Buying at the
Stock-Up Sale
Objective To guide children as they multiply using mental math
and the partial-products algorithm.
a
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Key Concepts and Skills
• Apply place-value concepts to find
partial products. [Number and Numeration Goal 1]
• Use multiplication facts to make estimates
and calculate partial products. [Operations and Computation Goal 3]
• Use the partial-products algorithm to
multiply 1-digit by multidigit numbers. [Operations and Computation Goal 4]
• Make reasonable estimates. [Operations and Computation Goal 5]
Key Activities
Children make up and solve problems
about costs of multiple items advertised
on the Stock-Up Sale posters.
Materials
Math Journal 2, p. 217
Student Reference Book, pp. 216 and 217
Home Link 9 4
Math Masters, pp. 399 and 400 (optional)
slate tool-kit coins (optional)
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing Fraction Top-It
Student Reference Book, p. 287
Math Masters, p. 398
per partnership: 1 deck of
Fraction Cards
Children practice comparing fractions.
Ongoing Assessment:
Recognizing Student Achievement
Use an Exit Slip (Math Masters,
page 398). [Number and Numeration Goal 6]
Math Boxes 9 5
Math Journal 2, p. 218
Children practice and maintain skills
through Math Box problems.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Estimating Costs
Math Masters, p. 284; p. 399 (from Part 1)
Student Reference Book, pp. 216 and 217
tool-kit dimes
Children estimate the money they need
to make purchases at the Stock-Up Sale.
ENRICHMENT
Solving Multistep Number Stories
Student Reference Book, pp. 216 and 217
Math Masters, p. 285
Children estimate and solve multistep
number stories.
Home Link 9 5
Math Masters, p. 283
Children practice and maintain skills
through Home Link activities.
Advance Preparation
Copy and cut apart the play money on Math Masters, pages 399 and 400 (optional).
Teacher’s Reference Manual, Grades 1– 3 p. 190
736
Unit 9
Multiplication and Division
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Getting Started
Mental Math and Reflexes
Math Message
Have children practice quick recall of basic multiplication
facts. Suggestions:
Turn to page 217 in your Student Reference Book.
Estimate whether $10 is enough to buy 4 rolls of
gift-wrapping paper. Record your estimate on your slate.
Discuss your estimation strategy with a partner.
6 × 6 36
7 × 7 49
8 × 8 64
9 × 9 81
4 × 8 32
6 × 8 48
7 × 8 56
9 × 8 72
40 × 9 360 600 × 7 4,200 70 × 80 5,600 60 × 900 54,000
Home Link 9 4 Follow-Up
Briefly review answers. Have volunteers model the
partial-products algorithm for some of the problems.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
(Student Reference Book, p. 217;
Math Masters, pp. 399 and 400)
Discuss children’s answers. Possible estimation strategies:
Change $2.35 to a close-but-easier amount, such as $2.50.
4 × $2.50 = $10.00 (double $2.50 twice). $10 would be enough
to buy 4 rolls if they were $2.50 per roll. Because $2.50 is more
than $2.35, the cost of 4 rolls at $2.35 is less than $10.
Round $2.35 to the nearest $0.10, which is $2.40.
4 × $2.00 = $8.00, and 4 × $0.40 = $1.60. Therefore,
4 × $2.40 = $9.60. Because $2.40 is more than $2.35, the
cost is less than $10.
Remind children that many problems can be solved with
estimation instead of exact calculation. An efficient estimation
strategy requires simple mental math and gives an answer that
is reasonably close to the exact answer.
