EM07TLG2_G3_U08_L05.qxd
1/17/06
10:39 AM
Page 672
Getting Started
Mental Math and Reflexes
Math Message
Children solve division number stories. They write
answers on slates and explain their strategies to the
class. Provide counters.
Take an envelope. Carefully cut apart the 32
Fraction Cards on Activity Sheets 5–8 at the back of your journal.
Put them in the envelope.
There are 36 children in the class. They sit in rows of 4.
How many rows are there? 9 rows
8 children share 72 pennies. How many pennies per child?
9 pennies
5 children share 56 strawberries. How many strawberries
per child? 11 strawberries, with 1 left over
Home Link 8 4 Follow-Up
䉬
Briefly review answers. Place new items in the
Fractions Museum.
1 Teaching the Lesson
䉴 Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Math Journal 2, Activity Sheets 5–8)
Check that children have cut out all 32 Fraction Cards.
䉴 Using Fraction Cards to
WHOLE-CLASS
DISCUSSION
Extend Fraction Concepts
(Math Journal 2, Activity Sheets 5–8)
Ask children to turn their cards to the picture side. Share
observations. (Keep this part of the lesson brief.)
Student Page
Date
Time
LESSON
Fraction Cards
8 5
䉬
䉯 Each card represents a whole, or ONE. All cards are the
same size.
䉯 The number of strips (or bars) varies from card to card.
Some strips are shaded; others are unshaded.
2
2
3
4
䉯 The fraction shown on the back of the card represents the
shaded fractional part of the ONE.
1
3
2
3
䉯 Some fractions have the same numerator and different
denominators. That means the ONE is divided into different
numbers of equal parts.
䉯 The larger the denominator, the more parts the ONE is divided
into, and the smaller each part.
3
6
1
4
Point out that any fraction with 1 in the numerator is called a
1
unit fraction. For example, ᎏ2ᎏ is a unit fraction.
1 1
S
1
2
2
6
f
Math Journal 2, Activity Sheet 5
672
Unit 8 Fractions
Ask children to name other unit fractions. Sample answers: ᎏ3ᎏ, ᎏ4ᎏ,
1
1
ᎏᎏ, ᎏᎏ To support English language learners, write unit fraction on
10 98
the board along with a list of examples.
EM07TLG2_G3_U08_L05.qxd
1/17/06
10:39 AM
Page 673
Student Page
䉴 Investigating Equivalent
WHOLE-CLASS
ACTIVITY
Fractions
Date
Time
LESSON
Table of Equivalent Fractions
8 5
䉬
Use your deck of Fraction Cards to find equivalent fractions.
Record them in the table.
(Math Journal 2, p. 194)
Fraction
Equivalent Fractions
0
ᎏᎏ
4
2 3
ᎏᎏ, ᎏᎏ,
4 6
4 5
ᎏᎏ, ᎏᎏ,
4 5
2 3
ᎏᎏ, ᎏᎏ,
6 9
4 6
ᎏᎏ, ᎏᎏ,
6 9
2
ᎏᎏ
8
6
ᎏᎏ
8
2
ᎏᎏ
10
8
ᎏᎏ
10
0
ᎏᎏ
2
1
ᎏᎏ
2
Each partnership uses one set of 32 Fraction Cards. Guide the
class through the following activities.
2
ᎏᎏ
2
1
ᎏᎏ
3
2
ᎏᎏ
3
Adjusting the Activity
1
ᎏᎏ
4
3
ᎏᎏ
4
At first, use the 16 cards on Activity Sheets 5 and 6. Then use the full
deck of 32 cards.
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
1
ᎏᎏ
5
4
ᎏᎏ
5
2
ᎏᎏ
12
1
ᎏᎏ
6
V I S U A L
䉬
10
ᎏᎏ
12
5
ᎏᎏ
6
1
Have children find the ᎏ2ᎏ card. Their task is to find as many other
cards in the deck as they can that have exactly the same amount
shaded. Demonstrate side-by-side comparisons for exact matches.
1
As children name fractions equivalent to ᎏ2ᎏ, they record them in
the Table of Equivalent Fractions on journal page 194. Remind
them that these fractions are called equivalent fractions.
Equivalent fractions name the same fractional part of the ONE.
