each chapter includes 4 targeted strategic...rounding 4.nbt.3 chapter 1, lesson 5 check my progress...

EACH CHAPTER INCLUDES: •Prescriptivetargetedstrategic

interventioncharts. •Studentactivitypages

alignedtotheCommonCoreStateStandards.

•Completelessonplanpageswithlessonobjectives,gettingstartedactivities,teachingsuggestions,andquestionstocheckstudentunderstanding.

Grade 4

Targeted Strategic Intervention

Grade 4, Chapter 4

Based on student performance on Am I Ready?, Check My Progress, and Review, use these charts to select the strategic intervention lessons found in this packet to provide remediation.

Am I Ready?

If Students miss

Exercises…

Then use this Strategic

Intervention Activity… Concept

Where is this concept in My Math?

1-5 4-A: Multiplication

Practice Multiplication 4.NBT.5 Grade 3,

Chapters 6, 7, and 8

6-8

4-B: Base-Ten Blocks Place value 4.NBT.1 Chapter 1,

Lesson 1

9-12 4-C: Round to the Given Place Value

Rounding 4.NBT.3 Chapter 1, Lesson 5

Check My Progress 1

If Students miss

Exercises…




2-4 4-D: Multiplication Patterns

Multiplication patterns

4.NBT.1, 4.NBT.5

Chapter 4, Lesson 1

4-E: Comparing Numbers

5-6

4-F: Round to the Nearest Ten, Hundred,

or Thousand

Estimation 4.NBT.3, 4.NBT.5

Chapter 4, Lesson 2

7-8 4-G: Use an Area Model to Multiply

Multiply using models 4.NBT.5 Chapter 4,

Lesson 4

Check My Progress 2

If Students miss

Exercises…




4-7 4-H: Multiply Whole

Numbers Multiply with one-

digit numbers 4.NBT.5 Chapter 4, Lessons 5-9

Review

If Students miss

Exercises…




8-9 4-I: Multiplying with Multiples of 10, 100,

or 1,000

Multiplication patterns

4.NBT.1, 4.NBT.5

Chapter 4, Lesson 1

4-J: Use Place Value to Compare Numbers

10-11

4-K: Round Whole Numbers

Estimation 4.NBT.3, 4.NBT.5

Chapter 4, Lesson 2

12-17 4-L: Two-Digit by One-Digit Multiplication

Multiply with one-digit numbers

4.NBT.5 Chapter 4, Lessons 5-9

Program: SI_Chart Component: SEPDF Pass

Vendor: Laserwords Grade: 4

Name

Multiplication Practice

Use a Multiplication Table.

Example: To find 7 times 8, look across the 7 row until you are under the 8. The product is 56.

Adding can help you multiply. Complete each pair of problems to see how.

1. 6 + 6 + 6 =

3 × 6 =

2. 8 + 8 =

2 × 8 =

3. 3 + 3 + 3 + 3 =

4 × 3 =

4. 4 + 4 + 4 + 4 =

4 × 4 =

5. 2 + 2 + 2 =

3 × 2 =

6. 7 + 7 =

2 × 7 =

Multiply.

7. 6 × 6 = 8. 7 × 5 = 9. 8 × 2 = 10. 3 × 9 =

11. 4 × 8 = 12. 4 × 5 = 13. 7 × 9 = 14. 2 × 5 =

Lesson

4-A

0 0 0 0 0 0 0 0 0 0 0

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What Can I Do?I want to multiply

two numbers.

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Program: SI_Chart Component: TEPDF Pass


WHAT IF THE STUDENT NEEDS HELP TO

USING LESSON 4-A

Lesson Goal• Multiply using a multiplication

table or repeated addition.

What the Student Needs to Know• Read a table.

• Add numbers in repetition.

Getting StartedFind out what students know about multiplication. Have them solve the following addition sentence: 4 + 4 + 4 + 4 = ____ (16). Ask:

• How can this addition sentence be written as a multiplication fact? (4 × 4 = 16)

What Can I Do?Read the question and the response. Then read and discuss the example. Ask:

• How can the example be written as a multiplication fact? (7 × 8 = 56)

• How is a multiplication table like an addition table? How are the two different? (Both show the results of performing an operation with two numbers. A multiplication table shows multiplication, while an addition table shows addition.)

Try It• Have students complete

Exercises 1–6. Then have them demonstrate on a multiplication table the correct answers to the multiplication sentences.

Power Practice• Have students complete the

practice items. Then review each answer. Be sure that students understand that repeated addition and using the multiplication table should yield the same answer.

Read a Table• Use an addition table. Show

the student how finding the intersection of a column and a row gives the sum of two numbers. Have the student practice writing addition sentences using the table.

• Illustrate how a multiplication table works on the same principle.

Add Numbers in Repetition• Use counters to demonstrate

repeated addition of a number. Show, for example, that 4 + 4 = 8, 4 + 4 + 4 = 12, and so on.

• Show the student how repeated addition can also be written as multiplication, so that 4 + 4 + 4 + 4 + 4 = 20 becomes 5 × 4 = 20. Have the student practice converting examples of repeated addition into multiplication sentences until the student can do so with ease.

Complete the Power Practice• Discuss each incorrect answer.

Have the student show you the correct answer on the multiplication table. Then have the student use repeated addition to demonstrate the correctness of the answer.

Name

Multiplication Practice

Use a Multiplication Table.

Example: To find 7 times 8, look across the 7 row until you are under the 8. The product is 56.

Adding can help you multiply. Complete each pair of problems to see how.

1. 6 + 6 + 6 = 18

3 × 6 = 18

2. 8 + 8 = 16

2 × 8 = 16

3. 3 + 3 + 3 + 3 = 12

4 × 3 = 12

4. 4 + 4 + 4 + 4 = 16

4 × 4 = 16

5. 2 + 2 + 2 = 6

3 × 2 = 6

6. 7 + 7 = 14

2 × 7 = 14

Multiply.

7. 6 × 6 = 36 8. 7 × 5 = 35 9. 8 × 2 = 16 10. 3 × 9 = 27

11. 4 × 8 = 32 12. 4 × 5 = 20 13. 7 × 9 = 63 14. 2 × 5 = 10

Lesson

4-A

0 0 0 0 0 0 0 0 0 0 0

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0 10 15 20 25 30 35 40 45 50

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0 16 24 32 40 48 56 64 72 80

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0× 1 2 3 4 5 6 7 8 9 10

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two numbers.

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Name

Count the hundreds, tens, and ones.

3 hundreds

4 tens

7 ones

Use a place-value chart.

A place-value chart can show the same number as the models.

Base-Ten Blocks

Complete the place-value chart for each model.

1.

2.

3.

4.

hundreds tens ones

hundreds tens ones

hundreds tens ones

hundreds tens ones

hundreds tens ones

Lesson

4-B

What Can I Do?I want to use

models to write numbers.

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Name

5.

tens ones

6.

tens ones

7.

ten ones

8.

tens ones

9.

hundreds tens ones

10.

hundred tens ones

11.

hundreds tens ones

Complete the expanded form for each model.

