Objective
To guide the development and use of a rule for
generating equivalent fractions.
1
materials
Teaching the Lesson
Key Activities
Students use examples of equivalent fractions to develop a rule for finding equivalent fractions.
ⵧ Math Journal 2, pp. 201, 342
and 343
ⵧ Study Link 7 6
䉬
Key Concepts and Skills
• Identify fractional parts of regions. [Number and Numeration Goal 2]
• Name equivalent fractions. [Number and Numeration Goal 5]
• Use a rule for generating equivalent fractions. [Number and Numeration Goal 5]
• Develop a rule for generating equivalent fractions. [Patterns, Functions, and Algebra Goal 1]
ⵧ Teaching Master (Math Masters,
p. 225)
ⵧ calculator
ⵧ colored chalk
ⵧ slate
Key Vocabulary
equivalent fractions • Equivalent Fractions Rule
Ongoing Assessment: Informing Instruction See page 605.
Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page 225.
[Number and Numeration Goal 5]
2
materials
Ongoing Learning & Practice
Students play Fraction Match to practice naming equivalent fractions.
Students practice and maintain skills through Math Boxes and Study Link activities.
3
Students use a
Fraction NumberLine Poster to
identify equivalent
fractions.
ENRICHMENT
Students investigate
how early Egyptians
represented a fraction as the sum of
unit fractions.
ⵧ Study Link Master (Math Masters,
p. 223)
ⵧ Game Masters (Math Masters,
pp. 473–476)
materials
Differentiation Options
READINESS
ⵧ Student Reference Book, p. 243
ⵧ Math Journal 2, p. 202
EXTRA PRACTICE
Students complete
name-collection
boxes for fractions.
EXTRA PRACTICE
Students practice
finding equivalent
fractions.
ⵧ Teaching Master (Math Masters,
p. 224)
ⵧ Teaching Aid Masters (Math Masters,
p. 388 or 389 and 397)
ⵧ 5-Minute Math, pp. 1, 17, 79, and 165
ⵧ Fraction Number-Line Poster
(Math Masters, pp. 204 and 205)
ⵧ straightedge
Technology
Assessment Management System
Math Masters, page 225
See the iTLG.
Lesson 7 7
䉬
603
Getting Started
Mental Math and Reflexes
6 1, 2, 3, 6
4 1, 2, 4
5 1, 5
Have students name all the factors for
numbers under 100. Suggestions:
12 1, 2, 3, 4, 6, 12
15 1, 3, 5, 15
21 1, 3, 7, 21
50 1, 2, 5, 10, 25, 50
52 1, 2, 4, 13, 26, 52
72 1, 2, 3, 4, 6, 8, 9,
12, 18, 24, 36, 72
Math Message
Study Link 7 6 Follow-Up
Complete journal page 201.
Have small groups compare answers. Ask volunteers to draw additional
representations of the fractions in Problems 1–4.
䉬
1 Teaching the Lesson
䉴 Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
(Math Journal 2, p. 201)
Ask students to examine the squares they colored on journal
page 201. Point out that the three fractions they wrote for each
problem all name the same fractional part of the square. Such
fractions are called equivalent fractions. To support English
language learners, have students write equivalent fractions next
to the examples in the journals.
Students should notice that whenever the total number of equal
parts is doubled (or quadrupled), the number of colored parts is
also doubled (or quadrupled), but the fractional part represented
by the colored parts does not change.
Tell students that in this lesson they will develop a rule for finding
equivalent fractions.
Student Page
Date
Time
LESSON
Many Names for Fractions
77
䉬
Color the squares and write the missing numerators.
1
1. Color of each large square.
2
Whole
䉴 Developing a Rule for
49
square
WHOLE-CLASS
DISCUSSION
Finding Equivalent Fractions
(Math Journal 2, p. 201)
1
is colored.
2
2. Color
1
2
is colored.
4
1
4
4
In each problem on journal page 201, the numerator and
denominator of the first fraction are each multiplied by 2 to
obtain the second fraction. They are each multiplied by 4 to
obtain the third fraction.
is colored.
8
of each large square.
is colored.
4
2
is colored.
8
4
To support English language learners, write the following on
the board.
is colored.
