Download Adding and Subtracting Mixed Numbers

Chapter 7
Lesson
Lesson
4
-1 -1
11
Adding and Subtracting
Mixed Numbers
NCTM Standards 1, 2, 6, 7, 8, 9, 10
Common Core State Standards 4.NF 3
STUDENT OBJECTIVES
Lesson Planner
• n
• n
o write fractions that have a numerator greater than the denominator
T
as mixed numbers
To add and subtract mixed numbers with like denominators
(CCRG p. CC 37)
Open Ended Problem Solving/Headline Story
Skills Practice and Review—
Fractions Less Than 1 and Fractions Greater
Than 1
(CCRG pp. CC 38–CC 40)
Fractions or Mixed Numbers? (CCRG p. CC 38)
Adding and Subtracting Mixed
Numbers (CCRG p. CC 39)
•CCRG: Activity Master, Adding and Subtracting
Mixed Numbers
•CCRG: Explore Master, Fractions or Mixed
Numbers
Adding and Subtracting Mixed
Numbers (CCRG p. CC 40)
•transparency of Explore Master (optional)
•
LAB Masters, CCRG pp. CC 41–CC 42)
(CCRG p. CC 41)
Leveled Problem Solving (CCRG p. CC 41)
Practice Master, CCRG p. CC 44
Intervention Activity (CCRG p. CC 41)
Extension Master, CCRG p. CC 45
Extension Activity (CCRG p. CC 41)
Lesson Notes
Lesson 7.11-1 has been added. Use this lesson after Lesson 7.11.
About the Lesson
About the Mathematics
In this lesson students become more familiar with
mixed numbers and their equivalent fractions.
Students add and subtract mixed numbers with the
same denominator by using properties of operations.
Finally, they extend what they have learned to the
challenge of changing mixed numbers to improper
fractions and adding.
There are two different ways you can add mixed
numbers: by replacing each mixed number with
an equivalent fraction or by using properties of
operations. This lesson encourages students to use
what they know about the properties of addition and
subtraction to regroup the parts of mixed numbers to
find sums and differences. In the extension students
are challenged to find fractions equivalent to mixed
numbers in order to add.
CC 36 Common Core Resource Guide
Chapter 7 • Lesson 11-1
Developing
Mathematical
Language
Vocabulary: mixed number,
numerator, denominator
A number that is made up of a
whole number and a fraction is
a mixed number. The numerator
of a fraction is the number above
the fraction bar. The numerator
shows how many equal parts of
the whole you are talking about.
The denominator of a fraction is
the number below the fraction
bar. The denominator shows into
how many equal parts the whole
is divided.
Open-Ended Problem Solving
Read the Headline Story to the class. Encourage students to solve the
problem by drawing a picture and using information from the story.
Create a story to match this
number sentence:
(8 1 8) 2 (8 1 2) 5 ?
Possible responses:
Josie and Pedro each have 8 model trains. Josie bought 8 more at
the fair. Pedro bought 2 more at the fair. How many more trains does
Josie have than Pedro?
Beginning Write a mixed
number on the board and point to
the parts of the number while you
say whole number, numerator and
denominator.
Skills Practice and Review
Intermediate Write several
Fractions Less Than 1 and Fractions Greater Than 1
mixed numbers on the board. Ask
students to identify the whole
number, the numerator of the
fraction, and the denominator of
the fraction.
List several fractions on the board and draw two large circles. Label
one circle “Less Than 1” and label the other “Greater Than 1.” Have
students come to the board one at a time and write one of the
fractions in the appropriate circle. Use fractions such as
Advanced Tell students that you
3 6 7 8 1 10 17 2 10
, , , , , , , , ,
5 7 6 4 12 17 10 8 5
and 91.
are thinking of a mixed number.
Describe it and have them write it
down. For example, “I am thinking
of a mixed number which is made
up of the whole number 3 and a
fraction that has a numerator of 5
and a denominator of 7.”
Common Core Resource Guide TMG4CCRG_CH07_L11-1_TG_p36-p41.indd 37
CC 37
12/28/10 12:45:39 PM
20
MIN
Materials
• For the teacher:
transparency of Explore
(optional)
NCTM Standards 1, 2, 6, 7, 8, 9, 10
CCSS 4.NF 3
Concept Alert
Problem 7 may be tricky for
some students. Students
must express 4 as a simpler
8
fraction. They should see that
half of the second rectangle
is shaded so this quantity can
be represented as 11.
2
Above Level Ask students to
come up with a method for
changing any mixed number
into an equivalent fraction.
Possible explanation:
2 is equivalent to
6
2
8
3
2 is equal to so 2 is equal
3
6
2 83
to 1 or .
3
3
Purpose To give students the opportunity to see that a quantity made up of several
fractional parts can be expressed as both a fraction and a mixed number
Introduce Have students work independently or with a partner on Explore Master:
Fractions or Mixed Numbers? Before they begin tell them that they are going to be filling
in the squares to complete the mixed number and the fraction next to each picture. Both
are good ways to describe how much of something is represented. Point out that a mixed
number like 12 is read “one and two fifths.” This can also be translated as 1 1 2. Pointing
5
5
this out now will help students understand a method for
transforming mixed numbers into equivalent fractions.
Name
Chapter 7
Lesson 11-1
Task Direct students to fill in the missing pieces for