Lesson

4-B

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USING LESSON 4-B


Lesson Goal• Use base-ten blocks to model

two- and three-digit numbers.

What the Student Needs to Know• Identify the digits in a number.

• Identify the places in two- and three-digit numbers.

• Count by tens using base-ten blocks.

• Count by hundreds using base-ten blocks.

Getting StartedHave students work in small groups. Provide each group with a supply of base-ten blocks for ones, tens, and hundreds. Hold up and identify a 1-cube, a 10-rod, and a 100-flat in turn. Ask:

• How are these blocks used to model numbers? (Numbers may have hundreds, tens, and ones. The blocks show the meanings of the digits in numbers.)

• Have students take turns modeling numbers for others in the group to identify. Start with two-digit numbers and then move on to three-digit numbers.


• How many hundreds are pictured? (3) How many tens? (4) How many ones? (7) What number does this stand for? (347) How does the place-value chart show what the number means? (The chart shows the value of each of the three digits in the number. If necessary, review the term “digit.”)

Have students use their base-ten blocks to show 347. Then ask questions such as:

• Take away one hundreds square. What number is left? (247)

• Add two more tens rods. What number do you have now? (267)

Identify the Digits in a Number• Write the term digit and the

symbols 0 through 9 on the board. Ask:

• How do we use digits to make numbers? (The digits are combined in different ways.)

• Does a digit always have the same value in a number? (No, the value of the digit depends on its place in the number.)

• Use the digits 1, 2, and 3 to make some different numbers. (Answers will vary.)

Identify the Places in Two- and Three-Digit Numbers• Provide the student with blank

place-value charts for tens and ones. Have him or her show two-digit numbers with base-ten blocks and record their work in the charts.

• Repeat the activity for three-digit numbers.

• Give the student pairs of numbers such as 84 and 48. Ask him or her to explain how the numbers are the same and how they are different. Repeat with pairs such as 412 and 214. Encourage the student to use the names of the places in their discussions.

Name

Count the hundreds, tens, and ones.

3 hundreds

4 tens

7 ones

Use a place-value chart.

A place-value chart can show the same number as the models.

Base-Ten Blocks

Complete the place-value chart for each model.

1.

2.

3.

4.

8

hundreds tens ones

61 3

hundreds tens ones

24 5

hundreds tens ones

02 8

hundreds tens ones

13 2

hundreds tens ones

43 7

Lesson

4-B

What Can I Do?I want to use

models to write numbers.

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Lesson 4-B




Count by Tens Using Base-Ten Blocks• Have students work in pairs.

Provide each pair with a supply of tens rods. One student selects rods; the other student counts the rods by tens.

• One student grabs some tens rods and counts them. The other student must say the ten that is one more.

Count by Hundreds Using Base-Ten Blocks• Have students work in pairs

using hundreds squares. One student shows a number; the other counts by hundreds to find that number.

Complete the Power Practice• Have the student use base-ten

blocks to show each number before they write the answers.

• Provide extra help by working with the student using base-ten blocks. Show a number and ask him or her to name it. Begin with tens and ones; then go on to hundreds.

• Play money may also be used to model three-digit numbers. Use play pennies, dimes, and dollars with students who need more practice.

Try ItPoint out that each problem has a picture of base-ten blocks and a place-value chart. These are two different ways to show a number. Ask:

• How many hundreds are in the first problem? (1) How does this help you fill in the chart? (You write a 1 under “hundreds” to show there is 1 hundred in the number.) Repeat for the tens and ones in the first problem. If students are still not sure what to do, go over the second problem in the same way.

• Next, direct students’ attention to Exercise 3. Ask: What is different about this problem? (It has no tens.) What number is used to show nothing? (zero) Where does the zero go in this number? (In the tens place, or in the middle of the chart.)

• Have students complete the Try It section. Have base-ten blocks available for any student who needs them.

Power PracticeHave students look over the exercises before they begin. Ask:

• Which exercises show tens and ones, but no hundreds? (Exercises 5–8) Do you need to use zeros because there are no hundreds? Why or why not? (No, it is not necessary to use a zero at the beginning of a number.)

• When all students have finished, have them say and write the standard form of the number for each exercise.

Reinforce the work students have done on the page by asking questions such as:

• Which number on the page has zero tens? (305) Which is the greatest number? (305) the least number? (18)

Name

5.

2 tens 5 ones

6.

7 tens 1 ones

7.

1 ten 8 ones

8.

4 tens 4 ones

9.

2 hundreds 4 tens 3 ones

10.

1 hundred 8 tens 0 ones

11.

3 hundreds 0 tens 5 ones

Complete the expanded form for each model.

Lesson

4-B

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109_110_S_G4_C04_SI_119816.indd 110 09/07/12 12:40 PM




Name

Round to the Given Place Value

Round to the given place value.

To round to the nearest ten, use the ones digit.

26 rounds to 30. 32 rounds to 30.

To round to the nearest hundred, use the tens digit.


To round to the nearest thousand, use the hundreds digit.

2,901 rounds to 3,000. 3,472 rounds to 3,000.

Circle the numbers.

1. Circle the numbers that round to 50.

42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58


530 540 550 560 570 580 590 600 610 620 630 640 650 660

Round each number to the nearest ten.

3. 76 4. 36 5. 24 6. 57

7. 85 8. 71 9. 91 10. 65

Round each number to the nearest hundred.

11. 631 12. 923 13. 349 14. 558

15. 815 16. 128 17. 644 18. 157

Lesson

4-C

What Can I Do?I want to round

to the nearest ten or hundred.

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USING LESSON 4-C

Lesson Goal• Round numbers to the nearest

ten or hundred.

What the Student Needs to Know• Count by tens.

• Count by hundreds and thousands.

Getting StartedFind out what students know about tens, hundreds, and thousands. Have them count by 10s to 100, 100s to 1,000, and 1,000s to 10,000. Ask:

• When you count by 10s, 100s, and 1,000s, what happens to the first (left) digit of the numbers as you count? (It increases by one.)

• What happens to the other digits in the numbers? (They remain zero.)

What Can I Do?Read the question and the response. Then read and discuss the examples. Ask:

• What does it mean to say that 26 rounds to 30? (26 is closer to 30 than 20)

• What does it mean to say that 302 rounds to 300? (302 is closer to 300 than 400)

• What does it mean to say that 3,472 rounds to 3,000? (3,472 is closer to 3,000 than 4,000)

Try it• Choose volunteers to identify and

say the numbers in Exercise 1.

• When a digit you are rounding is a 5, do you round up or down? (up)

• What digits round a number up?(5 through 9)

• What digits round a number down? (0 through 4)

• Have students complete Exercises 1 through 18.

Count by Tens• Have the student use base-ten

blocks to illustrate the numbers that result when you count by tens. Then have the student write the sequence of numbers.

• Have the student practice counting by 10s to 100 until it can be done with ease.

Count by Hundreds and Thousands• Use base-ten blocks to

represent hundreds and thousands. Have the student count the blocks by ones. Then explain what each block represents and have the student count again, this time identifying what is being counted as a hundred or as a thousand.

