each chapter includes 10 targeted...round to the nearest ten or hundred using place value you can...

Grade 5

EACH CHAPTER INCLUDES: •Prescriptivetargetedstrategic

interventioncharts. •Studentactivitypages

alignedtotheCommonCoreStateStandards.

•Completelessonplanpageswithlessonobjectives,gettingstartedactivities,teachingsuggestions,andquestionstocheckstudentunderstanding.

Targeted Strategic Intervention

Grade 5, Chapter 10

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?

1-3 10-A: Use a Number Line

to Round Fractions

Estimate sums and differences of

mixed numbers 5.NF.2 Chapter 9,

Lessons 11 and 12

10-B: Find Products and Quotients

4-7 10-C: Round to the Nearest Ten or Hundred

Using Place Value

Estimate products and quotients 5.NBT.6

Chapter 2, Lesson 8;

Chapter 3, Lesson 5

10-D: Find the Least Common Denominator

with Multiples 8-11

10-E: Use Strategies to Simplify Fractions

Add and subtract fractions 5.NF.2

Chapter 9, Lessons 2, 3,

and 5

Check My Progress 1

If Students miss

Exercises…




4-6 10-F: Write the

Numerator of a Fraction Estimate products

of fractions 5.NF.4, 5.NF.4a

Chapter 10, Lesson 2

7 10-G: Model and Add

Fractions Model fraction multiplication

5.NF.4, 5.NF.4a


8-10 10-H: Simplifying Improper Fractions

Multiply whole numbers and

fractions

5.NF.4, 5.NF.4a


Check My Progress 2

If Students miss

Exercises…




2-3 10-I: Multiplication Practice

Multiply fractions using models

5.NF.4, 5.NF.4a, 5.NF.4b


4-7 10-J: Renaming Mixed

Numbers

Multiply fractions and mixed numbers

5.NF.6 Chapter 10, Lesson 7

8-9 10-K: Multiplying

Fractions and Whole Numbers

Interpret multiplication as

scaling

5.NF.5, 5.NF.5a, 5.NF.5b, 5.NF.6


Review

If Students miss

Exercises…




9-10 10-L: Make Equal Groups to Divide

Estimate products of fractions and whole numbers

5.NF.4, 5.NF.4a


11-16 10-M: Improper

Fractions and Mixed Numbers

Multiply fractions

5.NF.4, 5.NF.4a, 5.NF.5b, 5.NF.6

Chapter 10, Lessons 6 and 7

17-18 10-N: Fractions

Equivalent to One Whole

Divide whole numbers by unit

fractions and unit fractions by whole

numbers using models

5.NF.7, 5.NF.7a, 5.NF.7b

Chapter 10, Lessons 10 and 11

Name

Estimate the value of each fraction by rounding to 0, 1 __ 2 , or 1. Draw pictures to help you.

1. 7 ___ 12 2. 6 __ 8

Use a number line to estimate the value of each fraction. Label the number line and round to 0, 1 _

2 , or 1.

3. 5 ___ 12 4. 4 __ 5

5. 1 __ 7 6. 5 __ 9

7. 8 __ 9 8. 3 __ 6

9. 2 ___ 10 10. 1 __ 5

Use a Number Line to Round Fractions

Program: SI_Chart Component: SEPDF Pass

Vendor: Laserwords Grade: 5

Lesson

10-A

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Program: SI_Chart Component: TEPDF Pass


USING LESSON 10-A

WHAT IF THE STUDENT NEEDS HELP TO

Lesson Goal• Use a number line to round

fractions to 0, 1 __ 2 , or 1.

What the Student Needs to Know• Count on a fraction number line.

• Compare models to round fractions.

Getting Started• Distribute paper for students to

make and name fraction models with fraction tiles.

• Write the fraction 4 __ 6 on the board.

• Ask student volunteers to identify the numerator (4) and denominator (6) in the fraction.

• How can you model the denominator? (Draw a model divided into 6 equal sections.)

• How can you model the numerator? (Shade 4 sections of the model.)

• Continue to have students’ model fractions with fraction tiles. Have them identify the numerator and denominator of the fractions, as needed.

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

• How many equal sections is the model divided into? (12)

• How many sections do we need to shade to show 7 __ 12 ? (7 sections)

• With seven out of twelve squares

shaded, is the fraction 7 __ 12 closer to

0, 1 __ 2 , or 1? ( 7 __ 12 is closer to 1 __ 2 )• How do you know 7 __ 12 is closer to 1 __ 2

and not 0 or 1? (The fraction 6 __ 12 is

equal to 1 __ 2 . Therefore, 7 __ 12 is closer

to 6 __ 12 .)

Practice• Have students read the directions

and complete Exercises 2 through 10.

Count on a Fraction Number Line• Display a number line from 0 to

20. Point to each number and count each number aloud.

• Display a number line divided into sixths. Read the fractions aloud.

• Emphasize the similarity between counting whole numbers and fractions 1, 2, 3,

and 1 __ 6 , 2 __ 6 , and 3 __ 6 .

• Repeat the activity with a variety of number lines divided into equal intervals with fractions.

Compare Models to Round Fractions• Have the student draw a model

of a circle divided into sixths.Ask the student to shade 3 parts.

• Have the student make another circle model to represent 1 __ 2 .

The circle model should be the same size as the first circle.

• Have the student compare the fraction models.

Name

Estimate the value of each fraction by rounding to 0, 1 __ 2 , or 1. Draw pictures to help you.

1. 7 ___ 12 1 __ 2

2. 6 __ 8 1

Use a number line to estimate the value of each fraction. Label the number line and round to 0, 1 _

2 , or 1.

3. 5 ___ 12 1 __ 2

4. 4 __ 5 1

0 1

122

123

124

125

126

127

128

129

121012

1112

1212

0 1

525

35

45

55

5. 1 __ 7 0 6. 5 __ 9 1 __ 2

0 1

727

37

47

57

67

77

0 1

929

39

49

59

69

79

89

99

7. 8 __ 9 1 8. 3 __ 6 1 __ 2

0 1

929

39

49

59

69

79

89

99

0 1

626

36

46

56

66

9. 2 ___ 10 0 10. 1 __ 5 0

0 1

102

103

104

105

106

107

108

109

101010

0 1

525

35

45

55

Use a Number Line to Round Fractions

Lesson

10-A

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Name

Find Products and Quotients

Use basic facts.

Multiply or divide.

30× 6180

6 � �� 66

-6 06 -6 0

Use basic facts. Complete to find each product or quotient.

1. 40× 2

2. 50× 4

3. 5 � �� 70

-5 20

4. 5 � �� 80

-5 30

Find each product or quotient. Show your work.

5. 30× 3

6. 60× 5

7. 80× 7

8. 10× 9

9. 5 � �� 90 10. 7 � �� 91 11. 4 � �� 60 12. 6 � �� 72

11

1 1

↓

↓ ↓

Lesson

10-B

What Can I Do?I want to multiply

by a 1-digit factor and divide by a 1-digit divisor.

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USING LESSON 10-B


Lesson Goal• Multiply by a 1-digit factor and

divide by a 1-digit divisor.

What the Student Needs to Know• Recall basic multiplication and

division facts.

Getting StartedFind out what students know about basic multiplication and division facts.

• What is the product of 7 and 4? (28) What does the number 28 mean? (2 tens 8 ones)

• Say: I want to divide 9 by 3. How many times does 3 go into 9? (3) Does 3 divide evenly into 9? (yes)

What Can I Do?Read the question and the response. Then read and discuss the examples. For the multiplication example, ask:

• What is the product of 6 × 0? (0) What does 0 represent? (0 ones)

• What is the product of 6 × 3? (18) What does 18 represent? (18 tens)

• What number is represented by 18 tens 0 ones? (180)

For the division example, ask:

• What division do you perform first? (Divide 6 into 6.) What is the quotient? (1)

• What do you do next? (Subtract 6 from 6 in the tens place. Next, bring down the 6 from the ones place. Then divide 6 into 6.)

