portableruptbreakerupt, interruptscribwritedescribe, scripturespectlookinspect, spectatorstructbuildconstruct, structuretelefar offtelescope, televisionterrlandterritory, terrainthermheatthermal, thermostractpull, dragtractor, attractvid / visseevideo, visiblevocvoice, callvocal, advocateformshapetransform, uniformmit / misssendtransmit, missioncredbelievecredit, incredibleON A TESTSplit the unknown word, translate each part, then check it against the sentence.Greek & Latin Rootslittleactivity.com
Literacy

Greek & Latin Roots

Twenty-four roots with meanings and two example words each.

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Paragraph & Essay FrameThe five-paragraph skeleton plus sentence starters for each…5th GradeINTRODUCTIONstart hereHook · background · thesis“Have you ever…”“In this essay I will show that…”BODY 1paragraph 2Strongest reason first“One reason is…”“For example,…”“This shows that…”BODY 2paragraph 3Second reason“Another reason is…”“For instance,…”“This means…”BODY 3paragraph 4Last reason“Finally,…”“According to…”“As a result,…”CONCLUSIONfinish hereRestate · sum up · leave a thought“In conclusion,…”“This is why…”ORDERWrite the body first. The introduction is easiest once you know what you said.Paragraph & Essay Framelittleactivity.com
Literacy

Paragraph & Essay Frame

The five-paragraph skeleton plus sentence starters for each slot.

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Body SystemsSix systems, what each does, and the organs that belong to it.5th GradeCirculatoryMoves blood, oxygen and nutrients around the body.heart · blood · arteries · veinsRespiratoryTakes in oxygen and gets rid of carbon dioxide.lungs · trachea · diaphragmDigestiveBreaks food down so the body can absorb it.mouth · stomach · intestines · liverSkeletalSupports and protects, and makes blood cells.206 bones · joints · cartilageMuscularMoves the skeleton and keeps the heart beating.skeletal · smooth · cardiac muscleNervousSenses, decides and sends signals — fast.brain · spinal cord · nervesTHEY WORK TOGETHERYou breathe in oxygen (respiratory), blood carries it (circulatory) to muscles(muscular) that move bones (skeletal) — all directed by the nervous system.Body Systemslittleactivity.com
Science

Body Systems

Six systems, what each does, and the organs that belong to it.

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3 Branches of GovernmentLegislative, executive, judicial — powers, people, and the…5th GradeLEGISLATIVECongressMakes the lawsSenate — 100 members, 2per stateHouse — 435 members, bypopulationControls spending andtaxesDeclares warEXECUTIVEPresidentCarries out the lawsPresident and VicePresidentThe Cabinet and federalagenciesCommander in chiefSigns or vetoes billsJUDICIALSupreme CourtInterprets the laws9 justices, appointed forlifeDecides if a law isconstitutionalHears appealsJudicial reviewCHECKS & BALANCES — nobody gets to act aloneCongress→ Presidentcan override a veto, controls the budget, can impeachCongress→ Courtsconfirms judges, can propose amendmentsPresident→ Congresscan veto a billPresident→ Courtsappoints the justicesCourts→ Congresscan rule a law unconstitutionalCourts→ Presidentcan rule an action unconstitutionalTHE POINTPower is split three ways on purpose — so no single branch can run the country alone.3 Branches of Governmentlittleactivity.com
Social Studies

3 Branches of Government

Legislative, executive, judicial — powers, people, and the checks between them.

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