Chapter Resources GRADE 4, CHAPTER 8

Transcription

1 Chapter Resources GRADE 4, CHAPTER 8 Contents Family Letter for Unit 4 Chapter Pretest (3 pages) Resources for Lessons (6 pages/lesson) Reteach Practice Enrichment Problem Solving Homework English Learners Chapter Test (2 pages) Unit 4 Record Sheet Copyright by Houghton Mifflin Company. All rights reserved. Permission is hereby granted to teachers to reprint or photocopy classroom quantities of the pages or sheets in this work that carry a Houghton Mifflin copyright notice. These pages are designed to be reproduced by teachers for use in their classes with accompanying Houghton Mifflin material, provided each copy made shows the copyright notice. Such copies may not be sold, and further distribution is expressly prohibited. Except as authorized above, prior written permission must be obtained from Houghton Mifflin Company to reproduce or transmit this work or portions thereof in any form or by any electronic or mechanical means, including any information storage or retrieval system, unless expressly permitted by federal copyright law. Address inquiries to School Permissions, 222 Berkeley Street, Boston, MA Printed in the U.S.A. Booklet 8 of 25

2 Family Letter for Unit 4 Dear Family, During the next few weeks, our math class will be learning about and practicing division of whole numbers. You can expect to see work that provides practice with dividing numbers with up to four digits by one- and two-digit numbers. As we use division to learn about prime and composite numbers, you may wish to use this sample as a guide. prime number A whole number that has only itself and 1 as factors. composite number A whole number that has more than two factors. divisible One number is divisible by another if the quotient is a whole number and the remainder is 0. average The number found by dividing the sum of a set of numbers by the number of addends. Prime and Composite Numbers You can use the factors of a number to tell if the number is prime or composite. Examples of Prime Numbers Prime Number Factors 2 1 and and and 13 Notice that each number has exactly two factors. Examples of Composite Numbers Composite Number Factors 4 1, 2, and , 2, 5, and , 2, 3, 4, 6, and 12 Notice that each number has more than two factors. The number 2 is the only prime even number. The number 1 is neither prime nor composite. During this unit, students should continue to practice and memorize basic multiplication and division facts. Sincerely, Your Child s Teacher Check out Education Place at eduplace.com/kids/mw/ for e Glossary, e Word Games, test prep practice, and more. Unit 4 Family Letter

3 Are You Ready? Divide. Check your answers Chapter 8 Pretest Write a division fact for each picture. 5. x x x x x x x x x x x x x x x x x x x x 6. Divide. Tell if there is a remainder Solve. Explain why your answer makes sense. 10. A van can hold 6 passengers. If 20 people need a ride to the museum, how many vans are needed? Go on

4 Check What You Know Divide. Tell if there is a remainder. Chapter 8 Pretest continued Divide. Check your answers Divide , , , ,800 8 Go on

5 Estimate. Write the basic fact you used Chapter 8 Pretest continued Solve. Explain why your answer makes sense. 18. Carly is placing postcards in a scrapbook. She can fit 4 postcards on a page. How many pages does Carly need for 26 postcards? 19. Sean has 30 days to work on a class project. How many full weeks does he have? 20. Andy buys as many $3-books as he can for $20. How much money does he have left over after he buys the books? STOP

6 Model Division Use models to understand division. Reteach 8.1 Use money to find Place 14 one-dollar bills in groups of 5. Look at the picture. It shows how to make as many groups of 5 as possible. Ask yourself how many groups of 5 are there? You should count 2 Look at the one-dollar bills left over. Count them. How many one-dollar bills are left over? R4 Divide 13 into groups with 3 in each group. Use the counters below for Exercises Circle as many groups of 3 counters as you can. How many groups of 3 are there? 2. How many are left over? 3. What is the quotient? 4. Draw a picture to show 10 divided equally into 2 groups. 5. How many are in each equal group? 6. How many are left over? 7. What is the quotient? Use with text pages

7 Model Division Use base-ten blocks to complete the table. Practice 8.1 Number Number of Number in Number Number Equal Groups Each Group Left Sentence Draw a picture to show 30 divided into 5 equal groups. Write a number sentence to show division. 7. Draw a picture to show 17 divided into groups of 4 in each group. Write a number sentence to show division. Test Prep 8. If you divide 20 one-dollar bills into 4 equal groups how many one-dollar bills would be in each group? A 4 C 5 B 3 D 1 9. Mr. Marris is building a birdhouse. He has 23 nails and 5 boards. Does he have enough nails to hammer 4 nails in each board? If so, how many nails will he have left over? Use with text pages

8 Name Enrichment 8.1 Picture Match-Up For each picture, choose a division equation from the box that represents the picture. Each equation will only be used once. Some equations may not be used R R R R R R R R R Use with text pages

9 Model Division Use base-ten blocks to model and solve each problem. 1. Mrs. Murphy had 66 apples. She used 6 apples in each pie she baked. How many pies did Mrs. Murphy bake? Show your work. Problem Solving Mr. Thomas picked several baskets of strawberries. He picked a total of 65 strawberries. He equally divided the strawberries into 3 containers. He ate any remaining strawberries. How many strawberries did Mr. Thomas eat? How can you tell? 3. The grocery store had a total of 56 oranges. The oranges were divided evenly into bags of 5 oranges each. How many bags of oranges were there? Were there any oranges left over? 4. Write About It Explain how the model of 54 5 is similar to Use with text pages

