# 4 Enrichment

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<p>11</p>
<p>Name</p>
<p>Date</p>
<p>EnrichThink of It</p>
<p>Read each riddle and write the answer in the form requested. 1. It is a three-digit number whose tens digit is 3. Its hundreds digit is 4 more than its ones digit, which is an odd number less than 5. No two digits are the same. Write it in standard form:</p>
<p>2. It is the greatest even two-digit number. The product of its digits is 72. Write it in word form:</p>
<p>3. It is the least four-digit number that can be rounded up to the nearest hundred as 4,100.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>Write it in expanded form:</p>
<p>4. It is a four-digit number greater than 7,000. None of its digits are the same and all of them are even numbers. Its ones digit is 6 and the sum of its digits is 20. Write it in standard form:</p>
<p>5. Both the sum and the product of its three digits are 6. The least digit is in the hundreds place and the greatest digit is in the ones place. Write it in word form:</p>
<p>Grade 4</p>
<p>12</p>
<p>Chapter 1</p>
<p>12</p>
<p>Name</p>
<p>Date</p>
<p>EnrichChapter Resources</p>
<p>Telephone Fun</p>
<p>Use what you know about place value and telephone numbers to complete this chart.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>Telephone Number</p>
<p>Standard Form</p>
<p>Expanded Form</p>
<p>Word Form Two million, six hundred thirty-seven thousand, four hundred twenty</p>
<p>905-9618</p>
<p>7,000,000 + 300,000 + 10,000 + 5,000 + 800 + 80 + 2Write your telephone number in standard form:</p>
<p>Grade 4</p>
<p>17</p>
<p>Chapter 1</p>
<p>13</p>
<p>Name</p>
<p>Date</p>
<p>EnrichBig Time</p>
<p>One million is a big number, and these are big questions. A good problem-solving plan and a calculator will help you find the answers. 1. About how many years old were you by the time you had lived a million minutes?</p>
<p>2. About how old would you be if you lived a million hours?</p>
<p>3. About how old would you be if you lived a million days?</p>
<p>4. About how old would you be if you lived a million weeks?</p>
<p>5. About how many months is a million weeks?</p>
<p>6. About how many years is a million months?</p>
<p>Grade 4</p>
<p>22</p>
<p>Chapter 1</p>
<p>14</p>
<p>Name</p>
<p>Date</p>
<p>EnrichChapter ResourcesChapter 1</p>
<p>More or LessRead each question. Then write your answers on the lines provided. 1. How many different three-digit numbers can you make using 1, 2, and 3 as digits?</p>
<p>2. From least to greatest, write the 6 three-digit numbers you can make using the digits 1, 2, and 3.</p>
<p>3. How many different three-digit numbers can you make using 4, 5, and 6 as digits?</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>4. From least to greatest write the 6 three-digit numbers you can make using the digits 4, 5, and 6.</p>
<p>5. Write the greatest and least numbers you can make using all four of these digits: 0, 3, 5, 7 Use the signs >, or < to show which package weighs more. Then multiply to check your answers. 37 tons 42 56 tons 21</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>78 pounds 11</p>
<p>42 pounds 98</p>
<p>87 ounces 84</p>
<p>65 ounces 33</p>
<p>57 kilograms 59</p>
<p>84 kilograms 29</p>
<p>Grade 4</p>
<p>17</p>
<p>Chapter 7</p>
<p>73</p>
<p>Name</p>
<p>Date</p>
<p>EnrichAsked and Answered</p>
<p>Almost 2,000 kids went to Camp Guthrie last summer884 boys and 965 girls. Most of them bought clothes at the Guthrie Gift Shop. Write three questions you can ask and answer by multiplying. 1.</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>2.</p>
<p>3.</p>
<p>Add 3 items to the Guthrie Gift Shop price list. Create two more questions that you can ask and answer by multiplying. Be sure to use the new items in your questions! 4.</p>
<p>5.</p>
<p>Trade with a partner to check each others work.</p>
<p>Grade 4</p>
<p>22</p>
<p>Chapter 7</p>
<p>74</p>
<p>Name</p>
<p>Date</p>
<p>EnrichChapter ResourcesChapter 7</p>
