[PDF] Unit 05 Big Numbers Estimation and Computation.pdf | Plain Text

STUDY LINK 5 1 139 17 Name Date Time Copyright © Wright Group/McGraw-Hill Solve the multiplication/division puzzles mentally. Fill in the blank boxes. Examples: 1. 2. 3. 4. 5. 6. Make up and solve some puzzles of your own. 7. 8. º, / 300 2,000 2 600 4, 000 3 900 6, 000 º, / 80 50 4 320 200 8 640 400 º, / 70 400 8 9 º, / 5 7 80 600 º, / 9 4 50 7,000 º, / 600 7 3,500 2,400 º, / 80 30 2,700 56,000 º, / 4,000 36,000 20 10,000 º, / º, / 9. 0.56 0.92 10. 2.86 1.73 11. 19.11 10.94  12. 0.52  0.25 Practice Multiplication/Division Puzzles

STUDY LINK 5 2 Extended Multiplication Facts Copyright © Wright Group/McGraw-Hill 140 17 Name Date Time 1. 6 º 7  2. 9 º 3  6 º 70 9 º 30  60 º 7 90 º 3  60 º 70 90 º 30  600 º 7 900 º 3  60 º 700 90 º 300  3. 4 º 8  4. 5 º 15 4 º 80 30 º 150 40 º 8 30 º 1,500 40 º 80 º 50 150 400 º 8 º 500 1,500 40 º 800 30 º 15,000 5. º 9 54 6. 8 º 40 º 90 540 8 º 4,000 º 90 5,400 80 º 4,000 60 º 540 º 50 400 6 º 5,400 º 5 400 6 º 54,000 º 500 400,000 7. 6.3 8.7 8. 7.36 2.14 9. 9.74 5.48 10. 4.6 2.8 Practice Solve mentally.

LESSON 5 2 Name Date Time Partial-Sums Addition 141 Copyright © Wright Group/McGraw-Hill Example:2,000 280 300 42 ? 2,000 280 300 42 Add the thousands: 2,000 Add the hundreds: 500 (200 300) Add the tens: 120 (80 40) Add the ones:2 Find the total: 2,622 Solve each problem. 1. 800 120 160 24  2. 700 420 50 30  3. 600 180 40 12 4. 2,400 160 420 28 5. 1,500 90 240 24 6. 5,600 420 400 30  10

LESSON 5 2 Name Date Time A Multiplication WrestlingCompetition 142 Copyright © Wright Group/McGraw-Hill 1. Twelve players entered a Multiplication Wrestlingcompetition. The numbers they chose are shown in the following table. The score of each player is the product of the two numbers. For example, Aidan’s score is 741, because 13 º 57 741. Which of the 12 players do you think has the highest score? Check your guess with the following procedure. Do not do any arithmetic for Steps 2 and 3. 2. In each pair below, cross out the player with the lower score. Find that player’s name in the table above and cross it out as well. 3. Two players are left in Group A. Cross out the one with the lower score. Two players are left in Group B. Cross out the one with the lower score. Two players are left in Group C. Cross out the one with the lower score. Which 3 players are still left? 4. Of the 3 players who are left, which player has the lowest score? Cross out that player’s name. 5. There are 2 players left. What are their scores? 6. Who won the competition? Group A Group B Group C Aidan: 13 º 57 Indira: 15 º 73 Miguel: 17 º 35 Colette: 13 º 75 Jelani: 15 º 37 Rex: 17 º 53 Emily: 31 º 75 Kuniko: 51 º 37 Sarah: 71 º 53 Gunnar: 31 º 57 Liza: 51 º 73 Tanisha: 71 º 35 Aidan; Colette Indira; Jelani Miguel; Rex Emily; Gunnar Kuniko; Liza Sarah; Tanisha

LESSON 5 3 Name Date Time Flight Coupons 143 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill The airline you are using on the World Tour will give you a $200 discount coupon for every 15,000 miles you fly. Suppose you have flown the distances shown in the table below. Washington, D.C. ∑ Cairo 5,980 mi Cairo ∑ Accra 2,420 mi Accra ∑ Cairo 2,420 mi Cairo ∑ Budapest 1,380 mi Budapest ∑ London 1,040 mi 1. Have you flown enough miles to get a discount coupon? 2. Describe the strategy you used to solve the problem. LESSON 5 3 Name Date Time Flight Coupons The airline you are using on the World Tour will give you a $200 discount coupon for every 15,000 miles you fly. Suppose you have flown the distances shown in the table below. Washington, D.C. ∑ Cairo 5,980 mi Cairo ∑ Accra 2,420 mi Accra ∑ Cairo 2,420 mi Cairo ∑ Budapest 1,380 mi Budapest ∑ London 1,040 mi 1. Have you flown enough miles to get a discount coupon? 2. Describe the strategy you used to solve the problem.

