Objective
To develop addition concepts related to
mixed numbers.
1
materials
Teaching the Lesson
Key Activities
Students review fraction addition. They add mixed numbers in which the fractional parts have
like or unlike denominators and rename the sums in simplest form.
Key Concepts and Skills
• Find equivalent fractions in simplest form.
Щ— Math Journal 2, pp. 251 and 252
Щ— Study Link 8 1
б­њ
Щ— Teaching Aid Master (Math Masters,
p. 414; optional)
Щ— slates
Щ— Class Data Pad (optional)
[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]
Ongoing Assessment: Informing Instruction See page 626.
Ongoing Assessment: Recognizing Student Achievement Use journal page 252.
[Operations and Computation Goal 4]
2
Ongoing Learning & Practice
Students practice and maintain skills through Math Boxes and Study Link activities.
3
Students explore an alternate method for
adding mixed numbers.
Щ— Math Journal 2, p. 253
Щ— Study Link Master (Math Masters,
p. 223)
materials
Differentiation Options
READINESS
materials
EXTRA PRACTICE
Students play Fraction Capture to practice
comparing fractions and finding equivalent
fractions.
Щ— Math Journal 1, p. 198
Щ— Math Journal 2, p. 252
Щ— Game Master (Math Masters,
p. 460)
Щ— 2 six-sided dice
Technology
Assessment Management System
Journal page 252
See the iTLG.
624
Unit 8 Fractions and Ratios
Getting Started
Mental Math and Reflexes
Math Message
Have students rename each fraction as a whole
number or mixed number and each mixed number as
an improper fraction.
Solve Problems 1–9 at the top of journal page 251.
3
бЋЏбЋЏ 1
3
1 5
2бЋЏ2бЋЏ бЋЏ2бЋЏ
3 1
бЋЏбЋЏ 1бЋЏбЋЏ
2 2
13 5
бЋЏбЋЏ 1бЋЏбЋЏ
8 8
1 33
4бЋЏ8бЋЏ бЋЏ8бЋЏ
17 2
бЋЏбЋЏ 3бЋЏбЋЏ
5 5
37 2
бЋЏбЋЏ 7бЋЏбЋЏ
5 5
62
2
бЋЏбЋЏ 12бЋЏбЋЏ
5
5
1 45
бЋЏ
бЋЏ
бЋЏ
11 4 4бЋЏ
Study Link 8 1 Follow-Up
б­њ
Have partners compare answers and resolve
differences. Ask volunteers to share their
explanations for Problems 7, 14, and 21.
1 Teaching the Lesson
б­¤ Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Math Journal 2, p. 251)
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 the
denominator, 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.
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.
Student Page
Date
Time
LESSON
8 2
Math Message
Add. Write the sums in simplest form.
3
1
1. бЋЏбЋЏ П© бЋЏбЋЏ П­
5
5
3
4. бЋЏбЋЏ
7
б­¤ Adding Mixed Numbers with
Adding Fractions
б­њ
П©
5
бЋЏбЋЏ П­
7
4
бЋЏбЋЏ
5
1бЋЏ17бЋЏ
3
1
2. бЋЏбЋЏ П© бЋЏбЋЏ П­
8
8
5
бЋЏбЋЏ
6
2
2
8. бЋЏбЋЏ П© бЋЏбЋЏ П­
3
5
1
2
7. бЋЏбЋЏ П© бЋЏбЋЏ П­
6
3
WHOLE-CLASS
ACTIVITY
Fractions Having Like Denominators
Explain that one way to find the sum of mixed numbers is to treat
the fraction and whole number parts separately. Write the
problem on the next page onto the board or a transparency:
7
5. бЋЏбЋЏ
10
П©
1
бЋЏбЋЏ
2
2
2
2
3. бЋЏбЋЏ П© бЋЏбЋЏ П© бЋЏбЋЏ П­
3
3
3
1бЋЏ25бЋЏ
7
бЋЏбЋЏ П­
10
1бЋЏ11бЋЏ5
2
5
7
6. бЋЏбЋЏ П© бЋЏбЋЏ П­
9
9
1бЋЏ13бЋЏ
5
5
9. бЋЏбЋЏ П© бЋЏбЋЏ П­
6
8
1бЋЏ12бЋЏ14
Adding Mixed Numbers
Add. Write each sum as a whole number or mixed number.
