Naming Parts
with Fractions
Objective To guide children as they use fractions to name a of b
equal parts.
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Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Practicing with Fact Triangles
• Use manipulatives to solve problems
involving fractional parts of collections. ×, ÷ Fact Triangles
Children practice multiplication and
division facts with Fact Triangles.
[Number and Numeration Goal 2]
• Identify equivalent halves and fourths
of a shaded region. [Number and Numeration Goal 5]
• Use shaded regions to compare fractions. Math Boxes 8 1
Math Journal 2, p. 182
Children practice and maintain skills
through Math Box problems.
[Number and Numeration Goal 6]
• Use equal sharing to solve fractional
part-of-a-collection problems. [Operations and Computation Goal 6]
Home Link 8 1
Math Masters, p. 237
Children practice and maintain skills
through Home Link activities.
Key Activities
Children review basic fraction concepts
and notation. They name fractional parts
of regions and sets of objects.
Ongoing Assessment:
Informing Instruction See pages 650
and 651.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 180. [Number and Numeration Goal 2]
Key Vocabulary
equal whole (the ONE) denominator numerator unit fraction
Materials
Math Journal 2, pp. 180 and 181
slate 25 pennies or counters
Advance Preparation
Teacher’s Reference Manual, Grades 1–3 pp. 59–62
648
Unit 8
Fractions
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Exploring Fractions
Math Masters, p. 238
counters ruler or straightedge
Children explore the concept of a fraction
of a set.
ENRICHMENT
Solving Fraction Puzzles
Math Masters, p. 239
centimeter cubes
Children solve Fraction Puzzles to create
the whole when a part is given.
ELL SUPPORT
Building a Math Word Bank
Differentiation Handbook, p. 132
Children add the terms numerator and
denominator to their Math Word Banks.
Mathematical Practices
SMP2, SMP3, SMP4, SMP5, SMP6
Getting Started
Content Standards
3.NF.1, 3.NF.3c, 3.G.2
Mental Math and Reflexes
Math Message
Pose problems like the following. Children write their answers on slates and
share their strategies. Encourage children to write number models to show
their strategies.
Turn to page 180 in your
journal. Do Problems 1–5
only.
A fin whale weighs about 50 tons. About how much do 6 fin whales weigh?
6 × 50 T = 300 T
1 ton = 2,000 pounds. About how much does 1 fin whale weigh in pounds?
50 × 2,000 lb = 100,000 lb
A 9-year-old’s heart beats about 90 times per minute. About how many times does
it beat per hour? 60 × 90 beats = 5,400 beats About how many times does it beat
in 10 hours? 54,000 beats
1 Teaching the Lesson
Math Message Follow-Up
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
WHOLE-CLASS
DISCUSSION
(Math Journal 2, p. 180)
Go over the answers to the Math Message problems while
reviewing the use of fractions to express parts of wholes. Be sure
to include the following points in the discussion:
NOTE To extend fraction review, have
children compare the fractions in
Problems 2– 5, Math Journal 2, page 180.
Fraction notation is one way to express equal parts of any
whole. (Decimal notation is another way.)
Fractions are not meaningful unless they refer to a part
of a particular whole (the ONE). Throughout this unit,
consistently ask children to identify the ONE in problem
situations. For example, __14 of a large pizza is not the same
as __14 of a small pizza.
A fraction has two parts. The denominator names the number
of equal parts into which the whole (the ONE) has been divided.
The numerator names the number of those equal parts being
used or considered.
3
7
numerator
denominator
A fraction with the same numerator and denominator names
all the parts of the whole (the ONE). For example, __33 , __44 , and
5
__
are all equivalent names for 1.
5
A fraction with 1 in the numerator is called a unit fraction.
1 __
1
__
, 1 , and __
are examples of unit fractions.
4 8
25
Student Page
Date
Time
LESSON
81
Fraction Review
Math Message
2
_
1. Draw an X through 3 of the circles.
0 1 1 2
, or –34.
Label each picture with one of the following numbers: 0, –4, –4, –2, –
4
2.
4
–
4
3.
4.
0
0 or _
4
or 1
5.
3
_
1
_
1
2
_
_
2 or 4
4
4
Each whole figure represents ONE.
Write a fraction that names each region inside the figure.
6.
7.
1
2
1
2
9.
1
2
1
4
1
4
1
4
1
4
10.
1
2
1
4
1
4
1
2
8.
11.
1
3
1
3
1
3
1
2
1
4
1
4
Try This
Each whole figure represents ONE. Write a fraction that names each
region inside the figure.
12.
13.
