Adding Mixed Numbers
Objectives To develop addition concepts related
to
t mixed numbers.
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Key Concepts and Skills
Math Boxes 8 2
• Find equivalent fractions in simplest form. Math Journal 2, p. 253
Students practice and maintain skills
through Math Box problems.
[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]
Study Link 8 2
Math Masters, p. 223
Students practice and maintain skills
through Study Link activities.
• Use benchmarks to estimate sums. [Operations and Computation Goal 6]
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. 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]
Materials
Math Journal 2, pp. 251 and 252
Study Link 81
Math Masters, p. 414
slate Class Data Pad (optional)
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 142, 143
624
Unit 8
Fractions and Ratios
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Adding Mixed Numbers
Math Journal 2, p. 252
Students explore an alternate method
for adding mixed numbers.
EXTRA PRACTICE
Playing Fraction Capture
Math 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
Problems
Math Masters, p. 253A
Students practice adding mixed numbers
with like and unlike denominators.
Mathematical Practices
SMP1, SMP2, SMP3, SMP5, SMP6, SMP8
Content Standards
Getting Started
5.NF.1, 5.NF.2
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.
Use benchmarks to estimate the sums and to check the
reasonableness of your solutions.
3
_
1
3
1 5
2_ _
2 2
3 _
1
_
1
2 2
13 _
5
_
1
8
8
33
1 _
_
48 8
17 _
2
_
35
5
37 _
2
_
7
5
5
Study Link 8 1 Follow-Up
62
2
_
12 _
5
5
45
1 _
11 _
4 4
Have partners compare answers and resolve
differences. Ask volunteers to share their
explanations for Problems 7, 14, and 21.
1 Teaching the Lesson
▶ Math Message Follow-Up
(Math Journal 2, p. 251)
WHOLE-CLASS
ACTIVITY
ELL
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 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.
Ask students to share their estimating strategies for Problem 7
using benchmarks. Sample answer: _16 is less than _12 , and _23 is
greater than _12 . 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.
Student Page
Date
Time
LESSON
Adding Fractions
82
Math Message
Add. Write the sums in simplest form.
1.
1
3
_
+_
=
4.
3
5
_
+_
=
7.
1
2
_
+_
=
_4
5
1
1_
7
_5
5
5
7
7
6
6
3
_1
2.
3
1
_
+_
=
5.
7
7
_
+_
=
8.
2
2
_
+_
=
8
2
8
10
3
10
5
2
1_
5
1
1_
15
3.
2
2
2
_
+_
+_
=
6.
5
7
_
+_
=
9.
5
5
_
+_
=
3
9
6
3
9
8
3
1
1_
3
2
11
1_
24
Adding Mixed Numbers
Add. Write each sum as a whole number or mixed number.
3
1_
5
10.
1_
2
1
11.
12.
1
4
2_
1
+ 1_
1
+_
3
+ 3_
4
2_
5
2
6
2
5
4
Fill in the missing numbers.
13.
12
5
5_ = 6 _
16.
=5
4_
3
7
5
7
2
_
3
8
3
_
14.
=
7_
5
17.
5
11
= 13 _
12 _
6
6
8
5
15.
1
5
=3 _
2_
4
4
18.
3
13
= 10 _
9_
10
10
Add. Write each sum as a mixed number in simplest form.
19.
3_
3
2
2
+ 5_
3
1
9_
3
20.
4_
7
6
4
+ 2_
7
7_
7
3
21.
3_
9
4
8
+ 6_
9
1
10 _
3
Math Journal 2, p. 251
248-287_EMCS_S_MJ2_U08_576434.indd 251
2/16/11 1:01 PM
Lesson 8 2
625
▶ Adding Mixed Numbers with
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 below on the board or a transparency:
1
3_
8
3
+ 5_
8
4
1
_
8 or 8_
8
2
Add the whole-number parts.
Then add the fraction parts.
7
2_
8
5
+ 3_
Ask students to solve
the following problem:
8
Discuss students’ solution strategies. Make sure the following
strategy is presented:
7
1. Add the whole-number parts.
2_
8
Ongoing Assessment:
Informing Instruction
Watch for students who have difficulty
12
renaming mixed-number sums such as 5_
8.