7
5
 
3
7
or 1 1
6
8
3
9
4
 4
3

5
or 1 1
2
 record their answers on a transparency or on the board.
Point out that the two forms are the same (or equivalent)
ways of expressing the same amount.
2
or 1
3
2
6
 Talk Math
Date
EXPLORE
Fractions or Mixed Numbers?
Fill in the blanks to describe each picture with a fraction and a
mixed number.
each fraction and mixed number on Explore Master:
Fractions or Mixed Numbers? Each figure is divided into
a different number of equal parts. For each set of figures
decide what fraction or mixed number is represented.
Share Ask students to share their answers. You can
Differentiated
Instruction
2
3
Fractions or Mixed Numbers?
© School Specialty
pairs
12
8
2
or 2
3
or
or
or 1
1
2
1
4
8
4
1
3
or 1
1
2
Common Core Resource Guide
CC 47
Explore Master: Fractions or
Mixed Numbers?
Why is 4 1 called a mixed number? Possible answer: It
2
mixes whole numbers and fractions to express a quantity.
What whole number is 2 5 equivalent to? Possible answer: 55 is the same
5
as 1. So 2 55 is really like saying “2 and 1” or 3.
Compare the numerator and denominator of the first fraction in each
problem on Explore Master: Fractions or Mixed Numbers? What do
you notice? Possible answer: The numerator is always greater than the
denominator.
CC 38 Common Core Resource Guide
TMG4CCRG_CH07_L11-1_TG_p36-p41.indd 38
Chapter 7 • Lesson 11-1
12/28/10 12:45:41 PM
Adding and Subtracting Mixed Numbers
whole class
20
MIN
Materials
Purpose To add and subtract mixed numbers with like denominators
• For each student: AM:
Adding and Subtracting
Mixed Numbers
Introduce To introduce students to the idea of combining mixed numbers, present
a problem in context.
NCTM Standards 1, 2, 6, 7, 8, 9, 10
CCSS 4.NF 3
Task Ask students to find the sum of two mixed numbers and explain the
process. Pose this question to your students (or one similar to it): Your family ordered
pizzas that were cut into 8 slices each. You and your sister ate 1 whole pizza and 38 of
another pizza. Your parents ate 1 whole pizza and 28 of another pizza. How much pizza
did your family eat?
• Do students understand
that a mixed number is
made up of a whole number
part and a fraction part?
• Do students understand
that adding fractions with
like denominators is similar
to adding like objects, such
as 4 movie tickets + 8
movie tickets?
• Do students understand
that if a fraction’s
numerator is greater than
its denominator its value is
greater than 1? Ask students to think of an addition sentence that models this question. Have someone
write it on the board or you can write 138 1 128. Ask, “How could we find the sum of
these numbers?” Guide students through the process of regrouping and adding the
whole number parts of the mixed numbers first and then adding the fractional parts.
