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STUDY LINK 4 1 Uses of Division Copyright © Wright Group/McGraw-Hill 102 Name Date TimeName Date Time Practice Solve. Then write the other problems in the fact families. 5. 1,803 925  6. 498 377  11 21 Use multiplication and division facts to solve the following problems mentally. Remember:Break the number into two or more friendly parts. Example:How many 4s in 71? Break 71 into smaller, friendly numbers. Here are two ways. ◆40 and 31. Ask yourself: How many 4s in 40?(10) How many 4s in 31?(7 and 3 left over) Think: What multiplication fact for 4 has a product near 31?(4  7 28) Total  17 and 3 left over. ◆20, 20, 20, and 11. Ask yourself: How many 4s in 20?(5) How many 4s in three 20s? (15) How many 4s in 11?(2 and 3 left over) Total 17 and 3 left over. So 71 divided by 4 equals 17 with 3 left over. 1. 57 divided by 3 equals . 2. 96 divided by 8 equals . (friendly parts for 57) (friendly parts for 96) 3. The diameter of Earth, about 8,000 miles, 4. The weight of an object on Earth is is about 4 times the diameter of the 6 times heavier than its weight on the moon. What is the approximate moon. An object that weighs 30 lb diameter of the moon? on Earth weighs how many pounds on the moon? unit unit 8,000 mi

LESSON 4 1 Name Date Time Testing for Divisibility by 7, 11, and 13 103 Copyright © Wright Group/McGraw-Hill Use these divisibility rules to test large numbers. To test if a number is divisible by 7: 1. Is 33,992 divisible by 7? To test if a number is divisible by 11: 2. Is 9,723 divisible by 11? To test if a number is divisible by 13: 3. Is 89,362 divisible by 13? ◆Take the rightmost digit. 25,809 ◆Double it. 9 2 18 ◆Subtract the result from the 2,580 18 2,562 remaining digits. ◆Repeat, each time doubling the 2,562 2 2 4 256 4 252 rightmost digit and subtracting, 252 2 2 4 25 4 21 until the result is small enough to know that it is, or is not, 21 is divisible by 7, so 25,809 is divisible by 7.divisible by 7. ◆Find the sum of every other digit. 1 0,6 48 1  6  8 15 ◆Find the sum of the digits that are left. 0 4 4 ◆Subtract. 15 4 11 11 is divisible by 11, so 10,648 is divisible by 11. ◆Multiply the rightmost digit by 4. 1,166,932 2 4 8 ◆Add the result to the remaining 116,693  8116,701 digits. ◆Repeat, each time multiplying 116,701 1 4 4 the rightmost digit and adding, 11,670  411,674 4 4 16 until the result is small enough to 1,167  16 1,183 3 4 12 know that it is, or is not, divisible 118  12  130 by 13. 130 13 10, so 1,166,923 is divisible by 13.

STUDY LINK 4 2 Division Copyright © Wright Group/McGraw-Hill 104 Name Date Time Here is the partial-quotients algorithm using a friendly numbers strategy. 72  37 Rename dividend (use multiples of the divisor): 237 210 21 6 How many 7s are in 210? 30 30 The first partial quotient. 30  7 210 Subtract. 27 is left to divide. How many 7s are in 27? 3 The second partial quotient. 3  7 21 Subtract. 6 is left to divide. Add the partial quotients: 30 3 33 1. Another way to rename 237 with multiples of 7 is 237 70 70 70 21 6 If the example had used this name for 237, what would the partial quotients have been? 2. 6166 3. 214 / 5 Answer: Answer: 4. 485 15 5. 174  08 Answer: Answer: 210 27 21 6 3 33 Practice 6. 3,817 168  Check: 7. 52,517 281  Check: Remainder Quotient Answer: 33 R6 → → 22 23

