STUDENT WORKSHEETS - Springer978-94-6209-104-7/1.pdf · STUDENT WORKSHEETS UNIT 1: PART-PART-WHOLE PROBLEM REPRESENTATION Lesson 2 Part-Part-Whole Problem Representation Modeling

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APPENDIX A

STUDENT WORKSHEETS

UNIT 1: PART-PART-WHOLE PROBLEM REPRESENTATION

Lesson 2 Part-Part-Whole Problem Representation

Modeling PPW story representation 1, 2, and 31. Heather had 54 crayons. Then, her sister, Tara, gave her 32 more crayons. Now Heather has 86 crayons.

Part Part

+ =

Whole

2. Rachel had 48 flowers in a big vase. Then, 19 of the flowers wilted, so Rachel took them out of the vase. There were then 29 flowers left in the vase.

Part Part

+ =

Whole

3. It rained 45 inches in 2006, and it rained 57 inches in 2005. It rained a total of 102 inches in the two years combined.

Part Part

+ =

Whole

APPENDIX A

192

Try It Out–PPW story representation 4, 5, and 64. The pound had 67 dogs in cages waiting to be adopted. One week, 24 of the dogs were adopted. There were still 43 left at the pound.

Part Part

+ =

Whole

5. A basketball player named Sarah scored 43 points in the first half of a game. Then, she scored 12 more points in the second half. By the end of the game, she had scored 55 points.

Part Part

+ =

Whole

6. Alex had 164 colored pencils. 57 of them were different shades of blue. There were 107 colored pencils which were not blue.

Part Part

+ =

Whole

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Independent Worksheet–PPW story representation 7, 8 and 97. One teacher had 23 flashcards for his students. Another teacher had 89 flashcards. In total the two teachers had 112 flashcards.

Part Part

+ =

Whole

8. One student’s mom baked 56 cookies for the class party. Her son and his friends ate 32 of the cookies before she woke up. There were only 24 cookies left for the party.

Part Part

+ =

Whole

9. A cat caught 23 mice the spring and summer. In the fall and winter, the same cat got 53 mice. The cat caught a total of 76 mice that year.

Part Part

+ =

Whole

APPENDIX A

194

UNIT 2: SOLVING PART-PART WHOLE PROBLEMS

Lesson 3 Solving PPW problems

Modeling PPW problem solving 1–61. Christie read two books over the summer. One book was 193 pages and the other book was 267 pages. How many pages did Christie read over the summer?

Part Part

+ =

Whole

ANSWER:__________________________

2. The Girl Scouts were selling cookies at the mall. They brought 93 boxes of cookies with them, and they sold 47 boxes that day. How many boxes of cookies will the Girl Scouts have to take back home?

Part Part

+ =

Whole

ANSWER:__________________________

3. Travis ordered 68 baseball cards from a magazine. Then, he ordered some more for his brother. In all, he ordered 129 baseball cards. How many did he order for his brother?

Part Part

+ =

Whole

ANSWER:__________________________

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4. Two people in a particular music group have written 48 songs. If one member wrote 27 of the songs, how many did the other one write?

Part Part

+ =

Whole

ANSWER:__________________________

5. After a hard day’s work, a mailman delivered 203 letters, but he still has 148 letters left in his bag. How many letters did he have in his bag at the beginning of the day?

Part Part

+ =

Whole

ANSWER:__________________________

6. Mary wrote 54 poems over the summer, but then she realized she didn’t like some of them and tore them up. Afterwards, she had only 35 poems left. How many did she tear up?

Part Part

+ =

Whole

ANSWER:__________________________

APPENDIX A

196

Independent Worksheet–PPW problem solving 7, 8 and 97. A school fundraiser made $308 in both parent and student contributions. The students contributed $111. How much did the parents contribute?

Part Part

+ =

Whole

ANSWER:__________________________

8. Larry had a big bag of candy after Halloween night. He ate 45 pieces and gave the remaining 57 pieces to his friends. How many pieces of candy did Larry originally have?

Part Part

+ =

Whole

ANSWER:__________________________

9. Gilbert had several paperback books. Then, his brother, Sean, gave him 57 more paperback books. Now Gilbert has 113 paperback books. How many paperback books did Gilbert have in the beginning?

Part Part

+ =

Whole

ANSWER:__________________________

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UNIT 3: REPRESENTING ADDITIVE COMPARE PROBLEMS

Lesson 4: Representing AC-more problems

Modeling AC problem representation 1, 2, & 31. Christine has 43 toy cars. Bob has 66 more toy cars than Christine. Bob has 109 toy cars.

Part Part

+ =

Whole

Smaller DifferenceBigger

2. Lauren has 110 Carnival tickets. Lauren has 50 more tickets than Alex. Alex has 60 tickets.

Part Part

+ =

Whole


3. Rob has 79 glue sticks. Felipe has 38 glue sticks. Rob has 41 more glue sticks than Felipe.

Part Part

+ =

Whole


APPENDIX A

198

Try It Out–AC story representation 4, 5, and 64. Diego has 30 cats. Ronald has 64 more cats than Diego. Ronald has 94 cats.

Part Part

+ =

Whole


5. Celina has 112 bikes. Also, Celina has 64 more bikes than Autumn. Autumn has 48 bikes.

Part Part

+ =

Whole


6. Tracey has 106 necklaces. Simone has 69 necklaces. Tracey has 37 more necklace than Simone.

Part Part

+ =

Whole


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Independent Worksheet—AC story representation 7, 8 and 97. Malcolm has 61 balls. Dale has 60 more balls than Malcolm. How many balls does Dale have.

Part Part

+ =

Whole


8. A girl Melissa has 119 books. Melissa has 72 more books than Alicia. Alicia has 47 books.

Part Part

+ =

Whole


9. Avery has 35 more notebooks than Martin. Martin has 65 notebooks. Avery has 100 notebooks.

Part Part

+ =

Whole


APPENDIX A

200


Lesson 5: Representing AC-less Problems

Modeling AC problem representation 10, 11, and1210. If Cristal has 29 pens and she has 71 fewer pens than a boy named Warren. Warren has 100 pens.

Part Part

+ =

Whole


11. Eugene says he has 88 cards. If Abigail has 35 fewer cards than Eugene, Abigail has 53 cards.

Part Part

+ =

Whole


12. Melissa has 119 books. Melissa has 72 more books than Alicia. Alicia has 47 books.

Part Part

+ =

Whole


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Independent Work–AC problem representation 13, 14, and 15 13. Jorge has 43 flags. Terrell has 80 flags. Jorge has 37 fewer flags than Terrel.