• What is the quotient? (1) Subtract 6 from 6 to equal zero.

• What is 66 divided by 6? (11)

Try It• Have students use basic facts to

complete the process to find each quotient or product.

Power Practice• Have students complete the

practice items. Then review each answer.

Recall Basic Multiplication and Division Facts• Practice multiplication and

division facts for 10 to 15 minutes daily until the student can recall the products for multiplication facts and the quotients for division facts automatically.

Complete the Power Practice• Discuss each incorrect answer.

Have the student model how he or she arrived at their answer.

Name

Find Products and Quotients

Use basic facts.

Multiply or divide.

30× 6180

6 � �� 66

-6 06 -6 0

Use basic facts. Complete to find each product or quotient.

1. 40× 280

2. 50× 4200

3. 5 � �� 70

-5 20 -20 0

4. 5 � �� 80

-5 30 -30 0

Find each product or quotient. Show your work.

5. 30× 390

6. 60× 5300

7. 80× 7560

8. 10× 990

9. 5 � �� 90 10. 7 � �� 91 11. 4 � �� 60 12. 6 � �� 72

11

14 16

18 13 15 12

↓

↓ ↓

Lesson

10-B

What Can I Do?I want to multiply

by a 1-digit factor and divide by a 1-digit divisor.

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Name

Round to the Nearest Ten or Hundred Using Place Value

You can round numbers by using place value.

hundreds tens ones

3 6 1

Round 361 to the nearest hundred.

• Find the hundreds place. 361• Look at the digit to its right.

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

Since 6 > 5, round up.

To the nearest hundred, 361 rounds up to 400.

Round 361 to the nearest ten.

• Find the tens place. 361• Look at the digit to its right.


Since 1 < 5, round down.

To the nearest ten, 361 rounds down to 360.

Round each number to the nearest ten.

1. 35 2. 83 3. 671

4. 982 5. 309 6. 357

Round each number to the nearest hundred.

7. 293 8. 646 9. 485

10. 128 11. 151 12. 207

Lesson

10-C

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

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Name

Round each number to the underlined place.

13. 147 14. 281 15. 867

16. 54 17. 163 18. 247

19. 724 20. 855 21. 299

22. 709 23. 277 24. 529

Round to the nearest ten.

25. 49 26. 23 27. 22

28. 34 29. 83 30. 81

31. 35 32. 69 33. 65

34. 92 35. 55 36. 18

Round to the nearest hundred.

37. 779 38. 789 39. 615

40. 583 41. 488 42. 883

43. 814 44. 698 45. 712

46. 479 47. 656 48. 344

Lesson

10-C

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USING LESSON 10-C


Lesson Goal• Round to the nearest ten or

hundred.

What the Student Needs to Know• Identify the tens place.

• Identify the hundreds place.

• Identify multiples of 10 and 100.

Getting Started • Write 40, 50, and 60 on the board.

Remind students that these are called multiples of 10.

• Ask: What are the two multiples of 10 nearest to 43? (40 and 50) To 57? (50 and 60)

• Write 400, 500, and 600 on the board. Remind students that these are called multiples of 100.

• Ask: What are the two multiples of 100 nearest to 438? (400 and 500) To 572? (500 and 600)

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

• Ask students to mark 11 and 18 on a number line and draw an arrow connecting each number with the number they round to. Point out that on the number line, each number is closer to the multiple of ten that it rounds to.

11 15131210 14 17 1916 2018

• Repeat the activity with 15. Students should find that 15 appears exactly halfway between two tens. Tell students that if a number is halfway between two tens, it is rounded to the greater ten.

Identify the Tens Place• Use place-value charts for

two- and three-digit numbers.

• Use base-ten blocks to review the meaning of the digits in two- and three-digit numbers.

Identify the Hundreds Place• Use place-value charts for

three-digit numbers.

• Use base-ten blocks to model three-digit numbers.

• Use color-coded cards. Give each pair of students 3 crayons and 3 index cards. Students should write a number from 1 to 9 on each card, using a different color for each. The colors should be red, yellow,

and blue. Create three-digit place-value charts. Have the students shade the columns: ones, red; tens, yellow; hundreds, blue. Have pairs match each number card by its color to a column on the chart.

Identify Multiples of 10 and 100• Count aloud with the student

by 10s from 10 to 100. Have the student write the multiples of 10 on the board. Have the student name several multiples of 10 that are greater than 100. Point out that a multiple of 10 has a zero in the ones place. Repeat the activity with multiples of 100.

Name

Round to the Nearest Ten or Hundred Using Place Value

You can round numbers by using place value.

hundreds tens ones

3 6 1

Round 361 to the nearest hundred.

• Find the hundreds place. 361• Look at the digit to its right.


Since 6 > 5, round up.

To the nearest hundred, 361 rounds up to 400.

Round 361 to the nearest ten.

• Find the tens place. 361• Look at the digit to its right.


Since 1 < 5, round down.

To the nearest ten, 361 rounds down to 360.

Round each number to the nearest ten.

1. 35 40 2. 83 80 3. 671 670

4. 982 980 5. 309 310 6. 357 360

Round each number to the nearest hundred.

7. 293 300 8. 646 600 9. 485 500

10. 128 100 11. 151 200 12. 207 200

Lesson

10-C

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

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Lesson 10-C




Complete the Power Practice• Have the student draw number

lines to show the exercises. When rounding to the nearest ten, the number line is num-bered by 1s. When rounding to the nearest hundred, the num-ber line is numbered by 10s.

• Have the student underline the number in the place he or she is rounding to, then circle the digit to the right.

• The student may have difficulty finding the halfway point on a number line. Distribute number lines marked 0–100, 100–200, 300–400, and so on up to

900–1,000. Have the student point and follow on their number lines as you model how to count forward to find the middle or halfway point. Mark each halfway point with a symbol such as a stop sign. Repeat with different marked number lines until the student recognizes the pattern that the halfway point always includes the number 50.

• Have students write 361 in a place-value chart and round it to the nearest ten, explaining the rule used. (360; If the ones digit is less than 5, round down.)

• Ask students to round 361 to the nearest hundred. Explain that instead of using the ones digit, they will use the tens digit and the same rules for rounding. Have students identify the digit in the tens place and determine whether to round to the next greater hundred. (6 tens; Round 361 to 400.)

Try It• Work through Exercises 1 and 2

with students. Have students copy the numbers and underline the digit of the place they are round-ing. Then have students circle the digit to the right of the underlined digit. Have students demonstrate or explain how they found their answers to each exercise. For Exercises 3–6, have students tell you the tens digit in each number. For Exercises 7–12, have them tell you the hundreds digit.

Power PracticeBefore doing the exercises, check that students fully grasp the importance of using the digit in the ones place to determine how the digit in the tens place is rounded.

Have the students read the directions and look over the practice items. Ask:

• To which place will you round the underlined number in Exercise 13? (tens)

Name

Round each number to the underlined place.

13. 147 150 14. 281 300 15. 867 870

16. 54 50 17. 163 200 18. 247 250

19. 724 700 20. 855 900 21. 299 300

22. 709 710 23. 277 300 24. 529 500

Round to the nearest ten.

25. 49 50 26. 23 20 27. 22 20

28. 34 30 29. 83 80 30. 81 80

31. 35 40 32. 69 70 33. 65 70

34. 92 90 35. 55 60 36. 18 20

Round to the nearest hundred.