LESSON 4 2 Name Date Time Divisibility by the Digits 105 Copyright © Wright Group/McGraw-Hill Ms. Winters asked Vito and Jacob to make answer cards for a division puzzle. They had to find numbers that met all of the following characteristics. 1. Jacob knew that with divisibility rules, it should be easy. The boys started with 3-digit numbers and found 123 and 242. Latoya checked their work. What should she tell them? Example: ◆The first digit is divisible by 1. 1 ◆The first two digits are divisible by 2. 12 ◆The first three digits are divisible by 3. 120 ◆The first four digits are divisible by 4. 1,204 ◆The first five digits are divisible by 5. 12,040 ◆The first six digits are divisible by 6. 120,402 ◆The first seven digits are divisible by 7. 1,204,021 ◆The first eight digits are divisible by 8. 12,049,216 ◆The first nine digits are divisible by 9. 120,402,162 Puzzle Numbers 4-digit 5-digit 6-digit 7-digit 8-digit 9-digit 2. Use the characteristics listed above to find as many puzzle numbers as you can. Record them in the boxes below.

STUDY LINK 4 3 Distance to School Copyright © Wright Group/McGraw-Hill 106 Name Date Time There are two ways to go from Josephina’s house to school. She can take Elm Street and then Washington Avenue. She can also take Snakey Lane. Use the map and scale below to answer the questions. 1. Josephina started walking from home to school along Elm Street. a. How far would Josephina walk before she turned onto Washington Avenue? b. How far would she be from school when she turned the corner? 2. Suppose Josephina could take a straight path from her house to school. Estimate the distance. a. Draw and measure a straight line on the map from Josephina’s house to the school. b. Use the scale to measure this distance in miles. Washington Avenue Elm Street Snakey Lane School Josephina’s house 01 1 2 1 inch represents 1 2mile 3. 376 188  Check:  4. 3,997 151  Check:  Practice 211 212

LESSON 4 3 Name Date Time Estimating Curved-Path Distances 107 Copyright © Wright Group/McGraw-Hill Use a ruler, string, compass, paper and pencil, or any other tool. 1. The map below shows the border between Mexico and the United States. Estimate the length of the border. mi 0 1 inch 200 miles CALIF. MEXICO ARIZONA NEW MEXICO TEXAS 2. a. Estimate the lengths of the following rivers. Use the map on pages 386 and 387 of the Student Reference Book. River Length (miles) Arkansas (CO, KS, OK, and AR) Missouri (MT, ND, SD, NE, IA, KS, and MO) Brazos (NM and TX) Chattahoochee (GA, AL, FL) b. Explain how you found the length of the Chattahoochee River.

LESSON 4 3 Name Date Time A Trip through the Panama Canal 108 Copyright © Wright Group/McGraw-Hill The Panama Canal crosses the country of Panama near its capital city, Panama City. The canal connects the Atlantic Ocean and the Pacific Ocean. Pretend that you will travel by ship from New York, through the Panama Canal, to Los Angeles. 1. Use the map below to decide on a route your ship will take. Then use a pencil to draw this route on the map. 2. Estimate the length of the route you have chosen. Use a ruler, string, compass, paper and pencil, or any other tool. mi 3. How much longer is your route than the straight-line distance from New York to Los Angeles? mi ATLANTIC OCEAN PACIFIC OCEAN Caribbean Sea Gulf of Mexico Los Angeles 0 250 500 1 inch represents 500 milesNew York UNITED STATES MEXICO SOUTH AMERICA Panama City PANAMA N WE S

LESSON 4 4 Name Date Time Easy Multiples 109 Copyright © Wright Group/McGraw-Hill 1,000 º1,000 º 100 º100 º 50 º50 º 20 º20 º 10 º10 º 5º5 º 1,000 º1,000 º 100 º100 º 50 º50 º 20 º20 º 10 º10 º 5º5 º 1,000 º1,000 º 100 º100 º 50 º50 º 20 º20 º 10 º10 º 5º5 º

STUDY LINK 4 4 Division Copyright © Wright Group/McGraw-Hill 110 22 23 Name Date Time Here is an example of the partial-quotients algorithm using an “at least...not more than” strategy. 81 85 Begin estimating with multiples of 10. How many 8s are in 185? At least 10. 10 The first partial quotient. 10 º 8 80 Subtract. 105 is left to divide. How many 8s are in 105? At least 10. 10 The second partial quotient. 10 º 8 80 Subtract. 25 is left to divide. How many 8s are in 25? At least 3. The third partial quotient. 3 º 8 24 3 Subtract. 1 is left to divide. 1 23 Add the partial quotients: 10 10 3 23 Remainder Quotient Answer: 23 R1 Solve. 1. 639 9 2. 954 18 Answer: Answer: 3. 1,990 / 24 4. 972 / 37 Answer: Answer: 5. Robert is making a photo album. 6 photos fit on a page. How many pages will he need for 497 photos? pages Practice 6. 2,746 68  Check:   7. 3,461 165  Check:   80105 80  25 24  → →