Have children work in small groups to find the exact cost, using
mental math or an algorithm. $9.40 Take time to have children
share strategies. For example:
4 × $2.00 = $8.00
Student Page
Data Bank
Stock-Up Sale Poster #2
5
4 × $0.30 = $1.20
OR M ORE
S ALE
You pay $2.63
per box
Gift Wrapping Paper
$2.35 per roll
Bath Soap
Greeting Cards
Box of 12 $3.29
$0.88
5
Toothbrush
OR M ORE
S ALE
You pay $0.65
per bar
5
Garbage Bags
$1.38
OR M ORE
S ALE
You pay $1.86
per roll
Night Light Bulbs
2-Pack
$0.96
$3.75
4 × $0.05 = $0.20
$8.00 + $1.20 + $0.20 = $9.40
5
OR M ORE
S ALE
You pay $1.13
per brush
5
Glue
K I N E S T H E T I C
5
OR M ORE
S ALE
You pay $0.76
per pack
Shoelaces
per pair
$1.27
ELL
Provide dollar bills (Math Masters, pages 399 and 400) and tool-kit
coins for children to use as they act out the problems.
A U D I T O R Y
You pay $3.18
per box
Construction Paper
$0.67 per pad
$1.15
Adjusting the Activity
OR M ORE
S ALE
T A C T I L E
5
OR M ORE
S ALE
You pay $0.94
per bottle
5
OR M ORE
S ALE
You pay $0.54
per pad
5
OR M ORE
S ALE
You pay $1.08
per pair
V I S U A L
Student Reference Book, p. 217
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Lesson 9 5
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Student Page
Applying the Partial-Products
Data Bank
Stock-Up Sale Poster #1
Light Bulbs
4-Pack
$1.09
WHOLE-CLASS
ACTIVITY
Algorithm
Extension Cord
Tissues
$3.25
(Student Reference Book, pp. 216 and 217)
$0.73
PROBLEM
PR
PRO
P
RO
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OBL
BLE
B
LE
L
LEM
EM
SOLVING
SO
S
OL
O
LV
VIN
IIN
NG
N
G
5
OR M ORE
S ALE
You pay $0.88
per pack
5
$0.84
OR M ORE
S ALE
You pay $0.65
per roll
5
$0.39
OR M ORE
S ALE
You pay $0.27
per pen
5
OR M ORE
S ALE
You pay $2.90
per pack
5
OR M ORE
S ALE
You pay $1.86
per can
OR M ORE
S ALE
Various items are advertised on the two Stock-Up Sale Posters.
You or the children use the given prices to suggest number stories
that can be solved in two steps. Prior to solving each number
story, have children estimate the answer. Next they represent
the number story with a number model and use a letter for the
unknown quantity and parentheses to show the first calculation.
Then they find the answer using the partial-products algorithm
(Lesson 9-4) with dollars and cents. For the first few stories, write
the problems on the board while the children suggest the number
models for the partial products.
You pay $0.57
per box
Toothpaste
$1.39
5
Tennis Balls
Can of 3 $2.59
Ballpoint Pen
5
You pay $2.79
per cord
Batteries
4-Pack
$3.59
Transparent Tape
5
OR M ORE
S ALE
OR M ORE
S ALE
You pay $1.14
per tube
Paperback Book
$2.99
5
OR M ORE
S ALE
You pay $2.25
per book
Student Reference Book, p. 216
211_248_EMCS_S_G3_SRB_DBA_577260.indd 216
NOTE Explain to children that stores often
encourage customers to spend more by
reducing the price of an item purchased in
bulk. Stores make up for the lower profit per
item by selling more items.
2/17/11 9:48 AM
For example: How much change would you receive if you bought
5 packs of batteries at the stock-up sale price and paid with a
$20 bill? (Story examples are based on Student Reference Book,
pages 216 and 217.)
Remind children of the Guide to Solving Number Stories on Math
Masters, page 406.
●
What do you want to find out? The amount of change you would
receive from $20
●
What do you know from reading the story and looking at the
Stock-Up Sale Poster? 5 packs of batteries are purchased and
each pack costs the sale price of $2.90.
Ask partners to work together to estimate the answer. After a
few minutes, discuss children’s answers. One possible estimation
strategy is to round $2.90 to the nearest dollar, which is $3.00.
$3.00 × 5 is $15.00. The difference between $20.00 and $15.00 is
$5, so the answer to the number story should be about $5.