STUDY LINK 5 3 Estimating Sums Copyright © Wright Group/McGraw-Hill 144 Name Date Time 181 For all problems, write a number model to estimate the sum. If the estimate is greater than or equal to 1,500, find the exact sum. If the estimate is less than 1,500, do not solve the problem. 1. 867 734  Number model: 3. 382 744  Number model: 5. 318 295 493  Number model: 7. 694 210 386  Number model: 9. 756 381 201  Number model: 2. 374 962 488  Number model: 4. 581 648 366  Number model: 6. 845 702  Number model: 8. 132 692 803  Number model: 10. 575 832  Number model: 11. 60 º 80  12. 30 º 70  13. 50 º 900  14. 40 º 800  Practice

LESSON 5 3 Name Date Time “Closer To” with Base-10 Blocks 145 Copyright © Wright Group/McGraw-Hill You can use base-10 blocks to help you roundnumbers. Example:Round 64 to the nearest ten. Build a model for 64 with base-10 blocks. Think:What multiples of 10are nearest to 64? If I take the ones (cubes) away, I would have 60. If I add more ones to make the next ten, I would have 70. Build models for 60 and 70. Think:Is 64 closer to 60 or 70? 64 is closer to 60. So, 64 rounded to the nearest ten is 60. Build models to help you choose the closer number. 1. Round 87 to the nearest ten. List the three numbers you will build models for: , , 87 is closer to .So, 87 rounded to the nearest ten is . 2. Round 43 to the nearest ten. List the three numbers you will build models for: , , 43 is closer to .So, 43 rounded to the nearest ten is . 3. Round 138 to the nearest ten. List the three numbers you will build models for: , , 138 is closer to .So, 138 rounded to the nearest ten is . 4. Round 138 to the nearest hundred. List the three numbers you will build models for: , , 138 is closer to .So, 138 rounded to the nearest hundred is . 70 64 60

LESSON 5 3 Name Date Time A Traveling Salesperson Problem 146 Copyright © Wright Group/McGraw-Hill A salesperson plans to visit several cities. To save time and money, the trip should be as short as possible. If the salesperson were visiting only a few cities, it would be possible to figure the shortest route in a reasonable time. But what if the trip includes 10 cities? There would be 3,628,800 possible routes! Computer scientists are trying to find ways to solve this problem on the computer without having to do an impossible number of calculations. Think like a computer. Imagine that you begin a trip in Seattle and have to visit Denver, Birmingham, and Bangor for business. 1. Estimate to find the shortest routethat would include each city. Use the map on journal page 112. 2. Describe your route between each of the four cities. Try This 3. Describe a route that includes each city that would take the shortest amount of time.

LESSON 5 4 Name Date Time What Do Americans Eat? 147 Copyright © Wright Group/McGraw-HillCopyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Answer the following questions: 1. How many eggs did you eat in the last 7 days? 2. How many cups of milk did you drink in the last 7 days? 3. How many cups of yogurt did you eat in the last 7 days? LESSON 5 4 Name Date Time What Do Americans Eat? LESSON 5 4 Name Date Time What Do Americans Eat? Answer the following questions: 1. How many eggs did you eat in the last 7 days? 2. How many cups of milk did you drink in the last 7 days? 3. How many cups of yogurt did you eat in the last 7 days? Answer the following questions: 1. How many eggs did you eat in the last 7 days? 2. How many cups of milk did you drink in the last 7 days? 3. How many cups of yogurt did you eat in the last 7 days?