3
5
1бЋЏ бЋЏ
10.
1
2
1бЋЏбЋЏ
11.
12.
1
4
2 бЋЏбЋЏ
П© 1бЋЏ бЋЏ
1
5
П© бЋЏбЋЏ
1
2
П© 3 бЋЏбЋЏ
2бЋЏ45бЋЏ
2
6
3
4
Fill in the missing numbers.
12
13. 5 бЋЏбЋЏ П­ 6
7
5
16. 4 бЋЏбЋЏ П­ 5
3
5
7
2
3
8
14. 7 бЋЏбЋЏ П­
5
8
11
17. 12 бЋЏбЋЏ П­ 13
6
3
бЋЏбЋЏ
5
5
6
5
15. 2бЋЏбЋЏ П­ 3
4
13
18. 9 бЋЏбЋЏ П­ 10
10
1
4
3
10
Add. Write each sum as a mixed number in simplest form.
2
3
3 бЋЏбЋЏ
19.
П©
2
5 бЋЏбЋЏ
3
9бЋЏ13бЋЏ
6
7
4 бЋЏбЋЏ
20.
21.
4
9
3 бЋЏбЋЏ
8
9
4
2 бЋЏбЋЏ
7
П© 6 бЋЏбЋЏ
7бЋЏ37бЋЏ
10 бЋЏ13бЋЏ
П©
251
Math Journal 2, p. 251
Lesson 8 2
б­њ
625
1
3бЋЏ8бЋЏ
3
П© 5бЋЏ8бЋЏ
4
1
8бЋЏ8бЋЏ or 8бЋЏ2бЋЏ
Add the whole-number parts.
Then add the fraction parts.
7
2бЋЏ8бЋЏ
Ask students to solve
the following problem:
5
П© 3бЋЏ8бЋЏ
Discuss students’ solution strategies. Make sure the following
strategy is presented:
7
2бЋЏ8бЋЏ
1. Add the whole-number parts.
5
П© 3бЋЏ8бЋЏ
2. Add the fraction parts.
12
5бЋЏ8бЋЏ
12
3. Rename 5бЋЏ8бЋЏ in simplest form.
12
бЋЏбЋЏ
8
8
4
4
4
П­ бЋЏ8бЋЏ П© бЋЏ8бЋЏ П­ 1 П© бЋЏ8бЋЏ П­ 1бЋЏ8бЋЏ
12
4
12
4
4
1
Since бЋЏ8бЋЏ П­ 1бЋЏ8бЋЏ, then 5бЋЏ8бЋЏ П­ 5 П© 1 П© бЋЏ8бЋЏ П­ 6бЋЏ8бЋЏ or 6бЋЏ2бЋЏ.
Model renaming the sum with a picture.
12
4
бЋЏбЋЏ П­ 1бЋЏбЋЏ
8
8
Pose a few more addition problems in which the addends are
mixed numbers with like denominators. Suggestions:
4
3
в—Џ
1бЋЏ4бЋЏ П© 2бЋЏ4бЋЏ 4бЋЏ4бЋЏ, or 4бЋЏ2бЋЏ
1
в—Џ
8бЋЏ10бЋЏ П© 5бЋЏ10бЋЏ 14бЋЏ5бЋЏ
в—Џ
3бЋЏ7бЋЏ П© 4бЋЏ7бЋЏ 8
в—Џ
6бЋЏ23бЋЏ П© 2бЋЏ3бЋЏ 9
3
7
3
2
9
1
3
Ongoing Assessment: Informing Instruction
Watch for students who have difficulty renaming mixed-number sums such as
12
5бЋЏ8бЋЏ. Discuss the meanings of numerator and denominator, and have students
rename the fractional parts in the mixed numbers. Suggestions:
4бЋЏ75бЋЏ
8бЋЏ43бЋЏ
2бЋЏ74бЋЏ
626
Unit 8 Fractions and Ratios
7
бЋЏбЋЏ
5
4
бЋЏбЋЏ
3
7
бЋЏбЋЏ
4
П­
П­
П­
5
бЋЏбЋЏ
5
3
бЋЏбЋЏ
3
4
бЋЏбЋЏ
4
П©
П©
П©
2
бЋЏбЋЏ
5
1
бЋЏбЋЏ
3
3
бЋЏбЋЏ
4
П­1П©
П­1П©
П­1П©
2
бЋЏбЋЏ
5
1
бЋЏбЋЏ
3
3
бЋЏбЋЏ
4
б­¤ Adding Mixed Numbers with
WHOLE-CLASS
ACTIVITY
Fractions Having Unlike Denominators
Write the following problem on the board, and ask students to find
the sum:
3
3бЋЏ4бЋЏ
7
П© 2бЋЏ8бЋЏ
After a few minutes, ask students to share solution strategies.
