Transcript Gr04_Ch_08 - Etiwanda E

Chapter 8
Multiply by Two-Digit Numbers
Click the mouse or press the space bar to continue.
8
Multiply by Two-Digit Numbers
Lesson 8-1
Multiply by Tens
Lesson 8-2
Estimate Products
Lesson 8-3
Problem-Solving Strategy: Act It Out
Lesson 8-4
Multiply Two-Digit Numbers
Lesson 8-5
Multiply Three-Digit Numbers by
Two-Digit Numbers
Lesson 8-6
Problem-Solving Investigation:
Choose a Strategy
Lesson 8-7
Multiply Greater Numbers
8-1
Multiply by Tens
Five-Minute Check (over Chapter 7)
Main Idea
California Standards
Example 1: Multiply by Tens
Example 2: Multiply by Tens
8-1
Multiply by Tens
• I will multiply a whole number by a multiple of ten.
8-1
Multiply by Tens
Standard 4NS3.3 Solve problems
involving the multiplication of multidigit
numbers by two-digit numbers.
8-1
Multiply by Tens
Standard 4NS3.2 Demonstrate an
understanding of, and the ability to use,
standard algorithms for multiplying a multidigit
number by a two-digit number and for dividing a
multidigit number by a one-digit number; use
relationships between them to simplify computations
and to check results.
8-1
Multiply by Tens
There are 35 packs of markers in an art classroom.
Each pack contains 50 markers. How many markers
are there in all?
You need to find 35 × 50.
8-1
Multiply by Tens
One Way: Use Properties
35 × 50
35 × (10 × 5)
35 × (5 × 10)
(35 × 5) × 10
175 × 10
1,750
Write the problem.
Think of 50 as 10 × 5.
Commutative Property
Associative Property
Multiply. 35 × 5 = 175
Mental Math
8-1
Multiply by Tens
Another Way: Paper and Pencil
Step 1 Multiply the
ones.
35
× 50
0
Step 2 Multiply the
tens.
35
× 50
1,75 0
Answer: So, there are 1,750 markers in all.
8-1
Multiply by Tens
Find 45 × 30.
A. 1,350
B. 1,250
C. 135
D. 125
8-1
Multiply by Tens
A store has 20 children’s bicycles in stock that
cost $159 each. How much do the bicycles cost
altogether?
Step 1 Multiply the ones.
$159
× 20
0
8-1
Multiply by Tens
Step 2 Multiply the tens.
$159
× 20
$3,18 0
Answer: So, the bicycles cost $3,180 altogether.
8-1
Multiply by Tens
Check
Think of 20 × 159 as 2 × 10 × 159.
20 × $159
(2 × 10) × $159
(10 × 2) × $159
10 × (2 × $159)
10 × $318
$3,180
Write the problem.
Think of 20 as 2 × 10.
Commutative Property
Associative Property
Multiply. 2 × $159 = $318
Mental Math
So, the answer is correct.
8-1
Multiply by Tens
Find $179 × 30.
A. $6,370
B. $5,530
C. $5,370
D. $4,170
8-2
Estimate Products
Five-Minute Check (over Lesson 8-1)
Main Idea
California Standards
Example 1: Estimate Products
Example 2: Estimate Products
8-2
Estimate Products
• I will estimate products by rounding.
8-2
Estimate Products
Standard 4NS3.3 Solve problems involving
multiplication of multidigit numbers by two-digit
numbers.
Standard 4NS1.3 Round whole numbers
through the millions to the nearest ten, hundred,
thousand, ten thousand, or hundred thousand.
8-2
Estimate Products
Kaylee is awake for about 16 hours each day.
About how many hours is she awake in 4 weeks?
There are 28 days in 4 weeks. So, estimate 16 × 28.
Round each factor to its greatest place. Then multiply.
Step 1 Round each factor to the nearest ten.
16
× 28
20
× 30
8-2
Estimate Products
Step 2 Multiply.
20
× 30
600
Answer: So, Kaylee is awake for about 600 hours
in 4 weeks.
8-2
Estimate Products
A koala sleeps for about 19 hours a day. About
how many hours does one sleep in 3 weeks?
A. 400 hours
B. 425 hours
C. 450 hours
D. 500 hours
8-2
Estimate Products
A company bought 53 computers for $909 each.
About how much did they spend in all?
You need to estimate $909 × 53.
Step 1 Round each factor to its greatest place.
909
× 53
900
× 50
8-2
Estimate Products
Step 2 Multiply.
900
× 50
45,000
Answer: So, the company spent about $45,000.
8-2
Estimate Products
A school bought 57 laptops for $837 each. About
how much did the school spend in all?
A. $45,000
B. $48,000
C. $53,000
D. $56,000
8-3
Problem-Solving Strategy: Act It Out
Five-Minute Check (over Lesson 8-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
8-3
Problem-Solving Strategy: Act It Out
• I will solve a problem by acting it out.