37. 779 800 38. 789 800 39. 615 600

40. 583 600 41. 488 500 42. 883 900

43. 814 800 44. 698 700 45. 712 700

46. 479 500 47. 656 700 48. 344 300

Lesson

10-C

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Program: SI_Chart Component: SEPDF 2nd


Name

Find the Least Common Denominator with Multiples

The least common denominator (LCD) of two fractions is the least common multiple (LCM) of the denominators.

To find the LCD of 7 __ 8 and 5 ___ 12 , list some of the multiples of each denominator. The denominators are 8 and 12.

Multiples of 8: 8, 16, 24, 32, 40, 48, 56

Multiples of 12: 12, 24, 36, 48, 60

The common multiples in each list are 24 and 48.

The lesser number in each list is the least common multiple. The LCM of 8 and 12 is 24. So, the LCD of 7 __ 8 and 5 ___ 12 is 24.

Complete to find the LCM for each pair of numbers.

1. 3 and 5 Multiples of 3: 3, 6, , ,

Multiples of 5: 5, 10, , ,

LCM:

2. 6 and 8 Multiples of 6: 6, 12, ,

Multiples of 8: 8, ,

LCM:

Complete to find the LCD.

3. 2 __ 3 and 5 __ 6 Multiples of 3: Multiples of 6: LCD:

4. 1 __ 2 and 3 __ 5 Multiples of 2: Multiples of 5: LCD:

Lesson

10-D

What Can I Do?I want to find the least common denominator

of two fractions.

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Program: SI_Chart Component: TEPDF 2nd


USING LESSON 10-D


Lesson Goal• Find the least common

denominator of two fractions.

What the Student Needs to Know• List the multiples of a number.

• Recognize the numerator and the denominator of a fraction.

Getting Started• Find out what students recall

about finding the multiples of a number. For example, ask:

• What are the first 5 multiples of 2? How do you find each multiple? (2, 4, 6, 8, 10; Possible answers: count by twos or multiply 1, 2, 3, 4, and 5 each by 2.)

• You may want to review the multiples of several other numbers as well, to make sure students understand how to list the numbers in order.

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

• For the fractions 7 __ 8 and 5 __ 12 , how do you decide which pair of numbers to use to find the least common denominator? (Use the denominators of each fraction.)

• How many multiples do you have to list for each number to find the least common multiple? (List the multiples until a common number appears in both lists.)

• How can you recognize when the denominator of one of the fractions will be the LCD of the fractions? (When one denominator is a multiple of the other denominator, the greater denominator will be the LCD.)

Try It• Discuss the differences and

similarities between Exercises 1–2 and Exercises 3–4. (In Exercises 1–2, students are finding the LCM of a pair of numbers. In Exercises 3–4, students are finding the LCD of a pair of fractions.) The LCD is the LCM of the denominators.

List the Multiples of a Number• Review how to skip count

with whole numbers. Have the student list the multiples of some whole numbers by skip counting. Remind the student to think about adding the same number each time to help with skip counting. Then have the student use multiplication to list the multiples of various whole numbers.

Recognize the Numerator and the Denominator of a Fraction• Present the student with a list

of fractions. Have the student identify the numerator and the denominator of each fraction. Then have the student circle the denominator of each fraction in the exercises.

Name

Find the Least Common Denominator with Multiples

The least common denominator (LCD) of two fractions is the least common multiple (LCM) of the denominators.

To find the LCD of 7 __ 8 and 5 ___ 12 , list some of the multiples of each denominator. The denominators are 8 and 12.

Multiples of 8: 8, 16, 24, 32, 40, 48, 56

Multiples of 12: 12, 24, 36, 48, 60

The common multiples in each list are 24 and 48.

The lesser number in each list is the least common multiple. The LCM of 8 and 12 is 24. So, the LCD of 7 __ 8 and 5 ___ 12 is 24.

Complete to find the LCM for each pair of numbers.

1. 3 and 5 Multiples of 3: 3, 6, 9 , 12 , 15

Multiples of 5: 5, 10, 15 , 20 , 25

LCM: 15

2. 6 and 8 Multiples of 6: 6, 12, 18 , 24

Multiples of 8: 8, 16 , 24

LCM: 24

Complete to find the LCD.

3. 2 __ 3 and 5 __ 6 Multiples of 3: 3, 6

Multiples of 6: 6 LCD: 6

4. 1 __ 2 and 3 __ 5 Multiples of 2: 2, 4, 6, 8, 10

Multiples of 5: 5, 10

LCD: 10

Lesson

10-D

What Can I Do?I want to find the least common denominator

of two fractions.

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Name

Use Strategies to Simplify Fractions

Divide by common factors.

9 ÷ 3 _______ 24 ÷ 3 = 3 __ 8 Think: Both 9 and 24 have 3 as a factor.

Write in simplest form.

1. 15 ÷ 3 _______ 21 ÷ 3 = 2. 4 ÷ 4 _____ 8 ÷ 4 = 3. 12 ÷ 4 _______ 16 ÷ 4 =


4. 8 ___ 12 ÷ 4 ÷ 4

5. 9 ___ 18 ÷ 9 ÷ 9

6. 2 ___ 18 ÷ 2 ÷ 2

7. 3 ___ 18 ÷ 3 ÷ 3

8. 2 ___ 12 ÷ 2 ÷ 2

9. 2 __ 6 ÷ 2 ÷ 2

10. 12 ___ 14 ÷ 2 ÷ 2

11. 8 ___ 16 ÷ 8 ÷ 8

12. 2 ___ 10 ÷ 2 ÷ 2

13. 14 ___ 21 ÷ 7 ÷ 7

14. 10 ___ 15 ÷ 5 ÷ 5

15. 4 ___ 12 ÷ 4 ÷ 4

Lesson

10-E

What Can I Do?I want to write fractions

in simplest form.

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USING LESSON 10-E


Lesson Goal• Write fractions in simplest form.

What the Student Needs to Know• Recall division facts.

• Find common factors.

Getting Started• Present some division facts and

have students name the quotients.

• Ask students to find the common factors for 6 and 8. (1 and 2)


• How can you tell if a fraction is in simplest form? (If the fraction is in simplest form, the numerator and denominator have only 1 as a common factor.)

Try It• Ask: In Exercise 1, will dividing by 3

give a fraction in simplest form? How do you know? (Yes, 3 is the greatest common factor of 15 and 21.)

Power Practice• Have students explain the

difference between simplifying a fraction and writing it in simplest form. (Sometimes when a fraction is simplified by dividing, the new fraction can also be simplified. So, for example 8 __ 20 can be simplified to 4 __ 10 , but in simplest form 8 __ 20 = 2 __ 5 .)

• Tell students to be sure their answers are in simplest form.

Recall Division Facts• Remind the student to use

counters to model any division facts he or she is unsure about.

• Demonstrate how to divide on a number line using repeated subtraction. Tell the student to use this strategy when they cannot recall a division fact.

• Have pairs of students work together to practice division facts using manipulatives, flash cards, or number lines.

Find Common Factors• Ask the student to explain what

a common factor is. (A number that divides into both numbers in a pair.)


Isolate problem areas by having the student explain his or her reasoning step by step for each problem.

Name

Use Strategies to Simplify Fractions

Divide by common factors.

9 ÷ 3 _______ 24 ÷ 3 = 3 __ 8 Think: Both 9 and 24 have 3 as a factor.


