Comparing and
Ordering Fractions
Objectives To review equivalent fractions; and to provide
experience
with comparing and ordering fractions.
e
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Teaching the Lesson
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
1 2
4 3
• Find equivalent fractions using a length
model. [Number and Numeration Goal 5]
• Compare fractions to the benchmarks 0,
and 1. [Number and Numeration Goal 6]
• Order fractions from least to greatest. Family
Letters
1
_
2,
[Number and Numeration Goal 6]
• Solve fraction number stories using a
number-line model. [Operations and Computation Goal 4]
• Use fraction sticks to add fractions. Playing Fraction Top-It
Student Reference Book, p. 316
Fraction Cards (Math Journal 2,
Activity Sheets 5–7)
Students practice comparing fractions
by playing Fraction Top-It.
Math Boxes 5 3
Math Journal 1, p. 133
Students practice and maintain skills
through Math Box problems.
Study Link 5 3
[Operations and Computation Goal 4]
Key Activities
Students use the Fraction-Stick Chart to find
equivalent fractions and compare fractions to
the benchmarks 0, _12 , 1, and 1_12 . They use
the fraction-stick model to compare pairs of
fractions, find equivalent fractions, and
continue their exploration of fraction addition.
Math Masters, p. 131
Students practice and maintain skills
through Study Link activities.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Making Fraction Strips
6 strips of colored paper, each 2" by 8_12 "
Students use a length model to explore
comparing and ordering fractions by making
fraction strips.
ENRICHMENT
Exploring a Fraction-Stick Chart
Math Masters, p. 130
Students explore relationships between
the numerators and denominators of
equivalent fractions.
ELL SUPPORT
Building a Math Word Bank
Differentiation Handbook, p. 142
Students add the term equivalent fractions
to their Math Word Banks.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 129. [Number and Numeration Goal 6]
Ongoing Assessment:
Informing Instruction See page 305.
Key Vocabulary
benchmark fraction stick equivalent fractions
Materials
Math Journal 1, pp. 129–132
Study Link 52
transparency of Math Masters, p. 137 slate
Geometry Template straightedge (optional)
Advance Preparation
For Part 1, make a transparency of the chart on Math Masters, page 137. For the optional Readiness
activity in Part 3, each student will need 6 strips of colored paper, each 2" by 8_12 ". These can be prepared
ahead of time or during the activity.
Teacher’s Reference Manual, Grades 4–6 pp. 38, 44, 45, 60–74, 88, 89
302
Unit 5
Fractions, Decimals, and Percents
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Getting Started
Mental Math and Reflexes
Math Message
Use the benchmarks 0, _
,
2
and 1 to answer Problems 1–5
on journal page 129.
1
Have students use the rulers on their Geometry Templates.
Find 2_
inches on a ruler. How many half-inches is that? 5
2
1
Find 6 cm on a ruler. How many _
cm is that? 12
2
1
Study Link 5 2
Follow-Up
Find 2_
inches on a ruler. How many quarter-inches is that? 10
8
4
Find 3_
cm on a ruler. How many _
cm is that? 7
2
2
1
1
1
1
1
_
inch is what fraction of 2_ inches? _
Allow students five
minutes to compare answers and correct
any errors. Have volunteers share their
mixed-number problems.
5
2
2
3
3
1
_
_
_
inch
is
what
fraction
of
2
inches?
4
2
10
1 Teaching the Lesson
▶ Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
(Math Journal 1, p. 129)
Remind students that a benchmark is a well-known count or
measure that can serve as a reference point when estimating.
1
When working with fractions, the benchmarks 0, _
, and 1 are often
2
used. Discuss how students applied their knowledge of numerators,
denominators, and benchmarks to tell if each measurement is
1
closest to 0, _
, or 1.
2
Ongoing Assessment:
Recognizing Student Achievement
Journal
Page 129
Problem 5
Student Page
Date
Time
LESSON
Use journal page 129, Problem 5 to assess students’ understanding of the
structure of fractions. Students are making adequate progress if their explanations
correctly represent the relationship between the numerator and denominator and
1
the use of benchmarks such as 0, _
2 , and 1.