1
Have children find cards with fractions equivalent to the ᎏ3ᎏ card
and record them in the table.
4 5
6
ᎏᎏ, ᎏᎏ, ᎏᎏ
8 10 12
9
ᎏᎏ
9
4
ᎏᎏ
12
8
ᎏᎏ
12
Describe any patterns you see.
2
Sample answers: Each of the fractions equivalent to ᎏ2ᎏ has
the same numerator and denominator. Except for the row of
2
fractions equivalent to ᎏ2ᎏ, all the numerators and denominators
in each row are multiples of the numerators and denominators
of the given fraction for that row.
Math Journal 2, p. 194
2
Repeat with the ᎏ3ᎏ card, checking for patterns and predictions
before matching equivalent Fraction Cards.
Partners then sort the rest of the cards into as many sets of
equivalent fractions as they can and record them in the table.
Bring the class together to share the equivalent fractions found in
the deck and the patterns they observed among the equivalent
fractions.
1 Whole
0
䉴 Identifying Equivalent Fractions
1
WHOLE-CLASS
ACTIVITY
(Math Journal 2, p. 191)
Halves
1
2
0
2
2
2
Fourths
Discuss how to use the Fraction Number-Line Poster to identify
equivalent fractions.
0
4
1
4
2
4
3
4
4
4
Eighths
1
Ask: What part of the fourths strip is the same size as ᎏ2ᎏ of the ONE
2
2
1
strip? ᎏ4ᎏ Is ᎏ4ᎏ another name for ᎏ2ᎏ? Yes What are some other names
1 3 4
on the Fraction Number-Line Poster for ᎏ2ᎏ? ᎏ6ᎏ, ᎏ8ᎏ
Show how to place a straightedge vertically on the page next to
1
1
the fraction ᎏ2ᎏ to find fractions equivalent to ᎏ2ᎏ. Have children use a
1
3
1
2
straightedge to find other names for ᎏ4ᎏ, for ᎏ4ᎏ, for ᎏ3ᎏ, and for ᎏ3ᎏ. (You
may need to point out that equivalent fractions may not line up
exactly if they are off slightly in the gluing or cutting. Because the
intervals are so large, the error should not prevent children from
finding the equivalencies.)
0
8
1
8
2
8
3
8
4
8
5
8
6
8
7
8
8
8
Thirds
0
3
1
3
2
3
3
3
Sixths
0
6
1
6
2
6
3
6
4
6
5
6
6
6
A straightedge highlights equal fractions.
Ask: If the ONE strip were divided into 10 equal parts, how many
1
of these parts would be the same size as ᎏ2ᎏ of the ONE strip?
5
5 parts What fraction of the ONE strip is this? ᎏ1ᎏ
0
Lesson 8 5
䉬
673
EM07TLG2_G3_U08_L05.qxd
1/17/06
10:39 AM
Page 674
Student Page
Games
Equivalent Fractions Game
2
Skill
Recognizing fractions that are equivalent
WHOLE-CLASS
ACTIVITY
Fractions Game
Materials 䊐 1 deck of Fraction Cards (Math Journal 2,
Activity Sheets 5– 8)
Players
䉴 Playing the Equivalent
(Student Reference Book, pp. 283 and 284)
Object of the game To collect more Fraction Cards.
Directions
1. Shuffle the Fraction Cards and place the deck
picture-side down on the table.
2. Turn the top card over near the deck of cards.
3. Players take turns. When it is your turn, turn over the
top card from the deck. Try to match this card with a
picture-side up card on the table.
◆ If you find a match, take the 2 matching cards.
Then, if there are no cards left picture-side up, turn
the top card over near the deck.
◆ If you cannot find a match, place your card pictureside up next to the other cards. Your turn is over.
4. The game ends when all cards have been matched. The
player with more cards wins.
Have children read the rules for the Equivalent Fractions Game
on page 283 in the Student Reference Book. Demonstrate how to
play the game.
Before children put their cards in their tool kits, they should store
them in an envelope. The Fraction Cards will be used again in
Lesson 8-6.
Example The top card is turned over and put
4
on the table. The picture shows ᎏ6ᎏ.
Player 1 turns over the
2
ᎏᎏ
3
4
card. This card matches ᎏ6ᎏ.