16
3
3. Color 4 of each large square.
Problem 1:
1ⴱ2
2ⴱ2
3
4
is colored.
6
is colored.
8
1ⴱ4
2ⴱ4
8
1ⴱ4
4ⴱ4
16
4
Problem 2:
12 is colored.
16
201
1ⴱ2
4ⴱ2
Math Journal 2, p. 201
604
2
4
Unit 7 Fractions and Their Uses; Chance and Probability
2
8
4
Student Page
Date
Problem 3:
3ⴱ2
4ⴱ2
2
2
Equivalent Names for Fractions
3ⴱ4
4ⴱ4
6
8
Time
12
16
Fraction
Equivalent Fractions
Decimal
Percent
0
0%
1
100%
Decimal
Percent
0
2
4
4
Write and with colored chalk to emphasize that the numerator
and denominator were multiplied by the same number.
1
2
The Equivalent Fractions Rule can be used to rename any
fraction: If the numerator and denominator of a fraction are
multiplied by the same nonzero number, the result is a fraction
that is equivalent to the original fraction.
2
3
2 3
, 4 6
2
2
1
3
1
4
3
4
1
5
2
5
3
5
Adjusting the Activity
4
5
Present a more abstract rationale for this rule:
5
6
1
6
䉯 If any number is multiplied by 1, the product is the number you started with.
䉯 A fraction with the same numerator and denominator, such as 44, is
1
8
3
8
5
8
equivalent to 1.
7
8
䉯 Multiplying the numerator and denominator of a fraction by the same number
(not 0) is the same as multiplying the fraction by 1. So, the product is
equivalent to the original fraction.
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
䉴 Generating Equivalent Fractions
䉬
342
Math Journal 2, p. 342
V I S U A L
PARTNER
ACTIVITY
(Math Journal 2, pp. 342 and 343; Math Masters, p. 225)
Have students turn to the Equivalent Names for Fractions
table on journal page 342. Ask them to write 10 fractions that
1
are equivalent to 3.
Have students look for patterns in fractions that are equivalent
1
to 3. Point out how these patterns relate to the Equivalent
Fractions Rule.
Student Page
Date
Ongoing Assessment: Informing Instruction
Time
Equivalent Names for Fractions
Fraction
Watch for students who note that not every pair of equivalent fractions can be
found by multiplying (or dividing) by the same whole number. For example:
1
3 ⴱ 13
4
8
1
6 ⴱ 13
In this example, the numerator and denominator are both multiplied by the mixed
1
number 13.
Equivalent Fractions
continued
1
9
2
9
4
9
5
9
7
9
8
9
1
10
3
10
7
10
Working in pairs, students use the Equivalent Fractions Rule to
find three equivalent fractions for each of the remaining fractions
in the table.
Ask students to explain how to use a calculator to find equivalent
fractions. Sample answer: Enter a fraction. Multiply it by any
fraction whose numerator and denominator are the same.
9
10
1
12
5
12
7
12
11
12
343
Math Journal 2, p. 343
Lesson 7 7
䉬
605
Name
Date
LESSON
Time
An Equivalent Fractions Rule
77
䉬
夹
Margot says the value of a fraction does not change if you do the same thing to
the numerator and denominator. Margot says that she added 2 to the numerator
1
3
and the denominator in and got .
4
12
42
6
3
6
Therefore, she says that
1
4
3
.
6
When students complete their work on journal pages 342 and 343
ask them to solve the problem on Math Masters, page 225 on
their own.
How could you explain or show Margot that she is wrong?
1
3
Sample answer: 4 does not equal 6, because
3
1
equals . You can multiply or divide the
6
2
numerator and denominator by the same
number and not change the value of the fraction,
but you cannot just add or subtract the same
number from the numerator and denominator.
Ongoing Assessment:
Recognizing Student Achievement
Math Masters
Page 225
夹
Use Math Masters, page 225 to assess students’ understanding of
equivalent fractions. Students are making adequate progress if they are
able to draw a picture or use the Equivalent Fractions Rule to demonstrate that
1
3
(is not equal to) . Some students may rename the fractions as decimals
4
6
and show that 0.25 0.5.