1. 15 ÷ 3 _______ 21 ÷ 3 = 5 _ 7

2. 4 ÷ 4 _____ 8 ÷ 4 = 1 _ 2

3. 12 ÷ 4 _______ 16 ÷ 4 = 3 _ 4


4. 8 ___ 12 ÷ 4 ÷ 4

2 _ 3

5. 9 ___ 18 ÷ 9 ÷ 9

1 _ 2

6. 2 ___ 18 ÷ 2 ÷ 2

1 _ 9

7. 3 ___ 18 ÷ 3 ÷ 3

1 _ 6

8. 2 ___ 12 ÷ 2 ÷ 2

1 _ 6

9. 2 __ 6 ÷ 2 ÷ 2

1 _ 3

10. 12 ___ 14 ÷ 2 ÷ 2

6 _ 7

11. 8 ___ 16 ÷ 8 ÷ 8

1 _ 2

12. 2 ___ 10 ÷ 2 ÷ 2

1 _ 5

13. 14 ___ 21 ÷ 7 ÷ 7

2 _ 3

14. 10 ___ 15 ÷ 5 ÷ 5

2 _ 3

15. 4 ___ 12 ÷ 4 ÷ 4

1 _ 3

Lesson

10-E

What Can I Do?I want to write fractions

in simplest form.

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315_S_G5_C10_SI_119817.indd 315 12/07/12 7:33 PM


Name

number line

0 or 114

24

34

44

fractions

Write each numerator. Circle the fraction. Round each fraction to 0, 1 __

2 , or 1.

1. 2 __ 3

0

or 13 3 3

Rounds to

2. 3 __ 6

0

or 16 6 6 6 6 6

Rounds to

3. 1 __ 7

0

7 7 7 7 7 7or 1

7

Rounds to

4. 8 __ 9

0

9 9 9 9 9 9 9 9or 1

9

Rounds to

Write the Numerator of a Fraction



Lesson

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USING LESSON 10-F


Lesson Goal• Use a number line to identify the

numerator and denominator of a fraction.

What the Student Needs to Know• Identify fractions on a number line.

Getting Started• On the board, draw a number line

with six tick marks, equally spaced from 1 __ 5 to 5 __ 5 .

• Write a zero (0) at the first tick mark.

• Point to the remaining tick marks and explain to students that every tick mark represents a fraction.

• Help students label the remaining fraction tick marks. Have students identify the numerator and denominator of each fraction.

TeachRead and discuss the example at the top of the page. On the board, draw a number line with five tick marks start-ing at 0 and spaced equally from 1 __ 4 to 4 __ 4 . Write a zero (0) at the first tick mark.

• Point to the remaining tick marks and explain to students that every tick mark represents a fraction.

• Remind students that a fraction is part of a whole. After zero, label the first fraction tick mark 1 __ 4 . Tell students that this tick mark is the first part of the whole.

• Help students label the remaining fraction tick marks.

• What fraction would round to zero?

( 1 __ 4 )• What fraction would round to 1 __ 2 ? ( 2 __ 4 )• What fraction would round to 1? ( 3 __ 4 )Practice• Read the directions as students

complete Exercises 1 through 4. Check their work.

Identify Fractions on a Number Line• Make index cards with number

lines divided into halves, fourths, and eighths.

• Place a red dot on one tick mark on each number line.

• The fraction at the red dot should be written on the back of the card.

• Then label each tick mark on the number line with a fraction. Reminder: Do not label the fraction at the red dot.

• Place students in pairs.

• Give each pair a set of index cards.

• Place the cards in a pile with the number lines facing up.

• One partner picks a card and identifies the fraction represented by the red dot.

• If the fraction is correct, they keep the card.

• If the fraction is not correct, it is returned to the pile.

• Play continues until the pile is gone.

• The player with the most cards wins.

• To challenge players, encourage them to determine if the fraction on the number line would be rounded to 0, 1 _

2 or 1.

Name

number line

0 or 114

24

34

44

fractions

Write each numerator. Circle the fraction. Round each fraction to 0, 1 __

2 , or 1.

1. 2 __ 3

0

or 113

23

33

Rounds to 1

2. 3 __ 6

0

or 116

26

36

46

56

66

Rounds to 1 __ 2

3. 1 __ 7

0 1

727

37

47

57

67

or 177

Rounds to 0

4. 8 __ 9

0 1

929

39

49

59

69

79

89

or 199

Rounds to 1

Write the Numerator of a Fraction Lesson

10-F

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317_S_G5_C10_SI_119817.indd 317 12/07/12 7:35 PM


Name

Use drawings to help you add. Write each sum in simplest form.

1. 1 __ 3 + 1 __ 3 = 2. 2 __ 9 + 2 __ 9 =

3. 2 __ 6 + 2 __ 6 = 4. 3 ___ 10 + 3 ___ 10 =

Circle the correct answer in simplest form.

5. 2 ___ 14 + 2 ___ 14 = 2 __ 7 4 ___ 14 6. 3 ___ 12 + 3 ___ 12 = 6 ___ 12 1 __ 2

7. 1 __ 6 + 1 __ 6 = 1 __ 3 2 __ 6 8. 3 __ 9 + 3 __ 9 = 6 __ 9 2 __ 3

Use fraction tiles, fraction circles or drawings to add. Write each sum in simplest form.

9. 3 __ 8 + 3 __ 8 = 10. 4 ___ 11 + 4 ___ 11 =

11. 4 ___ 10 + 4 ___ 10 = 12. 1 __ 4 + 1 __ 4 =

13. 4 __ 9 + 4 __ 9 = 14. 1 __ 5 + 1 __ 5 =

15. 4 ___ 12 + 4 ___ 12 = 16. 1 __ 7 + 1 __ 7 =

Model and Add Fractions



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USING LESSON 10-G


Lesson Goal• Add fractions with common

denominators.

What the Student Needs to Know• Add like fractions.

Getting Started• Draw a circle divided into 5 equal

parts on the board. Write the

equation 1 __ 5 + 1 __ 5 above the circle.

• How would you shade the circle

to show 1 __ 5 + 1 __ 5 ? (Shade 1 part to

show 1 __ 5 and shade 1 part to show

another 1 __ 5 .)

• What fraction of the circle is shaded? ( 2 __ 5 )


• How many parts of the circle do we

need to shade to show 1 __ 3 ? (1 part)

• How many parts of the circle do we

need to shade to show 1 __ 3 ? (1 part)

• How many parts of the circle are shaded? (2)

• What fraction represents the shaded

part? ( 2 __ 3 )• Let’s check to make sure the fraction

is in simplest form.

• What are the factors of 2? (1, 2) What are the factors of 3? (1, 3)

• What is the greatest factor the numbers have in common? (1) Therefore, the fraction is in simplest form.

• What is 1 __ 3 + 1 __ 3 ? ( 2 __ 3

)Practice• Have students complete

Exercises 2 through 16. Check their work.

Add Like Fractions• For this activity, you will need

two measuring cups and a plastic cup of water.

• Have the student model adding fractions using measuring cups. Have the student measure to

solve 1 __ 8 + 1 __ 8 .

• Pour water into the first

measuring cup to the 1 __ 8 line.

• Pour water into the second

measuring cup to the 1 __ 8 line.

• Pour the 1 __ 8 cup of water from the second measuring cup into the first measuring cup. (The first measuring cup should now have 2 __ 8 cup of water.)

• How much water do we have in

the measuring cup now? ( 2 __ 8 )• What is that fraction in simplest

form? ( 1 __ 4 )• Provide additional examples for

the student to use measuring cups to practice adding fractions with common denominators.

Name

Use drawings to help you add. Write each sum in simplest form.

1. 1 __ 3 + 1 __ 3 = 2 __ 3

2. 2 __ 9 + 2 __ 9 =

4 __ 9

3. 2 __ 6 + 2 __ 6 = 4 __ 6

= 2 __ 3

4. 3 ___ 10 + 3 ___ 10 =

6 ___ 10

= 3 __ 5

Circle the correct answer in simplest form.

5. 2 ___ 14 + 2 ___ 14 = 2 __ 7 4 ___ 14 6. 3 ___ 12 + 3 ___ 12 = 6 ___ 12 1 __ 2

7. 1 __ 6 + 1 __ 6 = 1 __ 3 2 __ 6 8. 3 __ 9 + 3 __ 9 = 6 __ 9 2 __ 3

Use fraction tiles, fraction circles or drawings to add. Write each sum in simplest form.