Player 1 takes both cards. There are no cards left
4
6
2
3
4
6
2
3
6
8
0
4
6
8
0
4
picture-side up. So Player 1 turns over the top card
6
and puts it near the deck. The picture shows ᎏ8ᎏ.
Player 2 turns over the
0
ᎏᎏ
4
card. There is no match.
6
This card is placed next to ᎏ8ᎏ. It is Player 1’s turn again.
Student Reference Book, p. 283
Adjusting the Activity
Another version of Equivalent Fractions Game has players match the
fraction sides of cards with the picture sides of the cards. The rules for this
version are on page 284 in the Student Reference Book.
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
2 Ongoing Learning & Practice
䉴 Playing The Block-Drawing
SMALL-GROUP
ACTIVITY
Game
(Math Masters, p. 398; Student Reference Book,
pp. 280 and 281)
Children practice making and testing predictions by playing
The Block-Drawing Game, introduced in Lesson 8-2. Detailed
directions are on pages 280 and 281 in the Student Reference
Book. Have children record their predictions on an Exit Slip
(Math Masters, page 398).
Student Page
Games
Equivalent Fractions Game
(Advanced Version)
Materials 䊐 1 deck of Fraction Cards
(Math Journal 2,
Activity Sheets 5– 8)
6
8
Players
2
Skill
Recognizing fractions that are equivalent
2
8
1
3
Object of the game To collect more Fraction Cards.
Directions
1. Shuffle the Fraction Cards and place the deck
picture-side down on the table.
2. Turn the top card over near the deck of cards.
Ongoing Assessment:
Recognizing Student Achievement
◆ If there is no match, place your card next to the
other cards, picture-side up. Your turn is over.
◆ If there is a match but you did not find it, the other
player can take the matching cards.
4. The game ends when all cards have been matched. The
player with more cards wins.
Student Reference Book, p. 284
674
Unit 8 Fractions
夹
Use the Exit Slip to assess children’s progress toward making and testing
predictions for simple experiments. Children are making adequate progress if
they make reasonable predictions based on the data collected from the draws.
Some children may be able to make the connection between the number of
draws made and the reliability of their predictions.
[Data and Chance Goal 4]
3. Players take turns. When it is your turn, take the top
card from the deck, but do not turn it over (keep
the picture side down). Try to match the fraction
with one of the picture-side up cards on the table.
◆ If you find a match, turn the card over to see if you
matched the cards correctly. If you did, take both
cards. Then, if there are no cards left picture-side
up, turn the top card over.
Exit Slip
䉴 Math Boxes 8 5
䉬
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 195)
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 8-7. The skill in Problem 6
previews Unit 9 content.
EM07TLG2_G3_U08_L05.qxd
1/17/06
11:17 AM
Page 675
Student Page
䉴 Home Link 8 5
INDEPENDENT
ACTIVITY
䉬
(Math Masters, pp. 252 and 253)
Date
Time
LESSON
Math Boxes
8 5
䉬
1.
In the number 3.514:
Home Connection Children shade fractions of regions,
identify fractions of sets, and identify equivalent fractions.
2.
3 ones
the 3 means
1 hundredth
5 tenths
4 thousandths
the 1 means
the 5 means
the 4 means
Which is true? Fill in
the circle for the
best answer.
The spinner is
white
blue
A unlikely to
land on blue
B less likely to land on white
C equally likely to land on
blue or white
D likely to land on green
35
3 Differentiation Options
3.
Write 4 fractions equivalent to
Sample answers:
SMALL-GROUP
ACTIVITY
READINESS
䉴 Shading Equivalent Fractions
1
ᎏᎏ .
2
5.
5–15 Min
of Regions
2
4
13
26
50
100
7
14
4.
Use a straightedge. Draw the other
half of the symmetric shape.
6.
Solve.
122 123
30
9 children share 18 candies.
How many candies per child?
2 candies
54 ⫼ 9 ⫽
How many candies left over?
27 ⫼ 3 ⫽
0 candies
6
8
16 books in all. 3 books per shelf.
(Math Masters, p. 254)
How many shelves? 5 shelves
How many books left over?
To provide experience with equivalent fractions, have children
shade regions of similar shapes on Math Masters, page 254.
