# Lesson 4.4 Adding and Subtracting Mixed Numbers with Like

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Objective
To add and subtract mixed numbers with
like denominators.
1
materials
Teaching the Lesson
Key Activities
Students practice adding and subtracting mixed numbers that have fractions with
like denominators.
Щ— Math Journal 1, pp. 132 and 133
Щ— Student Reference Book,
pp. 84вЂ“86
Щ— Study Link 4 3
б­њ
Key Concepts and Skills
вЂў Convert between fractions and mixed numbers. [Number and Numeration Goal 5]
вЂў Use multiplication and division facts to find equivalent fractions and to simplify fractions.
[Operations and Computation Goal 2]
вЂў Add and subtract mixed numbers with like denominators. [Operations and Computation Goal 3]
Щ— Teaching Master (Math Masters,
p. 117)
Щ— scissors
See Advance Preparation
Key Vocabulary
mixed number вЂў proper fraction вЂў improper fraction вЂў simplest form
Ongoing Assessment: Recognizing Student Achievement Use journal page 133.
[Operations and Computation Goal 3]
2
materials
Ongoing Learning & Practice
Students practice estimating sums of fractions by playing Fraction Action, Fraction Friction.
Students practice and maintain skills through Math Boxes and Study Link activities.
3
materials
Differentiation Options
READINESS
Students use a calculator
to practice counting by
fractions and converting
between improper fractions
and mixed numbers.
ENRICHMENT
Students read a poem
about fractions.
EXTRA PRACTICE
Students use bills and
coins to model and simplify
mixed numbers.
Additional Information
Advance Preparation For the Math Message in Part 1, make one copy of
Math Masters, page 117 for every two students.
272
Unit 4 Rational Number Uses and Operations
Щ— Math Journal 1, p. 134
Щ— Student Reference Book, p. 317
Щ— Study Link Master (Math Masters,
p. 118)
Щ— Game Master (Math Masters,
p. 446)
Щ— Geometry Template; calculator
Щ— Teaching Master (Math Masters,
p. 119)
Щ— Math Talk: Mathematical Ideas in
Poems for Two Voices
Щ— calculator; coins and bills of various
denominations
Technology
Assessment Management System
Journal page 133, Problems 9, 12, 14,
and 15
See the iTLG.
Getting Started
Mental Math and Reflexes
Math Message
Students rename improper fractions as mixed
numbers. Suggestions:
Complete a copy of the Math Message problem.
3
1
бЋЏбЋЏ 1бЋЏбЋЏ
2
2
5
2
бЋЏбЋЏ 1бЋЏбЋЏ
3
3
75
3
бЋЏбЋЏ 18бЋЏбЋЏ
4
4
5
1
бЋЏбЋЏ 1бЋЏбЋЏ
4
4
13 1
бЋЏбЋЏ 2бЋЏбЋЏ
6
6
108
3
бЋЏбЋЏ 21бЋЏбЋЏ
5
5
Study Link 4 3 Follow-Up
б­њ
Go over the answers.
1 Teaching the Lesson
б­¤ Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
NOTE If students are fairly skilled at finding
(Math Masters, p. 117)
sums and differences of fractions, this lesson
may take less than one day.
Ask a volunteer to demonstrate and explain how to use the paper
ruler to measure the line segment. Sample answer: Line up the
right end of A
а·†B
а·† with the mark for 4 in. on the ruler. The left end
5
of а·†
AB
а·† is aligned with the mark for бЋЏ16бЋЏ in. The total length of A
а·†B
а·† is
5
5
бЋЏ
бЋЏ
бЋЏ
бЋЏ
4 in. П© 16 in., or 4 16 in. This ruler shows the two parts of a mixed
number: the whole number and the fraction. A mixed number
can be viewed as the sum of a whole number and a fraction.
Discuss why fractions greater than 1 are easier to interpret when
3
written as mixed numbers. For example, 2бЋЏ4бЋЏ clearly represents a
number greater than 2 but less than 3. This is not as obvious
3
11
when 2бЋЏ4бЋЏ is written as the improper fraction бЋЏ4бЋЏ.
б­¤ Writing Mixed Numbers
Teaching Master
Name
WHOLE-CLASS
DISCUSSION
in Simplest Form
Date
LESSON
Time
Math Message
4 4
б­њ
Cut out the ruler below. Use it to measure line segment AB to the
1
nearest бЋЏбЋЏ inch.