[Number and Numeration Goal 6]
Comparing and Ordering Fractions
53
Math Message
1
Decide whether each of these measurements is closer to the benchmark 0, _
2 , or
1 inch. Circle the closest benchmark.
1
_
1. 8
inch is closest to . . .
15 inch
2. _
16
5
3. _
8
is closest to . . .
inch is closest to . . .
3 inch is closest to . . .
4. _
8
▶ Ordering Fractions
PARTNER
ACTIVITY
(Math Journal 1, p. 129)
5.
0 inches.
1
_
2 inch.
1 inch.
0 inches.
1
_
2 inch.
1 inch.
0 inches.
1
_
2 inch.
1 inch.
0 inches.
1
_
2 inch.
1 inch.
Explain your solution for Problem 4.
3
1
_
Sample answer: I know that _
8 is only 8 away
3
4
1
1
_
_
_
from , which is . So must be closest to _
.
8
2
8
2
Ordering Fractions
On the board or a transparency, draw 4 horizontal lines in a row
to order the fractions from Problems 1–4 of the journal page.
Volunteers explain which of the Math Message fractions is least
1 is the least because it is the closest to 0;
and which is greatest. _
8
15 is the greatest because it is closest to 1. Write these fractions
_
16
5 and _
3 are
on the first and last lines, respectively. Ask: Since _
8
8
1 , how do we decide where to write them? Both
equally close to _
2
fractions are eighths, and 5 is more than 3, which means that
3 is the smaller fraction so it is closer to 0.
_
8
For each problem below, write the fractions in order from least to greatest.
6 _
3 _
5 _
8
_
6. 8 , 8 , 8 , 8
2 _
2 _
2 _
2
_
7. 7 , 9 , 5 , 12
3
2 _
1 _
1 _
_
8. 3 , 4 , 3 , 4
3 _
9 _
4 _
1
_
9. 5 , 10 , 20 , 25
3 _
5
1 _
7 _
_
10. 7 , 10 , 8 , 7
5 _
9
2 _
1 _
_
11. 9 , 5 , 6 , 10
3 _
4 _
4 _
4
_
12. 8 , 7 , 5 , 9
3
_
8
2
_
12
1
_
4
1
_
25
1
_
10
1
_
6
4
_
9
5
_
,
,
,
,
,
,
,
8
2
_
9
1
_
3
4
_
10
3
_
7
2
_
5
4
_
8
6
_
,
,
,
,
,
,
,
8
2
_
7
2
_
3
9
_
20
5
_
7
5
_
9
4
_
7
8
_
,
,
,
,
,
,
,
8
2
_
5
3
_
4
3
_
5
7
_
8
9
_
10
3
_
5
Math Journal 1, p. 129
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Lesson 5 3
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2/14/11 1:26 PM
Student Page
Date
Time
LESSON
Fraction-Stick Chart
53
䉬
0
1
4
1
8
1
10
1
12
1
16
9
—
7
6
2
3
—
4
9
—
8
12
12
3
4
14
8
—
1
2
1
3
1
1
4
4
1
1
5
5
1
1
1
6
6
6
1
1
1
7
7
7
1
1
1
8
8
8
1
1
1
1
9
9
9
9
1
1
1
1
10
10
10
10
1
1
1
1
1
12
12
12
12
12
1
1
1
1
1
1
1
16
16
16
16
16
16
16
—
6
4
2
1. 3
8
12 1
2
4
1
—
16
Examples:
4
7
or 8 ?
4
or 5 ?
6.
3.
2
Which is 5 closest to:
Which is closer to 1 2:
1
0 or 2 or 1?
1 3 or 1 5 ?
3
4
Which is larger:
4
7
Ask students to describe the fractions in Problem 6. The
denominators are the same. So we know that all the unit
fractions are the same size. Only the number of pieces (the
numerators) need to be compared.
1
3
2.
Which is larger:
7
12
1
9
1
10
5.
