Objective
1
To provide practice finding fractional parts of sets.
materials
Teaching the Lesson
Key Activities
Students find fractions of a whole when the whole is a collection of objects.
Key Concepts and Skills
•
•
•
•
Solve problems involving fractional parts of collections. [Number and Numeration Goal 2]
Identify the whole or the ONE when given the “fraction-of.” [Number and Numeration Goal 2]
Identify equivalent fractions. [Number and Numeration Goal 5]
Use an equal-sharing division strategy. [Operations and Computation Goal 4]
ⵧ Math Journal 2, pp. 189 and 190
ⵧ Study Link 7 1
䉬
ⵧ 20 pennies or other counters
ⵧ slate
ⵧ straws and quarter-sheets of paper
(optional)
See Advance Preparation
Ongoing Assessment: Recognizing Student Achievement Use journal page 190.
[Number and Numeration Goal 2]
Ongoing Assessment: Informing Instruction See page 578.
2
materials
Ongoing Learning & Practice
Students continue the World Tour.
Students practice and maintain skills through Math Boxes and Study Link activities.
3
materials
Differentiation Options
READINESS
Students act out a
fraction situation.
ENRICHMENT
Students solve “fraction-of”
hiking problems.
ⵧ Math Journal 2, pp. 191 and 329–333
ⵧ Student Reference Book
ⵧ Teaching Aid Masters (Math Masters,
pp. 419–421; optional)
ⵧ Study Link Master (Math Masters, p. 207)
EXTRA PRACTICE
Students play Fraction Of.
ⵧ Student Reference Book, pp. 244
and 245
ⵧ Teaching Master (Math Masters, p. 208)
ⵧ Teaching Aid Master (Math Masters,
p. 388 or 389)
ⵧ Game Masters (Math Masters,
pp. 477–480)
ⵧ counters (optional)
See Advance Preparation
Additional Information
Advance Preparation For Part 1, put a supply of pennies (or counters) next to the Math
Message (at least 20 per student). For the optional Extra Practice activity in Part 3, consider
copying Math Masters, pages 477, 478, and 480 on cardstock.
576
Unit 7 Fractions and Their Uses; Chance and Probability
Technology
Assessment Management System
Journal page 190, Problems 4a– 8a
See the iTLG.
Getting Started
Mental Math and Reflexes
Math Message
1
Take 20 pennies. Show 2 of 20.
Pose mental addition and subtraction problems. Have students share
solution strategies. Suggestions:
11 12 23
18 6 24
13 28 41
19 33 52
123 246 369
225 468 693
27 – 15 12
37 – 19 18
55 – 47 8
75 – 41 34
247 – 135 112
364 – 297 67
Study Link 7 1
Follow-Up
䉬
Have partnerships discuss how they
found the missing numbers on the number lines.
1 Teaching the Lesson
䉴 Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Partners compare answers and share their thinking or strategies.
Tell students that in this lesson they will investigate different
ways to divide sets into fractional parts.
䉴 Modeling “Fraction-of”
PARTNER
ACTIVITY
Problems with Pennies
Ask each partnership to place 24 pennies on the desk and count
2
out 3 of them. Emphasize that the whole is 24 pennies, or
24 cents, not 1 penny. Stress the importance of identifying the
whole in any problem involving fractions.
Whole
24 pennies
Have students share solution strategies. If no one suggests it,
model the following strategy:
Divide the 24 pennies into 3 equal groups, or 3 “fair shares.”
Separate the groups from one another with straws or pencils.
●
How much is the whole? 24 pennies, or 24¢
●
The pennies in each group represent what fraction of all
1
the pennies? 3
How many pennies are in each group (or share)? 8 pennies
●
●
2
How much is 3 of 24 pennies? 16 pennies, or 16¢
2
1
Summary: One way to find 3 of 24 is to first find 3 of 24. 8
1
2
If 3 of 24 is 8, 3 of 24 must be twice as much. 16
1
3
2
3
of 24 8
of 24 16
Lesson 7 2
䉬
577
Student Page
Date
Time
LESSON
Pose similar problems, and have students model the solutions with
pennies. Suggestions:
“Fraction-of” Problems
72
䉬
Whole
1.
59
●
16 nickels
3
a. Circle 4 of the nickels.
b. How much money is that?
0
$
.
60
1
How much is 4 of 32¢? 8¢
●
How much is
●
How much is
1
5
2
3
of 30¢? 6¢
of 27¢? 18¢
2
4
2
5
5
6
of 32¢? 16¢
of 30¢? 12¢
of 30¢? 25¢
3
4
4
5
3
8
of 32¢? 24¢
of 30¢? 24¢
of 40¢? 15¢
Whole
2.
12 dimes
5
b. Circle 6 of the dimes.
Have students place quarter-sheets of paper on their desks to
represent the number of equal groups. Ask them to divide the pennies into
equal groups by distributing them among the sheets. The total number of
sheets (groups) represents the denominator of the fraction.
How much money is that?
1
$
.
00
Whole
3.
ELL
Adjusting the Activity
a. Fill in the “whole” box.