Date
HOME LINK
䉬
Family
Note
9
73
52 53
Home Link Master
Name
Time
Date
HOME LINK
Equivalent Fractions
85
⫽ 64 ⫼ 8
Math Journal 2, p. 195
Home Link Master
Name
6
9
⫽ 36 ⫼ 6
45 ⫼ 5 ⫽
1 book
92 93
Equivalent Fractions
85
䉬
The class continues fraction work by finding equivalent names for fractions. Different fractions
that name the same amount are called equivalent fractions. The fractions that complete
Problems 4–6 are equivalent. If needed, help your child name the fractional parts in these
problems. Ask your child to explain the fraction name she or he chooses in Problem 9—a
fraction that is equivalent to ᎏ14ᎏ and describes the fraction of cats circled.
Time
7. Circle
1
ᎏᎏ
4
continued
of the cats.
27–30
Please return this Home Link to school tomorrow.
The pictures show three kinds of pie. Use a straightedge to do the following:
1. Divide the peach
pie into 4 equal
pieces. Shade 2 of
the pieces.
2. Divide the blueberry
pie into 6 equal
pieces. Shade 3 of
the pieces.
3. Divide the cherry
pie into 8 equal
pieces. Shade 4 of
the pieces.
8. How many cats did you circle?
4 cats
4
ᎏᎏ
16
9. Write a fraction that describes the group of
cats you circled and that is equivalent to 14 .
Each whole rectangle below is ONE. Write a fraction inside each part.
10.
peach pie
blueberry pie
What fraction of each pie did you shade?
ᎏ2ᎏ
4 of the peach pie.
Write another name for this fraction:
ᎏ1ᎏ
2
6 of the blueberry pie.
Write another name for this fraction:
ᎏ1ᎏ
2
4. I shaded
5. I shaded
6. I shaded
ᎏ3ᎏ
ᎏ4
8ᎏ
of the cherry pie.
Write another name for this fraction:
ᎏ1ᎏ
2
1
8
1
4
cherry pie
4
8
, 24 , or
1
2
11.
1
6
2
6
or
1
6
1
3
2
6
Math Masters, p. 252
1
8
or
1
3
Math Masters, p. 253
Lesson 8 5
䉬
675
EM07TLG2_G3_U08_L05.qxd
1/17/06
10:40 AM
Page 676
Teaching Master
Name
Date
LESSON
Time
85
䉬
PARTNER
ACTIVITY
ENRICHMENT
Equivalent Fractions in Shapes
䉴 Looking for a Rule
1
ᎏᎏ of each
2
circle. Complete the
fractions.
1. Shade
5–15 Min
(Math Journal 2, p. 194; Math Masters, p. 255)
2
1
ᎏᎏ
2
1
ᎏᎏ
2
111
⫽ ᎏᎏ
4
1
ᎏᎏ
3
1
ᎏᎏ
3
222
⫽ ᎏ
6
1
ᎏᎏ ⫽
2
3
222
ᎏ
6
1
ᎏᎏ of each
3
rectangle. Complete
the fractions.
2. Shade
2
1
ᎏᎏ
3
3
222
⫽ ᎏ
9
3. Make up your own:
222 of each
Shade ᎏ
square. Write the
fractions.
⫽
Answers vary.
⫽
To apply children’s understanding of equivalent fractions,
have them look for a rule about how fractions equivalent
1
to ᎏ2ᎏ are related to one another. (For example, equivalent
fractions can be generated by multiplying the numerator and the
denominator by the same whole number.) They use their rule to
complete the remaining problems on Math Masters, page 255.
NOTE Not every pair of equivalent fractions can be found easily with this rule,
3
4
for example, ᎏ6ᎏ and ᎏ8ᎏ. However, applying the rule when one of the fractions is a
1
unit fraction is usually easy. For example, if the numerator and denominator of ᎏ3ᎏ
2
are multiplied by 2, the result is the equivalent fraction ᎏ6ᎏ; if the multiplier is 3, the
3
result is ᎏ9ᎏ, and so on.
ENRICHMENT
Math Masters, p. 254
䉴 Making Name-Collection
SMALL-GROUP
ACTIVITY
15–30 Min
Boxes for Fractions
To apply children’s understanding of fraction concepts,
have them work in small groups to make poster-size
name-collection boxes for familiar fractions.