Which is larger:
13 or 3 ? 12. Which is 8 closest to:
1
16
8.
Which is larger:
1
4
1
12
1
5
1
6
1
7
1
8
1
9
1
10
1
12
1
16
1
16
1
1
3
1
4
1
8
1
143
1
3
1
9
1
10
1
16
1
4
1
12
1
1
5
2
1
6
1
7
1
8
1
9
1
10
1
12
1
16
1
16
1
2
0 or 2 or 1?
1
2
1
3
1
4
1
1
5
5
1
1
6
6
1
1
1
7
7
7
1
1
1
8
8
8
1
1
1
9
9
9
1
1
1
10
10
10
1
1
1
1
12
12
12
12
1
1
1
1
1
16
16
16
16
16
142
1
10
1
12
1
16
5
1
3
1
4
or 6 ? 9. Which is 1
6 closest to: 0 or 2 or 1?
4
1
2
1
3
1
1
4
4
1
1
5
5
1
1
1
6
6
6
1
1
1
7
7
7
1
1
1
8
8
8
1
1
1
1
9
9
9
9
1
1
1
1
10
10
10
10
1
1
1
1
1
12
12
12
12
12
1
1
1
1
1
1
1
16
16
16
16
16
16
16
2
11.
1
2
1
3
1
4
1
1
5
5
1
1
6
6
1
1
1
7
7
7
1
1
1
8
8
8
1
1
1
9
9
9
1
1
1
10
10
10
1
1
1
1
12
12
12
12
1
1
1
1
1
16
16
16
16
16
—
12
12
2
3
—
8
3
4
16
28
12
11
6
—
22
14 3
Fill in the blanks. Circle the correct answer.
—
6
5
3
4. 4
4
—
5
8
—
3
15 20
7. 16
10.
Explain that examining numerators and denominators is the first
step when comparing and ordering fractions. Refer students to
journal page 129.
Math Journal 1, p. 130
Ask students to describe the fractions in Problem 7. The
numerators are the same. Now what do we know? There are
the same number of pieces for each fraction. So only the size of
the pieces (the denominators) needs to be compared. Remind
students that the smaller the denominator is, the larger the
piece is.
Ask students to describe the fractions in Problem 8. There are
two different denominators; there are two unit fractions. First
1 and _
1 . The smaller denominator is
compare the unit fractions _
3
4
the larger fraction. The remaining fractions are within one
3 is _
1 away from 1, and _
2 is _
1 away from 1.
piece of 1—that is, _
4
4
3
3
1 is greater than _
1 , that makes _
2 farther away from 1.
Since _
3
4
3
Ask partners to complete the problems on the journal page. When
most students are finished, discuss their strategies for Problems
9–12, including the following:
1 . That leaves the other three
Problem 9: The least fraction is _
25
to compare. Change each to an equivalent fraction with a
denominator of 20.
Problem 10: One of these fractions is close to 0, one is close to
1.
1, and the other two are close to _
2
1 is to see if the
Problem 11: One way to compare a fraction to _
2
1
_
numerator is more or less than 2 of the denominator. Two of
1 . Their order is determined
the fractions are greater than _
2
5
9
1
_
_
_
because 9 is close to 2 and 10 is close to 1. Of the two fractions
1 , the denominators are close to each other,
that are less than _
Student Page
Date
Time
LESSON
Adding with Fraction Sticks
5 3
䉬
1.
2.
2 halves
8 eighths
4 quarters
16 sixteenths
and one numerator is 2 times the numerator of the other.
1 (the numerator is _
1 of the
Problem 12: One fraction equals _
2
2
1 , and _
4 is less than _
1.
denominator). The others are close to _
2
Use the fraction sticks to find equivalent fractions.
2
a. 1
8
—
d. 1
2
—
b.
16
2
4
4
—
8
6
—
8
12
16 8
3
4
e.
—
16
2
—
2
6
c.
—
4
4 —
8
8
—
8
3
4 1 2 8
8
3
8
2
4
1
4 9
1
6 12
,
16
or
3
4
5
8
1
6 16 14
,
16
or
7
8
a.