LESSON 4 4 Name Date Time Division Practice 111 Copyright © Wright Group/McGraw-Hill For each division problem, complete the list of multiples of the divisor. Then divide. 1. 234566 2.  Answer: Answer: 200 º 200 º  100 º 100 º  50 º 50 º  20 º 20 º  10 º 10 º  5 º 5 º  3. / 4.  Answer: Answer: 200 º 200 º  100 º 100 º  50 º 50 º  20 º 20 º  10 º 10 º  5 º 5 º 

LESSON 4 4 Name Date Time Using Expanded Notation 112 Copyright © Wright Group/McGraw-Hill ◆Work with a partner. Use a deck with 4 each of cards 1–9. ◆Take turns dealing 4 cards and forming a 4-digit number. ◆Write the number in standard notation and expanded notation. ◆Then write equivalent names for the value of each digit. 1. Write a 4-digit number. 2. Write the number in expanded notation.    3. Write equivalent names for the value of each digit. 4. Write a 4-digit number. 5. Write the number in expanded notation.    6. Write equivalent names for the value of each digit. 1st digit 2 nd digit 3 rd digit 4 th digit 1st digit 2 nd digit 3 rd digit 4 th digit 1st digit 2 nd digit 3 rd digit 4 th digit

STUDY LINK 4 5 Estimate and Calculate Quotients 113 Name Date Time Copyright © Wright Group/McGraw-Hill For each problem: ◆Make a magnitude estimate of the quotient. Ask yourself: Is the answer in the tenths, ones, tens, or hundreds? ◆Circle a box to show the magnitude of your estimate. ◆Write a number sentence to show how you estimated. ◆If there is a decimal point, ignore it. Divide the numbers. ◆Use your magnitude estimate to place the decimal point in the final answer. ◆Check that your final answer is reasonable. 1. 678.6 2. 3387 How I estimated: How I estimated: Answer: Answer: 3. $29.52 8 4. 989 43 How I estimated: How I estimated: Answer: Answer: 5. 845 / 5 6. 15.84 / 9 How I estimated: How I estimated: Answer: Answer: 1s 0.1s 10s 100s 1s 0.1s 10s 100s 1s 0.1s 10s 100s 1s 0.1s 10s 100s 1s 0.1s 10s 100s 1s 0.1s 10s 100s Practice 7. 8.54 6.004  Check:   22 23

LESSON 4 5 Name Date Time Division with Base-10 Blocks 114 Copyright © Wright Group/McGraw-Hill For each problem: ◆First use to represent the dividend with base-10 blocks. ◆Then use to show how you would distribute the blocks in equal groups to represent the division. ◆Record your answer with digits. Example:56  89 w w w w ww Answer: 56  89 w w w w ww 1. 3427ww0w0w0w ◆Show the dividend: ◆Show equal groups below. ◆Write the answer. 34 27ww0w0w0w 2. 4555w0w0w0w0w ◆Show the dividend: ◆Show equal groups below. ◆Write the answer. 45 55ww0w0w0w 137 R4

LESSON 4 5 Name Date Time A Division Challenge 115 Copyright © Wright Group/McGraw-Hill Judy and two friends bought a raffle ticket at the school fund-raiser. They agreed that if they won, they would share the winnings equally. They won $145! They received one $100 bill, four $10 bills, and five $1 bills. Judy used this division algorithm to calculate how much money each person should get. Can you figure out how the algorithm works? (Hint:There were 3 people in all. Judy realized that in order to share the $100 bill, they needed to trade it for ten $10 bills. Then they would have fourteen $10 bills and five $1 bills.) 1. Explain how you think the algorithm works. 2. Explain what Judy did when she had $1 left. 3. How much money did each person get? 4. Use the algorithm to divide: 45 1.6 100s 10s 1s 10 ths 100 ths 4833 314500 14 25 10 10 12 24 99 2111  

