Problem Solving and Reading Strategies Wo Wo r k b o o k PUPIL EDITION Grade 6
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CONTENTS
Unit 1: NUMBER SENSE AND OPERATIONS Chapter 1: Whole Number Applications 1.1 1.1 Esti Estima mate te with with Wh Whol ole e Num Numbe bers rs . . . . 1 1.2 1.2 Use Use Add Addit itio ion n and and Subt Subtrracti action on . . . . 2 1.3 1.3 Use Use Mul Multi tipl plic icat ation ion and and Div Divis isio ion n ...3 1.4 1.4 Read Readin ingg Stra Strate tegy gy:: Comp Compar are e.......4 1.5 1.5 Alge Algebr bra: a: Use Use Exp Expre ress ssio ions ns . . . . . . . . . 5 1.6 1.6 Alge Algebr bra: a: Ment Mental al Math Math and and Equations Equations . . . . . . . . . . . . . . . . . . . . . . 6 Chapter 2: Operation Operation Sense 2.1 2.1 Ment Mental al Mat Math: h: Use Use the the Prop Propert ertie iess . . 7 2.2 Alge Algebr bra: a: Expon Exponen ents ts . . . . . . . . . . . . . . 8 2.4 Algebr Algebra: a: Orde Orderr of Opera Operatio tions ns . . . . . 9 2.5 Read Readin ingg Str Strat ategy egy:: Seq Seque uenc nce e . . . . . 10 Chapter 3: Decimal Concepts 3.1 3.1 Repr Repres esen ent, t, Compa Compare re,, and and Orde Orderr Decimals . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 3.2 Read Readin ingg Stra Strate tegy gy:: Use Use Graphic Aids . . . . . . . . . . . . . . . . . . . 12 3.3 3.3 Esti Estima mate te with with Deci Decima mals ls . . . . . . . . . 13 3.4 3.4 Deci Decima mals ls and and Per Perce cent ntss . . . . . . . . . . 14 Chapter 4: Decimal Operations Operations 4.1 4.1 Add Add and and Subt Subtra ract ct Deci Decima mals ls . . . . . . 15 4.2 4.2 Mu Mult ltip iply ly Dec Decima imals ls . . . . . . . . . . . . . . 16 4.4 4.4 Divi Divide de with with Deci Decima mals ls . . . . . . . . . . . 17 4.5 4.5 Read Readin ingg Stra Strate tegy gy:: Use Use Cont Contex extt . . . 18 4.6 Algebr Algebra: a: Decima Decimall Expre Expressi ssions ons and Equations . . . . . . . . . . . . . . . . . . 19 Unit 2: STATISTICS AND GRAPHING Chapter 5: Collect and Organize Data 5.1 5.1 Samp Sample less . . . . . . . . . . . . . . . . . . . . . . 20 5.2 5.2 Bias Bias in Surv Survey eyss . . . . . . . . . . . . . . . . . 21 5.3 5.3 Read Readin ingg Stra Strate tegy gy:: Use Use Graphic Aids . . . . . . . . . . . . . . . . . . . 22
5.4 5.4 Freq Freque uenc ncy y Tab Table less and and Line Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . 23 5.5 Measu Measure ress of Centr Central al Tendenc endency y . . . 24 5.6 5.6 Outl Outlie iers rs and and Add Addit itio iona nall Dat Dataa . . . . 25 5.7 5.7 Data Data and and Con Concl clus usio ions ns . . . . . . . . . . 26
Chapter 6: Graph Data 6.1 6.1 Make Make and and Anal Analyz yze e Grap Graphs hs . . . . . . . 27 6.2 Find Find Unk Unkno nown wn Valu Values es . . . . . . . . . . . 28 6.3 Stem Stem-a -andnd-Le Leaf af Plot Plotss and and Histograms . . . . . . . . . . . . . . . . . . . . 29 6.5 BoxBox-and and-W -Whis hiske kerr Graph Graphss . . . . . . . . 30 6.6 Anal Analyz yze e Gra Graph phss . . . . . . . . . . . . . . . . 31 Unit 3: FRACTION CONCEPTS AND OPERATIONS Chapter 7: Number Theory 7.1 Divi Divisi sibi bili lity ty . . . . . . . . . . . . . . . . . . . . . 32 7.2 Prime Prime Fact Factori oriza zati tion on . . . . . . . . . . . . . 33 7.3 Leas Leastt Com Common mon Mu Mult ltip iple le and and Greate Greatest st Common Common Factor Factor . . . . . . . 34 7.4 Readi Reading ng Strat Strategy egy:: Synthe Synthesiz size e Information . . . . . . . . . . . . . . . . . . . . 35 Chapter 8: Fraction Concepts 8.1 8.1 Equi Equivvalen alentt Frac Fracti tion onss and and Simplest Simplest Form Form . . . . . . . . . . . . . . . . . 36 8.2 8.2 Mixe Mixed d Num Numbe bers rs and and FFra ract ctio ions ns . . . 37 8.3 8.3 Comp Compar are e and and Ord Order er Frac Fracti tion onss . . . 38 8.5 8.5 Frac Fracti tions ons,, Dec Decim imal als, s, and and Percents . . . . . . . . . . . . . . . . . . . . . . . 39 Chapter 9: Add and Subtract Fractions and Mixed Numbers 9.1 Esti Estima matte Sum Sumss and and Differences . . . . . . . . . . . . . . . . . . . . 40 9.3 Add Add and and Subt Subtra ract ct Fra Fract ctio ions ns . . . . . . 41 9.4 Add Add and and Subt Subtra ract ct Mix Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . 42 9.6 Subtr Subtract act Mixed Mixed Numb Numbers ers . . . . . . . . 43 9.7 Readi Reading ng Strat Strategy egy:: Summa Summarize rize . . . . 44
Chapter 10: Multiply and Divide Fractions and Mixed Numbers 10.1 10.1 Estima Estimate te Produ Products cts and Quotients Quotients . . . . . . . . . . . . . . . . . . . . . 45 10.2 10.2 Multip Multiply ly Fra Fracti ctions ons . . . . . . . . . . . . . 46 10.3 10.3 Mu Mult ltip iply ly Mix Mixed ed Num Numbe bers rs . . . . . . . 47 10.5 Divide Fractions Fractions and Mixed Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . 48 10.6 10.6 Readin Readingg Strat Strategy egy:: Multiple-Me Multiple-Meaning aning Words Words . . . . . . . 49 10.7 10.7 Algebra: Algebra: Fraction Fraction Expre Expressions ssions and Equatio Equations ns . . . . . . . . . . . . . . . . . 50 Unit 4: ALGEBRA: INTEGERS Chapter 11: Number Relationships 11. 11.1 Under Underst stan and d Inte Intege gers rs . . . . . . . . . . . . 51 11.2 11.2 Ratio Rational nal Numbers Numbers . . . . . . . . . . . . . . 52 11.3 11.3 Compar Compare e and and Order Order Ratio Rational nal Numbers Numbers . . . . . . . . . . . . . . . . . . . . . . 53 11.4 11.4 Readin Readingg Stra Strateg tegy: y: Analy Analyze ze Informati Information on . . . . . . . . . . . . . . . . . . . 54 Chapter 12: Add and Subtract with with Intege Integers rs 12.2 Algebr Algebra: a: Add Add Integ Integers ers . . . . . . . . . . . 55 12.4 Algebra: Algebra: Subtract Subtract Integ Integers ers . . . . . . . 56 Chapter 13: Multiply and Divide with with Intege Integers rs 13.2 13.2 Algebr Algebra: a: Multi Multiply ply Inte Integer gerss . . . . . . . 57 13.3 13.3 Algebr Algebra: a: Divid Divide e Intege Integers rs . . . . . . . . . 58 13.4 13.4 Combin Combine e Operat Operations ions with with Integers Integers . . . . . . . . . . . . . . . . . . . . . . . 59 Unit 5: ALGEBRA: EXPRESSIONS AND EQUATIONS Chapter 14: Expressions 14.1 14.1 Write Write Expre Expressi ssions ons . . . . . . . . . . . . . . 60 14.2 14.2 Evalu Evaluat ate e Expre Expressi ssions ons . . . . . . . . . . . . 61 14.4 Expression Expressionss with with Squar Squares es and and Square Square Roots . . . . . . . . . . . . . . . . . . 62 Chapter 15: Addition and Subtraction Equations 15.1 15.1 Connec Connectt Wor Words ds and and Equa Equatio tions ns . . . 63
15.3 15.3 Solve Solve Additi Addition on EEqua quatio tions ns . . . . . . . 64 15.4 Solve Solve Subtrac Subtraction tion Equations Equations . . . . . 65
Chapter 16: Multiplication and Division Division Equations Equations 16.2 Solve Solve Multiplica Multiplication tion and Division Division Equations Equations . . . . . . . . . . . . . 66 16.3 16.3 Use Formul Formulas as . . . . . . . . . . . . . . . . . . 67 16.5 Reading Reading Strategy: Strategy: Draw Draw Conclusions Conclusions . . . . . . . . . . . . . . . . . . . 68 Unit 6: GEOMETRY AND SPATIAL REASONING Chapter 17: Geometric Figures 17. 17.1 Points oints,, Line Lines, s, and and Pla Plane ness . . . . . . . . 69 17.3 17.3 Angle Angle Rela Relatio tionsh nships ips . . . . . . . . . . . . 70 17.4 17.4 Classi Classify fy Line Liness . . . . . . . . . . . . . . . . . . 71 Chapter 18: Plane Figures 18.1 18.1 Triangl riangles es . . . . . . . . . . . . . . . . . . . . . . 72 18.2 Reading Reading Strategy: Strategy: Make Make Inferences Inferences . . . . . . . . . . . . . . . . . . . . . 73 18.3 18.3 Quadri Quadrila later terals als . . . . . . . . . . . . . . . . . 74 18.4 18.4 Dra Draw Two Two-Di -Dimen mensio sional nal Figur Figures es . . 75 18.5 18.5 Circle Circless . . . . . . . . . . . . . . . . . . . . . . . . 76 Chapter 19: Solid Figures 19. 19.1 Types ypes of of Soli Solid d Figu Figure ress . . . . . . . . . . 77 19.2 19.2 Differe Different nt Views Views of Solid Solid Figures Figures . . 78 19.4 19.4 Readin Readingg Strat Strategy egy:: Para Paraphr phrase ase . . . . 79 Unit 7: RATIO, PROPORTION, PERCENT, AND PROBABILITY Chapter 20: Ratio and Proportion 20.1 20.1 Ratio Ratioss and and Rate Ratess . . . . . . . . . . . . . . . 80 20.3 Reading Reading Strategy: Strategy: Follow Follow Directions Directions . . . . . . . . . . . . . . . . . . . . . 81 20.4 Algebra: Algebra: Ratios Ratios and Similar Similar Figures . . . . . . . . . . . . . . . . . . . . . . . . 82 20.5 Algebra: Algebra: Proport Proportions ions and Similar Similar Figures Figures . . . . . . . . . . . . . . . . . 83 20.6 Algebra: Scale Scale Drawings Drawings . . . . . . . . . 84 20.7 20.7 Algebr Algebra: a: Maps Maps . . . . . . . . . . . . . . . . . 85
Chapter 21: Percent and Change 21.1 21.1 Perc Percent ent . . . . . . . . . . . . . . . . . . . . . . . 86 21.2 Percent Percents, s, Decimals, Decimals, and Fractions . . . . . . . . . . . . . . . . . . . . . . 87 21.3 Estimate Estimate and and Find Find Perc Percent ent of of a Number . . . . . . . . . . . . . . . . . . . . . . . 88 21.5 21.5 Discou Discount nt and and Sale Saless Tax Tax . . . . . . . . . 89 21.6 21.6 Simple Simple Inter Interest est . . . . . . . . . . . . . . . . 90 Chapter 22: Probability of Simple Events 22.1 22.1 Theoretica Theoreticall Probabi Probability lity . . . . . . . . . . 91 22.2 Reading Reading Strat Strategy: egy: Choose Choose Relevant Relevant Information . . . . . . . . . . . 92 22.4 Experimenta Experimentall Probabil Probability ity . . . . . . . . 93 Chapter 23: Probability of Compound Compound Events Events 23.1 23.1 Readin Readingg Strat Strategy egy:: Classi Classify fy and Catego Categorize rize . . . . . . . . . . . . . . . . 94 23.2 Compound Compound Events Events . . . . . . . . . . . . . . 95 23.3 Independent Independent and Dependent Dependent Events Events . . . . . . . . . . . . . . . . . . . . . . . . 96 23.4 23.4 Make Make Predi Predicti ctions ons . . . . . . . . . . . . . . 97 Unit 8: MEASUREMENT Chapter 24: Units of Measure 24.1 24.1 Algebr Algebra: a: Custo Customar mary y Measurements . . . . . . . . . . . . . . . . . 98 24.2 Algebra: Algebra: Metric Measurements . . . . . . . . . . . . . . . . . 99 24.3 Relate Relate Customary Customary and Metric Metric . . . . . . . . . . . . . . . . . . . . . . . 100 24.4 Appropria Appropriate te Tools Tools and and Units . . . . 101 24.5 Reading Reading Strat Strategy: egy: Make Make Predictio Predictions ns . . . . . . . . . . . . . . . . . . . 102 Chapter 25: Length and Perimeter Perimeter 25.2 Perimete Perimeterr . . . . . . . . . . . . . . . . . . . . . 103 25.3 Reading Reading Strategy Strategy:: Use Use Graphic Aids . . . . . . . . . . . . . . . . . . 104 25.5 25.5 Circum Circumfe fere renc nce e . . . . . . . . . . . . . . . . 105 Chapter 26: Area 26.1 26.1 Estima Estimate te and Find Find Area Area . . . . . . . . 106 26.2 Algebra: Areas of Parallelograms Parallelograms and Trapezoids . . . . . . . . . . . . . . . . 107
26.4 Algebra: Algebra: Area Areass of Circles Circles . . . . . . . 108 26.5 Algebra: Algebra: Surfac Surface e Areas Areas of Prisms and Pyramids . . . . . . . . . . . 109
Chapter 27: Volume 27. 27.1 Estima Estimate te and and Find Find Volu Volume me . . . . . . 110 27.2 27.2 Reading Reading Strategy: Strategy: Activa Activate te Prior Knowl Knowledge edge . . . . . . . . . . . . . . . 111 27.3 27.3 Algebra: Algebra: Volumes Volumes of of Pyramids Pyramids . . . 112 27.5 27.5 Volumes Volumes of Cylinde Cylinders rs . . . . . . . . . . . 113 Unit 9: ALGEBRA: PATTERNS AND RELATIONSHIPS Chapter 28: Patterns 28.1 28.1 Reading Reading Stra Strategy: tegy: Cause and Effect Effect . . . . . . . . . . . . . . . . . . . . . . . . 114 28.2 Pattern Patternss in Sequen Sequences ces . . . . . . . . . . 115 28.3 Number Number Patt Patterns erns and Functions Functions . . . . . . . . . . . . . . . . . . . . . 116 28.4 Geometric Geometric Patt Patterns erns . . . . . . . . . . . . 117 Chapter 29: Geometry and Motion 29. 29.1 Transform ransformatio ations ns of of Plane Plane Figures Figures . . . . . . . . . . . . . . . . . . . . . . . 118 29.2 29.2 Tessellat essellations ions . . . . . . . . . . . . . . . . . . 119 29.3 29.3 Reading Reading Strate Strategy: gy: Form Form Mental Images Images . . . . . . . . . . . . . . . . . . . . . . . 120 29.4 29.4 Transform ransformatio ations ns of Solid Figures Figures . . . . . . . . . . . . . . . . . . . . . . . 121 29.5 29.5 Symmet Symmetry ry . . . . . . . . . . . . . . . . . . . . 122 Chapter 30: Graph Relationships 30. 30.1 Ineq Inequa uali liti ties es on on a Numb Number er Lin Line e . . 123 30.2 Graph Graph on the Coordi Coordinat nate e Plane . . . . . . . . . . . . . . . . . . . . . . . . 124 30.3 Graph Graph Functions Functions . . . . . . . . . . . . . . . 125 30.4 Reading Reading Strate Strategy: gy: Make Make Generaliza Generalizations tions . . . . . . . . . . . . . . . 126 30.6 Graph Graph Trans Transforma formations tions . . . . . . . . . 127
LESSON 1.1 1.1
Name
Estimate with Whole Numbers Write the correct answer. 1. Use clustering to estimate the sum.
2. Use rounding to estimate the product.
7,843 8,213 8,107
3. The The loca locall museu museum m esti estima mate tess that that abou aboutt
5,47 5,475 5 peop people le visi visite ted d the the muse museum um in the the last last 9 days days.. Abou Aboutt ho how w man any y peopl eople e visi visite ted d the the muse museum um each each day? day?
33 21
4. Ruby made a quilt using 588 squares.
There were 28 rows of squares in the quilt. About how many squares were in each row?
Choose the letter for the best answer. 5. What is the place value of the
underlined digit? A B C D
1,345.835 hundredths tenths tens hundreds
7. The Rockwells traveled 4,476 miles in
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11 days. Each Each day they traveled traveled about about the same number of miles. What is a good estimate of how many miles they traveled each day? A 200 mi C 400 mi B 300 mi D 500 mi
6. What is 2,768 rounded to the nearest
hundred? F 3,000 G 2,800 H 2,770 J 2,700
8. June gets paid about $1,550 each
month. What is a reasonable estimate of how much she makes in a year? F Less than $10,000 G Between $10,000 and $15,000 H Between $15,000 and $20,000 J More than $20,000
9. Write About It Explain how to use clustering to estimate the sum of
385 408 396 411.
Problem Solving
PS1
LESSON 1.2
Name
Use Addition and Subtraction Subtraction Solve. 1. In 1995, there were about 58,000 farms
in North Carolina and about 22,000 farms in South Carolina. There were about 100,000 farms in Iowa in 1995. About how many more farms were there in Iowa than in North Carolina and South Carolina combined in 1995?
3. Give the value represented by the digit
8 in the number 258,034,199.
2. Carrie participated in a bird census
during three days last week. She counted 435 birds on Monday, 206 birds on Tuesday, and 359 birds on Wednesday Wednesday.. How many birds did she count in all during these three days?
4. Use clustering to estimate the sum.
65 57 62 54
Choose the letter for the best answer. 5.
In 1999 1999,, a worl world d reco recorrd for for the the larg larges estt gath gather erin ing g of twin twinss was was set set in Taipe aipei, i, Taiwa aiwan, n, with with 3,96 3,961 1 pair pairss of twin twinss in atte attenda ndance nce.. The numbe numberr of twins twins shatt shatter ered ed the previ previou ouss recor record d of 2,900 2,900 pairs pairs set set in Twinsb winsbur urg, g, Ohio Ohio,, in 1998. 1998. What is a reasonable estimate of the incr increa ease se in the the numb number er of pair pairss of twin twins? s? A 60 pairs B 160 pairs C 900 pairs D 1,100 pairs
7. What 2 numbers have a sum of 4,949
and a difference of 1,963? A 1,999 and 2,950 B 1,493 and 3,456 C 1,358 and 3,591 D 1,078 and 3,871
6. When a children’ children’s museum opened
near Roberto’ Roberto’s home, he was among 14,756 children who visited it during the first month it was open. The next month, 18,355 children visited, while 27,982 children visited during the third month. What is a reasonable estimate of the number of children who visited the museum during the first three months it was open? F 40,000 children H 60,000 children G 50,000 children J 70,000 children 8. Which is the greatest number of the
four shown below? 23,887; 32,109; 24,999; 32,190 F 23,887 G 32,109 H 24,999 J 32,190
9. Write About It Which operation would you use to solve a problem
in which you are asked to find an amount of increase? Explain.
PS2
Problem So Solving
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LESSON 1.3 1.3
Name
Use Multiplication and Division Write the correct answer. 1. Larry washed 58 windows. He charged
2. Claire had 108 balloons that she
$4 for every window he washed. How much money did he make washing windows?
wanted to give to her 6 friends. f riends. If each person got the same number, how many balloons did each person get?
3. Write the numbers in order from least
4. What is the value of the 2 in 3,927,648?
to greatest. Use . 80,808, 80,080, 80,088
Choose the letter for the best answer. 5. What is the difference dif ference between
2,403,615 and 1,417,528? A 1,096,133 B 1,086,197 C 986,087 D 985,987 7. Pauline rides to and from school on
her bike every day. day. Each round-trip round-trip is 6 miles. miles. What What is a good estimate estimate for the number number of miles she she rides in 180 school school days? days? A 1,000 mi B 1,500 mi C 2,000 mi D 2,500 mi t r u o c r a H ©
6. What is the product of 1,010 and 100?
1,010,000 G 110,101 H 101,000 J 100,110
F
8. Sam has 9 friends in the gardening
club. He orders 340 tomato seeds for his friends to share. What is a good estimate of how many seeds each person would get if they share the seeds equally? F 40 seeds G 25 seeds H 20 seeds J 15 seeds
9. Write About It Which operation would you use to solve a problem
in which objects are being shared equally? Explain your choice.
Problem Solving
PS3
LESSON 1.4
Name
Compare When you compare two or more things, you examine how they are alike. It can be helpful helpful to compare information in in a problem. Read the following following problem.
VOCABULAR VOCAB ULARY Y
compare
Ralph has some chickens and some pigs. Together, the animals have 38 legs. They have 15 heads. How many of each kind of animal does he have? predi ct and test This is a problem for which you might want to use the predict strategy. When you use this strategy, you think of possible solutions. Then you compare to see whether your solution fits the information given in the problem. You can use a table to compare information. 1. Complete the table. Compare the information about heads and
legs in the chart with the information given in the problem.
Predict
Test
Numbe Numberr of of Chi Chick ckens ens Number Number of Pigs Pigs Numbe Numberr of of Leg Legss Numbe Numberr of of Hea Heads ds 7
8
9
6
46
2. Solve the problem.
Make a table to compare the facts. Solve. 3. The Ping-P Ping-Pong ong Paddler Paddlerss table-tenni table-tenniss
team played 15 games. They lost 4 fewer games than they won. They tied 2 more games than they lost. What was the team’s team’s record? rec ord?
PS4
Reading St Strategy
4. Janine bought 20 pieces of fruit. Ten
can be eaten without peeling. Eight are yellow and 6 are orange. She has 2 more pears than bananas. She bought grapefruit, lemons, bananas, apples, yellow pears, and oranges. How many of each fruit did she buy?
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LESSON 1.5 1.5
Name
Algebra: Use Expressions Write the correct answer. 1. Write an algebraic expression for the
word expression. 15 less than a number, a
3. Fred scored 8 points more than Dale
during the game. If together they scored 32 points, determine the number of points Dale scored.
2. Write a numerical expression for the
word expression. 24 times 8
4. Patricia wants to share her package of
36 pretzels pretzels equally equally among her 5 friends and herself. How many pretzels will each person receive?
Choose the letter for the best answer. 5. Which algebraic expression represents
the word expression? the sum of 9 and a number, a , squared A 9 a 2 C 9 a 2 B 9 a 2 D 9 a 2
7. What 2 numbers have a product of 48
and a quotient of 48? A 8 and 6 B 12 and 4 C 48 and 1 D 96 and 2
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6. Which word expression represents the
numerical expression? 24 6 F 24 decreased by 6 G the sum of 24 and 6 H 24 increased by 6 J the quotient of 24 and 6 8. Joan bought 5 yards of fabric for $2.85
a yard, including tax. Which equation could be used to find the change Joan received, a , if she gave the cashier $50? F a 50 (5 2.85) G a 50 (5 2.85) H a 50 (5 2.85) J a 50 5 2.85
9. Write About It Give examples of phrases that can usually be
translated into subtraction expressions. e xpressions.
Problem Solving
PS5
LESSON 1.6
Name
Algebra: Mental Math and Equations Write the correct answer. 1. Shania is saving $25 each week for a
bicycle. When she began saving, she used the equation 25 y 200 to find out how many weeks she needed to save the money for the the bike. How How many many weeks will it take her to save enough for the bike?
3. Write the number 86,003 in words.
2. An average of 2 million people visited a
new encyclopedia web site each day during the first 5 days it was open. You can use the equation n 2 5 to determine how many millions of people visited the site during the 5 days. How How many visitors were there? there?
4. Write 40,610 in expanded form.
Choose the letter for the best answer. 5. Determine which of the values is a
solution of the equation 5 x 55. A 5 B 10 C 11 D 55 7. It is 12 bloc blocks ks from from Hiro iro’s ho hou use to the the
stor store e. He uses uses the the equa equati tion on 12 b 24 to fin find ou outt ho how w much uch fart farthe herr he need needss to walk alk to get to the library, ry, which is 24 bloc blocks ks from from his his ho hous use e. How far far does does he have to walk? A 2 blocks B 12 blocks C 36 blocks D 268 blocks
6. Which of the following numbers is
divisible by 3, 4, and 9? F 9,164 G 6,372 H 4,581 J 3,762 8. A video costs $16.48. Sondra has saved
$7.95. Which equation could she use to find how much more money she needs to buy the video? F $16.48 n $7.95 G $7.95 n $16.48 H $7.95 $16.48 n J n $16.48 $7.95
9. Write About It How would you use mental math to solve the
equation z 8 9?
PS6
Problem So Solving
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LESSON 2.1 2.1
Name
Use the Properties Write the correct answer. 1. Use compensation to add.
2. Use mental math to find the value of
48 35
3. In the auditorium, there are 32 rows of
seats. Each row has 24 chairs. How many students can the auditorium seat?
(13 12) 7.
4. Brock sorted his toy cars into five
groups. The groups contained 18, 22, 16, 7, and 14 cars. Use mental math to find the total number of cars.
Choose the letter for the best answer. 5. Which expression shows how to use
compensation to subtract 22 from 47?
digit in 9,987.6532?
A (47
5 tens G 5 ones H 5 tenths J 5 hundredths
2) (22 2) B (47 3) (22 2) C (47 20) (22 2) D 47 22
7. If you swim between 35 and 45
minutes a day, what is a reasonable estimate of the number of minutes you swim in 15 days? A Less than 300 B Between 300 and 500 C Between 500 and 700 D More than 700 t r u o c r a H ©
6. What is the value of the underlined
F
8. Which equation illustrates the
Commutative Property?
(2 3) 4 (2 3) 4 G 2 (3 4) (2 3) 4 H (2 3) 4 (3 2) 4 J (2 3) 4 6 4 F
9. Write About It Explain how to use the Distributive Property to
multiply 48 and 17.