3
16
b.
1
c. 16
16
16
—
16
3
4
5
1
2
1
4 b.
1
2
3
8 c.
5
8
1
4
d.
1
4
7
2
WHOLE-CLASS
ACTIVITY
Fraction-Stick Chart
3
4
7
8
7
8
8 1
6 2
7
▶ Introducing the
Use the fraction sticks to add fractions with different denominators.
a.
9
1 but only by _
1 of a piece
The other two are greater than _
2
2
3 is _
4
1
1 , and _
1 of
_
_
each—that is, 7 is 2 of a seventh greater than _
2
5
2
1 . Because fifths are greater than sevenths,
a fifth greater than _
2
3 is greater than _
4.
_
12
—
Use the fraction sticks to add fractions with the same denominator.
Example:
3.
2
1
A whole stick is worth 1.
(Math Journal 1, p. 130; Math Masters, p. 137)
20
16 ,
4
1
116, or 14
Use a transparency of the chart from Math Masters, page 137 to
demonstrate how to use the Fraction-Stick Chart.
Math Journal 1, p. 131
304
Unit 5
Fractions, Decimals, and Percents
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1. Skip-Counting with Fractions
Please refer students to journal page 130. Explain that a
fraction stick is a model for the whole, or the ONE, that shows
unit fractions for the interval between 0 and 1. Each row of the
Fraction-Stick Chart combines 2 fraction sticks to show the
interval from 0 to 2, divided into unit fractions for a particular
denominator.
NOTE A fraction stick is a narrow rectangle
divided into pieces that represents fractions.
Sometimes it is helpful to make physical
fraction sticks, as in Part 3 of this lesson.
Example: The third row shows two sticks, each divided into
1 . The pieces
thirds. There are 6 pieces in this row, each labeled _
3
can be used to count by thirds.
2. Finding Equivalent Fractions
The Fraction-Stick Chart on Math Masters, page 137 can be used
to find equivalent fractions. Survey the class for examples of
pairs of fractions that name the same part of a whole. Emphasize
that these are equivalent fractions and list the examples on the
3 is equivalent to _
1.
board. For example, _
6
2
2.
Example: Find equivalent fractions for _
1
3
1
3
1
3
0
3
1
3
1
3
2
3
1
3
3
3
1
3
4
3
5
3
6
3
The third row of the Fraction-Stick Chart
3
Step 1: The denominator is 3, so use the thirds stick to locate the
2 . Count the pieces from left to right. The right edge of the
fraction _
3
2.
second piece is _
3
2 , that is, along the
Step 2: Place one edge of a straightedge at _
3
1 piece. The straightedge should be
right edge of the second _
3
parallel to the sides of the Fraction-Stick Chart. Now look for
other fraction sticks on the chart along the straightedge.
On the sixths stick, the straightedge touches the right edge of a
piece. Count the sixths-stick pieces from left to right. The
4 . So _
4 is
straightedge is at the end of the fourth piece, which is _
6
6
2
_
equivalent to 3 .
Ongoing Assessment:
Informing Instruction
Watch for students who confuse the fraction
labels with the actual end of the fraction stick.
Remind students that the labels are in the
center of a portion, not at its end. Have
students draw a light pencil line along the
straightedge and use the line instead of the
straightedge to identify equivalent portions.
On the ninths stick, the straightedge touches the end of the sixth
6 . So _
6 =_
2.
piece, which is _
9
9
3
On the twelfths stick, the straightedge touches the end of the
8 . So _
8 =_
6 , and _
8
2 . The fractions _
2, _
4, _
eighth piece, which is _
12
12
3
3 6 9
12
are equivalent. They name the same distance on the FractionStick Chart.
0
1
4
On the other sticks, the straightedge cuts through some of the
2 cannot be written as an equivalent fraction using the
pieces, so _
3
denominator on those sticks.
