Comparing Fractions
Objective To guide children as they compare fractions using
region models.
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Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Read fractions. [Number and Numeration Goal 2]
• Compare fractions to _12 . [Number and Numeration Goal 6]
• Use an area model to compare fractions. [Number and Numeration Goal 6]
• Identify patterns and relationships between
numerators and denominators of fractions. [Patterns, Functions, and Algebra Goal 1]
Key Activities
Children use Fraction Cards to identify
fractions that are greater than _12 , less than _12 ,
equal to _12 , close to 0, and close to 1.
Children play Fraction Top-It.
Family
Letters
Assessment
Management
Common
Core State
Standards
Curriculum
Focal Points
Ongoing Learning & Practice
1 2
4 3
Playing Fraction Top-It
Student Reference Book, pp. 287
and 288
per partnership: 1 deck of
Fraction Cards
Children practice comparing fractions.
Math Boxes 8 6
Math Journal 2, p. 196
Children practice and maintain skills
through Math Box problems.
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Exploring Fraction Patterns
Math Masters, p. 257
straightedge
Children construct fractions on a grid.
ENRICHMENT
Comparing and Ordering Fractions
per group: 2 six-sided dice, 3" by 5" index
cards, 3 sheets of 8_12 " by 11" paper
Children compare and order fractions.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problem 2. [Measurement and Reference Frames
Goal 3]
Home Link 8 6
Materials
Student Reference Book, pp. 287 and 288
Home Link 85
Fraction Cards
Math Masters, p. 256
Children practice and maintain skills
through Home Link activities.
Advance Preparation
For the optional Enrichment activity in Part 3, label three sheets of blank 8_12 " by 11" paper with one
of the following measures: 0, _12 , and 1.
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Getting Started
Mental Math and Reflexes
Math Message
Pose problems like the following:
Take out your Fraction Cards. Turn them so the
picture sides (sides with the shaded parts) are faceup. Find all
the unit fractions (fractions that have 1 in the numerator). Put them
in order, from the card with the smallest part shaded to the card
with the largest part shaded. What pattern do you notice?
3 [30s] 90
30 [30s] 900
300 [30s] 9,000
70 [60s] 4,200
700 [60s] 42,000
7,000 [60s] 420,000
50 [400s] 20,000
500 [400s] 200,000
5,000 [400s] 2,000,000
Home Link 8 5 Follow-Up
Have children share their answers for Problems 7–9.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Check to make sure that children have their unit fraction cards
in order from smallest to largest (__16 , __15 , __41 , __13 , and __12 ). Have them
share their observations about the cards. Expect children to point
out that all of the fractions have 1 in the numerator and that
the denominators get smaller from left to right. Guide children
to conclude that when the numerators are the same, the larger
the denominator, the smaller the shaded part, and, therefore, the
smaller the fraction. Ask children to use different fraction cards to
show that this holds true for other fractions with the same
numerator.
Next, have children find and order the following fraction cards
8
2 __
from smallest to largest: __
, 5 , and __
. Ask: What do you notice
10 10
10
about the cards? They each have 10 in the denominator. Describe
which fraction is smallest and which is largest. Sample answer:
The smallest fraction has the smallest numerator and the largest
fraction has the largest numerator. Guide them to conclude that
when the denominators are the same, the larger the numerator,
the larger the shaded part, and, therefore, the larger the fraction.
Ask children to use different fraction cards to show that this holds
true for other fractions with the same denominator.
678
Unit 8 Fractions
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Student Page
Comparing Fractions to
0, and 1
1
_
,
2
Games
WHOLE-CLASS
ACTIVITY
Materials 䊐 1 deck of Fraction Cards (Math Journal 2,
Activity Sheets 5–8)
1 _
2 _
_
, 1, _
, 10 ,
2 4 10 12
Ask children to take out the following Fraction Cards:
4 _
_
, 4 , _3 , _0 , _2 , and _23 . Guide them in the following activities:
8 5 9 4 2
●
●
1
_
2
Use the card to help you find all the cards that are less
2 _
than half-shaded. _14 , _
, 3 , and _04 Compare the numerators and
10 9
denominators of these fractions. What do you observe? The
numerator is less than half of the denominator. Ask children to
name a fraction that is less than half and has a denominator of
8. Sample answers: _38 , _28 , _18 , _08
●
●
2
Skill
Comparing fractions
Object of the game To collect more cards.
Directions
1. Shuffle the Fraction Cards and place the deck
picture-side down on the table.
2. Each player turns over a card from the top of the deck.
Players compare the shaded parts of the cards. The
player with the larger fraction shaded takes both cards.
3. If the shaded parts are equal, the fractions are
equivalent. Each player then turns over another
card. The player with the larger fraction shaded
takes all the cards from both plays.
4. The game is over when all cards have been taken from
the deck. The player with more cards wins.
3
Put all the cards back in the deck and take out the following
10
2 _
2
cards: _14 , _34 , _15 , _45 , _16 , _56 , _
, 8,_
, and _
Find all the cards that
10 10 12
12
Find all the cards that show less than _14 of the card shaded.