Problem Solving
PS 7
LESSON 2.2
Name
Exponents Write the correct answer. 1. Write in exponent form.
55555555
3. Claire is working on her reading
assignment for school. On Monday she read three pages. Then, on each day after the first day, she read triple the amount of the previous day. day. Using exponent form, write the number of pages she will read on the fifth day.
2. Compare the fractions
Use or .
3 7 . and 4 8
4. Bill needs to know the decimal
equivalent of 136 to solve a problem in his math homework. He changes the fraction to a decimal by dividing the numerator by the denominator. denominator. What decimal does he get?
Choose the letter for the best answer. 5. Find the value of 7 3. A 73
343 C 21 D 10
B
7. Which group of numbers is listed from
greatest to least? A 3.045, 3.04, 3.05 B 4.2, 4.013, 4.01 C 2.7, 2.86, 2.68 D 5.10, 5.010, 5.02
6. Which is the exponent e xponent form of
n n n n n ? F n 5 H 5n G 5 J 5n 5 n
8. A salesman travels 517 miles a week to
cover his territory. Which is a good estimate for the number of miles he travels in 4 weeks? F 500 mi G 1,000 mi H 1,500 mi J 2,000 mi
9. Write About It Explain how you can tell which is greater, 8 6 or 126,
without finding their values.
PS 8
Problem Solving
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LESSON 2.4 2.4
Name
Order of Operations For Problems 1–2, write and evaluate an expression to solve each problem. 1. Rita and Ken worked as volunteers in
a fund-raising fund-raising effort effort for a candidate candidate in the Georgia primary. Rita stuffed 132 envelopes envelopes per hour for 4 hours hours and Ken stuffed stuffed 116 116 per hour hour for 6 hours. How many envelopes did they get done?
3. Use mental math to find the value of
234 w , for w 6.
2. The Academy School District filled 21
buses to capacity when it announced it would transport students to the state championship football game. If each bus holds 52 students and 145 more students went by car, how many attended the championship game?
4. Give two numbers between 4.8 and
4.9.
Choose the letter for the best answer. 5. Maureen plans to walk 2 miles a day
for the first week in her exercise plan and 3 miles a day for the next 12 days after that. Which of the following expressions shows how far she plans to walk walk?? A (2 7) (3 12) B (2 7) (3 12) C (2 3) (7 12) D (2 3) 12 7. Which of the following f ollowing is the value of 5 4? A 20
125 C 625 D 1,024
B
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6. Denzel bought 14 boxes of cups for a
party. Each box of cups cost $1.99. He also bought 5 bottles of juice that cost $2.39 each and paid $1.99 in sales tax. How much did he spend in all? F $6.37 G $31.69 H $39.81 J $41.80 8. Evaluate the expression
42 7 8 (15 2). F 51 G 59 H 85 J 167
9. Write About It Explain the steps you would use in finding the
value of 82 3 7 21 (5 8).
Problem Solving
PS 9
LESSON 2.5
Name
Sequence Whether you are reading a story or a math problem, putting events VOCA VOCABULAR BULARY Y in order, or in sequence, can help you understand it better. To put sequence events in sequence, you prioritize the order of the events. You can use clues in the text and common sense. Read this problem.
Albert Alber t gets ge ts home h ome at 5:15 5 :15 P.M. Dinner is at 5:30. Albert has four tasks to do tonight. In what order should he do them? ALBERT’S EVENING SCHEDULE Task
Time It Takes
Do homework
Factors That Affect Sequence
2 hr
Pack up backpack for the next day Wash the dinner dishes Make a salad for the family dinner
3 hr 4 1 hr 2 1 hr 4
1. Next to each task in the chart above, write the factors that will help
you sequence the events. 2. Using the information from the table and common sense, write a
possible sequence for Albert’s Albert’s tasks.
Use the schedule below. Each event lasts 50 minutes. Sequence the events to solve.
CHITTENDEN COUNTY FAIR Event Pie Judging Dog Judging Pig Races Juggling Show Tractor Pull Traine rained d Bear Bear Show Show
Times Offered 10:00 A.M. 11:00 A.M. 10:00 A.M., 12 noon, 2:00 P.M. 9:00 A.M., 10:00 A.M., 11:00 A.M., 12 noon 9:00 A.M., 11:00 A.M., 1:00 P.M. 9:00 9:0 0 A.M., 1:00 P.M., 3:00 P.M.
3. Antoine and Penny get to the county
fair at 9:45 A .M. They both both want want to go to to as many activities as possible, with no breaks. What is the best schedule for Antoine and Penny?
PS 10
Reading St Strategy
4.
Helen and Raoul want to see at least one judged event and they they want to eat lunch at noon. They want to see the juggling show right after the tractor pull event. What is the best schedule for them? them?
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LESSON 3.1
Name
Represent, Compare, and Order Decimals Write the correct answer. 1. Write the numbers in order from least
2. Write the value of the digit 3 in the
number 145.36.
to greatest. 6.2; 6.002; 6.02
3. Kirk ran 2.6 miles on Monday, 4.2 miles
on Tuesday, 1.8 miles on Wednesday, and 5.1 miles on Thursday. Thursday. Estimate how many miles he ran in the 4 days.
4. Morgan carries between 4 and 6 logs at
a time. At this rate, what is a reasonable number of trips it will take her to move a pile of 118 logs?
Choose the letter for the best answer. 5. Which group of decimals is listed in
order from least to greatest? A 1.010, 1.001, 1.100 B 2.10, 2.200, 2.3 C 1.400, 1.040, 1.44 D 2.03, 2.33, 2.003
7. What is the value of the underlined
digit in 34.17? A 1 ten B 1 one C 1 tenth D 1 hundredth t r u o c r a H ©
6. Jill went to the store with $20. She
bought 6 cans of soup, 3 gallons of milk, and 2 packages of spaghetti. What else do you need to know to find how much change Jill received? F The brand of milk Jill bought G The size of a can of soup H The weight of a package of spaghetti J The cost of each item 8. Simeon played the piano between 2
and 3 hours. What is a reasonable estimate of the number of minutes he played? F Less than 60 minutes G Between 60 and 120 minutes H Between 120 and 180 minutes J More than 180 minutes
9. Write About It Explain how you would compare 4.08 and 4.3.
Problem Solving
PS 11
LESSON 3.2
Name
Use Graphic Aids You have used graphic aids such as tables to find information. You can make a table to organize data with numbers to help you solve problems. Read the following problem.
VOCABULAR VOCA BULARY Y
graphic aids
Five friends have saved different amounts of money. money. Bob has $18.94; Dot, Dot, $25.37 $25.37;; Caro Carol, l, $9.59; $9.59; Ruth, Ruth, $34.75 $34.75;; and and Ann, Ann, $12.38 $12.38.. Who has has save saved d the second greatest amount of money? the second least amount? 1. Order the data in the table below to make the problem easier to solve.
Name
Amount Saved
2. Solve the problem.
3. Explain the strategy you used to solve the problem. problem.
Reorder the data in the table to solve.
MR. FRENCH’S OFFICE Equipment sc ann er copy machine pr in ter phone system co m p u t e r
fax machine
Price $ 29 9 $1,769 $9 9 5 $ 48 8 $2 ,5 00
$547
4. Mr. French is buying new office
equipment. The store requires him to pay for the least and most expensive items in advance. How much does he have to pay now?
PS 12
Reading St Strategy
GIRLS’ BASKETBALL Team
Games Won and Lost
Di am on d s
1 wi n, 3 l os s es
T iger s
0 wi n s, 4 lo s se s
Hawks
3 wi ns , 1 lo ss
Astros
2 win s , 2 lo ss es
Ru bie s
1 wi n, 3 l os s es
5. There are five girls’ basketball teams in
the district. Which team is in second place?
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LESSON 3.3
Name
Estimate Estimate with Decimals Write the correct answer. 1. Is 18 or 24 a better estimate for the
product 3.98 6.02?
3. The owner of a computer store had 12
copies of a popular software program in stock. She ordered 8 more cartons, each of which contained 20 copies of the program. She used the expression 12 8 20 to determine how many copies she would have. What total did she find?
2. Use estimation to determine which is
greater, 209.4 81.6 or 241.54 3.
4. Malik wants to read a 210-page book
during his 12-day vacation. He estimates that he can read 20 pages per day in his free time. If Malik keeps to his estimate, will he be able to finish the book in the 12 days? If so, on which day will he finish?
Choose the letter for the best answer. 5. Kaitlin spent $39.95, $17.80, $42.30,
and $59.89 on gifts for her family. Which is the best estimate for the total amount that she spent? A $150 B $160 C $170 D $180 7. On a bar graph comparing how students
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get to school, the bar representing those who ride bikes was half as tall as the bar representing those who ride a bus. The bar for those who walk was twice the height of the one for the students who ride a bus. If 40 students ride bikes to school, how many students walk? A 80 students B 120 students C 140 students D 160 students
6. Collin drove 79.9 miles in the morning
and 121.1 miles after lunch. What is the best estimate of the difference between the two distances? F 20 miles G 30 miles H 40 miles J 50 miles 8. The Master Disk Company had sales of
$2,800,000 in 1998. Creative CDs had sales of $1,900,000 in 1998. If Master’s Master’s sales grow by $100,000 per year and Creative’s grow by $200,000, in how many years will the sales of the two companies be equal? F 9 years G 10 years H 11 years J 12 years
9. Write About It Explain two different ways to estimate the product
47.92 8.7.
Problem Solving
PS 13
LESSON 3.4
Name
Decimals and Percents Write the correct answer. 1. Carl paid for a $0.25 box of crackers
and a $0.55 drink with a one-dollar bill. What percent of the dollar did he receive in change?
3. Rama’s bus ride to or from school takes
9 minutes. How long is she on the bus in a 5-day school week?
2. There are 26 students in class 6-A, 24
in class 6-B, 23 in class 6-C, and 27 in class 6-D. What percent of the sixth graders are in classes 6-A and 6-B?
4. A rectangular array of dots has 6 rows.
There are a total of 216 dots in the array. How many columns of dots are there?
Choose the letter for the best answer. 5. A computer computer in the school school library library has
100 web sites bookmarked. Of these, 68 are educational and 16 are travelrelated. What percent of the sites are not related to either education or travel? A 16% C 52% B 18% D 84% 7. Using one possible route, the driving
distance from New York York City to Philadelphia is 100 miles. If you drive 1 hour at 50 50 miles per per hour and and one hour at 45 miles per hour, what percent of the trip will you still have left? A 95% B 50% C 10% D 5%
6. Carlos is 7 years older than his sister.
The sum of their ages is 13 less than their mother’s mother’s age. If their mother is 30 years old, how old is Carlos? F 7 years old H 12 years old G 10 years old J 17 years old 8. During a sale on film, a store charges
$4.99 for a roll of 36 exposures. You You need enough film to take individual pictures of all 100 students in the sixth grade. If your budget for film is $25.00, how much extra money do you have? F $10.03 G $14.97 H $15.02 J $20.01
9. Write About It Explain how you would find an unknown percent
if you know that a figure consists of two regions and you know the percent represented by one region.
PS 14
Problem Solving
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LESSON 4.1 4.1
Name
Add and Subtract Decimals Write the correct answer. 1. Round 38.75 to the nearest whole
number.
3. Michael bought a CD for $11.87 and a
book for $8.76. How much money did he spend on the purchases?
2. Paul has a balance in his checkbook of
$268.53. He writes a check to the store for $35.78. What is the new balance in his checkbook?
4. The wall is covered with 27 rows of
colorful tiles. If there are 43 tiles in each row, how many tiles are on the wall?
Choose the letter for the best answer. 5. Which list of numbers numbers is in order order from from
greatest to least? A 0.034, 0.03, 0.8 B 0.065, 0.05, 0.012 C 0.008, 0.07, 0.3 D 0.12, 0.21, 0.030 7. Philip and George ran a race. Philip’s
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time was 38.45 seconds and George’s time was 34.76 seconds. Which expression can be used to find out how many seconds George finished before Philip? A 38.45 34.76 B 38.45 34.76 C 38.45 34.76 D 38.45 34.76
6. Which expression shows one way to
use compensation to add 58 F (58 3) (43 3) G (58 3) (43 3) H (58 2) (43 2) J (58 2) (58 2)
43?
8. Daniel has ridden a total of 58 miles on
his skateboard so far this month. He rides it about the same distance each day. What else do you need to know to find how many miles he rides each day? The number of days in the month G The length of the skateboard H What time he starts riding ridin g each day J How many days this month he has ridden F
9. Write About It Why is it important to align the decimal points
when you add decimals? de cimals?
Problem Solving
PS 15
LESSON 4.2
Name
Multiply Decimals Write the correct answer. 1. Which is greater, 0.108 or 0.091?
Use or .
2. Sonia wrote a check for $27.86. What is
the number of dollars written in words?
Choose the letter for the best answer. 3. Walter grew a pumpkin that weighed
38.73 pounds. Bill grew a pumpkin that weighed 42.1 pounds. How many more pounds did Bill’s Bill’s pumpkin weigh than Walter’ Walter’s pumpkin? A 4.67 more pounds B 4.63 more pounds C 3.67 more pounds D 3.37 more pounds
5. A pencil costs $0.85 and a pen costs
$1.76. Wayne buys 12 pencils and 8 pens. Which expression can be used use d to find the total cost of Wayne’s purchases? A (12 0.85) (8 1.76) B (12 0.85) (8 1.76) C (12 0.85) (8 1.76) D (12 0.85) (8 1.76)
4. Ted wants to use a special wallpaper
border in his living room. He has three pieces of border that are 11.7 meters, 6.05 meters, and 24.75 meters long. How many meters of border does he have in all? F 24.75 meters G 31.97 meters H 42.5 meters J 641.45 meters 6. A grocery store needs to stock a new
cereal on the shelf. There are 8 shelves that can hold 6 boxes in each row. What else do you need to know k now to find out how many boxes of the cereal the store can put out at once? F The height of the box G How many rows of boxes fit on a shelf H How much a box of cereal costs J The brand of cereal
7. Write About It Explain how you could use a decimal square to
model the product 0.3
PS 16
Problem So Solving
0.2.
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LESSON 4.4 4.4
Name
Divide with Decimals Write the correct answer. 1. Find the quotient.
2. Place the decimal point in the
quotient.
7.4 1 5 3 .9 2
235.468 8.6 2738
3. Jacob bought a new computer for
$2,124.00. He is paying $88.50 a month for the computer. For how many months will he have to make payments?
4. Selma needs a new notebook that
costs $18.75 and a calculator that costs $23.64. How much money does she need to make the purchases?
Choose the letter for the best answer. 5. Which expression is 211.68
12.6 rewritten so that the divisor is a whole number? A 2116.8 126 B 21168 126 C 211.68 126 D 21168 12.6
7. Loraine sleeps between 6 and 8 hours
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each night. What is a reasonable estimate of the number of minutes she sleeps in a week? A Less than 1,500 B Between 1,500 and 2,500 C Between 2,500 and 3,500 D Between 3,500 and 4,500
9. Write About It Describe a pattern you see
in the set of problems at the right.
6. Which is the exponent form of the
expression? 24 24 24 3 24 G 33
F
H 324 J
243
8. Hunter saves $3.50 each week to buy a
CD boxed set that sells for $52.50. He has already saved $10.50. How many more weeks does he need to save money? F 11 weeks G 12 weeks H 14 weeks J 15 weeks 600 10 60 6 10 0.6 60 10 6 0.6 10 0.06
Problem Solving
PS 17
LESSON 4.5
Name
Use Context If there is a word, phrase, or paragraph you do not understand, context can help you. Context means the words, phrases, pictures, or graphic aids that go along with what you are reading. Context can help you decide how to interpret the remainder.
VOCABULAR VOCA BULARY Y context
Read the following problem.
Thirty-eight sixth graders are going to see a band from Puerto Rico that specializes in Caribbean Caribbean music. Each driver can take 4 students. students. How How many drivers drivers are needed needed?? 1. Use context to help you decide how to treat the remainder, if there
is one. If there is a remainder, should you add 1 to the quotient, drop the remainder, or use it as the answer? Why?
2. Solve the problem.
Solve the problem. Use context to help you decide how to interpret the remainder. 3. The band needs 40 minutes of music
to make 1 CD. The songs they know last for 2 hours and 42 minutes. How many CDs could they cut now?
5. The concert was attended by 1,000
people. If there were 36 seats in a row, how many rows could have been filled?
7. How many containers for 1 dozen eggs
are needed for 2,000 eggs?
PS 18
Reading St Strategy
4. Alexis Rivera wants to take some
friends to the concert. She has $135 and each ticket costs $30. How many tickets can she buy?
6. The band has 5,000 copies of their new
CD. If 73 music stores each get the same number of copies of the CD, how many CDs will be left over?
8. If 25 books fit on a shelf, how many
shelves are needed for 465 books?
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LESSON 4.6 4.6
Name
Algebra: Decimal Expressions and Equations Write the correct answer. 1. Each child’s child’s meal at a fast-food
restaurant costs $2.79. What is the greatest number of these meals that can be bought with $20.00?
3. The winning car in a race had an
average speed of 203.7 miles per hour. This was b miles per hour faster than the second-place car. Write an expression for the average speed of the second-place car. car.
2. Felipe is a teenager who is 10 years
older than his sister Irene. In 6 years, Felipe will be twice as old as his sister. How old is Felipe now?
4. The round-trip distance between
Kaitlin’s house and her school is 3.2 mile miless. Ka Kait itli lin n ride ridess her her bike bike tosc to scho hool ol 3 days per week. Write an expression that can be used to find the number of miles Kaitlin rides in w weeks. weeks.
Choose the letter for the best answer. 5. At a self-service self-ser vice copy center, the cost
of making copies is $0.08 per copy for the first 100 copies, $0.06 per copy for copies 101–200, and $0.05 per copy for any above 200. Stan needs to make 7 copies of a 30-page report. How much should he expect to pay? A $16.80 C $12.60 B $14.50 D $10.50 7. After driving 159.7 miles, Rasheed had
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r miles left to travel. If the total distance he needed to travel was 201.3 miles, which equation can you use to find the value of r ? A r 159.7 201.3 B r 201.3 159.7 C 159.7r 201.3 D 201.3 r 159.7
6. Marla poured out g glasses of juice for
a party she is hosting. If each glass contained 0.2 liter of juice, which expression describes the total amount of juice she poured? F
g H 0.2
0.2g
0.2 G g
J
0.2 g
8. At a school cafeteria, cafeter ia, 6 carrot sticks are
served with each lunch order. Carrot sticks are purchased in bags of 120. If 310 lunches were served ser ved today, how many bags of carrots were opened? F 13 bags G 14 bags H 15 bags J 16 bags
9. Write About It Describe how you decided which operation was
needed to find the total distance Kaitlin rides in w weeks weeks in Problem 4.
Problem Solving
PS 19
LESSON 5.1
Name
Samples Write the correct answer. 1. Find the product.
2. Evaluate the expression.
(72 (5 3) 22) 40
65.35 80.6
3. Fred wanted to find out the favorite
4. Cecily is ordering sodas for the class
color of all the students in his middle school. He surveyed all the students in his class. Is this a random sample? Explain.
party. She asks a student in the lunch line for her favorite soda and then asks every tenth student. What kind of sample is she using?
Choose the letter for the best answer. 5. Thad conducted a survey on hair color
at his school. His results were 23 students had blonde hair, 38 students had black hair, 7 students had red hair, and 19 students had brown hair. If he sampled 1 out of every 10 students at his school, how many people attend the school? A 900 people
870 people C 820 people D 750 people
B
7. The owner of a grocery store ordered
56 cases of cups. Each case holds 16 packages. How many packages of cups did the store owner order? A 896 packages C 1,026 packages B 1,006 packages D 1,128 packages
6.
Jill surveyed students about their choice for a new school color. The results were that 45 people liked red, 33 liked green, 16 liked orange, and 8 liked blue. If she chose a student at random from the school’s school’s enrollment list and then asked every tenth student on the list, which describes the school’s school’s enrollment and her sample? F 1,020 students; random sample G 1,002 students; systematic sample H 1,020 students; systematic sample J 1,002 students; convenience sample
8. Paul has 1,716 eggs to put into cartons.
Each carton holds one dozen eggs. How many cartons does Paul need to store all the eggs? F 163 cartons H 143 cartons G 153 cartons J 133 cartons
9. Write About It Why does a large sample generally give better
results than a small sample?
PS 20
Problem Solving
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LESSON 5.2 5.2
Name
Bias in Surveys Write the correct answer. 1. Bruce surveyed everyone in his math math
class to find out the favorite subject of the students in his school. Is his sample biased? Explain.
3. Tell how how many people people you would would
survey out of a group of 970, if you survey 1 out of every 10 people.
2. Lisa randomly surveyed 1 out of every
10 people in her school to find out their favorite item in the cafeteria. Is her sample biased? Explain.
4. Tell how many people you would
survey out of a group of 320, if you survey 1 out of every 10 people.
Choose the letter for the best answer. 5. A supermarket wants to know the
favorite brand of juice of its customers. Which group of customers should the store randomly survey to get results that are not biased? A 1 out of every 50 child customers B 1 out of every 100 adult customers C 10 out of every 100 customers as they leave the store D 2 out of every 5 female customers 7. Larry needs to buy 60 cookies for his
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party. A dozen cookies cost $3.50, including tax. Which expression can be used to find find the total total cost of the the cookies that Larry wants to buy? A 60 12 3.50 B 60 12 3.50 C 60 12 3.50 D 60 12 3.50
6. Rachel sold tickets for the local charity.
On Monday she sold 245 tickets, on Tuesday she sold 188 tickets, and on Thursday she sold 96 tickets. Which is the best estimate of how many tickets Rachel sold? F 300 tickets G 400 tickets H 450 tickets J 500 tickets 8. The head cook at a school wants to
know the favorite meal of the 870 students who attend the school. Which sample of students in the lunchroom would not be biased? F 1 out of every 100 male students G 1 out of every 10 female students H Every eighth student passing through the lunch line J Every student seated at one table
9. Write About It Why is it important to base your survey on a
random sample that is not biased?
Problem Solving
PS 21
LESSON 5.3
Name
Use Graphic Aids Often you must look for relationships between data. You may have to compare two or more numbers and add amounts. This is easier to do if you use a graphic aid such as a tally table.
VOCABULAR VOCA BULARY Y
graphic aid
Read the following problem.
Mr. Quang asked his students to name their favorite favorite animal. The results are shown below below. Which animal do most students like best? Which animal was third in rank?
monkey cat rabbit dog
squirrel cat dog cat
dog monkey cat mouse
squirrel dog cat snake
cat monkey monkey dog
1. Make a tally table to organize the data. Read the data. Make one
tally mark for each animal below its name. Monkey
Cat
Rabbit
Squirrel
Dog
Mouse
Snake
2. Solve the problem.
Make a table to organize the data. Solve. 3. The Belle School Student Council sold
bags of nuts to raise money. These are their results. peanuts walnuts peanuts brazil nuts almonds almonds brazil nuts peanuts almonds walnuts pecans pecans pecans almonds walnuts walnuts walnuts peanuts How many bags of pecans or almonds were sold in all? Which type of nut sold best?
PS 22
Reading St Strategy
4. The principal of a middle school needed
to know how students travel to school. She randomly surveyed 20 students.
bike
bike
car
bus
bus
walk
bike
bike
walk
bus
bus
bike
bike
bike
bus
walk
walk
bike
bike
bike
What fraction of students bike to school? What fraction of students travel by car or bus?
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LESSON 5.4 5.4
Name
Frequency Tables and Line Plots Write the correct answer. 1. The scores on the last quiz are given
below. below. What is the range of the data?
Scores 15 11 8 19 20 16 14 18 20 19 16 14 11 19 20
2. The line plot shows the average length
of a student’s student’s stride in centimeters. How many students participated in the survey?
30 31 32 33 34 35 36 37 38 39 40
Choose the letter for the best answer. 3. The recorded temperatures of selected
cities were: 67°, 54°, 98°, 77°, 92°, 85°, 83°, 90°, 63°, 74°, and 96°. What is the range of the temperatures? A 29° B 31° C 35° D 44°
5. George helped his father plant 4,836
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trees last month. This month they planted 6,981 trees. Which is the best estimate of how many more trees George and his father planted this month than last month? A 2,000 trees B 2,500 trees C 3,000 trees D 3,500 trees
4. Sara Sara likes to to swim between between 20 and and 30
laps in her pool each day for exercise. What is a reasonable estimate of the number of laps she would swim in 35 days? F Less than 300 G Between 300 and 500 H Between 500 and 700 J More than 700 6. The results of the last test were: 67, 84,
98, 70, 72, 66, 78, 74, 90, 92, 77, 93, 95, 79, 91, 87, 88, 86, 68, 71, 62, and 78. If the data were grouped by 60s, 70s, 80s, and 90s, what would the frequency be for the 90s? F 3 G 4 H 6 J 8
7. Write About It If the results of a survey are displayed on a line
plot, how can you tell which answer was the most popular?
Problem Solving
PS 23
LESSON 5.5
Name
Measures of Central Tendency Write the correct answer. 1. Find the mean of the numbers.
23, 86, 97, 45, 12
3. Find the median of the numbers.
13, 8, 9, 16, 18
2. Evaluate the expression below.
a b 12.7 for a 4.9 and b 28.6
4. If you survey 1 out of every 10 people,
how many would you survey out of a group of 23,800 people?
Choose the letter for the best answer. 5. Yolanda Yolanda has received scores of 98, 76,
6. Fred conducted a survey regarding hair
87, 98, and 80 so far this year on her math tests. What is the mean of her test scores? A 98 B 87.8 C 87.5 D 87
color. color. Which measure of central tendency should he use to report the hair color that occurs most often? F range G mean H median J mode
7. A pilot logged 87,984 87, 984 miles of flight
time in one month. If he flew the same route every day for 20 days, what is a good estimate for the length of his route? A 3,500 mi B 4,000 mi C 4,500 mi D 5,000 mi
8. Mr. Jacob works between 9 and 12
hours each day, 5 days a week. What is a reasonable estimate of the number of hours he works in 50 weeks? F Less than 400 hr G Between 400 and 1,000 hr H Between 1,000 and 2,000 hr J More than 2,000 hr
9. Write About It Explain why the mean of a set of data is sometimes
a number that is not in the set of data.
PS 24
Problem Solving
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LESSON 5.6 5.6
Name
Outliers and Additional Data Write the correct answer. 1. Brittany had test scores of 80, 85, 85,
92, and 90. If her score on the next test is 65, which measures of central tendency change?