16
A
Review the meanings of proper fraction, improper fraction, and
simplest form with the class.
B
вЂ”
length of AB П­
б­џ A fraction in which the numerator is less than the
denominator is called a proper fraction. A proper fraction
names a number that is less than 1.
3
9
5
бЋЏбЋЏ
16
4 in.
0
1
2
3
4
5
inches
0
Examples: бЋЏ8бЋЏ, бЋЏ10бЋЏ, бЋЏ4бЋЏ
б­џ A fraction in which the numerator is equal to or greater than
the denominator is called an improper fraction. An
improper fraction names a number that is greater than or
equal to 1.
5 7 9
Examples: бЋЏ5бЋЏ, бЋЏ2бЋЏ, бЋЏ3бЋЏ
Name
Date
LESSON
Time
Math Message
4 4
б­њ
Cut out the ruler below. Use it to measure line segment AB to the
1
nearest бЋЏбЋЏ inch.
16
A
B
вЂ”
length of AB П­
0
1
2
3
4
5
inches
Math Masters, p. 117
Lesson 4 4
б­њ
273
Student Page
Date
Time
LESSON
б­џ A mixed number is in simplest form if the fraction part is a
proper fraction in simplest form.
Adding and Subtracting Mixed Numbers
4 4
б­њ
2
5
4
5
Example 1: 1бЋЏбЋЏ П© 2бЋЏбЋЏ П­ ?
84вЂ“86
Step 1
Add the fractions. Then add the
whole numbers.
6
3 бЋЏ65бЋЏ П­ 3 П© бЋЏ5бЋЏ
2
1бЋЏ5бЋЏ
П©
5
1
П­ 3 П© бЋЏ5бЋЏ П© бЋЏ5бЋЏ
4
2 бЋЏ5бЋЏ
1
П­ 3 П© 1 П© бЋЏ5бЋЏ
1
П­ 4 бЋЏ5бЋЏ
6
3 бЋЏ5бЋЏ
Add. Write your answers in simplest form.
1
4 бЋЏ5бЋЏ
1.
2
1бЋЏ4бЋЏ
2.
2
П© 3 бЋЏ5бЋЏ
3
П© 1 бЋЏ4бЋЏ
4бЋЏ14бЋЏ
7
7бЋЏ35бЋЏ
5
4 бЋЏ8бЋЏ
Example 2:
ПЄ
1
2 бЋЏ8бЋЏ
1
5 бЋЏ4бЋЏ
3.
3
П© 2 бЋЏ4бЋЏ
2
Step 2
If necessary, rename the difference.
5
4 бЋЏ8бЋЏ
5
4 бЋЏ8бЋЏ
ПЄ
1
ПЄ 2 бЋЏ8бЋЏ
1
2 бЋЏ8бЋЏ
4
4
Example 3:
ПЄ
2
1бЋЏ3бЋЏ
1
2 бЋЏ8бЋЏ П­ 2 бЋЏ2бЋЏ
2 бЋЏ8бЋЏ
1
5 бЋЏ3бЋЏ
9
be written using proper fractions, the fraction part is not required to be in
simplest form. Students should know how to name fractions in simplest form
for standardized tests. However, they may often find it helpful to work with
fractions or mixed numbers that are not in simplest form when they are
computing with fractions.
2
П© 1бЋЏ8бЋЏ
3
бЋЏбЋЏ
4
П­?
Step 1
Subtract the fractions.
Then subtract the whole numbers.
8
NOTE While Everyday Mathematics requests that mixed-number answers
4
1бЋЏ8бЋЏ
4.
4
Examples: 2бЋЏ7бЋЏ is in simplest form. 4бЋЏ5бЋЏ and 3бЋЏ9бЋЏ are not in
simplest form because they contain an improper fraction.
4
4
3бЋЏ8бЋЏ is not in simplest form because бЋЏ8бЋЏ is not in simplest form.
Step 2
If necessary, rename the sum.
5
Write 3бЋЏ4бЋЏ on the board and ask a volunteer to rename it in
simplest form. Use pictures similar to those below to show
the procedure.
П­?
Notice that the fraction in the first mixed number is less than the fraction in the second
2
1
1
mixed number. Because you canвЂ™t subtract бЋЏ3бЋЏ from бЋЏ3бЋЏ, you need to rename 5 бЋЏ3бЋЏ.