1
1
2
1
3
3. Comparing Fractions
The Fraction-Stick Chart on Math Masters, page 137 can be used
3 . (See margin.)
4 and _
to compare fractions, for example, compare _
9
8
Step 1: The denominator of the first fraction is 9, so use the
4 . Count the pieces from left to right. The
ninths stick to locate _
9
4 . Place the straightedge along
right edge of the fourth piece is _
9
this edge.
2
4
1
3
1
4
1
5
eighths
ninths
1
4
1
5
1
5
1
1
1
6
6
6
1
1
1
7
7
7
1
1
1
8
8
8
1
1
1
1
9
9
9
9
1
1
1
1
10
10
10
10
1
1
1
1
1
12
12
12
12
12
1
1
1
1
1
1
1
16
16
16
16
16
16
16
1
7
1
8
1
9
1
10
1
12
1
16
Lesson 5 3
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12/4/10 7:59 AM
Student Page
Date
3 (the right edge of the third piece on the eighths
Step 2: Locate _
8
3 is to the left of _
4 , it is less than _
4 . Conversely, _
4 is
stick). Since _
8
9
9
9
3
3
_
_
to the right of 8 , so it is greater than 8 . Ask partners to complete
journal page 130. Ask volunteers to explain their solutions.
Time
LESSON
Fraction Number Stories
5 3
䉬
Shade the fraction sticks to help you solve these fraction number stories.
Write a number model for each story.
1.
2.
3.
5
ᎏ7ᎏ
8
1
ᎏᎏ ⫽ ᎏ7ᎏ
4
8
a.
How much flour did he use in all?
b.
Number model:
ᎏ5ᎏ
8
⫹
cup
1
Sheryl’s puppy weighed 1ᎏ2ᎏ pounds
when it was born. After two weeks,
3
the puppy had gained ᎏ8ᎏ pounds.
a.
How much did the puppy weigh after two weeks?
b.
Number model:
1ᎏ12ᎏ ⫹
ᎏ3ᎏ
8
⫽ 1ᎏ78ᎏ
1ᎏ78ᎏ
▶ Adding with Fraction Sticks
pounds
5
8
⫹ ᎏᎏ =
1ᎏ38ᎏ
The five fraction sticks at the top of journal page 131 provide a
length model for fraction work. Note that the denominators are
restricted to 1, 2, 4, 8, and 16. This model will be used to formally
introduce the addition of fractions. All these problems can be
solved visually. The correct amount of shading for any fraction
can be decided by using the appropriate fraction stick at the
top of the page.
Answers vary.
Number story:
b.
Make up your own fraction number story. Draw and shade fraction sticks to solve it.
Write a number model for your story.
Answers vary.
a.
Number story:
b.
Number model:
c.
Solution:
PARTNER
ACTIVITY
(Math Journal 1, p. 131)
Shade the fraction sticks to solve the number model. Then write a fraction number
story that fits the number model.
3
a. ᎏᎏ
4
4.
1
Chris made pizza dough with ᎏ8ᎏ cup of white flour and ᎏ4ᎏ cup of whole wheat flour.
▶ Solving Fraction Number Stories
Math Journal 1, p. 132
(Math Journal 1, p. 132)
INDEPENDENT
ACTIVITY
PROBLEM
PRO
PR
P
RO
R
OB
BLE
BL
L
LE
LEM
EM
SO
S
SOLVING
OL
O
LV
VIN
IIN
NG
Students solve the fraction number stories on journal page 132.
Circulate and assist. Encourage students to use the benchmarks
1 , and 1 when explaining their solutions and assessing the
0, _
2
reasonableness of answers. Discuss the answers and write the
strategies on the board.
2 Ongoing Learning & Practice
▶ Playing Fraction Top-It
Student Page
Date
Math Boxes
53
䉬
1.
(Student Reference Book, p. 316; Math Journal 2,
Activity Sheets 5–7)
Time
LESSON
Write a 10-digit numeral that has
9
3
5
7
1
6
in
in
in
in
in
in
2.
the tens place,
the millions place,
the billions place,
the hundred-millions place,
the thousands place, and
all other places.