2. While shopping, Debra estimated the
sum of $48.99 and $78.85 as $130. How did she know that the result was an overestimate?
3. Robert’s scores on six math tests are
4. In Grades 6 through 8 at Adams Middle
90, 80, 80, 85, 88, and 45. How much higher is the mean of his scores without the outlier than when the outlier is included?
School, 45% of the members of the computer club are eighth graders and 19% are seventh graders. What percent are sixth graders?
Choose the letter for the best answer. 5. John wants to pay for a book that costs
$28. He has 3 ten-dollar bills, 4 fivedollar bills, and 5 one-dollar bills. In how many different ways can John pay exactly $28 for the book using his money? A 1 way C 3 ways B 2 ways D 4 ways
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6. A custodian is changing all the
lightbulbs in an auditorium. The bulbs come in packages of 4. There are 17 light fixtures in the auditorium and each has 5 bulbs in it. How many packages of bulbs must the custodian open? F 20 packages H 22 packages G 21 packages J 23 packages
7. Danielle’s first 3 test scores were 86, 87,
8. The five linemen on the football team
and 91. If a perfect score is 100, what is the highest mean score she can have after 4 tests? A 89 B 90 C 91 D 92
weigh 240 pounds, 228 pounds, 230 pounds, 256 pounds, and 266 pounds. The quarterback weighs 172 pounds. How much greater is the mean weight of the five linemen than the mean weight of the six players? F 244 pounds H 20 pounds G 232 pounds J 12 pounds
9. Write About It In Exercise 3, what is the effect on the median and
the mode of Robert’s scores if the outlier is removed from his scores?
Problem Solving
PS 25
LESSON 5.7
Name
Data and Conclusions
PERCENT OF GLASS RECYCLED
Write the correct answer. Use the table at the right for 1–2.
Britain Japan
17 % 55%
Netherlands
57%
United States
20% 2. Stefon concludes that the percent of
1. Karin concludes from the table that
glass recycled in the Netherlands is 4 times that in Britain. Is he correct?
the percent of glass recycled in Japan is more than twice that recycled in the United States. States. Is she correct? Use the table below for 3–4.
Watches at Sea Starting Time Length of Watch
N o on
4 P.M.
8 P.M.
Midnight
4 A.M.
8 A.M.
10 A.M.
4 hr
4 hr
4 hr
4 hr
4 hr
2 hr
2 hr
3. If 15 sailors stand watch one at a time
in order, what is the greatest number of hours a sailor must stand watch in any 48-hour period?
4. If each watch is taken by a different
sailor, how many sailors will stand a watch during one week at sea?
Choose the letter for the best answer. Use the survey results given in the chart below for 5–7.
WHAT DID YOU HAVE FOR BREAKFAST? Toast
17 students
Cereal
39 students
Waffles
12 students
Nothing
14 students
6. Angela correctly concludes that the
percent of students who had cereal is ? about . F 25% G 50% H 75% J 90%
5. Mark correctly concludes that the least ? common breakfast was . A Toast C Waffles B Cereal D Nothing
7. How How many more students had
something for breakfast than had nothing for breakfast? A 14 more students B 54 more students C 68 more students D 82 more students
8. Write About It For Exercise 6, how did you estimate the percent of
students who had cereal?
PS 26
Problem Solving
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LESSON 6.1 6.1
Name
Make and Analyze Graphs Write the correct answer. 1. Jane wants to make a graph to
2. The double-line graph shows the
profits of two companies in millions of dollars. Which company made more money in 1996?
compare the types of music students listen to. She also wants to show whether there is a difference dif ference between the music girls like and the music boys like. What type of graph should Jane use?
) s y r e l a n l 50 o o d 40 M f f o o 30 t s n n o 20 u i l o l i 10 m m 0 A (
3. A city in the West West recorded a high
temperature of 87°F and a low temperature of 32°F. What was the range of the temperatures?
PROFITS Company A Company B
93 94 95 96 97 Year Year
Write the letter of the best answer. 4. When Dave was 9 years old, his
5. The Fredrickson family drove across
parents started recording his height every year. He started with a height of 45 inches and is now 62 inches tall. What is the range of his height? A 21 in. C 19 in. B 20 in. D 17 in. 6. Albert gets paid about $225 a week.
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the country on vacation. They drove through 36 states in 9 days. What is the average number of states they drove through each day? F 6 H 4 G 5 J 3 7. Which type of graph would be most
What is a reasonable estimate of how much he makes in a year? A Less than $12,000 B Between $12,000 and $14,000 C Between $14,000 and $18,000 D Between $18,000 and $20,000
appropriate for displaying the number of students in each of six homerooms for a sixth-grade class? F bar graph H line graph G circle graph J double-line graph
8. Write About It When making a double-bar graph or a double-line
graph, why is it necessary to include a key?
Problem Solving
PS 27
LESSON 6.2
Name
Find Unknown Values Write the correct answer. 1. While driving from Cincinnati to
Toledo, Ohio, a distance of 200 mi, Jamie averages 40 mi per hr. If she left at 10:30 A .M., at what time should she expect to arrive arr ive in Toledo? Toledo?
3. Kiona kept a record of how much she
saved by using an on-line grocery shopping service. Over the first 6 weeks she has used this service, ser vice, she saved $102. If her savings continue at the same rate, about how much can she expect to save during the seventh week she uses the shopping service? serv ice?
2. In the 1990 Census, the population of
Los Angeles was 3,485,557. About how many more people would it take for the population to reach 4,000,000?
4. Carmen pays $5.95 per month for a
long-distance calling plan that charges her $0.07 per min for her long-distance calls. She averages about 2 hr of long distance calls per month. About how much does she save each month over a plan that charges $0.15 per min for her calls, with no monthly fee?
Write the letter of the best answer. 5. Ty mows lawns after school for $45 per
week. He wants to use the money to pay for a trip that will cost $350. If he spends $20 each week and saves the rest, what is the least number of weeks he must work to pay for f or the trip? A 12 weeks C 14 weeks B 13 weeks D 15 weeks 7. An airplane is climbing at a steady rate
of 600 ft per min. From the time it reaches an altitude of 3,600 ft, how many more minutes will it take to reach an altitude of 9,000 ft? A 6 min C 8 min B 7 min D 9 min
6. For an art project, you need to cut
squares that measure 4 in. on each side from a rectangular sheet of paper that measures 8 in. by 12 in. What is the greatest number of squares that you can cut? F 4 squares H 8 squares G 6 squares J 10 squares 8. Brady counted 240 words on the first
page of a reading assignment. If the reading assignment is 6 pages long, about how many words should he expect to read? F 1,200 words H 1,440 words G 1,340 words J 1,500 words
9. Write About It In Exercise 1, what formula could you use to find
the time Jamie would arrive in Toledo? Toledo?
PS 28
Problem Solving
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LESSON 6.3 6.3
Name
Stem-and-Leaf Plots and Histograms Write the correct answer. 1. Harry wants to make a graph to show
the number of cars that go down his street during 1-hour intervals during the day. Would a bar graph or a histogram be more appropriate?
3. If you survey 1 out of every 10 people,
how many would you survey out of a group of 930 girls?
2. A contest to see who could jump the
farthest was conducted. The shortest jump was 87 centimeters and the longest jump was 162 centimeters. What is the range for the data?
4. Gregg wants to compare the
population in five states. Would Would a bar graph or a histogram be more appropriate?
Write the letter of the best answer. 5. A set of data ranges from 12 to 86.
What intervals would you use to display this data in a histogram with 4 intervals? A 10–39, 40–49, 50–69, 70–89 B 10–19, 20–39, 40–59, 60–89 C 10–29, 30–49, 50–69, 70–89 D 10–29, 30–39, 40–49, 50–89 7. Dolly and her three friends pool their
baby-sitting money. money. Last month they earned a total of $90. If they share the money equally, how much would each girl receive? A $21.50 C $23.50 B $22.50 D $30.00 t r u o c r a H ©
6. This year Mary has scored 87, 89, 93,
94, 78, 76, 99, and 100 on her math tests. Which could be the stems of a stem-and-leaf plot of the data? F 7, 8, 9, 10 G 1, 7, 8, 9 H 70, 80, 90, 100 J 7, 8, 9 8. Rick has a book with 48 pages of
stickers. Each page has between 12 and 23 stickers. What is a reasonable estimate of the total number of stickers in Rick’s book? F Fewer than 550 G Between 550 and 1,100 H Between 1,100 and 1,600 J More than 1,600
9. Write About It Why are the bars in a histogram connected rather
than separated?
Problem Solving
PS 29
LESSON LESSON 6.5 6.5
Name
Box-and-Whisker Graphs Write the correct answer. 1. What is the lower quartile of the data?
24, 26, 28, 29, 30, 32, 34, 36, 37
3. George is 145 centimeters tall and his
brother is 167 centimeters tall. What is the mean of their heights?
2. What is the upper quartile of the data?
56, 58, 58, 59, 60, 62, 64, 64, 90
4. If you survey 1 out of every 10 people,
how many would you survey out of a group of 145,910 people?
Write the letter of the best answer. 5. Ashley dusts the house for her mother
every 5 days. How many times in a year does Ashley dust the house for her mother? A 52 C 73 B 63 D 75 7. Kate took 131 pictures of her
classmates during the year. She gave each of the 31 students in the class 2 pictures. Which Which number sentence could be used to find p , the number of pictures Kate has left after giving some to her classmates? A p 131 (31 2) B p 131 (31 2) C p 131 (31 2) D p 131 (31 2)
6. Peter wants to use a box-and-whisker
graph to display his test scores. If his scores are 100, 79, 64, 89, 80, 86, and 89, what is the median? F 89 H 81 G 86 J 25 8. On the last test, nine students scored
64, 68, 68, 70, 72, 78, 82, 84, and 100 points. What is the upper quartile of the data? F 78, 82, 84, and 100 G 68 H 72 J 83
9. Write About It Into how many equal parts does the lower quartile
divide the lower half of the data? Explain. t r u o c r a H ©
PS 30
Problem Solving
LESSON 6.6 6.6
Name
Analyze Graphs Write the correct answer. Use the graph below for 1–3. s ) n s e 1.1 o l i i l l i m1.0 m e 0.9 r n a i ( u 0.8 q a s e r f 0.7 A o0.6
LAND AREAS
so that Casey would not have made the mistake he did.
Write the letter of the best answer. Use the graph below for 4–6. DOMINIQUE’S DOG
Jan Feb Mar Apr May Month
5. If the scale started at 0 and ended at
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decided that the area of Argentina was about three times the area of Mexico. Explain why Casey’s Casey’s conclusion is wrong.
Mexico Argentina Country
2. Explain how the graph could be fixed
) s d n 58 u o 56 p n 54 i ( 52 t h 50 g i e 0 W
1. After looking at the graph, Casey
60, with intervals of 2, how would the appearance of the graph change? A The line would be steeper. B The line would be flatter. C The line would look the same as it does now. D The line would be a straight line.
3. Use the graph to estimate the total
combined area of Mexico and Argentina.
4. During which of these times did
Dominique’s dog gain the least amount of weight? F from January to February G from February to March H from March to April J from April to May
6. If the scale began at 0, which interval
would make Dominique’s Dominique’s dog’s dog’s weight gain seem the greatest? F an interval of 2 lb G an interval of 5 lb H an interval of 10 lb J an interval of 15 lb
7. Write About It Why does increasing the size of the interval used in
the vertical scale of a line graph make the line seem flatter?
Problem Solving
PS 31
LESSON 7.1
Name
Divisibility Write the correct answer. 1. A bolt manufacturing company has
12,885 bolts to be put into bags. The packing machine can be set to seal either 3, 5, or 6 bolts into each bag. Can the machine be set for any of the three numbers without any bolts being left over? If so, which setting or settings can be used?
3. What is the least number that is
divisible by 2, 3, 4, 5, 6, 8, 9 and 10? What is the least number if 7 is included?
2. Scott earned $35, $40, $40, $25, and
$45 for 5 weeks of part-time work. During a school break, he worked fulltime for one week and earned $187. How much greater were his mean weekly earnings with the full-time week included than without it?
4. A supermarket manager wants to make
a pyramid of 110 cereal boxes for display. If cereal boxes are packed in cartons of 12, what is the least number of cartons she needs to open?
Choose the letter for the best answer. 5. A warehouse received 1,448 copies of a
book. The manager wants to place them on shelves. Which number of shelves can he use if he wants the same number of books on each shelf? A 3 shelves C 5 shelves B 4 shelves D 6 shelves 7. Max sells popcorn and potato chips at
the ballpark. During one game, he sold a total of 136 bags. He sold 12 fewer bags of chips than popcorn. How many bags of chips did he sell? A 124 bags C 74 bags B 84 bags D 62 bags
6. Amy had a total of $81.60 to spend on
4 gifts. She bought 3 copies of the same book and then had $27 left to spend on a sweater. How much did she pay for each copy of the book? F $9.00 H $27.00 G $18.20 J $54.60 8. A commercial jet made 3 trips tri ps during duri ng
one 24-hour period, each time carrying the same number of passengers. How many passengers might the plane have carried that day? F 516 passengers H 620 passengers G 586 passengers J 634 passengers
9. Write About It Explain how you solved Problem 8.
PS 32
Problem Solving
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LESSON 7.2 7.2
Name
Prime Factorization Write the correct answer. 1. Write the prime factorization of 42.
2. List the factors of 30.
3. The prime factors of a number are
4. Roger agreed to watch his younger
greater than 6 and less than 12. The smallest prime factor is used twice; the other(s), only once. What are the factors? What is the number?
siblings on August 7th and every seventh day after that. How many days will Roger watch his younger siblings in August?
Choose the letter for the best answer. 5. What is the prime pr ime factorization of 18 in
exponent form? A 22 32 B 29 C 36 D 2 32
6. Which number is composite?
13 G 21 H 23 J 29 F
7. Lucille is having a party. She invited 8
friends and wants to have between 4 and 8 balloons for herself and each friend. What is a reasonable number of balloons to buy for the party? A 27 balloons B 32 balloons C 45 balloons D 81 balloons
8. In her last 4 basketball games, Tara Tara
scored 26, 18, 34, and 27 points. Which is the best estimate of Tara’s total points scored for the 4 games? Less than 100 G Between 100 and 120 H Between 120 and 140 J Between 140 and 160 F
9. Write About It Explain how you can tell which prime factorization t r u o c r a H ©
is for the greater number. 23 32
22 33
Problem Solving
PS 33
LESSON LESSON 7.3 7.3
Name
Least Common Multiple and Greatest Common Factor Write the correct answer. 1. What is the GCF of 8 and 20?
2. Name the first four multiples of 30.
3. Balloons come in packages of 10 and
4. Write the prime factorization in
party favors come in packages of 8. Bill wants to have the same number of balloons and favors. What is the least number of packages of balloons and party favors he needs to buy so that he has none left over?
exponent form. 2233555
Choose the letter for the best answer. 5. Which is the GCF G CF of 72 and 200? A 2
6. Which is the LCM of 4, 5, and 6?
1 G 20 H 60 J 120 F
8 C 12 D 16
B
7. Charley bought 7 packs of gum for
$0.65 each, including tax. He gave the clerk $20. Which number sentence could be used to find c , the change the clerk gave him back from his purchase? A c $20
(7 $0.65) B c $20 (7 $0.65) C c $20 (7 $0.65) D c $20 (7 $0.65)
8. Wesley Wesley needs 6 cans of paint, a brush,
and a roller to paint his room. He has $127 saved to buy the supplies. What else do you need to know to determine whether Wesley Wesley has enough e nough money to paint his room? F The cost of the paint, brush, and roller G The size of the paint cans H The height of his room J The length of his room
9. Write About It Explain how you can tell the number of prime
factors a number has when its prime factorization is written in exponent form.
PS 34
Problem Solving
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LESSON 7.4 7.4
Name
Synthesize Information To synthesize means to form a whole by combining parts. You can combine new information to make something from the separate parts. One way to do this is to make an organized list. Read the following problem.
VOCABULAR VOCAB ULARY Y
synthesize
Al, Jo-Jo, Jo-Jo, and Tom Tom are standing on the first step of a staircase.There staircase. There are are 16 steps in all. Al goes up the staircase one step at a time. Jo-Jo Jo-Jo skips one step each time. Tom skips two steps each time. time. On which steps steps will they all place a foot? 1. Make a list to show on which step each person steps.
Al: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 Jo-Jo: Tom: 2. Synthesize the information by finding the number that appears in
all three lists. Solve the problem.
Synthesize the information by making an organized list. Solve 3. Al, Jo-Jo, Jo-Jo, and Tom Tom are climbing the
staircase, as described above. All three boys start on their left foot. Which is the next step on which they will all place their left foot?
5. Al, Jo-Jo, Jo-Jo, and Tom Tom are climbing the
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staircase. They all start on their left foot. Will all three boys ever step on the same stair with their right foot? Explain.
4. Al walks 1 mi in 14 min. Jo-Jo bikes 1
mi in 6 min. Tom runs 1 mi in 7 min. If they all start from the same place on a 1-mi track, how many miles will each boy have traveled when they are all on that spot again?
6. Jo-Jo jogs every fourth day of each
month. Al jogs every sixth day of each month. On which days of each month can they jog together?
Reading Strategy
PS 35
LESSON 8.1
Name
Equivalent Fractions and Simplest Form Write the correct answer.
12 20
1. Write in simplest form.
2. What is the LCM of 4 and 6?
3. Pauline has 8 adventure books, 4 books
4. Vickie made 20 cookies to share
of poems, and 6 animals books. What fraction of the books are books of poems? Write Write the fraction in simplest form.
equally with friends. She will give the same number of cookies to each friend and keep that same number for herself. With how many friends can she share the cookies? List all the possible numbers of friends.
Choose the letter for the best answer.
5. What number is missing from the
factor tree? 36 2 18 2 33 C 9 D 16
A 2 B
3
7. Which is the simplest form of the
fraction 2 A 5 B
4 9
32 ? 72
8 18
C
D
1 2
6. What are are the factors factors common common to the
numerator and denominator of 2544? F 1, 2, 3, 6 G 1, 2, 3, 6, 8 H 1, 2, 3, 4, 6 J 1, 2, 3, 6, 18
8. Abigail saved $3.58, $12.64, $9.45, and
$23.60 in the last four weeks. What is a good estimate of how much Abigail saved in the last four weeks? F Less than $20 G Between $20 and $40 H Between $40 and $60 J Between $60 and $80
9. Write About It Explain why dividing the numerator and the
denominator of a fraction by the GCF is the most efficient way of simplifying the fraction.
PS 36
Problem So Solving
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LESSON 8.2 8.2
Name
Mixed Numbers and Fractions Write the correct answer.
3 5
24 40
1. Write 4 as a fraction.
2. Write in simplest form.
3. Alex found a piece of lumber in the
4. Jane has envelopes in packets of 4 and
7 feet long. He needs 4
wood pile that is 3 feet to do a projec project. t. Does he have have enough lumber for the project? Explain.
note cards in packets of 6. What is the least number of packets of each she needs in order to have an equal number of envelopes and note cards?
Choose the letter for the best answer.
7 8
5. Which fraction is equivalent to 5 ?
61 A 8 47 B 8
40 C 8 35 D 8
7. Betty’s Betty’s father earned $38,967.43 last
year. Each month $245.32 was taken out of his pay for deductions. Which number sentence could be used to find m , the amount of money he took home each month? A m ($38,967.43 12) $245.32 B m ($38,967.43 12) $245.32 C m ($38,967.43 $245.32) 12 D m ($38,967.43 $245.32) 12 t r u o c r a H ©
6. Which mixed number is equivalent
to 897? F
7 8 9
H 9
5 9
G
4 9 9
J
2 9 3
8. Devin has between $12 and $20
deducted from his check every month for charity. What is a reasonable estimate for the amount of money he will have deducted for donations to charity in a year? F $50 G $200 H $300 J $400
9. Write About It Can any whole number be written as a fraction?
Explain.
Problem Solving
PS 37
LESSON 8.3
Name
Compare and Order Fractions Write the correct answer.
1. Beth has a box of 20 red pencils and a
box of 16 blue pencils. If she makes equal-size groups of all red or all blue pencils, what is the greatest number that can be in each group so that no pencils will be left over?
3. A doughnut shop uses the following
formula when selling its doughnuts: P $0.75 d , where d is the number of doughnuts purchased and P is the price the customer pays. What is the greatest number of doughnuts a customer can buy with $5?
2. Kim called her brother from her hotel
after stopping for the night while on a trip. She told him she had completed 58 of her trip. Had she completed at least half the trip? Explain.
4. José read a cake recipe that called for
3 4
cup flour, 12 cup sugar, and 23 cup milk. He lined up the ingredients in order by the amount, from least to greatest. Which ingredient did José put at the end of the line?
Choose the letter for the best answer.
5. Evelyn said that she had finished less
than half of her homework problems. What fraction of the problems might Evelyn have completed? 3 5 A C 5 8 B
3 8
D
4 5
7. This year’s year’s sixth grade in Glenn Middle
School has 6 classes. Which is the number of sixth-grade students if there are the same number of students in each class? A 184 students C 170 students B 172 students D 168 students
6. Four friends are all reading the same
book. Gordon has read 12 the book, Nick has read 23, Yvonne Yvonne has read 26, and Curtis has read 25. Which of them has read the greatest part of the book? F Gordon H Nick G Yvonne J Curtis
8. Di has 1 red marker, 1 blue marker,
and 1 green marker. She plans to make a design having 3 vertical stripes, one of each color. color. How many different designs can Di make? F 3 designs H 9 designs G 6 designs J 12 designs 1 2
9. Write About It What are some different ways to compare a fraction to ?
PS 38
Problem So Solving
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LESSON 8.5 8.5
Name
Fractions, Decimals, and Percents Write the correct answer.
1. Amir had
3 4
of a dollar and Dale had $0.83. Who had more money?
3. The winning times for the men’s
100-meter run in three recent Olympics are given below. Put the winning times in order from fastest to slowest. 19 8 8 1 9 92 1 99 6 9.92 sec 9.96 sec 9.84 sec
2. Kate read the number 0.345 as “345
hundredths.” Was she correct? Explain.
4. The winning times for the women’s
400-meter relay in the 1988, 1992, and 1996 Olympics are given below. In which year was the fastest time run? 19 8 8 1 99 2 19 9 6 41.98 sec 42.11 sec 41.95 sec
Choose the letter for the best answer.
5. Polly listens to 5 hours of classical
music each week. Which is the best estimate of how many minutes of classical music she listens to in 19 weeks? A 4,000 min B 6,000 min C 8,000 min D 10,000 min 7. The distance from Shania’s house to 3 5
school is of the distance from Faith’s house to school. What percent of the distance that Faith travels each morning does Shania travel? A 3.5% C 50% B 35% D 60% t r u o c r a H ©
6. Nancy wants to buy 24 sodas for her
party. A 6-pack of soda costs $2, including tax. Which expression can be used to find the total cost of the sodas that Nancy wants to buy? F 24 $2 G 6 $2 H (24 6) $2 J (24 6) $2 8. Park ran 0.8 mile. Nicholas said that he
ran the same fraction of a mile. How far did Nicholas run? 4 mi 5 3 G mi 5
F
9. Write About It Explain how to compare the fraction
decimal 0.7 to see which is greater.
H
J
1 mi 5 1 mi 8
2 and the 3
Problem Solving
PS 39
LESSON LESSON 9.1 9.1
Name
Estimate Sums and Differences Write the correct answer. 1
1. Jon wo won n 3 of his his tenn tennis is matc matche hes. s. Tori
won 0.45 of her matches and Tim won 2 5 of his. If they all played the same numb nu mber er of matc matche hes, s, who who wo won n the the most most??
3
3. Ma Mary ry has has 4 gal of milk. She need eeds to use 1 3
1 4
gal in one recipe and gal in another recipe. Does she have enough milk?
2. Working Working on the computer, Julie used
15% of the available time. At that point 60% of the time was left. How much of the computer time was available before Julie worked?
4. Thad practiced playing the flute for
134 hr before dinner and 2 81 hr after dinner. About how long did Thad practice playing his flute?
Choose the letter for the best answer. 5. Sid has two pieces of fabric. One piece
is 152 yd and the other piece is 16 yd. Estimate the total amount of fabric he has.
1 A – 4 yd 1 B – 2 yd
F
2 ft
D 1 yd
G
1–2 ft
7. On Monday 45,789 people attended
a game in the stadium. On Tuesday 36,984 people attended a game in the stadium. Which is the best estimate of how many more people attended the game on Monday than on Tuesday? Tuesday? A 7,000 B 8,000 C 9,000 D 10,000
fraction to 0,
PS 40
1 , 2
1
H 1 ft J
1 – 2 ft
8. Nancy measured her stride to be
45.7 cm. She then went for a walk and counted 352 steps. Which expression can be used to find the distance she walked in centimeters? 352 45.7 G 352 45.7 H 352 45.7 J 352 45.7 F
Explain how you know whether to round a or 1.
Problem Solving
1
his friend. About how much twine does he have left?
–3 yd 4
C
9. Write About It
5
6. Kyle has 18 ft of twine. He gave 2 ft to
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LESSON 9.3
Name
Add and Subtract Fractions Write the correct answer. 1. List all the factors of 24.
2. What is the prime factorization
3 3 5 7 11 11 written in exponent form?
3
3. Olga has 4 yd of blue ribbon. She also
has 38 yd of red ribbon. r ibbon. How much ribbon does she have altogether?
7
4. Bruce walks 8 mi to school and 1
his friend friend walks walks 3 mi to school. How much farther does Bruce have to walk than his friend?
Choose the letter for the best answer. 5. What is the prime factorization of 48?
22222 C 22223 D 22233
B
1 – 8 gal 3 G – 8 gal
F
1
7. The third-grade class painted 4 of the
school fence, the fourth-grade class painted 15 of it, and the fifth-grade class class painte painted d 25 of it. How much of the fence has been painted?
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1
on one proje project ct and and 4 gal on another project. How much paint does he have left?
A 2 2 3
4 A – 5 13 — B 15 17 — C 20 9 — D 10
7
6. Todd had 8 gal of paint. He used 2 gal 1
5 H – 8 gal 5 J – 3 gal
8. In the last four days, the local
swimming pool has been used by 348 people, 276 people, 573 people, and 621 people. Which is the best estimate of the total number of people who have used the pool in the last four days? 1,850 G 2,000
F
H 2,200 J
2,350
Explain how you found the least common denominator for Exercise 6.