2
and _
Ask children which card they used to guide
12
their comparisons. _14 What do you observe about the
numerators and denominators of these fractions? When a very
small part of a card is shaded, the numerator of the fraction is
very small compared to the denominator. The difference
between the numerator and denominator is large.
4
Players turn over a ᎏ4ᎏ card and a ᎏ6ᎏ card.
The
the
3
ᎏᎏ card has a larger shaded
4
3
ᎏᎏ card takes both cards.
4
area. The player holding
4
6
3
4
1
4
ᎏᎏ card and a ᎏᎏ card.
2
8
The shaded parts are equal. Each player turns over
another card. The player with the larger Fraction Card
takes all the cards.
Players turn over a
1
2
4
8
1
2
4
8
two hundred eighty-seven
287
Student Reference Book, p. 287
Find all the cards that are exactly half-shaded. _12 and _48
Compare the numerators and denominators of these fractions.
What do you observe? The numerator is exactly half of the
denominator. Ask children to name a fraction that is equal to
6
half and that has a denominator of 12. _
12
10 _
8
, 4 , and _
Ask
show more than _34 of the card shaded. _56 , _
12 5
10
children which card they used to guide their comparisons. _34
What do you observe about the numerators and denominators
of these fractions? When most of a card is shaded, the
numerator of the fraction is close to the denominator. The
difference between the numerator and denominator is small.
●
Players
10
4 _
_
, 2, _
,
5 2 12
Find all the cards that are more than half-shaded.
and
Compare the numerators and denominators of these
fractions. What do you observe? The numerator is more than
half of the denominator. Ask children to name a fraction that is
more than half and has a denominator of 8. Sample answers: _58 ,
6 _
_
, 7 , _8 , _9 , and so on
8 8 8 8
2
_
3
Fraction Top-It
Adjusting
the Activity
ELL
Play the advanced version of Fraction Top-It.
Directions are on page 288 in the Student
Reference Book.
AUDITORY
1 _
_
, 2 , _1 ,
5 10 6
KINESTHETIC
TACTILE
VISUAL
Student Page
Games
Fraction Top-It
(Advanced Version)
Materials 䊐 1 deck of Fraction Cards (Math Journal 2,
Activity Sheets 5–8)
Players
2
Skill
Comparing fractions
Object of the game To collect more cards.
Directions
Playing Fraction Top-It
WHOLE-CLASS
ACTIVITY
(Student Reference Book, pp. 287 and 288)
Have children read the rules for Fraction Top-It in the Student
Reference Book on page 287. Demonstrate a few rounds and then
have partners play the game.
1. Shuffle the Fraction Cards and place the deck picture-side
down on the table.
2. Each player takes a card from the top of the deck but does
not turn it over. The cards remain picture-side down.
3. Players take turns. When it is your turn:
◆ Say whether you think your fraction is greater than,
less than, or equivalent to the other player’s fraction.
◆ Turn the cards over and compare the shaded parts. If
you were correct, take both cards. If you were wrong,
the other player takes both cards.
4. The game is over when all cards have been taken from the
deck. The player with more cards wins.
2
1
Joel draws a ᎏ8ᎏ card. Sue draws a ᎏ4ᎏ
card. It is Sue’s turn, and she says that her
fraction is less than Joel’s. They turn their
cards over and find that the shaded areas
are equal. The fractions are equivalent. Sue
was wrong, so Joel takes both cards.
288
2
8
1
4
two hundred eighty-eight
Student Reference Book, p. 288
Lesson 8 6
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Student Page
Date
Time
LESSON
1
Write 4 fractions equivalent to _
4.
Sample answers:
10
_
2
_
40
8
4
_
2.
Complete.
24
3
100
_1
2
4.
_1
4
hour
247
Children continue to practice comparing fractions by playing
Fraction Top-It. Have children use half-sheets of paper to record
each round using <, >, or = to compare the fraction pairs.
Draw a set of 12 Xs. Circle 9 of
them. What fraction of the whole
set are the 9 Xs?
9
3
4
12
_ or _
circle(s).
Math Boxes 8 6
Solve. Fill in the circle that shows
the best answer.
6.
(2 × 90) + 7 =
Solve. Use your calculator. Pretend
the division key is broken.
(Math Journal 2, p. 196)
Christopher and Rochelle are
packing 212 cookies in boxes.
Each box holds 20 cookies. How
many full boxes can they pack?
A 98
B 99
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 8-8. The skill in Problem 6
previews Unit 9 content.
10 boxes
Answer:
C 187
(unit)
D 194
INDEPENDENT
ACTIVITY
24
5.
PARTNER
ACTIVITY
(Student Reference Book, pp. 287 and 288)
1
minutes = __
hour
2
15 minutes =
30
Playing Fraction Top-It
day
weeks = 21 days
30
If I wanted to have an equal
chance of taking out a circle
or a square, I would put in
4
hours = 1 day
12 hours =
25
_
16
3.