Step 1
Rename the first mixed number.
1
1
5 бЋЏ3бЋЏ П­ 4 П© 1 П© бЋЏ3бЋЏ
3
Step 2
Subtract the fractions.
Then subtract the whole numbers.
1
П­ 4 П© бЋЏ3бЋЏ П© бЋЏ3бЋЏ
4
5 бЋЏ3бЋЏ
1
4 бЋЏ3бЋЏ
2
ПЄ 1бЋЏ3бЋЏ
1
4
4
1
2
ПЄ 1бЋЏ3бЋЏ
4
П­ 4 П© бЋЏ3бЋЏ П­ 4 бЋЏ3бЋЏ
1
1
1
4
1
4
1
4
1
4
2
3 бЋЏ3бЋЏ
132
Math Journal 1, p. 132
5
34 П­
1
1
П­
1
1
Time
4 4
5
П­ 7 П© бЋЏ88бЋЏ
7 бЋЏ8бЋЏ
5
ПЄ 3 бЋЏ8бЋЏ
а¬™
6.
1
4 бЋЏ5бЋЏ
ПЄ 2 бЋЏ4бЋЏ
3
ПЄ 2 бЋЏ5бЋЏ
1
бЋЏбЋЏ
2
4
бЋЏбЋЏ
5
5
7.
2
10.
1
2
1
3 бЋЏ5бЋЏ
5
11.
ПЄ 1 бЋЏ5бЋЏ
3
ПЄ 1бЋЏ4бЋЏ
3
1
бЋЏбЋЏ
3
3
бЋЏбЋЏ
5
1
бЋЏбЋЏ
4
3
1
а¬™
3
7
6 бЋЏ8бЋЏ
1
5
4бЋЏ2бЋЏ 5бЋЏ2бЋЏ
2
9
2бЋЏ3бЋЏ 3бЋЏ3бЋЏ
10
A U D I T O R Y
1
бЋЏбЋЏ
4
7 бЋЏ12бЋЏ inches
14. Mr. Ventrelli is making bread. He adds
cups
1
of white flour and 1бЋЏ4бЋЏ cups of wheat flour. The
recipe calls for the same number of cups of
water as cups of flour. How much water
should he add?
2 бЋЏ12бЋЏ cups of water
15. EvelynвЂ™s house is between RobertвЂ™s
and ElizabethвЂ™s. How far is RobertвЂ™s
house from ElizabethвЂ™s?
1
бЋЏбЋЏ
2
3
4
mi
3
1 4 mi
2 miles
RobertвЂ™s
EvelynвЂ™s
1
1бЋЏ6бЋЏ 2бЋЏ2бЋЏ
ELL
3
П© 3 бЋЏ8бЋЏ
1
1бЋЏ4бЋЏ
ElizabethвЂ™s
133
Math Journal 1, p. 133
274
1
П­44
Have students model mixed numbers using bills and quarters. To
5
model 3бЋЏ4бЋЏ, use \$3 and 5 quarters. Five quarters is equal to \$1 and 1 quarter.
Therefore, \$3 and 5 quarters П­ \$4 and 1 quarter.
1
ПЄ 3 бЋЏ4бЋЏ
3
бЋЏбЋЏ
4
12.
П© 2 бЋЏ6бЋЏ
6
7
8.
3
13. Joe has a board that is 8 бЋЏ4бЋЏ inches long. He cuts
1
off 1бЋЏ4бЋЏ inches. How long is the remaining piece?
а¬™
а¬™
1
4
Adjusting the Activity
2
ПЄ 2 бЋЏ3бЋЏ
1
бЋЏбЋЏ
3
1
1
П©
3
Add or subtract.
4 бЋЏ6бЋЏ
1
4
5
4 бЋЏ8бЋЏ
9.
1
4
8
8
ПЄ 3 бЋЏ8бЋЏ
8
П­ 7 бЋЏ8бЋЏ
3
7бЋЏ5бЋЏ 8
Step 2
Subtract the fractions. Then subtract
the whole numbers.
8П­7П©1
1
П©
84вЂ“86
Step 1
Rename the whole number.
3 бЋЏ4бЋЏ
П­1
1
4
Write several such mixed numbers on the board. Have students
rename them in simplest form. Suggestions:
5
Example 4: 8 ПЄ 3 бЋЏ8бЋЏ П­ ?
5.
