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624 Unit 8 Fractions and Ratios

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Key Concepts and Skills• Find equivalent fractions in simplest form. 

[Number and Numeration Goal 5]

• Convert between and simplify fractions and

mixed numbers. 

[Number and Numeration Goal 5]

• Add fractions and mixed numbers. 

[Operations and Computation Goal 4]

• Use benchmarks to estimate sums. 

[Operations and Computation Goal 6]

Key ActivitiesStudents review fraction addition. They add

mixed numbers in which the fractional parts

have like or unlike denominators and rename

the sums in simplest form. Students use

benchmarks to estimate sums.

Ongoing Assessment: Informing Instruction See page 626.

Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, page 414). [Number and Numeration Goal 5;

Operations and Computation Goal 4]

MaterialsMath Journal 2, pp. 251 and 252

Study Link 8�1

Math Masters, p. 414

slate � Class Data Pad (optional)

Math Boxes 8�2Math Journal 2, p. 253

Students practice and maintain skills

through Math Box problems.

Study Link 8�2Math Masters, p. 223

Students practice and maintain skills

through Study Link activities.

READINESS

Adding Mixed NumbersMath Journal 2, p. 252

Students explore an alternate method

for adding mixed numbers.

EXTRA PRACTICE

Playing Fraction CaptureMath Journal 1, p. 198

Math Masters, p. 460

per partnership: 2 six-sided dice

Students practice comparing fractions and

finding equivalent fractions.

EXTRA PRACTICE

Solving Mixed-Number Addition ProblemsMath Masters, p. 253A

Students practice adding mixed numbers

with like and unlike denominators.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Adding Mixed NumbersObjectives To develop addition concepts related

to mixed numbers.t

Advance Preparation

Teacher’s Reference Manual, Grades 4–6 pp. 142, 143

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

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Date Time

Math Message

Add. Write the sums in simplest form.

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Adding Mixed Numbers

Add. Write each sum as a whole number or mixed number.

10. 11. 12.

Fill in the missing numbers.

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Add. Write each sum as a mixed number in simplest form.

19. 20. 21.

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Adding FractionsLESSON

8 �2

Math Journal 2, p. 251

Student Page

Lesson 8�2 625

Getting Started

1 Teaching the Lesson

▶ Math Message Follow-Up WHOLE-CLASS

ACTIVITY (Math Journal 2, p. 251)

Ask students to share their strategies for estimating the sums for Problems 1–6. Make sure students make reference to the benchmarks when estimating their sums.

Ask volunteers to share their strategies for renaming the sums in Problems 3–6 to a whole or mixed number. Encourage students to use their understanding of multiplication facts to recognize when the simplest form will be a whole number. If the sum is an improper fraction and the numerator is not a multiple of the denominator, the simplest form will be a mixed number. If the numerator is a multiple of the denominator, the simplest form will be a whole number. Ask volunteers to explain how to recognize an improper fraction. If the numerator is greater than or equal to thedenominator, the fraction is an improper fraction. To support English language learners, write and label examples of improper fractions on the board or Class Data Pad.

Ask students to share their estimating strategies for Problem 7 using benchmarks. Sample answer: 1_6 is less than 1_2, and 2_3 is greater than 1_

2. I estimated my answer to be about 1. Survey

students for what methods they used to find the common denominators for Problems 7–9. Expect a mixture of the methods discussed in Lesson 8-1. Summarize the methods on the board or Class Data Pad for student reference throughout the lesson.

ELL

3

_ 3 1

2 1

_ 2 5

_ 2

3

_ 2 1

1

_ 2

13

_ 8 1

5

_ 8

4 1

_ 8 33

_ 8

17

_ 5 3

2

_ 5

37

_ 5 7

2

_ 5

62

_ 5 12

2

_ 5

11 1

_ 4 45

_ 4

Math MessageSolve Problems 1–9 at the top of journal page 251. Use benchmarks to estimate the sums and to check the reasonableness of your solutions.

Study Link 8�1 Follow-UpHave partners compare answers and resolve differences. Ask volunteers to share their explanations for Problems 7, 14, and 21.

Mental Math and Reflexes Have students rename each fraction as a whole number or mixed number and each mixed number as an improper fraction.

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626 Unit 8 Fractions and Ratios

▶ Adding Mixed Numbers with

WHOLE-CLASS ACTIVITY

Fractions Having Like DenominatorsExplain that one way to find the sum of mixed numbers is to treat the fraction and whole number parts separately. Write the problem below on the board or a transparency:

3 1 _ 8

+ 5 3 _ 8

8 4 _8 or 8 1 _ 2

Add the whole-number parts. Then add the fraction parts.