Write each fraction as a whole number or
a mixed number.
4ᎏ14ᎏ
8
2ᎏ12ᎏ
17
a. ᎏᎏ ⫽
4
24
b. ᎏᎏ
3
5, 7 6 3, 6 6 1, 6 9 6
Write the numeral in words.
Five billion, seven hundred
sixty-three million, six
hundred sixty-one thousand,
six hundred ninety-six
⫽
5
c. ᎏᎏ
2
⫽
9
d. ᎏᎏ
8
⫽
32
e. ᎏᎏ
5
1ᎏ18ᎏ
6ᎏ25ᎏ
⫽
what fraction of the students
traveled within their state?
b.
what fraction traveled
to Europe?
c.
62 63
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 5-1. The skill in Problem 5
previews Unit 6 content.
Vacation Travel
11
ᎏ
ᎏ
32
ᎏ4ᎏ
32
, or
what fraction traveled to
Canada or Mexico?
ᎏ8ᎏ
32
, or
within state
11
ᎏ1ᎏ
8
Canada
or Mexico
8
stayed
home 3
another
state
6
Europe
4
ᎏ1ᎏ
4
59 125
4.
Divide.
5.
a.
21冄4
苶9
苶3
苶∑
23 R10
b.
35冄6
苶2
苶3
苶∑
17 R28
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 133)
Where 32 students vacationed, ...
a.
Students practice comparing fractions by playing Fraction Top-It.
Students use the Fraction Cards that were stored in Lesson 5-1.
▶ Math Boxes 5 3
4
3.
PARTNER
ACTIVITY
22–24
Find the following landmarks for this set of
numbers: 929, 842, 986, 978, 869, 732,
898, 986, 900, 899, 986, 920, 842
a.
Minimum:
b.
Maximum:
c.
Mode:
d.
Range:
e.
Median:
732
986
986
254
900
Writing/Reasoning Have students write a response to the
following: Explain how you converted the fractions to mixed
numbers in Problem 2. Sample answer: For the whole number
part, I found how many groups of the denominator were in the
numerator. The fraction part was what was left.
119
Math Journal 1, p. 133
306
Unit 5
Fractions, Decimals, and Percents
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Study Link Master
▶ Study Link 5 3
INDEPENDENT
ACTIVITY
(Math Masters, p. 131)
Name
Date
STUDY LINK
Time
Fraction-Stick Problems
53
䉬
Shade the fraction sticks to help you find equivalent fractions.
59
Home Connection Students find equivalent fractions,
add fractions, and solve fraction number stories using
fraction sticks.
3 Differentiation Options
4
1
1. 2
—
8
3
2. 4
—
16
12
1
4
2
8
—
16
—
3.
4
Shade the fraction sticks to help you solve the addition problems.
1
4. 4
1
5. 2
1
6. 2
4
1
4
6
3
8
4
5
1
1
4
4
3
4
2
8
3
4
Shade the fraction sticks to help you solve the fraction number stories.
3
3
Joe was baking a cake. He added cup of white sugar and cup of brown
4
8
sugar. How much sugar did he use in all?
7.
9
,
8
118 cups
or
(unit)
READINESS
▶ Making Fraction Strips
SMALL-GROUP
ACTIVITY
On the back of this page, write a number story using fractions. Then write a
number model to show how you solved it.
8.
Practice
15–30 Min
To explore comparing and ordering fractions using a length model,
have students make fraction strips. Students cut 6 strips of paper,
1 " and then fold and label them to represent halves,
each 2" by 8_
2
thirds, fourths, fifths, sixths, and eighths. (See margin.)
297
3冄苶8
苶9
苶1
苶
9.
74 R3
12冄苶8
苶9
苶1
苶→
11.
→
10.
6冄苶8
苶9
苶1
苶
12.
24冄苶8
苶9
苶1
苶 →
148 R3
37 R3
Math Masters, p. 131
To fold into thirds, fold one end in so the doubled parts and the
single part are the same size.