• Have the student practice counting by hundreds and thousands until it can be done with ease.

Name

Round to the Given Place Value

Round to the given place value.

To round to the nearest ten, use the ones digit.


To round to the nearest hundred, use the tens digit.


To round to the nearest thousand, use the hundreds digit.

2,901 rounds to 3,000. 3,472 rounds to 3,000.

Circle the numbers.


42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58


530 540 550 560 570 580 590 600 610 620 630 640 650 660

Round each number to the nearest ten.

3. 76 80 4. 36 40 5. 24 20 6. 57 60

7. 85 90 8. 71 70 9. 91 90 10. 65 70

Round each number to the nearest hundred.

11. 631 600 12. 923 900 13. 349 300 14. 558 600

15. 815 800 16. 128 100 17. 644 600 18. 157 200

Lesson

4-C

What Can I Do?I want to round

to the nearest ten or hundred.

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113_S_G4_C04_SI_119816.indd 113 09/07/12 12:45 PM




Name

Multiplication Patterns

Look for a pattern.

The number of zeros in the product is the same as in the power of ten.

1 zero → 4 × 10 = 40

2 zeros → 4 × 100 = 400

3 zeros → 4 × 1,000 = 4,000

Complete each pattern.

1. 7 × 10 =

7 × 100 =

7 × 1,000 =

2. 2 × 10 =

2 × 100 =

2 × 1,000 =

3. 9 × 10 =

9 × 100 =

9 × 1,000 =

4. 3 × 10 =

3 × 100 =

3 × 1,000 =

5. 8 × 10 =

8 × 100 =

8 × 1,000 =

6. 5 × 10 =

5 × 100 =

5 × 1,000 =

Find each product.

7. 9 × 100 = 8. 3 × 1,000 = 9. 7 × 10 =

10. 6 × 10 = 11. 5 × 100 = 12. 3 × 1,000 =

13. 8 × 1,000 = 14. 4 × 10 = 15. 8 × 10 =

16. 4 × 100 = 17. 6 × 1,000 = 18. 2 × 100 =

Lesson

4-D

What Can I Do?I want to multiply by 10, 100, or 1,000.

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USING LESSON 4-D

Lesson Goal• Multiply numbers by 10, 100,

and 1,000.

What the Student Needs to Know• Multiply by one.

• Understand the relationship between 10, 100, and 1,000.

Getting StartedFind out what students know about the relationship between 10, 100, and 1,000. Ask:

• How many zeros are there in 10? 100? 1,000? (1, 2, 3)


• What is a simple way of multiplying 4 times 10, 100, or 1,000? (Possible answer: take the number 4 and write 1, 2, or 3 zeros after it.)

Try ItHave students answer Exercises 1 and 2 aloud. Then have students complete Exercises 3–6. Ask:

• As you move from multiplying by 10 to multiplying by 100, then by 1,000, what happens to your products? (They increase by a factor of ten each time.)


practice items. Then review each answer.

• Compare any incorrect answers with similar exercises on the page that the student answered correctly. For example, if the student answers 4 × 100 incorrectly, it can be compared with a correct answer for 4 × 10 or 9 × 100.

Multiply by One• Use counters to demonstrate

simple multiplication equa-tions, such as 4 × 2 and 4 × 3. Then show how multiplying a number by one results in a product of that number.

• Have the student practice multiplying the numbers 1 through 9 by 1 until the concept is clear.

Understand the Relationship between 10, 100, and 1,000• Use grid strips and grid paper

to model the relationship between the three numbers.

• Demonstrate how it takes 10 strips of 10 grid squares to make 100, and 10 grids of 100 squares to make 1,000.


Have the student identify the number of zeros in the second factor. Then have the student write the answer by attaching those zeros to the 1-digit factor.

Name

Multiplication Patterns

Look for a pattern.

The number of zeros in the product is the same as in the power of ten.

1 zero → 4 × 10 = 40

2 zeros → 4 × 100 = 400

3 zeros → 4 × 1,000 = 4,000

Complete each pattern.

1. 7 × 10 = 70

7 × 100 = 700

7 × 1,000 = 7,000

2. 2 × 10 = 20

2 × 100 = 200

2 × 1,000 = 2,000

3. 9 × 10 = 90

9 × 100 = 900

9 × 1,000 = 9,000

4. 3 × 10 = 30

3 × 100 = 300

3 × 1,000 = 3,000

5. 8 × 10 = 80

8 × 100 = 800

8 × 1,000 = 8,000

6. 5 × 10 = 50

5 × 100 = 500

5 × 1,000 = 5,000

Find each product.

7. 9 × 100 = 900 8. 3 × 1,000 = 3,000 9. 7 × 10 = 70

10. 6 × 10 = 60 11. 5 × 100 = 500 12. 3 × 1,000 = 3,000

13. 8 × 1,000 = 8,000 14. 4 × 10 = 40 15. 8 × 10 = 80

16. 4 × 100 = 400 17. 6 × 1,000 = 6,000 18. 2 × 100 = 200

Lesson

4-D

What Can I Do?I want to multiply by 10, 100, or 1,000.

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Name

Comparing Numbers

Use a number line.

Find each number on a number line.

The number to the right is greater than the number to the left.

So 12 is greater than 8.

Write 12 > 8.

Use place value.

Look at the place of the greatest value.

541 > 728

Since 5 is less than 7, 541 is less than 728.

541 < 728

If the digits of the greatest place are the same, look at the next place.

689 > 624

Since 8 is greater than 2, 689 is greater than 624.

689 > 624

Use the number line. Compare. Write >, <, or =.

1. 38 40 2. 35 23 3. 12 27

4. 36 39 5. 24 16 6. 40 38

7. 25 28 8. 33 26 9. 16 8

Use place value. Start at the greatest place. Compare. Write >, <, or =.

10. 46 51 11. 73 85 12. 91 37

13. 193 184 14. 277 391 15. 444 441

16. 2,856 2,890 17. 5,318 5,318 18. 7,251 7,521

Lesson

4-E

What Can I Do?I want to

compare two numbers.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

7 8 9 10 11 12 13

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

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Name

Compare. Write >, <, or =.

19. 78 45 20. 56 65 21. 39 42

22. 203 196 23. 308 304 24. 628 628

25. 956 963 26. 79 59 27. 854 954

28. 748 748 29. 680 694 30. 980 980

31. 943 929 32. 210 212 33. 453 453

34. 296 296

35. 597 579

36. 35 32

37. 867 861

38. 425 999

39. 658 682

40. 621 612

41. 963 938

42. 620 619

43. 101 100

44. 673 967

45. 742 839

Lesson

4-E

Top This If You Can!

Play a game to help you learn to compare numbers.

• Use index cards. Make 2 sets of number cards for each number from 1 to 100.

• Shuffle the cards well. Deal out 10 cards to each player. Place the other cards facedown in the center.

• Each player picks one card from their hand. Players place the cards on the table. The player whose card shows the greater number keeps both cards.

• If the cards show equal numbers, players show one more card until a player wins the hand. The player who runs out of cards can pick 10 cards from the pile. Play continues until one player has all the cards.

