Collections of Things
Objective To guide children as they use fractions to name
parts of collections.
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Common
Core State
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Ongoing Learning & Practice
Key Concepts and Skills
Counting Equal Parts
• Describe and name fractional parts of
a collection of objects. Math Journal 2, p. 193
straightedge or Pattern-Block
Template pattern blocks (optional)
Children divide shapes into equal parts
and count the parts.
[Number and Numeration Goal 3]
• Use manipulatives to model fractions
as equal parts of a collection of things. [Number and Numeration Goal 3]
Key Activities
Children identify fractions of collections of
pennies; they also identify equal shares and
translate them into fractions. Children color
fractional parts of a set.
Ongoing Assessment:
Informing Instruction See page 618.
Math Boxes 8 3
Math Journal 2, p. 194
blue, yellow, and red crayons
Children practice and maintain skills
through Math Box problems.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problem 4. [Operations and Computation Goal 2]
Materials
Math Journal 2, pp. 191 and 192
Home Link 8 2
penny, nickel, dime, quarter, and dollar bill collection of 3 to 6 same-sized books and
various sets of objects, such as crayons,
chairs, or buttons 15 pennies per child counters (optional)
Home Link 8 3
Math Masters, p. 235
Children practice and maintain skills
through Home Link activities.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Exploring Fractions
Math Masters, p. 236
12 pennies or counters per child
Children explore the concept of a fraction
of a set.
ENRICHMENT
Finding All the Marbles
Math Masters, p. 237
counters
Children draw pictures or use counters
to solve a fraction puzzle.
EXTRA PRACTICE
Using Fractions to Name Parts
of Regions and Sets
Math Masters, p. 238
25 pennies or counters per child
Children use fractions to name parts
of regions and sets.
Advance Preparation
For a mathematics and literacy connection, obtain copies of Only One by Marc Harshman
(Dutton Children’s, 1993) and Apple Fractions by Jerry Pallotta (Scholastic Inc., 2002).
Teacher’s Reference Manual, Grades 1–3 pp. 59–61
616
Unit 8
Fractions
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Getting Started
Mental Math and Reflexes
Math Message
Illustrate the following questions by holding up coins and
a $1 bill.
1
Tyrone had 12 marbles. He gave _
3 of the marbles
1
_
to Ling and 3 of the marbles to Mike. How many
marbles did he keep for himself? 4 marbles
How many nickels make one dime? 2
How many pennies make one dime? 10
If a dime is ONE, then what is a nickel? one-half
Home Link 8 2 Follow-Up
How do we write this fraction? _12
If $1 is ONE, then what is a quarter?
1
_
4
A dime?
As you review answers, emphasize the idea that
the size of a fractional part depends on the size
of the whole. A fraction has no meaning unless we know what
the whole is. Have children share strategies for Problem 3.
1
_
10
1
If a dime is ONE, then what is $1? 10 What is a penny? _
10
If a quarter is ONE, then what is $1? 4 A nickel? _15
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Have children share solution strategies. If necessary, model the
story with 12 pennies or counters.
Reviewing Fractions with
WHOLE-CLASS
ACTIVITY
Reference to Collections of Objects
Display a pile of same-sized books. Have someone count the books.
Then, pointing to the pile of books, ask: What fraction of the pile is
1 book? What fraction is 2 books? Write each fraction on the board
as you talk. Follow the same procedure with other collections, such
as a new box of crayons or chairs in rows.
Identifying Fractions of
Collections of Pennies
WHOLE-CLASS
ACTIVITY
PROBLEM
PRO
PR
P
RO
R
OB
BLE
BL
L
LE
LEM
EM
SOLVING
SO
S
OL
O
LV
L
VIN
V
ING
Each child should have about 15 pennies. Pose the following
problems verbally:
●
Make a pile of 4 pennies. What fraction of the pile is 1 penny? _14
2 pennies? _24 or _12 4 pennies? _44 0 pennies? _04
●
Make a pile of 5 pennies. Show me _15 of this pile; 1 penny _25 of
the pile; 2 pennies _55 of the pile. 5 pennies How many pennies
are in _05 of the pile? 0 pennies
●
Take 12 pennies. Show how you would share them equally with
another person. How many pennies would each person get? 6
pennies Show equal shares among 3 people. How many pennies
would each person get? 4 pennies
Adjusting the Activity
Pose problems like the following:
There are 8 crayons in 1 box. How many
1
crayons are in 2 boxes? 16 crayons In 12_
boxes? There are 8 crayons in 1 box, so
there are 4 crayons in half of a box.
Therefore, there are 8 + 4, or 12 crayons in
1_12 boxes.