Part Part

+ =

Whole


14. Kaylin has 48 candies. Kaylin has 70 fewer candies than Melody. Melody has 118 candies.

Part Part

+ =

Whole


15. Malcolm has 51 balls. Malcolm has 60 fewer balls than Dale. Dale has 111 balls.

Part Part

+ =

Whole


APPENDIX A

202

UNIT 4: SOLVING ADDITIVE COMPARISON PROBLEMS

Lesson 6: Solving AC-more and AC-less problems

Modeling AC Problem Solving 1, 2, 3, and 4 1. Malcolm has 51 tennis balls. David has 60 more tennis balls than Malcolm. How many tennis balls does David have?

Part Part

+ =

Whole


ANSWER:__________________________

2. Kaylin has 48 candies. Kaylin has 70 fewer candies than Melody. How many Candies does Melody have?

Part Part

+ =

Whole


ANSWER:__________________________

3. Patrick has 119 sports cards. Patrick has 72 more sports cards than Joy. How many Sports cards does Joy have?

Part Part

+ =

Whole


ANSWER:__________________________

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4. Stacey has 106 necklaces. If Jill has 69 less necklaces than Stacey, how many necklaces does Jill have?

Part Part

+ =

Whole


ANSWER:__________________________

Try It Out Worksheet–AC problem solving 5 & 6 5. Phillip has 64 worms. Phillip has 34 more worms than Harley. How many worms does Harley have?

Part Part

+ =

Whole


ANSWER:__________________________

6. Lucas has 30 stamps. Lucas has 44 fewer stamps than Ben. How many stamps does Ben have?

Part Part

+ =

Whole


ANSWER:__________________________

APPENDIX A

204

Independent worksheet- AC problem solving 7, 8 & 97. Ariana has 70 cows. Michelle has 75 more cows than Ariana. How many cows does Michelle have?

Part Part

+ =

Whole


ANSWER:__________________________

8. Felipe has 38 glue sticks. Rodolfo has 41 more glue sticks than Felipe. How many glue sticks does Rodolfo have?

Part Part

+ =

Whole


ANSWER:__________________________

9. Marlene has 49 fewer shirts than Jack. Jack has 96 shirts. How many shirts does Marlene have?

Part Part

+ =

Whole


ANSWER:__________________________

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UNIT 5: SOLVING MIXED PPW AND AC PROBLEMS

Lesson 7: Solving Mixed PPW and AC problems

Modeling PPW and AC Problem Solving 1, 2, 3, and 4 1. Bobby has 87 basketball cards. He has 13 more basketball cards than Jeff. How many basketball cards does Jeff have?

+ =Smaller Difference Bigger

ANSWER:__________________________

2. Nick has 118 cups. Nick gives his sister 22 cups. How many cups does Nick have left?

+ =Part Part Whole

ANSWER:__________________________

3. Lauren has 14 pencils. Lauren has 26 fewer pencils than Brenna. How many pencils does Brenna have?


ANSWER:__________________________

4. Andy and Bill were in a spelling bee. Andy spelled 29 words correctly. Bill spelled 37 words correctly. How many more words did Bill spell correct?


ANSWER:__________________________

APPENDIX A

206

Try-It-Out Worksheet 5 and 6

5. Mike planted 148 tulip bulbs. He planted 59 more than Henry. How many bulbs did Henry plant?


ANSWER:_________________________

6. Angela had many dolls. Then, she gave away 26 of her dolls to her little sister. Now, Angela has 49 dolls. How many dolls did Angela have in the beginning?

+ =Part Part Whole

ANSWER:__________________________

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Independent Worksheet-Mixed Problem Solving 7, 8 ,9 and 10

7. Kelsie said she had 82 apples. If Lee had 32 fewer apples than Kelsie, how many apples did Lee have?


ANSWER:__________________________

8. Selina had some video games. Then, her brother Andy gave her 24 more video games. Now Selina has 67 video games. How many video games did Selina have in the beginning?

+ =Part Part Whole

ANSWER:__________________________

9. Taylor and her friend Wendy collect marbles. As of today, Taylor has 93 marbles. Taylor has 53 more marbles than Wendy. How many marbles does Wendy have?


ANSWER:__________________________

10. Dana has 28 gold fish in her aquarium. She has 32 fewer gold fish than her friend Gesell. How many gold fish does Gisela have in her aquarium?


ANSWER:__________________________

APPENDIX A

208

UNIT 6: EQUAL GROUP PROBLEM REPRESENTATION

Modeling EG story representation 1, 2, and 31. Emily has 9 bags of marbles. Each bag has 6 marbles. There should be a total of 54 marbles.

Unit Rate # of Units Product

X =

2. There are 48 sandwiches to be arranged equally in 6 trays. 8 sandwiches should be arranged in each tray.


X =

3. Each movie ticket costs $7. If Emily needs to buy 8 tickets, the total cost would be $56.


X =

Try It Out–EG story representation 4, 5, and 6 4. Rudy got 442 crayons from the art room. He can put 26 crayons in one crayon box. He will need 17 boxes to hold all of the crayons he got from the art room.


X =

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5. If there are 13 neighborhoods in the town, There are a total of 702 houses in the town. If each neighborrhood has the same number of house, then each neighborrhood has 54 houses in it.


X =

6. Each movie we rented was 93 minutes long. It took us 651 minutes to watch 7 of the movies.


X =

Independent Worksheet–EG Story Representation 7, 8 and 97. Gary made 41 buttons when running for class president. It takes 23 drops of glue to make each button. Gary used 943 drops of glue.


X =

8. Sue wants to buy presents for all her friends. She has $153 and each present costs $9. She can buy 17 presents.


X =

9. Bobby found 7 boxes in the attic of his house. In each box there were an equal number of crystal drinking glasses. If there were 91 total glasses, there were 13 glasses in each box.


X =

APPENDIX A

210

UNIT 7: MODELING EG PROBLEM SOLVING

Modeling EG problem solving 1, 2, and 31. There are 22 ice cream bars in each box. How many ice cream bars would you have if you bought 37 boxes of ice cream bars?


X =

ANSWER:__________________________

2. Lucky Luke hits the exact same number of home runs in each game he plays. Last year, he played 93 games and hit 558 home runs! How many home runs does he hit each game?


X =

ANSWER:__________________________

3. Sue wants to buy presents for all her friends. She has $153 and each present costs $9. How many presents can she buy?


X =

ANSWER:__________________________

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Try It Out–EG problem solving 4, 5, and 6 4. Uncle Jim is a painter. He says that it takes 8 gallons of paint to paint one entire house. How many houses could he paint with 408 gallons of paint?


X =

ANSWER:__________________________

5. Tina gets paid an hourly wage for selling cookies at the mall. She worked 16 hours last week and made $96. How much does Tina make each hour?