Make sure the following method is discussed:
3
7
1. Find a common denominator for бЋЏ4бЋЏ and бЋЏ8бЋЏ 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.
3бЋЏ4бЋЏ
3
3бЋЏ8бЋЏ
6
7
П© 2бЋЏ8бЋЏ
7
П© 2бЋЏ8бЋЏ
13
5бЋЏ8бЋЏ
3. Add.
13
8
5
5
5
5бЋЏ8бЋЏ П­ 5 П© бЋЏ8бЋЏ П© бЋЏ8бЋЏ П­ 5 П© 1 П© бЋЏ8бЋЏ П­ 6бЋЏ8бЋЏ
4. Rename the sum.
Pose a few more problems that involve finding common
denominators to add mixed numbers. Suggestions:
1
3
7
2
5
3
4
1
1
5
3
13
7
1
1
в—Џ
2бЋЏ2бЋЏ П© 4бЋЏ8бЋЏ 6бЋЏ8бЋЏ
в—Џ
5бЋЏ3бЋЏ П© 1бЋЏ6бЋЏ 7бЋЏ6бЋЏ, or 7бЋЏ2бЋЏ
в—Џ
3бЋЏ5бЋЏ П© 2бЋЏ4бЋЏ 6бЋЏ20бЋЏ
в—Џ
6бЋЏ6бЋЏ П© 3бЋЏ5бЋЏ 10бЋЏ3бЋЏ0
в—Џ
1бЋЏ8бЋЏ П© 8бЋЏ6бЋЏ 10бЋЏ2бЋЏ4
1
Student Page
б­¤ Adding Mixed Numbers
Date
PARTNER
ACTIVITY
(Math Journal 2, pp. 251 and 252)
Time
LESSON
Adding Mixed Numbers
8 2
б­њ
continued
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.
Have students complete journal pages 251 and 252. Circulate
and assist.
3
5
2
3
Example: 2 бЋЏбЋЏ П© 4 бЋЏбЋЏ П­ ?
3
5
б­њ Write the problem in vertical form, and rename the fractions.
3
5
9
15
2 бЋЏбЋЏ
2 бЋЏбЋЏ
П©
Ongoing Assessment:
Recognizing Student Achievement
ଙ
Journal
Page 252
Problem 4
[Operations and Computation Goal 4]
2
4 бЋЏбЋЏ
3
∑
П© 4 бЋЏ10бЋЏ
15
6 бЋЏ19бЋЏ
б­њ Add.
б­њ Rename the sum.
19
6 бЋЏбЋЏ
15
П­6П©
15
бЋЏбЋЏ
15
15
4
15
4
15
4
15
П© бЋЏбЋЏ П­ 6 П© 1 П© бЋЏбЋЏ П­ 7бЋЏбЋЏ
Add. Write each sum as a mixed number in simplest form. Show your work.
7бЋЏ190бЋЏ
5бЋЏ17бЋЏ2
1
1
1
2
1. 2бЋЏбЋЏ П© 3 бЋЏбЋЏ П­
2. 5 бЋЏбЋЏ П© 2бЋЏбЋЏ П­
3
Use journal page 252, Problem 4 to assess students’ facility with adding mixed
numbers. Have students complete an Exit Slip (Math Masters, 414) for the
following: Explain how you 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.
2
3
᭜ Find a common denominator. The QCD of ᎏᎏ and ᎏᎏ is 5 ‫ ء‬3 ϭ 15.