9. Write About It
Problem Solving
PS 41
LESSON 9.4
Name
Add and Subtract Mixed Numbers Write the correct answer. 15
1. Write 25 in simplest form.
2. List all of the factors of 42.
3. Devon worked on her homework for
4. Victoria taped a piece of ribbon that
243
1 12
hr on Friday and hr on Saturday. How much longer did she work on Friday than on Saturday?
was 3 31 yd long to a piece that was 1 41 yd long. How long are the two pieces of ribbon together?
Choose the letter for the best answer. 5. What is the GCF G CF of 30 and 40?
A 2
10 C 30 D 40
B
1
7. Hank walks 44 blocks to school and
6 38
his friend Jonas walks blocks to school. How much farther does Jonas have to walk? 7 A 1– 8 blocks 1 B 2– 8 blocks 1 C 2– 4 blocks 3 D 2– 8 blocks
45
6. What is 7 written as a mixed number? 3 F 7– 5 3 G 6– 7 5 H 6– 7 5 J 5– 7 8. At a flea market, Theresa bought
523 yd of lace trim and 8 43 yd of ribbon trim. How much trim did she buy altogether? 5
F
13–8 yd
G
— yd 1312
5
7 — H 1312 yd 5 — J 1412 yd
9. Write About It When adding mixed numbers, what do you do
when the fraction part of the sum has a numerator that is greater than the denominator?
P S 42
Problem Solving
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LESSON 9.6
Name
Subtract Mixed Numbers Write the correct answer. 2
52
1. Write 79 as a fraction.
2. Write 11 as a mixed number or whole
number.
1
3. The nature club hiked 5 8 km on
Saturday and 4 34 km on Sunday. How much farther did they hike on Saturday than on Sunday?
1
4. Rachel bought 8 2 yd of fabric. fabr ic. She used
423 yd to make a blouse and skirt. s kirt. How much fabric did she have left?
Choose the letter for the best answer. 5. What is the LCM of 4, 7, and 8?
2 G 4 H 5 J 7
A 14
F
28 C 56 D 224
B
1
7. The electrician had 45 2 ft of wire.
He used used 378 ft of it to wire a CD player. How How much wire wire did he have have left? 5 A 41– 8 ft 7 B 41– 8 ft 3 C 42– 8 ft 5 D 42– 8 ft
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9. Write About It
6. What is the GCF of 20 and 28?
2
8. In 1998, a northern city had 24 3 ft of
snow. In 1999 that same city had only 843 ft of snow. snow. What was the difference in the snowfall amounts? 7
F
16–8 ft
G
16–8 ft
1
11 — ft H 1512 7 — J 1512 ft
Explain how to write a mixed number as
a fraction.
Problem Solving
P S 43
LESSON 9.7
Name
Summarize To summarize is to stat state e some someth thin ing g in a brie brieff way way. Kn Kno owing wing ho how w to summ summari arize ze infor informa mati tion on is a usef useful ul skil skill. l. Some Someti time mess draw drawin ing ga diagr diagram am to displ display ay inform informati ation on is a goo good d way to summa summarize rize information.
VOCABULAR VOCA BULARY Y
summarize
Read the following problem.
Rosie walks dogs to earn money. money. She leaves home with her own dog, dog, Loki, Loki, and picks picks up up a poodle, poodle, Dante, Dante, 21 mi east of her home. Next Next she gets Noni, Noni, another another poodle, who lives lives 43 mi east of Dante. Another 14 mi east, east, she picks picks up a spaniel, spaniel, Higgins. Higgins. Rosie then drops drops off the dogs at their their houses houses in this order: order: first Loki, Loki, then Dante, Dante, then Noni, Noni, then Higgins Higgins.. Then Rosie Rosie walks walks home. How How far have Rosie and each dog walked? 1. Draw a diagram to summarize the information.
2. Solve the problem.
Rosie walked
mi.
Loki walked
Noni walked
mi.
Higgins walke alked d
mi.
Dante walked
mi.
mi.
Draw a diagram to summarize the information. Solve the problem. 3. Bill, Samantha, and Tim are doing a science project together.
Samantha lives 170 mi west of the school. Tim lives 52 mi west of Samantha. Bill lives 31 mi east of the school. After school, they walk to Bill’s house to pick up some equipment. Then they go to Tim’s house to work. When they are finished, Bill and Samantha walk home. How far did each student walk after school? t r u o c r a H ©
Bill walked PS 44
mi.
Reading St Strategy
Samantha walked
mi. Tim walked
mi.
LESSON 10.1
Name
Estimate Products and Quotients Write the correct answer. 1. The water behind a dam begins rising at
1 45
a rate of in. per hr during a spring thaw. The water will spill over the dam if it rises 72 in. Estimate the number of hours before the dam will overflow.
1
3. Mikel used 3 6 qt of potting soil per plant
to pot 15 small shrubs. About how much potting soil did Mikel use for all of the shrubs?
2. Dillon wants to survey 1 out of every 10
adults in his neighborhood between the ages of 25 and 40. He has generated a list of 220 people in this age group. How many people should he survey?
4. Ann is 136.8 centimeters tall tall and
Theresa is 128.9 centimeters tall. How much taller is Ann than Theresa?
Write the letter of the best answer. 3
6. Nikki’s 8 dogs each get 4 6 c of dry dog
7. Karl found that a garden measured
8. About how how many 3 lb boxes of raisins
chip cookies. About how many packages can be filled from a 44 lb container of chocolate chip cookies? A about 33 packages B about 44 packages C about 60 packages D about 66 packages 478 yd by 1256 yd. Which Which is the best estimate of the area of the garden? 2 A (4 12) yd 2 B (4 13) yd 2 C (5 12) yd 2 D (5 13) yd
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1
5. Al is filling 4 lb packages of chocolate
food every day. Estimate the total amount of dry dog food that she provides for the dogs each day. F about 4 c G about 12 c H about 33 c J about 100 c 2
can be filled from a 15 12 lb bag of raisins?
about 10 boxes G about 15 boxes H about 20 boxes J about 25 boxes F
9. Write About It When is it appropriate to use an estimate?
Problem Solving
PS 45
LESSON 10.2
Name
Multiply Fractions Write the correct answer. 12
1. Write 18 in simplest form.
2. List the first four multiples of 9.
3. Write the multiplicati multiplication on shown by by the
4. Write Write the multiplication multiplication shown by by the
model. Then write the product.
model. Then write the product.
Write the letter of the best answer. 5. Which is the missing number? number?
7 8
5
B
C
2
5, 10 G 2, 5, 10, 25 H 1, 2, 5, 10, 25, 50 J 1, 2, 5, 10, 15, 20, 25, 50 F
7 10
3 D 4
A 1
6. Which is a list of all the factors of 50?
3
7. Luke exercises 4 hr each morning. He 1
spends 3 of this time riding an exercise bike. What part of an hour does Luke spend riding the bike?
A
1 hr 4
C
1 hr 2
B
1 hr 3
D
3 hr 4
8. Sally is reading a book for school. She
has read 27 pages every day for the last 15 days. How many pages has Sally read so far? F 42 pages G 300 pages H 405 pages J 450 pages
9. Write About It Look at the model in Problem 3. Explain how you can
tell which two fractions are factors and which fraction is the product.
PS 46
Problem Solving
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LESSON 10.3
Name
Multiply Mixed Numbers Write the correct answer. 1. Rewrite the problem by changing each
mixed number to a fraction. Then multiply; write the answer in simplest form. 2 3
2. Rewrite the problem by changing each
mixed number to a fraction. Then multiply; write the answer in simplest form.
2 5
1 4
4 3
2 9
7 5
1
3. Peter needs 8 of a cup of butter to 1
make cookies cookies and 8 of a cup of butter to make bread. How How much much butter in all does Peter need to make cookies and bread?
3
4. Darla needs to exercise 4 hour each day.
So far today she has exercised for hour. How much longer does Darla need to exercise today?
1 2
Write the letter of the best answer. 5. In the long jump, Bryn’s longest jump is
1413
1 18
ft. April’s best jump is times as far as Bryn Br yn’’s. What is April’s April’s longest lo ngest jump? 1 8 1 D 16 ft 2
11 A 13 ft 24
B
C
11 24
15 ft
16 ft
1
7. Derick spent 1 2 hours cleaning up after
an event. Charles spent 2 14
times as many hours as Derick did cleaning up. Which number sentence sentence can be used to find c , the amount of time Charles spent cleaning up?
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1 1 A c 2 1 4 2 1 1 B c 2 1 4 2
1 1 4 2 1 1 D c 2 1 4 2
C
c 2 1
6. Andrew has a collection collection of 36 baseball
cards. Jared has 1 56 times as many baseball cards as Andrew. How many baseball cards does Jared have in his collection? F 38 cards H 66 cards G 60 cards J 396 cards
8. Sam worked four different jobs last
week. On the first job he earned $28.75, on the second job he earned $18.03, on the third job he earned $50, and on the fourth job he earned $68.93. Which Which is the best estimate of how much Sam earned last week? F $200 H $120 G $170 J $100
9. Write About It When rewriting rewriting a mixed number as a fraction, why do
you multiply the whole whole number by the denominator denominator of the fraction?
Problem Solving
PS 47
LESSON 10.5
Name
Divide Fractions and Mixed Numbers Write the correct answer. 5
1. Write the reciprocal reciprocal of 9.
1
3. Bill used 7 8 cups of flour to bake a batch
of bread. He started with 12 12 cups of flour. Does Bill have enough flour to bake another batch of bread? Explain.
2. Write Write the reciprocal reciprocal of 15.
3
4. Nancy has 194 feet of wallpaper
border. border. She bought an an additional 5 238 feet. How much wallpaper border does Nancy have in all?
Write the letter of the best answer. 5. Which is a list of all the factors of 26?
multipl multiples es of 5? F 1, 5, 10, 15 G 5, 10, 15, 20 H 5, 15, 25, 35 J 10, 20, 30, 40
A 1, 2, 3, 9, 13, 26
1, 13, 26 C 1, 2, 13, 26 D 26, 52, 78, 104
B
7. Julie is hanging wallpaper in her house.
5 12
The job requires rolls of wallpaper. If she can hang 1 34 rolls of wallpaper each hour, how long will it take her to complete the job? 1 A 2 hr 4 1 B 3 hr 7
6. Which is a list of the first four
3 4 1 D 7 hr 4
C
3 hr
8. Evan has has a board that is 8 feet long. long. He
wants to cut it into pieces that are are 34 foot each. Which Which number sentence can be used to determine p , the number of pieces he will get from the board? 3 4 3 G p 8 4
F
p 8
3 H p 8 4 3 J p 8 4
9. Write About It Explain what a reciprocal is and how to find the
reciprocal of a fraction and of a whole number. t r u o c r a H ©
PS 48
Problem Solving
LESSON 10.6
Name
Multiple-Meaning Words Some problems contain words that have have more than one meaning. The words may have the same spelling and different pronunciations or the same sound but different meanings. You You can use information given in the problem to determine which meaning of the word is being used. Read the following problem.
VOCABULAR VOCABU LARY Y
multiplemeaning
The Continental Divide, or Great Great Divide, Divide, is the watershed of North America. This means that it is the high high point of land that separates the waters that flow east from those that flow west. The chart below shows precipitation information for the Continental Divide. How How much greater is the annual precipitation precipitation at the highest elevation than at the lowest elevation? Elevation
4,000–7,000 ft
7,000–11,000 ft
11,000–14,000 ft
1 1 in .
2 0 in .
4 0 in .
Annual Precipitation
1. Which word word has both a mathematical meaning meaning and an everyday meaning? 2. What operation is needed needed to solve the problem? 3. Solve the problem.
Read each problem carefully. Then solve. Mr. Mr. Winston is building an addition onto his house. The area of the t he addition is 150 square feet. The contractor is charging him $200 per square foot. How much will the addition cost? 4. Which word word has both a mathematical meaning meaning and an everyday meaning? 5. What operation is needed needed to solve the problem? 6. Solve the problem.
Mr. Winston’s house is in a suburban area. The original house had an area of 1,750 square feet. When construction is complete, what will be the area of the new house? t r u o c r a H ©
7. Which Which word word has both both a mathe mathemati matical cal meaning meaning and an everyday everyday meaning meaning?? 8. What operation is needed needed to solve the problem? 9. Solve the problem.
Reading Strategy
PS 49
LESSON 10.7
Name
Algebra: Fraction Expressions and Equations Write the correct answer. 1. Use GCFs to simplify the factors. Write
the new problem. 2 5
2. Use GCFs to simplify the factors. Write
the new problem. 5 9
4 7
3 8
3. A 45-inch-tall rain rain barrel is filling up 3 4
with water at a rate of in. per hr. The time it takes to fill can be found by solving the equation 45 34 h for h. How How long will it take the rain barrel to fill?
4. Some videotapes are made so that the
first 113 ft of the tape cannot be recorded on. Find how much of a 180-foot videotape can be recorded on by solving the equation 180 t 113 for t.
Write the letter of the best answer. 3
5. x 5 is the solution to which of the
following equations?
3 A 3 x 5
B
3 5 x
2 1 x 5 5 D 3x 3
C
7. Carlos rode his skateboard for 48 min
each day for the last 25 days. How many hours has Carlos ridden on his skateboard over the last 25 days? A 20 hr B 23 hr C 25 hr D 1200 hr
6. What is the value of the expression expression 3 7
3
7
F
y, for y 37?
3 7
G 0 H J
9 49 12 49
8. Brad bought a new basketball for
$35.87, including tax. He gave the cashier a $100 bill. How much change did the cashier give back to Brad? F $75.87 G $64.87 H $64.13 J $35.87
9. Write About It How is evaluating expressions involving fractions
different from evaluating expressions that do not involve fractions?
PS 50
Problem Solving
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LESSON 11.1
Name
Understand Integers Write the correct answer. 1. Write Write an integer that represents represents the
situation.
2. Write an integer integer that represents represents the
situation.
52 feet above sea level
3. There are three bags of apples. They
weigh 3.1 pounds, pounds, 3.2 pounds, and 3.05 pounds. Write the weights in order from greatest to least. Use >.
losing 25 yards in football
4. A hiker is 30 feet feet above above sea level, level, on a
cliff. His friend is 15 feet below sea level, in a valley below the hiker. What is the difference in elevation of the two hikers?
Choose the letter for the best answer. 5. Maggie went deep-sea diving. She
explored a sunken ship at 78 feet below sea level and a reef at 45 feet below sea level. Which Which is the position of the sunken ship written as an integer? A 78 45 B C 45 D 78
7. Luis scored 98, 88, 76, 78, 98, and 65 on
his last 6 test. What is the range of Luis’s test scores? A 98 B 83 C 33 D 22
6. Jon was in a hot-air balloon at 23,500
feet above sea level. Phil was in a hot-air balloon at 15,200 feet above sea level. Which is the elevation of Jon’s hot-air balloon written as an integer? F 23,500 15,200 G H 15,200 J 23,500
8. Kim works between 32 and 38 hours a
week. Which is a reasonable estimate estimate of how many hours Kim works in a year? F Less than 2,000 hr G Between 2,000 and 3,000 hr H Between 3,000 and 4,000 hr J Between 4,000 and 5,000 hr
9. Write About It On a number line, what value would best represent t r u o c r a H ©
sea level? Explain.
Problem Solving
PS 51
LESSON 11.2
Name
Rational Numbers Write the correct answer. 1. Write 832 as a rational number in the
2. Find a rational number between 18 and 13.
3. Write an integer integer that represents represents the
4. Write Write an integer that represents represents the
a form b .
situation. climbing up a cliff 856 ft
situation. a drop in temperature of 48 degrees
Choose the letter for the best answer. 5. The temperature outside was 36°F. The
temperature inside was 72°F. Which is the inside temperature written as an integer? A 72 B 36 C 36 D 72
7. The local newspaper wants to use a
graph to report the number of tourists that have visited the town each month for the last year. Which type of graph should the newspaper use? A bar graph B line graph C histogram D line plot
6. Which rational rational number is equivalent
to 259 ? 2 2 9 3 G 2 9 24 H 9 25 J 9 F
8. Nancy checked the gauge on her
propane tank and found that the tank was between 14 and 12 full. Which fraction could represent how full the tank was when Nancy Nancy checked? F 7 16 1 G 1 16 9 H 16 13 J 16
a 9. Write About It Explain how 0 can be written in the form b .
PS 52
Problem Solving
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LESSON 11.3
Name
Compare and Order Rational Numbers Write the correct answer. 1. Compare the rational numbers and
2. Compare the rational numbers and
order them from least to greatest.
order them from least to greatest.
4.2, 4.083, 54, 92
3. Find a rational number between 38 and 34.
514, 538, 5.1, 5.4
4. Write 2334 as a rational number in the a form b .
Choose the letter for the best answer. 5. The temperature outside was 67°F on
Monday and 75°F on Tuesday. Which is the temperature on Monday written as an integer? A C 67 75 B D 75 67
7. Larry is making punch for a large
gathering of people. The recipe calls for 3 scoops of punch powder for every 10 cups. He needs to make 85 cups. Which is a reasonable estimate for how many scoops of powder Larry needs to use? A 18 scoops B
22 scoops
26 scoops D 30 scoops
C
6. Jason’s times for the 100-meter dash are
11.72 sec, 11 34 sec, 1145 sec, and 11.85 sec. What is his lowest time time for this race? F 114 sec H 113 sec 5 4 G 11.72 sec
J
11.85 sec
8. Which group of rational rational numbers is in
order from least to greatest? 2 3
6 8 7 9 G 3.4, 31, 3.3, 3.1 3
F
H
J
,
4 5
,
,
8.7, 8.07, 8.007, 8.7 21, 21, 0, 21 2
3
4
9. Write About It Explain how you would order a group of rational
numbers in which some are positive and some are negative. t r u o c r a H ©
Problem Solving
PS 53
LESSON 11.4
Name
Analyze Information The information in a problem can offer clues about how to solve it. Analyze, or look carefully at, the problem. Underline or record details that help you understand the problem.
VOCABULARY VOCABU LARY
analyze
Read the following problem.
Abigail, Bart, Carlotta, and Donald each play a different sport, soccer, soccer, basketball, basketball, ice hockey hockey,, or lacrosse, lacrosse, but not necessa necessarily rily in that order. order. Abigail plays a sport that that uses a round ball. Carlotta needs a stick to play her sport. Donald can’t can’t play his his sport outside in the summer. summer. Bart’s Bart’s sport isn’t isn’t played on grass. grass. Which sport does each play? 1. Analyze the problem. Underline Underline or record record details that will will help you solve the
problem. Which Which sport does each clue suggest?
2. Solve the problem.
Analyze the problem. Underline or record details that help you reach an understanding. Then solve. 3. Ari, Latanya, Mary, Mary, and Jed each make a
different dinner course, soup, salad, main course, or dessert, but not necessarily in that order. Mary is the only one whose recipe doesn’t require vegetables. Latanya is the only one who doesn’t need to use a stove. Jed’s course is the only one that requires a spoon. What did they each prepare? prepare?
4. Fred, Georgia, Hal, and Inez all
participated participated in the Geo-Bee. Their scores were 92%, 75%, 100%, and 83%, but not necessarily in that order. Georgia’s score was 43 of Hal’s score. Inez’s score was 9 points less than Fred’s score. What score did each receive? t r u o c r a H ©
PS 54
Reading St Strategy
LESSON 12.2
Name
Algebra: Add Integers Write the correct answer.
1. Find the missing number in the pattern.
2. Find the missing number in the pattern.
325
3 1 2
314
3 0 3
303
3 1 4
3 1 2
3 2 5
3 2 1
3 3 6
3 3
3 4
3. Carmen wants to share her money with
4. Five students were waiting in line to
her cousin Jasmine. Together they have $48. If Carmen gives Jasmine $3, they will each have the same amount of money. How much money does each girl have now?
return books at the library. There There were 3 students ahead of John. There were 3 students behind Leila. Carla was first in line. Paul was last. What number in line was Sara?
Choose the letter for the best answer.
5. On three consecutive plays, a football
6. By 10:00 A.M., the temperature had
team lost 2 yards, gained 5 yards, and gained 7 yards. Which expression could be used to find the total yards gained by the team on these three plays? A 2 5 7 C 2 5 7 B 2 5 7 D 2 5 7 7. Kirk is 131.9 centimeters tall and Thad is
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risen 7°C from a morning low temperature of 15°C. What was the temperature at 10:00 A.M.? F 8°C H 7°C G 7°C J 8°C 8. Patty had 25.8 meters of wire to install
162.3 centimeters tall. Which is the best estimate of how much taller Thad is than Kirk? A 10 cm C 30 cm B 20 cm D 40 cm
lights in her backyard. She used only 19.4 meters. How much wire was left? F 7.4 m H 5.4 m G 6.4 m J 3.4 m
9. Write About It Explain why 8 3 3 8.
Problem Solving
PS 55
LESSON 12.4
Name
Algebra: Subtract Integers Write the correct answer.
1. Find the missing number in the pattern.
2. Find the missing number in the pattern.
422
2 1 3
413
2 0 2
404
2 1 1
4 1 5
2 2 0
4 2 6
2 3 1
4 3
2 4
3. Five years ago, Sean was three times as
old as his brother. Today Sean is twice as old as his brother. How many years older than his brother is Sean? How old is Sean now?
4. For one week of work, Roberto earned
$615. He worked 25 hours at his regular pay of $15 per hour. hour. He also worked overtime hours, for which he was paid $20 per hour. How many overtime hours did Roberto work?
Choose the letter for the best answer.
5. Which addition problem is equivalent to
the subtraction problem8 17? A 8 17 B 8 17 C 8 17 D 8 17 7. John collected n gadgets. Frank gave
him 18 more gadgets. John now has 51 gadgets. Which Which equation could be used to find the number of gadgets John had before Frank gave him more? A n 18 51 C n 51 18 B n 51 18 D n 18 51 9. Write About It Explain why 3 2 2 3.
PS 56
Problem So Solving
6. Four hours ago, the temperature outside
was +6°F. +6°F. Since then the temperature has dropped 13°F. What is the temperature outside now? F 19°F H 7°F G 7°F J 19°F 8. Maria keeps old records stored in
special boxes. Each box can hold 45 old records. If she has 16 boxes full of old records, how many old records does she have? F 690 records H 710 records G 700 records J 720 records
t r u o c r a H ©
LESSON 13.2
Name
Algebra: Multiply Integers Write the correct answer.
1. Find the missing number in the
2. Find the missing number in the
pattern.
pattern.
3 2 6 3 1 3 3 0 0 3 1 3 3 2 6 3 3
428 414 400 4 1 4 4 2 8 4 3
3. Compare the rational numbers and
4. Compare the rational numbers and
order them from least to greatest.
order them from greatest to least.
3 4 , 0.01, 0.55 5 25
7 6 1.8, 1.74 4 3
,
, ,
Choose the letter for the best answer.
5. The temperatur temperature e dropped by by 4° each
hour from midnight until 5 A .M. How much did the temperature change in that time? A 24° B 20° C 20° D 24° 7. Which rational number is between
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1.45 and 1.5? A 1.4 B 1.44 C 1.48 D 1.52 9. Write About It Explain why 5
6. Stock in XYZ.com dropped 8 points
each day from Monday to Friday. Friday. How How much did the stock stock price change change that week? F 48 points G 20 points H 40 points J 56 points 8. Which rational number is not between 2 7 and ? 3 8
19 24 5 G 6
F
H J
3 4 1 2
2 2 5.
Problem Solving
PS 57
LESSON 13.3
Name
Algebra: Divide Integers Write the correct answer.
1. Find the missing number in the
2. Find the missing number in the
pattern.
pattern. 6 2 3 4 2 2 2 2 1 0 2 0 2 2 1 4 2
12 3 4 12 2 6 12 1 12 12 1 12 12 2 6 12 3
3. Compare the rational numbers and
order them from least to greatest. 1
4 , 5 5.62, 5. 5.7, 5 2
5 4. Write 48 as a rational number in the a 8 . form b
5
Choose the letter for the best answer.
5. The temperatur temperature e changed 28° over over a
period of 7 hours. If the temperature dropped at a constant rate, what was the change per hour? A 7° B 4° C 1° D 7° 7. Grace scored 8, 7, 8, 8, 10, 6, 7, 8, 7, 6,
and 9 on her last 11 quizzes. Grace scored 8 most of the time. What term describes the most frequent score? A mean C mode B median D range
9. Write About It Explain why 8
PS 58
Problem So Solving
2 2 8.
6. A theme park recorded 1,800 fewer
visitors this year than last year. What was the shortage of visitors in an average month? F 150 visitors G 140 visitors H 130 visitors J 120 visitors 8. Mr. Frank earns $4,987.34 each month
and Mrs. Frank earns $5,198.22 each month. Estimate how much the two earn together each month. F $8,000 H $10,000 G $9,000 J $11,000
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LESSON 13.4
Name
Combine Operations with Integers Write the correct answer.
1. The Li family camped in a valley at an
altitude of 25 ft, or 25 ft below sea level. During the morning they hiked to the top of a hill where the altitude was 575 ft, or 575 ft above sea level. What is the difference dif ference in altitude of the two places?
3. At 8 A .M. the outside temperature was
10° C. By noon the temperature had risen 15° C. Between noon and 5 P.M. the temperature dropped 12° C. What was the temperature tempe rature at 5 P.M.?
2. Renee’s checking account allows her to
write checks for more than is in her account. She began with a balance of $326 and, after writing some checks, ended with a balance of $108. What was the total amount of the checks she wrote?
1 are green, 4. In a box of 48 candies, 1 4 4 are red, and 12 are orange. If you give
away all the candies except the green ones, how many candies will you have given away?
Choose the letter for the best answer.
5. Chris bought a pen for $0.79. He gave
the cashier a $1 bill. The cashier accidentally gave him $0.35 in change. How much extra did the cashier accidentally give Chris? A $0.44 C $0.14 B $0.21 D $0.06 7. A movie you want to see begins at
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3:00 P.M. and ends ends at 5:15 5:15 P.M. If you leave leave your house 30 min before the movie begins and arrive home 15 min after it ends, how long are you away? A 2 hr 45 min B 3 hr C 3 hr 15 min D 3 hr 30 min
6. Joann dove from a 6-ft-high diving
board into a 9-ft-deep pool and then touched the bottom of the pool. How far did she travel from the top of the board to the bottom of the pool? F 3 ft H 15 ft G 6 ft J 54 ft 8. You You buy several boxes of markers for
an art project and spread them out on your desk. Adding 3 other markers that you already had, you now have 43 markers. How many markers could possibly come in a box? F 6 markers G 7 markers H 8 markers J 9 markers
9. Write About It How did you decide how many markers could have
been in each box?