Discuss the meanings of numerator and
denominator, and have students rename
the fractional parts in the mixed numbers.
Suggestions:
7
4_5
4
8_
3
7
_
24
8
12 in simplest form.
3. Rename 5_
8
8 +_
12 = _
4 =1+_
4 = 1_
4
_
8
=
=
5
_3
3
_4
4
+
+
5
_1
3
_3
4
=1+
=1+
8
8
8
8
12 = 1_
4 , then 5_
12 = 5 + 1 + _
4 = 6_
4 , or 6_
1.
Since _
8
8
8
8
8
2
12 with a picture.
Model renaming _
8
_7 = _5 + _2 = 1 + _2
5
_4
3
_7
4
5
+ 3_
8
12
5_
2. Add the fraction parts.
5
_1
3
_3
4
12
4
_
_
8 = 18
Pose a few more addition problems in which the addends are
mixed numbers with like denominators. Suggestions:
●
●
626
Unit 8
Fractions and Ratios
3 8
4 + 4_
3_
7
7
2
_
_
6 + 21 9
3
3
●
●
3 + 2_
3 4_
2 , or 4_
1
1_
4
4 4
2
7
9
3
_
_
_
8
+ 5 14
10
10
5
●
5 yards of red ribbon and 4_
7 yards of
Madeleine purchased 3_
8
8
4,
purple ribbon. How much ribbon did Madeleine purchase? 8_
8
1 yards
or 8_
2
●
3 pizzas and Mr. Samuel’s class ate 4_
2
Mr. Marcus’s class ate 6_
4
4
1
_
pizzas. How many pizzas did the two classes eat? 11 4 pizzas
▶ 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
3_
4
7
+ 2_
8
After a few minutes, ask students to share solution strategies.
Make sure the following method is discussed:
3 and _
7 8, 16, 24, 32, ...
1. Find a common denominator for _
4
8
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
6
3_
3_
4
8
7
+ 2_
8
7
+ 2_
8
13
5_
8
3. Add.
4. Rename the sum.
8 +_
5 =5+1+_
5 = 6_
5
13 = 5 + _
5_
8
8
8
8
8
Pose a few more problems that involve finding common
denominators to add mixed numbers. Suggestions:
●
3 6_
7
1 + 4_
2_
2
8 8
●
5 + 3_
3 10_
13
6_
6
5
30
●
5 7_
3 , or 7_
2 + 1_
1
5_
3
6 6
2
●
7 + 8_
1 10_
1
1_
8
6
24
●
4 + 2_
1 6_
1
3_
5
4 20
●
7 yards of fabric for a dress and 5_
1 yards for a
Juanita needs 1_
8
6
1
_
jacket. How many total yards does she need? 7 24 yards
●
The costumes for the lead roles in the school musical require
5 yards of one type of fabric and 2_
1 yards of another type of
4_
8
3
23 yards
fabric. How much fabric needs to be purchased? 6_
24
Student Page
Date
Time
LESSON
8 2
Adding Mixed Numbers
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.
▶ Adding Mixed Numbers
PARTNER
ACTIVITY
3
2
_
Example: 2 _
5 + 43 = ?
3
_2
∗
Find a common denominator. The QCD of _
5 and 3 is 5 3 = 15.
Write the problem in vertical form, and rename the fractions.
(Math Journal 2, pp. 251 and 252)
3
2_
5
+ 4_23
Add.
Have students complete journal pages 251 and 252. Circulate
and assist.
2_
15
9
∑
10
+ 4_
15
19
6_
15
19
15
4
4
4
_
_
_
_
Rename the sum. 6 _
15 = 6 + 15 + 15 = 6 + 1 + 15 = 7 15
Add. Write each sum as a mixed number in simplest form. Show your work.
Ongoing Assessment:
Recognizing Student Achievement
Exit Slip
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.
7
5_
12
1
1
_
2_
3 + 34 =
3.