Explain that because the number story asks for the amount of
change, we need to calculate to find the exact answer. Ask: Will the
exact answer be more or less than $5? More, because we rounded
the price of one pack of batteries up to $3.
NOTE Some children might use mental
arithmetic to find the exact answer, thinking
of the solution as: 5 × $0.10 = $0.50;
$15 − $0.50 = $14.50; $20 − $14.50 =
$5.50. Praise this strategy; however, since
the focus of this lesson is on the partialproducts algorithm, make sure to emphasize
the strategy described in this activity.
738
●
What is a first step to solve the problem? Find the cost of
5 packs of batteries.
●
How might you do this? Multiply $2.90 × 5. Write $2.90 × 5
on the board.
●
What symbols can we use in the number model to show that
this is the first step? Add parentheses around $2.90 × 5.
●
What is the second step? Subtract that product from $20.00.
●
How can we write this step? Indicate the first step using
parentheses, then subtract from $20. Write the step on the
board: $20 – ($2.90 × 5). Since we want to find the amount of
change, use C for the unknown quantity in the open sentence:
$20 − ($2.90 × 5) = C.
Unit 9 Multiplication and Division
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Student Page
Date
Links to the Future
At this time, children are not expected to know the conventional order of
operations, so parentheses tell them which operation comes first. Understanding
that grouping symbols can be used to affect the order in which operations
are carried out is a Grade 3 Grade-Level Goal. Describing and applying the
conventional order of operations is a Grade 6 Grade-Level Goal.
Time
LESSON
Shopping at the Stock-Up Sale
95
Use the Stock-Up Sale Posters on pages 216 and 217 in the Student
Reference Book. Solve each number story below. There is no sales tax.
For each problem:
Estimate the answer.
Write a number model with parentheses to show which step is first.
Use a letter to show what you want to find out.
Solve for the exact answer.
Show your work.
1.
workspace
Jeff bought 5 toothbrushes and 1 tube of toothpaste.
Sample answer:
$7.40
Estimate: The total cost is about
What is the total cost?
Take a few minutes to reconnect each expression in the number
model with the problem situation. What is $20? The amount of
money used to pay for the batteries What is $2.90? The cost of
1 pack of batteries Why are we multiplying $2.90 by 5? To find the
cost of 5 packs of batteries
Because the calculation in parentheses is solved first, write the
multiplication problem on the board. Ask children to suggest
number models for the partial products.
Number model:
.
(5 × $1.13) + $1.39 = T
$7.04
Answer:
Does your answer make sense? Explain.
Sample answer: Yes, my estimate was about $7.40 and my
answer was $7.04. They are close.
2.
Mr. De la Garza pays for 8 boxes of tissues with a $5.00 bill.
How much change will he get? Sample answer:
Estimate: He will get about
Number model:
$0.20
.
$5.00 – (8 × $0.57) = C
$0.44
Answer:
Does your answer make sense? Explain.
$2.90
× 5
5 [$2.00s]→ 10.00
5 [$0.90s]→ + 4.50
$14.50
Sample answers: Yes, because the amount of change is less
than what he started with; my answer is close to my estimate.
Math Journal 2, p. 217
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Ask: Is $14.50 the answer to the number story? no Why? $14.50
tells how much 5 packs of batteries cost, but we still need to find
out how much change is left from $20. What is the second step?
Subtract $14.50 from $20. Have children complete the calculation:
$20 – $14.50 = $5.50.
●
What is the answer to the number story? You would get $5.50
change.
●
Does your answer make sense? yes
●
How do you know? Sample answers: Before I solved for the
exact answer, I estimated the change to be about $5. $5.50 is
close to $5; I know my answer has to be less than $20 because
some of the money was spent on batteries.
●
Does your answer make the number model true? yes Write a
summary number model on the board: $20 − ($2.90 × 5) =
$5.50.
Pose another number story: How much would it cost to buy 5 pads
of construction paper and 1 bottle of glue?
●
●
Student Page
Games
Fraction Top-It
Materials □ 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
What do you want to find out? The total cost of the construction
paper and 1 bottle of glue
1. Shuffle the Fraction Cards and place the deck
picture-side down on the table.