<p>Fill the GridUse a number cube to roll the top two numbers for each multiplication problem in the grid. Trade with a partner to check each others work.</p>
<p> 14</p>
<p> 35</p>
<p> 62</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p> 53</p>
<p> 89</p>
<p> 71</p>
<p> 27</p>
<p> 94</p>
<p> 56</p>
<p>Grade 4</p>
<p>27</p>
<p>75</p>
<p>Name</p>
<p>Date</p>
<p>EnrichDigit Detective</p>
<p>Fill in the missing digits in the multiplication problems below. 1.</p>
<p>83 4 2 1674 33 351 8 4 14 5 5484 4570 5 184 4 7 2430 3 02 36450 6</p>
<p>2.</p>
<p>6</p>
<p>2</p>
<p>3 8 5376 2 01 24.</p>
<p>536Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>3.</p>
<p>5</p>
<p>5 25</p>
<p>7 1 3675 376.</p>
<p>75 95 8</p>
<p>5.</p>
<p>3160 790 11 60</p>
<p>Grade 4</p>
<p>32</p>
<p>Chapter 7</p>
<p>76</p>
<p>Name</p>
<p>Date</p>
<p>EnrichChapter Resources INDEX</p>
<p>Napiers BonesIn the 17th century, John Napier invented a simple calculator that multiplied by adding. Use Napiers Bones to find 49 37. 1. Cut out the ten strips below. Place the 4, 9, and index strips next to each other. 2. Fold the strips so that rows 3 and 7 of the index are next to each other. See how the diagonal lines form a pattern of diagonal columns. 3. To find the product, add the numbers along the diagonal columns starting from the bottom right. The first diagonal (3) is the ones digit. The next diagonal (7 + 6 + 8 = 21) is the tens. Write 1 under the tens column and regroup 2 to the next diagonal. Add the next diagonal, 2 + 2 + 2 + 2 = 8, for the hundreds. The last diagonal (1) is the thousands. So, the product of 49 37 is 1,813. Use the strips to find each product.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>1. 57 34 = 4. 32 33 =</p>
<p>2. 61 76 = 5. 94 65 =</p>
<p>3. 85 29 = 6. 56 48 =</p>
<p>91 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1</p>
<p>81 6 2 4 3 2 4 0 4 8 5 6 6 4 7 2</p>
<p>71 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3</p>
<p>61 2 1 8 2 4 3 0 3 6 4 2 4 8 5 4</p>
<p>51 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5</p>
<p>48 1 2 1 6 2 0 2 4 2 8 3 2 3 6</p>
<p>36 9 1 2 1 5 1 8 2 1 2 4 2 7</p>
<p>24 6 8 1 0 1 2 1 4 1 6 1 8</p>
<p>12 3 4 5 6 7 8 9</p>
<p>1 2 3 4 5 6 7 8 9</p>
<p>Grade 4</p>
<p>37</p>
<p>Chapter 7</p>
<p>77</p>
<p>Name</p>
<p>Date</p>
<p>EnrichEight Million or More</p>
<p>Using the digits 3, 4, 5, 6, 7, 8, and 9, write at least 5 multiplication problems with a product of eight million or more. You may not use the same digit more than once in the same problem. Multiply to check your answers.</p>
<p>Using the same digits (3, 4, 5, 6, 7, 8, and 9), write at least 5 numbers that round to six million. Round to check your answers.</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>Now, create a problem for a partner. Choose seven digits. ___ ___ ___ ___ ___ ___ ___ Create a question. For example, write at least 5 addition problems with a sum less than four million.</p>
<p>Trade with a partner, and complete each others problems.</p>
<p>Grade 4</p>
<p>42</p>
<p>Chapter 7</p>
<p>81</p>
<p>Name</p>
<p>Date</p>
<p>EnrichDivision Rules</p>
<p>Work across each row of problems to discover a division rule. 36 2 = 42 2 = 12 2 = 54 3 = 48 3 = 30 3 = 3= 3= 3= 2= 2= 2= 36 6 = 42 6 = 12 6 = 54 6 = 48 6 = 30 6 =</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>Complete this statement: If a number can be divided evenly by 2 and by 3, then it is also divisible by .</p>
<p>Keep in mind 1. All even numbers are divisible by 2.</p>
<p>2. If the sum of the digits in a number is divisible by 3, then the number is divisible by 3.</p>
<p>Circle the numbers that are divisible by 6. 432 746 330 895 546</p>
<p>Grade 4</p>
<p>12</p>
<p>Chapter 8</p>
<p>82</p>
<p>Name</p>
<p>Date</p>
<p>EnrichChapter Resources</p>
<p>Timed Ten</p>
<p>Use a stopwatch or a second hand, to see how quickly you can complete these division chains using mental math. Ready, set, GO! 1. 3,500 70 = 2. 420 6 = 3. 81,000 900 =Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p> 10 = 7= 3=</p>