9. 3 __ 8 + 3 __ 8 = 6 __ 8

= 3 __ 4

10. 4 ___ 11 + 4 ___ 11 =

8 ___ 11

11. 4 ___ 10 + 4 ___ 10 = 8 ___ 10

= 4 __ 5

12. 1 __ 4 + 1 __ 4 =

2 __ 4

= 1 __ 2

13. 4 __ 9 + 4 __ 9 = 8 __ 9

14. 1 __ 5 + 1 __ 5 =

2 __ 5

15. 4 ___ 12 + 4 ___ 12 = 8 ___ 12

= 2 __ 3

16. 1 __ 7 + 1 __ 7 =

2 __ 7

Model and Add Fractions Lesson

10-G

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319_S_G5_C10_SI_119817.indd 319 12/07/12 7:45 PM




Name

Simplifying Improper Fractions

You can recognize an improper fraction because the numerator is greater than the denominator.

To simplify, divide the numerator by the denominator:

4 __ 2 = 4 ÷ 2 = 2 75 ___ 5 = 75 ÷ 5 = 15

Complete to simplify each fraction.

1. 18 ___ 3 = 18 ÷ 3 = 2. 14 ___ 2 = 14 ÷ 2 =

3. 16 ___ 2 = 16 ÷ = 4. 16 ___ 4 = 16 ÷ =

5. 20 ___ 5 = ÷ = 6. 22 ___ 2 = ÷ =

Simplify.

7. 24 ___ 6 = ÷ = 8. 30 ___ 3 = ÷ =

9. 27 ___ 9 = ÷ = 10. 25 ___ 5 = ÷ =

11. 28 ___ 2 = ÷ = 12. 30 ___ 15 = ÷ =

13. 36 ___ 3 = ÷ = 14. 36 ___ 6 = ÷ =

15. 72 ___ 4 = ÷ = 16. 81 ___ 9 = ÷ =

Lesson

10-H

What Can I Do?I want to simplify an

improper fraction.

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USING LESSON 10-H


Lesson Goal• Simplify improper fractions as

whole numbers.

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

• Recognize an improper fraction.

Getting Started• Review basic division facts and the

parts of a division sentence with students. For example, ask:

• What is 27 ÷ 3? (9)

• Can you name each part of the division sentence: 27 ÷ 3 = 9? (27 is the dividend, 3 is the divisor, and 9 is the quotient.)

• Which is greater, the dividend or the divisor? (the dividend)


• When you simplify an improper fraction using division, which part of the fraction corresponds to the dividend? To the divisor? (The numerator corresponds to the dividend and the denominator corresponds to the divisor.)

• What if the numerator is equal to the denominator, as in 8 __ 8 . Can you still divide to simplify the fraction? (Yes, 8 __ 8 = 1 because 8 ÷ 8 = 1.)

Try It• Have students explain what has to

be done to simplify the improper fractions in each exercise. (Divide the numerator by the denominator.)


practice items. Encourage them to use mental math to simplify each fraction. Then review each answer.

Recall Basic Division Facts• Practice division facts for 10

to 15 minutes daily until the student can recall the quotient for division facts automatically.

Recognize an Improper Fraction• Have the student compare pairs

of whole numbers. Then have the student look at a list of fractions and identify the fractions in which the numerator is greater than the denominator.

• Once the student can recognize an improper fraction, have the student write the fraction as a quotient following the rule:numerator ÷ denominator.


Have the student explain why the fraction should be simplified. Then have the student identify and compute the quotient that corresponds to the improper fraction.

Name

Simplifying Improper Fractions

You can recognize an improper fraction because the numerator is greater than the denominator.

To simplify, divide the numerator by the denominator:

4 __ 2 = 4 ÷ 2 = 2 75 ___ 5 = 75 ÷ 5 = 15

Complete to simplify each fraction.

1. 18 ___ 3 = 18 ÷ 3 = 6 2. 14 ___ 2 = 14 ÷ 2 = 7

3. 16 ___ 2 = 16 ÷ 2 = 8 4. 16 ___ 4 = 16 ÷ 4 = 4

5. 20 ___ 5 = 20 ÷ 5 = 4 6. 22 ___ 2 = 22 ÷ 2 = 11

Simplify.

7. 24 ___ 6 = 24 ÷ 6 = 4 8. 30 ___ 3 = 30 ÷ 3 = 10

9. 27 ___ 9 = 27 ÷ 9 = 3 10. 25 ___ 5 = 25 ÷ 5 = 5

11. 28 ___ 2 = 28 ÷ 2 = 14 12. 30 ___ 15 = 30 ÷ 15 = 2

13. 36 ___ 3 = 36 ÷ 3 = 12 14. 36 ___ 6 = 36 ÷ 6 = 6

15. 72 ___ 4 = 72 ÷ 4 = 18 16. 81 ___ 9 = 81 ÷ 9 = 9

Lesson

10-H

What Can I Do?I want to simplify an

improper fraction.

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321_S_G5_C10_SI_119817.indd 321 12/07/12 7:46 PM




Name

Draw an array to model each multiplication fact. Find the product. Then write the related multiplication fact.

1. 4 × 5 = ; 2. 5 × 10 = ;

Multiply by using repeated addition.

3. 2 × 6 = 4. 3 × 2 =

5. 5 × 6 = 6. 3 × 8 =

Use an array to find the missing number.

7. 5 × = 25 8. 3 × = 21


9. 2 × 7 = 10. 3 × 4 =

11. 2 × 9 = 12. 5 × 2 =

Use an array to find the product.

13. 5 × 8 = 14. 3 × 9 =

Multiplication Practice Lesson

10-IC

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USING LESSON 10-I


Lesson Goal• Use strategies to multiply two

whole numbers.

What the Student Needs to Know• Create arrays to represent

multiplication.

• Recall multiplication facts.

Getting Started• Write the following equation on

the board: 8 × 2 = 16

• What are the factors in this equation? (8 and 2) What is the product? (16)

• How can we represent this equation using illustrations? (use an array)

• Have students use connecting cubes to create an 8 × 2 array.


• Let’s find the product of 4 and 5 with an array.

• What is the first factor? (4) How many rows should the array have? (4)

• What is the second factor? (5) How many columns should the array have? (5)

• Use connecting cubes to create an array with 4 rows and 5 columns. Have students draw the array in Exercise 1.

• How many connecting cubes do we have in all? (20)

• Switch the rows and columns of your connecting cube array to find the related multiplication fact.

• How many rows will your array have for the related multiplication fact? (5) How many columns will your array have for the related multiplication fact? (4)

• What is the related multiplication fact? (5 × 4 = 20)

Practice• Read the directions as students

complete Exercises 2 through 14. Check student work.

Create Arrays to Represent Multiplication• Give each pair of students a set

of counters. Write the multiplication sentence 2 × 6 = 12 on the board.

• Explain that the sentence can be represented by an array of 2 rows with 6 counters in each row.

• Have students work together to make an array that represents the multiplication sentence. Encourage students to explain to each other how the array represents the multiplication sentence.

• Write another multiplication sentence on the board and have students repeat the steps.

Recall Multiplication Facts• Have the student make a

two-column table.

• One column will be numbered from 0 to 10. The other column will be the product of a factor being multiplied.

• For instance, when multiplying by 2, the first row will be 0 and 0, the second row will be 1 and 2, the third row will be 2 and 4, and so on.

• The student can create additional columns for multiplication facts in which they need extra practice.

• The student should also create flash cards to practice daily until products for the multiplication facts can be recalled with ease.

Name

Draw an array to model each multiplication fact. Find the product. Then write the related multiplication fact.

