Sharing Money
Objective To guide children as they share whole-dollar
amounts equally.
a
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Model money exchanges with
manipulatives. [Number and Numeration Goal 1]
• Solve equal-sharing division stories
involving money amounts. [Operations and Computation Goal 6]
Key Activities
Children solve problems about sharing
whole-dollar amounts equally in preparation
for more formal division procedures.
Ongoing Assessment:
Informing Instruction See page 750.
Materials
Math Journal 2, p. 222
Home Link 9 6
Math Masters, pp. 399 – 402
tool-kit coins scissors half-sheet of
paper slate quarter-sheet of paper
(optional)
Family
Letters
Assessment
Management
Common
Core State
Standards
Curriculum
Focal Points
Ongoing Learning & Practice
1 2
4 3
Playing Factor Bingo
Math Masters, p. 448 (one per player)
Student Reference Book pp. 285
and 286
per partnership: 4 each of number
cards 2– 9 (from the Everything Math
Deck, if available), 24 counters
Children apply their understanding
of factors.
Math Boxes 9 7
Math Journal 2, p. 223
Children practice and maintain skills
through Math Box problems.
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Trading Money
Math Masters, p. 146 (one per player)
per partnership: 2 dollar bills, 20 dimes, and
40 pennies; 2 dice
Children trade money to practice finding
equivalent coin and bill values.
ENRICHMENT
Sharing Money Equally
Math Masters, p. 289
Children solve a problem with equal shares
of money.
Ongoing Assessment:
Recognizing Student Achievement
Use Math Boxes, Problem 5. [Number and Numeration Goal 2]
Home Link 9 7
Math Masters, p. 288
Children practice and maintain skills
through Home Link activities.
Advance Preparation
Each partnership will need six $100 bills, forty $10 bills, and forty-eight $1 bills. Copy Math Masters,
pages 399– 402. Have children cut the bills apart.
Teacher’s Reference Manual, Grades 1– 3 pp. 111–113
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Unit 9
Multiplication and Division
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Getting Started
Mental Math
and Reflexes
Math Message
What is each person’s share if $1 is shared equally among 5 people? 20¢
If $2 is shared equally among 4 people? 50¢ $3 among 6 people? 50¢ $2 among
5 people? 40¢ Record your answers on a half-sheet of paper.
Children write fractions on their slates
and show whether each fraction is
(thumbs-up), equal to _
greater than _
2
2
1
1
Home Link 9 6 Follow-Up
1
(fists), or less than _ (thumbs-down).
2
1
1 less than _
_
, thumbs-down
2
4
1
3 equal to _, fist
_
Ask volunteers to draw arrays with 18 dots on the board. Ask someone to
explain how knowing all of the ways to arrange 18 chairs in equal rows
can help them name the factors of 18. When 18 chairs are arranged in rows with the
same number of chairs in each row with no chairs left over, the number of rows and the
number of chairs in each row are factors of 18. Knowing the different arrays for
18 visually shows the factors of 18.
2
6
1
3 less than _
_
, thumbs-down
2
8
1
7 greater than _
_
, thumbs-up
8
2
5
2
1
2 greater than _
_
, thumbs-up
2
3
1
3 greater than _, thumbs-up
_
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Children share their solutions and strategies. Possible strategies
for $1 shared by 5 people include:
There are 5 [20s] in 100 so there are five $0.20 in $1.00.
Change the dollars to cents and divide: $1 = 100¢, and 100¢
divided equally among 5 people is 20¢ apiece.
Change the dollars to dimes and divide: $1 = 10 dimes, and
10 dimes divided equally among 5 people is 2 dimes, or
20¢ apiece.
Sharing Play Money
Teaching Aid Master
Name
Date
Time
$1 Bills
WHOLE-CLASS
ACTIVITY
(Math Journal 2, p. 222; Math Masters,
pp. 399–402)
PROBLEM
PRO
P
RO
R
OBL
BLE
B
L
LE
LEM
EM
SOLVING
SO
S
OL
O
LV
L
VIN
V
IIN
NG
Children work with partners. Have them turn to journal page 222.