X =

ANSWER:__________________________

6. Your class is involved in a relay race. Each student must carry a bucket of water 22 feet. How far would the bucket travel if there were 15 people in your class?


X =

ANSWER:__________________________

APPENDIX A

212

Independent Work–EG problem solving 7, 8 and 97. Gary made 41 buttons when running for class president. It takes 23 drops of glue to make each button. How many drops of glue did Gary use?


X =

ANSWER:__________________________



X =

ANSWER:__________________________

9. Bobby found 7 boxes in the attic of his house. In each box there were an equal number of crystal drinking glasses. If there were 91 total glasses, how many glasses were in each box?


X =

ANSWER:__________________________

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UNIT 8: REPRESENTING MULTIPLICATIVE COMPARE PROBLEM

Modeling MC story representation 1, 2, and 31. Cara has 15 marbles. John has 8 times as many marbles as Cara. John has 120 marbles.

Unit Multiplier Product

X =

2. Sara completed 288 problems for her math homework. She completed 12 times as many problems as Joe. So Joe completed 24 problems.


X =

3. Marie spent $288 during last weekend holiday shopping. She spent 4 times as much as Dianne. Dianne spent $72 during the holiday shopping.


X =

Try It Out–MC Story Representation 4, 5 and 64. Sara completed 24 problems for her math homework. She completed 4 times as many problems as Joe. So Joe completed 6 problems.


X =

5. Bobby scored 21 goals in soccer. Rickie scored 3 times as many goals as Bobby. So Rickie scored 63 goals in soccer.


X =

APPENDIX A

214

6. Mary has 8 red markers and 4 green markers. So she has 2 times as many red markers as green markers.


X =

Independent Worksheet–MC Story Representation 7, 8 and 97. Tara accurately solved 72 problems. Ben accurately solved 9 problems. So Tara accurately solved 8 times as many problems as Ben.


X =

8. Mary spent $120 during last weekend holiday shopping. She spent 3 times as much as Dianne. So Dianne spent $40.


X =

9. Rod biked 56 miles during the season. Ted biked 3 times as many miles as Rod. So Ted biked 168 miles.


X =

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UNIT 9: SOLVING MULTIPLICATIVE COMPARE PROBLEMS

Modeling MC problem solving 1, 2, and 31. Ray has 125 crayons. Crystal has 5 times as many crayons as Ray. How many crayons does Crystal have?


X =

ANSWER:__________________________

2. Both Johnny and Greg play little league baseball. Greg hit 60 home runs. Greg hit 3 times as many home runs as Johnny. How many home runs did Johnny hit during the season?


X =

ANSWER:__________________________

3. Carol has 112 black pens and 14 red pens. How many times as many black pens as red pens does Carol have?


X =

ANSWER:__________________________

APPENDIX A

216

Try-It-Out–MC Problem Solving 4, 5 and 64. Bill watched 63 Phillies games. He watched 7 times as many games as Courtney. How many Phillies games did Courtney watch?


X =

ANSWER:__________________________

5. Dean has 480 drawings. Andre has 24 drawings. Dean has how many times as many drawing as Andre?


X =

ANSWER:__________________________

6. Julie spent $8 at the craft store. Mike spent 3 times as much time as Julia at the store. How much did Mike spend at the craft store?


X =

ANSWER:__________________________

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Independent Worksheet–MC Problem Solving 7, 8 and 97. A student named Macy has 475 pencils. Another student, Francis, has 25 pencils. How many times as many pencils does Macy have as Francis?


X =

ANSWER:__________________________

8. Edwin has 192 oranges. Brandon has 16 times as many oranges as Edward. How many oranges does Brandon have?


X =

ANSWER:__________________________

9. Cameron has 242 monkeys. Cameron has a brother named Isaac. Cameron has 22 times as many monkeys as Isaac. How many monkeys does Isaac have?


X =

ANSWER:__________________________

APPENDIX A

218

UNIT 10: SOLVING MIXED EQUAL GROUPS (EG) AND MULTIPLICATIVE COMPARE (MC) PROBLEMS

Modeling EG and MC Problem Solving 1–61. Your class is involved in a relay race. Each student must carry a bucket of water 22 feet. How far would the bucket travel if there were 15 students in your class?

X =Unit Rate # of Units Product

ANSWER:__________________________


X =UNIT Product

ANSWER:__________________________

3. There are 437 members of the neighborhood football league. If there are 23 teams and each team must have an equal number of players, how many players are on each team?


ANSWER:__________________________

4. Janelle received a total of $360 for her birthday. She wants to buy some giant stuffed animals. Each giant stuffed animal costs $24. How many giant stuffed animals can she buy?


ANSWER:__________________________

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5. Both Lisa and Menghua were volunteers for the Chinese New Year celebration event. Lisa gave out 28 flyers about this event to students across the campus. Her friend Menghua gave out 7 times as many. How many flyers did Menghua give out?

X =UNIT Product

ANSWER:__________________________

6. Evan has 16 Holiday greeting cards for sending out to his friends. Mick has 112 greeting cards for the holiday seasons. The number of greeting cards Mick has is how many times as many as Evan’s?

X =UNIT Product

ANSWER:__________________________

Independent Worksheet-Mixed Problem Solving 7–127. There are 256 students outside on the playground. This is eight times as many students as those who are inside the cafeteria. How many students are inside the cafeteria?

X =UNIT Product

ANSWER:__________________________

8. Eddie spent 45 days reading a novel. On average, he read 38 pages everyday. How many pages does the book have?


ANSWER:__________________________

APPENDIX A

220

9. There are a total of 360 students in Grade four. If one classroom can hold 40 students. How many classrooms does the school need for Grade four?


ANSWER:__________________________

10. The plane goes 700 miles an hour. The car goes 50 miles an hour. The plan is how many times faster as the car?

X =UNIT Product

ANSWER:__________________________

11. Wendy has 96 books. She has a bookshelf with 6 shelves on it. If Wendy puts the same number of books on each shelf, how many books will be on each shelf?


ANSWER:__________________________

12. Franklin Middle School has 1,593 students. An elementary school nearby, Roosevelt Elementary, has 3 times as many students as Franklin. How many students attend Roosevelt Elementary School?

X =UNIT Product

ANSWER:__________________________

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UNIT 11: SOLVING COMPLEX WORD PROBLEMS

Modeling Complex Problem Solving 1–4 1. The table below shows the total number of sport cards Mike collected over 4 weeks. If Mike collected the same number of soccer cards in each week, how many soccer cards did he collect each week?

SportTotal # of cards

collected Football 64Soccer 96Baseball 110Basketball 35


ANSWER:__________________________

2. Susan is putting her collection of 146 rocks into egg cartons. Each carton can hold 12 rocks. How many cartons does she need for all 146 rocks?