4
4
1
4
3бЋЏ54бЋЏ can be renamed as 4бЋЏ14бЋЏ.
Adding and Subtracting Mixed Numbers cont.
б­њ
1
4
1
4
Student Page
LESSON
1
4
П©
П­
Date
1
4
1
3
1
5
4
П©
3
Unit 4 Rational Number Uses and Operations
б­њ
K I N E S T H E T I C
б­њ
T A C T I L E
б­њ
V I S U A L
Student Page
б­¤ Adding Mixed Numbers
INDEPENDENT
ACTIVITY
with Like Denominators
Fractions
Addition of Mixed Numbers
One way to add mixed numbers is to add the fractions and the
whole numbers separately. This may require renaming the sum.
(Math Journal 1, p. 132; Student Reference Book, p. 84)
5
Example
7
Find 4бЋЏ8бЋЏ П© 2бЋЏ8бЋЏ.
Step 1: Add the fractions.
Step 2: Add the whole
Step 3: Rename the sum.
numbers.
2
4
Write the following problem on the board: 1бЋЏ5бЋЏ П© 2бЋЏ5бЋЏ П­ ?
Ask students to solve and then share their strategies. Go over
the steps on journal page 132 before having students complete
Problems 1вЂ“4 on their own. Bring the class together to share
solutions. If necessary, provide more practice, particularly with
problems that require renaming. Refer students to page 84 in the
Student Reference Book.
5
4
5
бЋЏбЋЏ
8
4
П©2
7
бЋЏбЋЏ
8
12
бЋЏбЋЏ
8
П©2
7
5
бЋЏбЋЏ
8
6
12
бЋЏбЋЏ
8
7
бЋЏбЋЏ
8
12
6 бЋЏ8бЋЏ
П­6П©
8
бЋЏбЋЏ
8
П©
П­6П©1П©
4
бЋЏбЋЏ
8
1
бЋЏбЋЏ
2
П­7
П­7
1
4бЋЏ8бЋЏ П© 2бЋЏ8бЋЏ П­ 7бЋЏ2бЋЏ
4
бЋЏбЋЏ
8
4
бЋЏбЋЏ
8
If the fractions do not have the same denominator, first rename
the fractions so they have a common denominator.
3
Example
2
Find 3бЋЏ4бЋЏ П© 5бЋЏ3бЋЏ.
Step 1: Rename and add
П©5
3
3
бЋЏбЋЏ
4
2
бЋЏбЋЏ
3
П­
3
П­П© 5
2
Step 3: Rename the sum.
Step 2: Add the whole
numbers.
the fractions.
3
9
бЋЏбЋЏ
12
8
бЋЏбЋЏ
12
17
бЋЏбЋЏ
12
3
П©5
8
9
бЋЏбЋЏ
12
8
бЋЏбЋЏ
12
17
бЋЏбЋЏ
12
8
17
бЋЏбЋЏ
12
П­ 8 П©
12
бЋЏбЋЏ
12
П©
П­ 8 П© 1 П©
П­ 9
5
бЋЏбЋЏ
12
5
бЋЏбЋЏ
12
5
бЋЏбЋЏ
12
5
3бЋЏ4бЋЏ П© 5бЋЏ3бЋЏ П­ 9бЋЏ12бЋЏ
б­¤ Subtracting Mixed Numbers
PARTNER
ACTIVITY
Some calculators have special keys for entering mixed numbers.
3
Example
2
Solve 3бЋЏ4бЋЏ П© 5бЋЏ3бЋЏ on a calculator.
On Calculator A: Key in 3
with Like Denominators
Unit
On Calculator B: Key in 3
(Math Journal 1, pp. 132 and 133; Student Reference Book, p. 85)
3
3
4
n
d
4
5
+
5
Unit
2
2
n
3
Enter
=
d
3
Check Your Understanding
Solve Problems 1вЂ“3 without a calculator. Solve Problem 4 with a calculator.
1
Go over the three subtraction examples on journal pages 132
and 133 (Examples 2вЂ“4). Ask students to solve Problem 5. If
successful, they should continue and complete the page. You may
need to provide additional practice before continuing or refer
students to page 85 in the Student Reference Book.