STUDY LINK 5 4 Estimating Products Copyright © Wright Group/McGraw-Hill 148 Name Date Time 184 Estimate whether the answer will be in the tens, hundreds, thousands, or more. Write a number model to show how you estimated. Then circle the box that shows your estimate. 1. A koala sleeps an average of 22 hours each day. About how many hours does a koala sleep in a year? Number model: 2. A prairie vole (a mouselike rodent) has an average of 9 babies per litter. If it has 17 litters in a season, about how many babies are produced? Number model: 3. Golfers lose, on average, about 5 golf balls per round of play. About how many golf balls will an average golfer lose playing one round every day for one year? Number model: 4. In the next hour, the people in France will save 12,000 trees by recycling paper. About how many trees will they save in two days? Number model: 5. How many digits can the product of two 2-digit numbers have? Give examples to support your answer. Practice 6. 60 7  7. 4 80  8. 200 9 1,000,000s 100,000s 10,000s 100s 10s 1,000s 1,000,000s 100,000s 10,000s 100s 10s 1,000s 1,000,000s 100,000s 10,000s 100s 10s 1,000s 1,000,000s 100,000s 10,000s 100s 10s 1,000s Try This

LESSON 5 4 Name Date Time A Curved Number Line 149 Copyright © Wright Group/McGraw-Hill The number lines below are curved like hills. Use them to help you roundnumbers. Example 1: Example 2: 65 64 60 70 150 175 100 200 Round 64 to the nearest ten.  Which multiples of 10are nearest to 64? and  What number is halfway between 60 and 70?  Will 64 “slide” down the hill to 60 or to 70?  64 rounded to the nearest ten is 60.Round 175 to the nearest hundred.  Which multiples of 100are nearest to 175? and  What number is halfway between 100 and 200?  Will 175 “slide” down the hill to 100 or 200?  175 rounded to the nearest hundred is 200. 1. Round 37 to the nearest ten. Label the curved number line. Mark 37. 37 will “slide” down to . 37 rounded to the nearest ten is . 2. Round 432 to the nearest hundred. Label the curved number line. Mark 432. 432 will “slide” down to . 432 rounded to the nearest hundred is .

LESSON 5 4 Name Date Time Missing Numbers and Digits 150 Copyright © Wright Group/McGraw-Hill 1. Complete the number sentences. Fill in the circles using the numbers 3, 4, 6, or 7. Fill in the rectangles using the numbers 47, 62, 74, or 86. Some numbers will be used more than once. a. b. c. d. e. f. 2. For each problem, fill in the squares using the digits 4, 6, and 7. a. b. c. 3. Use the digits 6, 7, 8, and 9 to make the largest product possible. 4. Use the digits 6, 7, 8, and 9 to make the smallest product possible.  258  372  329  248  444  296 448 322 268

STUDY LINK 5 5 Multiplication 151 18 184 Name Date Time Copyright © Wright Group/McGraw-Hill Multiply using the partial-product method. Show your work in the grid below. 1. 56 º 7  2. 8 º 275  3. 1,324 9 4. Maya goes to school for 7 hours each day. If she does not miss any of the 181 school days, how many hours will Maya spend in school this year? a. Estimate whether the answer will be in the tens, hundreds, thousands, or more. Write a number model to show how you estimated. Circle the box that shows your estimate. Number model: b. Exact answer: hours 5. The average eye blinks once every 5 seconds. Is that more than or less than a hundred thousand times per day? Explain your answer. 6. 495 7,389 7. 5,638 5,798  8. 3,007 1,749  9. 8,561 3,872 1,000,000s 100,000s 10,000s 100s 10s 1,000s Practice

LESSON 5 5 Name Date Time Patterns in Extended Facts 152 Copyright © Wright Group/McGraw-Hill 1. Use base-10 blocks to help you solve the problems in the first 2 columns. Use the patterns to help you solve the problems in the third column. Use a calculator to check your work. 2 º 1 20 º 1 200 º 1  2 º 10 20 º 10 200 º 10  2 º 100 20 º 100 200 º 100  2 º 4 20 º 4 200 º 4  2 º 40 20 º 40 200 º 40  2 º 400 20 º 400 200 º 400  2. Use what you learned in Problem 1 to help you solve the problems in the table below. Use a calculator to check your work. 4. Make up and solve some problems of your own that use this pattern. 3. Explain how knowing 2 º 4 can help you find the answer to 20 º 40.