Problem Solving
PS 59
LESSON 14.1
Name
Write Expressions Write the correct answer.
1. James is baking bread for his class
picnic so he needs to triple his bread recipe. The recipe calls for 2 43 cups of flour. How How much flour should he use?
3. Fred scored 8 points more than Dale
during the game. Write Write an algebraic expression that represents the number of points Fred scored. Let b represent the number of points Dale scored.
2. The length of the athletic field is three
times its width. Write an algebraic expression that represents the length of the field. Let l represent the length, and w, the width of the field.
4. Some of the students will make
sandwiches for the picnic. For each sandwich, they need 18 lb of turkey. How much turkey is required to make 46 sandwiches?
Choose the letter for the best answer.
5. John’s dog, Rocky, weighs 15 kg.
How many grams is that? A 150,000 g B 15,000 g C 1,500 g D 150 g
7. Patricia wants to share her package of
30 pretzels equally among her 5 friends and herself. How many pretzels will each person receive? A 4 B 5 C 6 D 7
6. For the class trip the bus driver
charges $45.00 plus $3.10 for each student. Which expression represents the cost for n students? F 45 3.1n G 45 3.1n H 45 3.1n J 45 3.1n 8. Joan bought 5 yards of fabric for $2.85
a yard, including tax. Which expression could be used to find the change Joan received if she gave the cashier $50? F 50 (5 2.85) G 50 – (5 2.85) H 50 – (5 2.85) J 50 5 2.85
9. Write About It Give examples of phrases that can usually be translated into
subtraction expressions.
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Problem So Solving
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LESSON 14.2
Name
Evaluate Expressions Write the correct answer.
1. Write an expression for one hundred
less than the product of 5 and a number, c . Evaluate for c 15.
3. Compare the rational numbers and
2. Four times a number, z , is added to 12.
This sum is then divided by 2. Write an expression, then evaluate for z 8.
9
4. What is 6 written as a decimal?
order them from greatest to least. 1
1 , 6 , 6.05, 6.3 6 10 4
Choose the letter for the best answer.
5. To evaluate the numerical expression,
6. To evaluate the numerical expression,
in which order would you perform the operations?
in which order would you perform the operations?
23 16 8 2
15 3 2 7
A add, subtract, multiply
subtract, multiply, add C multiply, add, subtract D subtract, add, multiply
B
7. Greg made deposits to his checking
account of $105.32, $295.00, and $62.50. He wrote checks for $129.00, $57.43, $6.98, and $357.19. He started with a balance of $133.89. What is his present balance? A $221.67 C $46.11 B D $221.67 $46.11 t r u o c r a H ©
divide, subtract, multiply G divide, multiply, subtract H multiply, subtract, divide J subtract, divide, multiply
F
8. Blaine earned $115.89 on Monday, Monday,
$87.33 on Tuesday, $121.08 on Wednesday Wednesday,, $68.03 on Thursday, and $110.20 on Friday. What is a reasonable estimate for how much Blaine earned during the five days? F $300 H $500 G $400 J $600
9. Write About It Explain the difference between an algebraic
expression and a numerical expression.
Problem Solving
PS 61
LESSON 14.4
Name
Expressions with Squares and Square Roots Write the correct answer.
1. A square room needs exactly 169
square tiles to cover the floor. Each tile is 1 foot on a side. If a wallpaper border is hung near the ceiling, how long will the border be?
3. Connie loves dressing up in strange
outfits. She has 4 pairs of jeans: a red pair, a striped pair, a green pair, and a yellow pair. pair. She also has 3 tops, none of which match any of the jeans. How many strange outfits can Connie make from these clothes?
2. Another square room, 12 ft by 12 ft,
was tiled with the same square tiles. The tiles in a 4 ft by 2 ft area in the center of the room were painted. How many tiles are unpainted?
4. In basketball, there are 2-point and
3-point baskets and 1-point foul shots. During one game, Felipe scored 26 points. He scored at least five 2-point baskets and at least three 3-point baskets. What is the greatest number of foul shots Felipe could have made?
Choose the letter for the best answer.
5. Kate is three times as old as her cousin,
Pam. The girls found an interesting relationship between their ages. When Pam is twice her current age, how old will Kate be? A Twice as old as Pam 1 B 2 times as old as Pam 2 C 3 times as old as Pam D 4 times as old as Pam 7. A contractor has 7 boxes of 1-ft
square tiles. Each box contains 20 tiles. What is the length of the side of the largest square he can cover with these tiles? A 10 ft C 12 ft B 11 ft D 13 ft
6. Scot Scottt is readi eading ng a no nove vell that that has has 70
page pages. s. If he mult multip ipli lies es the the nu numb mber er of page pagess he has has alr already eady read ead by 5 an and d then then subt subtra ract ctss 5 he will will have have the the nu numb mber er of page pagess in the the book book.. How many many page pagess has has Scott Scott alread already y read? read? F 8 G 12 H 15 J 18 8. A contractor has 8 boxes of 1-ft square sq uare
glass blocks. Each box contains 10 blocks. To To build a square wall, what is the greatest number of blocks that can be used? F 100 H 80 G 81 J 64
9. Write About It Explain how you eliminated some answer choices
in Exercise 8.
PS 62
Problem So Solving
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Name
LESSON 15.1
Connect Words and Equations Write the correct answer.
1. A redwood tree that is 320 ft high is 6
times the height of a pine tree. Write an equation.
3. In the school baseball game, the
number of runs scored by the winning team was 6 more than the 3 runs scored by the losing team. Write Write an equation.
2. The school-supplies store sold 35
review books for a total of $278.25. What was the price pr ice of each book?
4. It takes Shakeia 12 min to walk to
school. She also stops for 3 min at a store for a snack. If she must be at school no later than 8:20 A .M., what is the latest she should leave home?
Choose the letter for the best answer.
5. To celebrate her birthday, Julie took 5
6. When the school held a cookie sale, sale, the
of her friends to the science museum. The total cost for the tickets was $40.50. Choose the correct equation. A t 6 40.50 B 6 t 40.50 C t 6 40.50 D 6t 40.50
sixth grade made $65 more than the fifth grade. The sixth grade made a total of $230. Choose the correct equation. F x 65 230 G 65x 230 H x 65 230 J 23 230 0 ÷ 65 x
7. Your Your new compact car averages 27
miles per gallon of gas and you are going on a 247-mi trip. About how many gallons of gas do you expect to use? A 14 gal C 10 gal B 12 gal D 6 gal
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8. A community is building 65 new
homes. The builder has 780 windows to use in the new homes. What is the average number of windows per house? F 12 windows H 15 windows G 14 windows J 16 windows
9. Write About It Explain how you chose the correct equation in Exercise 6.
Problem Solving
PS 63
LESSON 15.3
Name
Solve Addition Equations Write the correct answer.
1. The CN Tower in Toronto is 1,815 ft
tall. It is 1,353 ft taller than the Chicago Tribune building. Write and solve an addition equation to find the height of the Chicago Tribune building.
3. After paying for fo r 3 adults’ movie tickets
at $7.50 each, 2 children’s tickets at $4.75 each, and snacks, that cost a total of $9.50, Mr. Gould had $18.75 left. How much did he have before he arrived at the theater?
2. Yesterday Yesterday,, the temperature rose from
3°F at 6 A .M. to 15°F 15°F at 3 P.M. Write rite and solve an equation to find how many degrees the temperature increased.
4. During a basketball game, a player
attempted only three-point shots. He made one out of every two shots he tried and scored a total of 12 points. How many three-point shots did the player attempt during the game?
Choose the letter for the best answer.
5. The moving van traveled 455 mi in 8 hr
and 45 min. What was the average speed? A 58 mph B
55 mph
52 mph D 50 mph
C
7. The athletic field is 134 ft long. The
playground is 56 ft shorter. How long is the playground? Choose the correct equation and solution. A x 56 134; x 190 B x 56 134; x 190 C x 2 56; x 112 D x 56 134; x 78
6. A grandfather clock chimes every
15 min on the quarter hour. hour. How many times will it chime between 11:10 P.M. and 5:35 A .M.? F 26 H 24 G 25 J 23 8. Joann planted 38 more pansies than
tulips. She planted 72 pansies. How many tulips did she plant? Choose the correct equation and solution. F 2t 72; t 36 G t 38 72; t 110 H t 38 72; t 34 J 110 t 72; t 38
9. Write About It How did you use the Subtraction Property of
Equality to solve Exercise 1?
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Problem So Solving
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LESSON 15.4
Name
Solve Subtraction Equations Write the correct answer.
1. The weather service recorded rainfall
of 1.4 in., 2.1 in., 0.85 in., 0.45 in., and 1.75 in. during a 5-day period. How much rain fell during that period?
3. Lacy scored 6 points lower on her test
than her friend Opal. Lacy scored a 77 on her test. Write and solve an equation to find Opal’s score.
2. Tom had 6 bags of mulch to use in his
garden. Each bag contained 8 31 lb of mulch. What was the total weight of the mulch?
4. Jon cut down 12 old trees on his
property. He now has 17 trees left. Write and solve an equation eq uation to find how many trees Jon had on his property before he started cutting.
Choose the letter for the best answer.
5. Sixteen kittens were adopted from the
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6. Tom is 5 years older than his brother,
animal shelter today. There are 25 kittens left. How many kittens did the shelter have to be adopted? A x 16 25; x 41 B x 16 25; x 9 C 25 x 16; x 9 D x 9 16; x 25
Jerry. Jerry is 7 years old. How old is Tom?
7. Warren Warren ran a race in 65.71 sec. He came
8. Sharon is saving to buy a new car. The
in second, behind his friend Kyle. What else do you need to know to find out how much faster Kyle ran the race? A Who finished third B When the race started C Kyle’s race time D The length of the race
y 5 7; y 2 G y 7 12; y 19 H y 7 12; y 5 J y 5 7; y 12 F
car costs $18,595. She wants to have at least $5,000 saved before she buys the car. If she saves $350 a week, how long will it take her to save the money? F 14 wk H 16 wk G 15 wk J 17 wk
9. Write About It Explain why you use addition to solve a
subtraction equation.
Problem Solving
PS 65
LESSON 16.2
Name
Solve Multiplication and Division Equations Write the correct answer. 1. After exercising for 1 week, Ned was
able to do 60 push-ups. This was 5 times as many as he could do before. How How many push-ups could Ned do before? Write and solve an equation.
3. An Internet company’s company’s stock started
the week at $39.50 per share. share. The stock 1 3 went up 4 4, up 24, down 5, up 3 12, and down 214 for the week. What was the ending price of the stock at the end of the week?
2. All of the money raised by students at
the town carnival was divided among 7 charities. Each charity received $406. How much was raised at the carnival? Write and solve an equation. eq uation.
4. A state university has 18,500 freshmen,
14,780 sophomores, 16,290 juniors, and 15,820 seniors. About how many students attend the university?
Choose the letter for the best answer. 5. The soccer club is divided into 4 teams.
Each team has 20 players. Which equation can be used to find how many players are in the soccer club? s A – 4 20 B 4s 20
s 4 20 D s 4 20
C
7. Kara’s history grades for the term are
89, 83, 79, 90, 81, and 88. Find the mean of her grades. A 87 C 85 B 86 D 84
6. Each set of chair pads requires 3 yd of
fabric. Which equation can be used to find how many sets can be made from 27 yd of fabric? F g 3 27 G 27 g 3 g H – 3 27 J 3g 27
8. Craig can fit 28 books in each box. box. He
packed 21 boxes. Estimate how many books Craig has packed. F 200 H 600 G 400 J 800
9. Write About It What is the reciprocal of 8? Explain.
PS 66
Problem So Solving
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LESSON 16.3
Name
Use Formulas Write the correct answer. 1. One day in Florida, the temperature fell
to 10°C. What was the temperature in degrees Fahrenheit (°F)?
1
3. Maria’s muffin recipe requires 2 3 cups
of whole-wheat flour. She wants to triple the recipe. How much flour does she need?
2. Sally timed a snail crawling at the rate
of 3 feet per minute. How far would the snail travel in 8 min?
4. The Krazy Bread Co. sells Maria’s
muffins at $12.98 per dozen. What will it cost the Garden Club to buy 48 muffins?
Choose the letter for the best answer. 5. A jet pilot flew a distance of 3,311 mi
in 5 hr and 30 min. Find the plane’ plane’s average rate of speed. A 662 mi per hr C 602 mi per hr B 625 mi per hr D 595 mi per hr 7. Luis earned $23.58 working part-time
and an additional $12.25 from his regular allowance. How much money did Luis earn in all? A $11.33 C $35.83 B $35.73 D $36.73
6. Kerri had to heat the candy mixture to
a temperature of 190°F. What is the temperature in degrees Celsius (°C)? F 93.5°C H 83.1°C G 87.8°C J 80.7°C 8. The museum has admitted 58 people
per hour for the last 6 hours. During that period, 129 people have left. How many people are still in the museum? F 71 H 187 G 123 J 219
9. Write About it Think about the formula d rt . Explain how t r u o c r a H ©
distance is affected when time is increased or decreased and when the rate is increased or decreased.
Problem Solving
PS 67
LESSON 16.5
Name
Draw Draw Conclusions When you look at the evidence and apply what you know to find the answer, answer, you are drawing conclusions. Read the following problem.
Bobbie rode her bike to the Green Mountain Hiking Center Center.. She parked in the parking lot and hiked for a couple of hours. Bobbie Bobbie did not walk any loop loop more than than once. She walked walked 2.9 mi. What loops did she take?
Parking Lot to Center Spot Garden Loop River Loop Hilly Loop Forest Loop
0.5 mi 0.45 mi 0.6 mi 0.5 mi 0.8 mi
1. In the first column, complete the statements with information
contained in the problem. In the second column, write some conclusions you can draw. Examine the Evidence
Draw Conclusions
Bobb Bo bbie ie walk walked ed
.
She didn didn’’t walk alk
.
Bobbie Bobb ie must must have have walk walked ed from from the the parking lot to the center spot and back, ack, for for a total tal of . The total number of miles walked on the loops would be .
2. Solve the problem.
Solve. 3. The next day, Bobbie walked a total of
2.9 mi again. She walked some loops twice. Which loops did she walk?
4. The Hiking Center added a new path
called the Gazebo Loop. It is 0.55 mi long. Bobbie walked a total of 2.9 mi, which included the Gazebo Loop. She walked one loop twice. Which loops did she walk? t r u o c r a H ©
PS 68
Reading Strategy
LESSON 17.1
Name
Points, Lines, and Planes Write the correct answer.
1. Mr. Morgan wants to hang 13 triangles
on the bulletin board. If he puts a pin in each corner of each triangle, how many pins does he need?
3. What geometric figure is suggested by
the surface of a lake?
2. Jean’s bowling scores for the month
are 95, 130, 124, 103, 88, 137, 110, 121, and 127. Find the mean, median, and range.
4. What geometric figure is suggested by
the tip of a pencil?
Choose the letter for the best answer.
5. A company picnic was being held in
6. Which is a name for the figure?
the park. Every table was set to hold 12 people and all 132 tables were completely filled. How many people attended the company picnic? A 1,584 C 132 B 144 D 12
J L
K
F line segment JK G ray JK H line JK J 7. Fred’s Fred’s class of 32 students is planning
a trip to the zoo in school vans. If each van can hold 10 students, how many vans will be needed? A 1 C 132 B 2 D 4 t r u o c r a H ©
plane JKL
8. Which is a name for the figure? B A
line BA G ray AB H line AB J plane AB F
9. Write rite Abou Aboutt It What geometric figure would you get if you
joined the endpoints of two rays and pointed the rays in opposite directions?
Problem Solving
PS 69
LESSON 17.3
Name
Angle Relationships Write the correct answer.
1. The N, S, E, and W on a compass are at
90° angles angles from one another another. What are the measures of 1, 2, and 3?
2. Gavin designed a garden as shown.
What are the measures of and 4?
1, 2, 3,
N
3 1 2
W
E
48°
1 2
4 3
11 1 °
15°
S
3. During their last camping trip, the
scouts hiked 1.25 mi east, 2.1 mi south, 1.43 mi west, and 3.54 mi north. How far did they hike?
4. Gavin’s sister bought 2 flats of pansies
at $1.19 and 5 flats of zinnias at $1.98 each each.. How much much chan change ge did did she she recei eceive ve from $20.00?
Choose the letter for the best answer.
5. What are the measures of the two
complementary angles if one angle measure measure is 30° less than the the other? A 150°, 30° C 75°, 45° B 60°, 30° D 15°, 30° 7. How many bows can be made from 3 4
10 yd of ribbon if it takes yd of ribbon to make one bow? A 15 bows C 13 bows B 14 bows D 12 bows
6. What are the measures of the two
supplementary angles if one angle measure is three times the other? F 22.5°, 67.5° H 20°, 60° G 45°, 135° J 60°, 180° 8. Angela had $100. She spent $39.15 on a
sweater and earned $22.75. How much does Angela have now? F $116.40 H $61.90 G $83.60 J $16.40
9. Write rite Abou Aboutt It Explain how you found the answer to Exercise 6.
PS 70
Problem Solving
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LESSON 17.4
Name
Classify Lines Write the correct answer.
1. Jon is twice as old as his sister, Jane,
less 4 years. Jon is 18 years old. How old is Jane?
3. Name the point where the two lines
intersect.
2. Vicki is
1 3
as old as her cousin, Ricky, plus 5 years. Vicki is 14 years old. How old is Ricky?
4. Name the two lines that are parallel to
each other. B
B
D
E
C E
D
F
A
A
C
Choose the letter for the best answer.
5. Which names the point where line AE
and line BD intersect? D
C E
A
A point A B
B
point C D point D
point B
A
E
C
G
F
B H
A line EG B
line EF
cans and 70 lb of newpapers. In each bag he has 128 cans. How many cans has George saved? F 1,950 H 1,800 G 1,920 J 128
C
7. Line AB is parallel to which line?
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6. George has saved 15 bags of recycled
D
8. Jane wants to cut a piece of ribbon into
13 equal pieces. If the ribbon is 156 in. long, how long will each piece be? F 13 in. H 11 in. G 12 in. J 10 in.
line BA D line CD
C
9. Write rite Abou Aboutt It Give an example of something that reminds you of
parallel lines.
Problem Solving
PS 71
LESSON 18.1
Name
Triangles Write the correct answer.
1. Sandra drew an acute triangle. She
labeled the three angles as follows: 71°, 53°, and 46°. How do you know Sandra made an error?
3. At the Downtown Downtown Cafe, Cafe, donuts cost $0.75
and muffins cost $1.05. If you bought a dozen of each, how much would you pay?
2. When Eric tried to draw a triangle with
an obtuse angle and a right angle, he realized that he had made an error. How did he know that?
4. Jermaine bought a box of donuts and ate
half of them himself. He gave one to each of his two sisters and had one left. How many donuts did he buy?
Choose the letter for the best answer.
5. A triangle was formed by by the school’s school’s
20-ft flagpole, the wire from the top of the pole to a point 12 ft from the pole, and the ground. Which of the following best describes the triangle? A acute scalene B right scalene C obtuse isosceles D equilateral 7. When Mike kicked a ball against the
handball court wall, the angle between the path of the ball and the wall was 75°. What was the angle between the path of the ball and the ground? A 15° C 75° B 25° D 105°
6. James arrives at school at 7:50 A .M. At 8:00 A .M., the clock chimes once. At 9:00 A .M.,
it chimes twice. At 10:00 A .M., it chimes three times. If the pattern continues, how many chimes will James hear by 3:20 P.M.? F 8 H 28 G 16 J 36
8. A building has 5 floors and and each floor has
6 apartments. Each apartment has 2 bedrooms and each bedroom has 1 closet. Each closet has 4 shelves. How many shelves are there in all? F 60 H 240 G 120 J 480
9. Write Write About It How How did you find the angle between the path of the ball
and the ground in Problem 7?
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Problem So Solving
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LESSON 18.2
Name
Make Inferences You You can make inferences, inferences, or logical connections, connections, to help you solve a problem. Examine all the given facts and combine them to reach understandings that are not stated directly in the problem. Read the following problem. Ernesto’ Ernesto’s classroom has triangular tables. If the tables are placed side-toside, Ernesto wants to know how many students can be seated. Two Two students can sit on each side si de of a table. Find a pattern that will allow Ernesto to predict how many students can sit at a given number of tables. 1. Examine the information given in the problem. Then make inferences.
Information
Inference
• Triangular riangular tables tables are placed placed side-to-sid side-to-side. e. • Two students students can can sit on each each side side of a table 2. Fill in the table to show the pattern.
Number of Tables (t )
Number of Sides (s )
Number of Students (n )
1
3
6
2
4
3 4 3. Describe the pattern. Solve the problem.
Make inferences based on the evidence. Then solve.
4. Ling’s classroom has square tables where
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2 students can sit at each side. Find the pattern that will allow her to predict how many students can sit at a given number of tables placed side-to-side.
5. Della’s classroom has hexagonal tables
where 2 students can can sit at each side. Find the pattern that will allow her to predict how many students can sit at a given number number of tables placed placed side-to-side.
Reading Strategy
PS 73
LESSON 18.3
Name
Quadrilaterals Write the correct answer.
1. A football field is a rectangle rectangle 300 ft long
and 160 ft wide. The end zones add another 30 ft of length at each end. How much greater is the perimeter of the field with the end zones than without them?
3. Karen found that the length of her
classroom is just 1 ft greater than the width. The perimeter of of the room is 138 ft. What are the length and and width?
2. A baseball diamond is a square whose
side measures 90 ft. For a home run, a player must run around the square. If a player hits 35 home runs, what is the least number of feet he or she must run?
4. James James has $30.00 $30.00 to pay pay for a $28.0 $28.00 0 book. If the sales tax is $1.96, how much change will James get?
Choose the letter for the best answer.
5. The school flagpole cast a shadow 15 ft
long. Mr. Hansen cast a shadow 4 ft long. Mr. Mr. Hansen is 6 ft tall. tall . How tall is the flagpole? A 90 ft C 22.5 ft B 60 ft D 18 ft
6. Mrs. Gibson bought 13 yd red ribbon, ribbon, 34 yd
blue ribbon, 112 yd yellow ribbon, ribbon, and 4 yd white ribbon. How How much ribbon did she buy altogether? F 7152 yd H 5172 yd G 6172 yd J 5112 yd
7. Erik gave the following descriptions of
8. Jules gave the following descriptions of
parallelograms. Which description is incorrect? A A quadrilateral with two pairs of parallel opposite sides B A quadrilateral with opposite sides congruent C A four-sided polygon with opposite sides parallel D A polygon with opposite sides parallel
rectangles. Which description is incorrect? F A quadrilateral containing four right angles G A parallelogram containing four congruent angles H A parallelogram containing four congruent sides J A four-sided polygon with four right angles
9. Write About It How How did you find the incorrect answer in 7?
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Problem Solving
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LESSON 18.4
Name
Draw Two-Dimensional Figures Write the correct answer.
1. A basketball court is a rectangle. rectangle. A line
segment drawn between opposite corners divides the court into two congruent figures. Describe these figures.
3. A target in a game of darts has three
sections: 1 point, 3 points, and 6 points. If you throw 3 darts at the target and they all stick, how many different scores are possible?
2. Harry cut out a rhombus with no right
angles. He drew the longer diagonal, then folded the rhombus along the diagonal to make two congruent figures. Describe these figures.
4. At the finals of the school school contest, the
sixth-grade basketball team scored 6 three-point baskets, 13 two-point baskets, and 5 one-point foul shots. How many points did they score?
Choose the letter for the best answer.
5. Adrianna has drawn three sides of a
quadrilateral. They are 3 in., 7 in., and 4 in. long. What is the only quadrilateral she can complete by drawing the last side? A rectangle B trapezoid C rhombus D parallelogram 7. For every $5.00 Matthew earns, he
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spends $2.00 and saves the rest. How much should he be able to save if he earns a total of $150? A $30 C $90 B $60 D $120
6. Josh Josh drew drew an equilater equilateral al triangle, triangle, which which
he labeled ABC . Then he drew a line segment from vertex A to the middle of side BC. What kind of triangles did he form? F right isosceles G acute isosceles H right scalene J acute scalene 8. When Sophia was born, her father father was
30 years old. How old will Sophia’s father be when he is three times as old as his daughter? F 40 years old H 50 years old G 45 years old J 60 years old
9. Write About About It In Exercise 6, would the result be the same if the line
segment were drawn from vertex B to the middle of side AC ? Explain your reasoning.
Problem Solving
PS 75
LESSON 18.5
Name
Circles Write the correct answer.
1. A merry-go-round in the shape of a circle
rotates around a central post. The distance from the center of the post to the edge of the merry-go-round is 27 ft. What is the diameter of the merry-go-round?
3. The Muffin Man has muffins on sale for
$0.75 each or $1.75 for 3 muffins. What is the greatest number of muffins that you can buy for $5.00?
2. A circular target has three sections, all
with the same center. The diameter of the largest section is 18 in. The radius of the smallest section is 4 in. Halfway between these circles is the middle circle. What is its diameter?
4. After saving for three months, Kali had
$20 more than 3 times her initial deposit in her savings account. If she had $200, what was her initial deposit?
Choose the letter for the best answer.
5. The radius of a large truck tire is 19 in.
The back of the truck is supported by a row of 3 tires from front to back. There is 4 in. of space between tires. What is the distance from the front of the row of tires to the rear? A 10 ft 2 in. C 10 ft 10 in. B 10 ft 6 in. D 11 ft 7. An amusement park charges $15.50 for
admission. One day it collected $10,695. Which is the best estimate of the number of customers? A 600 customers B 700 customers C 800 customers D 900 customers
6. A circle circle graph graph shows shows how how 120 studen students ts
voted in an election for class president. The sector that represents the winner’s votes is twice the size of the sector that shows the runner-up’s votes. How many votes did the winner receive? F 40 votes H 80 votes G 60 votes J 100 votes 8. During the day, 102 T-shirts were sold.
Each shirt cost $12.95. How How much did the park earn from the sale of the shirts? F G H J
$129.50 $132.90 $1,295.00 $1,320.90
9. Write Write About It How How does knowing the relationship between the radius
and diameter of a circle help you answer questions?