What do you know from reading the story and looking at the
poster? I know that if you buy 5 or more pads you get the stockup sale price. One pad of construction paper at the sale price is
$0.54 and 1 bottle of glue at the regular price costs $1.15.
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.
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.
4. The game is over when all cards have been taken from
the deck. The player with more cards wins.
Players turn over a _34 card and a _46 card.
A possible number model for the story is ($0.54 × 5) + $1.15 = T.
The
3
_
4
card has a larger shaded area. The player holding
the
3
_
4
card takes both cards.
●
Players turn over a
What is the answer? The total cost is $3.85.
As needed, continue to suggest number stories involving two or
more steps to solve with the class.
3
4
1
_
card and a _48 card.
2
The shaded parts are equal. Each player turns over
another card. The player with the larger Fraction Card
takes all the cards.
4
6
1
2
4
8
1
2
4
8
Student Reference Book, p. 287
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Lesson 9 5
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Student Page
Date
Math Boxes
95
1.
Solving Stock-Up
Time
LESSON
2.
Fill in the oval for the best
answer. The perimeter of the
quadrangle is
Sale Stories
Draw a 4-by-9 array of Xs.
6 yd
15 yd
24 yd.
How many Xs in all?
Write a number model.
42 yd.
Use the partial-products algorithm
to solve.
5.
92
× 6
37
× 5
540
+ 12
552
150
+ 35
185
4.
60
200
(7 × 80) + 140 = 700
(40 × 3) ÷ 2 =
68 69
16
6.
Solve.
2 grams =
5
1
Color _
6 of the set green.
B R R G
B
grams = 5,000 milligrams
1 kilogram =
4
R R G
2 Ongoing Learning & Practice
1,000 milligrams
2,000 milligrams
1 gram =
1
Color _
3 of the set red.
B
64 65
Solve.
5
Color _
12 of the set blue.
B
Children work together in partnerships to solve 2-step problems
on journal page 217 using the information on pages 216 and 217
in the Student Reference Book. Children write the number models
using a letter variable for the unknown quantity.
4 × (300 ÷ 6) =
Draw a set of 12 circles.
B
36
4 × 9 = 36
150 151
3.
PROBLEM
PRO
PR
P
RO
R
OB
BLE
BL
LE
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LEM
EM
SOLVING
SO
S
OL
O
LV
VIN
IIN
NG
(Math Journal 2, p. 217; Student Reference
Book, pp. 216 and 217)
21 yd.
30 yd.
PARTNER
ACTIVITY
Playing Fraction Top-It
1,000 grams
kilograms = 4,000 grams
24
(Student Reference Book, p. 287; Math Masters, p. 398)
162
Math Journal 2, p. 218
204-239_EMCS_S_MJ2_G3_U09_576418.indd 218
PARTNER
ACTIVITY
3/11/11 1:45 PM
Children practice comparing fractions by playing Fraction Top-It.
For game instructions, see Lesson 8-6 or page 287 in the Student
Reference Book. Have children use an Exit Slip to record at least
five rounds using the symbols >, <, and = to compare the
fraction pairs.
Ongoing Assessment:
Recognizing Student Achievement
Exit Slip
Use an Exit Slip (Math Masters, page 398) to assess children’s progress
toward comparing fractions. Children are making adequate progress if they are
able to record at least 5 pairs of fractions with the appropriate comparison
symbols. Some children may be able to compare the fractions without using
Fraction Cards.
Home Link Master
Name
Date
[Number and Numeration Goal 6]
Time
Saving at the Stock-Up Sale
HOME LINK
95
Family
Note
Today the class used mental math and the partial-products algorithm to solve problems. For each
problem below, have your child estimate the answer and then write a number model to represent
the story, using a letter for the unknown quantity and parentheses to show which calculation
they do first. Note that any letter can be used to represent the unknown quantity.
16 17
68 69
192
Please return this Home Link to school tomorrow.
For each problem, make an estimate and then solve for the exact answer.