4
1
4
3. 6 бЋЏбЋЏ П© 2бЋЏбЋЏ П­
3
9
1
5
5. 7бЋЏбЋЏ П© 2 бЋЏбЋЏ П­
4
6
2
8бЋЏ79бЋЏ
10бЋЏ112бЋЏ
5
ଙ
1
3
4. 1бЋЏбЋЏ П© 4бЋЏбЋЏ П­
2
4
5
3
6. 3 бЋЏбЋЏ П© 3 бЋЏбЋЏ П­
6
4
6бЋЏ14бЋЏ
7бЋЏ172бЋЏ
252
Math Journal 2, p. 252
Lesson 8 2
б­њ
627
Student Page
Date
Time
LESSON
2 Ongoing Learning & Practice
Math Boxes
8 2
б­њ
1. Add.
2. Use the patterns to fill in the missing
1
2
a. бЋЏбЋЏ П© бЋЏбЋЏ П­
4
4
3
1
b. бЋЏбЋЏ П© бЋЏбЋЏ П­
8
4
1
c. бЋЏбЋЏ
2
П©
1
бЋЏбЋЏ
8
numbers.
3
бЋЏбЋЏ
4
5
бЋЏбЋЏ
8
П­
2
1
d. бЋЏбЋЏ П© бЋЏбЋЏ П­
3
6
8
a. 1, 2, 4,
5
бЋЏбЋЏ
8
5
бЋЏбЋЏ
6
4
2
2
e. бЋЏбЋЏ П© бЋЏбЋЏ П­ бЋЏ6бЋЏ
6
6
, or
32
,
41
c. 4, 34, 64,
94
,
124
62
d. 20, 34, 48,
2
бЋЏбЋЏ
3
68
e. 100, 152, 204,
3
3. The school band practiced 2бЋЏбЋЏ hours on
4
2
Saturday and 3 бЋЏбЋЏ hours on Sunday. Was
3
16
,
b. 5, 14, 23,
,
б­¤ Math Boxes 8 2
(Math Journal 2, p. 253)
76
256 , 308
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.
parentheses.
a. 18 ПЄ 11 П© 3 П­ 10
More than 6 hours
b. 18 ПЄ 11 П© 3 П­ 4
Sample answer:
Explain.
2бЋЏ34бЋЏ П© 3бЋЏ23бЋЏ П­ 5П© бЋЏ19бЋЏ2 П© бЋЏ18бЋЏ2 П­
5П© бЋЏ11бЋЏ72 П­ 5П© бЋЏ11бЋЏ22 П© бЋЏ152бЋЏ П­
5П© 1П© бЋЏ15бЋЏ2 П­ 6П© бЋЏ152бЋЏ
c. 14 ПЄ 7 П© 5 П© 1 П­ 13
(
)
(
)
)
(
(
(
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.
)
d. 14 ПЄ 7 П© 5 П© 1 П­ 1
)
e. 14 ПЄ 7 П© 5 П© 1 П­ 3
71
5. Solve.
230
4. Make each sentence true by inserting
the band’s total practice time more or less
than 6 hours?
222
Solution
6. Circle the congruent line segments.
x
5
a. бЋЏбЋЏ П­ бЋЏбЋЏ
18
9
x П­ 10
a.
40
8
b. бЋЏбЋЏ П­ бЋЏбЋЏ
y
25
y П­ 125
b.
6
w
c. бЋЏбЋЏ П­ бЋЏбЋЏ
14
49
w П­ 21
c.
28
7
d. бЋЏбЋЏ П­ бЋЏбЋЏ
z
9
z П­ 36
d.
44
4
e. бЋЏбЋЏ П­ бЋЏбЋЏ
77
v
vП­7
INDEPENDENT
ACTIVITY
б­њ
155
108 109
253
Math Journal 2, p. 253
NOTE Alternately, students may use a table or chart to find an equivalent
fraction with the given denominator or numerator.
б­¤ Study Link 8 2
INDEPENDENT
ACTIVITY
б­њ
(Math Masters, p. 223)
Home Connection Students practice adding mixed
numbers and renaming improper fractions as mixed
numbers in simplest form.
3 Differentiation Options
Study Link Master
Name
Date
STUDY LINK
Time
82
Rename each mixed number in simplest form.
1
4бЋЏ5бЋЏ
6
5
1.
3 бЋЏбЋЏ П­
3.
9 бЋЏбЋЏ П­
5.
4 бЋЏбЋЏ П­
16
2. бЋЏбЋЏ
8
2
2бЋЏ5бЋЏ
7
5
4.
1 бЋЏбЋЏ П­
6.