Ask students to solve 2 7 _ 8 the following problem: + 3 5 _ 8

Discuss students’ solution strategies. Make sure the following strategy is presented:

1. Add the whole-number parts. 2 7 _ 8

2. Add the fraction parts. + 3 5 _ 8

5 12 _ 8

3. Rename 5 12 _ 8 in simplest form.

12 _ 8 = 8 _ 8 + 4 _ 8 = 1 + 4 _ 8 = 1 4 _ 8

Since 12 _ 8 = 1 4 _ 8 , then 5 12 _ 8 = 5 + 1 + 4 _ 8 = 6 4 _ 8 , or 6 1 _ 2 .

Model renaming 12 _ 8 with a picture.

12

_ 8 = 1 4 _ 8

Pose a few more addition problems in which the addends are mixed numbers with like denominators. Suggestions:

● 3 4 _ 7 + 4 3 _ 7 8 ● 1 3 _ 4 + 2 3 _ 4 4 2 _ 4 , or 4 1 _ 2

● 6 2 _ 3 + 2 1 _ 3 9 ● 8 7 _ 10 + 5 9 _ 10 14 3 _ 5

● Madeleine purchased 3 5 _ 8 yards of red ribbon and 4 7 _ 8 yards of purple ribbon. How much ribbon did Madeleine purchase? 8 4 _ 8 , or 8 1 _ 2 yards

● Mr. Marcus’s class ate 6 3 _ 4 pizzas and Mr. Samuel’s class ate 4 2 _ 4 pizzas. How many pizzas did the two classes eat? 11 1 _ 4 pizzas

Ongoing Assessment: Informing Instruction

Watch for students who have difficulty

renaming mixed-number sums such as 5 12

_ 8 .

Discuss the meanings of numerator and

denominator, and have students rename

the fractional parts in the mixed numbers.

Suggestions:

4 7 _ 5 7 _

5 = 5 _

5 + 2 _

5 = 1 + 2 _

5

8 4 _ 3 4 _

3 = 3 _

3 + 1 _

3 = 1 + 1 _

3

2 7 _ 4 7 _

4 = 4 _

4 + 3 _

4 = 1 + 3 _

4

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Date Time

To add mixed numbers in which the fractions do not have the same denominator,

you must first rename one or both fractions so that both fractions have a

common denominator.

Example: 2 3

_ 5 + 4 2 _ 3 = ?

� Find a common denominator. The QCD of 3

_ 5 and 2

_ 3 is 5 ∗ 3 = 15.

� Write the problem in vertical form, and rename the fractions.

� Add.

2 9

_ 15

+ 4 10

_ 15

6 19

_ 15

2 3

_ 5

+ 4 2

_ 3 ∑

� Rename the sum. 6 19

_ 15 = 6 +

15

_ 15 + 4 _ 15 = 6 + 1 + 4

_ 15 = 7 4 _ 15

Add. Write each sum as a mixed number in simplest form. Show your work.

1. 2 1 _ 3 + 3 1

_ 4 = 2. 5 1 _ 2 + 2 2

_ 5 =

3. 6 1 _ 3 + 2 4

_ 9 = 4. 1 1 _ 2 + 4

3

_ 4 =

5. Sam purchased 4 3

_ 8 yards of fleece fabric for a jacket and 6 1 _ 3 yards of fleece

fabric to make a blanket. How much fabric did he purchase?

Adding Mixed NumbersLESSON

8 � 2

10 17

_ 24 yards

5 7 _ 12 7 9 _ 10

8 7 _ 9 6 1 _ 4

�

248-287_EMCS_S_MJ2_G5_U08_576434.indd 252 4/1/11 8:59 AM

Math Journal 2, p. 252

Student Page

Lesson 8�2 627

▶ Adding Mixed Numbers with

WHOLE-CLASS ACTIVITY

Fractions Having Unlike DenominatorsWrite the following problem on the board, and ask students to find the sum:

3 3 _ 4

+ 2 7 _ 8

After a few minutes, ask students to share solution strategies. Make sure the following method is discussed:

1. Find a common denominator for 3 _ 4 and 7 _ 8 8, 16, 24, 32, ...

2. Rename the fraction parts of the mixed numbers so they have the same denominator. In this case, the least common denominator, 8, is the easiest to use.