1. 4 × 5 = 20 ; 5 × 4 = 20 2. 5 × 10 = 50 ; 10 × 5 = 50


3. 2 × 6 = 6 + 6 = 12 4. 3 × 2 = 2 + 2 + 2 = 6

5. 5 × 6 = 6 + 6 + 6 + 6 + 6 = 30 6. 3 × 8 = 8 + 8 + 8 = 24

Use an array to find the missing number.

7. 5 × 5 = 25 8. 3 × 7 = 21


9. 2 × 7 = 7 + 7 = 14 10. 3 × 4 = 4 + 4 + 4 = 12

11. 2 × 9 = 9 + 9 = 18 12. 5 × 2 = 2 + 2 + 2 + 2 + 2= 10

Use an array to find the product.

13. 5 × 8 = 40 14. 3 × 9 = 27

Multiplication Practice Lesson

10-I

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323_S_G5_C10_SI_119817.indd 323 7/13/12 3:25 PM




Name

Renaming Mixed Numbers

Use multiplication and addition.

Rename this mixed number as an improper fraction.

5 7 __ 8 Multiply the whole number by the denominator of the fraction. Add that to the numerator of the fraction.

5 × 8 = 4040 + 7 = 47

This number now becomes the numerator of the improper fraction. Use the same denominator.

5 7 __ 8 = 47 ___ 8

Use multiplication and addition. Rename eachmixed number as an improper fraction.

1. 3 1 __ 3 = ___ 3 2. 2 1 __ 6 = ___ 6 3. 6 3 __ 4 = ___ 4

4. 3 2 __ 5 = ___ 5 5. 4 7 __ 9 = ___ 9 6. 2 9 ___ 10 = ___ 10

Rename each mixed number as an improper fraction.

7. 8 1 __ 2 = 8. 6 3 __ 5 = 9. 8 1 __ 9 =

5 7 __ 8 +×

��

Lesson

10-J

What Can I Do?I want to rename a mixed number as an improper fraction.

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10. 8 2 __ 3 = 11. 5 1 __ 7 = 12. 4 5 __ 6 =

13. 9 3 __ 8 = 14. 4 1 __ 8 = 15. 5 4 __ 9 =

16. 8 5 __ 8 = 17. 2 3 ___ 10 = 18. 3 3 __ 8 =

19. 5 3 __ 7 = 20. 7 2 __ 5 =

21. 1 7 ___ 10 = 22. 9 1 __ 2 =

23. 7 1 __ 6 = 24. 3 4 __ 5 =

25. 4 3 __ 4 = 26. 5 5 __ 6 =

27. 3 1 __ 2 = 28. 7 4 __ 5 =

29. 12 2 __ 3 = 30. 5 2 __ 3 =

Properly ImproperPlay with a partner. Take turns.

• Mix up 4 sets of number cards and deal them all out to the players.

• The first player places 3 cards from his or her hand face up to make a mixed number. The other player must rename the mixed number as an improper fraction.

• Correct answers are worth 3 points. The first player to get 21 points wins the game.

When you have mastered this game, use 4 cards to make each mixed number.

Lesson

10-J

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USING LESSON 10-J


Lesson Goal• Rename a mixed number as an

improper fraction.

What the Student Needs to Know• Recall basic multiplication and

addition facts.

• Recognize mixed numbers and improper fractions.

Getting StartedFind out what students know about mixed numbers and improper fractions. Ask:

• What is a mixed number? (a number made up of a whole number and a fraction)

• What is an improper fraction? (a fraction whose numerator is greater than its denominator)

Draw four rectangles on the board. Shade the first three rectangles completely. Divide the fourth rectangle in half and shade one half. Ask:

• What mixed number can you write for the shaded parts of the rectangles? (3 1 __ 2 )

Now divide the other threerectangles in half. Ask:

• How many shaded halves are there in all now? (7)

• What improper fraction can you write for the number of shaded halves? ( 7 __ 2 )

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

• What is the whole number part of

the mixed number 5 7 __ 8 ? (5) What is

the fraction part? ( 7 __ 8 )• What does the denominator of 7 __ 8 represent? (It tells that there are

8 equal parts in each whole, or 8 eighths in each whole.)

• How many wholes are there in 5 7 __ 8 ? (5) How many eighths are there in 5

wholes? (40 eighths)

Recall Basic Multiplication and Addition Facts• Practice multiplication and

addition facts for 10–15 minutes daily until the student can recall the products for multiplication facts and the sums for the addition facts easily.

Recognize Mixed Numbers and Improper Fractions• Have the student draw

rectangular models for a mixed number, such as 2 1 __ 3 .

• The student should see that each completely shaded rectangle represents 3 thirds

( 3 __ 3 ). So, the two rectangles would have 6 thirds ( 6 __ 3 ). The extra shaded section of the third rectangle is 1 __ 3 . The total number of shaded thirds is 7 __ 3 .

Name

Renaming Mixed Numbers

Use multiplication and addition.

Rename this mixed number as an improper fraction.

5 7 __ 8 Multiply the whole number by the denominator of the fraction. Add that to the numerator of the fraction.

5 × 8 = 4040 + 7 = 47

This number now becomes the numerator of the improper fraction. Use the same denominator.

5 7 __ 8 = 47 ___ 8

Use multiplication and addition. Rename eachmixed number as an improper fraction.

1. 3 1 __ 3 = 10 ___ 3 2. 2 1 __ 6 = 13 ___ 6 3. 6 3 __ 4 = 27 ___ 4

4. 3 2 __ 5 = 17 ___ 5 5. 4 7 __ 9 = 43 ___ 9 6. 2 9 ___ 10 = 29 ___ 10


7. 8 1 __ 2 = 17 ___ 2 8. 6 3 __ 5 = 33 ___ 5 9. 8 1 __ 9 = 73 ___ 9

5 7 __ 8 +×

��

Lesson

10-J

What Can I Do?I want to rename a mixed number as an improper fraction.

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325_326_S_G5_C10_SI_119817.indd 325 12/07/12 8:01 PM


Lesson 10-J




Complete the Power Practice• Have the student review the

steps for renaming a mixed number as an improper fraction. Multiply the whole number by the denominator. Add that to the numerator. This number now becomes the numerator of the improper fraction. Use the same denominator.

• How much is 40 eighths plus

7 eighths? (47 eighths or 47 __ 8 )

Try It• Be sure that students notice

that the denominator of the improper fraction is the same as the denominator of the mixed number.

• Be sure students multiply the whole number by the denominator and add that product to the numerator of the fraction. The result is the numerator of the equivalent improper fraction.


practice items. Then review each answer. Remind students that the denominator of the mixed number and improper fraction should be the same.

Learn with Partners & Parents• It is important when students

and their partners are making the mixed numbers from the cards that they realize that in the fraction part of a mixed number, the denominator must be larger than the numerator.

• Have students record the mixed number they made with the cards. Have partners write the improper fraction for the mixed number next to it.

Name


10. 8 2 __ 3 = 263

11. 5 1 __ 7 = 367

12. 4 5 __ 6 = 296

13. 9 3 __ 8 = 758

14. 4 1 __ 8 = 338

15. 5 4 __ 9 = 499

16. 8 5 __ 8 = 698

17. 2 3 ___ 10 = 2310

18. 3 3 __ 8 = 278

19. 5 3 __ 7 = 387

20. 7 2 __ 5 = 375

21. 1 7 ___ 10 = 1710

22. 9 1 __ 2 = 192

23. 7 1 __ 6 = 436

24. 3 4 __ 5 = 195

25. 4 3 __ 4 = 194

26. 5 5 __ 6 = 356

27. 3 1 __ 2 = 72

28. 7 4 __ 5 = 395

29. 12 2 __ 3 = 383

30. 5 2 __ 3 = 173

Properly ImproperPlay with a partner. Take turns.