5 бЋЏбЋЏ П­
6бЋЏ3бЋЏ
10
6
Add. Write each sum as a whole number or mixed number in simplest form.
1
4
3
4
1
3
2
3
7.
3 бЋЏбЋЏ П© 2 бЋЏ бЋЏ П­
9.
9 бЋЏбЋЏ П© 4 бЋЏ бЋЏ П­
6
1
5
4
5
5
7
6
7
2
9
5
9
8.
4 бЋЏбЋЏ П© 3 бЋЏбЋЏ П­
10.
3 бЋЏбЋЏ П© 8 бЋЏбЋЏ П­
3
8
П© 3 бЋЏбЋЏ П­
12.
4 бЋЏбЋЏ П© 5 бЋЏбЋЏ П­
8
4
14
1
15
11. бЋЏбЋЏ
8
15–30 Min
2
1
5бЋЏ2бЋЏ
6
4
б­¤ Adding Mixed Numbers
(Math Journal 2, p. 252)
2
10бЋЏ3бЋЏ
5
3
61 63
70
2
П­
SMALL-GROUP
ACTIVITY
READINESS
Adding Mixed Numbers
б­њ
12бЋЏ7бЋЏ
To explore mixed-number addition, have students use an oppositechange algorithm. Have students change one of the addends to a
whole number. Pose the following problem:
2
5
1бЋЏ3бЋЏ П© 7бЋЏ6бЋЏ
7
5бЋЏ4бЋЏ
9бЋЏ9бЋЏ
2
1
2
1
1. Change 1 and бЋЏ3бЋЏ to a whole number by adding бЋЏ3бЋЏ: 1бЋЏ3бЋЏ П© бЋЏ3бЋЏ П­ 2
Add.
13.
5
8
3
4
2 бЋЏбЋЏ
14.
1
2
2
3
7 бЋЏбЋЏ
6
9
7
12
4 бЋЏбЋЏ
15.
П© 6 бЋЏбЋЏ
П© 3 бЋЏбЋЏ
П© 3 бЋЏбЋЏ
3
11бЋЏ6бЋЏ
1
8бЋЏ4бЋЏ
9бЋЏ8бЋЏ
16.
3
4
4
5
5 бЋЏбЋЏ
П© 2 бЋЏбЋЏ
1
11
8бЋЏ2бЋЏ0
Practice
17.
3,540 П¬ 6 П­
590
18.
1,770 П¬ 3 П­
590
19.
7,080 / 12 П­
590
20.
(590 ‫ ء‬5) Ϭ 2 ϭ
1,475
Math Masters, p. 223
628
Unit 8 Fractions and Ratios
1
5 1
2
5
2
3
2. Subtract ᎏ3ᎏ from 7ᎏ6ᎏ: ᎏ3ᎏ ϭ ᎏ6ᎏ; 7ᎏ6ᎏ – ᎏ6ᎏ ϭ 7ᎏ6ᎏ.
3
3
1
3. Add the new addends: 2 П© 7бЋЏ6бЋЏ П­ 9бЋЏ6бЋЏ, or 9бЋЏ2бЋЏ.
This strategy is most efficient when the sum of the fraction parts
is greater than 1. Have students use this method to solve the
following problems. Discuss how to recognize that the fraction
parts are greater than 1:
Game Master
в—Џ
8
1
3
Name
3бЋЏ2бЋЏ П© 7бЋЏ10бЋЏ 11бЋЏ1бЋЏ0
3
в—Џ 2бЋЏбЋЏ
4
8
П©
9
6бЋЏ12бЋЏ
1
6
9бЋЏ1бЋЏ2 ,
5бЋЏ9бЋЏ П© 7бЋЏ3бЋЏ 13бЋЏ9бЋЏ
в—Џ
4бЋЏ10бЋЏ П© 3бЋЏ6бЋЏ 8бЋЏ3бЋЏ0
5
Time
1 2
4 3
Fraction Capture Gameboard
1
9бЋЏ2бЋЏ
1
2
2
в—Џ
8
or
Date
1
2
1
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Before students begin journal page 252, have them identify
problems for which this algorithm might apply. Problems 4–6
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15–30 Min
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(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.
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PARTNER
ACTIVITY
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б­¤ Playing Fraction Capture
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EXTRA PRACTICE
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Math Masters, p. 460
Lesson 8 2
б­њ
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