3 3 _ 4 3 6 _ 8

+ 2 7 _ 8 + 2 7 _ 8 3. Add. 5 13 _ 8

4. Rename the sum. 5 13 _ 8 = 5 + 8 _ 8 + 5 _ 8 = 5 + 1 + 5 _ 8 = 6 5 _ 8

Pose a few more problems that involve finding common denominators to add mixed numbers. Suggestions:

● 2 1 _ 2 + 4 3 _ 8 6 7 _ 8

● 5 2 _ 3 + 1 5 _ 6 7 3 _ 6 , or 7 1 _ 2

● 3 4 _ 5 + 2 1 _ 4 6 1 _ 20

● Juanita needs 1 7 _ 8 yards of fabric for a dress and 5 1 _ 6 yards for a jacket. How many total yards does she need? 7 1 _ 24 yards

● The costumes for the lead roles in the school musical require 4 5 _ 8 yards of one type of fabric and 2 1 _ 3 yards of another type of fabric. How much fabric needs to be purchased? 6 23 _ 24 yards

▶ Adding Mixed Numbers PARTNER ACTIVITY

(Math Journal 2, pp. 251 and 252)

Have students complete journal pages 251 and 252. Circulate and assist.

Ongoing Assessment: Exit Slip

�

Recognizing Student Achievement

Use an Exit Slip (Math Masters, page 414) to assess students’ facility with

adding mixed numbers. Have students explain how they found the answer to

Problem 4 on journal page 252. Students are making adequate progress if their

responses demonstrate an understanding of renaming fractions to have common

denominators and to be in simplest form.

[Number and Numeration Goal 5; Operations and Computation Goal 4]

● 6 5 _ 6 + 3 3 _ 5 10 13 _ 30

● 1 7 _ 8 + 8 1 _ 6 10 1 _ 24

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Date Time

5. Solve. Solution

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the band’s total practice time more or less

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Explain. Sample answer:

More than 6 hours

4. Make each sentence true by inserting

parentheses.

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b. 18 �(11 � 3)� 4

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d. 14 �(7 � 5 � 1)� 1

e. 14 �(7 � 5)� 1 � 3

2. Use the patterns to fill in the missing

numbers.

a. 1, 2, 4, ,

b. 5, 14, 23, ,

c. 4, 34, 64, ,

d. 20, 34, 48, ,

e. 100, 152, 204, , 308256

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Math BoxesLESSON

8 �2

68

71

108 109

230

222

155

(

(

Math Journal 2, p. 253

Student Page

STUDY LINK

8�2 Adding Mixed Numbers

61 6370

Name Date Time

17. 3,540 � 6 � 18. 1,770 � 3 �

19. 7,080 / 12 � 20. (590 � 5) � 2 � 1,475590

590590

Rename each mixed number in simplest form.

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6� �

3. 9 �5

3� � 4. 1�

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5. 4 �6

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Add. Write each sum as a whole number or mixed number in simplest form.

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Practice

Math Masters, p. 223

Study Link Master

628 Unit 8 Fractions and Ratios

2 Ongoing Learning & Practice

▶ Math Boxes 8�2

INDEPENDENT ACTIVITY

(Math Journal 2, p. 253)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 8-4. The skill in Problem 6 previews Unit 9 content.

Writing/Reasoning Have students write a response to the following: Explain your strategy for finding the values of the variables in Problem 5. Sample answer:

I looked for the common factor of the numerators or denominators that were complete. Then I used the multiplication rule or the division rule to multiply or divide to find the values for the variables.

NOTE Alternately, students may use a table or chart to find an equivalent

fraction with the given denominator or numerator.

▶ Study Link 8�2

INDEPENDENT ACTIVITY

(Math Masters, p. 223)

Home Connection Students practice adding mixed numbers and renaming improper fractions as mixed numbers in simplest form.