1 1 1 1 38 1 28
Tell them that since the denominators of the fractional parts of each mixed number are
the same you can add them just as if you were adding 3 slices of pizza 1 2 slices of
pizza.
Practice Write some additional mixed number addition and subtraction sentences
on the board or use Activity Master: Adding and Subtracting Mixed Numbers to give
students more examples to work with. Ask students to find each answer.
Share Once students have completed the problems ask for volunteers to provide
answers and explain how they found the sum or difference. Problem 6 from Activity
Master: Adding and Subtracting Mixed Numbers results in a mixed number whose
fractional part is 55. Students should recognize that this fraction is equivalent to 1 and
so the answer will be a whole number.
Differentiated
Instruction
On Level Students should
use the same process for
subtracting mixed numbers as
they have been using for adding
mixed numbers: subtract the
whole number parts, then
subtract the fraction parts,
then combine the two pieces.
Talk Math
How would you complete this number sentence: 315 1
5 345?
3
5
that the whole number part of the answer is the same, so all you need
to add is a fraction. You know that the fractional part of the answer
1
4
Talia had to find the answer to this number sentence: 315
1 215
1
2
1
4
2
.
415. She wrote this number sentence to help her: 9 1 15 1 15 1 15
Explain what Talia did and then find the sum. Possible answer: Talia
regrouped the sentence and added the whole number parts first and
7
will then add the fraction parts. 916
Name
Date
Activity
ActivityMaster
MasterX
Adding and Subtracting Mixed Numbers
1
4
2
11
7
7
27
3
4
2
21
7
7
27
1
1
14
5
5
55
7
3
21
11
11
4
211
1
3
3
4
12
9
9
6
2
2
7
29
© School Specialty
must be 45 so you need 3 more fifths to make 45.
Explain how to find the answer. Possible explanation: You know
1
4
1
11
5
5
5
25 or 3
CC 46 Common Core Resource Guide
Activity Master: Adding and
Subtracting Mixed Numbers
Chapter 7 • Lesson 11-1
TMG4CCRG_CH07_L11-1_TG_p36-p41.indd 39
Common Core Resource Guide CC 39
12/28/10 12:45:43 PM
Adding and Subtracting Mixed Numbers individuals
LAB Masters, CCRG pp. CC 42–CC 43
Purpose To add and subtract mixed numbers with like denominators using
NCTM Standards 1, 2, 6, 7, 8, 9, 10
CCSS 4.NF 3
properties of operations
Lesson Activity Book Master, CCRG p. CC 42
Chapter 7
Name
Lesson
20
MIN
Lesson Activity Book Master, CCRG p. CC 43
Date/Time
11-1 Adding and Subtracting
3
3
1
2 12 52121
5
5
5
2
5 23 55231
8
8
1
1
1
1
2 11 13 5 7
2
2
2
2
1
3
1
2
3 22 5 1
8
8
8
3
5
1
2 11 5 4
7
7
7
Mixed Numbers
5
1
1
5
5 4
4
5
5 2
3
8
NCTM Standards 1, 2, 6, 7, 8, 9, 10
Common Core State Standards 4.NF 3
Fill in the missing pieces of each number sentence.

