# 4 enrichment

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11

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EnrichThink of It

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:

2. It is the greatest even two-digit number. The product of its digits is 72. Write it in word form:

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.

Write it in expanded form:

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:

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:

Grade 4

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Chapter 1

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EnrichChapter Resources

Telephone Fun

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.

Telephone Number

Standard Form

Expanded Form

Word Form Two million, six hundred thirty-seven thousand, four hundred twenty

905-9618

7,000,000 + 300,000 + 10,000 + 5,000 + 800 + 80 + 2Write your telephone number in standard form:

Grade 4

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Chapter 1

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EnrichBig Time

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?

2. About how old would you be if you lived a million hours?

3. About how old would you be if you lived a million days?

4. About how old would you be if you lived a million weeks?

5. About how many months is a million weeks?

6. About how many years is a million months?

Grade 4

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Chapter 1

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EnrichChapter ResourcesChapter 1

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?

2. From least to greatest, write the 6 three-digit numbers you can make using the digits 1, 2, and 3.

3. How many different three-digit numbers can you make using 4, 5, and 6 as digits?

Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

4. From least to greatest write the 6 three-digit numbers you can make using the digits 4, 5, and 6.

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

Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

78 pounds 11

42 pounds 98

87 ounces 84

65 ounces 33

57 kilograms 59

84 kilograms 29

Grade 4

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Chapter 7

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EnrichAsked and Answered

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.

Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

2.

3.

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.

5.

Trade with a partner to check each others work.

Grade 4

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Chapter 7

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EnrichChapter ResourcesChapter 7

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.

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35

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Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

53

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27

94

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Grade 4

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EnrichDigit Detective

Fill in the missing digits in the multiplication problems below. 1.

83 4 2 1674 33 351 8 4 14 5 5484 4570 5 184 4 7 2430 3 02 36450 6

2.

6

2

3 8 5376 2 01 24.

536Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

3.

5

5 25

7 1 3675 376.

75 95 8

5.

3160 790 11 60

Grade 4

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Chapter 7

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EnrichChapter Resources INDEX

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.

1. 57 34 = 4. 32 33 =

2. 61 76 = 5. 94 65 =

3. 85 29 = 6. 56 48 =

91 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1

81 6 2 4 3 2 4 0 4 8 5 6 6 4 7 2

71 4 2 1 2 8 3 5 4 2 4 9 5 6 6 3

61 2 1 8 2 4 3 0 3 6 4 2 4 8 5 4

51 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5

48 1 2 1 6 2 0 2 4 2 8 3 2 3 6

36 9 1 2 1 5 1 8 2 1 2 4 2 7

24 6 8 1 0 1 2 1 4 1 6 1 8

12 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

Grade 4

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Chapter 7

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EnrichEight Million or More

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.

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.

Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

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.

Trade with a partner, and complete each others problems.

Grade 4

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Chapter 7

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EnrichDivision Rules

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 =

Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Complete this statement: If a number can be divided evenly by 2 and by 3, then it is also divisible by .

Keep in mind 1. All even numbers are divisible by 2.

2. If the sum of the digits in a number is divisible by 3, then the number is divisible by 3.

Circle the numbers that are divisible by 6. 432 746 330 895 546

Grade 4

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Chapter 8

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Timed Ten

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.

10 = 7= 3=

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=

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=

10 = 2=

20 = 6=

60 = 30 = 10 =

Grade 4

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Chapter 8

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EnrichThe Bike Path

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.

Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Explain your thinking.

Grade 4

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Chapter 8

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EnrichChapter ResourcesChapter 8

Estimate QuotientsEstimate. Check your estimate. 1. 7 428 2. 3 605 3. 4 316

4. 9 8,140

5. 5 5,165

6. 8 3,999

7. 6 3,546

8. 2 196

9. 4 85

10. 9 98

11. 8 725

12. 5 5,620

Copyright Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Use the problems above to spell the name of the treasure state. Write the estimated quotient from above beside th

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