3
4
1
4
1
4
1
4
1 1
8 8
1
4
180
Math Journal 2, p. 180
EM3MJ2_G3_U08_180-203.indd 180
1/30/11 10:37 AM
Lesson 8 1
649
NOTE The numerator of a fraction can be 0;
0 0
0
for example, _1 , _2 , and _3 are names for no
parts of the whole, or 0. The denominator of a
fraction cannot be 0. Because the reason for
this is beyond the grasp of most third graders,
do not mention this unless someone makes
up a fraction with 0 in the denominator. You
3
might also enter a fraction such as _0 into a
calculator to see what the display shows.
Some calculators will display an error
message when the = key is pressed. Others
will not allow 0 to be entered.
Any whole number can be named as a fraction with 1 in the
denominator. For example, a fraction name for 6 is _61 . The
numerator 6 tells how many copies you have of the unit fraction
with the denominator 1:
6
1
_
=6×_
1
1
1
1 +_
1 +_
1 +_
1 +_
1
=_+_
1
1
1
1
1
1
=1+1+1+1+1+1
=6
Ongoing Assessment: Informing Instruction
Watch for children who have difficulty remembering which part of a fraction is the
numerator and which part is the denominator. Explain that they might remember
the numerator by thinking that the word has a u for up and denominator has a d
for down.
As you continue to discuss fractions with children, emphasize the
importance of equal parts and consistently ask them to identify
the ONE in problem situations.
Reviewing Fractions as Names
WHOLE-CLASS
ACTIVITY
for Parts of Regions
When a slate is divided into equal parts, each part can be
expressed as a fraction. The slate’s drawing surface is the ONE.
Lead the class in activities such as the following:
Adjusting
the Activity
●
Divide the slate into 2 equal parts. First shade one part, and
then the other. What is equal to the two halves? The whole
slate, or the ONE How would you write this as a fraction? _22
●
Divide the slate into 3 equal parts. What fraction of the slate
is each part? _13 of the slate Divide it into 6 equal parts. What is
each part called? _16 of the slate Share your strategies for
dividing the slate to show 6 equal parts. Use one line to divide
the thirds in half. Or add three more parts by dividing each
third with a line.
●
Divide the slate into 4 equal parts. Shade 3 of the 4 parts.
What fractional part of the slate have you shaded? _34 of the
slate What fractional part is not shaded? _14 of the slate
●
Which is larger, _12 or _14 of the slate? _12 Why? With the fraction _12 ,
the slate is divided into fewer equal parts so each of those parts
is larger. Which is smaller, _12 or _24 ? Neither; they’re equal. Why?
The same amount is shaded.
●
Divide the slate into 6 equal parts. Shade 0 sixths. How much
of the slate is shaded? Nothing is shaded. How would you write
that as a fraction? _06
ELL
Have one child divide a slate in half and
shade one half, and another child divide
another slate into 4 equal parts and shade
2 fourths. Then compare the shaded parts.
1
2
Explain that _2 and _4 are equivalent fractions.
AUDITORY
650
KINESTHETIC
Unit 8 Fractions
TACTILE
VISUAL
Reviewing Fractions as Names
for Parts of Sets
Student Page
WHOLE-CLASS
ACTIVITY
ELL
Date
Time
LESSON
81
Fraction Review
continued
You need at least 25 pennies or other counters to help you solve
these problems. Share solution strategies with others in your group.
Unit
counters
Ask 5 children to lend their journals to make a set of books. Show
the pile of 5 books. The 5 books are the whole set, or the ONE. To
support English language learners, discuss the meaning of the
word set in this context. Hold up several books, and ask children
to name the fractional part of the set.
1
_
14. a. Show 4 of a set of
8 counters. How
many counters
is that?
Name a fractional part, and ask children to tell you how many
books to hold up.
Ask: How many books are _25 of the set? 2 books _45 of the set? 4 books
3
_
c. Show 4 of the set. How
many counters?
many counters?
2
1
_
15. a. Show 3 of a set of
12 counters. How
many counters
is that?
4
2
_
b. Show 3 of the set. How
16. a. Show 5 of a set of
15 counters. How
many counters
is that?
many counters?
8
4
_
b. Show 5 of the set. How
19. Five counters is 5 of
18 counters. How
many counters?
12
20 counters. How
many counters?
12
1
_
2
_
12
3
_
17. Show 4 of a set of
many counters?
3
18. Show 3 of a set of
6
3
_
c. Show 3 of the set. How
many counters?
4
1
_
Ask: What fractional part of the set is 1 book? _15 3 books? _35 No
books? _05 5 books? _55 , the whole set, or the ONE
2
_
b. Show 4 of the set. How
a set. How many
counters are in the
whole set?
a set. How many
counters are in the
whole set?