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USING LESSON 4-E


Lesson Goal• Compare two numbers using a

number line or place value.

What the Student Needs to Know• Read a number line.

• Read and use mathematical notations of >, <, and =.

• Identify place value.

Getting StartedReview the meaning of greater than and less than with the student. Ask:

• Why would we want to know which of two numbers is greater? (Answers will vary.)

• What symbol do we use to show that a number is greater than another number? (>) What symbol is used to show a number is less than another number? (<) What symbol is used to show that two numbers are equal? (=)


• How does a number line show the order of numbers? (The numbers are written in order from left to right.)

• Choose a number on the number line. What can you tell about the numbers to the left and the numbers to the right? (The numbers to the right are greater than the number chosen, and the numbers to the left are less than the number chosen.)

• Is a whole number with 4 digits greater or less than a whole number with 3 digits? (greater than)

• Consider these two numbers: 527 and 524. Which digit will determine which number is greater? (the digit in the ones place)

Read a Number Line• Review the order of the

numbers 1–20 with the student. Demonstrate how these numbers can be shown in order on a number line.

• Have the student locate several numbers on the number line.

• Have the student draw a number line from 20 to 40, locating all the whole numbers and labeling them properly.

Read and Use Mathematical Notations of >, <, and =• Remind the student that the

equals sign (=) is used to show that two quantities or numbers are the same or equal.

• The student may better remember how to interpret the greater than (>) and less than (<) symbols when he or she understands that the point of the symbol shows the lesser number. Have the student practice writing inequalities you give verbally.

Name

Comparing Numbers

Use a number line.



So 12 is greater than 8.

Write 12 > 8.

Use place value.


541 > 728


541 < 728


689 > 624


689 > 624


1. 38 < 40 2. 35 > 23 3. 12 < 27

4. 36 < 39 5. 24 > 16 6. 40 > 38

7. 25 < 28 8. 33 > 26 9. 16 > 8

Use place value. Start at the greatest place. Compare. Write >, <, or =.

10. 46 < 51 11. 73 < 85 12. 91 > 37

13. 193 > 184 14. 277 < 391 15. 444 > 441

16. 2,856 < 2,890 17. 5,318 = 5,318 18. 7,251 < 7,521

Lesson

4-E



0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

7 8 9 10 11 12 13

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

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117_118_S_G4_C04_SI_119816.indd 117 09/07/12 12:55 PM


Lesson 4-E




Identify Place Value• Write a 3-digit number on the

board and have the student identify the place value of each digit as you point to it. Repeat with 4-digit numbers.

• Provide a place-value chart. Have the student write numbers you say into the chart. Discuss how place value clues are given by the names of the numbers in thousands and hundreds.

Complete the Power Practice• Review answers with the

student. For each incorrect answer, have him or her use either a number line or place-value chart to demonstrate how the answer was deter-mined. Correct any errors in these methods at this time.

Try ItHave students draw a circle around each number on the number line for each exercise.

• Check to see that students’ use of the mathematical symbols is correct by asking them to read several answers aloud.

• Reinforce students’ understanding of place value by asking them to name the place value where the important comparison occurs in Exercises 10–18. For example, in Exercise 14, they need to compare the hundreds digits. In Exercise 15, however, the hundreds and tens digits are equal, so they must compare the ones digit to find the greater number.

Power Practice• Select several exercises and have

students tell the key place value they need to look at before determining the greater number.

• Remind students that they can draw a number line or cross out equal digits to help decide which number is greater. Discuss which symbol would be used if the first number is greater, or if the second number is greater.

Name

Compare. Write >, <, or =.

19. 78 > 45 20. 56 < 65 21. 39 < 42

22. 203 > 196 23. 308 > 304 24. 628 = 628

25. 956 < 963 26. 79 > 59 27. 854 < 954

28. 748 = 748 29. 680 < 694 30. 980 = 980

31. 943 > 929 32. 210 < 212 33. 453 = 453

34. 296 = 296

35. 597 > 579

36. 35 > 32

37. 867 > 861

38. 425 < 999

39. 658 < 682

40. 621 > 612

41. 963 > 938

42. 620 > 619

43. 101 > 100

44. 673 < 967

45. 742 < 839

Lesson

4-E

Top This If You Can!

Play a game to help you learn to compare numbers.

• Use index cards. Make 2 sets of number cards for each number from 1 to 100.

• Shuffle the cards well. Deal out 10 cards to each player. Place the other cards facedown in the center.

• Each player picks one card from their hand. Players place the cards on the table. The player whose card shows the greater number keeps both cards.

• If the cards show equal numbers, players show one more card until a player wins the hand. The player who runs out of cards can pick 10 cards from the pile. Play continues until one player has all the cards.

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117_118_S_G4_C04_SI_119816.indd 118 09/07/12 12:55 PM

Learn with Partners & Parents• Have students write a number

sentence with >, <, or = for each hand played.

• Advanced players can deal two cards at a time and add them together. The winner of each hand would be the student whose total is greater.




Name

Round to the Nearest Ten, Hundred, or Thousand

Round to the nearest hundred.

Round to the nearest thousand.

Round to the nearest ten or hundred. Fill in the blanks.

Round 6,803 to the nearest thousand.

Step 1

Look at the place to the right of the thousands place.

6,803

Step 2

If the digit is less than 5, round down to 6,000.

If the digit is 5 or greater, round up to 7,000.

8 > 5, so round 6,803 up to 7,000.

So, 6,803 rounded to the nearest thousand is 7,000.

Round to the nearest ten.

3. 22 4. 86 5. 45

6. 271 7. 749 8. 615

9. 4,672 10. 3,333 11. 8,501

1. Round 29 to the nearest ten.

29 is between and .

29 rounds to .

2. Round 538 to the nearest hundred.

538 is between and .

538 rounds to .

Lesson

4-F

What Can I Do?I want to round to the nearest ten, hundred,

or thousand.

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USING LESSON 4-F

Lesson Goal• Round numbers to the nearest ten,

hundred, or thousand.

What the Student Needs to Know• Count by tens, hundreds, and

thousands.

• Identify digits in the ones, tens, hundreds, and thousands place.

Getting StartedWrite the number 4,321 on the board. Ask:

• What number is in the hundreds place? (3) What number is in the ones place? (1) What number is in the thousands place? (4) What number is in the tens place? (2)

What Can I Do? Read the question and the response. Then read and discuss the examples. Ask:

• What does “round to the nearest thousand” mean? (to go up or down to the nearest thousand)

• Should we round 6,803 up or down? (up) Why should we round this number up? (The digit to the right of the thousands place is 8. 8 is greater than 5, so we round up.)

• What is 6,803 rounded to the nearest thousand? (7,000)

Try It For each of the exercises, have the students say the number to be rounded and then tell which multiples of 10 or 100 it falls between. Ask:

• In Exercise 1, should you round 29 up or down? (up) Why? (because 9 ones is greater than 5 ones)

• In Exercise 2, is 538 closer to 500 or 600? (500) Should you round up or down? (down) Why? (because 3 tens is less than 5 tens)

Power Practice• Have the student complete the


Count by Tens, Hundreds, and Thousands• Practice counting by tens,

hundreds, and thousands a few times each day until the student can do so with ease.

