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SFDRCISD Pre-Algebra- 7th Grade PDF

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SFDR 7th Grade Pre-Algebra SFDR Math 7 Maria Sigley Arturo Padilla Angie Jasso Tiffany Perez SayThankstotheAuthors Clickhttp://www.ck12.org/saythanks (Nosigninrequired) www.ck12.org AUTHORS SFDRMath7 To access a customizable version of this book, as well as other MariaSigley interactivecontent,visitwww.ck12.org ArturoPadilla AngieJasso TiffanyPerez SOURCES CK-12 Foundation is a non-profit organization with a mission to GoogleYouTube reduce the cost of textbook materials for the K-12 market both in JamesSousa–Videos theU.S.andworldwide. Usinganopen-source,collaborative,and KhanAcademy web-based compilation model, CK-12 pioneers and promotes the Pearson creationanddistributionofhigh-quality,adaptiveonlinetextbooks McGraw-Hill that can be mixed, modified and printed (i.e., the FlexBook® CK12.org textbooks). TeksingTowardSTAAR Copyright©2016CK-12Foundation,www.ck12.org The names “CK-12” and “CK12” and associated logos and the terms “FlexBook®” and “FlexBook Platform®” (collectively “CK-12 Marks”) are trademarks and service marks of CK-12 Foundation and are protected by federal, state, and international laws. Any form of reproduction of this book in any format or medium, in whole or in sections must include the referral attribution link http://www.ck12.org/saythanks (placed in a visible location) in additiontothefollowingterms. Except as otherwise noted, all CK-12 Content (including CK-12 Curriculum Material) is made available to Users in accordance with the Creative Commons Attribution-Non-Commercial 3.0 Unported (CC BY-NC 3.0) License (http://creativecommons.org/ licenses/by-nc/3.0/), as amended and updated by Creative Com- monsfromtimetotime(the“CCLicense”),whichisincorporated hereinbythisreference. Complete terms can be found at http://www.ck12.org/about/ terms-of-use. Printed: August22,2016 iii Contents www.ck12.org Contents 1 RelationshipswithRealNumberSystem 1 1.1 RationalNumberRelationships(7.2aand8.2a) . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 RationalNumberOperations 15 2.1 RationalNumbers(7.3aand7.3b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2 AddingandSubtractingDecimals(7.3aand7.3b) . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3 CombiningRationalNumbers(7.3aand7.3b) . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4 MultiplyandDivideRationalNumbers(7.3aand7.3b) . . . . . . . . . . . . . . . . . . . . . . 37 2.5 ApproximatingIrrationalNumbers(8.2b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3 EquationsandInequalities 46 3.1 ModelandSolveOne-Variable,Two-StepEquations(7.11a) . . . . . . . . . . . . . . . . . . . 47 3.2 ModelandSolveOne-Variable,One-StepInequalities(7.11a) . . . . . . . . . . . . . . . . . . . 57 3.3 ModelandSolveOne-Variable,Two-StepInequalities(7.11a) . . . . . . . . . . . . . . . . . . . 63 3.4 ModelandSolveOne-VariableEquationswithVariablesonBothSides(7.11a,8.8a) . . . . . . . 73 3.5 ModelandSolveEquationswithGeometryConcepts(7.11c) . . . . . . . . . . . . . . . . . . . 84 3.6 SolvingEquationsusingSubstitution(7.11b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.7 SolvingInequalitiesUsingSubstitution(7.11b) . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.8 WritingEquationsGivenSituations–additionandsubtraction(7.10a) . . . . . . . . . . . . . . 102 3.9 WritingEquationsGivenSituations–MultiplicationandDivision(7.10a) . . . . . . . . . . . . 109 3.10 WritingInequalitiesGivenaSituation(7.10a) . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.11 RepresentingSolutionsforEquationsasFunctionTable(7.10b) . . . . . . . . . . . . . . . . . . 128 3.12 RepresentingSolutionsforEquationsasGraphs(7.10b) . . . . . . . . . . . . . . . . . . . . . . 149 3.13 RepresentingSolutionsforInequalities(7.10b) . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 3.14 RepresentingRealLifeSituationsUsingEquations(7.10c) . . . . . . . . . . . . . . . . . . . . 163 3.15 RepresentingRealLifeSituationsusingInequalities(7.10c) . . . . . . . . . . . . . . . . . . . . 168 4 ConstantRatesofChangeandConstantofProportionality 173 4.1 RatiosandRates(7.4b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4.2 ConstantRateofChange(7.4a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 4.3 CalculatingUnitRates(7.4b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191 4.4 DeterminingConstantofProportionality(7.4c) . . . . . . . . . . . . . . . . . . . . . . . . . . 197 5 ProportionandNon-ProportionalRelationships 204 5.1 GraphsofLinearRelationships(7.7a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 5.2 LinearEquations(7.7a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 5.3 RepresentationTabletoGraph(7.7a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220 5.4 FindingSlope(7.7a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231 5.5 WritingEquationsfromTablesandGraphs(7.7a) . . . . . . . . . . . . . . . . . . . . . . . . . 240 5.6 ApplicationsofLinearRelationships(7.7a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246 6 RatesandPercentages–FinancialLiteracyI 258 iv www.ck12.org Contents 6.1 Percent–Estimation(7.4d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 6.2 Percent–Proportions(7.4d). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 6.3 Percent–Equations(7.4d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279 6.4 Percent–PercentofChange(7.4d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 6.5 Percent–SalesTaxandTip(7.4d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 6.6 Percent–Discounts(7.4d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 6.7 SimpleInterest(7.13eand8.12d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 6.8 CompoundInterest(7.13eand8.12d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 6.9 MonetaryIncentives(7.13f) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 7 SimilarShapes 321 7.1 AttributesofCongruency(7.5a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 7.2 AttributesofSimilarity(7.5a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 7.3 FindingtheMissingSidesofSimilarFigures(7.5a) . . . . . . . . . . . . . . . . . . . . . . . . 337 7.4 ScaleDrawings(7.5c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 8 MeasurementConversions 358 8.1 WriteandSolveProportionsbyUsingEquivalentRates(7.4e) . . . . . . . . . . . . . . . . . . 359 8.2 WriteandSolveProportionsbyUsingCross-Products(7.4e) . . . . . . . . . . . . . . . . . . . 364 8.3 ConvertCustomaryUnitsofMeasurement(7.4e) . . . . . . . . . . . . . . . . . . . . . . . . . 369 8.4 ConvertCustomaryUnitsofMeasurementinReal-WorldSituations(7.4e) . . . . . . . . . . . . 374 8.5 ConvertMetricUnitsofMeasurement(7.4e) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380 8.6 ConvertMetricUnitsofMeasurementinReal-WorldSituations(7.4e) . . . . . . . . . . . . . . 385 8.7 ConversionApplicationsInvolvingRatesandUnitAnalysis(7.4e) . . . . . . . . . . . . . . . . 391 9 Circumference,Area,andSurfaceArea 396 9.1 CircumferenceofaCircle(7.9b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397 9.2 AreaofaCircle(7.9b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401 9.3 AreaofCompositeFigures(7.9c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 9.4 NetsofPrismsandPyramids(7.9d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 9.5 LateralandTotalSurfaceAreaofPrisms(7.9d) . . . . . . . . . . . . . . . . . . . . . . . . . . 420 9.6 LateralandTotalSurfaceAreaofPyramids(7.9d) . . . . . . . . . . . . . . . . . . . . . . . . . 429 9.7 Circumference,Area,andSurfaceAreaApplicationSituations(7.9d) . . . . . . . . . . . . . . . 437 10 Volumeof3-DFigures 440 10.1 RelationshipBetweenVolumeofPrismsandPyramids(7.8a) . . . . . . . . . . . . . . . . . . . 441 10.2 RectangularPrisms(7.9a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442 10.3 TriangularPrisms(7.9a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449 10.4 RectangularandTriangularPyramids(7.9a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 10.5 Cylinders(8.7a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 10.6 Cones(8.7a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472 10.7 Spheres(8.7a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 10.8 VolumeApplications(7.9a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 11 Probability 487 11.1 SampleSpaces(7.6a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 11.2 TheoreticalProbability–SimpleEvents(7.6dand7.6i) . . . . . . . . . . . . . . . . . . . . . . 495 11.3 TheoreticalProbability–CompoundEvents(7.6i) . . . . . . . . . . . . . . . . . . . . . . . . . 500 11.4 ExperimentalProbability(7.6cand7.6i) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 11.5 ProbabilityApplications(7.6h) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 12 Graphs 515 v Contents www.ck12.org 12.1 BarGraphs(7.6g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 12.2 CircleGraphs(7.6g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 12.3 DotPlots(7.6g) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530 12.4 BoxPlots(7.12a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533 12.5 ComparingGroupsofData(7.12a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 12.6 PopulationInferences(7.12c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550 12.7 InterpretingData(7.6gand7.12b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 12.8 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 13 FinancialLiteracyII 562 13.1 IncomeTax(7.13a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 13.2 PersonalBudget(7.13b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568 13.3 FamilyBudget(7.13d) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 13.4 NetWorth-AssetsandLiabilities(7.13c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579 14 PythagoreanTheorem 583 14.1 ModelsandDiagramstoExplainPythagoreanTheorem(8.6c) . . . . . . . . . . . . . . . . . . 584 14.2 PythagoreanTheoremanditsConverse(8.7c) . . . . . . . . . . . . . . . . . . . . . . . . . . . 591 14.3 DeterminingDistanceUsingPythagoreanTheorem(8.7d) . . . . . . . . . . . . . . . . . . . . . 598 15 Transformations 607 15.1 PropertiesofCongruence(8.10a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608 15.2 Translations,Rotations,andReflections(8.10a) . . . . . . . . . . . . . . . . . . . . . . . . . . 