Math Masters, page 225
[Number and Numeration Goal 5]
2 Ongoing Learning & Practice
䉴 Playing Fraction Match
SMALL-GROUP
ACTIVITY
(Student Reference Book, p. 243; Math Masters, pp. 473–476)
Students play Fraction Match to practice naming
equivalent fractions.
Adjusting the Activity
Have a table of equivalent fractions available, such as Math Journal 2,
pages 342 and 343 or Student Reference Book, page 51.
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
Student Page
Games
Fraction Match
Materials 䊐 1 deck of Fraction Match Cards
(Math Masters, pp. 473–476)
Players
2 to 4
Skill
Recognizing equivalent fractions
2
3
2
3
2
3
Object of the game To match all of your cards and have none left.
1. Shuffle the deck and deal 7 cards to each player. Place the
remaining cards facedown on the table. Turn over the top
card and place it beside the deck. This is the target card.
If a WILD card is drawn, return it to the deck and continue
drawing until the first target card is a fraction.
1
5
1
5
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 7-5. The skill in Problem 6
previews Unit 8 content.
Writing/Reasoning Have students write a response to the
following: How did you determine the number of squares
you needed to circle in Problem 1? Sample answer: There
are 24 total squares. I divided them into 8 equal groups with 3
squares in each group. Then I circled 3 of the groups.
♦ a card with an equivalent fraction
♦ a card with a like denominator
♦ a WILD card.
is the target card. It can be matched with:
8
, or
♦ an equivalent fraction card such as 46 , 69 , or 12
♦ a like denominator card such as 30 , 13 , or 33 , or
♦ a WILD card. The player names any fraction (with a denominator
of 2, 3, 4, 5, 6, 8, 9, 10, or 12) that is equivalent to the target card.
8 . The player may not
The player can match 23 by saying 46 , 69 , or 12
match 2 by saying 2 .
3
3
3. If a match is made, the player’s matching card is placed on
top of the pile and becomes the new target card. It is now the
next player’s turn. When a WILD card is played, the next
player uses the fraction just stated for the new target card.
4. If no match can be made, the player takes 1 card from the
deck. If the card drawn matches the target card, it may be
played. If not, the player keeps the card and the turn ends.
5. The game is over when one of the players runs out of cards,
when there are no cards left in the Fraction Match deck, or
time runs out. The player with the fewest cards wins.
WILD
WILD
WILD
Name an
equivalent
fraction with a
denominator of
2, 3, 4, 5, 6, 8, 9,
10, or 12.
Student Reference Book, p. 243
606
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 202)
2. Players take turns trying to match the target card with
a card from their hand in one of 3 possible ways:
2
3
䉬
1
5
Directions
Example
䉴 Math Boxes 7 7
Unit 7 Fractions and Their Uses; Chance and Probability
Student Page
䉴 Study Link 7 7
INDEPENDENT
ACTIVITY
䉬
(Math Masters, p. 223)
Date
Time
LESSON
Math Boxes
77
1. Circle
3
8
1
2. Insert parentheses to make these
of all the squares. Mark Xs on 6
of all the squares.
Home Connection Students identify the missing
numerator or denominator of equivalent fractions to
complete name-collection boxes.
number sentences true.
(3
a. 2
Sample answer:
b. 12
) 26
(6 4)
10
6
)
c. 24
(
5
d. 12
24
2
38
3
(6 6)
59
150
4. Draw and label a 125° angle.
3. Plot and label each point on the
coordinate grid.
A (0,2)
3 Differentiation Options
C
5
3
C (1,5)
1
D (5,5)
0
0
T
E
A
2
Sample answer:
D
4
B (4,0)
1
2
3
B
4
O
obtuse
This angle is an
(acute or obtuse) angle.
144
SMALL-GROUP
ACTIVITY
READINESS
䉴 Identifying Equivalent Fractions
5. A bag contains
5
6
1
3
5–15 Min
on the Fraction Number-Line
Poster
92 93
143
6. If 1 inch on a map represents 40 miles,
then how many inches represent
10 miles? Fill in the circle next to the
best answer.
green blocks,
red blocks,
blue block, and
yellow blocks.
You put your hand in the bag and, without
looking, pull out a block. About what
fraction of the time would you expect to
get a blue block?
1
15
(Math Masters, pp. 204, 205, and 388 or 389 )
P
5
E (5,3)
A
2 in.