STUDY LINK 4 6 Division Number Stories with Remainders Copyright © Wright Group/McGraw-Hill 116 Name Date Time For each number story draw a picture or write a number sentence on the back of this page. Then divide to solve the problem. Decide what to do about the remainder. Explain what you did. Example: You need to set up benches for a picnic. Each bench seats 7 people. You expect 25 people to attend. How many benches do you need? Circle what you did with the remainder. Ignored it Reported it as a fraction or decimal Rounded the answer up Why? 3 benches seat 21 people. One more bench is needed. 1. It costs $50.00 to be a member of a soccer team. The team plays 8 games during the season. What is the cost per game? $ Circle what you did with the remainder. Ignored it Reported it as a fraction or decimal Rounded the answer up Why? 2. Lynn is having a party. Pizzas cost $8.00 each. How many pizzas can she buy with $60.00? pizzas Circle what you did with the remainder. Ignored it Reported it as a fraction or decimal Rounded the answer up Why? 257b 25 people How many benches? 7 seats per bench benches 4 3. 31 2→ 4. 629 84  Practice 226 243

LESSON 4 6 Name Date Time Finding Number Story Information 117 Copyright © Wright Group/McGraw-Hill For each problem, write the number of the sentence that has the information for each part of the situation diagram. Then complete the situation diagram. Problem 1 1. Ms. Haag is rearranging her classroom. 2. There are 32 students. 3. The students sit at tables. 4. Four students can sit at each table. 5. How many tables does she need? Sentence(s): Problem 2 1. Marc needs 3 yards of fabric to make a cape for a costume party. 2. His friends want capes that match his. 3. If Marc has 15 yards of fabric, how many capes can he make? Sentence(s): per tables total students ?4 in all per 226 243

LESSON 4 7 Name Date Time Math Message 118 Math Message Name: 1st die 2nd die Product (P) 20 P Math Message Name: 1st die 2nd die Product (P) 20 P Math Message Name: 1st die 2nd die Product (P) 20 P Math Message Name: 1st die 2nd die Product (P) 20 P Math Message Name: 1st die 2nd die Product (P) 20 P Math Message Name: 1st die 2nd die Product (P) 20 P Copyright © Wright Group/McGraw-Hill

STUDY LINK 4 7 Variables 119 Name Date Time Copyright © Wright Group/McGraw-Hill For Problems 1–3: ◆ Find the value of xin the first number sentence. ◆ Use this value to complete the second number sentence. 1. xnumber of days in a week 2. x 11 0of 100 x 2x78  3. xlargest sum possible with 2 six-sided dice 598 x 4. Count the number of letters in your first name and in your last name. a. My first name has letters. b. My last name has letters. c. Find the product of these 2 numbers. Product  Answer the questions in Problems 5–11 by replacing xwith the product you found in Problem 4. 5. Is xa prime or a composite number? 6. Is 3x 0less than 1? 7. Which is larger, 3 x,or x100? 8. What is the median and the range for this set of 3 weights: 30 pounds, 52 pounds, xpounds? 9. There are 200 students at Henry Clissold School. x% speak Spanish. How many students speak Spanish? 10. (3x5) 7  11. True or false: x 230 x 12. 3,817 168  13. 52,517 281  218 Practice

LESSON 4 7 Name Date Time Solving for Unknown Quantities 120 226 For each number story: ◆ Draw a situation diagram. ◆ Fill in the numbers. Write a ? for the unknown quantity. ◆ Write a number sentence with for the unknown. ◆ Solve the problem. Example: Fran bought a bag of 14 marbles from a game store. She added them to her collection. She now has 47 marbles. How many marbles did she have before she bought more? Number sentence: 1447 Solution: 33 1. It was 68 when Nadine left for school. By lunchtime, it was 75 . By how many degrees had the temperature gone up? Number sentence: Solution: 2. Michael wants to buy a milkshake. With tax, it costs $3.92, and he has $3.43. How much more money does he need? Number sentence: Solution: 3. Lora bought 5 packages of pencils. Each package had 12 pencils in it. How many pencils did she buy in all? Number sentence: Solution: 4. Make up a problem of your own on the back of this page. 47 14 ? Diagram Copyright © Wright Group/McGraw-Hill