• Mix up 4 sets of number cards and deal them all out to the players.

• The first player places 3 cards from his or her hand face up to make a mixed number. The other player must rename the mixed number as an improper fraction.

• Correct answers are worth 3 points. The first player to get 21 points wins the game.

When you have mastered this game, use 4 cards to make each mixed number.

Lesson

10-J

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325_326_S_G5_C10_SI_119817.indd 326 12/07/12 8:02 PM




Name

Multiplying Fractions and Whole Numbers

To multiply a fraction and a whole number, write the whole number as an improper fraction. Then multiply the fractions. Write the product in simplest form.

1 __ 8 × 32

1 __ 8 × 32 ___ 1 Write 32 as 32 ___ 1 .

1 × 32 ______ 8 × 1 Multiplying the fractions.

32 ___ 8 = 4 Write in simplest form.

Multiply. Write in simplest form.

1. 1 __ 3 × 9 = 1 __ 3 × 9 __ 1 = 1 × 9 _____ 3 × 1 = 9 __ 3 =

2. 1 __ 8 × 16 = 1 __ 8 × 16 ___ 1 = 1 × 16 ______ 8 × 1 = 16 ___ 8 =

3. 1 __ 6 × 18 = 1 __ 6 × 18 ___ 1 = 4. 1 __ 5 × 20 = 1 __ 5 × 20 ___ 1 =


5. 1 __ 7 × 14 = 1 __ 7 × 14 ___ 1 = 14 ___ 7 =

6. 1 __ 3 × 12 = 1 __ 3 × 12 ___ 1 = 12 ___ 3 =

7. 1 __ 5 × 15 = 1 __ 5 × 15 ___ 1 = 15 ___ 5 =

8. 1 __ 4 × 20 = 1 __ 4 × 20 ___ 1 = 20 ___ 4 =

Lesson

10-K

What Can I Do?I want to multiply a unit fraction and a

whole number.

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USING LESSON 10-K


Lesson Goal• Multiply a unit fraction and a

whole number.

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

• Write a whole number as an improper fraction.

Getting StartedReview the definition of animproper fraction. Ask:

• Which is larger in an improper fraction, the numerator or the denominator? (numerator)

• What is the value of 12 __ 3 ? (4) What is a way of writing 4 as an improper fraction? ( 4 __ 1 )

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

• How do you write 32 as an improper

fraction? ( 32 __ 1 ) What is the product of the numerators 1 × 32? (32) What is the product of the denominators 8 × 1? (8) What does 32 __ 8 simplify to? (4)

Try It• Have students study the

multiplication in Exercises 1 and 2 and simplify the fraction in the product. Have students complete the multiplication and simplify in Exercises 3 and 4.


practice items. Then review each answer. Students can use a multiplication table, as needed.

• Ask students if they see a shortcut method for multiplying a unit fraction by a whole number. Some students may realize that instead of multiplying, they can divide the whole number by the denominator of the fraction.

Recall Basic Division Facts• Practice basic division facts for

10 to 15 minutes daily until the student can recall the quotients of division facts automatically.

Write a Whole Number as an Improper Fraction • Have the student divide 8 by 1.

Point out that 8 divided by 1 is 8 and the division can also be represented as 8 __ 1 . Have the

student practice writing other whole numbers as improper fractions.


Have the student find the product and divide the numerator by the denominator again for each incorrect answer.

Name

Multiplying Fractions and Whole Numbers

To multiply a fraction and a whole number, write the whole number as an improper fraction. Then multiply the fractions. Write the product in simplest form.

1 __ 8 × 32

1 __ 8 × 32 ___ 1 Write 32 as 32 ___ 1 .

1 × 32 ______ 8 × 1 Multiplying the fractions.

32 ___ 8 = 4 Write in simplest form.


1. 1 __ 3 × 9 = 1 __ 3 × 9 __ 1 = 1 × 9 _____ 3 × 1 = 9 __ 3 = 3

2. 1 __ 8 × 16 = 1 __ 8 × 16 ___ 1 = 1 × 16 ______ 8 × 1 = 16 ___ 8 = 2

3. 1 __ 6 × 18 = 1 __ 6 × 18 ___ 1 = 3 4. 1 __ 5 × 20 = 1 __ 5 × 20 ___ 1 = 4


5. 1 __ 7 × 14 = 1 __ 7 × 14 ___ 1 = 14 ___ 7 = 2

6. 1 __ 3 × 12 = 1 __ 3 × 12 ___ 1 = 12 ___ 3 = 4

7. 1 __ 5 × 15 = 1 __ 5 × 15 ___ 1 = 15 ___ 5 = 3

8. 1 __ 4 × 20 = 1 __ 4 × 20 ___ 1 = 20 ___ 4 = 5

Lesson

10-K

What Can I Do?I want to multiply a unit fraction and a

whole number.

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329_S_G5_C10_SI_119817.indd 329 12/07/12 8:08 PM




Name

Make Equal Groups to Divide

Put the same number in each group.

12 stars4 stars in each group

Count the groups.3 groups of stars

Make equal groups.

18 circles3 equal groups of circles

Count the number in each group. 6 circles in each group

Use counters or small objects.

1. Use 20 counters. Put 4 counters in each group. How many groups do you get?

groups of counters

2. Use 18 counters. Make 2 equal groups. How many counters are there in each group?

counters in each group


groups of counters


counters in each group

Lesson

10-L

What Can I Do?I want to draw

pictures for division problems.

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Name

Draw each picture. Then tell how many equal groups, or how many are in each group.

5. 8 squares 6. 10 triangles

4 squares in each group 2 equal groups of triangles

groups of squares triangles in each group

7. 6 stars 8. 9 circles

3 stars in each group 3 equal groups of circles

groups of stars circles in each group

9. 16 triangles 10. 12 squares

8 triangles in each group 3 equal groups of squares

groups of triangles squares in each group

Lesson

10-L

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USING LESSON 10-L


Lesson Goal• Learn the principle of division.

What the Student Needs to Know• Understand the idea of dividing

a large group of items into equal, smaller groups.

• Add numbers in repetition.

Getting StartedFind out what students know about division. Draw 6 squares on the board. Say:

• There are 6 squares on the board. How can you divide the squares into 2 equal groups? (2 equal groups of 3)


• If you want to draw 12 stars and you know that there are 4 stars in each group, how can you find out how many groups there are? (Find out how many times you have to add 4 to get 12.)

• If you want to draw 18 circles and you know that there are 3 equal groups, how can you find out how many circles are in each group? (Evenly distribute the circles into 3 groups. There will be 6 circles in each group.) Understand the Idea of

Dividing a Large Group of Items into Equal, Smaller Groups• Use counters to demonstrate

how to divide even numbers into 2 equal groups. Have the student practice evenly dividing the numbers 2 through 18 until the student can do so easily. For example, have the student evenly divide 6 connecting cubes into 2 groups. The student will find each group has 3 connecting cubes.

• From here, move on to the idea of 3, 4, 5, 6, 7, 8, and 9 equal groups.

• Demonstrate how repeated addition or multiplication can be used to be sure that a number has been divided correctly.

Name

Make Equal Groups to Divide

Put the same number in each group.

12 stars4 stars in each group

Count the groups.3 groups of stars

Make equal groups.

18 circles3 equal groups of circles

Count the number in each group. 6 circles in each group

Use counters or small objects.


5 groups of counters


9 counters in each group


5 groups of counters


6 counters in each group

Lesson

10-L

What Can I Do?I want to draw

pictures for division problems.

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331_332_S_G5_C10_SI_119817.indd 331 12/07/12 8:14 PM


Lesson 10-L




Add Numbers in Repetition• Use counters to demonstrate

how a number may be added to itself repeatedly and that the sum increases each time the number is added. For example: 3 + 3 = 6; 3 + 3 + 3 = 9; 3 + 3 + 3 + 3 = 12; and so on.