ANSWER:__________________________

3. The Vincent elementary school is planning a spring field trip for a total of 152 students. If each minivan can carry a maximum of 16 students, how many minivans are needed to carry all students to the field trip?


ANSWER:__________________________

4. When born, baby kangaroos, or joeys, spend about 235 days in their mother’s pouch before they leave for food. About how many weeks is this?


ANSWER:__________________________

APPENDIX A

222

Try-it-Out and Independent Worksheet–Solving Complex Problems 5–85. Jimmy spent the same amount of money on sports each of 5 months. How much did he spend on sports in each month?

Entries Money spent for 5 months

Books 240Food 1100Transportation 330Sports 250


ANSWER:__________________________

6. There are 1,343 athletes and parents signed up for a sports picnic. Each table will seat 6 people. How many tables will be needed?


ANSWER:__________________________

7. Marilyn is putting her CD collection of 152 CDs into cabinets. Each cabinet can hold 25 CDs. How many cabinets does she need?


ANSWER:__________________________

8. In 1940, a man set a world record by riding his bike for 505 days. About how many weeks did he ride?


ANSWER:__________________________

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UNIT 12: SOLVING MIXED MULTI-STEP PROBLEMS

Modeling Mixed Problem Solving 1–4 1. Emily has 6 dolls and Dana has 11. If Laura has 8 more than Emily and Dana combined, how many dolls does Laura have? (From Harcourt Math, 4th grade, p. 11)

+ =Part Part Whole


ANSWER:__________________________

2. Bart had 6 checkers and found 7 more. Jenny has 8 checkers. How many more checkers will she need so that she and Bart have the same number of checkers? (From Harcourt Math, 4th grade, p. 81)

+ =Part Part Whole


ANSWER:__________________________

3. The Ricardos family paid $14.00 for parking. Parking cost $5.00 for the first hour and $1.50 for each additional hours. How many hours were they parked? (From Harcourt Math, 5th grade, p. 105)

+ =Part Part Whole

x =Unit Rate # of Units Product

ANSWER:__________________________

APPENDIX A

224

4. Maria earned $110, which is $86 more than twice the amount Joan earned. How much did Joan earn? (from Harcourt Math, 5th grade, p. 73)

+ =Part Part Whole

x =UNIT Product

ANSWER:__________________________

Try-it-Out and Independent Worksheet–Solving Mixed Problems 5–105. Bobby has 17 basketball cards. Greg has 12 cards. If Jeff has 13 more than Bobby and Greg combined, how many cards does Jeff have?

+ =Part Part Whole


ANSWER:__________________________

6. The Central Florida Zoo covers 109 acres. The National Zoo, in Washington, D.C., covers 163 acres. If the Central Florida Zoo bought another 55 acres for expansion, which zoo would be larger? How much larger? (Harcourt Math, Grade 4, p. 42)

+ =Part Part Whole


ANSWER:__________________________

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7. Use data: What was the total attendance at the festival in 2003 for all 3 days?

1. Fall foliage festival attendance

Day 2003 2004Thursday 13,789 15,034Friday 23,681 27,950Saturday 34,625 41,393

+ =Part Part Whole

+ =Part Part Whole

OR simply use below diagram:

+ =Part Part Whole

+Part

ANSWER:__________________________

8. The cafeteria served 124 school lunches. There were a total of 11 pizzas cut into 12 slices each. If each student received 1 slice, how many slices were left? (Harcourt Math, Grade 4, p. 177)

+ =Part Part Whole


ANSWER:__________________________

APPENDIX A

226

9. Tyler collects comic books. He displays his collection in 3 binders, with 10 comic books in each. On a trip to the store, Tyler bought 2 new comic books. How many comic books does he have in his collection now? (Harcourt, Grade 4, p. 184)


+ =Part Part Whole

ANSWER:__________________________

10. Mountain cabins are available to rent for $170 a night during the summer or $140 a night during the winter. You want to rent a cabin for 6 nights. How much less would your stay cost during the winter than during the summer? (Harcourt, Grade 4, p. 227)





OR


ANSWER:__________________________

227

APPENDIX B

REFERENCE GUIDE

UNIT 1: PART-PART-WHOLE PROBLEM REPRESENTATION

Lesson 2 Part-Part-Whole Problem Representation

Modeling PPW story representation 1, 2, and 31. Heather had 54 crayons. Then, her sister, Tara, gave her 32 more crayons. Now Heather has 86 crayons.

Part Part

+ =

Whole

54 32 86

2. Rachel had 48 flowers in a big vase. Then, 19 of the flowers wilted, so Rachel took them out of the vase. There were then 29 flowers left in the vase.

Part Part

+ =

Whole

19 29 48

3. It rained 45 inches in 2006, and it rained 57 inches in 2005. It rained a total of 102 inches in the two years combined.

Part Part

+ =

Whole

45 57 102

APPENDIX B

228

Try It Out–PPW story representation 4, 5, and 64. The pound had 67 dogs in cages waiting to be adopted. One week, 24 of the dogs were adopted. There were still 43 left at the pound.

Part Part

+ =

Whole

24 43 67

5. A basketball player named Sarah scored 43 points in the first half of a game. Then, she scored 12 more points in the second half. By the end of the game, she had scored 55 points.

Part Part

+ =

Whole

43 12 55

6. Alex had 164 colored pencils. 57 of them were different shades of blue. There were 107 colored pencils which were not blue.

Part Part

+ =

Whole

57 107 164

Independent Worksheet–PPW story representation 7, 8 and 97. One teacher had 23 flashcards for his students. Another teacher had 89 flashcards. In total the two teachers had 112 flashcards.

Part Part

+ =

Whole

23 89 112

REFERENCE GUIDE

229

8. One student’s mom baked 56 cookies for the class party. Her son and his friends ate 32 of the cookies before she woke up. There were only 24 cookies left for the party.

Part Part

+ =

Whole

32 24 56

9. A cat caught 23 mice the spring and summer. In the fall and winter, the same cat got 53 mice. The cat caught a total of 76 mice that year.

Part Part

+ =

Whole

23 53 76

APPENDIX B

230

UNIT 2: SOLVING PART-PART WHOLE PROBLEMS

Lesson 3 Solving PPW problems

Modeling PPW problem solving 1–61. Christie read two books over the summer. One book was 193 pages and the other book was 267 pages. How many pages did Christie read over the summer?

Part Part

+ =

Whole

193 267 ?

ANSWER: 460 pages.

2. The Girl Scouts were selling cookies at the mall. They brought 93 boxes of cookies with them, and they sold 47 boxes that day. How many boxes of cookies will the Girl Scouts have to take back home?