1
1
4
1

1
 2
4
2
4
or 2
1
2

7
1
16
2
2

3
16
1
2
1
1 12
2
3
2
1
2
1
1 12
 1
2
inches
1
4
inches
 1
3
4
inches
8
1
4
2
7
1
13
5 4
15 15
15
15
or 1
1
4
1
3
 3 inches
© School Specialty
1

1
3
2
16
© School Specialty
inches
1

8
2
9

2
5
1
is the same as 3 . Is she
Challenge Patricia thinks that 13
4
4
correct? Use a diagram to explain your answer.
Patricia is correct. Possible explanation:
NOTE: Your child is learning to solve story problems involving comparisons. Play a game where you and
your child guess numbers from clues, such as, “My number is 18 more than 53.”
CC 42
CommonCore Resource Guide
TMG4CCRG_CH07_L11-1_LAB_p42-p43.indd 42
CC 43
Common Core Resource Guide
12/23/10 11:44:18 AM
Teaching Notes for LAB Master, CCRG
page CC 42
Teaching Notes for LAB Master, CCRG
page CC 43
Have students complete the page individually or with partners.
On this page students are shown diagrams of mixed number
addition and subtraction sentences. Students complete the
sentences by filling in the missing pieces and finding the sum
or difference. The diagram in Problem 1 shows a sum of 212.
But, an answer of 224 is also acceptable.
Students can complete this page individually or with partners.
The first two problems show students how to regroup the
mixed numbers to aid in finding the answers. Encourage
students to use this process for the remaining problems on
the page.
Challenge Problem Problem 13 requires students to use
a diagram to show that the fraction 13
is the same as the mixed
4
number 314.
Reflect and Summarize the Lesson
Add the mixed numbers. Explain how you found the sum.
5 45; Possible explanation: I added the whole number parts and
I added the fraction parts.
CC 40 Common Core Resource Guide
TMG4CCRG_CH07_L11-1_TG_p36-p41.indd 40
3
1
25 + 35
Chapter 7 • Lesson 11-1
12/28/10 12:45:46 PM
Leveled Problem Solving
Deana bought 434 yards of fabric. Selena bought 214 yards of fabric.
Basic Level
How many total yards of fabric
did Deana and Selena buy?
Explain how you know. 7 yards
Possible explanation:
434
644
1
214
3
4
1
4
54121 1 5
On Level
How much more fabric did Deana
buy than Selena? 212 yards.
Possible explanation:
Above Level
Monica bought twice as much
fabric as Selena. How much fabric
did the three girls buy in all? 1112 yards. Possible explanation:
Monica bought 214 1 214 or 412 yards
434 2 214 5 4 2 2 1 34 2 14 5 224
644
224 5 212
5 6 1 15 7
434 1 214 1 412 5 4 1 2 14 1 34 1
1
4
1 12 5 1064
2
4
5 1112
1064 5 1044 1 24 5 10 1 1 1
Practice Master, CCRG p. CC 44
Name
Extension Master, CCRG p. CC 45
Practice
Lesson
Lesson11-1
44
Date
Name Adding and Subtracting Mixed Numbers
Extension
Lesson 11-1
Date Adding Mixed Numbers
Solvebywritingequivalentfractionsandthenadding.

1
6
1
2

4
3

6
5
6
3
5
1
2
1
1 12
2
2 12
3

inches
1
1

1
2

5
1
1 12
2 12
2
1
3
4

1
4
5
2 15 57
8
8
8
1
3
4
1 1 9
8
Sampleworkisshown.
4
8
8
4
and 8
8
1 21
12
5
8
8
2
5
3
inches
1
1
8
8
1
and 8
8

2
1 
3
1
1 1 2 7
7
3 25
10
15
1 5
7
7
7
3
4
1 1 10
10
1
1
1 1 4 3
3
1
3
10 1 1 5
5
33
10
1 14
10
5
47
10
5
3
1
2
7 5 52
5
5
5
CC 44 Common Core Resource Guide
Intervention Activity
© School Specialty
Adafoundthesumbelow.Whichmixednumberis
equivalenttoAda’sanswer?
8
8
16
11
52
1
15
15
15
11
A. 3
C.
15
1
8
B. 3
D. 2
15
15
© School Specialty
Test Prep
4
13
17
1 5
3
3
3
51
8
59
1 5
5
5
5
1
1
2
2 1 3 1 1 1 2 2
2
4
4
2
1 7
2
1
3
2
1 5
2
5
19
2
Common Core Resource Guide
CC 45
Extension Activity
Mixed Number Dollar Amounts
Fraction and Mixed Number Match
Give students strips of paper to represent one dollar bills
and have them tear some of them into halves and some
into quarters. Ask them to show you 13 dollars. Then ask
4
them to show you 21 dollars. Have them add the two
2
numbers to get the total amount. Repeat this with other
mixed number dollar amounts.
Prepare cards in pairs. One half of the pair should have
a mixed number. The other half of the pair should have
its equivalent fraction. Mix up the cards and hand one
to each student. Students need to find the match to the
card they receive.
Chapter 7 • Lesson 11-1
TMG4CCRG_CH07_L11-1_TG_p36-p41.indd 41
Common Core Resource Guide CC 41
12/28/10 12:45:49 PM
Chapter 77
Chapter
Name
Name
11
Lesson
Lesson11-1-1
Date/Time Date
Adding and Subtracting
Mixed Numbers
NCTM Standards 1, 2, 6, 7, 8, 9, 10
Common Core State Standards 4.NF 3
Fill in the missing pieces of each number sentence.