10 Model Division Use base-ten blocks to complete the table. Homework 8.1 Number Number of Number in Number Number Equal Groups Each Group Left Sentence R Problem Solving 5. Martin had 37 shells. He put them in 3 equal piles. How many shells were left over? Show your work. Use with text pages

11 Model Division Read this explanation. English Learners 8.1 In math, divide means to separate into equal parts or to put in equal groups. 2" 2" 2" The process of dividing is called division. In a division problem, the process of dividing is shown in numbers. The total number being divided is called the dividend. The number of groups or portions the number is being divided into is called the divisor. The answer the size of each portion or the number in each group is called the quotient. Any amount left over when the equal portions are made is called the remainder. 2" 2" 2" Write words from the box to fill the blanks. divide division dividend divisor quotient remainder This is a problem. In this problem you must 12 by 6. The number that must be divided, 12, is called the. The number it must be divided by, 6, is called the This division problem has been solved. The answer, 3, is called the. 3 r This division problem has 1 left over. This amount is called the. Use with text pages

12 Divide With Remainders Reteach 8.2 Divide You can use dimes and pennies to show 25 cents. Divide the money into 2 equal groups. Put 1 dime in each group. Put two pennies in each group. There is one penny left over. Count the dimes and pennies in one group. This is the quotient. The penny left over is the remainder. So, 12 R or R1 Divide. Tell if there is a remainder Use with text pages

13 Divide With Remainders Divide. Tell if there is a remainder. Practice Algebra Symbols Write or for each Test Prep 30. Find A 20 R1 B 22 R1 C 21 R1 D 23 R3 31. Marsha, Ashley, Peter and Dawn have 45 pieces of candy to share equally. How many pieces will each get? How many are left over? Explain your answers. Use with text pages

14 Division Riddles Enrichment 8.2 Digit Detective needs help on a mission. He must organize the dividends, divisors, quotients, and remainders into 4 groups. The problem is that he doesn t know which numbers are which. Your job is to help him solve these division riddles to find each number. Then, organize the numbers into the four groups. 1. Divide me by 3, and you ll get a remainder of 2. My digits have a sum of 8 and a difference of 2. I am less than 6 6. What dividend am I? 2. If you divide 48 by me, you ll get no remainder. But if you divide 46 by me, you ll get a remainder of 2. What divisor am I? 3. Divide 56 or 71 by 5 and me as a remainder you ll see. What remainder am I? 4. I am an odd number. When you divide 38 by me, the remainder is 2. What divisors could I be? 5. Divide me by 5 and you ll get a remainder of 2. I am greater than 9 6, but less than What dividend am I? 6. Add me to the product of the divisor and the quotient and you ll get the dividend of 41. That is if the divisor was 3 and the quotient was 13. What remainder am I? 7. Divide 98 by an odd number and you ll get me with a remainder of 8. What quotients can I be? 8. If you divide an even number by 2, I will be your remainder. What remainder am I? Dividends Divisors Quotients Remainders Use with text pages

15 Divide With Remainders Solve. 1. Jordan has 42 files on his computer. He saved an equal number of files on 2 disks. How many files are on each disk? Show your work. Problem Solving Jordan has 89 CDs in his collection. He wants to organize them evenly into 4 cases. How many CDs will he put in each case? How many will be left over? 3. The music store displays CDs on 8 shelves and on the counter. The same number of CDs are displayed on each shelf. If the store displays a total of 83 CDs. How many CDs are on the counter? 4. Randy spent $65 at the music store. He bought 5 CDs. How much did each CD cost? 5. You Decide Harvey has 56 songs stored on his computer. He wants to save them to 3 CDs. How many different ways can he divide the songs? Explain how you found your answer. Use with text pages

16 Divide With Remainders Divide. Tell if there is a remainder. Homework Multiply 1 ten 4. Subtract 4 4. Compare R Bring down 9 ones. Multiply 2 ones 4. Subtract 9 8. Compare R Mental Math Write or for each Problem Solving 12. Jan has 38 baseball caps. She wants to put them in groups of 3 caps each. How many groups of caps will she have? Will she have any caps left over? If so, how many? Show your work. Use with text pages

17 Divide With Remainders Read this information. English Learners 8.2 Model is a word with many meanings. It can be used as a noun, a verb, or an adjective. The dictionary entry below gives the noun meanings. mod el (mod l) noun. 1. a small copy of something: This model of a race car is 6 inches long. 2. a tiny example of something not yet made: The builder showed the family a model of the house he planned to build. 3. a style or design: This year s model of the Speedycar is much better looking than last year s model. 4. a person serving as a subject for an artist: Rhonda asked her friend Beth to be a model for a painting she wanted to make. 5. a person paid to display clothes by wearing them: Helen will be a model in the fashion show tomorrow. Match each picture to the definition that fits it. 1. a small copy of something 2. a tiny example of something not yet made 3. a style or design 4. a person serving as a subject for an artist 5. a person paid to display clothes by wearing them Use with text pages