Part Part

+ =

Whole

47 ? 93

ANSWER: 46 boxes of cookies

3. Travis ordered 68 baseball cards from a magazine. Then, he ordered some more for his brother. In all, he ordered 129 baseball cards. How many did he order for his brother?

Part Part

+ =

Whole

68 a 129

ANSWER: 61 baseball cards

REFERENCE GUIDE

231

4. Two people in a particular music group have written 48 songs. If one member wrote 27 of the songs, how many did the other one write?

Part Part

+ =

Whole

27 a 48

ANSWER: 21 songs

5. After a hard day’s work, a mailman delivered 203 letters, but he still has 148 letters left in his bag. How many letters did he have in his bag at the beginning of the day?

Part Part

+ =

Whole

203 148 a

ANSWER: 351 letters

6. Mary wrote 54 poems over the summer, but then she realized she didn’t like some of them and tore them up. Afterwards, she had only 35 poems left. How many did she tear up?

Part Part

+ =

Whole

a 35 54

ANSWER: 19 poems

APPENDIX B

232

Independent Worksheet–PPW problem solving 7, 8 and 97. A school fundraiser made $308 in both parent and student contributions. The students contributed $111. How much did the parents contribute?

Part Part

+ =

Whole

111 a 308

ANSWER: $ 197

8. Larry had a big bag of candy after Halloween night. He ate 45 pieces and gave the remaining 57 pieces to his friends. How many pieces of candy did Larry originally have?

Part Part

+ =

Whole

45 57 a

ANSWER: 102 pieces

9. Gilbert had several paperback books. Then, his brother, Sean, gave him 57 more paperback books. Now Gilbert has 113 paperback books. How many paperback books did Gilbert have in the beginning?

Part Part

+ =

Whole

a 57 113

ANSWER: 56 paperback books

REFERENCE GUIDE

233


Lesson 4: Representing AC-more problems

Modeling AC problem representation 1, 2, & 31. Christine has 43 toy cars. Bob has 66 more toy cars than Christine. Bob has 109 toy cars.

Part Part

+ =

Whole


43 66 109

2. Lauren has 110 Carnival tickets. Lauren has 50 more tickets than Alex. Alex has 60 tickets.

Part Part

+ =

Whole


60 50 110

3. Rob has 79 glue sticks. Felipe has 38 glue sticks. Rob has 41 more glue sticks than Felipe.

Part Part

+ =

Whole


38 41 79

APPENDIX B

234

Try It Out–AC story representation 4, 5, and 64. Diego has 30 cats. Ronald has 64 more cats than Diego. Ronald has 94 cats.

Part Part

+ =

Whole


30 64 94

5. Celina has 112 bikes. Also, Celina has 64 more bikes than Autumn. Autumn has 48 bikes.

Part Part

+ =

Whole


48 64 112

6. Tracey has 106 necklaces. Simone has 69 necklaces. Tracey has 37 more necklace than Simone.

Part Part

+ =

Whole


69 37 106

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Independent Worksheet—AC story representation 7, 8, and 97. Malcolm has 61 balls. Dale has 60 more balls than Malcolm. Dale has 121 balls.

Part Part

+ =

Whole


60 61 121

8. A girl Melissa has 119 books. Melissa has 72 more books than Alicia. Alicia has 47 books.

Part Part

+ =

Whole


47 92 119

9. Avery has 35 more notebooks than Martin. Martin has 65 notebooks. Avery has100 notebooks.

Part Part

+ =

Whole


65 35 100

APPENDIX B

236


Lesson 5: Representing AC-less problems

Modeling AC problem representation 10, 11, and 1210. If Cristal has 29 pens and she has 71 fewer pens than a boy named Warren. Warren has 100 pens.

Part Part

+ =

Whole


29 71 100

11. Eugene says he has 88 cards. If Abigail has 35 fewer cards than Eugene, Abigail has 53 cards.

Part Part

+ =

Whole


53 35 88

12. Melissa has 119 books. Melissa has 72 more books than Alicia. Alicia has 47 books.

Part Part

+ =

Whole


47 72 119

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Independent Work–AC problem representation 13, 14, and 15 13. Jorge has 43 flags. Terrell has 80 flags. Jorge has 37 fewer flags than Terrel.

Part Part

+ =

Whole


43 37 80

14. Kaylin has 48 candies. Kaylin has 70 fewer candies than Melody. Melody has 118 candies.

Part Part

+ =

Whole


48 70 118

15. Malcolm has 51 balls. Malcolm has 60 fewer balls than Dale. Dale has 111 balls.

Part Part

+ =

Whole


51 60 111

APPENDIX B

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UNIT 4: SOLVING ADDITIVE COMPARISON PROBLEMS

Lesson 6: Solving AC-more and AC-less problems

Modeling AC Problem Solving 1, 2, 3, and 4 1. Malcolm has 51 tennis balls. David has 60 more tennis balls than Malcolm. How many tennis balls does David have?

Part Part

+ =

Whole

51 60 a


ANSWER: 111 tennis balls

2. Kaylin has 48 candies. Kaylin has 70 fewer candies than Melody. How many candies does Melody have?

Part Part

+ =

Whole

48 70 a


ANSWER: 118 candies

3. Patrick has 119 sports cards. Patrick has 72 more sports cards than Joy. How many Sports cards does Joy have?

Part Part

+ =

Whole

a 72 119


ANSWER: 47 sports cards

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4. Stacey has 106 necklaces. If Jill has 69 fewer necklaces than Stacey, how many necklaces does Jill have?

Part Part

+ =

Whole

a 69 106


ANSWER: 37 necklaces

Try It Out Worksheet–AC problem solving 5 & 6 5. Phillip has 64 worms. Phillip has 34 more worms than Harley. How many worms does Harley have?

Part Part

+ =

Whole

a 34 64


ANSWER: 30 worms

6. Lucas has 30 stamps. Lucas has 44 fewer stamps than Ben. How many stamps does Ben have?

Part Part

+ =

Whole

30 44 a


ANSWER: 74 stamps

APPENDIX B

240

Independent worksheet–AC problem solving 7, 8 & 97. Ariana has 70 cows. Michelle has 75 more cows than Ariana. How many cows does Michelle have?