1
4
_
6_
3 + 29 =
5.
3
1
_
Sam purchased 4_
8 yards of fleece fabric for a jacket and 6 3 yards of fleece
fabric to make a blanket. How much fabric did he purchase?
8_79
2.
4.
1
2
_
5_
2 + 25 =
9
7_
10
1.
3
1
_
1_
2 + 44 =
6_14
17
10_
24 yards
[Number and Numeration Goal 5; Operations and Computation Goal 4]
Math Journal 2, p. 252
248-287_EMCS_S_MJ2_G5_U08_576434.indd 252
4/1/11 8:59 AM
Lesson 8 2
627
Student Page
Date
Time
LESSON
8 2
Add.
1.
2.
1
a. 4
3
b. 8
1
c. 2
2
4
3
4
5
8
5
8
5
6
1
4
1
8
2
d. 3
2
e. 6
4
2
6,
6
1
6
or
2
3
68
3
The school band practiced 2 hours on
4
2
Saturday and 3 hours on Sunday. Was
3
the band’s total practice time more or less
than 6 hours?
3.
4.
Use the patterns to fill in the missing
numbers.
8
16
a.
1, 2, 4,
b.
5, 14, 23,
32
,
41
c.
4, 34, 64,
94
,
124
d.
20, 34, 48,
e.
100, 152, 204,
,
62
,
▶ Math Boxes 8 2
(
(Math Journal 2, p. 253)
76
256 , 308
Sample answer:
Explain.
234 323 5 192 182 5 1172 5 1122 152 5 1 152 6 152
5
a. 9
)
(
18 11 3 4
c.
222
Solution
x
18
6.
Circle the congruent line segments.
x 10
a.
40
y
y 125
b.
w
49
w 21
c.
7
9
z 36
4
v
v7
8
b. 25
6
c. 14
28
d. z
44
e. 77
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.
18 11 3 10
71
Solve.
230
)
(14 7) 5 1 13
d. 14 (7 5 1) 1
e. 14 (7 5) 1 3
b.
INDEPENDENT
ACTIVITY
Make each sentence true by inserting
parentheses.
a.
More than 6 hours
5.
2 Ongoing Learning & Practice
Math Boxes
䉬
d.
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.
155
108 109
NOTE Alternately, students may use a table or chart to find an equivalent
Math Journal 2, p. 253
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
Study Link Master
Name
Date
STUDY LINK
Adding Mixed Numbers
82
䉬
Rename each mixed number in simplest form.
1
5
4
6
5
3 1.
5
3
9 3.
4.
1 6.
5 6
4
61 63
70
2
1
52
4 5.
16
2. 8
2
103
1
4
3
4
1
3
2
3
3 2 7
5
2
9.
9 4 15
11. 8
3
8
3 6
63
10
6
1
5
4
5
5
7
6
7
8.
4 3 10.
3 8 8
4
14
1
54
12.
2
9
5
9
4 5 127
5
8
3
4
2 14.
1
2
2
3
7 6
9
7
12
4 15.
6 3 3 3
116
1
84
98
Practice
16.
3
4
4
5
5 2 1
11
820
17.
3,540 6 590
18.
1,770 3 19.
7,080 / 12 590
20.
(590 ⴱ 5) 2 590
1,475
Math Masters, p. 223
628
Unit 8
15–30 Min
(Math Journal 2, p. 252)
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:
5
2 + 7_
1_
3
7
99
Add.
13.
▶ Adding Mixed Numbers
2
25
Add. Write each sum as a whole number or mixed number in simplest form.
7.
SMALL-GROUP
ACTIVITY
READINESS
Time
Fractions and Ratios
6
2 to a whole number by adding _
1 : 1_
2 +_
1 = 2.