121 Copyright © Wright Group/McGraw-Hill Fractions, Decimals, and Percents Unit 5 focuses on naming numbers as fractions, decimals, and percents. Your child will use pattern blocks to review basic fraction and mixed-number concepts as well as notations. Your child will also formulate rules for finding equivalent fractions. InFourth Grade Everyday Mathematics,your child learned to convert easy fractions, such as 1 2,1 4,11 0, and 3 4, to equivalent decimals and percents. For example, 1 2can be renamed as 0.5 or 50%. Your child will now learn (with the use of a calculator) how to rename any fraction as a decimal and as a percent. Unit 5 also introduces two new games: Estimation Squeeze,to practice estimating products; and Frac-Tac-Toe, to practice converting fractions to decimals and percents. These games, like others introduced earlier, are used to reinforce arithmetic skills. Both games use simple materials (calculator, number cards, and pennies or other counters) so you can play them at home. Your child will study data about the past and compare it with current information as the American Tour continues. Please keep this Family Letter for reference as your child works through Unit 5. STUDY LINK 4 8 Unit 5: Family Letter Name Date Time

Copyright © Wright Group/McGraw-Hill 122 bar graph A graph that uses horizontal or vertical bars to represent data. circle graph A graph in which a circle and its interior are divided through its center into parts to show the parts of a set of data. The whole circle represents the whole set of data. denominator The number below the line in a fraction. In a fraction representing a whole, or ONE, divided into equal parts, the denominator is the total number of equal parts. In the fraction ba,bis the denominator. equivalent fractions Fractions that have different denominators but name the same amount. For example, 1 2and 4 8are equivalent fractions. improper fraction A fraction whose numerator is greater than or equal to its denominator. For example, 4 3,5 2,4 4, and 2 14 2are improper fractions. In Everyday Mathematics,improper fractions are sometimes called “top-heavy” fractions. mixed number A number that is written using both a whole number and a fraction. For example, 2 1 4is a mixed number equal to 2  1 4. numerator The number above the line in a fraction. In a fraction representing a whole, or ONE, divided into equal parts, the numerator is the number of equal parts that are being considered. In the fraction ba,ais the numerator. percent (%) Per hundred, or out of a hundred. For example,48% of the students in the school are boys means that, on average, 48 out of every 100 students in the school are boys. Percent Circle A tool on the Geometry Template that is used to measure or draw figures that involve percents, such as circle graphs. repeating decimal A decimal in which one digit or a group of digits is repeated without end. For example, 0.333... and 0. are repeating decimals. 147 Vocabulary Important terms in Unit 5: 5% 15% 30% 35% 40% 45% 55% 60% 65% 70%80%85%90%95% 0% 10% 20% 25% 50% 75% 1/5 1/6 1/101/8 1/3 3/4 1/4 2/3 1/2 PERCENT CIRCLE Unit 5: Family Letter cont. STUDY LINK 48

123 Copyright © Wright Group/McGraw-Hill Do-Anytime Activities To work with your child on the concepts taught in this unit and in previous units, try these interesting and rewarding activities. 1.Help your child find fractions, decimals, and percents in the everyday world—in newspaper advertisements, on measuring tools, in recipes, in the sports section of the newspaper, and so on. 2.Over a period of time, have your child record daily temperatures in the morning and in the evening. Keep track of the temperatures in a chart. Then have your child make a graph from the data. Ask questions about the data. For example, have your child find the differences in temperatures from morning to evening or from one day to the next. 3.Practice using percents in the context of tips. For example, have your child calculate 11 0or 10% of amounts of money. Invite your child to find the tip the next time the family goes out for dinner. 4.Ask your child to identify 2-dimensional and 3-dimensional shapes around the house. Unit 5: Family Letter cont. STUDY LINK 48 In Unit 5, your child will practice operations and computation skills by playing the following games. For detailed instructions, see the Student Reference Book. Estimation SqueezeSeeStudent Reference Book,page 304. This is a game for two players who use a single calculator. The game provides practice in estimating products. Frac-Tac-ToeSeeStudent Reference Book,pages 309–311. This is a game for two players. Game materials include 4 each of the number cards 0–10, pennies or counters of two colors, a calculator, and a gameboard. The gameboard is a 5-by-5 number grid that resembles a bingo card. Several versions of the gameboard are shown in the Student Reference Book. Frac-Tac-Toehelps students practice converting fractions to decimals and percents. Fraction OfSeeStudent Reference Book,pages 313 and 314. This is a game for two players. Game materials include 1 deck each of Fraction OfFraction Cards and Set Cards, the Fraction OfGameboard, and a record sheet. This game provides practice with multiplication of fractions and whole numbers. Fraction/Percent ConcentrationSeeStudent Reference Book,page 315. This game helps students memorize some of the easy fraction/percent equivalencies. Two or three players use 1 set of Fraction/Percent Concentrationtiles and a calculator to play. Fraction Top–It SeeStudent Reference Book,page 316. This game is for 2–4 players. Game materials include 1 deck of 32 Fraction Cards. This game provides practice with comparing fractions. Building Skills through Games

