SFDRCISD Pre-Algebra- 7th Grade

690 Pages·2016·35.73 MB·English

SFDR 7th Grade Pre-Algebra
SFDR Math 7
Maria Sigley
Arturo Padilla
Angie Jasso
Tiffany Perez
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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
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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
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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
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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.
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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