1. Change 1_
3
3
3
3
5
5
3
1
1
2
2
_
_
_
_
_
_
_
2. Subtract from 7 : = ; 7 - = 7 .
3
6 3
6
3. Add the new addends: 2 +
6
6
3
3,
7_
= 9_
6
6
6
1.
or 9_
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:
Game Master
●
●
8 11_
3
1 + 7_
3_
2
10
10
3 + 6_
9 9_
6 , or 9_
1
2_
4
12
12
●
8 + 7_
1 13_
2
5_
9
3
9
●
8 + 3_
5 8_
19
4_
10
6 30
Name
Date
1
2
1
2
1
2
1
2
1
3
1
3
1
3
1
3
1
4
1
4
1
4
15–30 Min
1
5
1
5
1
5
1
3
1
3
1
3
1
3
1
4
1
5
1
4
1
4
1
4
1
4
1
5
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
4
1
4
1
5
1
5
1
5
1
6
1
5
1
5
1
5
1
6
1
4
1
5
1
5
1
5
1
6
1
4
1
4
1
4
1
6
1
6
1
3
1
4
1
4
1
5
1
5
1
5
1
5
1
5
(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.
1
2
1
3
1
3
PARTNER
ACTIVITY
1
2
1
2
1
2
1
3
Before students begin journal page 252, have them identify
problems for which this algorithm might apply. Problem 4
▶ Playing Fraction Capture
1 2
4 3
Fraction Capture Gameboard
2
EXTRA PRACTICE
Time
1
6
1
5
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
Math Masters, p. 460
429-431_460_EMCS_B_MM_G5_U06Proj_576973.indd 460
EXTRA PRACTICE
▶ Solving Mixed-Number
3/8/11 11:21 AM
PARTNER
ACTIVITY
15–30 Min
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.
Teaching Master
Name
Date
LESSON
Time
Solving Mixed-Number Addition Problems
82
Add. Write each sum as a mixed number in simplest form. Show your work.
7
3
1
4
2
_
_
_
_
10
1. 5 + 2 =
2. 3 + 5
=
5
8 __
8
5
5
6 _6
10
5.
3
1
+ 2_ =
4_
4
12
7 __
12
5
5
3.
4.
3
2
+ 2_ =
4_
3
4
Josiah was painting his garage. Before lunch, he painted 1 _
walls.
3
2
After lunch, he painted another 1 _
walls. How many walls did he
3
paint during the day?
1
3
2
3 _ walls
6.
Julie’s mom made muffins for Julie and her friends to share.
3
1
Julie ate 1 _
muffins. Her friends ate 3 _
muffins. How many
4
2
muffins did Julie and her friends eat altogether?
1
4
5 _ muffins
Without adding the mixed numbers, insert <, >, or =.
Explain how you got your answer.
7.
8.
3
2
1_ + 6_
>
8
8
3
3
3
2
Sample answer: The sum of 1 _9 and 6 _3 is 8. But _8 is
3
greater than _9 , so the sum is greater than 8.
5
<
1
7
2_ + 2_
5
8
1
7
Sample answer: You only need to add _8 to _8 to get another
1
1
1
7
_
whole. But 5 is greater than _8 , so 2 _5 + 2 _8 is greater than 5.
Math Masters, p. 253A
253A-253B_EMCS_B_MM_G5_U08_576973 .indd 253A
3/16/11 1:26 PM
Lesson 8 2
629
Name
Date
LESSON
Time
Solving Mixed-Number Addition Problems
82
Add. Write each sum as a mixed number in simplest form. Show your work.
1.
+ 2_ =
5_
5
5
2.
+ 5_ =
3_
5
10
3.
3
1
+ 2_ =
4_
4
12
4.
3
2
+ 2_ =
4_
3
4
5.
6.
1
4
2
3
Josiah was painting his garage. Before lunch, he painted 1 _
walls.
3
2
_
After lunch, he painted another 1 3 walls. How many walls did he
paint during the day?
2
Julie’s mom made muffins for Julie and her friends to share.
3
1
_
Julie ate 1 _
muffins.
Her
friends
ate
3
muffins. How many
4
2
muffins did Julie and her friends eat altogether?
Without adding the mixed numbers, insert <, >, or =.
Explain how you got your answer.
3
2
+ 6_
1_
8
3
8.
5
253A
8
1
7
2_
+ 2_
5
8
Copyright © Wright Group/McGraw-Hill
7.