Encourage them to include region, collection, and number-line
representations as well as equivalent fractions, expressions with
numbers, and expressions with words. Assign each small group a
1
1
fraction for their name-collection box—for example, ᎏ3ᎏ or ᎏ4ᎏ.
ELL SUPPORT
Teaching Master
Name
Date
LESSON
Time
Rules for Equivalent Fractions
85
䉬
䉴 Building a Math Word Bank
SMALL-GROUP
ACTIVITY
5–15 Min
(Differentiation Handbook)
1. Look at Math Journal 2, page 194. Record the fractions equivalent
to ᎏ12ᎏ below. As you record them, put them in an order that will help
you find a pattern.
1
ᎏᎏ
2
2
ᎏ
4
3
ᎏ
6
4
ᎏ
8
5
ᎏ
10
6
ᎏ
12
2. Use your pattern to write a rule for finding equivalent fractions.
Write your rule on the lines below.
Sample answer:
Multiply the numerator and denominator by the same whole
number to find equivalent fractions.
Try your rule to see whether it works. List 3 other fractions equivalent to ᎏ12ᎏ
using your rule. (Use pictures or counters to check your fractions.)
8
ᎏᎏ
16
7
ᎏᎏ
14
9
ᎏᎏ
18
1
3
3. Use your rule to find 2 fractions equivalent to ᎏᎏ.
Check your answers with the Fraction Cards.
2
ᎏᎏ
6
3
ᎏᎏ
9
Try This
4. Use your rule to find equivalent fractions for the fractions in the table
below. Show any work that you do on the back of this page.
Fraction
Equivalent Fractions
1
ᎏᎏ
8
2
3
4
5
ᎏᎏ, ᎏᎏ, ᎏᎏ, ᎏᎏ
16 24 32 40
5
ᎏᎏ
8
10 15 20
ᎏᎏ, ᎏᎏ, ᎏᎏ
16 24 32
2
ᎏᎏ
9
4
6
8
ᎏᎏ, ᎏᎏ, ᎏᎏ
18 27 36
Math Masters, p. 255
676
Unit 8 Fractions
Sample answers:
To provide language support for fractions, have children use the
Word Bank template found in the Differentiation Handbook. Ask
children to write the term equivalent fraction, draw a picture
representing the term, and write other related words. See the
Differentiation Handbook for more information.
EM07TLG2_G3_U08_LOP06.qxd
1/17/06
1:47 PM
Page 677
Objective To guide children as they compare fractions using
region models.
1
materials
Teaching the Lesson
Key Activities
1
1
Children use Fraction Cards to identify fractions that are greater than ᎏ2ᎏ, less than ᎏ2ᎏ,
1
equal to ᎏ2ᎏ, close to 0, and close to 1. Children play Fraction Top-It.
Key Concepts and Skills
ⵧ Student Reference Book,
pp. 287 and 288
ⵧ Home Link 8 5
䉬
ⵧ Fraction Cards
• Read fractions.
[Number and Numeration Goal 2]
1
• Compare fractions to ᎏ2ᎏ.
[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]
2
Ongoing Learning & Practice
Children play the Equivalent Fractions Game.
Children practice and maintain skills through Math Boxes and Home Link activities.
Ongoing Assessment: Recognizing Student Achievement Use journal page 196.
[Measurement and Reference Frames Goal 3]
3
Children construct fractions on a grid.
ⵧ Math Journal 2, p. 196
ⵧ Student Reference Book,
pp. 283 and 284
ⵧ Home Link Master (Math Masters,
p. 256)
ⵧ Fraction Cards
materials
Differentiation Options
READINESS
materials
ENRICHMENT
Children compare and order fractions.
ⵧ Teaching Master (Math Masters,
p. 257)
ⵧ dice
ⵧ 3" by 5" index cards
ⵧ 3 sheets of 8 ᎏ12ᎏ" by 11" paper
ⵧ straightedge
See Advance Preparation
Additional Information
Advance Preparation For the optional Enrichment activity in Part 3, label three sheets of
1
1
blank 8ᎏ2ᎏ-by-11 paper with one of the following measures: 0, ᎏ2ᎏ, and 1.
Technology
Assessment Management System
Math Boxes, Problem 2
See the iTLG.