153 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill LESSON 5 5 Name Date Time An Old Puzzle An old puzzle begins like this: “A man has 6 houses. In each house, he keeps 6 cats. Each cat has 6 whiskers. On each whisker sit 6 fleas.” 1. Answer the last line of the puzzle: “Houses, cats, whiskers, fleas—how many are there in all?” 2. Use number models or illustrations to explain how you solved the puzzle. An old puzzle begins like this: “A man has 6 houses. In each house, he keeps 6 cats. Each cat has 6 whiskers. On each whisker sit 6 fleas.” 1. Answer the last line of the puzzle: “Houses, cats, whiskers, fleas—how many are there in all?” 2. Use number models or illustrations to explain how you solved the puzzle. LESSON 5 5 Name Date Time An Old Puzzle

STUDY LINK 5 6 More Multiplication Copyright © Wright Group/McGraw-Hill 154 Name Date Time 18 Multiply using the partial-products algorithm. Show your work. 1. 582 º 7  2. 56 º 30  3. 42 º 50  4. 27 º 18 5. 46 º 71 6. 340 º 50  Try This 7. 241 º 31 8. 768 º 49 9. 283 5,439 10. 6,473 4,278  11. 5,583 4,667  12. 9,141 6,372 Practice

LESSON 5 6 Name Date Time A Dart Game 155 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Vanessa played a game of darts. She threw 9 darts. Each dart hit the target. She scored 550 points. Where might each of her 9 darts have hit? Use the table to show all possible solutions. 200 100 50 25 200 100 50 25 LESSON 5 6 Name Date Time A Dart Game Vanessa played a game of darts. She threw 9 darts. Each dart hit the target. She scored 550 points. Where might each of her 9 darts have hit? Use the table to show all possible solutions. 200 100 50 25 200 100 50 25

LESSON 5 6 Name Date Time Sorting Numbers 156 Copyright © Wright Group/McGraw-Hill Study the Venn diagrams in Problems 1 and 2. Label each circle and add at least one number to each section. 1. Try This 2. 720 2,400300 180 4,200 80 5,600 160 990 1,230 360 750 1,200210 840 4,200 6,300 350 7,000 250 4,000 650560 490 280

STUDY LINK 5 7 Lattice Multiplication 157 19 Name Date Time Copyright © Wright Group/McGraw-Hill Use the lattice method to find the following products. 1. 5 º 46  2. 8 º 67  3. 7 º 836  4. 4 º 329  5. 25 º 31  6. 49 º 52  7. Use the lattice method and the partial-products method to find the product. 84 º 78  5 4 6 8. 33.67 5.9 9. 68.4 5.82  10. 71.44 37.67  11. 101.06 29.91 Practice

LESSON 5 7 Name Date Time Napier’s Rods 158 Copyright © Wright Group/McGraw-Hill Scottish mathematician John Napier (1550 –1617) devised a multiplication method using rods made of bone, wood, or heavy paper. These rods were used to solve multiplication and division problems. Example 1: Example 2: 4 º 67 268 8 º 5,239 41,912 Cut out the rods on Math Masters,page 159. Use the rods and the board on Math Masters,page 160 to solve the following problems and some of your own. Use another method to check your answers. 1. 5 º 79  2. 7 º 92  3. 6 º 236 4. 9 º 5,841 Try This 5. Show a friend how you would use Napier’s Rods to solve 3 º 407 or 9 º 5,038. 1 2 3 4 5 6 7 8 9 6 0 6 1 2 1 8 2 4 3 0 3 6 4 2 4 8 5 4 7 0 7 1 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3 1 2 3 4 5 6 7 8 9 5 0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 2 0 2 0 4 0 6 0 8 1 0 1 2 1 4 1 6 1 8 3 0 3 0 6 0 9 1 2 1 5 1 8 2 1 2 4 2 7 9 0 9 1 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1 2 42 8 68 2 4 01 6 19 4 21 47 2 12

LESSON 5 7 Name Date Time Napier’s Rods continued 159 Copyright © Wright Group/McGraw-Hill 123456789 0 10 20 30 40 50 60 70 80 9 0 20 40 60 81 01 21 41 61 8 0 30 60 91 21 51 82 12 42 7 0 40 81 21 62 02 42 83 23 6 0 51 01 52 02 53 03 54 04 5 0 61 21 82 43 03 64 24 85 4 0 71 42 12 83 54 24 95 66 3 0 81 62 43 24 04 85 66 47 2 0 91 82 73 64 55 46 37 28 1