PS 76
Problem So Solving
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LESSON LESSON 19.1 19.1
Name
Types of Solid Figures Write the correct answer. 1. Paula carved a block of wood in the
shape of a hexagonal prism. How many faces does the block have?
3. Irene has 17 quarters, 13 nickels, and
34 pennies. How much does she have?
2. Ned made a clay pyramid with six
faces. How many sides does the base of his pyramid have?
4. Alex has math scores of 97, 85, 88, 78,
83, and 91. What is the mean of his scores?
Choose the letter for the best answer. 3
1
5. Blai Blain n used used 34 yd of a 62 yd long piece of
fabric. Then she bought an additional 513 yd. Which number sentence can be used to find t, the total amount of fabric Blain has now? 1 –3 A t 6– 2 34 1 –3 B t 6– 3 2 4 1 –3 C t 6– 2 34 1 –3 D t 6– 2 34
changed jobs and earned $36,924 this year. How How much more did he earn this year than last year?
1
5–3 1 5–3 1 5–3 1 5–3
7. Janet bought a crystal paperweight
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6. Roger earned $27,785 last year. He
F
$8,861
G
$9,139
H $10,861 J
$10,139
8. George carved an ornament in the
shaped like a triangular prism. How many edges and vertices does it have?
shape of an octagonal pyramid. How many faces and edges does it have?
A 9 edges, 6 vertices
8 faces, 24 edges G 10 faces, 10 edges H 8 faces, 12 edges J 9 faces, 16 edges
8 edges, 4 vertices C 12 edges, 8 vertices D 6 edges, 6 vertices
B
F
9. Write About It Explain why a cylinder is not a prism.
Problem Solving
PS 77
LESSON LESSON 19.2 19.2
Name
Different Views of Solid Figures Write the correct answer. 1. Name the solid
figure that has the given views.
2. Name the solid
figure that has the given views.
top
front
front
side
3. The entire middle school is going on a
field trip. The school has 893 students. If each bus can hold 45 students, how many buses do they need?
top
side
4. Tina bought a printer for $435. She
made a down payment of $120 and paid the rest in equal payments of $45 per month. How long did it take her to pay for the printer?
Choose the letter for the best answer. 5. Every side view of a pentagonal
pyramid shows what shape? A pentagon B circle C rectangle D triangle 7. Jack ran two laps in 45.8 sec each
and then the last two laps in 58.7 sec each. Then he rested for 60 sec. Which expression can be used to find Jack’s total running time? A (2
45.8) (2 58.7) B (2 45.8) (2 58.7) C (2 45.8) (2 58.7) D (2 45.8) (2 58.7)
6. Every side view of a hexagonal prism
shows what shape? F hexagon G circle H rectangle J triangle 8. Jill worked for 3 hours each Saturday
for 2 years helping her favorite charity. What else do you need to know to find out how many total hours Jill has donated to her favorite charity? F How many baskets she handed out G How many Saturdays there were in each year H What type of food she gave out J The name of the charity
9. Write About It Describe the top, front, and side views of a
triangular prism.
PS 78
Problem So Solving
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LESSON LESSON 19.4 19.4
Name
Paraphrase When you paraphrase, or restate, something in your own words, you show your understanding. Paraphrasing a problem helps you clarify and identify what you are asked to find and the facts that are given in the problem.
VOCABULAR VOCAB ULARY Y
paraphrase
Read the following problem.
The movie theater is having a benefit to raise money to build a park. Movie Movie tickets tickets cost $5 $5 for adults, adults, $1 for senior senior citizens, citizens, and $0.10 for children. children. In the first hour hour, they sell 100 tickets tickets worth $100. Some of each kind kind of ticket were were sold. How How many of each kind of ticket were purchased? 1. Paraphrase the problem by restating it in your own words.
2. How would you use the strategy solve a simpler problem to solve
this problem? Use your restatement of the problem.
3. Solve the problem.
Paraphrase the problem. Try solving a simpler problem first. Then solve. 4. The appliance department where
Shawn works is having a sale. Blenders are $16, popcorn makers are $10, and mixers are $11. Shawn takes in $400 and sells at least one of each kind of appliance. How many of each might he have sold? t r u o c r a H ©
1
5. Harold owned 3 of a group of horses.
Moira owned 91 and Sandy owned 12 of the group. But they couldn’t split up the horses until Joe joined the group with his own horse. Harold, Moira, and Sandy each took the correct number of horses, and Joe kept his. How many horses did each one own?
Reading Strategy
PS 79
LESSON LESSON 20.1 20.1
Name
Ratios and Rates Write the correct answer. 1. There are 15 girls and 17 boys in one
2. A box holds 4 green apples, 3 red
class. What is the ratio of boys to the total number of students? Write Write the ratio three different ways.
apples, and 8 yellow apples. Write the ratio of red apples to green apples three different ways.
3. Last month 156,980 people visited a
4. Peter can hop a distance of 29 cm. To
them theme e park park.. This This mont month h 18 188, 8,10 103 3 peopl people e visited the park. Estimate how many more people visited the park this month than last month.
raise money for the school carnival, he hopped that distance 147 times. How far did he hop?
Choose the letter for the best answer. 5. Nina can walk 10 blocks in 5 minutes.
At this rate, how many blocks could Nina walk in 1 minute? A 3 C 1 1 B 2 D – 2
1
yd of fabric for a 7. Sharon used 3 3
seat cover on her chair. She used an additional 1 12 yd to cover the arms. How much fabric did Sharon use for the chair? 5 A 4– 6 yd 1 B 4– 2 yd
C
2
4–5 yd
1 D 4– 3 yd
6. Jason paid $8.50 for 5 lb of apricots.
Lorren wants to buy 1 lb at the same rate. How much will Lorren Lorren have to pay for 1 lb of apricots? F $1.90 H $1.80 G $1.85 J $1.70 8. The forest service bought 24,975 blue
spruce trees to plant on 15 hills. If they want an equal number planted on each hill, how many trees will they plant on each? F 1,685 H 1,665 G 1,675 J 1,655
9. Write About It In a unit rate, which number always equals 1?
Explain.
PS 80
Problem Solving
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LESSON LESSON 20.3 20.3
Name
Follow Directions Read and follow directions carefully to solve a problem. Look for words that state the operation or process to follow f ollow.. Sometimes, a problem requires you to work within certain limits. Make sure you follow the rules that are given.
VOCABULAR VOCAB ULARY Y
follow directions
Read the following problem.
Melina is from Greece.When Greece. When she came to the United States, she exchanged 1,500 Greek drachma and received $4.08 in U.S. dollars. Choose another amount of drachma that is not not a multiple or factor of 1,500. How much would Melina receive receive if she exchanged that number of drachma for U.S. dollars? 1. Write the directions you must follow to solve the problem.
2. What information is given?
3. Choose a number and solve the problem. What equation can you
write in the form of a proportion to solve the problem?
Follow directions to choose a number. Write a proportion. Then solve. 4. Brian exchanged 6 British pounds for t r u o c r a H ©
$9.31 $9.3 1 in U.S. U.S. doll dollar arss. Choo Choose se an amou amount nt in pounds that is neither a multiple nor a factor of 6. Write a proportion and find the amount’s amount’s equivalent in U.S. dollars.
5. Renata exchanged 100 German marks
for $47 in U.S. currency. Select an amount in marks that is not a factor or a multiple of 100. Write a proportion and find out how much the amount is worth in the United States?
Reading Strategy
PS 81
LESSON LESSON 20.4 20.4
Name
Algebra: Ratios and Similar Figures Write the correct answer. 1. The two figures below are similar.
Which angle corresponds to A ?
2. How many pairs of similar circles can
you find in the figure below?
A
8 cm
8 cm
M
3 cm
4 cm C
6 cm
B
N
4 cm L
3. Irene has 23 quarters, 15 dimes, and
6 nickels. How much money does she have?
4. A roll of quarters contains 40 quarters.
How many rolls of quarters would Jake get for two $20 bills?
Choose the letter for the best answer. 5. Triangle ABC has sides of 6 in., 8 in.,
and 9 in. Which is a similar triangle? A 12 in., 16 in., 20 in. B 10 in., 16 in., 18 in. C 12 in., 16 in., 18 in. D 12 in., 14 in., 18 in.
7. Oscar scored an 88 and a 92 on his last
two tests. What is the mean of Oscar’s Oscar’s test scores? A 88 C 90 B 89 D 91
6. Triangle XYZ has sides of 5 mm,
10 mm, and 12 mm. It is similar to triangle MNP . The two longest sides of triangle MNP are 30 mm and 36 mm. What is the length of the shortest shor test side? F 25 mm H 18 mm G 20 mm J 15 mm 8. Tom’s shuffleboard scores for the first
two rounds are 10 and 4. What is his total score? F 14 H 6 G 6 J 14
9. Write About It ABC is similar to DEF, A corresponds to D,
and B corresponds to E. Which side corresponds to side BC ? Explain.
PS 82
Problem Solving
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LESSON LESSON 20.5 20.5
Name
Algebra: Proportions and Similar Figures Write the correct answer. 1. Dale is 6 ft tall and his shadow is 4 ft
long. At the same time, a building casts a shadow that is 20 ft long. What is the height of the building?
3. Vivian bought 6 apples at $0.15 each e ach
and 7 bananas at $0.08 each. How much change did she get from $5.00?
2. A tree casts a shadow that is 12 m long.
Nearby a stick that is 2 m tall casts a shadow that is 3 m long. What is the height of the tree?
4. When a tree was cut down, its trunk
was found to contain 8 rings. Each ring is said to represent 13 yr of a tree’s life. How old was this tree?
Choose the letter for the best answer. 5. Tom is reading a book for English class.
He reads 8 pages in 15 minutes. At this rate how many pages can he read in 1 hour? A 8 C 24 B 16 D 32 7. Blake is in charge of stocking shelves.
He opened cases of soup and stocked the shelve shelvess with with 840 840 cans cans.. Each Each case case holds 24 cans of soup. Which equation can be used to find the number of cases, c , Blake opened? A 24 c 840 C 24c 840 B t r u o c r a H ©
24 c 840
24 D — c 840
6. Lisa Lisa has has 48 doll dollss. The The ratio atio of doll dollss from from
the U.S. to dolls from other countries is 3:5. How many dolls does she have from other countries? F 8 H 30 G 28 J 40 8. Maria recorded the weights of the
watermelons she harvested harv ested from her garden. They were 23.4, 19.8, 20.9, 28.7, 32.1, 18.8, 19.8, 22.3, and 33.8 kg. What was the median weight of Maria’ Maria’s watermelons? F 19.8 kg H 24.4 kg G 22.3 kg J 32.1 kg
9. Write About It When you are using the lengths of two shadows
to find an indirect measurement, why is it important that the lengths of the two shadows be taken at the same time of day?
Problem Solving
PS 83
LESSON LESSON 20.6 20.6
Name
Algebra: Scale Drawings Write the correct answer. 1. A playroom is 12 ft wide. How wide is
2. The school auditorium is 25 mm long
it on a floor plan drawn to the scale 1 in. 10 ft?
on a floor plan drawn to the scale 5 mm 4 m. Find the actual length of the auditorium.
3. Linda measured the height of 6 people
in her class. They were 187, 167, 192, 187, 190, and 181 cm. What is the mode of the heights?
4. Al is
1 5
as old as his cousin, Val. Sal, at 27, is two years older than Val. How How old is Al?
Choose the letter for the best answer. 5. The scale on a model airplane drawing
is 1 in. 18 ft. If the wing on the drawing is 4 in., how long is the actual airplane wing? A 36 ft C 60 ft B 48 ft D 72 ft
6. The scale on a drawing of a house is
1 in. 4 ft. The patio of the house will be circular with a diameter of 20 ft. What is the diameter of the patio on the drawing? F 10 in. H 5 in. G 8 in. J 4 in.
7. The stadium can hold 18,752 people. If
8. Michael gave away 58 model airplanes
the stadium has 32 equal rows of seats that that go comp comple lete tely ly arou around nd the the stad stadiu ium, m, how many seats are there in each row? A 556 C 576 B 566 D 586
he had built. He now has 133 left. Which equation could be used to find a, the total number of model airplanes Michael had before he gave any away? F a 58 133 H 58a 133 G a 58 133
J
9. Write rite Abou Aboutt It Two draw drawin ings gs of the the same same floo floorr plan plan are are draw drawn. n. The The
scale on one drawing is 1 in. 5 ft. The scale on the other drawing is 1 in. 10 ft. Explain how the sizes of the drawings will differ.
PS 84
Problem Solving
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LESSON LESSON 20.7 20.7
Name
Algebra: Maps Write the correct answer. 1. Use the scale 1 in.
50 mi to find the actual distance for a map distance of 7 in.
3. McKenna has to read a 647-page book
in 3 days. She read 176 pages the first day and 291 pages the second day. How many pages does she have left to read?
2. Use the scale 1 in.
80 mi to find the actual distance for a map distance of 9 in.
4. Kirk is playing a game with a 12-sided
geometric figure. If the figure has the numbers 1 through 12 on it, how many favorable chances does he have to roll a multiple of 4?
Choose the letter for the best answer. 5. A rectangle is 32 feet long and 16 feet
wide. A similar rectangle is 4 ft long. How wide is the similar rectangle? A 1 ft C 3 ft B 2 ft D 4 ft
7. The state capitol is 300 km from the
beach. How far is this on a map drawn to a scale of 1 cm 20 km? A 10 cm C 15 cm B 12 cm D 20 cm
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6. The map of the city is drawn to a scale
of 1 in. to 3 mi. The high school is 4 21 in. from the swim club. Find the actual distance. 1 F 4– H 12 mi 2 mi 1 G 9 mi J 13 – 2 mi
8. Jack and his three friends spent a total
of $24 for lunch. What was the mean price for the lunches? F $8 H $4 G $6 J $2
9. Write About It How can you measure a curvy road on a map?
Problem Solving
PS 85
LESSON LESSON 21.1 21.1
Name
Percent Write the correct answer. 1. The Panthers won 45 games last year.
They played 49 home games and 41 away games. What percent of their games did they win?
3. Harri arriet et is maki making ng a batc batch h of cook cookie iess an and d
is going to use 3 c of chocolate chips for every 24 cookies she makes. If she plans on making 48 cookies, how many cups of chocolate chips does she need?
2. Six out of 20 hiking club members
own their own tent. What percent of hiking club members do not own their own tent?
4. Carol saw 34 cars and 19 trucks drive
down down her her str street eet in a 2-ho 2-hour ur peri period od.. What is the ratio of cars to trucks? Write the ratio in three different ways.
Choose the letter for the best answer. 5. There are 25 students in a classroom.
Fourteen of them are boys. What percent of the class are boys? A 25% C 56% B 44% D 60% 3 7. Vicki colored – 4 of a picture. She left the
rest for her sister to color. color. What percent of the picture did Vicki leave for her sister to color?
A 75% B
50%
25% D 5%
C
6. Warren Warren ran the 100-m race in 48 sec. At
this rate, how long would it take him to run 10 m? F 48 sec H 0.48 sec G 4.8 sec J 0.048 sec
8. Joan bought a bag of green beans that
weighed 8.2 kg and Carrie bought a bag of green beans that weighed 12.1 kg. How much more did Carrie’s bag of beans weigh? F 3.9 kg H 4.1 kg G 4.0 kg J 4.2 kg
9. Write About It Why is it easy to change a fraction to a percent
when the denominator of the fraction is 100?
PS 86
Problem Solving
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LESSON LESSON 21.2 21.2
Name
Percents, Decimals, and Fractions Write the correct answer. 1. Cheryl has invited 68 people to a party.
She has has 4 tabl tables es that hat eac each seat seat 5 peopl eople e. A party-supply company rents tables that seat 6. How many tables does she need to rent?
3. In the school parking lot, the ratio of
sedans to minivans is 3 to 5. What percent of the cars are minivans?
2. Out of 1,450 books distributed at the
beginning of the school year, only 12% of them have not been returned. What fraction of the books have been returned?
4. Rosie’s Posies sells roses for $54.00 a
dozen. At that rate, what is the cost of two roses?
Choose the letter for the best answer. 5. Eighteen out of the 25 members of
the girls’ soccer team wear their hair in a ponytail. What percent of the girls on the soccer team wear their hair hair in a ponytai ponytail? l? A 80% C 28% B 72% D 18%
7. Devon bought 12 child tickets and
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23 adult tickets to a show. Each child ticket cost $3.25 and each adult ticket cost $6.75. What equation can be used to find a , the total cost of the tickets? A a 12 3.25 23 6.75 B a (23 3.25) (12 6.75) C a (12 3.25) (23 6.75) D a (12 3.25) (23 6.75)
6. Sami, ami, Tami, ami, an and d Ka Kami mi pain painte ted d the the fenc fence e
around their garden. Sami painted 35% of it, Tami painted 52 of it. What fraction of the fence did Kami paint? –2 5 1 G – 3
F
1 H – 4 1 J – 5
8. Karen earned 221 bonus points at
her local supermarket by buying the specials. Denise earned five times as many points and Beth earned 125 more points. How many bonus points did Denise earn? F 985 H 1,005 G 995 J 1,105
9. Write About It When changing a percent to a decimal, why do you
move the decimal point two places to the left?
Problem Solving
PS 87
LESSON LESSON 21.3 21.3
Name
Estimate and Find Percent of a Number Write the correct answer. 1. Greg found that 87.5% of the azalea
bushes he planted in the spring produced flowers. He planted 24 azalea bushes. How many bushes produced flowers?
3. Lawn chairs cost $34 and reclining
chairs cost twice as much. What is the cost of 2 lawn chairs and 2 reclining chairs?
2. The bill for dinner for your family of
five comes to $78.25. You You want to leave a 15% tip. If you give the waiter $87.00 is that enough? Explain.
4. Jon flew across the country in 5 hr
15 min. The distance is about 3,200 mi. About how fast was the plane flying?
Choose the letter for the best answer. 5. The bill for dinner for 8 people comes
to $126.67. Mr. Zamboni wants to leave 15% as a tip. How much should he leave? A $17.59 C $18.75 B $18.20 D $19.00
6. The sixth-grade class is 120% as large
as the seventh-grade class. There are 485 students in seventh grade. How many students are in sixth grade? F 582 H 465 G 505 J 388
7. Grace is moving all of her 249 books to
8. Peter ran the first 100 m of the race in
the large bookcase downstairs. She can carry 12 books at a time in her arms. What is a reasonable estimate of how many trips Grace will need to make? A 10 C 30 B 20 D 40
45.8 sec. The race is 400 m long. If he maintains this rate, which expression can be used to find the total number of seconds it will take Peter to run the race? F 45.8 45.8 H 45.8 4 G 400 100 J 400 100
9. Write About It What is always true about the answer to a problem
when you are finding less than 100% of a number?
PS 88
Problem Solving
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LESSON LESSON 21.5 21.5
Name
Discount and Sales Tax Write the correct answer. 1. A pair of shoes regularly sells for $36.80.
2. A jacket regularly sells for $140. It is on
They are on sale for for 40% off. ff. What is the sale price?
sale for 20% off. What is the sale price?
3. Paul bought a 3-pound bag of apples
for $2.58. Albert bought a 5-pound bag of the same kind of apples for $4.20. Which was the better buy? Explain.
4. Bruce has a bag of candy. In it he has
18 caramels and 15 chocolate-covered cherries. What is the ratio of caramels to chocolate-covered cherries? Write the ratio in three ways.
Choose the letter for the best answer. 5. Lacy bought a shirt that regularly
sells for $40. The clerk gave her a $10 discount. What percent of the regular price was the discount? A 50% C 15% B 25% D 10% 7. Ralph and his family drove 2,876 mi
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in 8 days. If they drove about the same amount each day, which is the best estimate of how many miles they drove each day? A 350 mi B 450 mi C 550 mi D 650 mi
6. Hank bought a power saw on sale. The
regular price was $120. He paid only $96. What percent of the regular price did Hank pay? F 80% H 40% G 60% J 20% 8. Patrick gave away 9 of his marbles.
He now has only 42 marbles. Which equation can be used to find the total number of marbles, m, Patrick had before he gave 9 away? F
m — 9 42
G m 9 42 H 9m 42 J
m 9 42
9. Write About It Why is it important to be able to estimate what the
discount is on sale items?
Problem Solving
PS 89
LESSON LESSON 21.6 21.6
Name
Simple Interest Write the correct answer. 1. If you invest $1,400 at a simple interest
rate of 6.5% for 7 years, how much interest will you earn?
3. The ratio of apples to oranges is 6 to 5.
If there are 25 oranges, how many apples are there?
2. If you take a loan of $2,800 at a simple
interest rate of 8.3% for 2 years, what is the total you will have to repay?
4. If 22 fine-tip art pencils cost $3.96, how
many pencils can you buy for $2.70?
Choose the letter for the best answer. 5. Fred put $400 in the bank at 10%
simple interest. How much will he have in the bank in 5 years? A $450 C $600 B $550 D $700
7. Ned made four consecutive jumps. His
first jump was 1.45 m, his second jump was 1.15 m, his third jump was 1.68 m, and his fourth jump was 1.52 m. What is the total distance he jumped? A 4.28 m B 4.35 m C 5.7 m D 5.8 m
6. Ka Karren put put $6 $600 00 in the the bank bank at 5% simp simple le
interest. How many years will it take for her to double her original $600? F 5 years H 20 years G 10 years J 30 years
8. Melissa and Amy earned $54.40
babysitting together. Amy earned $6.26 more than Melissa. How much did Melissa earn? How much did Amy earn? F $24.07; $30.33 G $20.94; $27.40 H $30.33; $24.07 J $27.20; $20.94
9. Write About It Explain how the amount of interest you earn when
money is invested in a bank is related to the amount of time the money is invested.
PS 90
Problem Solving
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LESSON 22.1
Name
Theoretical Probability Write the correct answer. 1. In a bag there are 12 red marbles, 3
green marbles, and 4 yellow marbles. What is the probability of randomly selecting a red marble from the bag?
3. A recipe for chili feeds 35 people and 1 2
calls for 3 lb of onions. Juan wants to make chili for 5 people. How many pounds of onions does he need?
2. Each letter of the alphabet is put into
a bag. What is the probability of randomly selecting an A , E , I , O , or U from the bag?
4. During a basketball game, Stella
attempted 30 foul shots. She made 80% of them. How many foul shots did she miss?
Choose the letter for the best answer. 5. Dale was paid $487.63 for the month
and Bob was paid $691.02 for the month. How much more did Bob make than Dale? A $203.39 B
$203.59
$204.38 D $204.59
C
7. A spinner is divided into five sections
and labeled 1, 2, 3, 4, and 5. If each number is equally likely to occur, what is the probability of the spinner landing on an even number? A B t r u o c r a H ©
1 5 1 2
2 5 2 D 6
C
6. Lyle kept track of the temperature for
a month. The lowest temperature he recorded was 45°F and the highest temperature was 82°F. What is the range of the temperatures? F 34°F H 36°F G 35°F J 37°F 8. Darla can select one friend to go on
vacation with her. She will put the names of her 15 best friends into a bag and randomly select one name. What is the probability she will select her friend Cheryl? F G
1 15 14 15
H J
1 16 15 16
9. Write About It Explain what a probability of 0 means.
Problem Solving
PS 91
LESSON 22.2
Name
Choose Relevant Information Sometimes a word problem contains information that may not help you solve the problem. You must decide which information is relevant , or or needed to solve the problem. Unnecessary information is irrelevant. On the other hand, there may be facts that you need that are not included in the problem. Read the following problem.
VOCABULARY VOCABU LARY
relevant irrelevant
Evan is employed at the Squeaky-Clean Soap Company, and he likes his job. He starts at 8 A.M. and ends ends his shift shift at 4:30 P.M. He must work a total total of 5 hr each day, day, but his job is divided di vided up. Every hour on the th e hour, hou r, he works wo rks for f or 15 min. He takes a 20 min break at 10:20 A.M. On the the hal halff hour of odd-numbered hours, he works for 25 min. He eats lunch at 12:15 P.M. After After 4:30, he he cleans cleans up for 45 min min and goes home. Does he work 5 hr on this schedule? Explain. 1. Read each fact from the problem. Is the fact relevant or irrelevant
to solve the problem? Write R for relevant and I for irrelevant . A Evan likes his job. B He works from 8 A .M. un until til 4:30 4:30 P.M. C He must work 5 hr. D He works 15 min every hour on the hour. E He takes a 20 min break. F He works 25 min on the half hour of odd-numbered hours. G He has lunch at 12:15. H He spends 45 min cleaning up after 4:30. 2. Solve the problem.
Solve. Choose relevant information to help you. 3. Edna drinks a lot of water each day.
She knows a glass is 8 oz. She has 10 oz when she wakes up and 14 oz in the middle of the morning. She has 8 oz of water with each meal. She drinks 16 oz and d 4 P.M. of water between 3 P.M. an Before Before bed, she has has a 12 oz mug of of apple cider. How many glasses of water does she have each day?
PS 92
Reading St Strategy
4. Paul left home at 2 P.M. He walked walked 3
blocks east and 1 block north to the drugstore. Then he walked 1 block east and 1 block north to the post office. After that, he walked 2 blocks west and 1 block north to the library. He continued 2 blocks west and 1 block south to his friend Roberto’s house, where he ate a snack. Then he walked 1 block west and 2 blocks south to his piano teacher’s house. How far was Paul from home?
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LESSON 22.4
Name
Experimental Probability Write the correct answer. 1. Oscar’s scores for the dart game are
45, 23, 32, 32, 32, 12, 25, 65, and and 78. Find Find the mean of his scores.
3. In a bag there are 9 green squares,
8 red squares, and 13 yellow squares. Is each color equally likely to be selected at random? Explain.
2. In soccer, Bernice scored 8 goals out of
25 tries. How many goals can she expect to score if she tries 100 times?
4. Jake flipped a coin 50 times. The
results from the flipping were 31 heads and 19 tails. Based on his results, what is his experimental probability of getting tails?
Choose the letter for the best answer. 5. Charles had
3 4
ft of plywood and cut off 1 ft for a doorstop. How much plywood 8 does he have left?
A B
7 ft 8 3 ft 4
5 ft 8 1 D ft 2
C
6. Dale randomly threw darts at a target
and recorded the following results: 21 hits on black and 79 hits on white. What is the ratio of the hits on black to the hits in all? F G
79 100 21 100
H
J
21 79 79 21
7. Roger randomly selected marbles from a bag one at a time and
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recorded the color. He put each marble back before selecting the next one. The results were 12 red, 25 blue, 16 green, and 2 yellow. What conclusion can he make from these results? A There are very few yellow marbles in the bag. B There are the same amount of red and green marbles. C There are 55 marbles in the bag. D There are no other colors of marbles in the bag. 8. Write About It Is it possible to flip a coin and get 25 heads in a row? Explain.