• Have the student practice adding the numbers 1 through 9 in repetition until the student can do so with ease.


Have the student use counting, repeated addition, or multiplication to show how they got their answer.

Try It• Have students look at Exercises

1–4. Make sure they understand that the same operation can be used to determine both the number of groups into which a greater number is broken down and to find how many items are in each group.


practice items. Then review each answer. For any incorrect answers, have students use counters to model the correct number of groups and items.

Name

Draw each picture. Then tell how many equal groups, or how many are in each group.

5. 8 squares 6. 10 triangles

4 squares in each group 2 equal groups of triangles

2 groups of squares 5 triangles in each group

7. 6 stars 8. 9 circles

3 stars in each group 3 equal groups of circles

2 groups of stars 3 circles in each group

9. 16 triangles 10. 12 squares

8 triangles in each group 3 equal groups of squares

2 groups of triangles 4 squares in each group

Lesson

10-L

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331_332_S_G5_C10_SI_119817.indd 332 12/07/12 8:14 PM


Name

Improper fractions can be written as mixed numbers. For example, 3 __ 2 is the same as 1 1 __ 2 .

Draw a line to connect the improper fraction with the mixed number that it equals. Then shade the model beside each mixed number.

1. 7 __ 3 2 1 __ 2

2. 8 __ 5 2 1 __ 3

3. 5 __ 2 1 3 __ 5

An improper fraction has a numerator that is greater than the denominator. A mixed number has a whole number part and a fraction part.

Label each number as an improper fraction or a mixed number.

4. 1 7 __ 8 5. 12 ___ 10

6. 7 __ 7 7. 8 8 __ 9

8. 1 2 __ 3 9. 5 __ 2

10. 4 3 __ 4 11. 6 __ 3

Improper Fractions and Mixed Numbers



Lesson

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335_S_G5_C10_SI_119817.indd 335335_S_G5_C10_SI_119817.indd 335 7/17/12 11:22 AM7/17/12 11:22 AM



USING LESSON 10-M


Lesson Goal• Identify mixed numbers and

improper fractions.

What the Student Needs to Know• Identify improper fractions.

• Model mixed numbers.

Getting Started• Draw two fraction circles on the

board divided into thirds.

• How many parts is each circle divided into? (3)

• Shade one whole circle (3 parts) and shade one part (one third) of the second circle.

• Count the number of thirds that are shaded in both circles. How many parts are shaded in all? (4)

• The improper fraction to represent

the shaded parts would be 4 __ 3 . This

fraction can also represent the

mixed number 1 1 __ 3 .

TeachRead and discuss the example at the top of the page.

• Let’s use the circles to model the improper fraction and mixed number.

• Look at the left side of the arrow. How many parts is each circle divided into? (2)

• We need to show 3 __ 2 . How many parts of each circle do we need to shade to represent 3 __ 2 ? (Shade 1 __ 2 of each circle.)

• Now, we need to shade the circles on the right side of the arrow to represent the mixed number 1 1 __ 2 .

What do we need to shade? (Shade the first circle and 1 __ 2 of the second circle.)

Practice• Read the directions and review the

definitions as students complete Exercises 1 through 11. Check student work.

Identify Improper Fractions• If the student is having

difficulty with identifying improper fractions, have him or her use fraction tiles or fraction circles to model the fractions. This will show the student visually that the fraction is greater than 1.

Model Mixed Numbers• Have students work in pairs or

individually.

• Hand out index cards to each pair or individual. Tell the student to shade in one card. Then tell the student to divide another card into fourths and shade in one fourth.

• How many completely shaded cards are there? (1)

• How many fourths are shaded on

the other card? ( 1 __ 4 )• Have the student name the

whole number (1) and fraction

( 1 _ 4

) represented with each card,

and name the mixed number

created by the cards (1 1 _ 4

).• Repeat with other mixed

numbers.

Name

Improper fractions can be written as mixed numbers. For example, 3 __ 2 is the same as 1 1 __ 2 .

Draw a line to connect the improper fraction with the mixed number that it equals. Then shade the model beside each mixed number.

1. 7 __ 3 2 1 __ 2

2. 8 __ 5 2 1 __ 3

3. 5 __ 2 1 3 __ 5

An improper fraction has a numerator that is greater than the denominator. A mixed number has a whole number part and a fraction part.

Label each number as an improper fraction or a mixed number.

4. 1 7 __ 8 mixed number 5. 12 ___ 10 improper fraction

6. 7 __ 7 improper fraction 7. 8 8 __ 9 mixed number

8. 1 2 __ 3 mixed number 9. 5 __ 2 improper fraction

10. 4 3 __ 4 mixed number 11. 6 __ 3 improper fraction

Improper Fractions and Mixed Numbers

Lesson

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Name

Fractions Equivalent to One Whole

Name the fraction for one whole.

1.

1 = 10

2.

1 = 8

3.

1 = 12

4.

1 = 14

5.

1 = 6

6.

1 = 12

equivalent

⎫ ⎬ ⎭

1 = 6 _ 6

1

6 _ 6

Shade the equivalent form of one. Name the fraction.

Lesson

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USING LESSON 10-N


Lesson Goal• Name a fraction equivalent to one

whole.

What the Student Needs to Know• Model equivalent forms of one.

• Identify fractions that name one whole.

Getting Started• Draw a square on the board. Divide

the square into four equal sections.

• What fraction does one shaded section of the square represent? ( 1 __ 4 )

• Shade another section. What fraction do two shaded sections of the square represent?

( 2 __ 4

or 1 __ 2 )• Shade another section of the

square. What fraction do three shaded sections of the square represent? ( 3 __ 4 )

• Shade the last section. What fraction do four shaded sections of the square represent? ( 4 __

4 )

• All four parts make up one square. Therefore, 4 __ 4 equals one whole square.

TeachRead and discuss the exercise at the top of the page.

• Hold up a one whole fraction tile. What does this fraction tile represent? (one whole)

• Below the one whole fraction tile, line up six sixths fraction tiles in a row.

• Point to the sixths fraction model. How many tiles do we have in all? (6) What fraction represents the total number of fraction tiles? ( 6 __

6 )

• 6 __ 6 is equivalent to one whole.

Practice• Have students complete Exercises 1

through 6. Check their work.

Model Equivalent Forms of One• Use fraction circles to model

equivalent forms of 1.

• Have the student model fractions, such as 1 __ 6 and 4 __ 6 .

Then have him or her model 6 __ 6 .• The student will see that 6 __ 6 makes a complete circle. How much does 6 __ 6 represent? (one

whole)• Continue to have the student

model additional equivalent forms of one with a variety of fractions.

Identify Fractions that Name One Whole• Present the fraction song sung

to the tune of “Doe, a Deer.” (Do) One half, two halves, they

make one whole,(Re) One third, two thirds, three

thirds make one whole,(Mi) One fourth, two fourths, three

fourths, four fourths, (Fa) Look they make another

whole,(So) One fifth, two fifths, three

fifths, four fifths,(La) Five fifths, one whole, one

sixth, two sixths,(Ti) Three sixths, four sixths, five

sixths, six sixths,That will bring us back to whole, whole, whole, whole.

Name

Fractions Equivalent to One Whole

Name the fraction for one whole.

1.

1 = 10

10

2.

1 = 8

8

3.

1 = 12

12

4.

1 = 14

14

5.

1 = 6

6

6.

1 = 12

12

equivalent

⎫ ⎬ ⎭ 1 = 6 _

6

1

6 _ 6

Shade the equivalent form of one. Name the fraction.

Lesson

10-N

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337_S_G5_C10_SI_119817.indd 337 12/07/12 8:45 PM


each chapter includes 10 targeted...round to the nearest ten or hundred using place value you can...

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