Work through Problems 1 and 2 with the class, while children use
$100, $10, and $1 bills to represent the amounts being shared.
Adjusting the Activity
ELL
Provide children with quarter-sheets of paper to use as a model for how
many groups they need. For example, if 5 people are sharing a dollar, children
use 5 quarter-sheets of paper to model dividing the dollar into 5 equal shares.
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
Math Masters, p. 399
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Lesson 9 7
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Student Page
Date
Time
LESSON
97
Problem 1: Share $54 equally among 3 people.
Sharing Money
Have the class read aloud Problem 1 on journal page 222. Discuss
what you want to find out and what you know from the problem.
Remind children that the division operation can be used to solve
equal-sharing problems. Ask a volunteer to write a division
number model for the story on the board while the rest of the
children write it in their journals. $54 ÷ 3 = ?
Work with a partner. Put your play money in a bank for both of you to use.
If $54 is shared equally by 3 people, how much does each person get?
1.
$54 ÷ 3 = ?
a.
Number model:
b.
How many $10 bills does each person get?
c.
How many dollars are left to share? $
d.
e.
1
24.00
8
How many $1 bills does each person get?
Answer: Each person gets $ 18.00 .
$10 bill(s)
$1 bill(s)
If $71 is shared equally by 5 people, how much does each person get?
2.
Number model:
b.
How many $10 bills does each person get?
c.
How many dollars are left to share? $
d.
How many $1 bills does each person get?
e.
How many $1 bills are left over?
f.
If the leftover $1 bill(s) are shared equally,
how many cents does each person get? $
g.
Answer: Each person gets $
3.
$84 ÷ 3 = $
5.
$181 ÷ 4 = $
To solve, have partners place five $10 bills and four $1 bills on
the table and set the rest of the bills aside. They make three
piles with the same amount in each pile. After they put a
$10 bill in each pile, there are still two $10 bills and four
$1 bills left to share. Because the $10 bills cannot be
distributed equally among the three piles, children exchange
them for twenty $1 bills. Now there are twenty-four $1 bills to
be shared, or eight $1 bills per pile. Each pile now has one
$10 bill and eight $1 bills, or $18 total.
$71 ÷ 5 = ?
a.
28.00
45.25
1
$10 bill(s)
21.00
4
1
$1 bill(s)
14.20
$1 bill(s)
0.20
.
4. $75 ÷ 6 = $
12.50
6. $617 ÷ 5 = $
123.40
Children record these transactions on page 222.
Math Journal 2, p. 222
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Ask: Does your answer make sense? yes How do you know? Sample
answer: I know that $54 is close to $60 and $60 ÷ 3 is $20. Since
$20 is close to $18, my answer makes sense. Write a summary
number model on the board: $54 ÷ 3 = $18.
Problem 2: Share $71 equally among 5 people.
Ongoing Assessment:
Informing Instruction
Watch for children who have trouble with
problems in which a share involves
dollars and cents. Have them exchange the
leftover $1 bills for coins and divide the coins
into equal shares.
NOTE The solution to a division problem
often consists of the quotient and a remainder.
Because such results are not entirely
analogous to the results obtained with the
other operations, the equal sign has been
replaced with an arrow in division number
models with remainders. When children
learn to express quotients with fractions or
decimals, Everyday Mathematics will use the
traditional form; for example, 12 ÷ 5 = 2.4
or 2_25 .
750
Have children read aloud Problem 2. Discuss what you want to
find out and what you know from the problem. Ask children to
write a number model for the story in their journals while you
write it on the board. $71 ÷ 5 = ?