Lesson 8 6
䉬
677
EM07TLG2_G3_U08_L06.qxd
1/17/06
10:40 AM
Page 678
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
䉬
Have children share their answers for Problems 7–9.
1 Teaching the Lesson
䉴 Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Have children share their observations about the unit fraction
cards— ᎏ16ᎏ, ᎏ51ᎏ, ᎏ41ᎏ, ᎏ31ᎏ, and ᎏ21ᎏ. Guide them to conclude that the larger
the denominator, the smaller the shaded part—and therefore, the
smaller the fraction. Clarify with children that this is the case in
this problem because all the numerators are 1.
䉴 Comparing Fractions to ᎏ12ᎏ,
WHOLE-CLASS
ACTIVITY
0, and 1
1 1
2
10
ᎏᎏ
Ask children to take out the following Fraction Cards: ᎏ2ᎏ, ᎏ4ᎏ, ᎏ1ᎏ
0 , 12 ,
4 4 3 0 2
2
ᎏᎏ, ᎏᎏ, ᎏᎏ, ᎏᎏ, ᎏᎏ, and ᎏᎏ. Guide them in the following activities:
8 5 9 4 2
3
Use the ᎏ2ᎏ card to help you find all the cards that are less
1 2 3
0
than half-shaded. ᎏ4ᎏ, ᎏ10ᎏ, ᎏ9ᎏ, and ᎏ4ᎏ Compare the numerators and
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
3 2 1 0
8. Sample answers: ᎏ8ᎏ, ᎏ8ᎏ, ᎏ8ᎏ, ᎏ8ᎏ
●
Find all the cards that are more than half-shaded. ᎏ5ᎏ, ᎏ2ᎏ, ᎏ1ᎏ
2 , and
2
ᎏᎏ Compare the numerators and denominators of these
3
fractions. What do you observe? The numerator is more than
half of the denominator. Ask children to name a fraction that is
5
more than half and has a denominator of 8. Sample answers: ᎏ8ᎏ,
6 7 8 9
ᎏᎏ, ᎏᎏ, ᎏᎏ, ᎏᎏ, and so on
8 8 8 8
1
4
Find all the cards that are exactly half-shaded. ᎏ2ᎏ and ᎏ8ᎏ
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. ᎏ12ᎏ
●
678
Unit 8 Fractions
1
●
4 2 10
EM07TLG2_G3_U08_L06.qxd
1/17/06
10:40 AM
Page 679
Student Page
●
Games
Put all the cards back in the deck and take out the following
8
2
1 3 1 4 1 5 2
10
ᎏᎏ
cards: ᎏ4ᎏ, ᎏ4ᎏ, ᎏ5ᎏ, ᎏ5ᎏ, ᎏ6ᎏ, ᎏ6ᎏ, ᎏ10ᎏ, ᎏ10ᎏ, ᎏ1ᎏ
2 , and 12 . Find all the cards that
3
ᎏᎏ
4
8
ᎏᎏ
10
5 10 4
ᎏᎏ, ᎏᎏ, ᎏᎏ,
6 12 5
show more than of the card shaded.
and
Ask
3
children which card they used to guide their comparisons. ᎏ4ᎏ
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.
●
1
ᎏᎏ
4
Find all the cards that show less than of the card shaded.
1 2 1
2
ᎏᎏ, ᎏᎏ, ᎏᎏ, and ᎏᎏ Ask children which card they used to guide
5 10 6
12
1
their comparisons. ᎏ4ᎏ 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.
䉴 Playing Fraction Top-It
WHOLE-CLASS
ACTIVITY
Fraction Top-It
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
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.
Examples Players turn over a ᎏ3ᎏ card and a ᎏ4ᎏ card.
4
6
The
the
3
ᎏᎏ card has a larger shaded
4
3
ᎏᎏ card takes both cards.
4
area. The player holding
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.
3
4
4
6
3
4
4
6
Players turn over a
1
2
4
8
1
2
4
8
Student Reference Book, p. 287
(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.
Adjusting the Activity
Play the advanced version of Fraction Top-It. Directions are on
page 288 in the Student Reference Book.
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
2 Ongoing Learning & Practice
Student Page
Games
䉴 Playing the Equivalent
PARTNER
ACTIVITY
Fractions Game
(Student Reference Book, pp. 283 and 284)
The Equivalent Fractions Game was introduced in Lesson 8-5. If
necessary, children can read the rules in the Student Reference
Book on pages 283 and 284.