LESSON 5 7 Name Date Time Napier’s Rods continued 160 Copyright © Wright Group/McGraw-Hill 1 2 3 4 5 6 7 8 9

LESSON 5 7 Name Date Time Fact Lattice Patterns 161 Copyright © Wright Group/McGraw-Hill 1. Look at a Multiplication/Division Facts Table. Find the shaded diagonal showing the doubles facts. 2. Find the doubles facts on the Fact Lattice on Math Masters,page 435. Shade the doubles facts lightly with a colored pencil. 3. Compare the two fact tables. a. List 3 things the tables have in common. b. List 3 things that are different on the Fact Lattice. 4. Describe 2 patterns that you see on the Fact Lattice. a. b. 5. Which of your Fact Lattice patterns is also in the Multiplication/Division Facts Table in your journal?

LESSON 5 8 Name Date Time A 50-by-40 Array 162 Copyright © Wright Group/McGraw-Hill

STUDY LINK 5 8 Place-Value Puzzle 163 4 Name Date Time Copyright © Wright Group/McGraw-Hill Use the clues below to fill in the place-value chart. Billions Millions Thousands Ones 100B 10B 1B , 100M 10M 1M , 100Th 10Th 1Th , 100 10 1 13. 74 º 5  14. 396 º 8 15. 92 º 18 16. 56 º 47  Practice 1. Find 1 2of 24. Subtract 4. Write the result in the hundreds place. 2. Find 1 2of 30. Divide the result by 3. Write the answer in the ten-thousands place. 3. Find 30 10. Double the result. Write it in the one-millions place. 4. Divide 12 by 4. Write the answer in the ones place. 5. Find 9 º 8. Reverse the digits in the result. Divide by 3. Write the answer in the hundred-thousands place. 6. Double 8. Divide the result by 4. Write the answer in the one-thousands place. 7. In the one-billions place, write the even number greater than 0 that has not been used yet. 8. Write the answer to 5 5 in the hundred-millions place. 9. In the tens place, write the odd number that has not been used yet. 10. Find the sum of all the digits in the chart so far. Divide the result by 5, and write it in the ten-billions place. 11. Write 0 in the empty column whose place value is less than billions. 12. Write the number in words. For example, 17,450,206 could be written as “17 million, 450 thousand, 206.”

LESSON 5 8 Name Date Time A Roomful of Dots 164 Copyright © Wright Group/McGraw-Hill 180–184 Suppose you filled your classroom from floor to ceiling with dot paper (2,000 dots per sheet). 1. About how many dots do you think there would be on all the paper needed to fill your classroom? Make a check mark next to your guess. less than a million between a million and a half billion between half a billion and a billion more than a billion 2. One ream of paper weighs about 5 pounds and has 500 sheets of paper. About how many pounds would the paper needed to fill your classroom weigh? Make a check mark next to your guess. less than 100,000 pounds between 100,000 pounds and 500,000 pounds between 500,000 pounds and a million pounds more than a million pounds 3. Now, work with your group to make more accurate estimates for Problems 1 and 2. Explain what you did. My group’s estimates: Number of dots: Weight of the paper:

LESSON 5 8 Name Date Time How Much Is a Million? 165 Copyright © Wright Group/McGraw-Hill Copyright © Wright Group/McGraw-Hill Name Date Time David M. Schwartz, the author of How Much Is a Million?,used 7 pages of his book to show approximately 100,000 tiny stars. He wrote, “If this book had a million tiny stars, they would fill seventy pages.... If this book had a billion tiny stars, its pages spread side by side would stretch almost ten miles.... If you put a trillion of our stars onto a gigantic roll of paper, it would stretch all the way from New York to New Zealand.” 1. About how many pages would be needed to show a trillion tiny stars? Explain. 2. Describe a strategy you could use, other than counting each star, to find the number of tiny stars on one page of How Much Is a Million? David M. Schwartz, the author of How Much Is a Million?,used 7 pages of his book to show approximately 100,000 tiny stars. He wrote, “If this book had a million tiny stars, they would fill seventy pages.... If this book had a billion tiny stars, its pages spread side by side would stretch almost ten miles.... If you put a trillion of our stars onto a gigantic roll of paper, it would stretch all the way from New York to New Zealand.” 1. About how many pages would be needed to show a trillion tiny stars? Explain. 2. Describe a strategy you could use, other than counting each star, to find the number of tiny stars on one page of How Much Is a Million? LESSON 5 8 How Much Is a Million?