3 Differentiation Options

READINESS

SMALL-GROUP ACTIVITY

▶ Adding Mixed Numbers 15–30 Min

(Math Journal 2, p. 252)

To explore mixed-number addition, have students use an opposite-change algorithm. Have students change one of the addends to a whole number. Pose the following problem:

1 2 _ 3 + 7 5 _ 6

1. Change 1 2 _ 3 to a whole number by adding 1 _ 3 : 1 2 _ 3 + 1 _ 3 = 2.

2. Subtract 1 _ 3 from 7 5 _ 6 : 1 _ 3 = 2 _ 6 ; 7 5 _ 6 - 2 _ 6 = 7 3 _ 6 .

3. Add the new addends: 2 + 7 3 _ 6 = 9 3 _ 6 , or 9 1 _ 2 .

This strategy is most efficient when the sum of the fraction parts is greater than 1. Discuss how to recognize that the fraction parts are greater than 1. Have students use this method to solve the following problems:

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Name Date Time

Fraction Capture Gameboard 132

4

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

14

13

13

13

13

13

13

12

12

12

12 1

2

12

12

12

13

13

13

13

13

13

15

15 1

5

15 1

5

15

15

15

15

15

15

15

15

15

15

15

15

15

1515

16

16

16

16

16

16

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16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

16

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Math Masters, p. 460

Game Master

LESSON

8�2

Name Date Time

Solving Mixed-Number Addition Problems

Add. Write each sum as a mixed number in simplest form. Show your work.

1. 5 1

_ 5 + 2

4

_ 5 = 8 2. 3

2

_ 5 + 5

3

_ 10

= 8

7

__ 10

3. 4 3

_ 4 + 2

1

_ 12

= 6

5

_ 6 4. 4

2

_ 3 + 2

3

_ 4 =

7 5

__ 12

5. Josiah was painting his garage. Before lunch, he painted 1 2

_ 3 walls.

After lunch, he painted another 1 2

_ 3 walls. How many walls did he

paint during the day?

3

1

_ 3 walls

6. Julie’s mom made muffins for Julie and her friends to share.

Julie ate 1 3

_ 4 muffins. Her friends ate 3

1

_ 2 muffins. How many

muffins did Julie and her friends eat altogether?

5

1

_ 4 muffins

Without adding the mixed numbers, insert <, >, or =.

Explain how you got your answer.

7. 1 3

_ 8 + 6

2

_ 3 > 8

Sample answer: The sum of 1 3

_ 9 and 6 2

_ 3 is 8. But 3

_ 8 is

greater than 3

_ 9 , so the sum is greater than 8.

8. 5 < 2 1

_ 5 + 2

7

_ 8

Sample answer: You only need to add 1

_ 8 to 7

_ 8 to get another

whole. But 1

_ 5 is greater than 1

_ 8 , so 2 1

_ 5 + 2 7

_ 8 is greater than 5.

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Math Masters, p. 253A

Teaching Master

Lesson 8�2 629

● 3 1 _ 2 + 7 8 _ 10 11 3 _ 10

● 2 3 _ 4 + 6 9 _ 12 9 6 _ 12 , or 9 1 _ 2

● 5 8 _ 9 + 7 1 _ 3 13 2 _ 9

● 4 8 _ 10 + 3 5 _ 6 8 19 _ 30

Before students begin journal page 252, have them identify problems for which this algorithm might apply. Problems 4–6

EXTRA PRACTICE PARTNER ACTIVITY

▶ Playing Fraction Capture 15–30 Min

(Math Journal 1, p. 198; Math Masters, p. 460)

Students practice comparing fractions and finding equivalent fractions by playing Fraction Capture. Players roll dice, form fractions, and claim corresponding sections of squares. The rules are on Math Journal 1, page 198, and the gameboard is on Math Masters, page 460.

EXTRA PRACTICE PARTNER ACTIVITY

▶ Solving Mixed-Number Addition Problems(Math Masters, p. 253A)

Students practice adding mixed numbers with like and unlike denominators and use reasoning skills to compare sums of mixed numbers with whole numbers.

15–30 Min

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253A

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LESSON

8�2

Name Date Time

Solving Mixed-Number Addition Problems

Add. Write each sum as a mixed number in simplest form. Show your work.

1. 5 1

_ 5 + 2

4

_ 5 = 2. 3

2

_ 5 + 5

3

_ 10

=

3. 4 3

_ 4 + 2

1

_ 12

= 4. 4 2

_ 3 + 2

3

_ 4 =

5. Josiah was painting his garage. Before lunch, he painted 1 2

_ 3 walls.

After lunch, he painted another 1 2

_ 3 walls. How many walls did he

paint during the day?

6. Julie’s mom made muffins for Julie and her friends to share.

Julie ate 1 3

_ 4 muffins. Her friends ate 3

1

_ 2 muffins. How many

muffins did Julie and her friends eat altogether?

Without adding the mixed numbers, insert <, >, or =.

Explain how you got your answer.

7. 1 3

_ 8 + 6

2

_ 3 8

8. 5 2 1

_ 5 + 2

7

_ 8

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