To solve, partners take seven $10 bills and one $1 bill and
make 5 equal piles with one $10 bill in each. There are two $10
bills and one $1 bill left over. They exchange the two $10 bills
for twenty $1 bills and distribute them among the five piles, or
four $1 bills per pile. If they cannot decide what to do with the
remaining $1 bill, remind them of the first Math Message
problem. (When $1 is divided among 5 people, each person gets
20¢.) Thus, each person’s share is $14.20.
Ask: Does your answer make sense? yes How do you know?
Sample answer: I know that $71 is close to $70. If I think of $70
as $60 + $10, I know that there are five $12 in 60 and five $2
in 10. So, there are five $14 in 70, which is very close to five
$14.20 in $71. Write a summary number model on the board:
$71 ÷ 5 = $14.20.
Pose the following questions: What if 71¢ had been shared equally
among 5 people? What would each person’s share have been? 14¢
Could the leftover penny have been shared equally? no What is a
number model for this problem? 71¢ ÷ 5 → 14¢ R1¢ The number
model is read “71 cents divided by 5 is 14 cents with a remainder
of 1 cent.”
Unit 9 Multiplication and Division
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Game Master
Name
Solving Division Problems
PARTNER
ACTIVITY
(Math Journal 2, p. 222)
Date
Time
1 2
4 3
Factor Bingo Game Mat
PROBLEM
PR
PRO
P
RO
R
OBL
BLE
B
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
VING
VIN
IIN
NG
N
G
Children model the remaining equal-sharing problems (Problems
3 through 6) on journal page 222 with play money and complete
the number models. Children will check their answers to Problems
3 through 6 with a calculator in the next lesson, so postpone a
class discussion of these problems until then.
Links to the Future
Many children will be able to divide, with the use of manipulatives, whole-dollar
amounts that can be shared equally, but remainders may confuse some children.
The activities in this lesson are laying a foundation for more formal division work
in fourth grade. Solving problems involving the division of multidigit whole
numbers with remainders is a Grade 5 Goal.
Write any of the numbers
2 through 90 on the grid
above.
2
3
4
5
6
7
8
9
10
11 12
13
14
15
16
17
18
19
20
21 22
23
24
25
26
27
28
29
30
You may use a number
only once.
31 32
33
34
35
36
37
38
39
40
41 42
43
44
45
46
47
48
49
50
To help you keep track
of the numbers you use,
circle them in the list.
51 52
53
54
55
56
57
58
59
60
61 62
63
64
65
66
67
68
69
70
71 72
73
74
75
76
77
78
79
80
81 82
83
84
85
86
87
88
89
90
448
Math Masters, p. 448
2 Ongoing Learning & Practice
Playing Factor Bingo
PARTNER
ACTIVITY
(Math Masters, p. 448; Student Reference Book,
pp. 285 and 286)
This game was introduced in Lesson 9-6. Have children make new
game boards on Math Masters, page 448. If necessary, review
the rules for the game on pages 285 and 286 in the Student
Reference Book.
Student Page
Student Page
Games
Games
Factor Bingo
Materials
□ number cards 2–9 (4 of each)
□ 1 Factor Bingo game mat for each player
(Math Masters, p. 448)
□ 12 counters for each player
Players
2 to 4
Skill
Finding factors of a number
Object of the game To get 5 counters in a row, column, or
diagonal; or to get 12 counters anywhere on the game mat.
Directions
1. Fill in your own game mat. Choose 25 different numbers
from the numbers 2 through 90.
2. Write each number you choose in exactly 1 square on
your game mat grid. Be sure to mix the numbers up as
you write them on the grid; they should not all be in
order. To help you keep track of the numbers you use,
circle them in the list below the game mat.
3. Shuffle the number cards and place them number-side
down on the table. Any player can turn over the top card.
This top card is the “factor.”
4. Players check their grids for a number that has the card
number as a factor. Players who find such a number cover
the number with a counter. A player may place only 1
counter on the grid for each card that is turned over.