I am thinking of a pile of pennies. There are
4 pennies in 2_1 of the pile. Show me the whole
pile. 8 pennies
1
What if 4 pennies are 3_ of the pile? How
many pennies are in the whole pile now? 12
pennies
AUDITORY
KINESTHETIC
TACTILE
Lesson 8 3
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VISUAL
617
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Student Page
Date
Finding Fractions of
Time
LESSON
8 3
Equal Shares
INDEPENDENT
ACTIVITY
Circle each person’s share.
Collections of Things
1. Two people share 10 pennies.
(Math Journal 2, pp. 191 and 192)
Use pennies to help you solve the problems.
PROBLEM
PR
PRO
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SOLVING
SO
S
OL
O
LV
VIN
IN
NG
G
How many pennies does
each person get?
5
Have children use pennies or counters to complete these journal
pages. You may need to go through the first problem, making sure
children know what they are supposed to do.
pennies
5
_1 of 10 pennies =
2
pennies.
2. Three people share 9 pennies.
How many pennies does each
person get?
3
pennies
_1 of 9 pennies =
3
_2 of 9 pennies =
3
3
6
Ongoing Assessment: Informing Instruction
pennies.
pennies.
Watch for children who have difficulty with finding the number of pennies or
counters represented by the fraction. Mention that the bottom number
(denominator) tells the total number of equal groups, and the top number
(numerator) tells the number of equal groups being considered. Children count
the objects in the number of groups given by the numerator to solve the problem.
Children may also act out each problem with manipulatives.
3. Four people share
12 pennies.
How many pennies does
each person get?
3
pennies
3
9
_1 of 12 pennies =
4
_3 of 12 pennies =
4
pennies.
pennies.
Math Journal 2, p. 191
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2 Ongoing Learning & Practice
Counting Equal Parts
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 193)
Children divide shapes into equal parts. Then they write the
number of halves, fourths, and thirds.
Student Page
Student Page
Date
LESSON
8 3
䉬
Time
Date
Fractions of Sets
LESSON
8 3
A fraction is given in each problem. Color that fraction of the checkers red.
1.
Time
Equal Parts
Use a straightedge or Pattern-Block Template.
1. Divide the shape in half.
2.
2. Divide the shape into 4 equal
parts.
1
ᎏᎏ
5
are red.
3.
2
ᎏᎏ
3
are red.
4
ᎏᎏ
6
are red.
4.
3
ᎏᎏ
4
are red.
5.
How many halves?
2
How many fourths?
4
6.
3. Divide the shape in half.
4. Divide the shape in 4 equal
parts.
1
ᎏᎏ
2
0
ᎏᎏ
7
are red.
are red.
Try This
How many halves?
7.
2
How many fourths?
8.
4
Try This
1
ᎏᎏ
3
are red.
9.
1
ᎏᎏ
4
are red.
3
ᎏᎏ
4
are red.
5. Use your Pattern-Block Template triangle.
Divide the shape into 3 equal parts.
10.
2
ᎏᎏ
3
are red.
Math Journal 2, p. 192
How many thirds?
Math Journal 2, p. 193
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618
3
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Unit 8 Fractions
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Student Page
Math Boxes 8 3
Date
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 194)
Time
LESSON
Math Boxes
8 3
䉬
1
ᎏᎏ blue. Color
4
Color ᎏ12ᎏ red.
1. Color
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 8-1. The skill in Problem 6
previews Unit 9 content.
e
2. Circle the figure that has only
yellow.
one line of symmetry. Draw the
line of symmetry.
Sample
answer:
red
blu
1
ᎏᎏ
4
w
llo
ye
60
夹
3. Complete the table.
Ongoing Assessment:
Recognizing Student Achievement
Math Boxes
Problem 4
Use Math Boxes, Problem 4 to assess children’s ability to calculate
coin combinations. Children are making adequate progress if they can
show $1.28. Some children may be able to show the amount in more than
one way.
[Operations and Computation Goal 2]
Rule
1 yd ⫽ 3 ft
4. Show 1 way to make $1.28.
yd
Use ‰, Í, Â, and Î.
ft
Sample answer:
‰‰‰‰ÍÍÂ
ÎÎÎ
6
2
3
9
5
15
10
30
Answers vary.
5. Circle the event that is likely to
88–90
6. Which unit makes sense?
happen.
Choose the best answer.
You will fly to the center of the
earth.
A can of soup may weigh:
8 ounces
You will have homework.
8 cups
You will eat a rock.
Home Link 8 3
8 pounds
INDEPENDENT
ACTIVITY
8 feet
Math Journal 2, p. 194
(Math Masters, p. 235)
Home Connection Children solve an equal-sharing
problem. Children also find additional items to add to the
Fractions Museum.