18 Problem-Solving Application: Interpret Remainders Reteach 8.3 Heather owns a trading-card shop. She is arranging 59 cards on a display. Each row of the display holds 5 cards. How many rows of cards will she need to display all the cards? What is the question? One way to find the answer is to divide. How many rows of cards will she need in the display? What do you know? She has 59 cards Each row will hold 5 cards 11 R Explanation: Eleven rows will hold 55 trading cards. Another row is needed for the extra 4 trading cards, so increase the quotient to the next whole number which is 12. The answer is 12 rows. Solve each problem. Show your work. 1. Brad collects trading cards. He has 68 cards in his collection. He wants to store them in a book. Each page of the book holds 6 cards. How many pages will Brad need to store all of his cards? 2. Complete the table to show how many pages Brad would need if he only had 48 cards. Page 1 6 cards Page 2 12 cards Page 3 3. Maria is putting 93 football trading cards on display for 72 days at the mall. How many full weeks will the cards be on display? 4. Jim is arranging 69 basketball trading cards in 6 equal rows. Any cards left over will not be placed in the display. How many cards will not be in the display? Use with text pages

19 Problem-Solving Application: Interpret Remainders Solve. Explain why your answer makes sense. Show your work. Practice Gordan s Pineapple Farm in Hawaii is shipping 69 pineapples in wooden boxes. Each box holds 6 pineapples. How many boxes are needed? 2. Ms. Ramon brought 26 pineapples home from her vacation to Hawaii. She divided the pineapples into 3 equal piles and ate the pineapples that were left over. How many pineapples did Ms. Ramon eat? 3. Mr. Kelly s class has $65 to spend at the pineapple farm. They decide to use their money to buy pineapples. Each pineapple costs $3. How many pineapples can the class buy? 4. Mr. Jack s class helps pack pineapples in shipping boxes. The class is given 94 pineapples to pack. Each shipping box holds 9 pineapples. How many boxes can the class fill? 5. At the grocery store, Alice is arranging pineapples in the produce case. She puts 7 pineapples in each row, one at a time. What row does she put the 29th pineapple in? Use with text pages

20 Problem-Solving Application: Interpret Remainders Enrichment 8.3 Problem For a vacation, Mrs. Kluthrow and her family drove 478 miles to Philadelphia to visit the museums and other historical places. On the trip, Mrs. Kluthrow took 118 pictures. Of the pictures, 29 are photos of her children and the rest are photos of the places they visited. 1. Mrs. Kluthrow divides the photos of her two children evenly between the two children. How many photos does each child get? Explain how you found your answer. Show your work. 2. Mrs. Kluthrow organized the photos of the places they visited into a photo album. If 4 photos can fit on each page of the album, how many pages did Mrs. Kluthrow use? Explain how you found your answer. 3. Write a division problem in which the remainder is the answer to the problem. Use with text pages

21 Problem-Solving Application: Interpret Remainders Problem Peter has 58 photos to put in an album. He puts 5 photos on each page. How many pages will he need for all 58 photos? Show your work. Problem Solving For the above problem, what does the quotient of 58 5 tell you? 2. What is the remainder? How do you use the remainder to find the answer? 3. How many pages does Peter need? 4. How many of the pages are full? How do you know? Use with text pages

22 Problem-Solving Application: Interpret Remainders Solve. Explain why your answer makes sense. Homework 8.3 A basket holds 4 dinner rolls. How many baskets are needed to hold 47 dinner rolls? How many baskets have 4 rolls? 11 baskets 11 R3 How many rolls are left over? 3 rolls Is another basket needed? yes Another basket is needed to hold the 3 extra rolls, so 12 baskets are needed. Solve each problem. Show your work. 1. A florist received 69 roses. He wants to place the roses in buckets of water. Each bucket holds 6 roses. How many buckets will have 6 roses? How many roses are left over? How many buckets are needed for all the roses? 2. Ms. Dale bought 35 roses to give to her friends. She divided the roses equally between her 3 friends and kept the leftover roses for herself. How many roses did Ms. Dale keep? Use with text pages

23 Problem-Solving Application: Interpret Remainders Read these definitions. English Learners 8.3 post card exhibit on display tour demonstration scrapbook printing plant museum a card used for sending a short message through the mail a display being shown to people to make a trip through a place for the purpose of seeing it a show of how something works a book with blank pages for pasting pictures in a building with machines that print words and pictures on paper a building in which art or historic items are displayed Complete these paragraphs. Fill in the blanks with words from the boxes. tour printing plant demonstration Mrs. Napoleon s class is studying newspapers. Today they are going to visit a to see how newspapers are printed. There they will see a of a printing press. After that, the students will the newspaper office to see where the writers and editors work. on display museum exhibit scrapbook post card Mr. Ortega s class is studying art. They are going to visit a to see the famous paintings that are there. They will also see an of children s art. After that, each child will be given a with a picture of the museum on it. Each child can send the card to a friend, or put it in a. Use with text pages