B
1
4
in.
C
1
2
in.
D
4 in.
145
45
Math Journal 2, p. 202
To explore equivalent fractions using a number-line model, have
students use a straightedge to vertically line up fractions on the
Fraction Number-Line Poster (see the optional Readiness activity
1 1 1 2
in Lesson 7-1) that are equivalent to ᎏ4ᎏ, ᎏ3ᎏ, ᎏ2ᎏ, ᎏ3ᎏ, and so on. Ask
students to record the results of their exploration in a Math Log or
on an Exit Slip.
1 Whole
0
1
Halves
1
2
0
2
2
2
Study Link Master
Fourths
0
4
1
4
2
4
3
4
4
4
Name
Date
STUDY LINK
77
Eighths
Time
Fraction Name-Collection Boxes
䉬
In each name-collection box:
0
8
1
8
2
8
3
8
4
8
5
8
6
8
7
8
8
8
49 50
Write the missing number in each fraction so that the fraction belongs
in the box. Write one more fraction that can go in the box.
Thirds
1.
0
3
1
3
2
3
1
6
2
6
3
6
4
6
5
6
6
6
A straightedge highlights equivalent fractions.
3.
2
ᎏᎏ
3
1
ᎏᎏ
4
6
3
4
9
12
5
12
5
10
18
20
2
3
3
Sixths
0
6
2.
1
ᎏᎏ
2
10
20
10
20
30
40
9
8
25
18
12
100
Answers
vary.
Answers
vary.
Answers
vary.
4. Make up your own
a.
b.
name-collection box
problems like the ones
above. Ask a friend to
solve your problems.
Check your friend’s work.
Answers vary.
Practice
5.
23 R3
⫽ 95 / 4
6. 57 ⫼ 3 ⫽
19
7.
42
⫽ 882 / 21
Math Masters, p. 223
Lesson 7 7
䉬
607
Teaching Master
Name
Date
LESSON
Time
ENRICHMENT
Egyptian Fractions
77
䉬
Ancient Egyptians only used fractions with 1 in the numerator. These are called
3
4
unit fractions. They wrote non-unit fractions, such as and , as sums of unit
4
9
fractions. They did not use the same unit fraction more than once in a sum.
55 57
3
4
1
2
1
4
4
9
1
2
1
4
1
3
1
9
1
3
1
9
Use drawings and what you know about equivalent fractions to help you find the
Egyptian form of each fraction.
7
3. 10
1
4
1
4
1
8
1
2
1
2
1
8
5
2. 12
1
3
1
3
1
2
3
5. 5
1
5
5
4. 6
1
5
1
10
1
12
1
1
2
4
6. 7
1
2
2
NOTE Egyptians also used the fraction 3.
1
3
To apply students’ understanding of fraction addition and
equivalent fractions, have students investigate how early
Egyptians represented a fraction as the sum of unit fractions.
To solve Problems 5 and 6, students need to divide the rectangle
into more regions than indicated by the denominator of
the fraction.
1
3
1
2
(Math Masters, p. 224)
1
14
EXTRA PRACTICE
1
2
15–30 Min
Fractions
Examples:
3
1. 8
䉴 Investigating Egyptian
SMALL-GROUP
ACTIVITY
1
10
1
2
䉴 Completing Name-Collection
1
14
INDEPENDENT
ACTIVITY
5–15 Min
Boxes
Math Masters, p. 224
(Math Masters, p. 397)
To provide practice generating equivalent names for fractions,
have students complete name-collection boxes. Encourage students
to complete the boxes with equivalent fractions and mathematical
expressions that include fractions.
Use Math Masters, page 397 to create problems to meet the needs
of individual students or have students create and solve their
own problems.
EXTRA PRACTICE
Teaching Aid Master
Name
Date
䉴 5-Minute Math
5–15 Min
Time
To offer students more experience with equivalent fractions,
see 5-Minute Math, pages 1, 17, 79, and 165.
Name-Collection Boxes
Name ____________________________
Name ____________________________
Date _____________________________
Date _____________________________
Name ____________________________
Name ____________________________
Date _____________________________
Date _____________________________
Math Masters, p. 397
608
SMALL-GROUP
ACTIVITY
Unit 7 Fractions and Their Uses; Chance and Probability