LESSON 5 9 Name Date Time Place Value and Powers of 10 166 Copyright © Wright Group/McGraw-Hill 5 Fill in this place-value chart as follows: 1. Write standard numbers in Row 1. 2. In Row 2, write the value of each place to show that it is 10 times the value of the place to its right. 3. In Row 3, write the place values as products of 10s. 4. In Row 4, show the values as powers of 10. Use exponents. The exponent shows how many times 10 is used as a factor. It also shows how many zeros are in the standard number. Hundred Ten Millions Thousands ThousandsThousands Hundreds Tens Ones 1,000,0001,000 100 1 10 [100,000s] 10 [100s] 10 [10s] 10 [tenths] 10 º 10 º 10 º 10 10 º 10 10 5 10 3 10 2 10 0

STUDY LINK 5 9 Many Names for Powers of 10 167 5 Name Date Time Copyright © Wright Group/McGraw-Hill 1,000,000 10,000 1,000 100 10 10 [100,000s] 10 [10,000s] 10 6 10 [1,000s] 10 3 10 º 10 º 10 º 10 one thousand 10 5 10 º 10 º 10 º 10 º 10 10 [10s] 10 º 10 ten 10 1 10 [tenths] 10 0 1 7. 63 º 7  8. 495 º 6 9. 97 º 53 Practice Below are different names for powers of 10. Write the names in the appropriate name-collection boxes. Circle the names that do not fit in any of the boxes. 100,000 10 2 one 1 million 10 10 10 10 4 1. 2. 3. 4. 5. 6.

LESSON 5 9 Name Date Time Powers of 10 on a Calculator 168 Copyright © Wright Group/McGraw-Hill Experiment to see what happens when your calculator can no longer display all of the digits in a power of 10. Clear your calculator’s memory, then program it to multiply over and over by 10 as follows: Calculator Key Sequence Calculator A and together 10 10 ... Calculator B 10 ... Op1 Op1 Op1 Op1 Æ Op1 Clear On/Off 1. What is the largest power of 10 that your calculator can display before it switches from decimal notation to exponential notation? 2. Write what the calculator displays after it switches from decimal notation to exponential notation. 3. If there are different kinds of calculators in your classroom, is the largest power of 10 that they can display the same or different from your calculator? If it is different, tell how. Write your answer on the back of this page. Try This 4. What is the smallest power of 10 that your calculator can display before it switches from decimal notation to exponential notation? Explain what you did to find out. 5 213 215

STUDY LINK 5 10 Rounding 169 182 183 Name Date Time Copyright © Wright Group/McGraw-Hill 1. Round the seating capacities in the table below to the nearest thousand. Women’s National Basketball Association Seating Capacity of Home Courts Team Seating CapacityRounded to the Nearest 1,000 Charlotte Sting 24,042 Cleveland Rockers 20,562 Detroit Shock 22,076 New York Liberty 19,763 Phoenix Mercury 19,023 Sacramento Monarchs 17,317 San Antonio Stars 18,500 Seattle Storm 17,072 U.S. Population by Official Census from 1940 to 2000 Year PopulationRounded to the Nearest Million 1940 132,164,569 1960 179,323,175 1980 226,542,203 2000 281,421,906 Source for both tables: The World Almanac and Book of Facts 2004 2. Look at your rounded numbers. Which stadiums have about the same capacity? 3. Round the population figures in the table below to the nearest million. Practice 4. 692 º 6 5. 38 º 21 6. 44 º 73 

LESSON 5 10 Name Date Time Number Lines 170 Copyright © Wright Group/McGraw-Hill 1. For each number line, record the number that is halfway between the lower and higher number. Then plot a number that is lessthan the halfway number. a. b. 2. For each number line, record the number that is halfway between the lower and higher number. Then plot a number that is greaterthan the halfway number. a. b. 3. Make up a problem of your own. lower number higher number halfway number 71,000 lower number 72,000 higher number halfway number 3,400 lower number 3,500 higher number halfway number 880 lower number 890 higher number halfway number 30 lower number 40 higher number halfway number 182 183