10 quarters
A U D I T O R Y
䉬
K I N E S T H E T I C
䉬
T A C T I L E
䉬
V I S U A L
a. Fill in the “whole” box.
3
b. Circle 5 of the quarters.
How much money is that?
1
$
.
50
䉴 Solving “Fraction-of” Problems
189
PARTNER
ACTIVITY
(Math Journal 2, pp. 189 and 190)
Math Journal 2, p. 189
Suggest that students use counters to model the “fraction-of”
problems on journal pages 189 and 190.
When students have completed the page, ask them to describe a
calculator strategy for solving Problem 4b. Sample answers: Enter
2
into the calculator and multiply by 12, or divide 12 by 3 and
3
multiply by 2.
Ongoing Assessment: Informing Instruction
Watch for the strategies students use to solve Problems 9 and 10. The strategy
1
2
of first finding 4 of 14 (or 22) and using the answer to find 4, while possible, is
2
1
2
not practical. Look for students to note that 4 is another name for 2. Renaming 4
1
as 2 makes it easier to solve the problems.
Student Page
Date
Time
LESSON
“Fraction-of” Problems
72
䉬
夹
夹
夹
夹
夹
continued
Solve.
4
3
1
4. a. of 12 3
1
5. a. of 15 5
of 32 2
10. of 22 4
3
b. of 36 4
5
b. 8
4
1
8. a. of 24 6
2
9. of 14 4
3
b. of 15 5
9
4
1
6. a. of 36 4
1
7. a. 8
2
b. of 12 3
of 32 4
b. of 24 6
8
9
5
c. of 12 3
7
c. of 15 5
27
20
6
c. of 36 4
c.
16
9
8
of 32 13
c. of 24 6
54
36
52
7
11
1
Ongoing Assessment:
Recognizing Student Achievement
20
21
Use journal page 190, Problems 4a–8a to assess students’ ability to solve
“fraction-of” problems. Students are making adequate progress if they are able
to find the fraction of a collection when the fraction is a unit fraction. Some
students may be able to solve “fraction-of” problems involving non-unit fractions
(Problems 4b–8b) and fractions greater than one (Problems 4c–8c).
12 2 Explain.
1
Sample answer: 2 of 25 is the same as dividing
1
25 by 2, which is 12 2.
11. What is
1
2
of 25?
1
12. Michael had 20 baseball cards. He gave of them to his friend Alana,
5
2
and to his brother Dean.
5
a. How many baseball cards did he give to Alana?
b. How many did he give to Dean?
c. How many did he keep for himself?
4
8
8
cards
cards
cards
Try This
1
13. Maurice spent of his money on lunch. He has $2.50 left.
2
How much money did he start with?
$5.00
3
14. Erika spent of her money on lunch. She has $2.00 left.
4
How much money did she start with?
$8.00
190
Math Journal 2, p. 190
578
夹
Journal
page 190
Problems 4a–8a
Unit 7 Fractions and Their Uses; Chance and Probability
[Number and Numeration Goal 2]
Student Page
Date
2 Ongoing Learning & Practice
Time
LESSON
Math Boxes
72
䉬
2. Draw angle ABC that measures 65°.
1. What fraction of the clock face is shaded?
Fill in the circle next to the best answer.
䉴 Resuming the World Tour
INDEPENDENT
ACTIVITY
(Math Journal 2, pp. 329–333; Student Reference Book;
Math Masters, pp. 419–421)
A
1
3
B
6
12
C
1
4
D
2
1
A
B
C
acute
⬔ABC is an
(acute or obtuse) angle.
93 142
143
56
Social Studies Link Students follow the established
World Tour routine.
1
3. Mary has 27 pictures. She gives of them
3
2
to her sister Barb and 3 to her cousin Sara.
2
9
80 R2, or 80 12
962 / 12 a. How many pictures does Barb get?
pictures
b. How many pictures does Sara get?
䉯 They update the Route Map by drawing a line to connect
Budapest, Hungary, and Brası́lia, Brazil.
䉯 They use the World Tour section of the Student Reference Book
to locate facts about Brazil and Brası́lia and then fill in the
Country Notes pages for this country and capital.
4. Divide. Use a paper-and-pencil algorithm.
18
pictures
c. How many pictures does Mary keep?
0
pictures
22 23
179
59
5. There are 29 students in Ms. Wright’s class. 6. Find the area of the figure.
Each collected 50 bottle caps. How many
bottle caps did the students collect in all?
1,450
1 square centimeter
bottle caps
䉯 If they are keeping a Route Log, they update it.
Area 䉴 Math Boxes 7 2
䉬
7.5
133
square cm
191
INDEPENDENT
ACTIVITY
Math Journal 2, p. 191
(Math Journal 2, p. 191)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 7-4. The skill in Problem 6
previews Unit 8 content.
Writing/Reasoning Have students write a response to the
following: Describe the relationship between the fraction
you chose in Problem 1 and the minutes on the clock face.