To fold into sixths, fold a strip into thirds and then in half.
For fifths, fold the two outside edges of the strip in toward the
middle but not together. Fold them so the doubled parts and
the space between them look like three equal parts. Now fold
the doubled parts back the other way at the point where the
folded ends first came down.
When folded into thirds, the edge of the folded
end divides the rest into halves.
Have students label the fractions on the folds. As they finish, ask
students to fold two strips so only the unit fraction shows and then
1 is less than _
1.
make a comparison statement. For example, _
5
3
When folded into fifths, the two folded ends are
equal in size to the space in the middle.
ENRICHMENT
▶ Exploring a Fraction-Stick Chart
PARTNER
ACTIVITY
15–30 Min
Teaching Master
Name
Date
LESSON
Time
Fraction-Stick Chart
53
䉬
1
4
0
2
4
3
4
124
114
1
1
1
2
(Math Masters, p. 130)
1
2
1
3
1
3
1
4
1
5
To apply students’ understanding of fractions, have them explore
the relationships between the numerators and denominators of
equivalent fractions. When they finish, have them share one of
their discoveries.
1
4
1
5
1
5
1
3
1
4
1
5
1
6
1
7
1
8
1
1
9
9
1
1
10
10
1
1
12
12
1
1
1
16
16
16
1
3
1
4
1
5
1
5
1
4
1
4
1
5
1
5
1
5
1
1
1
1
1
6
6
6
6
6
1
1
1
1
1
1
7
7
7
7
7
7
1
1
1
1
1
1
1
8
8
8
8
8
8
8
1
1
1
1
1
1
1
9
9
9
9
9
9
9
1
1
1
1
1
1
1
1
10
10
10
10
10
10
10
10
1
1
1
1
1
1
1
1
1
1
12
12
12
12
12
12
12
12
12
12
1
1
1
1
1
1
1
1
1
1
1
1
1
16
16
16
16
16
16
16
16
16
16
16
16
16
1
6
1
7
1
8
1
1
9
9
1
1
10
10
1
1
12
12
1
1
1
16
16
16
6
8
2 3 4 5
4 , 6 , 8 , 10 , 12 , 16
Using the Fraction-Stick Chart, list all the
1
fractions that are equivalent to .
2
a.
2
1
2
1
3
1
4
1
1
1
1
1
6
6
6
6
6
1
1
1
1
1
1
7
7
7
7
7
7
1
1
1
1
1
1
1
8
8
8
8
8
8
8
1
1
1
1
1
1
1
9
9
9
9
9
9
9
1
1
1
1
1
1
1
1
10
10
10
10
10
10
10
10
1
1
1
1
1
1
1
1
1
1
12
12
12
12
12
12
12
12
12
12
1
1
1
1
1
1
1
1
1
1
1
1
1
16
16
16
16
16
16
16
16
16
16
16
16
16
1.
1
2
1
3
1
4
1
5
134
1
What pattern do you notice in the numerators for these fractions?
Numerators increase by 1 until the last
one, which increases by 2.
ELL SUPPORT
▶ Building a Math Word Bank
SMALL-GROUP
ACTIVITY
b.
What pattern do you notice in the denominators for these fractions?
c.
Denominators increase by 2 until the last
one, which increases by 4.
Are the patterns complete? No
d.
What fraction is missing that would make the pattern complete?
15–30 Min
(Differentiation Handbook, p. 142)
2.
To provide language support for fractions, have students use
the Word Bank Template found on Differentiation Handbook,
page 142. They write the term equivalent fraction, draw pictures
related to the term, and write other related words. See the
Differentiation Handbook for more information.
7
14
1
3
Using the Fraction-Stick Chart, list all the fractions that are equivalent to .
2
6
a.
b.
3
, 9,
4
12
What pattern do you notice in these fractions?
Numerators increase by 1 and denominators
increase by 3.
5
6
7
1
Use this pattern to find the next 3 fractions that are equivalent to . 15 , 18 , 21
3
Math Masters, p. 130
Lesson 5 3
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