Problem Solving
PS 93
LESSON LESSON 23.1 23.1
Name
Classify and Categorize One way to organize information in a problem is to classify and categorize it. To classify information is to group information that is alike in some way. To categorize information is to label the groups that you have made by classifying.
VOCABULAR VOCA BULARY Y
classify categorize
Read the following problem.
Elena’s Elena’s family is giving her a special birthday treat. treat. She can choose one special outing to have with one special special friend. The friends Elena migh mightt choose choose are Brad, Brad, Helen, Helen, Angie, Angie, Erica, Erica, or Roy Roy. The outings she is considering are are horseback riding, dinner and a movie, movie, a rock concert, a ride in a private private plane, or a day day at an an amusement park. How many different birthday treats involving one friend and one outing are possible? 1. Complete the table to classify and categorize the information
from the problem. Friend
Outing
Brad Brad
hors ho rse, e, dinn dinner er/m /mo ovie, vie, conc concer ert, t, plan plane, e, amus amusem emen entt park park
Helen Helen
horse horse,, dinn dinner/ er/mo movie vie,, conc concert ert,, plan plane, e, amuse amusemen mentt park park
Angie
horse, dinner/movie dinner/movie,, concert, plane, amusement amusement park
Eric Erica a
hors ho rse, e, dinn dinner er/m /mo ovie, vie, conc concer ert, t, plan plane, e, amus amusem emen entt par park k
Roy
hors ho rse e, dinn dinner er/m /mo ovie vie, conc concer ert, t, plan plane e, amus amusem emen entt park park
2. Solve the problem.
Classify and categorize the information. Then solve. 3. Virgil is baking a pie. He can make a
coconut pie, banana cream pie, or vanilla pie. He can make a graham crack cracker er crust, crust, regul regular ar crust, crust, or chocol chocolate ate cookie crust. How can you classify and categorize the information? How many different pies can he make?
PS 94
Reading St Strategy
4. Anita is choosing her song for the spring
concert. She can sing a pop song, lullaby, folk song, or funny song. She can be accompanied by a piano, harp, or guitar. How can you classify and categorize the information? How many possible presentations can Anita make?
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LESSON LESSON 23.2 23.2
Name
Compound Events Write the correct answer. 1. As a lunch special, the Kozy Kitchen
2. Flo wants to wrap 16 gifts for her
offers a choice of 6 sandwiches, 3 salads, 3 kinds of soup, and iced tea or lemonade. How many different lunches could you make?
friends. She has 3 kinds of paper, bows in 4 different colors, and 2 kinds of ribbon. Can she wrap each package in a different combination? Explain.
3. Sneakers that usually sell for $75 are on
1 . 4
sale. The discount on Trek sneakers is The discount on Pro sneakers is 15. Which brand has the greater discount? Explain.
4. Kyle and 9 of his friends formed a
nature club last year in January. January. They each paid an initiation fee of $5 and $2 per month dues. dues. How How much did the club collect last year?
Choose the letter for the best answer. 5. Nat wants to watch a TV special on
computers. The program will be aired on Monday, Wednesday, and Friday at 11:00 A .M., 4:00 P.M., 8:00 P.M., and midnight. How many choices does Nat have? A 7 choices C 12 choices B 9 choices D 15 choices 7. Adam has a bag that contains 8 red,
16 blue blue,, 12 green green,, an and d 14 yell yello ow marb marble less. Without looking, Adam takes a marble from the bag. What is the probability that Adam gets a yellow marble? t r u o c r a H ©
2 — A 50 1 — B 14
7 — 25 8 — D 25
C
6. Carla is choosing cabinets for her new
kitchen. The cabinets come in 2 sizes; a choice of oak, cherry, or pine wood; and a choice of 6 finishes. How many choices does Carla have? 36 choices G 42 choices
H 48 choices
F
J
60 choices
8. The Greenthumb Nursery usually sells
a flat of petunias for $12.50. This week, each flat is 15 off with a coupon from the newspaper. What is the price of 2 flats of petunias if a coupon is used to buy one of them? F $19.50 H $22.50 G $20.00 J $25.00
9. Write Would you rather draw a tree diagram or use the rite Abou Aboutt It Would
Fundamental Counting Principle to find the number of possible outcomes for a compound event? Explain.
Problem Solving
PS 95
LESSON LESSON 23.3 23.3
Name
Independent and Dependent Events Write the correct answer. 1. Your Your sock drawer contains 6 black
sock socks, s, 4 blue blue sock socks, s, an and d 10 bro brown sock sockss. What is the probability that you will get a pair of blue socks if you pick 2 socks without looking in the drawer?
3. Rick has three times as many baseball
cards as Vic. Vic has one half as many as Nick, who has 12 cards. How many baseball cards do they have in all?
2. A bag contains 6 lettered tiles labeled
A, A, B, C, D, D. Without looking, you select a tile and keep it. Then you select another tile. What is the probability of selecting an A and then a D ?
4. Martha wants to make a decorative
frame for a rectangular painting that 2
5
measur measures es 4–3 f t b y 3–8 ft. ft. How much much wo wood od will she need to construct the frame?
Choose the letter for the best answer. 5. Sam and Renee have signed up with
eight other students to be Recycling Monitors. One student and an alternate will be selected by drawing names from a hat. What is the probability that Sam will be selected as the monitor and Renee will be selected as the alternate? 1 — A 10 1 — B 45
1 — 90 1 —– D 100
C
7. Petunias are sold in flats of 10 plants.
Daisies are sold in flats of 6 plants. You You want to buy an equal number of each plant. What is the least number of plants you can buy? A 60 of each B
40 of each
30 of each D 20 of each
C
6. There are 2 blue marbles, 5 red
marbles, and 3 green marbles in a bag. You You close your eyes, e yes, select a marble, and replace it. Then you close your eyes and select another marble. What is the probability of picking a red marble both times? F G
–3 4 1 – 2
H J
8. Hank jogs 1 2 mi per day 4 days each
week. Each week he increases the distance he jogs by 14 mi per day. In how many weeks will Hank be jogging 2 mi per day? 4 weeks G 6 weeks
F
H 8 weeks J
9. Write You roll a number cube twice. Are these dependent rite Abou Aboutt It You
or independent events? Explain.
PS 96
Problem Solving
1 – 3 1 – 4
10 weeks
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LESSON LESSON 23.4 23.4
Name
Make Predictions Write the correct answer. 1. In a survey of 150 randomly selected
sixth graders, 25 of them said that they read magazines on a regular basis. Predict about how many sixth graders out of 2,400 will indicate that they read magazines on a regular basis.
3. The probability of picking a yellow tile from a bag of 5 tiles is 52–. You add a red tile
to the bag. Now what is the probability of picking a yellow tile? Explain.
2. In a survey of 175 randomly selected
computer users, 25 of them said that they used their computer for research. Predict about how many computer users out of 4,200 will indicate that they used their computers for research.
4. A computer store charges monthly
interest at the following rate: 1 12% for the first $200, and 1% for any amount over $200. What is the interest charge and total charge for a customer with a bill of $512?
Choose the letter for the best answer. 5. In a random sample of 300 VCRs, the
quality control department found that 18 were were defec defectiv tive. e. If the compan company y manufactured 9,000 VCRs, about how many of them would you expect to be defective? A about 54 C about 270 B about 180 D about 540 7. Kale counted 50 rose bushes in the
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park’s rose gardens. Of those bushes, 14 of them were a variety known as tea roses. What percent of the rose bushes were tea roses? A 14% C 50% B 28% D 56%
6. When a random sample of 100 carrot
seeds was planted, 15 of the seeds did not germinate. If 2,500 carrot seeds were planted, about how many would you expect not to germinate? about 150 G about 250
F
H about 375 J
about 475
8. Fruit drinks are sold in 4 flavors:
strawberry, strawberry, banana, mango, and orange. They are sold in 3 sizes: small, medi medium um,, an and d larg large. e. How many many diffe differe rent nt choices are available? F 12 H 4 G 7 J 3
rite Abou Aboutt It How can you use a ratio to make predictions based 9. Write
on a sample?
Problem Solving
PS 97
LESSON 24.1
Name
Algebra: Customary Measurements Write the correct answer. 1. Find the missing measurement.
32 ft in.
3. Felix walked 2,530 feet f eet on Tuesday and
558 yards on Wednesday. How many feet did Felix walk altogether?
2. Find the missing measurement.
16 qt gal
4. Which unit of measurement is larger,
pints or cups? Explain.
Choose the letter for the best answer. 5. Bill’s car weighs 3,450 pounds. His
friend Jack has a truck that weighs 2 tons. How many more pounds does Jack’s truck weigh than Bill’s car? A 550 lb C 570 lb B 560 lb D 580 lb
7. Gail made a spinner with 24 congruent
sections. She labeled each section in order as follows: A, B, C, D, A, B, C, A, B, A, B, A, B, A, B, C, A, B, C, D, A, B, C, D. What is the probability of spinning the pointer and landing on D? 1 — A 12 –1 B 8
C D
6. Ellen is making punch for a party. The
recipe makes 2 quarts. If she makes 4 times the recipe, how many gallons of punch will she have? F 5 gal H 3 gal G 4 gal J 2 gal
8. The Garcia family has five children.
Thei Theirr ages ages are are 9, 11 11,, 13, 18 18,, an and d 19 19.. What What is the mean (average) of their ages? F 10 years H 13 years G 12 years J 14 years
–1 6 –1 4
9. Write rite Abou Aboutt It Explain how you can change 1 mile to inches.
PS 98
Problem Solving
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LESSON 24.2
Name
Algebra: Metric Measurements Write the correct answer. 1. Which unit is larger, kilometers or
2. Find the missing measurement.
meters? Explain. 30 km m
3. Claire’s baby brother is 19 months old
today, and Ellen’s baby sister is 3 years old today. How much older is Ellen’s baby sister than Claire’s baby brother?
4. Nancy measured her step to be 2 feet.
She went for a walk and counted 5,280 steps. How many miles did she walk?
Choose the letter for the best answer. 5. Thomas had 2 liters of water with him
6. Paul bought a piece of rope 6 meters
to drink. Larry had 2,500 milliliters of water to drink. How much more did Larry have to drink than Thomas? A 2,500 mL C 1,500 mL B 2,000 mL D 500 mL
long. He used 480 centimeters tying down a tarp in his backyard. How much rope does he have left? F 0.12 m H 5,520 cm G 1.2 m J 12 m
7. Bob played ski ball at the arcade and
won 630 coupons. He played 18 games and got the same number of coupons each time he played. Which equation can be used to find the number of coupons, c , he won each time he played? A 18c 630 C c 18 630 t r u o c r a H ©
B
18 c 630
D
18 — c 630
8. Mary made 3 long distance phone
calls last month. The first call was to Australia and cost $34.71, the second call was to Spain and cost $29.09, and the third call was to Japan and cost $58.12. Estimate the total cost of the calls. F $120 H $160 G $140 J $180
9. Writ Write e Abou Aboutt It Explain how you can change smaller metric units to larger
ones or larger metric units to smaller ones by moving the decimal point.
Problem Solving
PS 99
LESSON 24.3
Name
Relate Customary and Metric Write the correct answer. 1. In international track and field
competitions, race distances are measured in meters. One race is 400 m long. To To the nearest 10 yd, how long is the 400-meter race?
3. Carrie is choosing between these sizes
of the same cereal: 16 oz for $1.79, 20 oz for $2.59, and 25 oz for $3.29. She wants to pick the one that is the best buy. buy. Which box of cereal should Carrie choose?
2. On a cold winter morning, the
temperatures in five cities were 7°F, 9°F, 12°F, 4°F, and 13°F. What were the mean and median temperatures for these five cities?
4. Ana’ Ana’s fish tank holds 80 L of water. water.
The owner of the pet store where she bought a new fish told her that the fish needs to be in a tank that holds at least 30 gal. Does her tank hold enough water for the new fish? Explain.
Choose the letter for the best answer. 5. Haley lives in Canada. On a map
she sees that the distance from her hometown to Chicago, Illinois, is 1,875 km. She wants wants to know know this distance in miles. Which expression can she use to find the number of miles? A 1,875 1.61 B (1,875 1.61) 1,875 C (1,875 1.61) 1,875 D 1,875 1.61 7. Which expression can you use to find
the weight in kilograms that is equivalent to 16 lb? A 16 0.45 C 16 0.45 B 16 0.45 D 16 0.45
6. Mr. and Mrs. Rojas are taking their
3 children ice skating. The cost for adults is $5.75. The cost for children is $3.25. They will also spend $12.00 on traveling expenses. Which expression can Mrs. Rojas use to find the total cost for the entire family? F 12 2 5.75 3 3.25 G 12 5(5.75 3.25) H 12 2 5.75 3 3.25 J 12 5(5.75 3.25) 8. Marie is 24 years younger than her
mother. mother. Which equation can you use to find Marie’s age, x , if her mother is 36 years old? F x 24 36 H x 24 36 G x 24 36 J x 24 36
9. Write rite Abou Aboutt It Explain how you would change 75 meters to feet.
PS 100
Problem So Solving
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LESSON 24.4
Name
Appropriate Tools and Units Write the correct answer. 1. Cora filled a measuring cup with water.
She looked at the scale on the side of the cup and recorded the amount in the cup as 1 87 c. Later, she changed the amount she had written to 15 oz. Which measurement is more precise?
3. Nate is comparing the prices of trips to
Europe. If he leaves between October 1 and an d Marc arch 31, the the trip trip costs osts $1 $1,1 ,115 15.. The The same trip, taken between April 1 and May 13 cost costss $1,3 1,339 39.. If he trav travel elss duri during ng the summer, he will pay $380 more than for winter travel. How much will Nate pay if he leaves July 5?
2. Josie is measuring the length of a room
for carpeting. When she stretches the tape across the room, she has a choice of two ways to read the length, 9 21 ft or 114 in. Which is a more precise way of measuring the room’s length?
4. Nate plans to fly from New York York City to
London. London is 5 hr ahead of New York York City. City. His flight will leave New York York City at 7:45 P.M. on Tuesday Tuesday.. The flight 1 to London takes 6 2 hr. If the plane is on time, at what time and on what day will Nate arrive in London?
Choose the letter for the best answer. 1
5. A folded sheet s heet of paper is 8 2 in. long. It
is placed in an envelope that is 9 in. long so that its ends are the same distance from the envelope ends. How much space is between each end of the letter and the envelope? A
1 in.
C
B
–3 4 in.
D
–1 in. 2 –1 4 in.
7. A school hallway is being measured for
new floor floor tile tiles. s. Whic Which h of these these measu measure ress gives the more precise length of the hallway? t r u o c r a H ©
A 180 ft B
60 yd
6. When Adita took her water bottle out
of her backpack, she noticed that there were four measurement scales on the bottle. Which of these measurements is the more precise measurement of the amount of water in Adita’s bottle? F 0.5 L G 500 mL 8. Henry exercises 25 min per day 3 days
each week. If he increases the number of minutes per day by 5 each week, how long will it take him to reach 2 hr of exercise each week? F 1 week H 3 weeks G 2 weeks J 4 weeks 7
9. Writ Write e Abou Aboutt It The measurements 15 oz and 1 8 c are equivalent. Why is one
considered to be more precise?
Problem Solving
PS 101
LESSON 24.5
Name
Make Predictions An estimate is an approximate answer to a problem. If a problem asks you to find about how many or is phrased as a yes-or-no question, you can use estimation to make a prediction. When a problem asks for an exact answer, you can estimate to check the reasonableness of your answer. Read the following problem.
VOCABULAR VOCA BULARY Y
estimate
Mattie has $34.23 in his savings savings account. He has $13.65 in his piggy bank. He received received $75 in birthday birthday money. money. Does he have enough to buy a CD player that costs $129.95? 1. Do you need to estimate or give an exact answer? Explain.
2. What prediction can you make?
3. How can you use estimation?
4. Solve the problem.
Use estimation to make predictions. 5. Phyllis has the following items in her
grocery cart: a chicken for $7.93, a loaf of bread for $2.19, a gallon of milk for $2.98, a dozen eggs for $1.59, a bag of potatoes for $0.99, a pound of cheese for $4.49, and 6 apples for $0.50 each. Her budget for food is $20.00. Predict whether or not she will stay within her budget.
PS 102
Reading Strategy
6. Amy and Eddie are collecting food for
the town soup kitchen. Their goal is to collect 200 lb of food in 1 day. They have collected sixty-one 16-oz cans of vegetables, forty-three 32-oz cans of fruit, nineteen 24-oz boxes of cereal, and ninety-eight 8-oz cans of soup. Predict whether or not they will meet their goal.
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LESSON 25.2
Name
Perimeter Write the correct answer. 38 ft
1. Find the perimeter.
2. Find the perimeter per imeter..
8 yd
34 ft 7 yd
85 ft
12 yd 11 yd
13 yd 9 yd
56 ft
8 yd
62 ft
3. In order to put up a fence, Jane needed
to measure the sides of her rectangular garden. It was 102 in. long and 66 in. wide. Express the measurements of Jane’s garden in feet.
4. Jane bought 4 flowering bushes to put
at the corners of her square patio. Each bush cost $29.95. How much change did she get from $150.00?
Choose the letter for the best answer. 5. Todd started working on his science
project 12 days and 22 hours ago. How many hours has it been since he started working on his project? A 144 C 288 B 166 D 310
7. The lengths of the sides of a
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quadrilateral are 23.5 cm, 36.4 cm, 19.1 cm, and x cm. The perimeter is 107.3 cm. What is x ? A 19.1 cm C 28.3 cm B 26.8 cm D 42.6 cm
6. Bernice bought a fish tank and was told
it held 12,800 mL of water. How many liters does the tank hold? 12,800 L G 1,280 L
F
H 128 L J
12.8 L
8. The school playground was built in
the shape of a square. Its perimeter is 1,408 yd. Find the length of each side of the playground. F 704 yd H 176 yd G 352 yd J 140 yd
9. Writ Write e Abou Aboutt It Explain how to find the perimeter of any polygon.
Problem Solving
PS 103
LESSON 25.3
Name
Use Graphic Aids As you read a problem that can be solved using a geometrical approach, make a diagram to record the information. Then you can use the graphic aid that you have created to help you solve the problem. Be careful to use accurate labels, symbols, and abbreviations in creating and using your graphic aid. Read the following problem.
Yukio Yukio is designing a house for his hamster. He has 5 cube-shaped rooms. They can be attached to each other by any of the four walls so that any two t wo cubes form a rectangular prism. pr ism. How How many different-shaped houses can Yukio make for his hamster? (Do not count mirror-image shapes as two different shapes.) 1. In your diagram, what shape would best represent each cube?
2. How can you use diagrams to solve the problem?
3. Yukio drew these arrangements. Draw other possible
arrangements.
4. Solve the problem.
Solve the problem. Make and use a graphic aid to help you. 5. Raoul is using blocks shaped like equilateral triangles to make
larger and larger equilateral triangles. Complete the pattern. What kind of pattern do you see in the numbers of triangles? t r u o c r a H ©
1 PS 104
4
Reading Strategy
Name
LESSON 25.5
Circumference Write the correct answer. 1. Earth’s two closest neighbors are
2. The radius of Earth is 3,960 mi (the
Mars and Venus. Venus. The diameter of Mars is 4,214 mi. The diameter of Venus Venus is 7,522 mi. How much greater is the circumfer circumference ence of Venus than the circumference of Mars? Round to the nearest mile.
distance from the center of the planet to the surface). How much greater is the circumference of Earth than of Venus? How much greater is the circumference of Earth than of Mars? Round to the nearest mile.
3. Carmen had some wood, some chain
4. Students each paid $7 to go on a class
link fencing, and some iron fencing. She built a fence using wood for 21 of the fence, chain link for 41 of the fence, and iron for the rest. She used 70 ft of iron. How long was her fence?
trip to the theater. For every 6 students, 1 parent was admitted at no charge. The total cost of the trip was $210. How many students and parents in all went on the trip?
Choose the letter for the best answer. 5. During a special sale, a department
store sold shirts for $10 and pairs of jeans for $12. Martin bought twice as many shirts as pairs of jeans and spent less than $100. What was the greatest number of pairs of jeans he could have bought? A 10 C 4 B 6 D 3 7. The rim rim of a pass assenger car tire can have
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a diameter of 13 in., 14 in., or 15 in. To the nearest whole number, number, how much greater is the circumference of a rim that is 15 in. in diameter than one that is 13 in. in diameter? A 4 in. B 5 in. C 6 in. D 7 in.
6. A baseball diamond is a square. The
distance from home plate to first base is 90 ft. During the 1998 baseball season, one player hit 70 home runs. What is the least number of feet he could have run after hitting those home runs? F 6,000 ft H 32,400 ft G 25,200 ft J 64,800 ft 8. A light truck tire may have a diameter
of 31 in. If the tire is on a rim that is 15 in. in diameter, to the nearest whole number, number, how much greater is the circumference of the tire than the circumference of the rim? F 50 in. G 54 in. H 60 in. J 100 in.
9. Writ Write e Abou Aboutt It Explain why you had to use different formulas to answer
Exercises 1 and 2.
Problem Solving
PS 105
LESSON 26.1 00.0
Name
Estimate and Find Area Write the correct answer. 2. Find the area of the triangle.
1. Estimate the area of the figure. Each
small square on the grid represents 1 m . 2
22m 6m
3. A rectangle has a length of 23 ft f t and a
width of 6 ft. f t. What is the perimeter of the rectangle?
4. How many seconds are equal to
3 weeks and 5 days?
Choose the letter for the best answer. 5. Ron’s new house has a den that is 14 ft
by 16 ft. How many square feet of carpet should he buy to cover the floor? A 60 ft2 C 224 ft2 B 196 ft2 D 256 ft2 7. Mr. Jones is planning a field trip for the
entire middle school. The school has 893 students. If each bus can hold 45 students, how many buses do they need? A 19 buses C 21 buses B 20 buses D 22 buses
6. The high school athletic field is 45 yd
long and 30 yd wide. How many square yards of fertilizer should they order to fertilize the entire field twice this year? F 2,700 yd2 H 1,350 yd2 G 1,900 yd2 J 900 yd2 8. Cassie mailed 67 graduation
invitations to her friends and family. If each stamp costs $0.33, how much did it cost her to mail all of the invitations? $22.11 G $21.22
F
9. Write About It Why is area always written wr itten with square sq uare units?
PS 106
Problem Solving
H J
$13.40 $2.24
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LESSON 26.2 00.0
Name
Algebra: Areas of Parallelograms and Trapezoids Write the correct answer. 1. Find the area of the parallelogram.
2. Find the area of the trapezoid.
4 cm
9 cm
7 ft
12 cm
22.3 ft
3. The length of a rectangle is 15 yd and
the width is 4 yd. Find the area.
4. How many centimeters are equal to
2 km?
Choose the letter for the best answer. 5. A trapezoid has bases of 12 cm and
15 cm and a height of 20 cm. What is the area of the trapezoid? A 540 cm2 C 360 cm2 B 500 cm2 D 270 cm2 7. Paul decided to survey 1 out of every
10 people in his school. school. There There are 976 people in Paul’s school. What is a reasonable estimate for how many people Paul should survey?
A 10 B t r u o c r a H ©
76
98 D 196
C
6. A parallelogram has a base of 7.5 m
and a height of 2.5 m. What is the area of the parallelogram? F 18.75 m2 H 12.75 m2 G 15 m 2 J 10 m 2 8. At a recent gathering in the stadium,
there were about 52,980 people in attendance. If between 4 and 6 people came in each car parked in the stadium parking lot, estimate how many cars were at the stadium parking lot. F 1,000 cars H 10,000 cars G 5,000 cars J 20,000 cars
9. Write About It A rectangle and a parallelogram with
the same base and height have the same area. Draw a diagram and explain why this is true.
Problem Solving
PS 107
LESSON 26.4 00.0
Name
Algebra: Areas of Circles Write the correct answer. 1. Find the area of the circle. Use 3.14 for π
. Round to the nearest whole number.
2. Find the area of the circle. Use 3.14 for π
. Round to the nearest whole number.
6 ft
3. The height of a triangle is 20 cm and
the base is 15 cm. Find the area.
15 yd
4. The length of a rectangle is 12 in. and
the width is 4 in. Find the area.
Choose the letter for the best answer. 5. The diameter of a circle is 42 ft. What is
the area to the nearest whole number? A 5,539 ft2
1,385 ft2 C 441 ft2 D 132 ft2
B
7. Dennis walks up and down the stairs
at school between 6 and 9 times a day. day. Which is a reasonable estimate of how many times he walks up and down the stairs in 180 school days? A Less than 1,000 B Between 1,000 and 1,800 C Between 1,800 and 2,200 D More than 2,200
6. A semicircle has a radius of 10 m.
What is the area of the semicircle to the nearest whole number? F 1,256 m2 G 628 m2 H 314 m2 J 157 m2 8. John earned $48,600 last year. Which is
the best estimate for how much money he earned each week?
$800 G $1,000 H $1,200 J $1,400 F
9. Write About It Explain how the diameter of a circle is related to
the radius.
PS 108
Problem Solving
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LESSON 26.5 00.0
Name
Algebra: Surface Areas of Prisms and Pyramids Write the correct answer. 1. Find the surface area.
2. Find the surface area.
12ft
3m
5m
7m
3. The radius of a circle is 16 cm. Find the
area. Use 3.14 for π. Round to the nearest whole number. number.
2ft
5ft
4. The base of a parallelogram is 22 ft and
the height is 38 ft. Find the area.
Choose the letter for the best answer. 5. The height of a triangle is 40 m and the
base is 52 m. What is the area? A 1,040 m2 B 1,050 m2 C 2,080 m2 D 2,090 m2 7. A cube measures 5 cm on each edge.
What is its surface area? A 200 cm2
150 cm2 C 120 cm2 D 100 cm2
B
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6. Henry walked 3 mi. How many feet did
Henry walk? F 15,940 ft G 15,880 ft H 15,860 ft J 15,840 ft 8. A rectangular pyramid has a base 18 in.
by 10 in., and the triangular faces each have a height of 25 in. What is the surface area? F 4,500 in. 2 G 1,400 in. 2 H 880 in. 2 J 700 in. 2
9. Write About It How are the areas of opposite faces on a rectangular prism
related? How does knowing this relationship help you find the surface area?