<p>5= 2= Rate Yourself: 5= 5= 90 seconds or less: Mental Mathemagician! 91 119 seconds: Magnificent Multiplier! Two minutes or more: Dawdling Divider! 10 = 10 = 4= 3= 5=</p>
<p>4. 50,000 50 = 5. 560 7 = 6. 64,000 80 = 7. 2,400 8 = 8. 48,000 10 = 9. 5,400 2 = 10. 32,000 80 = 4=</p>
<p> 10 = 2=</p>
<p> 20 = 6=</p>
<p> 60 = 30 = 10 =</p>
<p>Grade 4</p>
<p>17</p>
<p>Chapter 8</p>
<p>83</p>
<p>Name</p>
<p>Date</p>
<p>EnrichThe Bike Path</p>
<p>The Tollivers live on a bike path. Last Saturday morning, in just five minutes, they counted eleven riders and 26 wheels passing by. There were no unicycles just bicycles and tricycles with one rider each. How many bicycles and tricycles did the Tollilvers see? Use the space below to draw, guess and check, or make a table to find the answer.</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>Explain your thinking.</p>
<p>Grade 4</p>
<p>22</p>
<p>Chapter 8</p>
<p>84</p>
<p>Name</p>
<p>Date</p>
<p>EnrichChapter ResourcesChapter 8</p>
<p>Estimate QuotientsEstimate. Check your estimate. 1. 7 428 2. 3 605 3. 4 316</p>
<p>4. 9 8,140</p>
<p>5. 5 5,165</p>
<p>6. 8 3,999</p>
<p>7. 6 3,546</p>
<p>8. 2 196</p>
<p>9. 4 85</p>
<p>10. 9 98</p>
<p>11. 8 725</p>
<p>12. 5 5,620</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>Use the problems above to spell the name of the treasure state. Write the estimated quotient from above beside the matching problem number below. The first one, problem 11, is done for you. Cross out the letters above the quotients with two digits. Circle the letters above the quotients with three or more digits.</p>
<p>H11. 9.</p>
<p>15.</p>
<p>A10.</p>
<p>D</p>
<p>N2. 4.</p>
<p>N6.</p>
<p>T8.</p>
<p>M</p>
<p>O7. 1.</p>
<p>B3.</p>
<p>P12.</p>
<p>A</p>
<p>Use the circled letters. Unscramble the letters to spell the name of the treasure state, where valuable ore is mined.</p>
<p>Grade 4</p>
<p>27</p>
<p>85</p>
<p>Name</p>
<p>Date</p>
<p>EnrichTricky Tracking</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>Write and solve a division problem for each set of clues. 1. The quotient is 7. There is no remainder. The dividend is a square number less than 50. 2. The remainder is 2. The quotient is 4. The quotient equals the divisor. 3. The divisor is 3. The quotient is 2 2 2. The remainder is 2. 4. The quotient is 5. The dividend is 48. The remainder is an odd number. 5. The dividend is 65. The remainder is 1. The quotient is between 5 and 10.Grade 4</p>
<p>32</p>
<p>Chapter 8</p>
<p>86</p>
<p>Name</p>
<p>Date</p>
<p>EnrichChapter Resources</p>
<p>Puzzling Pennies</p>
<p>1. Start with 27 pennies. Divide them into three equal piles. Now move just six pennies so that one pile has nine more than the other two.</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>Prove your answer.</p>
<p>2. Place six pennies in two rows as shown: Now move one penny so that you have two rows with four pennies in each row.</p>
<p>Grade 4</p>
<p>37</p>
<p>Chapter 8</p>
<p>87</p>
<p>Name</p>
<p>Date</p>
<p>EnrichPatterns & Similarities</p>
<p>Watch for patterns as you solve these division problems. 1. 9 189 2. 6 144 3. 7 189</p>
<p>What is one way the first three quotients are similar?</p>
<p>4. 2 486</p>
<p>5. 3 486</p>
<p>6. 6 486</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>What is one way problems 4, 5, & 6 are similar?</p>
<p>7. 9 108</p>
<p>8. 5 65</p>
<p>9. 8 112</p>
<p>What pattern do you see in problems 7, 8 & 9?</p>
<p>10. 5 248</p>
<p>11. 5 722</p>
<p>12. 3 244</p>
<p>What pattern do you see in problems 10, 11 & 12?</p>
<p>Grade 4</p>
<p>42</p>
<p>Chapter 8</p>
<p>88</p>
<p>Name</p>
<p>Date</p>
<p>EnrichChapter Resources</p>
<p>Strategic DivisionUse one-digit divisors to create 20 division problems. Choose divisors carefully to earn points as follows: Zeros in the quotients hundreds place are not worth any points. Zeros in the quotients tens place are worth 2 points. Zeros in the quotients ones place are worth 1 point.</p>