24 Regroup In Division Reteach 8.4 Divide You can use play money to solve the problem. Show 31 using ten-dollar bills and one-dollar bills. Divide the money into 2 equal groups. Start by moving the ten-dollar bills. You can place 1 ten-dollar bill in each group with 1 ten-dollar bill left over. Exchange the remaining ten-dollar bill for 10 one-dollar bills. Place the one-dollar bills into the 2 equal groups with the ten-dollar bill. You will place 5 one-dollar bills in each group with 1 one-dollar bill left over. Count the money in one of the groups. This is the quotient. The one-dollar bill left over is the remainder. So, 15R or R1 Divide. Check your answers Use with text pages

25 Regroup In Division Divide. Check your answers. Practice Algebra Functions Copy and complete each table. Rule: y x 2 x y Rule: y x 5 x y Rule: y x 7 x y Test Prep 33. Jason is trading baseball cards. He can get 1 pack of cards for 5 single cards. If Jason has 63 single cards to trade, how many packs can he get? 34. If you had 52 cookies to put into 4 bags, how many cookies would go into each bag? How many will be left over? A 5 C 12 B 10 D 15 Use with text pages

26 Remainder Game Enrichment 8.4 Materials: two sets of number cards labeled 1 9, game board, game pieces Number of Players: 1 or more Rules of the game: Each player chooses a game piece and places it at the start square. Players take turns drawing 3 cards from the bag. The player arranges the cards to make a division problem with a two-digit dividend and a one-digit divisor. The player solves the division problem and moves his or her game piece the number of spaces as given below: If the remainder equals 0 move your game piece 4 spaces. If the remainder equals 1 or 2 move your game piece 3 spaces. If the remainder equals 3 or greater move your game piece 2 spaces. Play continues until someone reaches the finish space. Use with text pages

27 Regroup in Division Solve. 1. Mrs. Rosenberg collected 84 leaves for her art class to use. If each student uses 5 leaves to make a design, how many designs will be made? How many leaves will be left over? Show your work. Problem Solving There are 52 sheets of drawing paper. The teacher wants to have as many sheets of paper as he can in 3 equal piles. How many sheets will be in each pile? 3. There were 98 crayons in a container. Timothy divided the crayons equally into boxes of 8 crayons each. How many boxes were completely filled? 4. In art class, 67 drawings were made. All of the students except Carla made 4 drawings. Carla made fewer than 4 drawings. How many drawings did Carla make? 5. Reasoning Kip bought 4 paint sets at the craft store. He gave the clerk $60. His change was $4. How much was each paint set? Explain how you found your answer. Use with text pages

28 Regroup In Division Divide. Check your answers. Homework R Regroup the one ten left as 10 ones R2 Check: Algebra Functions Complete each table. Rule: y x 4 Rule: y x 8 x y x y Problem Solving 15. Three friends made 44 cupcakes. If they share the cupcakes evenly, how many cupcakes will be left over? Show your work. Use with text pages

29 Regroup in Division Read the explanation and the definitions that follow. English Learners 8.4 The prefix re- usually means back or again. Knowing this can help you figure out the meanings of many words. regroup rearrange repay recount replace refund reorder to group again; to put into new groups to arrange again; to arrange in a new way to pay back; to pay people money you owe them to count again to put or give something in place of something that has been lost or broken When you are dividing, you to give back money can regroup ten as 10 ones to order again to help you solve the problem. Complete the sentences below. Fill in the blanks with words in bold type. 1. To make sure that the votes have been counted correctly, two students will the votes. 2. Edda Mae ordered pencils and pens for the office. They are almost gone, so she must some soon. 3. The big show has been canceled. The ticket company will money to everyone who bought a ticket. 4. Derek grouped the blocks in sets of 10 to solve the division problem. He must some of the blocks in order to get the answer. 5. Sveta broke a flowerpot. She must it. 6. Keenan borrowed five dollars from his brother last week. Keenan has now earned ten dollars, so he can his brother. 7. Greta does not like where the chairs and the tables have been placed. She will the furniture so it looks better. Use with text pages

30 Divide Multiples of 10, 100, and 1,000. Reteach 8.5 You can use facts and patterns to help you divide mentally. 3, ones 5 6 ones tens 5 6 tens 60 3, hundreds 5 6 hundreds 600 So, 3, Use basic facts and patterns to find each quotient , , , , tens 6 tens hundreds 3 hundreds tens 5 tens thousands 9 thousands ,400 6 Use with text pages

31 Divide Multiples of 10, 100, and 1,000 Divide. Practice , , , , , , , , ,000 4 Algebra Equations Solve each equation ,100 3 n x y q 17. 1,400 2 p c Test Prep 19. Which number sentence is NOT correct? A C 2, B D , Complete the problem Use with text pages

32 Quotient Mix-Up Enrichment 8.5 At the math factory, there has been a big mix-up. Some of the quotients have been mismatched with a division problem. Look at each problem below. Write correct or incorrect beside each number sentence. Write the correct answer to each problem beside each letter. Then write the letter above each number in the saying below to find out a secret to doing division mentally. 1. 1, A ,000 E 3. 2, F 4. 1, N 5. 6, O P R S 9. 3, T 10. 1, Z Use with text pages