Ongoing Assessment:
Recognizing Student Achievement
7
4
1. 2бЋЏ8бЋЏ П© 7бЋЏ8бЋЏ
1
2
2. 3бЋЏ5бЋЏ П© 2бЋЏ2бЋЏ
3
4
3. 6бЋЏ3бЋЏ П© 3бЋЏ4бЋЏ
Ch
k
6
4. 14бЋЏ9бЋЏ П© 8бЋЏ7бЋЏ
417
Student Reference Book, p. 84
Journal
Page 133
Problems
9, 12, 14, and 15
а¬™
Use journal page 133, Problems 9, 12, 14, and 15 to assess
studentsвЂ™ ability to add mixed numbers with like denominators. Students are making
adequate progress if they can calculate the sums in Problems 9, 12, 14, and 15.
Some students may be able to calculate the differences in Problems 5вЂ“8, 10, 11,
and 13.
[Operations and Computation Goal 3]
Student Page
Fractions
Subtraction of Mixed Numbers
If the fractions do not have the same denominator, first rename
them as fractions with a common denominator.
7
3
Find 3бЋЏ8бЋЏ ПЄ 1бЋЏ4бЋЏ.
Example
Step 1: Rename the
fractions.
3 бЋЏ7бЋЏ
8
ПЄ1 бЋЏ3бЋЏ
4
7
8
ПЄ1 бЋЏ6бЋЏ
8
П­
3
Step 2: Subtract the
Step 3: Subtract the whole
fractions.
3 бЋЏ7бЋЏ
П­
1
3бЋЏ8бЋЏ ПЄ 1бЋЏ4бЋЏ П­ 2бЋЏ8бЋЏ
numbers.
3 бЋЏ8бЋЏ
7
3 бЋЏ7бЋЏ
ПЄ1 бЋЏ6бЋЏ
ПЄ1 бЋЏ6бЋЏ
8
8
1
бЋЏбЋЏ
8
8
2 бЋЏ1бЋЏ
8
To subtract a mixed number from a whole number, first rename
the whole number as the sum of a whole number and a fraction
that is equivalent to 1.
2
Find 5 ПЄ 2бЋЏ3бЋЏ.
Example
Step 1: Rename the whole
number.
ПЄ2 бЋЏ2бЋЏ
3
2
3
ПЄ2 бЋЏ2бЋЏ
3
П­
Step 3: Subtract the whole
fractions.
4 бЋЏ3бЋЏ
П­
5
Step 2: Subtract the
1
5 ПЄ 2бЋЏ3бЋЏ П­ 2бЋЏ3бЋЏ
numbers.
4 бЋЏ3бЋЏ
4 бЋЏ3бЋЏ
3
ПЄ 2 бЋЏ2бЋЏ
3
1
бЋЏбЋЏ
3
3
ПЄ 2 бЋЏ2бЋЏ
3
1
3
2 бЋЏбЋЏ
When subtracting mixed numbers, rename the larger mixed
number if it contains a fraction that is less than the fraction in
the smaller mixed number.
Example
1
3
Find 7бЋЏ5бЋЏ ПЄ 3бЋЏ5бЋЏ.
Step 1: Rename the larger
mixed number.
7 бЋЏ1бЋЏ
5
ПЄ 3 бЋЏ3бЋЏ
5
1
3
Step 2: Subtract the
Step 3: Subtract the whole
fractions.
numbers.
6 бЋЏ6бЋЏ
5
6 бЋЏ6бЋЏ
5
6 бЋЏ6бЋЏ
П­ ПЄ3 бЋЏ3бЋЏ
ПЄ 3 бЋЏ3бЋЏ
ПЄ 3 бЋЏ3бЋЏ
П­
5
3
7бЋЏ5бЋЏ ПЄ 3бЋЏ5бЋЏ П­ 3бЋЏ5бЋЏ
5
5
3
бЋЏбЋЏ
5
5
3 бЋЏ3бЋЏ
5
Student Reference Book, p. 85
Lesson 4 4
б­њ
275
Game Master
Name
Date
Time
Fraction Action, Fraction Friction Card Deck
1
2
1
3
2
3
1 2
4 3
2 Ongoing Learning & Practice
1
4
б­¤ Playing Fraction Action,
PARTNER
ACTIVITY
Fraction Friction
3
4
1
6
1
6
5
6
1
12
1
12
5
12
5
12
7
12
7
12
11
12
11
12
(Student Reference Book, p. 317; Math Masters, p. 446)
Distribute one set of 16 Fraction Action, Fraction Friction cards
and one or more calculators to each group of two or three players.