<p>1.</p>
<p>604</p>
<p>2.</p>
<p>781</p>
<p>3.</p>
<p>852</p>
<p>4.</p>
<p>509</p>
<p>5.</p>
<p>619</p>
<p>6.</p>
<p>775</p>
<p>7.</p>
<p>423</p>
<p>8.</p>
<p>170</p>
<p>9.</p>
<p>875</p>
<p>10.</p>
<p>181</p>
<p>11.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>363</p>
<p>12.</p>
<p>725</p>
<p>13.</p>
<p>211</p>
<p>14.</p>
<p>321</p>
<p>15.</p>
<p>354</p>
<p>16.</p>
<p>104</p>
<p>17.</p>
<p>545</p>
<p>18.</p>
<p>323</p>
<p>19.</p>
<p>906</p>
<p>20.</p>
<p>806</p>
<p>Zeros in the 10s Place = _____ 2 = _____ Zeros in the 1s Place = _____ 1 = _____ Total Points Earned = _____</p>
<p>Grade 4</p>
<p>47</p>
<p>Chapter 8</p>
<p>89</p>
<p>Name</p>
<p>Date</p>
<p>EnrichTic-Tac-Toe</p>
<p>Play division tic-tac-toe. First, solve all the division problems.</p>
<p>4 81,332</p>
<p>6 60,624</p>
<p>3 30,737</p>
<p>5 15,102</p>
<p>9 72,275</p>
<p>2 61,279Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>8 16,726</p>
<p>4 32,364</p>
<p>7 42,284</p>
<p>How many ways can you make tic-tac-toe by finding three problems in a row that all have remainders?</p>
<p>Grade 4</p>
<p>52</p>
<p>Chapter 8</p>
<p>91</p>
<p>Name</p>
<p>Date</p>
<p>EnrichThree-Dimensional Figures</p>
<p>Look at the net below. What three-dimensional figure can you make from the net on this page? List two ways to name this three-dimensional figure.</p>
<p>Predict which numbers will be on opposite faces of the solid threedimensional. Use these as factors to write three multiplication sentences and three addition sentences.</p>
<p>Cut out the net and create a three-dimensional figure to check your answers!6</p>
<p>Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>4</p>
<p>8</p>
<p>5</p>
<p>7</p>
<p>9</p>
<p>Challenge: Renumber the faces of the three-dimensional figure so the product of each set of opposite faces is 36.</p>
<p>Grade 4</p>
<p>12</p>
<p>Chapter 9</p>
<p>92</p>
<p>Name</p>
<p>Date</p>
<p>EnrichChapter Resources</p>
<p>Polygon Challenge</p>
<p>Use the figure above to follow the directions below. 1. Shade the part of the figure that is not a polygon.Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>2. Name the largest polygon that appears in the figure.</p>
<p>3. Count all the triangles. How many?</p>
<p>4. Name the polygon that appears inside the square.</p>
<p>5. Draw a pentagon inside one of the large triangles. Hint: You can use the sides of the triangle for some of the sides of the pentagon.</p>
<p>6. Count all the rectangles. How many?</p>
<p>Grade 4</p>
<p>17</p>
<p>Chapter 9</p>
<p>9-3</p>
<p>Name</p>
<p>Date</p>
<p>EnrichPentadots</p>
<p>5 dots</p>
<p>10 dots</p>
<p>15 dots</p>
<p>Pentadots are made with dots in the shape of a regular pentagon. It takes 5 dots to make a pentadot with 2 dots per side. It takes 10 dots to make a pentadot with 3 dots per side, 15 dots to make a pentadot with 4 dots per side, and so on. 1. Describe the pattern you see:Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>2. How many dots will be on each side if the total number of dots is 40? dots</p>
<p>3. How many dots does it take to make a pentadot with 17 dots per side? dots</p>
<p>4. Draw a hexadot, a hexagon with 2 dots per side.</p>
<p>5. How many dots does it take to make a hexadot with 3 dots per side? dots</p>
<p>Grade 4</p>
<p>22</p>
<p>Chapter 9</p>
<p>94</p>
<p>Name</p>
<p>Date</p>
<p>EnrichChapter Resources</p>
<p>Time for Angles11 12 1</p>
<p>10 9 8</p>
<p>2 3 4</p>
<p>7 6</p>
<p>5</p>
<p>Imagine how the hands of the clock would appear at each time listed below. Think about each angle the hands would form as the minute hand moves in a clockwise direction away from the hour hand. Classify each angle by making a checkmark in one of the columns.</p>
<p>AnglesCopyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.</p>
<p>Time 9:00 1:30 4:30 11:00 12:15</p>
<p>Acute</p>
<p>Obtuse</p>
<p>Right</p>
<p>Now fill in a time when the clock is a...</p>

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