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www.everydaymathonline.com
748 Unit 9 Multiplication and Division
�������
Advance PreparationEach 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
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 ActivitiesChildren solve problems about sharing
whole-dollar amounts equally in preparation
for more formal division procedures.
Ongoing Assessment: Informing Instruction See page 750.
MaterialsMath 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)
Playing Factor BingoMath 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�7Math Journal 2, p. 223
Children practice and maintain skills
through Math Box problems.
Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 5. [Number and Numeration Goal 2]
Home Link 9�7Math Masters, p. 288
Children practice and maintain skills
through Home Link activities.
READINESS
Trading MoneyMath 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.
ENRICHMENTSharing Money EquallyMath Masters, p. 289
Children solve a problem with equal shares
of money.
Teaching the Lesson Ongoing Learning & Practice
132
4
Differentiation Options
Sharing MoneyObjective To guide children as they share whole-dollar
amounts equally.a
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
748_EMCS_T_TLG_G3_U09_L07_576892.indd 748748_EMCS_T_TLG_G3_U09_L07_576892.indd 748 2/17/11 3:42 PM2/17/11 3:42 PM
Name Date Time
$1 Bills
396-404_440_452_462_EMCS_B_MM_G3_U01Proj_576957.indd 399 3/11/11 12:45 PM
Math Masters, p. 399
Teaching Aid Master
Lesson 9�7 749
Getting Started
Math MessageWhat 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.
Home Link 9�6 Follow-Up 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.
Mental Math and Reflexes Children write fractions on their slates and show whether each fraction is
greater than 1
_ 2 (thumbs-up), equal to
1
_ 2
(fists), or less than 1
_ 2 (thumbs-down).
1 _ 4 less than
1
_ 2 , thumbs-down
3 _ 6 equal to
1
_ 2 , fist
3 _ 8 less than
1
_ 2 , thumbs-down
7 _ 8 greater than
1
_ 2 , thumbs-up
2 _ 3 greater than
1
_ 2 , thumbs-up
3 _ 5 greater than
1
_ 2 , thumbs-up
Adjusting the Activity
1 Teaching the Lesson
� Math Message Follow-Up WHOLE-CLASSDISCUSSION
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 WHOLE-CLASS ACTIVITY
(Math Journal 2, p. 222; Math Masters,
pp. 399–402)
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.
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
PROBLEMBBBBBBBBBBBOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMEEEEMMBLEBLLELBLLLLBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMOOOOOOOOOOBBBBBLBLBLBBBLBLLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELLELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMOOOOOOOOOBBBLBLBLBLBLBOOOROROROROROROROROROROO LELELELEEEEEELEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLLVINVINVINNNNVINVINVINNVINVINVINVINVINV GGGGGGGGGGOLOOOLOLOLOOLOO VINVVINLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOLOOLOLOLOLOLOLOOO VVVLLLLLLLLLLVVVVVVVVOSOSOOSOSOSOSOSOSOSOOSOSOSOOSOOOOOSOSOSOSOSOSSOOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLVVVVVVVVVLVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIISOLVING
ELL
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750 Unit 9 Multiplication and Division
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 2
_ 5 .
Problem 1: Share $54 equally among 3 people.
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 = ?
� 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.
� Children record these transactions on page 222.
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.
� 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.”
Sharing MoneyLESSON
9�7
Date Time
Work with a partner. Put your play money in a bank for both of you to use.
1. If $54 is shared equally by 3 people, how much does each person get?
a. Number model: $54 ÷ 3 = ?
b. How many $10 bills does each person get? 1 $10 bill(s)
c. How many dollars are left to share? $ 24.00
d. How many $1 bills does each person get? 8 $1 bill(s)
e. Answer: Each person gets $ 18.00 .
2. If $71 is shared equally by 5 people, how much does each person get?
a. Number model: $71 ÷ 5 = ?
b. How many $10 bills does each person get? 1 $10 bill(s)
c. How many dollars are left to share? $ 21.00
d. How many $1 bills does each person get? 4 $1 bill(s)
e. How many $1 bills are left over? 1 $1 bill(s)
f. If the leftover $1 bill(s) are shared equally,
how many cents does each person get? $ 0.20
g. Answer: Each person gets $ 14.20 .
3. $84 ÷ 3 = $ 28.00 4. $75 ÷ 6 = $ 12.50
5. $181 ÷ 4 = $ 45.25 6. $617 ÷ 5 = $ 123.40
204-239_EMCS_S_MJ2_G3_U09_576418.indd 222 3/11/11 1:45 PM
Math Journal 2, p. 222
Student Page
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.
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Lesson 9�7 751
Links to the Future
� Solving Division Problems PARTNER ACTIVITY
(Math Journal 2, p. 222)
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.
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.
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.
PROBLEMBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEMMMBLELBLELBLLLLBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMMOOOOOOOOOOOBBBBBBBLBLBLBLBLBLLLLLLPROPROPROPROPROPROPROPROPROPRPROPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROOROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEEEEEELELEELEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMMOOOOOOOOOBBBBLBLBBLBLBLBOOOOROROROROROROROROROO LELELELEEEEEELEEMMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLVVINVINVINVINNNVINVINNNVINVINVINVINVINGGGGGGGGGGGOLOOOLOOLOLOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINVINV NGGGGGGGGGGOOOLOLOLOLOLOLOOO VVVVVVVLLLLLLLLLLVVVVVVVVVOOSOSOOSOSOSOSOSOSOSOOSOSOSOSOSOOOOOSOSOSOSOSOSSOOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING
Factor Bingo Game Mat
448
Name Date Time
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
Write any of the numbers
2 through 90 on the grid
above.
You may use a number
only once.
To help you keep track
of the numbers you use,
circle them in the list.
132
4
Math Masters, p. 448
Game Master
Games
Factor BingoMaterials □ 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.
6. If all the cards are used before someone wins, shuffle the cards again and continue playing.
Student Reference Book, p. 285
Student PageGames
Factor Bingo Game MatSample 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
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.
Student Reference Book, p. 286
Student Page
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752 Unit 9 Multiplication and Division
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,
how many cents does each friend get?
f. Answer: Each friend gets a total of $ .
Name Date Time
Sharing Money with FriendsHOME LINK
9�7
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.
Please return this Home Link to school tomorrow.
Family Note
73
Practice
Use the partial-products method to solve these problems. Show your work.
2. 21 3. 48 4. 63
× 2 × 4 × 5
$77 ÷ 4 = ?
3
9
1
$0.25
19.25
31519242
1
267-318_EMCS_B_MM_G3_U09_576957.indd 288 3/10/11 2:42 PM
Math Masters, p. 288
Home Link Master
� Math Boxes 9�7 INDEPENDENTACTIVITY
(Math Journal 2, p. 223)
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.
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 1 _ 2 pieces.
Ongoing Assessment: Math Boxes
Problem 5 �Recognizing Student Achievement
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.
[Number and Numeration Goal 2]
� Home Link 9�7 INDEPENDENTACTIVITY
(Math Masters, p. 288)
Home Connection Children solve an equal-sharing problem involving money.
5. What part of this pizza
has been eaten?
2 _ 8 , or 1
_ 4
What part is left?
6 _ 8 , or 3
_ 4
3. Use the partial-products algorithm
to solve.
296× 4
800 360 + 24 1,184
183× 7
700 560 + 21 1,281
Date Time
2. Draw a 4-by-8 array of Xs.
How many Xs in all? 32Write a number model.
4 × 8 = 32
4. Put in the parentheses needed to
complete the number sentences.
15 + 80 × 90 = 7,215
14 – 6 × 800 = 6,400
60 × 79 + 1 = 4,800
6. Solve.
1,000 milligrams = 1 gram
3,000 milligrams = 3 grams
500 milligrams = 1 _ 2 gram
1,000 grams = 1 kilogram
6,000 grams = 6 kilograms
1. Draw a shape with a perimeter
of 20 centimeters.
Sample answer:
What is the area of your shape?
16 square centimeters
Math BoxesLESSON
9�7
150 151154 155
68 69
64 65
16 17
22 23 162
(
(
(
(
( (
�
204-239_EMCS_S_MJ2_G3_U09_576418.indd 223 3/11/11 1:45 PM
Math Journal 2, p. 223
Student Page
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3 Differentiation Options
READINESS PARTNER ACTIVITY
� Trading Money 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 GameYou 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.
Directions:
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 PARTNER ACTIVITY
� Sharing Money Equally 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.
Lesson 9�7 753
LESSON
9�7
Name 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.
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.
20
How many people could go to the show if you had $32.00?
Explain your answer.
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.
25Try This
Math Masters, p. 289
Teaching Master
LESSON
5�8
Name Date Time
Place-Value Mat
Do
llars
On
es
Fla
ts
$
1.0
0
1
Dim
es
Ten
ths
Lon
gs
$
0.1
0
0
.1
Pen
nie
s H
un
dre
dth
s Cu
bes
$
0.0
1
0
.01
EM3MM_G3_U05_119-166.indd 146 12/28/10 10:06 AM
Math Masters, p. 146
Teaching Master
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Copyrig
ht ©
Wrig
ht G
roup/M
cG
raw
-Hill
288
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,
how many cents does each friend get?
f. Answer: Each friend gets a total of $ .
Name Date Time
Sharing Money with FriendsHOME LINK
9�7
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.
Please return this Home Link to school tomorrow.
Family Note
73
Practice
Use the partial-products method to solve these problems. Show your work.
2. 21 3. 48 4. 63
× 2 × 4 × 5
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