LESSON 5 10 Name Date Time Rounding Bar Graph Data 171 Copyright © Wright Group/McGraw-Hill Each bar represents the 2003 population of a country. Source: The World Factbook 1. Estimate the population of each country to the nearest 10 million, to the nearest 5 million, and to the nearest 1 million. Organize your information in a table on the back of this sheet. 2. Describe the strategy you used to round to the nearest million. France Italy Poland Spain United Kingdom 30 40 50 60 70 Population 2003 Countries Number of People in Millions 76

STUDY LINK 5 11 Comparing Data Copyright © Wright Group/McGraw-Hill 172 Name Date Time 4 This table shows the number of pounds of fruit produced by the top 10 fruit-producing countries in 2001. Read each of these numbers to a friend or a family member. 1. Which country produced the most fruit? 2. Which country produced the least fruit? 4. Which two countries together produced about as much fruit as India? Practice Estimate the sum. Write a number model. 5. 687 935 6. 2,409 1,196 1,327 7. 11,899 35,201 Country Pounds of Fruit Brazil 77,268,294,000 China 167,046,420,000 France 26,823,740,000 India 118,036,194,000 Iran 28,599,912,000 Italy 44,410,538,000 Mexico 34,549,912,000 Philippines 27,028,556,000 Spain 36,260,392,000 United States 73,148,598,000 3. For each pair, circle the country that produced more fruit. a. India Mexico b. United States Iran c. Brazil Philippines d. Spain Italy

STUDY LINK 5 12 Unit 6: Family Letter 173 Name Date Time Copyright © Wright Group/McGraw-Hill Division; Map Reference Frames; Measures of Angles The first four lessons and the last lesson of Unit 6 focus on understanding the division operation, developing a method for dividing whole numbers, and solving division number stories. Though most adults reach for a calculator to do a long-division problem, it is useful to know a paper-and-pencil procedure for computations such as 567 6 and 152 35. Fortunately, there is a method that is similar to the one most of us learned in school but is much easier to understand and use. This method is called the partial-quotients method. Students have had considerable practice with extended division facts, such as 420 760, and questions, such as “About how many 12s are in 150?” Using the partial- quotients method, your child will apply these skills to build partial quotients until the exact quotient and remainder are determined. This unit also focuses on numbers in map coordinate systems. For maps of relatively small areas, rectangular coordinate grids are used. For world maps and the world globe, the system of latitude and longitude is used to locate places. Because this global system is based on angle measures, the class will practice measuring and drawing angles with full-circle (360°) and half-circle (180°) protractors. If you have a protractor, ask your child to show you how to use this tool. The class is well into the World Tour. Students have visited Africa and are now traveling in Europe. They are beginning to see how numerical information about a country helps them get a better understanding of the country—its size, climate, location, and population distribution—and how these characteristics affect the way people live. Your child may want to share with you information about some of the countries the class has visited. Encourage your child to take materials about Europe to school, such as magazine articles, travel brochures, and articles in the travel section of your newspaper. Please keep this Family Letter for reference as your child works through Unit 6. Full-circle (360°) protractor 12 6 11 5 10 4 1 72 83 9 360 90 80 70 60 50 40 30 20 10 100 110 120 130 140 150 160 170 180 0 100 110 120 130 140 150 160 170 80 70 60 50 40 30 20 10 0 180 Half-circle (180°) protractor