1
1
4
1

1
 2
4
2
4
or 2
1
2

1
7
16
2
2

3
16
9
16

2
1
2
1
1 12
2
3
2
1

1
2
1
1 12
1
3
 1
1
3
2
inches
1
4
inches
 1
3
4
inches
 3 inches
©
© School
School Specialty
Specialty
inches
1

NOTE: Your child is learning to solve story problems involving comparisons. Play a game where you and
your child guess numbers from clues, such as, “My number is 18 more than 53.”
CC 42 Common
CommonCore Resource Guide
TMG4CCRG_CH07_L11-1_LAB_p42-p43.indd 42
12/29/10
12/23/10 12:02:49
11:44:18 PM
AM
3
1
2 1 2 5 2 1 2 1
5
5
1
5 4 4
5
5
2
5 2 3 5 5 2 3 1
8
8
2
3
5 2 8
1
1
1
1
2 1 1 1 3 5 7 2
2
2
2
1
4
2
7
1 3 5 4 1 1
15 15
15
15
3
1
2
1
3 2 2 5 1 or 1 8
8
8
4
3
5
1
2 1 1 5 4 7
7
7
© School Specialty
1
is the same as 3 . Is she
Challenge Patricia thinks that 13
4
4
correct? Use a diagram to explain your answer.
Common Core Resource Guide CC 43
TMG4CCRG_CH07_L11-1_LAB_p42-p43.indd 43
12/28/10 4:13:23 PM
Name
Practice
Lesson
Lesson11-1
44
Date
Adding and Subtracting Mixed Numbers

1
6
1
2

4
3

6
5
6

2
3
5
1
2
1
1 12
2
2 12
3

inches
1
1

1
2

5
1
1 12
2 12
2
1
2
5
3
inches
3
1
4

1
4
5
2 1 5 5 7 8
8
8
1
3
4

5
3
1
2
7  5 5 2 5
5
5
Ada found the sum below. Which mixed number is
equivalent to Ada’s answer?
8
8
16
1 1 5 2 1
15
15
15
11
A. 3
C. 15
1
8
D. 2 B. 3 15
15
© School Specialty
Test Prep
CC 44 Common Core Resource Guide
TMG4CCRG_CH07_L11-1_Practice_p44.indd 44
12/28/10 12:44:26 PM
Name
Extension
Lesson 11-1
Date
Adding Mixed Numbers
Solve by writing equivalent fractions and then adding.
1 1
8
1 1
8
1
and 8
8
9
8
4
8
8
4
and
8
8
1 12
5
8
8
3
1
1 1 2 7
7
© School Specialty
7
1
7
3 5
3
4
1 1 10
10
10
1
10
5
1
1
1 1 4 3
3
1
3
10 1 1 5
5
1
5
1
10
5
1
1
2
2 1 3 1 1 1 2 2
2
4
2
1
2
1
2
1
2
5
Common Core Resource Guide CC 45
TMG4CCRG_CH07_L11-1_Extension_p45.indd 45
12/28/10 12:07:45 PM
Name
Date
Activity
ActivityMaster
MasterX
Adding and Subtracting Mixed Numbers
4
2
1 1 1 7
7
4
2
3 2 1 7
7
1
1
1 1 4 5
5
3 7
3
2 1 11
11
© School Specialty
3
4
1 2 9
9
4
1
1 1 1 5
5
CC 46 Common Core Resource Guide
TMG4CCRG_CH07_L11-1_AM_p46.indd 46
12/28/10 12:14:44 PM
Name
Date
EXPLORE
Lesson 11-1
Fractions or Mixed Numbers?
Chapter 7
Fill in the blanks to describe each picture with a fraction and a
mixed number.

7
5
 
or 1 1
2
7
or 1 1
6
8
3
 9
© School Specialty
4
 4
3

5
3
2
6
 2
or 1
12
8
2
or 2
3
or
or
or 1
1
2
1
4
8
4
1
3
or 1
1
2
Common Core Resource Guide CC 47
TMG4CCRG_CH07_L11-1_EM_p47.indd 47
12/28/10 12:37:07 PM