616 15.3 DilationsofTwo-DimensionalFigures(8.10a) . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 15.4 TransformationsPreservingandNotPreservingCongruence(8.10b) . . . . . . . . . . . . . . . 634 15.5 RulesforTranslations(8.10c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641 15.6 RulesforReflections(8.10c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650 15.7 RulesforRotations(8.10c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660 15.8 RulesforDilations(8.10c) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674 vi www.ck12.org Chapter1. RelationshipswithRealNumberSystem C 1 HAPTER Relationships with Real Number System Chapter Outline 1.1 RATIONAL NUMBER RELATIONSHIPS (7.2A AND 8.2A) 7.2a: Extendpreviousknowledgeofsetsandsubsetsusingavisualrepresentationtodescriberelationshipsbetween setsofrationalnumbers 8.2a: Extendpreviousknowledgeofsetsandsubsetsusingavisualrepresentationtodescriberelationshipsbetween setsofrationalnumbers 8.2c: Convertbetweenstandarddecimalnotationandscientificnotation 1 1.1. RationalNumberRelationships(7.2aand8.2a) www.ck12.org 1.1 Rational Number Relationships (7.2a and 8.2a) GUIDANCE RealNumbers All numbers belong to the set of numbers known as the real number system. The real number system consists of everynumberyouhaveeverdealtwithsinceyouwereoldenoughtocount. Thenumbersintherealnumbersystem are divided into two main groups. One group is called the rational numbers and the other is called the irrational numbers. Thesetofirrationalnumbersconsistsofallnumbersthatarenotrational. Thissetofirrationalnumbers includesthosenumbersthatcannotbewrittenastheratiooftwointegers,decimalnumbersthatarenon-terminating √ anddecimalsthatdonothavearepeatingpatternofdigits. Forexample, pi(π), 2,−2.345876921...areirrational numbers. Thesetofrationalnumbersincludesnaturalnumbers,wholenumbers,integers,numbersthatcanbeexpressedas theratiooftwointegers,decimalnumberthatterminateanddecimalnumbersthathavearepeatingpatternofdigits. The natural numbers are the set of positive integers. For example, 1, 2, 3... are all natural numbers. The whole numbers are the natural numbers and zero. For example, 0, 1, 2, 3... are all whole numbers. The integers are the whole numbers and their opposites. For example, -2, -1, 0, 1, 2... are all integers. A rational number is any numberthatcanbeexpressedintheform a whereb(cid:54)=0. Whenarationalnumberisexpressedasadecimalthenthe b √ decimalwillterminate(end)oritwillhavearepeatingpatternofdigits. Forexample, 1, 81,−7.456545654are 2 allrationalnumbers. When you classify numbers remember that they can often belong to more than one set of numbers. If you think of thenumber3,youcancallitanaturalnumber,awholenumber,anintegerandarationalnumber. Thefollowingtablemayhelpyoutobetterunderstandtherealnumbersystem. 2 www.ck12.org Chapter1. RelationshipswithRealNumberSystem GUIDEDPRACTICE Example1 Earlier, you were given a problem about Faith and her circular flower bed. She wants to compare the new circular flower bed to the original square one using exact measurements. First, Faith should compare the perimeter of the squaretothecircumferenceofthecircle. Then,sheshouldcomparetheareaofthesquaretotheareaofthecircle. First,determinethediameterofthecirclewhichwillbethesidelengthofthesquare. Thediameterofacircleistwotimesthelengthoftheradius. Theradiusofthecircleis3feet. d = 2r d = 2(3) d = 6 3 1.1. RationalNumberRelationships(7.2aand8.2a) www.ck12.org Theansweris6. Thediameterofthecircleis6feet. Eachsideofthesquareisalso6feetinlength. Theanswerof6isanaturalnumber,awholenumber,anintegerandarationalnumber. Next, determine the perimeterof the square. The perimeter of the squareis the distance around itsouter edges and canbefoundbyaddingthelengthsofeachsideorbysimplymultiplyingthesidelengthbyfour. P = 4s square P = 4(6) square P = 24 square Theansweris24. Theperimeterofthesquareis24feet. Theanswerof24isanaturalnumber,awholenumber,anintegerandarationalnumber. Next, determine the circumference of the circle. The perimeter of a circle is known as its circumference and is the distancearoundtheouteredgeofthecircle. Theperimeterofacirclecanbefoundbymultiplyingthediameterby π. C = πd C = (3.141592654)(6) C = 18.84955592 Usingthevalueforπfromthecalculator(3.141592654)givestheanswer18.84955592. Thecircumferenceofthecircleis18.84955592feet. Theanswerof18.84955592isanirrationalnumber. Itisanon-terminating,non-repeatingdecimal. Next,determinetheareaofthesquare. Theareaofthesquarecanbefoundusingtheformula: A=s2 where’s’isthesidelengthofthesquare. A = s2 A = (6)2 A = 36 Theansweris36. Theareaofthesquareflowerbedis36 ft2. Theanswerof36isanaturalnumber,awholenumber,anintegerandarationalnumber. Next,determinetheareaofthecircle. Theareaofthecirclecanbefoundusingtheformula: A=πr2 where’r’istheradiusofthecircle. A = πr2 A = (3.141592654)(3)2 A = (3.141592654)(9) A = 28.27433388 4

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SFDR 7th Grade Pre-Algebra. SFDR Math 7. Maria Sigley http://www.ck12.org/saythanks (placed in a visible location) in addition to the following
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