5. Turn over the next top card and continue in the same way.
You call out “Bingo!” and win the game if you are the first
player to get 5 counters in a row, column, or diagonal. You
also win if you get 12 counters anywhere on the game mat.
A 5-card is turned over. So the number 5 is the
“factor.” Any player may place one counter on a number
for which 5 is a factor, such as 5, 10, 15, 20, or 25. A
player may place only one counter on the game mat for
each card that is turned over.
Sample Factor Bingo Game Mat
Factor Bingo Game Mat
Choose any 25 different numbers from the
numbers 2 through 90. Write each
number you choose in exactly 1 square
on your game mat page. To help you keep
track of the numbers you use, circle them
in the list on your game mat page.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
6. If all the cards are used before someone wins, shuffle the
cards again and continue playing.
Student Reference Book, p. 285
Student Reference Book, p. 286
Lesson 9 7
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Student Page
Date
Time
LESSON
Math Boxes 9 7
Math Boxes
97
Draw a 4-by-8 array of Xs.
2.
(Math Journal 2, p. 223)
Sample answer:
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 9-5. The skill in Problem 6
previews Unit 10 content.
32
How many Xs in all?
Write a number model.
What is the area of your shape?
16
square centimeters
4 × 8 = 32
150 151
154 155
Use the partial-products algorithm
to solve.
3.
296
× 4
183
× 7
800
360
+ 24
1,184
700
560
+ 21
1,281
64 65
Put in the parentheses needed to
complete the number sentences.
4.
16 17
What part of this pizza
has been eaten?
2
1
8
4
Writing/Reasoning Have children write an answer to the
following: Explain how you could equally share the leftover
pizza from Problem 5 among 4 people. Sample answer:
Each person can have one complete piece and half of another piece,
giving each person 1_12 pieces.
(
(
(14 – 6(× 800 = 6,400
60 ×(79 + 1(= 4,800
15 + 80 × 90 = 7,215
68 69
5.
INDEPENDENT
ACTIVITY
Draw a shape with a perimeter
of 20 centimeters.
1.
6.
_, or _
Solve.
1,000 milligrams =
3,000 milligrams =
500
What part is left?
6
3
8
4
_, or _
1
3
gram
Ongoing Assessment:
Recognizing Student Achievement
grams
1
milligrams = _
2 gram
1,000 grams =
6,000 grams =
1
6
kilogram
kilograms
22 23
Use Math Boxes, Problem 5 to assess children’s progress in solving problems
involving fractional parts of a region. Children are making adequate progress if
they are able to solve Problem 5. Some children may be able to record 2 or more
equivalent fractions to answer each question.
162
Math Journal 2, p. 223
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Math Boxes
Problem 5
3/11/11 1:45 PM
[Number and Numeration Goal 2]
Home Link 9 7
INDEPENDENT
ACTIVITY
(Math Masters, p. 288)
Home Connection Children solve an equal-sharing
problem involving money.
Home Link Master
Name
Date
Time
Sharing Money with Friends
HOME LINK
97
Family
Note
In class we are thinking about division, but we have not yet introduced a procedure for division.
We will work with formal division algorithms in Fourth Grade Everyday Mathematics. Encourage
your child to solve the following problems in his or her own way and to explain the strategy
to you. These problems provide an opportunity to develop a sense of what division means and
how it works. Sometimes it helps to model problems with bills and coins or with pennies,
beans or other counters that stand for coins and bills.
73
Please return this Home Link to school tomorrow.
1. Four friends want to share $77. They have 7 ten-dollar bills and 7 one-dollar
bills. They can go to the bank to get smaller bills and coins if they need to.
$77 ÷ 4 = ?
a. Number model:
1
b. How many $10 bills could each friend get?
3
How many $10 bills would be left over?
c. Of the remaining money, how many $1 bills could each friend get?
(Remember, you can exchange larger bills for smaller ones.)