Write a number model using a letter for what you want to find out and use
parentheses to show which calculation you do first.
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 218)
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 9-7. The skill in Problem 6
previews Unit 10 content.
1. Phil has $6.00. He wants to buy Creepy
Creature erasers that cost $1.05 each. If he
buys 5 or more, they are $0.79 each. Does
he have enough money to buy 7 erasers?
Math Boxes 9 5
yes
Sample answer: If Phil buys 7
erasers, each costs $0.79. $0.79 is close to $0.80
and $0.80 × 7 is $5.60. That is less than $6.
Explain your estimate.
How much money will Phil have left if he buys 7 Creepy Creature erasers?
$6.00 - ($0.79 × 7) = M
0.47
Answer: Phil has $
left.
Number model:
(Math Masters, p. 283)
2. Mrs. Katz is buying apples and carrot cake
for a school party. The apples cost $2.12 per
pound. The carrot cake costs $19.75. Estimate
the cost for 3 pounds of apples and 1 cake.
INDEPENDENT
ACTIVITY
PROBLEM
PR
PRO
P
RO
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OB
BLE
BL
LE
L
LEM
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SO
S
SOLVING
OL
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LV
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VING
VIN
V
ING
Home Connection Children use mental math or the
partial-products algorithm to solve multiplication
number stories.
Sample answer: 26.00
Explain your estimate.
Sample answer: $2.12 is close to $2 so 3 pounds of
apples cost about $6. $19.75 is close to $20. So the
total cost is about $26.
Estimate: About $
What is the exact cost for 3 pounds of apples and 1 cake?
Number model:
Home Link 9 5
($2.12 × 3) + $19.75 = E
26.11
.
Answer: The exact cost is $
283
Math Masters, p. 283
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Unit 9 Multiplication and Division
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Teaching Master
Name
3 Differentiation Options
READINESS
Estimating Costs
Date
95
PARTNER
ACTIVITY
5–15 Min
Use the Stock-Up Sale posters on pages 216 and 217 in your
Student Reference Book. Suppose that you have only dollars and
dimes. Write the least amount of money you could use to buy
each item.
Items to Be Purchased
Dollars and Dimes Needed
Example: 1 box of 12 Greeting Cards
Total: $
3
3
3.30
Total: $
2
4
2.40
Total: $
0
9
0.90
Total: $
0
8
0.80
Total: $
3
0
3.00
1 roll of Gift-Wrapping Paper
Price:
To provide experience with estimating money amounts, have
children determine the number of dollar bills and dimes they
need to make purchases. Use the Stock-Up Sale posters on
pages 216 and 217 in the Student Reference Book. Children
record their work on Math Masters, page 284.
Solving Multistep
PARTNER
ACTIVITY
$2.35
1 roll of Transparent Tape
Price:
$0.84
1 box of Tissues
Price:
$0.73
1 Paperback Book
Price:
$2.99
15–30 Min
Number Stories
(Student Reference Book, pp. 216 and 217; Math Masters, p. 285)
To provide children with experience with multistep number
stories, have them use information from the Stock-Up Sale Posters
on Student Reference Book, pages 216 and 217 to solve stories
on Math Masters, page 285. For each story, have children
estimate and then solve. Explain that when writing number
models for number stories with more than two steps, more than
one set of parentheses is sometimes needed. For example, consider
the following story: Compare the cost of buying 4 paperback books
to the cost of buying 5 paperback books. A possible number model
could be ($2.99 × 4) – ($2.25 × 5) = D. The calculations for the
costs of 4 books at the regular price and 5 books at the sale price
must be done before subtracting to find the difference.
dollars
dimes
dollars
dimes
dollars
dimes
dollars
dimes
dollars
dimes
Math Masters, p. 284
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2/18/11 7:37 PM
Algorithm Project The focus of this
lesson is to apply the partial-products
algorithm to money amounts. For enrichment,
see Algorithm Project 4 on page A15 to teach
U.S. traditional multiplication of decimals
using money.