33 Divide Multiples of 10, 100, and 1,000 Solve. Show your work. Problem Solving The Yosemite waterfall has a height of about 2,400 feet. How many yards high is this? (Hint: There are 3 feet in a yard.) 2. A park had a total of 4,200 visitors last week. If the same number of visitors were there each day, how many visitors were at the park on Monday? 3. The number of people that go to the park to swim is 3 times the number of people that go to hike. If 270 people go to swim, how many people go to hike? 4. The snack bar sold $320 worth of sport drinks to hikers. If each drink cost $4, how many drinks did the snack bar sell? 5. Patty hiked a total of 1500 miles. If she hiked 5 miles each day how many days did she hike? Use with text pages

34 Divide Multiples of 10, 100, and 1,000 Homework 8.5 Divide zero 1 zero 4, zeros 2 zeros , , , , , , , , Solve each equation. 9. 2,500 5 x y ,600 n 800 Problem Solving 12. A giant panda may eat up to 420 pounds of food in a week. How many pounds of food can a panda eat in 1 day? Show your work. Use with text pages

35 Divide Multiples of 10, 100, and 1,000 Read these explanations. English Learners 8.5 Today it is December 1, Six months ago it was June 1, After one year it will be December 1 again. If you are fifty years old, it means you have had a birthday in each of 50 years. If you go to the store every week, it means you go to the store at least once every seven days. If you work for a full week, you work all seven days in that week. Match each phrase with its meaning. 1. a full week seven days in the future years ago seven days in a row 3. every week at least one time in a period of seven days 4. each of 10 years a date 10 years in the past 5. after one week every year in a period of 10 years Use with text pages

36 Estimate Quotients Reteach 8.6 Estimate Look at the first digit in the number 82. Think of a basic fact with 3 and a number that is close to the first digit of the dividend Choose 3 3 9, because 9 is close to 8. To find the second digit in the number multiply 9 by Divide So, 82 3 is about 30. Estimate. Write the basic fact you used Basic Fact: Estimate: Basic Fact: Estimate: Basic Fact: Estimate: Basic Fact: Estimate: Basic Fact: Estimate: Basic Fact: Estimate: Basic Fact: Estimate: Basic Fact: Estimate: Use with text pages

37 Estimate Quotients Estimate. Write the basic fact you used. Practice Decide whether the actual quotient is greater than or less than the estimate given. Write or for each Test Prep 22. Which is the best estimate of 132 3? A 30 C 50 B 40 D Notebooks cost $4 each at the school store. Chris has $15. How many notebooks can he buy? Explain. Use with text pages

38 Estimate Quotients Enrichment 8.6 For each quotient given, write two division problems that would give the estimated quotient. The first one has been done for you. Estimated Quotient Division Problems Use with text pages

39 Estimate Quotients The Finley family took a vacation to the beach. They stopped at the Sun N Fun Beach store to buy a few supplies. Use the table to answer problems How many T-shirts can Maggie buy with 3 ten-dollar bills? 2. Mr. Finley bought sunscreen and some postcards. He spent $19. How many postcards did he buy? Problem Solving 8.6 Sun N Fun Beach Store Item sunscreen postcard sunglasses T-shirt Price $5 $2 $6 $7 3. Georgia has $42. She bought 3 T- shirts. How many pairs of sunglasses can she buy with the amount she has left over? Show your work. 4. Four families went out for dinner. The total food bill came to $327. The families also left a $40 tip for the waitress. If each family spent the same amount, about how much did each family spend on dinner? Explain how you found your answer. Use with text pages

40 Estimate Quotients Estimate. Write the basic fact you used. Homework Use basic facts and multiples of 10 to find a new dividend Think: is about Decide whether the actual quotient is greater than or less than the estimate given. Write or for each Problem Solving 12. Jim used 29 beads to make a necklace for his sister. The beads he used come in packages of 5 beads each. About how many packages of beads did Jim use? Show your work. Use with text pages

41 Estimate Quotients Read these explanations. English Learners 8.6 Estimate means to use what you know to make a good guess at an answer. Find the exact amount means to figure out the precise number. Some terms in the box tell about estimating. Others tell about finding the exact amount. Write each term on any line in the web where it belongs. how much about how much guess calculate how many about how many almost precisely estimated quotient exact quotient possible certain estimate find the exact amount Use with text pages

42 Divide. Tell if there is a remainder. Chapter 8 Test Divide. Check your answers Divide , , , ,200 9 Go on

43 Estimate. Write the basic fact you used Chapter 8 Test continued Solve. Explain why your answer makes sense. 18. Mark is displaying toy cars on shelves. He can fit 6 cars on each shelf. How many shelves does Mark need to display 25 cars? 19. Sarah s birthday is in 40 days. How many full weeks is that? 20. Carlos buys as many $8-kites as he can for $35. How much money does he have left over after he buys the kites? STOP

44 Class Unit 4 Assessment Unit 4 Class Record Chapter 8 Chapter 9 Chapter 10 Chapter 11 Unit 4 Test Student Pre- Chapter Pre- Chapter Pre- Chapter Pre- Chapter test Test test Test test Test test Test Form A Form B