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Home Link Master
Name
Date
HOME LINK
83
䉬
Family
Note
MILK
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Time
Fractions of Collections
In this lesson, your child learned to use fractions to name part of a collection of objects. For
example, your child could identify 2 out of 4 objects as 24 or 12 . Show your child how to use
pennies to act out Problem 1. Help your child collect household items that can be separated
into fractional parts—or any other items that have fractions written on them. Encourage
your child to bring these items to school for the class’s Fractions Museum.
14
Please return this Home Link to school tomorrow.
1.
Three people share 12 pennies. Circle each person’s share.
How many pennies does each person get?
1
3
of 12 pennies 2
3
of 12 pennies 4
8
4
pennies
pennies.
pennies.
Practice
Unit
Solve.
2. 68 24 3. 53 45 44
98
Cars
4.
65
27
38
5.
64
26
90
Ask someone at home to help you find more things to bring to school
for the Fractions Museum.
Children bring items with written fractions to add to the Fractions Museum.
Math Masters, p. 235
Lesson 8 3
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3 Differentiation Options
Teaching Master
Name
Date
LESSON
83
䉬
Time
Exploring Fractions
1
4
1
4
These show ᎏᎏ.
These do NOT show ᎏᎏ.
1
4
1. Explain how you can tell if something shows ᎏᎏ.
1
Sample answer: Something shows ᎏ4ᎏ
when 1 part out of 4 equal parts is marked.
For each problem—
Take the number of
counters.
Figure out how to show
1
ᎏᎏ of the counters.
4
Use the rectangles to the
right to make four equal
piles of counters.
Record your answer in the
rectangles below each problem.
䉬
䉬
䉬
䉬
2. Take 4 counters.
SMALL-GROUP
ACTIVITY
READINESS
Exploring Fractions
5–15 Min
(Math Masters, p. 236)
To explore the concept of a fraction of a collection of objects, have
children solve the fraction problems on Math Masters, page 236.
Have them discuss how they can find _14 of any number. I can
divide the number into four equal piles. Each pile is _14 .
SMALL-GROUP
ACTIVITY
ENRICHMENT
3. Take 8 counters.
1
1
Show ᎏᎏ of
4
4 counters.
Show ᎏᎏ of
4
8 counters.
Finding All the Marbles
5–15 Min
(Math Masters, p. 237)
4. Take 12 counters.
5. Take
1
counters.
1
Show ᎏᎏ of
4
12 counters.
Show ᎏᎏ of
4
counters.
Math Masters, p. 236
To apply children’s understanding of fractions as equal parts of a
collection, have them draw pictures or use counters to solve a
fraction puzzle. Have children share their strategies.
INDEPENDENT
ACTIVITY
EXTRA PRACTICE
Using Fractions to Name
5–15 Min
Parts of Regions and Sets
(Math Masters, p. 238)
To build on children’s knowledge of fractions, have them use
counters to solve the problems on Math Masters, page 238.
Teaching Master
Name
Date
LESSON
83
䉬
Teaching Master
Time
A Fraction Puzzle
LESSON
83
䉬
Use counters or draw pictures to solve the fraction puzzle.
Show all of your work. If you have time, write a fraction puzzle
of your own on the back of this page.
José was playing a game with marbles.
In the first round of the game, he lost
1
ᎏᎏ
4
Date
of his marbles.
1
1
In the third round of the game, he lost ᎏᎏ of his remaining
2
marbles.
Time
Fractions of Sets
Use 25 pennies or other counters to help you solve these problems.
Share solution strategies with others in your group.
Make a set of 8 pennies to use with Problems 1–3.
1
4
1. Show ᎏᎏ of a set of 8 pennies.
In the second round of the game, he lost ᎏᎏ of his remaining
3
marbles.
How many pennies is that?
Unit
pennies
2
2. Put the pennies back.
2
4
Show ᎏᎏ of the set.
How many pennies is that?
4
3. Put the pennies back.
He gave 1 marble to his friend Shavana.
3
4
Show ᎏᎏ of the set.
He had 1 marble left.
How many marbles did José start with?
Sample answer:
Round 1
Name
8
How many pennies is that?
4
5
6
4. Show ᎏᎏ of a set of 15 pennies.
Round 1
How many pennies is that?
3
4
12
5. Show ᎏᎏ of a set of 20 pennies.
How many pennies is that?
Round 2
Round 2
15
Try This
1
5
6. Five pennies is ᎏᎏ of a set.
Round 3
Round 3
Can’t give one
away and keep one.
Can give one away and keep one.
So, José started with 8 marbles.
How many are in the whole set?
25
Make up your own problem.
Answers vary.
Math Masters, p. 237
620
Math Masters, p. 238
Unit 8 Fractions
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