25
18
Try This
3
_
21. Twelve counters is 4 of a set. How many
16 counters
counters are in the complete set?
Repeat with a set of 9 books.
15
1
_
20. Six counters is 3 of
22. Pretend that you have a set of 15 cheese
8
_
9
Ask: How many books are in of the set? 8 books How many books
are _13 of the books? 3 books What fractional part are 6 of the books?
6
_
or _23
9
1
cubes. What is _
2 of that set? Use a fraction
or decimal in your answer.
1
7—2 or 7.5 cheese
cubes
Math Journal 2, p. 181
180-203_EMCS_S_MJ2_G3_U08_576418.indd 181
2/10/11 12:50 PM
Continue with similar questions.
Adjusting the Activity
ELL
Ask children how many books each child would get if 3 children were to
1
share the 9 books equally. 3 books Each share is _3 of the set. Ask: How many
total books would 2 of the children get? 6 books What fraction of books do the
2
2 children get? _3 of the set Have children model this and other situations using
counters.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
V I S U A L
Say that you have a case of juice boxes. Five juice boxes are
1
_
of the case. Ask: How many juice boxes are in the whole case?
2
10 juice boxes
Say that 4 apples are _14 of a bag. How many apples are in the
whole bag? 16 apples
Say that 8 girls are __23 of a group. How many children are in the
group? 12 children
Say that the set is $1.00 or 100 cents. What fraction of $1.00 is 50
50
50
cents? _
of a dollar What is another way to write _
of a dollar?
100
100
25
1
_
_
of a dollar What fraction of $1.00 is 25 cents? 100 of a dollar What
2
25
is another way to write _
of a dollar? _14 of a dollar What fraction
100
75
75
of $1.00 is 75 cents? _
of a dollar What is another way to write _
100
100
of a dollar? _34 of a dollar
Ongoing Assessment:
Informing Instruction
Watch for children who are having difficulty
solving the fractional part-of-a-set number
stories. Have them divide their slates and act
3
out the problems. For example, to show _4 of
a set of 20 counters, have children divide
their slates into 4 sections. They distribute
the 20 counters equally among the sections
and then count to find the total in 3 of the
4 sections.
Continue with similar questions.
Lesson 8 1
651
Student Page
Date
Time
LESSON
81
1. Double each amount.
$0.25
$0.50
$0.75
$1.25
$5.00
3.
2.
$0.50
$1.00
$1.50
$2.50
$10.00
6
12
8
It has
It has
It has
Fill in the missing numbers.
×, ÷
700
of Regions and Sets
60
5,600 480
7 4,900 420
8
4.
This drawing shows
a rectangular prism.
faces.
(4 + 3) − 2 =
5
10 = 6 + (2 +
2
edges.
vertices.
6.
Children work alone or with a partner to complete the journal
pages. They can use counters to help solve problems involving
fractional parts of sets. Bring the class together to discuss
children’s solutions.
)
21
Ongoing Assessment:
Recognizing Student Achievement
16
9 cups. 9 ice cubes per cup. How
many ice cubes in all? Fill in the
circle for the best answer.
5
_
What fraction is unshaded?
8
PR
PRO
PROBLEM
P
ROBLEM
B
SOLVING
= 3 × (9 − 0)
(5 × 5) − 4 =
115
3
Shade _
8 of the circle.
INDEPENDENT
ACTIVITY
(Math Journal 2, pp. 180 and 181)
Complete the
number models.
27
5.
Using Fractions to Name Parts
Math Boxes
A
18 ice cubes
B
81 ice cubes
C
90 ice cubes
D
99 ice cubes
Journal
Page 180
Problems 6–9
Use journal page 180, Problems 6–9 to assess children’s ability to identify and
write fractions that name regions. Children are making adequate progress if they
are able to successfully complete Problems 6–9. Some children may be able to
complete problems 10 and 11.
22 23
[Number and Numeration Goal 2]
66 67
182
Math Journal 2, p. 182
180-203_EMCS_S_MJ2_G3_U08_576418.indd 182
3/29/11 11:24 AM
2 Ongoing Learning & Practice
Practicing with Fact Triangles
PARTNER
ACTIVITY
Partners practice basic facts by flashing ×, ÷ Fact Triangles.
Children can keep track of the facts they miss so they can focus on
those facts during a second round.
Home Link Master
Name
Date
HOME LINK
Math Boxes 8 1
Time
Fractions All Around
81
Family
Note
(Math Journal 2, p. 182)
Help your child understand the idea of the ONE as well as fractions of objects and
sets. Help your child look for objects and pictures that have fractions or
decimals printed on them.