2 Ongoing Learning & Practice
Math Boxes
86
1.
16
Math Journal 2, p. 196
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Ongoing Assessment:
Recognizing Student Achievement
2/10/11 12:50 PM
Math Boxes
Problem 2
Use Math Boxes, Problem 2 to assess children’s ability to describe relationships
between equivalent units of time. Children are making adequate progress if they
successfully complete Problem 2. Some children may be able to describe the
relationship between the number of hours in 1 day and the number of hours in
21 days.
[Measurement and Reference Frames Goal 3]
Home Link 8 6
INDEPENDENT
ACTIVITY
(Math Masters, p. 256)
Home Link Master
Name
Date
Home Connection Children shade rectangles to represent
given fractions. They use the shaded rectangles to
determine which fractions are greater than or equal to _12 .
Then they compare fractions without using shaded
rectangles.
Time
1
Comparing Fractions to _
2
HOME LINK
86
Family
Note
Your child’s class is comparing fractions to determine whether they are larger, smaller, or
1
equal to _
. Ask your child to explain how to tell which category a fraction fits into.
2
For more on this topic, see Student Reference Book pages 13, 31, and 32.
13
31 32
Please return this Home Link to school tomorrow.
Shade each rectangle to match the fraction below it. Example:
1.
2.
3.
4.
3
8
2
3
5.
2
5
6.
3
6
7.
1
4
2
4
8.
5
10
5
9
7
8
1
_
_2 , _7 , _5
3 8 9
5
_3 , _
6 10
9. List the fractions above that are greater than 2 .
1
_
10. List the fractions above that are equal to 2 .
Insert <, >, or = in each problem below. Draw pictures to help you.
6
_
>
>
11. 8
10
_
13. 12
1
_
2
_
12. 9
2
1
_
2
6
_
14. 12
<
=
1
_
< means is less than
> means is greater than
= means is equal to
2
1
_
2
Practice
Solve.
56
15. 7 × 8 =
17. 8 ×
3
16. 54 = 6 ×
= 24
18. 9 × 8 =
9
72
Math Masters, p. 256
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Unit 8 Fractions
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Teaching Master
Name
3 Differentiation Options
Date
LESSON
86
䉬
Time
Exploring Fraction Patterns
For each problem, record your work on the grid below.
1. Use a straightedge to divide the
PARTNER
ACTIVITY
READINESS
Exploring Fraction Patterns
square into halves. Label each
on your drawing.
1
ᎏᎏ
2
1
2
1
2
5–15 Min
(Math Masters, p. 257)
To explore the patterns between the numerators and
denominators of fractions, have children use a straightedge to
construct fractions on a grid. When children have finished with
Math Masters, page 257, have them discuss the patterns they see.
Sample answer: Every time the unit fractions are divided in half,
the numerators stay the same and the denominators double. The
numerators and denominators of the equivalent fractions are
1
multiples. Multiply _
× _12 to find the fraction that names the next
16
1
smallest section, _
. Continue with the pattern to find the next
32
1
1
_
smallest section. 32 × _12 = _
, and so on.
64
This is the WHOLE or ONE.
2. Use a straightedge to divide one of your halves into 2 equal parts.
What fraction of the WHOLE is each new section worth?
Write the fraction equivalent to ᎏ12ᎏ.
2
ᎏᎏ
4
1
ᎏᎏ
4
3. Use a straightedge to divide one of your smallest sections into
2 equal parts.
What fraction of the WHOLE is each new section worth?
Write the fraction equivalent to ᎏ12ᎏ.
1
ᎏᎏ
8
4
ᎏᎏ
8
4. If you were to divide your smallest section into 2 equal parts, what
fraction of the WHOLE would each new section be worth?
1
ᎏᎏ
16
Write the fraction equivalent to ᎏ12ᎏ.
8
ᎏᎏ
16
5. On the back of your paper, list at least three patterns you notice in the
fractions you have made on the grid and the fractions you have written
on this paper.
Math Masters, p. 257
SMALL-GROUP
ACTIVITY
ENRICHMENT
Comparing and Ordering
15–30 Min
Fractions
To apply children’s understanding of comparing and ordering
fractions based on relationships between numerators and
denominators, have them make a set of 10 Fraction Cards to
compare. Lay out the three labeled 8_12 " by 11" papers in line
from 0 to 1 with space between them. (See Advance Preparation.)
Children roll two dice, and make and record a 2-digit number from
the digits. They repeat this. They use one of the numbers as the
numerator of a fraction and the other as the denominator. (They
should begin by making all their fractions less than or equal to
one.) They write each fraction on a 3" by 5" index card.
When they have written 10 fractions, have them decide whether
to place each fraction between or on the 0, _12 , and 1 labels. Some
children may be able to put some of the fractions in order.
0
11
63
21
65
16
35
1
2
24
42
35
53
24
33
42
51
53
56
23
24
1
11
11
Variation: Roll only 1 die each time instead of 2
to generate 1-digit numbers.
Lesson 8 6
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