• The student might use tens and hundreds base-ten blocks to count by tens and hundreds.

Identify Digits in the Ones, Tens, Hundreds, and Thousands Place• Emphasize that in a whole

number the last digit is in the ones place. Make sure the student knows that the digit to the left of the ones place is in the tens place. Have the

student also point to the hundreds and thousands places.

• Have the student point to each number in the Power Practice and identify the digit in the ones, tens, hundreds, and thousands places as appropriate.

Complete the Power Practice • Discuss each incorrect answer.

Have the student model any exercise he or she missed using a sketched number line.

• Have the student identify the digit to the right of the place he or she is rounding to. Then have him or her round up or down according to the rule.

Name

Round to the Nearest Ten, Hundred, or Thousand

Round to the nearest hundred.

Round to the nearest thousand.

Round to the nearest ten or hundred. Fill in the blanks.

Round 6,803 to the nearest thousand.

Step 1

Look at the place to the right of the thousands place.

6,803

Step 2

If the digit is less than 5, round down to 6,000.

If the digit is 5 or greater, round up to 7,000.

8 > 5, so round 6,803 up to 7,000.

So, 6,803 rounded to the nearest thousand is 7,000.

Round to the nearest ten.

3. 22 20 4. 86 90 5. 45 50

6. 271 300 7. 749 700 8. 615 600

9. 4,672 5,000 10. 3,333 3,000 11. 8,501 9,000

1. Round 29 to the nearest ten.

29 is between 20 and 30 .

29 rounds to 30 .

2. Round 538 to the nearest hundred.

538 is between 500 and 600 .

538 rounds to 500 .

Lesson

4-F

What Can I Do?I want to round to the nearest ten, hundred,

or thousand.

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121_S_G4_C04_SI_119816.indd 121 09/07/12 12:59 PM


Name

Use an Area Model to Multiply

Shade the area model. Find each product.

1. rows of

4 × 2 =

2. rows of

3 × 5 =

3. rows of

3 × 3 =

4. rows of

4 × 5 =

5. rows of

3 × 2 =

6. rows of

5 × 5 =



Lesson

4-GC

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USING LESSON 4-G

Lesson Goal• Use an area model to create

an array.

• Multiply two factors to find the product.

What the Student Needs to Know• Recognize an area model as a

model for multiplication.

Getting Started• Explain to students that an area

model is like an array made of squares.

• Arrange 15 base-ten ones cubes to cover 5 rows and 3 columns on graph or grid paper. Explain that the cubes create an array.

• Shade in the squares that the cubes cover. Explain that the shaded squares show an area model.

• What multiplication number sentence can you write from this model? (5 × 3)

• What is the product? (15)

• Have students model 5 × 4 using an array and an area model. Have them identify the factors and the product.

TeachRead and discuss Exercise 1 at the top of the page. Ask:

• What does the first number in the multiplication sentence (4 × 2) tell us? (The total amount of rows.)How many rows will our area model have? (4)

• What does the 2 in the multiplication sentence tell us? (The total amount in each row.) How many squares will be shaded in each row? (2)

• Let’s shade 4 rows of 2 squares in our area model.

• How many total squares did we shade? (8) What is 4 × 2 = ? (8)

Practice• Have students complete Exercises

2 through 6. Check their work.

Recognize an Area Model as a Model for Multiplication• Start with an area model that

models the multiplication sentence 3 × 2.

• Work with the student to use base-ten blocks (ones cubes) or connecting cubes to create an array on grid or graph paper.

• Have the student shade the squares to create an area model.

• How many rows are in the area model? (3)

• How many are in each row? (2)

• If necessary, have the student count by 1s to find the total amount of cubes.

• Work up to skip counting or repeated addition to add each row. (2 + 2 + 2 = 6)

• What multiplication sentence represents the array? (3 × 2 = 6)

• Continue to have the student model arrays, shade area models, practice skip counting, use repeated addition, and follow the steps to write a multiplication sentence.

Name

Use an Area Model to Multiply

Shade the area model. Find each product.

1. 4 rows of 2

4 × 2 = 8

2. 3 rows of 5

3 × 5 = 15

3. 3 rows of 3

3 × 3 = 9

4. 4 rows of 5

4 × 5 = 20

5. 3 rows of 2

3 × 2 = 6

6. 5 rows of 5

5 × 5 = 25

Lesson

4-G

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123_S_G4_C04_SI_119816.indd 123 7/17/12 3:11 PM




Name

Multiply Whole Numbers

The first step is done. Find the rest of the product.

Multiply.

Start with the ones.

2

8 6 × 4 4

Multiply tens. Add.

2

8 6 × 4 344

4 × 8 = 3232 + 2 = 34

4 × 6 = 24

1. 56

× 8

8

2. 32

× 7

4

3. 63

× 5

5

4. 71

× 9

9

4 1 1

5. 72

× 5

6. 47

× 6

7. 36

× 8

8. 59

× 3

9. 62

× 9

10. 81

× 4

11. 75

× 2

12. 43

× 7

13. 67

× 5

14. 28

× 6

15. 39

× 7

16. 46

× 3

17. 24

× 9

18. 17

× 4

19. 37

× 8

Lesson

4-H

What Can I Do?I want to multiply one-digit

and two-digit numbers.

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Program: SI_Chart Component: TEPDF 2nd



USING LESSON 4-H

Lesson Goal• Multiply a one-digit number by a

two-digit number.

What the Student Needs to Know• Complete multiplication facts.

• Regroup in multiplication.

• Identify the ones and tens digits in a number.

Getting Started• Write on the board:

31

× 6

Have students identify the ones and tens digits in the top number. Then say: There are two steps in this problem. What are the two steps? (Multiply 6 times the ones digit (1); multiply 6 times the tens digit (3).)

• Discuss the problem 6 × 37. Ask: How is this problem different from 6 times 31? (In 6 × 37,the ones product of 6 × 7 is more than 10. Regroping is needed.) Have a student solve the problem at the board.


• Which digits do you multiply first? (the 4 and the 6) What is their product and where do you write it? (24; write the 4 ones below the line in the ones place; write the 2 tens above the 8 in the top number.)

• Explain what is done in the next step. (Multiply 4 times 8 tens to get 32 tens. Add 2 tens from the regrouping to get 34 tens.)

Try It• Have students look over the

exercises. Point out that the first step is done. They need to find the other digits of the product.

Power Practice• Have the students complete the


Complete Multiplication Facts• Post a multiplication facts table.

Model for the student how to use the table. He or she finds one factor in the left row and the other factor in the top column. Where the row and column meet is the product of the two factors.

Regroup in Multiplication • Use problems such as 18 × 3

and 24 × 5 that have fairly small numbers. Provide base-ten blocks so the student can show the regrouping process.

Identify the Ones and Tens Digits in a Number• Have the student write

two-digit numbers such as 56 in expanded form, as in 56 = 5 tens 6 ones. Then ask him or her to tell you the tens digit and the ones digit.