Teaching Master
Name
NOTE It is also acceptable for children to write a series of number models for
number stories with more than two steps.
193 194
Use dollars and dimes to help you.
Price: $3.29
(Math Masters, p. 284; Student Reference Book,
pp. 216 and 217)
ENRICHMENT
Time
Dollars and Dimes
LESSON
LESSON
95
Date
Time
Solving Multistep Number Stories
Use the Stock-Up Sale Posters on pages 216 and 217 in the Student
Reference Book. For each problem below, make an estimate and then
solve the number story. There is no sales tax.
1. How much more do 5 boxes of garbage
bags cost than 3 boxes of garbage bags?
3
Explain your estimate.Sample answer:
If I buy 5 boxes, I pay $3.18 for each box; if I buy
3 boxes, I pay $3.75 for each box. $3.18 is close to
$3 and $3.75 is close to $4. $3 × 5 = $15 and
$4 × 3 = $12. The difference is about $3.
Sample answer: (5 × $3.18) – (3 × $3.75) = D
Number model:
Estimate: About $
Solve. Show your work on the back of the page.
Answer: 5 boxes cost $
4.65
more than 3 boxes.
2. How much more does it cost to buy 5 rolls
of wrapping paper than 2 rolls of wrapping paper?
2.50 Explain your estimate. Sample answer:
If I buy 5 rolls, each roll costs $1.86. If I buy 3 rolls, each
roll costs $2.35. I know that $1.86 is close to $2 and
$2.35 is close to $2.50, so $2 × 5 = $10 and
$2.50 × 3 = $7.50. The difference will be about $2.50.
Sample answer: (5 × $1.86) – (3 × $2.35) = D
Number model:
Estimate: About $
Solve. Show your work on the back of the page.
Answer: 5 rolls cost $
2.25
more than 3 rolls.
Math Masters, p. 285
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Lesson 9 5
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3/11/11 3:16 PM
Name
HOME LINK
95
Family
Note
Date
Time
Saving at the Stock-Up Sale
Today the class used mental math and the partial-products algorithm to solve problems. For each
problem below, have your child estimate the answer and then write a number model to represent
the story, using a letter for the unknown quantity and parentheses to show which calculation
they do first. Note that any letter can be used to represent the unknown quantity.
16 17
68 69
192
Please return this Home Link to school tomorrow.
For each problem, make an estimate and then solve for the exact answer.
Write a number model using a letter for what you want to find out and use
parentheses to show which calculation you do first.
1. Phil has $6.00. He wants to buy Creepy
Creature erasers that cost $1.05 each. If he
buys 5 or more, they are $0.79 each. Does
he have enough money to buy 7 erasers?
Explain your estimate.
How much money will Phil have left if he buys 7 Creepy Creature erasers?
Number model:
$6.00 - ($0.79 × 7) = M
Copyright © Wright Group/McGraw-Hill
Answer: Phil has $
left.
2. Mrs. Katz is buying apples and carrot cake
for a school party. The apples cost $2.12 per
pound. The carrot cake costs $19.75. Estimate
the cost for 3 pounds of apples and 1 cake.
Estimate: About $
Explain your estimate.
What is the exact cost for 3 pounds of apples and 1 cake?
Number model:
Answer: The exact cost is $
.
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Name
LESSON
95
Date
Time
Solving Multistep Number Stories
Use the Stock-Up Sale Posters on pages 216 and 217 in the Student
Reference Book. For each problem below, make an estimate and then
solve the number story. There is no sales tax.
1. How much more do 5 boxes of garbage
bags cost than 3 boxes of garbage bags?
Estimate: About $
Explain your estimate.
Number model:
Solve. Show your work on the back of the page.
Answer: 5 boxes cost $
more than 3 boxes.
2. How much more does it cost to buy 5 rolls
of wrapping paper than 2 rolls of wrapping paper?
Copyright © Wright Group/McGraw-Hill
Estimate: About $
Explain your estimate.
Number model:
Solve. Show your work on the back of the page.
Answer: 5 rolls cost $
more than 3 rolls.
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