45 Chapter Resources GRADE 4, CHAPTER 8 Contents Family Letter for Unit 4 Chapter Pretest (3 pages) Resources for Lessons (6 pages/lesson) Reteach Practice Enrichment Problem Solving Homework English Learners Chapter Test (2 pages) Unit 4 Record Sheet Copyright by Houghton Mifflin Company. All rights reserved. Permission is hereby granted to teachers to reprint or photocopy classroom quantities of the pages or sheets in this work that carry a Houghton Mifflin copyright notice. These pages are designed to be reproduced by teachers for use in their classes with accompanying Houghton Mifflin material, provided each copy made shows the copyright notice. Such copies may not be sold, and further distribution is expressly prohibited. Except as authorized above, prior written permission must be obtained from Houghton Mifflin Company to reproduce or transmit this work or portions thereof in any form or by any electronic or mechanical means, including any information storage or retrieval system, unless expressly permitted by federal copyright law. Address inquiries to School Permissions, 222 Berkeley Street, Boston, MA Printed in the U.S.A. Booklet 8 of 25

46 Family Letter for Unit 4 Dear Family, During the next few weeks, our math class will be learning about and practicing division of whole numbers. You can expect to see work that provides practice with dividing numbers with up to four digits by one- and two-digit numbers. As we use division to learn about prime and composite numbers, you may wish to use this sample as a guide. prime number A whole number that has only itself and 1 as factors. composite number A whole number that has more than two factors. divisible One number is divisible by another if the quotient is a whole number and the remainder is 0. average The number found by dividing the sum of a set of numbers by the number of addends. Prime and Composite Numbers You can use the factors of a number to tell if the number is prime or composite. Examples of Prime Numbers Prime Number Factors 2 1 and and and 13 Notice that each number has exactly two factors. Examples of Composite Numbers Composite Number Factors 4 1, 2, and , 2, 5, and , 2, 3, 4, 6, and 12 Notice that each number has more than two factors. The number 2 is the only prime even number. The number 1 is neither prime nor composite. During this unit, students should continue to practice and memorize basic multiplication and division facts. Sincerely, Your Child s Teacher Check out Education Place at eduplace.com/kids/mw/ for e Glossary, e Word Games, test prep practice, and more. Unit 4 Family Letter

47 Are You Ready? Divide. Check your answers ; ; ; ; Chapter 8 Pretest Write a division fact for each picture. 5. x x x x x x x x x x x x x x x x x x x x Divide. Tell if there is a remainder R1 8 R Solve. Explain why your answer makes sense. 10. A van can hold 6 passengers. If 20 people need a ride to the museum, how many vans are needed? 4 vans; explanations may vary. Go on

48 Check What You Know Divide. Tell if there is a remainder R Chapter 8 Pretest continued 21 Divide. Check your answers. 9 R R3 16 R Divide , , , ,800 8 Go on

49 Estimates may vary. 5; ; Estimate. Write the basic fact you used Chapter 8 Pretest continued Solve. Explain why your answer makes sense. 18. Carly is placing postcards in a scrapbook. She can fit 4 postcards on a page. How many pages does Carly need for 26 postcards? 7 pages; explanations may vary. 19. Sean has 30 days to work on a class project. How many full weeks does he have? 4 weeks; explanations may vary. 20. Andy buys as many $3-books as he can for $20. How much money does he have left over after he buys the books? $2; explanations may vary. STOP

50 Model Division Use models to understand division. Reteach 8.1 Use money to find Place 14 one-dollar bills in groups of 5. Look at the picture. It shows how to make as many groups of 5 as possible. Ask yourself how many groups of 5 are there? You should count 2 Look at the one-dollar bills left over. Count them. How many one-dollar bills are left over? R4 Divide 13 into groups with 3 in each group. Use the counters below for Exercises Circle as many groups of 3 counters as you can. How many groups of 3 are there? 4 2. How many are left over? 1 3. What is the quotient? 4 R1 4. Draw a picture to show 10 divided equally into 2 groups. 5. How many are in each equal group? 6. How many are left over? 0 5 Picture should show 2 groups of 5 7. What is the quotient? 5 Use with text pages

51 Model Division Use base-ten blocks to complete the table. Practice 8.1 Number Number of Number in Number Number Equal Groups Each Group Left Sentence R R R Draw a picture to show 30 divided into 5 equal groups. Write a number sentence to show division. Answers may vary; Draw a picture to show 17 divided into groups of 4 in each group. Write a number sentence to show division. Answers may vary; R1 Test Prep 8. If you divide 20 one-dollar bills into 4 equal groups how many one-dollar bills would be in each group? A 4 C 5 C B 3 D 1 9. Mr. Marris is building a birdhouse. He has 23 nails and 5 boards. Does he have enough nails to hammer 4 nails in each board? If so, how many nails will he have left over? Yes; 3 nails left over Use with text pages

52 Name Enrichment 8.1 Picture Match-Up For each picture, choose a division equation from the box that represents the picture. Each equation will only be used once. Some equations may not be used R R R R R R R R R ⴜ 4 ⴝ 12 R ⴜ 3 ⴝ 21 R ⴜ 5 ⴝ 10 R ⴜ 3 ⴝ 22 R ⴜ 4 ⴝ 11 R1 81 ⴜ 2 ⴝ 40 R1 Use with text pages