Complete the Power Practice• If the student is making errors

in basic facts, provide extra practice using rectangle arrays on grid paper. A student shades a rectangle array and then writes a multiplication fact to show the total number of squares in the rectangle.

Name

Multiply Whole Numbers

The first step is done. Find the rest of the product.

Multiply.

Start with the ones.

2

8 6 × 4 4

Multiply tens. Add.

2

8 6 × 4 344

4 × 8 = 3232 + 2 = 34

4 × 6 = 24

1. 56

× 8

4 48

2. 32

× 7

2 24

3. 63

× 5

3 15

4. 71

× 9

6 39

4 1 1

5. 72

× 5360

6. 47

× 6282

7. 36

× 8288

8. 59

× 3177

9. 62

× 9558

10. 81

× 4324

11. 75

× 2150

12. 43

× 7301

13. 67

× 5335

14. 28

× 6168

15. 39

× 7273

16. 46

× 3138

17. 24

× 9216

18. 17

× 468

19. 37

× 8296

Lesson

4-H

What Can I Do?I want to multiply one-digit

and two-digit numbers.

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125_S_G4_C04_SI_119816.indd 125 09/07/12 1:02 PM




Name

Multiplying with Multiples of 10, 100, or 1,000

Use place value.

5 × 4,000 = 5 × 4 thousands

Use the basic fact.

5 × 4 thousands = 20 thousands = 20,000

Write each number in standard form.

1. 24 tens = 2. 56 hundreds = 3. 63 thousands =



Complete the steps to find each product.

10. 3 × 80 11. 7 × 400 12. 6 × 3,000

= 3 × tens = 7 × hundreds = 6 × thousands

= tens = hundreds = thousands

= = =

Lesson

4-I


with tens, hundreds, and thousands.

Think : 5 × 4 = 20

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Name

Use the basic fact to write each product.

13. 4 × 6 = 24 14. 7 × 9 = 63 15. 5 × 8 = 40

4 × 60 = 7 × 900 = 5 × 8,000 =

16. 3 × 9 = 27 17. 6 × 5 = 30 18. 2 × 6 = 12

3 × 90 = 6 × 500 = 2 × 6,000 =

19. 6 × 7 = 20. 8 × 3 = 21. 4 × 5 =

6 × 70 = 8 × 300 = 4 × 5,000 =

22. 5 × 3 = 23. 9 × 2 = 24. 8 × 8 =

5 × 30 = 9 × 200 = 8 × 8,000 =

Find each product.

25. 100 × 9

26. 10 × 7

27. 1,000 × 3

28. 10 × 8

29. 10 × 4

30. 1,000 × 4

31. 100 × 6

32. 1,000 × 6

33. 100 × 5

34. 10 × 4

35. 1,000 × 8

36. 10 × 7

37. 1,000 × 6

38. 100 × 9

39. 10 × 2

40. 100 × 6

Lesson

4-I

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USING LESSON 4-I


Lesson Goal• Multiply with multiples of 10,

100, or 1,000.

What the Student Needs to Know• Recall basic multiplication facts.

• Understand place value through thousands.

• Multiply by 10, 100, and 1,000.

Getting StartedHave students solve the following two number sentences:

8 × 1 = ____ (8)

8 × 10 = ____ (80)

• What is the relationship between the first answer and the second answer? (Possible answers: The second answer is ten times more than the first answer; The second answer is the first answer with a zero attached.)

What Can I Do? Read the question and the response. Then read and discuss the example. Ask:

• Which multiplication fact do you need to know to solve the problem 5 × 4,000? (5 × 4 = 20)

• What do you have to know about place value to solve the problem 5 × 4,000? (You have to know that 4,000 is the same as 4 thousands.)

• What would the answer be if the problem was 5 × 3,000? (15,000) 5 × 5,000? (25,000)

Recall Basic Multiplication Facts• Use counters or base-ten

blocks to demonstrate the products of multiplying two 1-digit numbers. Then have the student do the same.

• Have the student write multiplication facts on flash cards and practice until they can be recalled with ease.

Understand Place Value through Thousands• Have the student practice

writing two-digit through four-digit numbers in a place-value chart and reading them aloud until it can be done

with ease. Be sure the student understands that each place value must have a single digit from 0 to 9.

• Have the student write down the following numbers in aplace-value chart and in standard form: 3 tens (30); 4 thousands (4,000); 7 hundreds (700); 6 tens (600); 4 hundreds (400); 8 thousands (8,000). Be sure the student understands that a place value that isn’t specified can be assumed to have a value of 0.

Name

Multiplying with Multiples of 10, 100, or 1,000

Use place value.

5 × 4,000 = 5 × 4 thousands

Use the basic fact.

5 × 4 thousands = 20 thousands = 20,000

Write each number in standard form.

1. 24 tens = 240 2. 56 hundreds = 5,600 3. 63 thousands = 63,000



Complete the steps to find each product.

10. 3 × 80 11. 7 × 400 12. 6 × 3,000

= 3 × 8 tens = 7 × 4 hundreds = 6 × 3 thousands

= 24 tens = 28 hundreds = 18 thousands

= 240 = 2,800 = 18,000

Lesson

4-I


with tens, hundreds, and thousands.

Think : 5 × 4 = 20

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127_128_S_G4_C04_SI_119816.indd 127 09/07/12 1:07 PM


Lesson 4-I




Multiply by 10, 100, and 1,000• Use grids, grid strips, and

cubes to model multiplication sentences. Show the student how a number may be multiplied by 10, 100, or 1,000 by attaching one, two, or three zeros to the original number. For example, 13 × 10 = 130; 13 × 100 = 1,300; and 13 × 1,000 = 13,000.

• Have the student practice multiplying by 10, 100, and 1,000 until the procedure becomes familiar.


Have the student identify the multiplication fact central to the problem. Then have the student describe the first factor in terms of place value. Finally, have the student use words to describe the answer in terms of place value before converting it to standard form.

Try ItHave the students look at Exercises 1–3. Make sure students understand that to write each number in standard form, they must multiply the 2-digit number by its place value. For example, 24 tens = 24 × 10 = 240. If students are not comfortable multiplying, have them write the number out in a place-value chart. For example, 24 tens becomes 2 hundreds, 4 tens, and 0 ones, or 240. Then have the students complete Exercises 1–9. Ask:

• What is a quick way to write 27 tens in standard form? (Add a zero to the end of 27 to get 270.) 27 hundreds in standard form? (Add two zeros to the end of 27 to get 2,700.) 27 thousands in standard form? (Add three zeros to the end of 27 to get 27,000.)

Have students look at Exercise 10. Be sure they understand how to rewrite 80 as 8 tens to facilitate multiplication. Then have the students complete Exercises 10–15.

Have the students look at Exercises 16–24. Be sure they understand how to name the second factor in the second number sentence in terms of its place value. For example, in Exercises 16–18, 90 = 9 tens; 500 = 5 hundreds; and 6,000 = 6 thousands.


practice exercises. Then review each answer.

• Select several of the exercises and have students identify the multiplication fact central to each problem.