Part Part

+ =

Whole

70 75 a


ANSWER: 145 cows

8. Felipe has 38 glue sticks. Rodolfo has 41 more glue sticks than Felipe. How many glue sticks does Rodolfo have?

Part Part

+ =

Whole

38 41 a


ANSWER: 79 glue sticks

9. Marlene has 49 fewer shirts than Jack. Jack has 96 shirts. how many shirts does Marlene have?

Part Part

+ =

Whole

a 49 96


ANSWER: 47 shirts

REFERENCE GUIDE

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UNIT 5: SOLVING MIXED PPW AND AC PROBLEMS

Lesson 7: Solving Mixed PPW and AC problems

Modeling PPW and AC Problem Solving 1, 2, 3, and 4 1. Bobby has 87 basketball cards. He has 13 more basketball cards than Jeff. How many basketball cards does Jeff have?


a 13 87

ANSWER: 74 basketball cards

2. Nick has 118 cups. Nick gives his sister 22 cups. How many cups does Nick have left?

+ =Part Part Whole

a 22 118

ANSWER: 96 cups

3. Lauren has 14 pencils. Lauren has 26 fewer pencils than Brenna. How many pencils does Brenna have?


14 26 a

ANSWER: 40 pencils

4. Andy and Bill were in a spelling bee. Andy spelled 29 words correctly. Bill spelled 37 words correctly. How many more words did Bill spell correct?


29 a 37

ANSWER: 8 words

APPENDIX B

242

Try-It-Out Worksheet 5 and 65. Mike planted 148 tulip bulbs. He planted 59 more than Henry. How many bulbs did Henry plant?


a 59 148

ANSWER: 89 tulip bulbs

6. Angela had many dolls. Then, she gave away 26 of her dolls to her little sister. Now, Angela has 49 dolls. How many dolls did Angela have in the beginning?

+ =Part Part Whole

26 49 a

ANSWER: 75 dolls

Independent Worksheet-Mixed Problem Solving 7, 8 ,9 and 107. Kelsie said she had 82 apples. If Lee had 32 fewer apples than Kelsie, how many apples did Lee have?


a 32 82

ANSWER: 50 apples

8. Selina had some video games. Then, her brother Andy gave her 24 more video games. Now Selina has 67 video games. How many video games did Selina have in the beginning?

+ =Part Part Whole

a 24 67

ANSWER: 43 video games

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9. Taylor and her friend Wendy collect marbles. As of today, Taylor has 93 marbles. Taylor has 53 more marbles than Wendy. How many marbles does Wendy have?


a 53 93

ANSWER: 40 marbles

10. Dana has 28 gold fish in her aquarium. She has 32 fewer gold fish than her friend Gesell. How many gold fish does Gisela have in her aquarium?


28 32 a

ANSWER: 60 gold fish

APPENDIX B

244

UNIT 6: EQUAL GROUP PROBLEM REPRESENTATION

Modeling EG story representation 1, 2, and 31. Emily has 9 bags of marbles. Each bag has 6 marbles. There should be a total of 54 marbles.


6 9 54X =

2. There are 48 sandwiches to be arranged equally in 6 trays. 8 sandwiches should be arranged in each tray.


X =8 6 48

3. Each movie ticket costs $7. If Emily needs to buy 8 tickets, the total cost would be $56.


X =$7 8 56

Try It Out–EG story representation 4, 5, and 6 4. Rudy got 442 crayons from the art room. He can put 26 crayons in one crayon box. He will need 17 boxes to hold all of the crayons he got from the art room.


X =26 17 442

5. If there are 13 neighborhoods in the town, There are a total of 702 houses in the town. If each neighborhood has the same number of house, then each neighborhood has 54 houses in it.


X =54 13 702

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6. Each movie we rented was 93 minutes long. It took us 651 minutes to watch 7 of the movies.


X =93 7 651

Independent Worksheet–EG Story Representation 7, 8 and 97. Gary made 41 buttons when running for class president. It takes 23 drops of glue to make each button. Gary used 943 drops of glue.


X =23 41 943

8. Sue wants to buy presents for all her friends. She has $153 and each present costs $9. She can buy 17 presents.


X =9 17 153

9. Bobby found 7 boxes in the attic of his house. In each box there were an equal number of crystal drinking glasses. If there were 91 total glasses, there were 13 glasses in each box.


X =13 7 91

APPENDIX B

246

UNIT 7: MODELING EG PROBLEM SOLVING

Modeling EG problem solving 1, 2, and 31. There are 22 ice cream bars in each box. How many ice cream bars would you have if you bought 37 boxes of ice cream bars?


22 37 aX =

ANSWER: 814 ice cream bars

2. Lucky Luke hits the exact same number of home runs in each game he plays. Last year, he played 93 games and hit 558 home runs! How many home runs does he hit each game?


X =a 93 558

ANSWER: 6 home runs



X =9 a 153

ANSWER: 17 presents

REFERENCE GUIDE

247

Try It Out–EG problem solving 4, 5, and 6 4. Uncle Jim is a painter. He says that it takes 8 gallons of paint to paint one entire house. How many houses could he paint with 408 gallons of paint?


X =8 a 408

ANSWER: 51 houses

5. Tina gets paid an hourly wage for selling cookies at the mall. She worked 16 hours last week and made $96. How much does Tina make each hour?


X =a 16 96

ANSWER: $ 6

6. Your class is involved in a relay race. Each student must carry a bucket of water 22 feet. How far would the bucket travel if there were 15 people in your class?


X =22 15 a

ANSWER: 330 feet

APPENDIX B

248

Independent Work–EG problem solving 7, 8 and 97. Gary made 41 buttons when running for class president. It takes 23 drops of glue to make each button. How many drops of glue did Gary use?


X =23 41 a

ANSWER: 943 drops of glue



X =9 a 153

ANSWER: 17 presents

9. Bobby found 7 boxes in the attic of his house. In each box there were an equal number of crystal drinking glasses. If there were 91 total glasses, how many glasses were in each box?


X =a 7 91

ANSWER: 13 glasses

REFERENCE GUIDE

249

UNIT 8: REPRESENTING MULTIPLICATIVE COMPARE PROBLEM

Modeling MC story representation 1, 2, and 31. Cara has 15 marbles. John has 8 times as many marbles as Cara. John has 120 marbles.


15 8 120X =

2. Sara completed 288 problems for her math homework. She completed 12 times as many problems as Joe. So Joe completed 24 problems.


X =24 12 288

3. Marie spent $288 during last weekend holiday shopping. She spent 4 times as much as Dianne. Dianne spent $72 during the holiday shopping.


X =72 4 288

Try It Out–MC Story Representation 4, 5 and 64. Sara completed 24 problems for her math homework. She completed 4 times as many problems as Joe. So Joe completed 6 problems.


X =6 4 24

5. Bobby scored 21 goals in soccer. Rickie scored 3 times as many goals as Bobby. So Rickie scored 63 goals in soccer.


X =21 3 63

APPENDIX B

250

6. Mary has 8 red markers and 4 green markers. So she has 2 times as many red markers as green markers.


X =4 2 8

Independent Worksheet–MC Story Representation 7, 8 and 97. Tara accurately solved 72 problems. Ben accurately solved 9 problems. So Tara accurately solved 8 times as many problems as Ben.