53 Model Division Use base-ten blocks to model and solve each problem. 1. Mrs. Murphy had 66 apples. She used 6 apples in each pie she baked. How many pies did Mrs. Murphy bake? 66; check students models; Show your work. Problem Solving Mr. Thomas picked several baskets of strawberries. He picked a total of 65 strawberries. He equally divided the strawberries into 3 containers. He ate any remaining strawberries. How many strawberries did Mr. Thomas eat? How can you tell? He ate 2 strawberries. He ate the leftover strawberries, and the remainder was The grocery store had a total of 56 oranges. The oranges were divided evenly into bags of 5 oranges each. How many bags of oranges were there? Were there any oranges left over? There were 11 bags of oranges and 1 orange left over. 4. Write About It Explain how the model of 54 5 is similar to Answers will vary. Use with text pages

54 Model Division Use base-ten blocks to complete the table. Homework 8.1 Number Number of Number in Number Number Equal Groups Each Group Left Sentence R R R R3 Problem Solving 5. Martin had 37 shells. He put them in 3 equal piles. How many shells were left over? 1 shell Show your work. Use with text pages

55 Model Division Read this explanation. English Learners 8.1 In math, divide means to separate into equal parts or to put in equal groups. 2" 2" 2" The process of dividing is called division. In a division problem, the process of dividing is shown in numbers. The total number being divided is called the dividend. The number of groups or portions the number is being divided into is called the divisor. The answer the size of each portion or the number in each group is called the quotient. Any amount left over when the equal portions are made is called the remainder. 2" 2" 2" Write words from the box to fill the blanks. divide division dividend divisor quotient remainder division divide dividend divisor This is a problem. In this problem you must 12 by 6. The number that must be divided, 12, is called the. The number it must be divided by, 6, is called the r This division problem has been solved. The answer, 3, is called the quotient. This division problem has 1 left over. This amount is called the remainder. Use with text pages

56 Divide With Remainders Reteach 8.2 Divide You can use dimes and pennies to show 25 cents. Divide the money into 2 equal groups. Put 1 dime in each group. Put two pennies in each group. There is one penny left over. Count the dimes and pennies in one group. This is the quotient. The penny left over is the remainder. So, 12 R or R1 Divide. Tell if there is a remainder. 31 R R1 11 R R R Use with text pages

57 Divide With Remainders Divide. Tell if there is a remainder. 21 R R1 11 R Practice R4 11 R3 32 R1 11 R R2 21 R R R3 21 R2 Algebra Symbols Write or for each Test Prep 30. Find A 20 R1 B 22 R1 B C 21 R1 D 23 R3 31. Marsha, Ashley, Peter and Dawn have 45 pieces of candy to share equally. How many pieces will each get? How many are left over? Explain your answers. 11 pieces; 1 piece left over. Explanations will vary. Use with text pages

58 Division Riddles Digit Detective needs help on a mission. He must organize the dividends, divisors, quotients, and remainders into 4 groups. The problem is that he doesn t know which numbers are which. Your job is to help him solve these division riddles to find each number. Then, organize the numbers into the four groups. Enrichment Divide me by 3, and you ll get a remainder of 2. My digits have a sum of 8 and a difference of 2. I am less than 6 6. What dividend am I? 3. Divide 56 or 71 by 5 and me as a remainder you ll see. What remainder am I? 5. Divide me by 5 and you ll get a remainder of 2. I am greater than 9 6, but less than What dividend am I? 2. If you divide 48 by me, you ll get no remainder. But if you divide 46 by me, you ll get a remainder of 2. What divisor am I? Divide 98 by an odd number and you ll get me with a remainder of 8. What quotients can I be? 4. I am an odd number. When you divide 38 by me, the remainder is 2. What divisors could I be? 1 3 or 9 6. Add me to the product of the divisor and the quotient and you ll get the dividend of 41. That is if the divisor was 3 and the quotient was 13. What remainder am I? If you divide an even number by 2, I will be your remainder. What remainder am I? 2, 6, or 10 0 Dividends 35, 57 Divisors 4, 3, 9 Quotients 2, 6, 10 Remainders 1, 2, 0 Use with text pages

59 Divide With Remainders Solve. 1. Jordan has 42 files on his computer. He saved an equal number of files on 2 disks. How many files are on each disk? 21 files 2. Jordan has 89 CDs in his collection. He wants to organize them evenly into 4 cases. How many CDs will he put in each case? How many will be left over? 22 CDs; 1 CD 3. The music store displays CDs on 8 shelves and on the counter. The same number of CDs are displayed on each shelf. If the store displays a total of 83 CDs. How many CDs are on the counter? 3 CDs 4. Randy spent $65 at the music store. He bought 5 CDs. How much did each CD cost? $13 Show your work. Problem Solving You Decide Harvey has 56 songs stored on his computer. He wants to save them to 3 CDs. How many different ways can he divide the songs? Explain how you found your answer. Answers may vary. The CDs should have a total of 56 songs on them combined. Use with text pages