Sample answer: The clock face is divided into 12 sections. Six of
the 12 sections are shaded. Each section represents 5 minutes, so
30 minutes are shaded. 6 * 5 30
䉴 Study Link 7 2
䉬
INDEPENDENT
ACTIVITY
(Math Masters, p. 207)
Study Link Master
Name
Date
STUDY LINK
72
1.
Time
“Fraction-of” Problems
䉬
1
6
3
6
Theresa had 24 cookies. She gave to her sister and to her mother.
59
Whole
Rule
Home Connection Students solve “fraction-of” problems.
24 cookies
a.
Fill in the “whole” box.
b.
How many cookies did she give to her sister?
c.
How many did she give to her mother?
d.
How many did she have left?
8
4
12
cookies
cookies
cookies
Solve.
1
2. 3
of 18 4
5. 5
of 35 6
28
2
3. 3
of 18 1
6. 4
of 40 12
10
1
4. 5
of 35 3
7. 4
of 40 7
30
Try This
4
3
12
12
9. of 27 10. of 20 9
5
2 12 Explain. Sample answer:
If I share 10 cookies among 4 friends, each
gets 2 whole cookies and 21 of another cookie.
5
8. 8
11.
of 16 10
1
What is of 10?
4
Practice
12.
92 4 14.
13
23
13.
104 / 8
15.
19 R2, or 19 23
41 R7, or 4179
9冄苶3
苶7
苶6
苶
59 / 3 Math Masters, p. 207
Lesson 7 2
䉬
579
Teaching Master
Name
Date
LESSON
Time
Hiking Trails
72
䉬
59
Luis is staying in a large state park that has
8 hiking trails. In the table at the right, each trail
is labeled easy, moderate, or rugged, depending
on how difficult that trail is for hiking.
State Park Trails
Trail
Miles
Ice Age
11
easy
Kettle
2
moderate
Luis figures that it would take him about
20 minutes to walk 1 mile on an easy trail,
about 30 minutes on a moderate trail, and
about 40 minutes on a rugged trail.
1.
a.
Kettle Trail: About
b.
Cliff Trail: About
c.
Oak Trail: About
d.
Bluff Trail: About
Oak
60 minutes
30 minutes
30 minutes
70 minutes
Sky
3
3.
If he wants to hike for about 25 minutes,
which trail should he choose?
4.
About how long would it take him
to complete Pine Trail?
rugged
rugged
easy
Ice Age (or Pine) Trail
22–23
䉴 Exploring Fractions of a Set
SMALL-GROUP
ACTIVITY
5–15 Min
(Math Masters, p. 388 or 389)
moderate
Sky Trail
About
READINESS
moderate
1
3 2
Badger
If Luis wants to hike for about of an
4
hour, which trail should he choose?
moderate
3
4
11
2
11
2
Cliff
2.
5.
3
4
13
4
Bluff
About how long will it take Luis to walk
the following trails?
Type
4
Pine
3 Differentiation Options
minutes
yes
Sample answer: Badger is a moderate
trail. Luis can walk 1 mile on a moderate trail
in 30 minutes. So, he can walk 4 miles in
2 hours. Badger Trail is only 3 12 miles long, so
Luis could walk it in less than 2 hours.
To explore fractions of a set, have students use fractions to
describe various attributes of a small group of students. For
example, give one student a pencil. Ask: What fraction of the
students is holding a pencil? What fraction is not holding a pencil?
Use other attributes, such as clothing or eye color, to model
finding the fraction of a set.
Do you think Luis could walk Badger Trail in less than 2 hours?
Explain.
Math Masters, p. 208
When students have enough experience describing the group in
terms of fractions, have them find objects in the room that come in
sets and use fractions to describe attributes of these sets. Have
them record their work in a Math Log or on an Exit Slip. For
1
1
example, 8 of the markers in a box are yellow; 12 of a box of
4
colored chalk is pink; 4 of the students at our table have calculators.
ENRICHMENT
䉴 Solving “Fraction-of” Problems
INDEPENDENT
ACTIVITY
5–15 Min
(Math Masters, p. 208)
To apply students’ understanding of “fraction-of ” situations, have
them solve the hiking trail problems on Math Masters, page 208.
When discussing solution strategies, remind students that the
trail data are estimates. The lengths of the trails are given to the
1
nearest 4 mile. The times Luis thinks it will take him to walk a
mile are also estimates.
Game Master
Name
Date
Time
Fraction Of Gameboard and Record Sheet
WHOLE
(Choose 1 of these sets.)
Fraction
card
of
1 2
4 3
EXTRA PRACTICE
䉴 Playing Fraction Of
PARTNER
ACTIVITY
5–15 Min
(Student Reference Book, pp. 244 and 245;
Math Masters, pp. 477–480)
Set
card
To practice identifying fractions of collections, have students play
Fraction Of. See Lesson 7-3 for additional information.
Round
Sample
“Fraction-of” Problem
1
5
of 25
Points
5
Planning Ahead
Obtain one regular deck of playing cards for every two students
to use in Lesson 7-3.
1
2
3
4
5
6
7
8
Total score
Math Masters, p. 479
580
Unit 7 Fractions and Their Uses; Chance and Probability