Copyright © Wright Group/McGraw-Hill 174 Vocabulary Important terms in Unit 6: acute angle An angle with a measure greater than 0° and less than 90°. coordinate grid (also called a rectangular coordinate grid) A reference frame for locating points in a plane using ordered number pairs,or coordinates. equal-groups notation A way to denote a number of equal-sized groups. The size of the groups is written inside square brackets and the number of groups is written in front of the brackets. For example, 3 [6s] means 3 groups with 6 in each group. index of locations A list of places together with a reference frame for locating them on a map. For example, “Billings D3,” indicates that Billings can be found within the rectangle where column 3 and row D of a grid meet on the map. meridian bar A device on a globe that shows degrees of latitude north and south of the equator. multiplication/division diagram A diagram used for problems in which a total is made up of several equal groups. The diagram has three parts: a number of groups, a number in each group, and a total number. obtuse angle An angle with a measure greater than 90° and less than 180°. ordered number pair Two numbers that are used to locate a point on a coordinate grid.The first number gives the position along the horizontal axis, and the second number gives the position along the vertical axis. The numbers in an ordered pair are called coordinates.Ordered pairs are usually written inside parentheses: (2,3). protractor A tool used for measuring or drawing angles. A half-circle protractor can be used to measure and draw angles up to 180°. A full-circle protractor can be used to measure and draw angles up to 360°. One of each type is on the Geometry Template. quotient The result of dividing one number by another number. For example, in 35 ÷ 5 = 7, the quotient is 7. reflex angle An angle with a measure greater than 180° and less than 360°. straight angle An angle with a measure of 180°. vertex The point at which the rays of an angle, the sides of a polygon, or the edges of a polyhedron meet. Plural is vertexes or vertices. 1 2 3 1231 2 3 1 2 30 (2,3) obtuse angle acute angle Unit 6: Family Letter cont. STUDY LINK 512 rows chairs chairs per row in all 64 24

Copyright © Wright Group/McGraw-Hill Do-Anytime Activities To work with your child on concepts taught in this unit, try these interesting and rewarding activities: 1.Help your child practice division by solving problems for everyday situations. 2.Name places on the world globe and ask your child to give the latitude and longitude for each. 3.Encourage your child to identify and classify acute, right, obtuse, straight, and reflex angles in buildings, bridges, and other structures. 4.Work together with your child to construct a map, coordinate system, and index of locations for your neighborhood. Building Skills through Games In Unit 6, your child will practice using division and reference frames and measuring angles by playing the following games. For detailed instructions, see the Student Reference Book. Angle TangleSeeStudent Reference Book,page 230. This is a game for two players and will require a protractor. The game helps students practice drawing, estimating the measure of, and measuring angles. Division DashSeeStudent Reference Book,page 241. This is a game for one or two players. Each player will need a calculator. The game helps students practice division and mental calculation. Grid SearchSeeStudent Reference Book,pages 250 and 251. This is a game for two players, and each player will require twoplaying grids. The game helps students practice using a letter-number coordinate system and developing a search strategy. Over and Up SquaresSeeStudent Reference Book,page 257. This is a game for two players and will require a playing grid. The game helps students practice using ordered pairs of numbers to locate points on a rectangular grid. Unit 6: Family Letter cont. STUDY LINK 512 175

Copyright © Wright Group/McGraw-Hill As You Help Your Child with Homework As your child brings assignments home, you may want to go over the instructions together, clarifying them as necessary. The answers listed below will guide you through some of the Study Links in this unit. Study Link 6 1 1.8 rows2.120,000 quills3.21 boxes Study Link 6 2 1.382.233.47 Study Link 6 3 1.13 marbles; 5 left2.72 prizes, 0 left 3.22 R34.53 R3 Study Link 6 4 1.15 4 8or 15 1 2; Reported it as a fraction or decimal; Sample answer: You can cut the remaining strawberries into halves to divide them evenly among 8 students. 2.21; Ignored it; Sample answer: There are not enough remaining pens to form another group of 16. Study Link 6 5 1–7. Study Link 6 6 1.; 101°2.; 52° 3.; 144°4.; 137° 6.247.8 R28.1579.185 R3 Study Link 6 7 1.60°2.150°3.84°4.105° 5.32°6.300° Study Link 6 8 1. 2.K(4,8);L(7,7);M(10,5);N(1,8);O(6,2); P(8,4);Q(10,2);R(3,10) Study Link 6 9 1. 2.Eastern Hemisphere3.water 4.15 R25.146.43 R27.134 Study Link 6 10 1.8 pitchers; 0 oranges left 2.22 bouquets; 8 flowers left 3.45 R64.695.180 6.2,2337.1,8278.16,287 10 9 8 7 6 5 4 3 2 1 0 012345678910 A B C DE GH F 176 1 step Oak Tree N WE S 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 0 0 equator South Pole North Pole prime meridian latitude longitudeB A Unit 6: Family Letter cont. STUDY LINK 512