Review game directions on page 317 of the Student Reference
Book. Play a few practice rounds with the class.
б­¤ Math Boxes 4 4
INDEPENDENT
ACTIVITY
б­њ
(Math Journal 1, p. 134)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 4-2. The skill in Problem 5
previews Unit 5 content. Students will need the Percent
Circle on the Geometry Template to complete Problem 5.
Math Masters, p. 446
б­¤ Study Link 4 4
INDEPENDENT
ACTIVITY
б­њ
(Math Masters, p. 118)
Home Connection Students practice addition and
subtraction of mixed numbers.
Study Link Master
Student Page
Date
Time
LESSON
Name
4 4
18
бЋЏ
a. бЋЏ
45 П­
2
бЋЏбЋЏ
5
26
b. бЋЏбЋЏ П­
39
2
бЋЏбЋЏ
3
1
3
a. бЋЏбЋЏ П© бЋЏбЋЏ П­
10
5
7
бЋЏбЋЏ
10
56
c. бЋЏбЋЏ П­
80
7
бЋЏбЋЏ
10
25
d. бЋЏбЋЏ П­
625
1
бЋЏбЋЏ
25
5
1
b. бЋЏбЋЏ П© бЋЏбЋЏ П­
12
3
3
бЋЏбЋЏ
4
7
4
c. бЋЏбЋЏ ПЄ бЋЏбЋЏ П­
9
9
1
бЋЏбЋЏ
3
6
d. бЋЏбЋЏ
8
0
9
4
Write 2 fractions equivalent to бЋЏбЋЏ.
e.
27
бЋЏбЋЏ
12
18
бЋЏбЋЏ
8
ПЄ
3
бЋЏбЋЏ
4
П­
In a national test, eighth-grade students answered the problem shown in the
top of the table at the right. Also shown are the 5 possible answers they
were given and the percent of students who chose each answer.
Sample answers:
a.
4. Thomas Jefferson was born in 1743.
George Washington was born m years
earlier. In what year was Washington born?
Choose the best answer.
following set of numbers.
1.5, 2.8, 3.4, 4.5, 2.2, 8.4
3.1
b. mean
3.8
m ПЄ 1743
The mean would double.
1743 ПЄ m
240
5. The table below shows the results of a
survey in which people were asked
which winter Olympic sport they most
enjoyed watching. Use a Percent Circle
to make a circle graph of the results.
Favorite
Sport
Percent of
People Surveyed
Luge
35%
Ice hockey
15%
Figure skating
40%
Other
10%
Winter Olympic Sports Preferences
28%
D. 21
27%
14%
1
бЋЏбЋЏ
4
1 inches
(unit)
3
Add or subtract. Write your answers as mixed numbers in simplest form. Show your work on
the back of the page. Use number sense to check whether each answer is reasonable.
1
3
1
бЋЏбЋЏ
бЋЏбЋЏ
бЋЏбЋЏ
1
1
1
2
2
2
4
3
4. 3бЋЏбЋЏ П© 1бЋЏбЋЏ П­
5. 4 ПЄ 2бЋЏбЋЏ П­
6. 1бЋЏбЋЏ П© бЋЏбЋЏ П­
4
4
4
1
4
3
3
2
3
Circle the numbers that are equivalent to 2бЋЏ4бЋЏ.
7
6
бЋЏбЋЏ
4
3
бЋЏбЋЏ
7
11
бЋЏбЋЏ
4
Practice
Solve mentally.
8.
5 Вє 18 П­
90
9.
6 Вє 41 П­
246
145 146
Unit 4 Rational Number Uses and Operations
C. 19
Tim is making papier-mГўchГ©. The recipe calls for 1бЋЏ4бЋЏ cups of paste. Using only
1
1
1
бЋЏбЋЏ -cup, бЋЏбЋЏ -cup, and бЋЏбЋЏ -cup measures, how can he measure the correct amount?
2
4
3
1
Sample answer: He can use three бЋЏ2бЋЏ-cup measures and
1
one бЋЏ4бЋЏ-cup measure.
134
276
24%
3
1бЋЏ4бЋЏ
Math Journal 1, p. 134
7%
B. 2
3.
Luge
Other
Figure
skating
A. 1
A board is 6бЋЏ8бЋЏ inches long. Verna wants to cut enough
1
so that it will be 5бЋЏ8бЋЏ inches long. How much should she cut?
7.
Ice
hockey
Explain why B is the best estimate.