Name

Use the basic fact to write each product.

13. 4 × 6 = 24 14. 7 × 9 = 63 15. 5 × 8 = 40

4 × 60 = 240 7 × 900 = 6,300 5 × 8,000 = 40,000

16. 3 × 9 = 27 17. 6 × 5 = 30 18. 2 × 6 = 12

3 × 90 = 270 6 × 500 = 3,000 2 × 6,000 = 12,000

19. 6 × 7 = 42 20. 8 × 3 = 24 21. 4 × 5 = 20

6 × 70 = 420 8 × 300 = 2,400 4 × 5,000 = 20,000

22. 5 × 3 = 15 23. 9 × 2 = 18 24. 8 × 8 = 64

5 × 30 = 150 9 × 200 = 1,800 8 × 8,000 = 64,000

Find each product.

25. 100 × 9

900

26. 10 × 7

70

27. 1,000 × 3 3,000

28. 10 × 8

80

29. 10 × 4

40

30. 1,000 × 4 4,000

31. 100 × 6

600

32. 1,000 × 6 6,000

33. 100 × 5

500

34. 10 × 4

40

35. 1,000 × 8 8,000

36. 10 × 7

70

37. 1,000 × 6 6,000

38. 100 × 9

900

39. 10 × 2

20

40. 100 × 6

600

Lesson

4-I

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127_128_S_G4_C04_SI_119816.indd 128 09/07/12 1:07 PM




Name

Use Place Value to Compare Numbers

Use a number line.


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


7 8 9 10 11 12 13

So, 13 is greater than 9.

Write 13 > 9.

Use place value.


432 655


432 < 655


848 815


848 > 815


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

1. 13 40 2. 35 39 3. 5 5

4. 36 25 5. 24 25 6. 20 23

7. 28 28 8. 7 26 9. 38 18

Use place value. Start at the greatest place. Compare. Write >, < or =.

10. 32 48 11. 69 52 12. 21 17

13. 243 268 14. 941 232 15. 772 773

16. 1,511 1,502 17. 5,318 5,318 18. 1,409 1,609

Lesson

4-J



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USING LESSON 4-J


Lesson Goal• Compare two numbers using a

number line or place value.

What the Student Needs to Know• Read a number line.

• Read and use mathematical notations of >, <, and =.

Getting StartedReview the meaning of greater than and less than with the student. Ask:

• Why would we want to know which of two numbers is greater? (Answers will vary.)

• What symbol do we use to show that a number is greater than another number? (>) What symbol is used to show a number is less than another number? (<) What symbol is used to show that two numbers are equal? (=)


• How does a number line show the order of numbers? (The numbers are written in order from left to right.)

Try It Have students draw a circle around each number on the number line for each exercise.

• Check to see that students’ use of the mathematical symbols is correct by asking them to read several answers aloud.

• Select several exercises and have students name the place value they need to look at before determining the greater number.

Read a Number Line• Review the order of the

numbers 1–20 with the student. Demonstrate how these numbers can be shown in order on a number line.

• Have the student locate several numbers on the number line.

• Have the student draw a number line from 20 to 40, locating all the whole numbers and labeling them properly.

Read and Use Mathematical Notations of >, <, and =• Remind the student that the

equals sign (=) is used to show that two quantities or numbers are the same or equal.

• The student may better remember how to interpret the greater than (>) and less than (<) symbols when he or she understands that the point of the symbol shows the lesser number. Have the student practice writing inequalities you give verbally.

Name

Use Place Value to Compare Numbers

Use a number line.


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


7 8 9 10 11 12 13

So, 13 is greater than 9.

Write 13 > 9.

Use place value.


432 655


432 < 655


848 815


848 > 815


0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

1. 13 < 40 2. 35 < 39 3. 5 = 5

4. 36 > 25 5. 24 < 25 6. 20 < 23

7. 28 = 28 8. 7 < 26 9. 38 > 18

Use place value. Start at the greatest place. Compare. Write >, < or =.

10. 32 < 48 11. 69 > 52 12. 21 > 17

13. 243 < 268 14. 941 > 232 15. 772 < 773

16. 1,511 > 1,502 17. 5,318 = 5,318 18. 1,409 < 1,609

Lesson

4-J



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131_S_G4_C04_SI_119816.indd 131 09/07/12 7:12 PM


Program: SI_Chart Component: SEPDF 2nd


Name

Round Whole Numbers

Round to the greatest place.

Round 87 to the nearest ten. Look at the ones digit.

If it is 5 or greater, round up. If it is less than 5, round down.

Think: 7 is greater than 5, so round up. 87 → 90

Round 416 to the nearest hundred. Look at the tens digit.Think: 1 is less than 5, so round down. 416 → 400

Round 5,392 to the nearest thousand. Look at the hundreds digit.Think: 3 is less than 5, so round down. 5,392 → 5,000

What Can I Do?I want to round whole numbers.

Round each number to its greatest place.

1. 842 2. 65 3. 7,662

4. 21 5. 9,287 6. 485

7. 92 8. 538 9. 1,626

10. 279 11. 3,206 12. 58


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USING LESSON 4-K


Lesson Goal• Round whole numbers.

What the Student Needs to Know• Recall place value.

Getting StartedTell students that they will be rounding to the nearest ten, hundred, or thousand. Ask them to skip-count:

• by 10 to 100

• by 100 to 1,000

• by 1,000 to 10,000

Explain that when they round, their answer will be a multiple of 10, 100, or 1,000.


• How do you know what place to round 87 to? (The 8 is in the tens place. That is the greatest place, so round to the nearest ten.)

• How do you know what digit to use to round a number? (Use the digit to the right of the greatest digit.)

Try It• Ask students to name the greatest

place for each number.

• Ask them to explain why one digit is bold in each number. (That is the digit they use to decide whether to round the number up or down.)

Power Practice• Remind students to round to the

greatest place.

• Tell them to look at the digit to the right of the greatest place.

• Ask them to name the digits that will tell them to round down. (0, 1, 2, 3, 4)

• Ask them to name the digits that will tell them to round up. (5, 6, 7, 8, 9)

Recall Place ValueUse a place-value chart.

• Show a number such as 3,629 and ask the student to name the value of the greatest place.

• Show a number such as 4,693 and have the student identify the place of each digit you name. Ask questions like, “What place is the 6 in?”

• Show a number such as 832. Ask the student to identify the digit in a place you name. For example, ask, “What digit is in the tens place?”


Have the student identify the place to which he or she will round.

• Ask the student to name the digit he or she will use to round the number and to explain how he or she will use it to round the number.

Name

Round Whole Numbers

Round to the greatest place.

Round 87 to the nearest ten. Look at the ones digit.

If it is 5 or greater, round up. If it is less than 5, round down.

Think: 7 is greater than 5, so round up. 87 → 90

Round 416 to the nearest hundred. Look at the tens digit.Think: 1 is less than 5, so round down. 416 → 400

Round 5,392 to the nearest thousand. Look at the hundreds digit.Think: 3 is less than 5, so round down. 5,392 → 5,000

What Can I Do?I want to round whole numbers.