124 Copyright © Wright Group/McGraw-Hill Study Link 5 1 1.92.143. 1 26 0, or 4 5 4. 4 55 0, or 19 0 5.706.16 7.98. a.$9b.$20 c.Jen paid 2 5of the bill: 8 2 4. So that means each fifth of the total was $4. Then 3 5must be $12. And $12 $8$20. 9.1410.14011.1412.140 Study Link 5 2 1.2 1 2;5 2 2.2 4 6, or 2 2 3;1 66, or 8 3 3.1 2 3;5 3 4.2 1 6;1 63 5.2 5 6;1 67 7.2628.32 R49.12310.72 R3 Study Link 5 3 1.42.123.1; 4 4. 4 415. 6 8 3 4 6. 5 41 1 4 7. 9 8, or 1 1 8cups9.297 10.148 R311.74 R312.37 R3 Study Link 5 4 1.2. 3. 4.5. 6.7.8.9.610.21 11.412.4013.1214.8015.27 16.5617.15018.7019.$7.04 20.$20.0321.17 R1022.80 R4 Study Link 5 5 2.0.4; 1.9; 20.7; 24.0; 60.9; 160.6; 181.3; 297.9; 316.0 Study Link 5 6 1.7 17 09 0;7 17 08 0, or 7 3 59 0;6 12 01 0;4 17 0; 3 16 0, or 3 3 5 2. a. 1 45 5, or 1 3 b. 49 5, or 1 5 c. 43 5, or 11 5 3.0. ; 0.2; 0.04.714 R6 5.8 R46.67 R5 Study Link 5 7 Sample answers given for Problem 1–5. 1.0.25; 0.5; 0.752.2.25; 2.5; 2.75 3.0.65; 0.7; 0.7754.0.325; 0.35; 0.375 5.0.051; 0.055; 0.0596.0.53 7.0.28.0.779.0.10.0.051 11.0.043; 0.05; 0.1; 0.12; 0.2; 0.6; 0.78 12.$7.0613.6 R1714.8115.694 R3 Study Link 5 8 1. 3 40.7575%; 1 14 60.87588%; 1 25 50.660%; 1 27 00.8585%; 3 80.37538% 3. 3 8;1 25 5;3 4;1 27 0;1 14 6 4.$1305.10 questions 6.97 R57.48 R158.32 R159.24 R15 Study Link 5 9 2.Bar graph 3.Line graph; Temperature went up and down. Study Link 5 10 1. a.50%b.15%c.35% 3.25% of the students in my class have skateboards. 25% have rollerblades. 50% have bicycles. 4.6335.1.16366.10 R17.100 R4 Study Link 5 11 Check your child’s circle graph. 2.173.234.95.7 Study Link 5 12 1.Mona ate 1 more cookie than Tomas. 3 8of 24 is 9; but 2 5of 25 is 10. 2.12 students were sick. If 2 3is 24, that means 1 3is 12 students. So that means the rest of the class, or 1 3of the class, or 12 students, is sick. 4.35.246.227.24 8 6 3 As You Help Your Child with Homework As your child brings assignments home, you might want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through this unit’s Study Links. Unit 5: Family Letter cont. STUDY LINK 48