22–24
Please return this Home Link to school tomorrow.
Each square flag below represents the ONE. Write the fractions that name
each region inside each flag.
1.
2.
1
2
1
4
1
2
1
4
1
4
3.
1
4
1
4
4.
(Math Masters, p. 237)
of the buttons have 4 holes.
7
5.
of the buttons have 2 holes.
Look for items around your home that have fractions or decimals on them, such
as recipes, measuring cups, wrenches, package labels, or pictures in newspapers.
Ask permission to bring them to school to display in our Fractions Museum.
Practice
Unit
Solve. Show your work.
6.
275
- 88
187
7.
684
- 97
587
8.
429
- 237
192
Math Masters, p. 237
237-266_EMCS_B_MM_G3_U08_576957.indd 237
652
8/16/11 3:23 PM
Unit 8 Fractions
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 8-3. The skill in Problem 6
previews Unit 9 content.
Home Link 8 1
3
4
Write the fractions.
_5
7
_2
INDEPENDENT
ACTIVITY
INDEPENDENT
ACTIVITY
PR
PRO
PROBLEM
P
ROBLEM
B
SOLVING
Home Connection Children use fractions to name parts
of objects and sets. They are asked to bring in items
with fractions or decimals printed on them for the
Fractions Museum.
Teaching Master
Name
3 Differentiation Options
READINESS
Exploring Fractions
LESSON
81
䉬
Date
Time
Exploring Fractions
These show ᎏ14ᎏ.
These do NOT show ᎏ14ᎏ.
PARTNER
ACTIVITY
1
1. Explain how you can tell whether something shows ᎏ4ᎏ.
Sample answer: If something has four equal parts and
5–15 Min
(Math Masters, p. 238)
1
one part is represented, then that shows ᎏ4ᎏ.
For Problems 2 and 3—
䉬 Take the number of counters.
To explore the concept of a fraction of a collection, have children
solve the fraction problems on Math Masters, page 238. When
children have finished the page, have them discuss how they can
find _14 of any number. Sample answer: I can divide the number into
four equal piles or the area into 4 equal parts. Each pile or part
is _14 .
ENRICHMENT
Solving Fraction Puzzles
䉬 Figure out how to show
5–15 Min
of
䉬 Use the rectangles to the right to
make four equal piles of counters.
䉬 Draw a picture to record your answer.
2. Take 8 counters. Show
1
ᎏᎏ
4
of
3. Take 20 counters. Show
the counters.
1
ᎏᎏ
4
of 20 counters.
4. Divide the figure below into four
5. Divide the figure below into four
equal parts.
equal parts another way.
Sample
answer:
PARTNER
ACTIVITY
(Math Masters, p. 239)
1
ᎏᎏ
4
the counters.
Is ᎏ14ᎏ in Problem 4 larger or
back of your paper.
Sample
answer:
1
ᎏᎏ
4
in Problem 5 larger? Explain your answer on the
Math Masters, p. 238
To apply children’s understanding of fractions as parts of wholes,
have them solve Fraction Puzzles on Math Masters, page 239.
ELL SUPPORT
Building a Math Word Bank
PARTNER
ACTIVITY
5–15 Min
(Differentiation Handbook, p. 132)
To provide language support for fractions, have children use the
Word Bank template found on Differentiation Handbook, page 132.
Ask children to write the terms numerator and denominator, draw
a picture representing each term, and write other related words.
See the Differentiation Handbook for more information.
NOTE Remind children to continue to record
the sunrise, sunset, and length of day in their
journals on pages 279–281. They will also
continue to record the national high and low
temperatures on journal page 175 and then
graph the temperature ranges on journal
pages 176 and 177.
Teaching Master
Name
LESSON
81
䉬
Date
Time
Fraction Puzzles
Use centimeter cubes to help you solve the puzzles.
1. The 1st graders are building a
little house with centimeter
cubes. The drawing shows ᎏ23ᎏ of
the floor of their house. Use
centimeter cubes to build
the whole floor of the house.
Then finish the picture.
Sample
answer:
7
ᎏᎏ of a line segment. Use centimeter cubes to
10
figure out how long the line segment is. Figure out how much longer
the line segment should be to make it whole. Use a ruler to draw the
rest of the whole line segment.
2. This drawing shows
3. Make up a puzzle. Ask a partner to solve it.
This drawing shows
—
Answers vary.
of a
Draw the whole
.
.
Math Masters, p. 239
Lesson 8 1
653