9
d. How many $1 bills would be left over?
e. If the leftover money is shared equally,
how many cents does each friend get?
f. Answer: Each friend gets a total of $
1
$0.25
19.25 .
Practice
Use the partial-products method to solve these problems. Show your work.
2.
21
3.
48
4.
63
×2
×4
×5
42
192
315
Math Masters, p. 288
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Unit 9 Multiplication and Division
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Teaching Master
Name
3 Differentiation Options
Pennies
Hundredths Cubes
Dimes Tenths Longs
Dollars Ones Flats
PARTNER
ACTIVITY
$0.01
0.01
$0.10
0.1
Trading Money
58
$1.00
1
READINESS
Date
Time
Place-Value Mat
LESSON
5–15 Min
(Math Masters, p. 146)
To provide experience with money exchanges, have children make
dollar-dime-penny trades in the Money Trading Game. Children
make their trades on the Place-Value Mat on Math Masters,
page 146.
Money Trading Game
You will need 2 dollar bills, 20 dimes, 40 pennies, 2 dice, and one
Place-Value Mat per player. Each player begins with 1 dollar on
his or her Place-Value Mat. The bank should have 20 dimes and
40 pennies.
Math Masters, p. 146
Directions:
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Take turns. On each turn, a player does the following:
1. Roll the dice and find the sum of the dice.
2. Return that number of cents to the bank. Make exchanges
when needed.
3. The player not rolling the dice checks on the accuracy of
the transactions.
4. The first player to clear his or her Place-Value Mat wins
the game.
ENRICHMENT
Sharing Money Equally
PARTNER
ACTIVITY
Teaching Master
5–15 Min
(Math Masters, p. 289)
To apply children’s understanding of equal shares, have them
figure out how many people can go to the magic show for $25.
Children record their work on Math Masters, page 289. Have
children explain their strategies for solving the problems. Discuss
why they think the last problem might be a Try This. Sample
answer: It was harder to answer because there was money
left over.
Name
LESSON
97
䉬
Date
Time
Equal Shares of Money
The price of admission to the neighborhood magic show is $1.25 per
person. How many people could you take to the show if you had $25.00?
Show your work, and explain how you figured it out.
20
Sample answer: I wanted to find out how
many $1.25s are in $25.00. I figured out that
there are four $1.25s in $5.00. In $10.00, there
are eight $1.25s. In $20.00, there are sixteen
$1.25s. In $25.00, there are twenty $1.25s.
20 people can go to the magic show.
Try This
How many people could go to the show if you had $32.00?
Explain your answer.
25
Sample answer: 4 people can go for
every $5.00, so 24 people can go for $30.00.
One more person can go with the extra $2.00.
Math Masters, p. 289
Lesson 9 7
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Name
Date
HOME LINK
97
Family
Note
Time
Sharing Money with Friends
In class we are thinking about division, but we have not yet introduced a procedure for division.
We will work with formal division algorithms in Fourth Grade Everyday Mathematics. Encourage
your child to solve the following problems in his or her own way and to explain the strategy
to you. These problems provide an opportunity to develop a sense of what division means and
how it works. Sometimes it helps to model problems with bills and coins or with pennies,
beans or other counters that stand for coins and bills.
73
Please return this Home Link to school tomorrow.
1. Four friends want to share $77. They have 7 ten-dollar bills and 7 one-dollar
bills. They can go to the bank to get smaller bills and coins if they need to.
a. Number model:
b. How many $10 bills could each friend get?
How many $10 bills would be left over?
c. Of the remaining money, how many $1 bills could each friend get?
(Remember, you can exchange larger bills for smaller ones.)
d. How many $1 bills would be left over?
e. If the leftover money is shared equally,
f. Answer: Each friend gets a total of $
.
Practice
Use the partial-products method to solve these problems. Show your work.
2.
21
×2
3.
48
×4
4.
63
×5
Copyright © Wright Group/McGraw-Hill
how many cents does each friend get?
288
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