60 Divide With Remainders Divide. Tell if there is a remainder. Homework Multiply 1 ten 4. Subtract 4 4. Compare R Bring down 9 ones. Multiply 2 ones 4. Subtract 9 8. Compare R1 21 R R3 11 R2 12 R1 11 Mental Math Write or for each Problem Solving 12. Jan has 38 baseball caps. She wants to put them in groups of 3 caps each. How many groups of caps will she have? Will she have any caps left over? If so, how many? 12 caps Yes 2 caps Show your work. Use with text pages

61 Divide With Remainders Read this information. English Learners 8.2 Model is a word with many meanings. It can be used as a noun, a verb, or an adjective. The dictionary entry below gives the noun meanings. mod el (mod l) noun. 1. a small copy of something: This model of a race car is 6 inches long. 2. a tiny example of something not yet made: The builder showed the family a model of the house he planned to build. 3. a style or design: This year s model of the Speedycar is much better looking than last year s model. 4. a person serving as a subject for an artist: Rhonda asked her friend Beth to be a model for a painting she wanted to make. 5. a person paid to display clothes by wearing them: Helen will be a model in the fashion show tomorrow. Match each picture to the definition that fits it. 1. a small copy of something 2. a tiny example of something not yet made 3. a style or design 4. a person serving as a subject for an artist 5. a person paid to display clothes by wearing them Use with text pages

62 Problem-Solving Application: Interpret Remainders Reteach 8.3 Heather owns a trading-card shop. She is arranging 59 cards on a display. Each row of the display holds 5 cards. How many rows of cards will she need to display all the cards? What is the question? One way to find the answer is to divide. How many rows of cards will she need in the display? What do you know? She has 59 cards Each row will hold 5 cards 11 R Explanation: Eleven rows will hold 55 trading cards. Another row is needed for the extra 4 trading cards, so increase the quotient to the next whole number which is 12. The answer is 12 rows. Solve each problem. Show your work. 1. Brad collects trading cards. He has 68 cards in his collection. He wants to store them in a book. Each page of the book holds 6 cards. How many pages will Brad need to store all of his cards? 2. Complete the table to show how many pages Brad would need if he only had 48 cards. Page 1 6 cards Page 2 12 cards 12 pages Page 3 Page 4 3. Maria is putting 93 football trading cards on display for 72 days at the mall. How many full weeks will the cards be on display? 10 full weeks Page 5 Page 6 4. Jim is arranging 69 basketball trading cards in 6 equal rows. Any cards left over will not be placed in the display. How many cards will not be in the display? 3 cards not in the display Page 7 Page 8 18 cards 24 cards 30 cards 36 cards 42 cards 48 cards Use with text pages

63 Problem-Solving Application: Interpret Remainders Solve. Explain why your answer makes sense. Show your work. Practice Gordan s Pineapple Farm in Hawaii is shipping 69 pineapples in wooden boxes. Each box holds 6 pineapples. How many boxes are needed? 12 boxes 2. Ms. Ramon brought 26 pineapples home from her vacation to Hawaii. She divided the pineapples into 3 equal piles and ate the pineapples that were left over. How many pineapples did Ms. Ramon eat? 2 pineapples 3. Mr. Kelly s class has $65 to spend at the pineapple farm. They decide to use their money to buy pineapples. Each pineapple costs $3. How many pineapples can the class buy? 21 pineapples 4. Mr. Jack s class helps pack pineapples in shipping boxes. The class is given 94 pineapples to pack. Each shipping box holds 9 pineapples. How many boxes can the class fill? 10 boxes 5. At the grocery store, Alice is arranging pineapples in the produce case. She puts 7 pineapples in each row, one at a time. What row does she put the 29th pineapple in? Row 5 Use with text pages

64 Problem-Solving Application: Interpret Remainders Problem For a vacation, Mrs. Kluthrow and her family drove 478 miles to Philadelphia to visit the museums and other historical places. On the trip, Mrs. Kluthrow took 118 pictures. Of the pictures, 29 are photos of her children and the rest are photos of the places they visited. 1. Mrs. Kluthrow divides the photos of her two children evenly between the two children. How many photos does each child get? Explain how you found your answer. 2. Mrs. Kluthrow organized the photos of the places they visited into a photo album. If 4 photos can fit on each page of the album, how many pages did Mrs. Kluthrow use? Explain how you found your answer. 3. Write a division problem in which the remainder is the answer to the problem. Enrichment photos; R1. Each child got 14 photos, and there was 1 photo left over. Because you can t split 1 photo, I dropped the remainder. 23 pages; I subtracted Since each page can hold 4 photos, I divided R1. Another page is needed for the 1 Answers may vary. Explanations may vary. Show your work. extra photo. So, I increased the quotient to 23. Use with text pages

65 Problem-Solving Application: Interpret Remainders Problem Peter has 58 photos to put in an album. He puts 5 photos on each page. How many pages will he need for all 58 photos? 1. For the above problem, what does the quotient of 58 5 tell you? Possible answer: 58 photos will fit evenly on 11 pages with 3 photos left over. 2. What is the remainder? How do you use the remainder to find the answer? 3 photos; answers will vary. Show your work. Problem Solving How many pages does Peter need? 12 pages 4. How many of the pages are full? How do you know? 11 pages; the whole number of the quotient is 11, so 11 pages are full. Use with text pages