X =9 8 72

8. Mary spent $120 during last weekend holiday shopping. She spent 3 times as much as Dianne. So Dianne spent $40.


X =40 3 120

9. Rod biked 56 miles during the season. Ted biked 3 times as many miles as Rod. So Ted biked 168 miles.


X =56 3 168

REFERENCE GUIDE

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UNIT 9: SOLVING MULTIPLICATIVE COMPARE PROBLEMS

Modeling MC problem solving 1, 2, and 31. Ray has 125 crayons. Crystal has 5 times as many crayons as Ray. How many crayons does Crystal have?


125 5 aX =

ANSWER: 625 crayons

2. Both Johnny and Greg play little league baseball. Greg hit 60 home runs. Greg hit 3 times as many home runs as Johnny. How many home runs did Johnny hit during the season?


X =a 3 60

ANSWER: 20 home runs

3. Carol has 112 black pens and 14 red pens. How many times as many black pens as red pens does Carol have?


X =14 a 112

ANSWER: 8 times

APPENDIX B

252

Try-It-Out–MC Problem Solving 4, 5 and 64. Bill watched 63 Phillies games. He watched 7 times as many games as Courtney. How many Phillies games did Courtney watch?


X =a 7 63

ANSWER: 9 Phillies games

5. Dean has 480 drawings. Andre has 24 drawings. Dean has how many times as many drawing as Andre?


X =24 a 48

ANSWER: 2 times

6. Julie spent $8 at the craft store. Mike spent 3 times as much time as Julia at the store. How much did Mike spend at the craft store?


X =8 3 a

ANSWER: $ 24

REFERENCE GUIDE

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Independent Worksheet–MC Problem Solving 7, 8 and 97. A student named Macy has 475 pencils. Another student, Francis, has 25 pencils. How many times as many pencils does Macy have as Francis?


X =25 a 475

ANSWER: 19 times

8. Edwin has 192 oranges. Brandon has 16 times as many oranges as Edward. How many oranges does Brandon have?


X =192 16 a

ANSWER: 3072 oranges



X =a 22 242

ANSWER: 11 monkeys

APPENDIX B

254

UNIT 10: SOLVING MIXED EQUAL GROUPS (EG) AND MULTIPLICATIVE COMPARE (MC) PROBLEMS

Modeling EG and MC Problem Solving 1–61. Your class is involved in a relay race. Each student must carry a bucket of water 22 feet. How far would the bucket travel if there were 15 students in your class?


22 15 a

ANSWER: 330 feet


X =UNIT Product

a 22 242

ANSWER: 11 monkeys

3. There are 437 members of the neighborhood football league. If there are 23 teams and each team must have an equal number of players, how many players are on each team?


a 23 437

ANSWER: 19 players

4. Janelle received a total of $360 for her birthday. She wants to buy some giant stuffed animals. Each giant stuffed animal costs $24. How many giant stuffed animals can she buy?


24 a 360

ANSWER: 15 giant stuffed animals

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5. Both Lisa and Menghua were volunteers for the Chinese New Year celebration event. Lisa gave out 28 flyers about this event to students across the campus. Her friend Menghua gave out 7 times as many. How many flyers did Menghua give out?

X =UNIT Product

28 7 a

ANSWER: 196 flyers

6. Evan has 16 Holiday greeting cards for sending out to his friends. Mick has 112 greeting cards for the holiday seasons. The number of greeting cards Mick has is how many times as many as Evan’s?

X =UNIT Product

16 a 112

ANSWER: 7 times

Independent Worksheet-Mixed Problem Solving 7–127. There are 256 students outside on the playground. This is eight times as many students as those who are inside the cafeteria. How many students are inside the cafeteria?

X =UNIT Product

a 8 256

ANSWER: 32 students

8. Eddie spent 45 days reading a novel. On average, he read 38 pages everyday. How many pages does the book have?


38 45 a

ANSWER: 1710 pages

9. There are a total of 360 students in Grade four. If one classroom can hold 40 students. How many classrooms does the school need for Grade four?


40 a 360

ANSWER: 9 classrooms

APPENDIX B

256

10. The plane goes 700 miles an hour. The car goes 50 miles an hour. The plan is how many times faster as the car?

X =UNIT Product

50 a 700

ANSWER: 14 times

11. Wendy has 96 books. She has a bookshelf with 6 shelves on it. If Wendy puts the same number of books on each shelf, how many books will be on each shelf?


a 6 96

ANSWER: 16 books

12. Franklin Middle School has 1,593 students. An elementary school nearby, Roosevelt Elementary, has 3 times as many students as Franklin. How many students attend Roosevelt Elementary School?

X =

UNIT Product

1593 3 a

ANSWER: 4779 students

REFERENCE GUIDE

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UNIT 11: SOLVING COMPLEX WORD PROBLEMS

Modeling Complex Problem Solving 1–4 1. The table below shows the total number of sport cards Mike collected over 4 weeks. If Mike collected the same number of soccer cards in each week, how many soccer cards did he collect each week?

Sport Total # of cards collected

Football 64Soccer 96Baseball 110Basketball 35


a 4 96

ANSWER: 24 soccer cards

2. Susan is putting her collection of 146 rocks into egg cartons. Each carton can hold 12 rocks. How many cartons does she need for all 146 rocks?


12 a 146

ANSWER: 13 cartons

3. The Vincent elementary school is planning a spring field trip for a total of 152 students. If each minivan can carry a maximum of 16 students, how many minivans are needed to carry all students to the field trip?


16 a 152

ANSWER: 10 minivans

4. When born, baby kangaroos, or joeys, spend about 235 days in their mother’s pouch before they leave for food. About how many weeks is this?


7 a 235

ANSWER: 34 weeks

APPENDIX B

258

Try-it-Out and Independent Worksheet–Solving Complex Problems 5–85. Jimmy spent the same amount of money on sports each of 5 months. How much did he spend on sports in each month?

Entries Money spent for 5 months

Books 240Food 1100Transportation 330Sports 250


a 5 250

ANSWER: $ 50

6. There are 1,343 athletes and parents signed up for a sports picnic. Each table will seat 6 people. How many tables will be needed?


6 a 1343

ANSWER: 224 tables

7. Marilyn is putting her CD collection of 152 CDs into cabinets. Each cabinet can hold 25 CDs. How many cabinets does she need?