2.
1743 П© m
136 137
7
Percent Who Chose
This Answer
E. I donвЂ™t know.
m П© 1743
Suppose you multiplied each data value
by 2. What would happen to the mean?
Possible
Answers
Both fractions are close to
1, so their sum should be
close to 2.
83
74
12
Estimate the answer to бЋЏ13бЋЏ П© бЋЏ8бЋЏ.
You will not have enough time to solve
the problem using paper and pencil.
What mistake do you think the
students who chose C made?
They may have added
only the numerators.
b.
3. Find the median and mean for the
a. median
1.
2. Add or subtract. Then simplify.
Time
Ш‰, ШЉ Fractions and Mixed Numbers
4 4
б­њ
1. Write each fraction in simplest form.
Sample answers:
Date
STUDY LINK
Math Boxes
б­њ
Math Masters, p. 118
10.
9 Вє 48 П­
432
11.
7 Вє 45 П­
315
Teaching Master
Name
3 Differentiation Options
Date
LESSON
Time
Fraction Counts and Conversions
4 4
б­њ
Most calculators have a function that lets you repeat an operation, such
1
as adding бЋЏбЋЏ to a number. This is called the constant function. To use
4
1
the constant function of your calculator to count by бЋЏбЋЏs, follow one of the
4
key sequences below, depending on the calculator you are using.
PARTNER
ACTIVITY
READINESS
б­¤ Using a Calculator for
Calculator A
Calculator B
Op1 +
Press:
1
n
4
d
Op1
1
1бЋЏ4бЋЏ
Display: 5
Fraction Counts
Display:
1.
1
a.
b.
2.
1
4
6
4
1
бЋЏбЋЏ
4
1
1бЋЏбЋЏ?
2
6
6
How many counts of бЋЏбЋЏ are needed to display бЋЏбЋЏ?
How many counts of
are needed to display
Use a calculator to convert mixed numbers to improper
fractions or whole numbers.
11
11
бЋЏбЋЏ
бЋЏбЋЏ
3
7
4
4
a. 2 бЋЏбЋЏ П­
b. 1бЋЏбЋЏ П­
4
3.
5
бЋЏбЋЏ
4
K
Using a calculator, start at 0 and count by бЋЏ4бЋЏs to answer the
following questions.
c.
б­¤ Reading about Fractions
0
Display: 1бЋЏ4бЋЏ
Display: бЋЏбЋЏ
PARTNER
ACTIVITY
+ +
1
5
4
(Math Masters, p. 119)
ENRICHMENT
4
Press:
Press:
To provide experience with fractions and mixed numbers, have
students use the constant function on a calculator to define and
generate fraction counts. They also study and apply patterns
involving unit fractions, improper fractions, and mixed numbers.
1
Press:
Op1 Op1 Op1 Op1 Op1
5вЂ“15 Min
4
3
4
4
2 бЋЏбЋЏ П­
d.
6
12
4
3 бЋЏбЋЏ П­
1
4
How many бЋЏбЋЏs are between the following numbers?
3
a. бЋЏбЋЏ
4
c.
and 2
3
4
1бЋЏбЋЏ and 4
5
9
6
b. бЋЏбЋЏ
4
d.
3
4
and 2 бЋЏбЋЏ
1
2
3 and 4 бЋЏбЋЏ
5
6
5вЂ“15 Min
in Poetry
Math Masters, p. 119
Literature Link To further explore fractions, have students
read the poem вЂњProper FractionsвЂќ in Math Talk:
Mathematical Ideas in Poems for Two Voices. Suggest that
students recite the poem in their spare time and present it to
the class.
PARTNER
ACTIVITY
EXTRA PRACTICE
б­¤ Modeling Mixed Numbers
5вЂ“15 Min
with Bills and Coins
To provide extra practice simplifying mixed numbers, have
students use bills and coins to model renaming procedures.
Suggestions:
4
13
2бЋЏ4бЋЏ \$2 and 4 quarters; 3
9
3
бЋЏбЋЏ
2бЋЏ1бЋЏ
0 \$2 and 13 dimes; 3 10
1
1бЋЏ4бЋЏ \$1 and 9 quarters; 3бЋЏ4бЋЏ
31
11
бЋЏбЋЏ
3бЋЏ2бЋЏ
0 \$3 and 31 nickels; 4 20
Lesson 4 4
б­њ
277
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