Problem Solving
PS 109
LESSON 27.1
Name
Estimate and Find Volume Write the correct answer. 1. Find the volume of a moving carton used
as a wardrobe for clothes that is 5 ft wide, 4 ft deep, and 8 ft tall.
3. The radius of a circle is 4.5 yd. Find the
area. Use π = 3.14. Round to the nearest whole number. number.
2. Find the volume of an ice cream carton
shaped like a triangular prism. The carton is 9 cm tall and the bottom is a triangle with a base of 5 cm and a height of 6 cm.
4. The height of a triangle is 6 in. and the
base is 4 in. Find the area.
Choose the letter for the best answer. 5. Marty has decided to store all his garden
equipment in a big box that measures 3 m on each side. Find the volume. A 27 m 3 B 18 m 3 C 12 m 3 D 9 m3 7. Sharon bought 25 pieces of candy that
looked identical. Without looking, she selected one from the bag. If 18 are dark chocolate and 7 are light chocolate, what is the probability that Sharon picked a light chocolate one? A
18 7
C
7 18
B
18 25
D
7 25
9. Write About It
6. Rita bought a flower vase that is 10 in.
tall. The base is a square that measures 3.5 in. on each side. Find the volume. F 350.5 in.3 G 122.5 in.3 H 70 in.3 J 35 in.3 8. Mo Monica nica earns earns $3 $3 a day day doing doing chores chores
around the house. At this rate, what is a reasonable estimate for how much she makes in a year? Less than $200 G Between $400 and $600 H Between $600 and $800 J More than $1,000 F
Explain how the volume of a rectangular prism relates to the volume of a triangular prism if the prisms have the same length, width, and height.
PS 110
Problem Solving
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LESSON 27.2
Name
Activate Prior Knowledge Readers use what they already know about different topics to help them solve problems. Prior knowledge can give you insight into how to approach a solution. Read the following problem.
VOCABULAR VOCAB ULARY Y
prior knowledge
Barney has 120 ft of wire. He wants to use it as the edges of a rectangular prism with the largest possible volume. What length, width, and height should he choose? 1. Explain how your prior knowledge about each topic listed can help
you solve this problem. a. Making models with centimeter cubes
b. Symmetry
2. Make a model. Then complete the table.
L en g th
Wid th
Heig ht
Total length of wire needed
Total Volume
120 ft 120 ft 120 ft 120 ft 120 ft 3. Solve the problem by comparing the volumes in the table.
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Make a model. Solve using your prior knowledge. 4. Eliza has 100 centimeter-cubes. Find the
size of a rectangular prism that she can make that uses the greatest number of cubes?
5. Rob makes two rectangular prisms. One
is 8 cm long, 2 cm deep, and 2 cm high. The other is 4 cm long, 4 cm deep, and 2 cm high. Which one has the greater volume?
Reading Strategy
PS 111
LESSON 27.3
Name
Algebra: Volumes of Pyramids Write the correct answer. 1. Mark has a pyramid-shape box with a
rectangular base. The length is 4 cm, the width is 5 cm, and the height is 12 cm. Ming has a cube-shape box that measures 5 cm along each side. Which Which box has the greater volume? Explain.
3. A container with a volume of of 230.4 in.3
holds 1 gal of water. How How many gallons of water will a fish tank hold that is 24 in. long, 12 in. wide, and 12 in. high? hi gh?
2. Sara has a pyramid-shape box with a
square base. The The base is 6 in. on each side and its height is i s 6 in. Kyra has a rectangular prism-shape box. The length is 5 in., the width is 4 in., and the height is 3 in. in . Which box has the greater volume? Explain.
4. You You want to plant a bush every every 2 ft along
the curved side of a semi-circular patio that has a radius of 12 ft. How How many bushes do you need?
Choose the letter for the best answer. 5. Carlos planted a flower
6. The art gallery is showing a sculpture in
garden in this shape. Estimate Estimate the area area of the r 8 ft flower garden. A About 12 ft 2 C About 200 ft 2 B About 50 ft 2 D About 800 ft 2
7. Kristi spent $588 on bark mulch for her
plant beds. The landscape supply company has a sale price of 4 yd3 for $112. How many cubic yards of mulch did Kristi buy? 1 A 5 yd3 C 28 yd3 4 B 21 yd3 D 84 yd3 9. Write About It
PS 112
the shape of a square pyramid. It is 4 12 yd high. Each side of the base measures 123 yd. Find the volume. volume. 3 3 5 F 33 yd H 7 yd3 4 6 G
J
1
46 yd3
8. The volume of a cube that measures 4 cm
on each side is 64 cm 3. How does that compare to the volume of a pyramid with the same base and height? F Less than H Greater than G Equal to J Not related
Explain your solution to Exercise 8.
Problem Solving
1
122 yd3
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LESSON 27.5
Name
Volumes of Cylinders Write the correct answer. 6 cm
1. Find the volume of this
soup can. Use π 3.14. Round to the nearest whole number. number.
2. Find the volume of this
oil drum. Use π 3.14. Round to the nearest whole number. number.
10 cm
3. The school playground is a rectangle 2
with an area of 72 72 m . If the length is 12 m, what is the perimete perimeter? r?
8 yd
12 yd
4. The area of a triangular-shape island is
100 mi2. If the base of the triangle is 20 mi, what is the height? height?
Choose the letter for the best answer. 5. Our new hot water tank is 512 ft tall and
has a diameter of 30 in. About how much water will it hold? A 27 ft3 B 43 ft3 C 108 ft 3 D 518 ft 3 7. Paula rolled a number cube 78 times.
Her results are shown shown in the table. Based Based on Paula’s results, what is the probability of rolling a 5? Number Rolled 1 2 Frequency 12 8 1 6 11 B 67
A
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78 11 11 D 78
C
3 4 5 6 14 15 11 18
6. A cylindrical water bottle has a diameter diameter
of 5 in. and is 11 in. tall. About About how much water can it hold? F 86 in.3 G 173 in.3 H 216 in.3 J 864 in.3 8. According According to the newspaper, newspaper, the high
school graduating class for this year is 12% greater than last year’s class. Last year 734 students graduated. graduated. How How large is this year’s graduating class? 646 G 722 H 746 J 822 F
9. Write About It
Cylinder A and Cylinder B have the same size bases. The height of Cylinder A is twice the height of Cylinder B. How are the volumes of the two cylinders related?
Problem Solving
PS 113
LESSON 28.1
Name
Cause and Effect Information in a math problem is related to other information in the same problem. For example, a rule can cause a pattern to occur. The pattern is the effect of the rule.
VOCABULAR VOCA BULARY Y
cause, effect
Read the following problem.
Josh has an unusual way of saving saving money. money. On each day of the month, the number of coins he saves matches the date. The first month he saves pennies. The second month he saves nickels. The third month he saves dimes. Then he starts over. If he begins his plan on March 1, how much money will he have at the end of May? 1. Use the information in the problem above to complete the chart.
C a use
E f fe c t
Number of pennies per day to match the date—31 days
1 ¢ + 2¢ + 3¢ + . . . 31 ¢
2. What pattern can you use for for adding the numbers?
3. Solve the problem.
Solve. 4. Joylyn Joylyn is memorizing math facts. She
memorizes 1 fact on the first day, day, 2 on the second day, 3 on the third day, and so on. On which day will she know 28 facts?
PS 114
Read Readin ing g Stra trategy egy
5. Larry is learning to type. He alternates
learning 2 new letters a day and 3 new letters a day. If he starts on Tuesday, on what day of the week will he know know all 26 letter letters? s?
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LESSON 28.2
Name
Patterns in Sequences Write the correct answer. 1. The third term in a sequence is i s 35. The
rule is add 8 to each term. ter m. What are the first and sixth terms in the sequence?
2. If the trend continues, what will the sales
be in the year 1998? Growing Stronger Every Day 160
3. The fifth term in a sequence is 324. The
rule is multiply each term by 3. What are the second and seventh terms in the sequence?
) s d n a s u o h t ( s e l a S
140 120 100 80 60 40 20 0
4. George can type 125 words in 5 min. How
many words can he type in 1 min?
1997 1998 1999 2000 200 0011 Years Years
Choose the letter for the best answer. 5. Lisa had 7 friends each bring 25 CDs to
her party. She had 48 CDs. Which expression could be used to determine how many CDs were at the party? A 25 7 48 B 25 7 48 C 25 7 48 D 25 7 48 7. Mark started saving with $20. He plans to
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increase his savings by $10 each week. How How much will he save in the eighth week? A $70 C $90 B $80 D $100
6. Paul makes $50 a day by working
part-time. He works five days a week. At this rate, which is the best estimate of how much he will make in a year? F $5,000 G $8,000 H $10,000 J $13,000 1
8. Rainfall is expected to decrease by 2 in.
each year for the next 3 yr. Four inches of rain fell this year. How much rain is expected the year after next? 1 F 3 in. H 4 in. 2 G
1
32 in.
J
5 in.
9. Write About It A sequence of numbers begins with 6. Each term is
multiplied by 12 to get the next term. Explain how you can tell if the sequence is increasing or decreasing.
Problem Solving
PS 115
LESSON 28.3
Name
Number Patterns and Functions Write the correct answer. 1. Hiroshi earns $6.50 an hour. hour. He wants to
2. Jennifer is taking a cab to a museum that
buy a CD player that costs $117. Write Write an equation and find how many hours Hiroshi will have to work to buy the CD player.
is 5 mi away. away. The cost of the cab is $0.85 per mile plus pl us $1.50. Write Write an equation and find how much the cab ride will cost Jennifer.
3. The lunch menu in the cafeteria includes
4 kinds of sandwiches, 3 salads, 3 beverages, and 2 desserts. How How many lunch combinations do you have to choose from?
4. José is building a model ship from a kit.
The scale of the model is 2 cm to 5 m. If the length of the model ship is 30 cm, what is the actual length of the ship?
Choose the letter for the best answer. 5. The members of Mark’s football team 3 4
6. Rebecca is cutting rectangles to make a
average 2 lb for each inch of height. Which equation shows shows the relationship of weight to height for the members of Mark’s football team? 3 3 A w 2 h C w 2 h 4 4
F
B
G l 3 w 2
3 w 2h 4
3 D w 2h 4
7. Brent has a bag that contains 10 red,
12 blue, 8 green, green, and 6 yellow yellow marbles. Without looking, Adam Adam takes a marble from the bag. What is the probability of Adam getting a yellow yellow marble? 2 3 1 B 4
1 6 1 D 36
A
C
9. Write About It
collage. The length of each rectangle is 2 less than than 3 times the width. width. Which equation can you use to find the length of a rectangle that is 4 in. wide? l 3w 2
Problem Solving
J
l 3w 2
8. Irene’s plane leaves at 5:45 P.M. She wants wants
to allow 35 min to get to the airport from her house. If she allows another half hour for check-in and getting to the gate, what time should she leave her house? 5:10 P.M. G 4:40 P.M.
F
If x represents the color of a package and y represents the cost of mailing the package, is y a function of x ? Explain.
PS 116
H l 3w 2
H 4:30 P.M. J
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LESSON 28.4
Name
Geometric Patterns Write the correct answer. 1. Susan is building a
pattern with blocks. Describe the next figure in her pattern.
3. Morgan Morgan has 28 videos. The ratio of
cartoon videos to music videos is 3 to 4. How many cartoon videos does Morgan have?
2. Yuko Yuko is designing
a wall hanging using a pattern of squares. Describe the next figure in her pattern.
4. Sam tossed a coin 63 times and got
29 heads and 34 tails. Based upon Sam’ Sam’s results, what is the probability of getting heads?
Choose the letter for the best answer. 5. Donald bought 63 pens. He paid $2 each
for the pens, not including tax. What was the total price Donald paid for the pens, not including tax? A $124 C $128 B $126 D $130 7. The Tic Toc Nursery School has a big
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clock face on the wall. The numbers are painted in this order: red, yellow, yellow, green, starting at 12. What colors are the numbers 7 and 11? A green, yellow B yellow, red C red, green D yellow, green 9. Write About It
6. Roger traveled 4,644 mi in 18 days. He
traveled the same distance each day. How far did Roger travel each day? 260 mi G 259 mi
F
H 258 mi J
257 mi
8. Ms. Dunn used a circle, a triangle, a
square, then a pentagon to make name tags. The shapes were repeated in the same order. order. If this pattern continues, what shape was used for the 18th 18th name name tag? tag? circle G triangle
F
H square J
pentagon
How How could you use multiples to help you do Exercise 8?
Problem Solving
PS 117
LESSON 29.1
Name
Transformations of Plane Figures Write the correct answer. 1. Tell whether the second figure is a
reflection, translation, or rotation of the first figure.
2. Tell whether the second figure is a
reflection, translation, or rotation of the first figure.
3. Harr Harry y buil builtt a desk deskto top p that that fits fits perf perfec ectl tly y
4. An angle with a measure of 107.5°
into a corner, and it has three sides. What geometric shape is the desktop?
would be classified as what type of angle? Find its supplement.
Choose the letter for the best answer. 5. What transformation could make a
6 beco become me a 9? A B C D
the first job and 27.08 m on the second job. How many meters of of copper pipe did he use in all?
translation 90° rotation reflection 180° rotation
F 12.8 m G 15 m
7. What transformation could make an
arrow pointing south become an arrow pointing west? A B C D
translation 90° rotation reflection 180° rotation
9. Write About It
H 29.88 m J 39.88 m
8. At the start of her trip, Lucy wrote
down the odometer reading as 12,993.8 mi. At the end of her trip she recorded the odometer reading as 13,311.8 mi. How far did Lucy travel on her trip? F 428 mi G 418 mi
H 328 mi J 318 mi
Explain why an arrow pointing east will still be pointing east if
you translate it.
PS 118
6. Kirk used 12.8 m of copper pipe on
Problem Solving
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LESSON 29.2
Name
Tessellations Write the correct answer. 1. Can Grace make a tessellation out of
this figure?
2. Can Sam make a tessellation out of
this figure?
3. Chuck has to pack 12,881 baseballs
into cartons. If each carton holds 32 baseballs, how many cartons does Chuck need?
4. Miranda made a tablecloth shaped
like an octagon. Each side was 28 in. Find the perimeter of the tablecloth.
Choose the letter for the best answer. 5. Luci is choosing a figure to make a
tessellation. Which figure should she choose? A B C D
the letter “P” quarter circle half-moon triangle
7. Bob had a piece of rope
5 7
ft B 1 ft C 11 4 ft 5 D 1 12 ft
tessellation. Which figure should he not choose? F G H J
2 3
ft long that he laid end to end with another piece that was 34 ft long. How long were the two pieces together?
A
6. Harry is choosing a figure to make a
circle hexagon square trapezoid
8. Vinnie is looking at used trucks. He
has found the following prices: $15,595, $19,500, $16,300, and $21,650. What are the mean and the median? F $19,250.50; $17,400 G $18,565.25; $18,100 H $18,261.25; $17,900 J
$17,634.50; $18,300
If you rotate a shape about the origin and a corner of the shape is on the origin, that point never changes position. Explain why.
9. Write About It
Problem Solving
PS 119
LESSON 29.3
Name
Form Mental Images Sometimes it is helpful to form mental images, or draw a mental picture, of the information in a problem. Using the details or facts to make a picture in your mind can help you organize and understand information.
VOCABULAR VOCAB ULARY Y
form mental images
Read the following problem. Arthur is helping his family design a patio. He is using octagonal tiles and square tiles. Can he tessellate the plane with those two shapes? Show how he can do it.
1. Use the details to make a mental picture. Then use words to describe what you see. Details
What I See
Octagonal tiles (8 sides) Square tiles (4 sides) Tessellate the plane
2. Solve the problem.
Make a mental image for each problem. Then solve. 3. Erin is wondering if it is possible to
make a tessellating shape with a curved edge. She draws the shape below. Does her shape tessellate? Show how.
4. The middle school has decided to
allow students to decorate one inside wall. Tia and Al are designing a tessellating border for the wall. Can they use a triangle and a square to make their border? If so, show how. t r u o c r a H ©
PS 120
Rea Readin ding Str Strategy
LESSON 29.4
Name
Transformations of Solid Figures Write the correct answer. 2.
1.
Plug A
Plug B
Re ceptor
Use Use trans transfo forma rmati tions ons to decid decide e which which plug lug (A, B, or bot both) will will fit the rec recept eptor.
3. Five friends are standing in line for
tickets. Paula is standing between Chuck and Chris. Zack is first in line. Chris is directly in front of Maria. List the order in which they are standing.
B
Look at the first figure. Which image is a 180° rotation of the original figure?
4. Maria is stacking books in the library
storeroom. The shelves are 0.8 m apart, and the bottom shelf is 1.5 m from the floor. There are 5 shelves. How far from the floor is the top shelf?
6. The total monthly revenue for the
5.
This cube has one black face. Roll the cube along the line using 90° rotations. How many rotations will occur before the black face will appear on top again? A 3 C 5 B 4 D 6 7. If you double the length and width
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A
of a prism, how does this affect the volume? A doubles C quadruples B triples D stays the same 9. Write About It
gym is $8,000. Half of this is used to pay salaries and 25%, to pay rent and utilities. Finally, 12% is used to pay insurance. The remaining amount is set aside for the purchase of new equipment. How much remains to be spent on new equipment? F $7,913 H $1,760 G $6,960 J $1,040 8. Gia is buying a brush and a hair
ribbon. Each item costs $3.50. Sales tax is 5%. What is Gia’s total cost? F $0.35 H $7.35 G $7.05 J $10.50
Explain how you found the answer to Exercise 7.
Problem Solving
PS 121
LESSON 29.5
Name
Symmetry Write the correct answer. 1. Naomi drew this line of
symmetry. Was she correct? Explain.
3. Gail made placemats as a gift. Each
placemat had 4 equal sides but no right angles. What shape was the placemat?
2. Willie drew this line
of symmetry. Was he correct? Explain.
4. Find three consecutive odd integers
that have a sum of 249.
Choose the letter for the best answer. 5. How many lines of symmetry does
regular pentagon have? F 0 G 1 H 3 J 5
the figure have? A 8 B 2 C 1 D 0 7. A “2-by-4” piece of lumber is really 1 2
1 2
1 in. by 3 in. Find the area of a cross section of a “2-by-4.” 1
in.2 A 23
B 5 in.2
6. How many lines of symmetry does a
1
in.2 C 54 1
in.2 D 62
8. Paul’s budget for food is $10 more than 1 3
of his total budget. He spent $100 on food. What his total total budget.
F $250 G $270
Can a figure have line symmetry and not rotational symmetry? If so, give an example.
H $300 J $310
9. Write About It
PS 122
Problem Solving
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LESSON 30.0 30.1
Name
Inequalities on a Number Line Write the correct answer. 1. Jodi is
1 3
as old as her brother, Tom. Jodi is 6 years old. Write an equation to find Tom’s age and solve.
3. If 3 apples cost $0.59, how much will
16 apples cost?
2. We should all eat at least 4 servings
of vegetables every day. Represent that requirement with an inequality.
4. The speed limit is 55 mi per hr. Write
an inequality to represent the speed limit.
Choose the letter for the best answer. 5. All the trees in the yard are at least
6 ft tall. Which inequali inequality ty represents represents this statement?
6. Which classroom showed the least
increase in the number of books read from last year to this year? Books Read in April
A B C D
n6 n6 n6 n6
Last Year
Room 1 s m o o r s s a l C
This Year Room 2 Room 3 Room 4 0
25
F Room 1 G Room 2 7. All the sixth graders are younger than
14. Which inequality represents this statement? A B C D t r u o c r a H ©
x 14 x 14 x 14 x 14
50 75 100 125 Number of Books
150
H Room 3 J Room 4
8. Kyle started at an elevation of a ft
above sea sea level. level. He climbed climbed 1,200 ft in 4 hr and was at an elevation of 8,765 ft. Which equation could be used to determine the elevation at which he started climbing? F a 8,765 1,200 G a 8,765 1,200 H a 1,200 8,765 J a 1,200 8,765
Explain how you can tell from a graph of integers on a number line that the integers go on forever?
9. Write About It
Problem Solving
PS 123
LESSON 30.2
Name
Graph on the Coordinate Plane Write the correct answer. 1. In which quadrant does the point
2. Which point has coordinates ( 3,2)?
(4,5) lie?
y
6 4
3. Sherry had 57 quarter sandwiches left
over from the party. How many sandwiches is that?
B
-6
C A
2 G
-4
-2 D
x
H
0
2
-2 F
4
6
E
-4
4. Phil has 30 quarters, 28 dimes, and
-6
21 nickels. nickels. How much much does he have? have?
Choose the letter for the best answer. 5. Use the coordinate plane above and
connect points (3,2), (3,0), and ( 2,0) to form a triangle. What is the area of this triangle? A 10 units2 C 6 units2 B 8 units2 D 5 units2 7. Dave bought 9 pizzas to feed
32 people people at a party. party. What What is a reasonable estimate for how much pizza each person will get if everyone shares equally? 1 1 A 7 pizza C 5 pizza 1 1 B 6 pizza D 4 pizza 9. Write About It
connect points (3,2), ( 3,2), (3,–2), and (3,2) to form a rectangle. What is the area of this rectangle? F 36 units2 H 16 units2 G 24 units2 J 9 units2
8. The Weslake family drove 1,856 mi
and used 80 gal of gas. Which is the best estimate of how many miles they drove on 1 gal of gas? F 10 mi
H 30 mi
G 20 mi
J
40 mi
Describe the coordinates of an ordered pair for a point in
Quadrant II.
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6. Use the coordinate plane above and
Problem Solving
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LESSON 30.3 30.0
Name
Graph Functions Write the correct answer. 1. Use the first three values of x and y to
2. Use the coordinate plane to graph the
ordered pairs from the table.
complete the table.
Input (x )
1
2
3
Output (y )
5
10
15
4
5
Input (x )
3
4
5
6
7
Output (y )
0
1
2
3
4
8
3. Jon has a square pizza. He cuts it into
y
6
pieces along all the lines of symmetry of the square. How many pieces does he have?
4 2 x
-8
-6
-4
-2
0 -2
2
4
6
8
-4
4. Solve. 6 x
72
-6 -8
Choose the letter for the best answer. 5. During Math Challenge, Marge
challenged Hal to name a rational number between 56 and 78. Which number should Hal not choose ? A 0.86 B 0.85
C 0.84 D 0.83
7. Each time Tony gets a paycheck, he
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6. Mrs. Harris found that 7 math books
filled one shelf in the bookcase. Which ordered pair represents this relationship if x equals the number of books? F (1,7) H (21,3) G (1,14) J (7,7) 8. To win the game, Sam needs to spin
keeps $5 and puts the rest in his savings account. Which ordered pair represents this relationship if x equals the amount of his paycheck?
a 4 or 7. The spinner is divided equally into 10 sections and numbered from 1 through 10. What is the probability that Sam will win on his next turn?
A (25,30)
C (50,10)
F
1 5
H
B (50,45)
D (1,10)
G
11 10
J
1 2
9. Write About It
1 10
Explain how to graph the ordered pair (4, 2).
Problem Solving
PS 125
LESSON 30.4
Name
Make Generalizations Generalizations are broad conclusions drawn from experiences or from pieces of information. Generalizations are statements about a group of similar situations. Equations that show the relationship between two variables are one kind of generalization. Read the following problem.
Agatha’s family bought a car for $7,600. They paid $456 in sales tax. Tim’s grandfather bought a car for $11,900. He paid $714 in sales tax. Cindy’s aunt Amelia bought a car for $5,400. She paid $324 in sales tax. How much sales tax would there be on a car that cost $9,300? 1. Complete the table.
cost of car, sales tax,
x
y
$7,600 $456
2. Find the relationship between x and y . Divide the amount of
the sales tax by the cost of the car in each case to find the generalization.
3. Use the generalization to solve the problem.
Solve by making a generalization. 4. For each cup of dry white beans that
you want to cook, you need 3 c of water. How many cups of white beans would you be cooking if you were using 20 c of water?
cups of beans (x )
1
2
3
4
cups of water (y )
3
6
9
12
PS 126
Rea Readin ding Strategy egy
5. Duane biked across the county to
raise money for charity. In the morning, he rode for 2.5 hr and traveled 20 mi. In the afternoon, he rode for 1.5 hr and traveled 12 mi. That evening he biked for 3 14 hr and traveled 26 mi. How far did he travel in 334 hr?
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LESSON 30.6
Name
Graph Transformations Write the correct answer. 1. Rectangle A(3,4) B(1,4) C (1,1)
D(3,1) was transformed into rectangle A (0,5) B (2,5) C (2,2) D (0,2). Describe the transformation ′
′
′
′
that took place.
3. Al is older than Mac. Nan is older
than Al but younger than Don. Don is younger than Bob. List the people in order from oldest to youngest.
2. Rectangle W (0,2) (0,2) X (3,2) (3,2) Y (3,0) (3,0) Z(0,0)
was transformed into rectangle W (0,2) X (3,2) Y (3,0) Z (0,0). Describe the transformation that took place. ′
′
′
′
takess 4. The train leaves at 7:30 A.M. It take Dana 20 min to walk to the train station and 15 min to eat breakfast there. When should she leave home?
Choose the letter for the best answer. 5. Lori bought $23.80 worth of groceries.
The tax was $1.90. What was Lori’s total bill, including tax? A $26.80 C $25.90 B $26.87 D $25.70
6. Dale had
7 8
ft of rope. Gregg borrowed ft of rope from Dale. How much rope does Dale have left ? F 3 H 3 4 ft 8 ft 1 1 G 2 ft J 4 ft 1 2
7. Triangle ABC has coordinates A(1,4),
(2,2), 8. Triangle XYZ has coordinates X (2,2),
B(3,4), and C (1,6). (1,6). If it is translated
Y (2,7), (2,7), and Z(5,8). If it is reflected across the x-axis, which are the
left 4 units, which are the coordinates of the new triangle? A A (3,4), B (1, 4), C (3,6) B A (2,4), B (0,4), C (2,6) C A (4,4), B (2,4), C (4,6) D A (1,0), B (3,0), C (1,2) ′
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coordinates of the new triangle? F X (2,2), Y (2,7), Z (5,8) G X (2,2), Y (2,7), Z (5,8) H X (2,2), Y (2,7), Z (5,8) J X (0,2), Y (7,2), Z (8,5) ′
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Describe how the coordinates of a figure change when you reflect it across the x-axis.
9. Write About It t r u o c r a H ©
Problem Solving
PS 127