25 a 152

ANSWER: 7 cabinets

8. In 1940, a man set a world record by riding his bike for 505 days. About how many weeks did he ride?


7 a 505

ANSWER: About 72 weeks

REFERENCE GUIDE

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UNIT 12: SOLVING MIXED MULTI-STEP PROBLEMS

Modeling Mixed Problem Solving 1–4 1. Emily has 6 dolls and Dana has 11. If Laura has 8 more than Emily and Dana combined, how many dolls does Laura have? (From Harcourt Math, 4th grade, p. 11)

(1) Find out the total of Emily and Dana combined

+ =Part Part Whole

6 11 ?

? = 6 + 11

? = 17

That is, the total of Emily and Dana combined: 17 dolls.

(2) Find out the # of dolls that Laura has


17 8 a

a = 17 + 8

a = 25

ANSWER: 25 dolls

2. Bart had 6 checkers and found 7 more. Jenny has 8 checkers. How many more checkers will she need so that she and Bart have the same number of checkers? (From Harcourt Math, 4th grade, p. 81)

(1) Find out the total # of checkers that Bart has

+ =Part Part Whole

6 7 ?

? = 6 + 7

? = 13

That is, Bart has a total of 13 checkers.

(2) Find out how many more checkers that Jenny needs to have so that she and Bart will have the same # of checkers (i.e., 13)


8 a 13

APPENDIX B

260

a = 13 – 8

a = 5

ANSWER: 5 more checkers

3. The Ricardos family paid $14.00 for parking. Parking cost $5.00 for the first hour and $1.50 for each additional hours. How many hours they parked? (From Harcourt Math, 5th grade, p. 105)

(1) Find out how much was charged for the parking after the first hour

+ =Part Part Whole

5 ? 14

? = 14 – 5

? = 9

That is, $9 was charged for the additional hours parked after the first hour.

(2) Find out # of hours parked (at the $1.5/ hour rate) after the first hour


1.5 a 9

a = 9 ÷ 1.5

a = 6

That is, they parked 6 additional hours after the first hour.

(3) Find out the total # of hours they parked

From (2), we know that they parked 6 additional hours (at the $1.5 rate) after the first hour ($5), thus the total hours they parked would be:

6 + 1 = 7

ANSWER: They parked 7 hours.

4. Maria earned $110, which is $86 more than twice the amount Joan earned. How much did Joan earn? (from Harcourt Math, 5th grade, p.73)

(1) Find out “twice the amount Joan earned”

+ =Small Difference Bigger

? 86 110

REFERENCE GUIDE

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? = 110 – 86

? = 24

That is, “twice the amount Joan earned” is $24.

(2) Find out the amount Joan earned

x =UNIT Product

a 2 24

a = 24 ÷ 2

a = 12

ANSWER: Joan earned $ 12.

Try-it-Out and Independent Worksheet–Solving Mixed Problems 5–105. Bobby has 17 basketball cards. Greg has 12 cards. If Jeff has 13 more than Bobby and Greg combined, how many cards does Jeff have?

(1) Find out the # of basketball cards Bobby and Greg combined

+ =Part Part Whole

17 12 ?

? = 17 + 12

? = 29

That is, together, Bobby and Greg has a total of 29 basketball cards.

(2) Find out the # of basketball cards the Jeff has


29 13 ?

a = 29 + 13

a = 42

ANSWER: Jeff has 42 basketball cards.

6. The Central Florida Zoo covers 109 acres. The National Zoo, in Washington, D.C., covers 163 acres. If the Central Florida Zoo bought another 55 acres for expansion, which zoo would be larger? How much larger? (Harcourt, Grade 4, p. 42)

(1) Find out the total # of acres Central Florida Zoo covers

+ =Part Part Whole

109 55 ?

APPENDIX B

262

? = 109 + 55

? = 164

That is, Central Florida Zoo covers a total of 164 acres.

(2) Find out which zoo would be larger? How much larger (the difference)?


163 a 164

a = 164 – 163

a = 1

ANSWER: The Central Florida Zoo is larger; it is 1 acre larger.

7. Use data: What was the total attendance at the festival in 2003 for all 3 days?

1. Fall foliage festival attendance

Day 2003 2004Thursday 13,789 15,034Friday 23,681 27,950Saturday 34,625 41,393

As the question asks for year 2003 only, we will only pay attention the column for year 2003.

(1) Find out the total # of attendance for Thursday and Friday

+ =

Part Part Whole

13789 23681 ?

? = 13789 + 23681

? = 37470

(2) Find out the total # of attendance for all three days

+ =Part Part Whole

37470 34625 ?

a = 37470+ 34,625

a = 72095

REFERENCE GUIDE

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OR simply use below diagram:

+ =Part Part Whole

+Part

13789 23681 34625 a

a = 13789 +23681 +34625

a = 72095

ANSWER: Total attendance in 2003 is 72095 people.

8. The cafeteria served 124 school lunches. There were a total of 11 pizzas cut into 12 slices each. If each student received 1 slice, how many slices were left? (Harcourt, Grade 4, p. 177)

(1) Find out the total # of slices


12 11 ?

? = 12 × 11

? = 132

(2) Find out how many slices were left


124 a 132

a = 132 – 124

a = 8

ANSWER: There were 8 slices left.

9. Tyler collects comic books. He displays his collection in 3 binders, with 10 comic books in each. On a trip to the store, Tyler bought 2 new comic books. How many comic books does he have in his collection now? (Harcourt, Grade 4, p.184)

(1) Find out the total # of comic books in his collection in 3 binders


10 3 ?

? = 10 × 3

? = 30

APPENDIX B

264

(2) Find out the total # of comic books in his collection now

+ =Part Part Whole

30 2 a

a = 30 + 2

a = 32

ANSWER: He has 32 comic books in his collection now.

10. Mountain cabins are available to rent for $170 a night during the summer or $140 a night during the winter. You want to rent a cabin for 6 nights. How much less would your stay cost during the winter than during the summer? (Harcourt, Grade 4, p. 227)

(1) Find out the cost for 6 nights during the summer


170 6 S

S = 170 × 6

S = 1020

That is, the cost for summer stay would be $1020.

(2) Find out the cost for 6 nights during the summer


140 6 W

W = 140 × 6

W = 840

That is, the cost for winter stay would be $840.

(3) Find out the difference between the summer and winter costs

You can either directly subtract the two numbers or use the model; it will result the same math sentence:

+ =Small Difference Bigger840 a 1020

a = 1020 – 840

a = 180

ANSWER: $ 180 less

REFERENCE GUIDE

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OR

(1) Find out the difference in cost for 1 night stay between summer and winter

+ =Small Difference Bigger140 ? 170

? = 170 – 140

? = 30

That is, it will cost $30 less for each night stay during the winter than summer.

(2) Find out the total saving for 6-night stay


30 6 a

a = 30 × 6

a = 180

ANSWER: $ 180 less.

267

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