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
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.
Example
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.
2
8
1
4
2
8
1
4
Student Reference Book, p. 288
Lesson 8 6
䉬
679
EM07TLG2_G3_U08_L06.qxd
1/17/06
1:22 PM
Page 680
Student Page
Date
86
1
4
Write 4 fractions equivalent to ᎏᎏ.
Sample answers:
2
10
8
40
4
16
夹
2.
24
hours ⫽ 1 day
1
ᎏᎏ
2 day
12 hours ⫽
3
weeks ⫽ 21 days
30
1 hour
minutes ⫽ ᎏ
4.
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.
2
1
ᎏᎏ
4 hour
15 minutes ⫽
If I wanted to have an equal
chance of taking out a circle
or a square, I would put in
4
(Math Journal 2, p. 196)
Complete.
25
100
30
3.
247
Draw a set of 12 Xs. Circle 9 of
them. What fraction of the whole
set are the 9 Xs?
9
ᎏᎏ
12
circle(s).
or
3
ᎏᎏ
4
24
5.
INDEPENDENT
ACTIVITY
䉬
Math Boxes
䉬
1.
䉴 Math Boxes 8 6
Time
LESSON
Solve. Fill in the circle that shows
the best answer.
6.
(2 ⫻ 90) ⫹ 7 ⫽
Solve. Use your calculator. Pretend
the division key is broken.
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
D 194
Math Boxes
Problem 2
夹
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 minutes in a ᎏ21ᎏ day and the number of hours
in 21 days.
[Measurement and Reference Frames Goal 3]
10 boxes
Answer:
C 187
Ongoing Assessment:
Recognizing Student Achievement
(unit)
16
䉴 Home Link 8 6
䉬
Math Journal 2, p. 196
INDEPENDENT
ACTIVITY
(Math Masters, p. 256)
Home Connection Children shade rectangles to represent
given fractions. They use the shaded rectangles to
1
determine which fractions are greater than or equal to ᎏ2ᎏ.
Then they compare fractions without using shaded
rectangles.
Home Link Master
Name
Date
HOME LINK
Time
Comparing Fractions to
86
䉬
Family
Note
1
ᎏᎏ
2
Your child’s class is comparing fractions to determine whether they are larger, smaller, or
equal to ᎏ12ᎏ . Ask your child to explain how to tell which category a fraction fits into.
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.
2
3
4.
3
8
5.
2
5
6.
3
6
7.
1
4
2
4
8.
5
10
5
9
7
8
2 7 5
ᎏᎏ, ᎏᎏ, ᎏᎏ
1
ᎏᎏ. 3
8 9
2
3 5
ᎏᎏ, ᎏᎏ
6 10
9. List the fractions above that are greater than
1
10. List the fractions above that are equal to ᎏ2ᎏ.
Insert ⬍, ⬎, or ⫽ in each problem below. Draw pictures to help you.
11.
6
ᎏᎏ
8
13.
10
ᎏᎏ
12
⬎
⬎
1
ᎏᎏ
2
1
ᎏᎏ
2
12.
2
ᎏᎏ
9
14.
6
ᎏᎏ
12
⬍
⫽
⬍ means is less than
⬎ means is greater than
⫽ means is equal to
1
ᎏᎏ
2
1
ᎏᎏ
2
Practice
Solve.
56
15. 7 ⫻ 8 ⫽
17. 8 ⫻
3
16. 54 ⫽ 6 ⫻
⫽ 24
Math Masters, p. 256
680
Unit 8 Fractions
18. 9 ⫻ 8 ⫽
9
72
EM07TLG2_G3_U08_L06.qxd
1/17/06
10:40 AM
Page 681
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
䉴 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
1
multiples. Multiply 16 2 to find the fraction that names the next
1
smallest section, 32. Continue with the pattern to find the next
1
1
1
smallest section. 32 2 64, and so on.
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.
4
ᎏᎏ
8
1
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
䉴 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
1
compare. Lay out the three labeled 82 in. by 11 in. 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 in. by 5 in. index card.
When they have written 10 fractions, have them decide whether
1
to place each fraction between or on the 0, 2, 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
䉬
681