1. 842 800 2. 65 70 3. 7,662 8,000

4. 21 20 5. 9,287 9,000 6. 485 500

7. 92 90 8. 538 500 9. 1,626 2,000

10. 279 300 11. 3,206 3,000 12. 58 60


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133_S_G4_C04_SI_119816.indd 133 7/12/12 5:38 PM




Name

Two-Digit by One-Digit Multiplication

Step 1 Step 2Multiply the ones. Multiply the tens. Regroup if needed. Add.

Finish each problem.

What Can I Do?I want to multiply a

one-digit number by a two-digit number.

2 7× 6

2

42 7

× 6162

4

9. 46× 8

8

4 10. 68

× 34

2 11. 59

× 64

5 12. 65

× 75

3

1. 38× 5

0

4 2. 76

× 38

1 3. 54

× 78

2 4. 27

× 93

6

6. 38× 9

2

7 5. 84

× 46

1 7. 54

× 64

2 8. 37

× 24

1

Lesson

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Think: 6 × 7 = 42Think: 6 × 2 = 12Then add. 12 + 4 = 16

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Name

Find each product.

Find each product.

18. 62× 5

13. 32× 1

17. 91× 5

19. 78× 3

20. 34× 2

29. 88× 3

30. 39× 5

31. 26× 8

32. 57× 6

33. 47× 2

34. 83× 4

35. 65× 5

36. 45× 9

21. 32× 6

22. 68× 2

23. 24× 7

24. 69× 4

25. 24× 9

26. 53× 7

27. 78× 3

28. 46× 8

14. 73× 3

15. 53× 7

16. 43× 2

Greatest Product Game

You will need one set of 0 to 9 digit cards.

• Turn the cards over and mix them up. Each player draws three cards.

• Make a problem like this:

× Find your product.• The player with the

greater product gets one point. Play until one player has 7 points.

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USING LESSON 4-L


Lesson Goal• Multiply one-digit numbers by

two-digit numbers.

What the Student Needs to Know• Recall multiplication facts.

• Understand place value.

• Understand regrouping.

Getting StartedFind out what students know about regrouping. Write the following multiplication on the board:

6

× 2

12

• Why do you write a 1 in the tens column in the answer? (because 6 × 2 = 12, which is 1 ten and 2 ones)

Write the following multiplication sentences on the board:

10

× 6

60

12

× 6

72

• What number is in the tens column in the answer to the first problem? (6) In the answer to the second problem? (7) Why is there a change? (Because in the second problem, the ones need to be regrouped after you multiply.) How would you solve 12 × 6? (In the answer, you write a 2 in the ones place, and write 1 ten above the tens column and add it to the product of 6 × 1.)

What Can I Do? Read the question and the response. Then read and discuss the example. Ask:

• In what order do you multiply the digits of a two-digit number? (Start with the ones, then multiply the tens.)

• When do you need to regroup to the next place value in a multiplication problem? (when the number in a place value is more than 9)

Recall Multiplication Facts• Use counters or base-ten

blocks to demonstrate the products of multiplying 2 one-digit numbers. Then have the student do the same.

• Have the student write out a multiplication table for the numbers 0 through 9.

• Have the student write multiplication facts on flash cards and practice until they can be recalled with ease.

Understand Place Value• Have the student write a

two-digit number and read it aloud. Then have the student tell you how many tens and ones are in the number.

• Have the student practice writing two-digit numbers in a place-value chart until it can be done with ease.

Name

Two-Digit by One-Digit Multiplication

Step 1 Step 2Multiply the ones. Multiply the tens. Regroup if needed. Add.

Finish each problem.

What Can I Do?I want to multiply a

one-digit number by a two-digit number.

2 7× 6

2

42 7

× 6162

4

9. 46× 8368

4 10. 68

× 3204

2 11. 59

× 6354

5 12. 65

× 7455

3

1. 38× 5190

4 2. 76

× 3228

1 3. 54

× 7378

2 4. 27

× 9243

6

6. 38× 9342

7 5. 84

× 4336

1 7. 54

× 6324

2 8. 37

× 274

1

Lesson

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Think: 6 × 7 = 42Think: 6 × 2 = 12Then add. 12 + 4 = 16

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135_136_S_G4_C04_SI_119816.indd 135 09/07/12 1:19 PM


Lesson 4-L




Understand Regrouping• Use grid strips and squares

to illustrate a situation where regrouping is required. For example: 1 ten, 7 ones (17) + 2 tens, 8 ones (28) = 3 tens, 15 ones. Since a number in the ones place may only be 9 or less, the ones must be regrouped. To get the answer of 45, 10 of the ones are converted to 1 ten, making a total of 4 tens. The 5 ones remain in the ones column.


Have the student write out the multiplication of the ones column as a multiplication fact. Then have the student write down the ones digit and regroup the tens. Finally, have the student multiply the tens column and add the results of the regrouping.

• Have the student use the Dis tributive Property of Multi plication to check the correctness of each revised answer. For example, 32 × 6 = 192 can be broken into (30 × 6) + (2 × 6) = 180 + 12 = 192.

• How do you regroup? (After multiplying, write down the digit in the ones place in the product and add the digit in the tens place to the product of the next column.)

Try It• Look at Exercise 1 with students.

Ask:

• How can you complete this problem? (Multiply 5 by 3, then add 4.)

Be sure students understand that they should first multiply the tens column, and then add any numbers resulting from regrouping. Then have them complete Exercises 1–12.

Have the students look at Exercise 15. Check to be sure they understand the order in which they should multiply the digits of the two-digit number. Ask:

• How can you find the answer to this problem? (Multiply 3 by 7 to get 21, then write 1 in the ones column. Remember that you need to regroup 2 tens. Multiply 5 by 7 to get 35, then write a 3 in the hundreds column and a 7 in the tens column because you add the 2 tens from regrouping.)

Have the students complete Exercises 13–20.



• Select a few of the exercises. Have volunteers demonstrate how to get the correct answer by regrouping.

Name

Find each product.

Find each product.

18. 62× 5310

13. 32× 132

17. 91× 5455

19. 78× 3234

20. 34× 268

29. 88× 3264

30. 39× 5195

31. 26× 8208

32. 57× 6342

33. 47× 294

34. 83× 4332

35. 65× 5325

36. 45× 9405

21. 32× 6192

22. 68× 2136

23. 24× 7168

24. 69× 4276

25. 24× 9216

26. 53× 7371

27. 78× 3234

28. 46× 8368

14. 73× 3219

15. 53× 7371

16. 43× 286

Greatest Product Game

You will need one set of 0 to 9 digit cards.

• Turn the cards over and mix them up. Each player draws three cards.

• Make a problem like this:

× Find your product.• The player with the

greater product gets one point. Play until one player has 7 points.

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135_136_S_G4_C04_SI_119816.indd 136 09/07/12 1:19 PM

Learn with Partners & Parents• Players may enjoy playing a

reverse game where they try to get products that are low.


each chapter includes 4 targeted strategic...rounding 4.nbt.3 chapter 1, lesson 5 check my progress...

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