8-3
Problem-Solving Strategy: Act It Out
Standard 4MR2.3 Use a variety of methods,
such as words, numbers, symbols, charts,
graphs, tables, diagrams, and models, to
explain mathematical reasoning.
8-3
Problem-Solving Strategy: Act It Out
Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.
8-3
Problem-Solving Strategy: Act It Out
Sonoda has 6 coins in his
bank. The coins equal 65¢.
What combination of coins
does he have in his bank?
8-3
Problem-Solving Strategy: Act It Out
Understand
What facts do you know?
• Sonoda has 6 coins.
• The value of the 6 coins is 65¢.
What do you need to find?
• Find the coins Sonoda has in his bank.
8-3
Problem-Solving Strategy: Act It Out
Plan
You can use play money to act out different
combinations of 65¢.
8-3
Problem-Solving Strategy: Act It Out
Solve
One way to make 65¢ is
with 2 quarters, 1 dime,
and 1 nickel. But, that is
only 4 coins. You need
two more coins.
8-3
Problem-Solving Strategy: Act It Out
Solve
Take 1 quarter and
exchange it for
2 dimes and 1 nickel.
The value stays the
same, and the number
of coins increases to 6.
Answer: So, Sonoda has 1 quarter, 3 dimes, and
2 nickels.
8-3
Problem-Solving Strategy: Act It Out
Check
Look back at the problem.
1 quarter + 3 dimes + 2 nickels
= (1 × 25 ) + (3 × 10 ) + (2 × 5 )
=
=
25
+
30
65
So, the answer is correct.
+
10
8-4
Multiply Two-Digit Numbers
Five-Minute Check (over Lesson 8-3)
Main Idea
California Standards
Example 1: Real-World Example
Example 2: Multiply Money
8-4
Multiply Two-Digit Numbers
• I will multiply two-digit numbers.
8-4
Multiply Two-Digit Numbers
Preparation for Standard 4NS3.2
Demonstrate an understanding of, and the ability to
use, standard algorithms for multiplying a multidigit
number by a two-digit number and for dividing a
multidigit number by a one-digit number; use the
relationships between them to simplify computations
and to check results.
8-4
Multiply Two-Digit Numbers
Preparation for Standard 4NS3.3 Solve
problems involving multiplication of multidigit
numbers by two-digit numbers.
8-4
Multiply Two-Digit Numbers
How far can a truck travel in 14 hours if it is
traveling an average of 57 miles per hour?
8-4
Multiply Two-Digit Numbers
One Way: Partial Products
57
× 14
28
200
70
+ 500
798
Multiply 4 × 7.
Multiply 4 × 50.
Multiply 10 × 7.
Multiply 10 × 50.
Add partial products.
8-4
Multiply Two-Digit Numbers
One Way: Partial Products
8-4
Multiply Two-Digit Numbers
Another Way: Paper and Pencil
Step 1 Multiply the ones.
2
57
× 14
228
8-4
Multiply Two-Digit Numbers
Another Way: Paper and Pencil
Step 2 Multiply the tens.
2
57
× 14
228
570
8-4
Multiply Two-Digit Numbers
Another Way: Paper and Pencil
Step 3 Add the
products.
2
57
× 14
228
+ 570
798
Answer: So, the truck can travel 798 miles
in 14 hours at 57 miles per hour.
8-4
Multiply Two-Digit Numbers
How far can a car travel in 15 hours if it is traveling
an average of 63 miles per hour?
A. 368 miles
B. 378 miles
C. 935 miles
D. 945 miles
8-4
Multiply Two-Digit Numbers
The Jones family spends an average of $48 a
month going to the movies. How much does the
family spend in 3 years?
There are 12 months in one year and 36 months in
3 years.
Estimate 50 × 40 = 2,000
8-4
Multiply Two-Digit Numbers
Step 1 Multiply the ones.
$48
× 36
288
Step 2 Multiply the tens.
$48
× 36
288
+ 1,440
8-4
Multiply Two-Digit Numbers
Step 3 Add the products.
$48
× 36
288
+ 1,440
1,728
Answer: So, the Jones family spends $1,728 going
to the movies in 3 years.
8-4
Multiply Two-Digit Numbers
Check
1,200 + 240 + 240 + 48 = 1,728
Check for Reasonableness
Since 1,728 is close to the estimate of 2,000, the
answer is reasonable.
8-4
Multiply Two-Digit Numbers
Lauren spends about $72 a month on gas for her
car. How much does she spend on gas in 4 years?
A. $3,456
B. $3,157
C. $2,456
D. $2,157
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Five-Minute Check (over Lesson 8-4)
Main Idea
California Standards
Example 1: Real-World Example
Example 2: Real-World Example
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
• I will multiply a three-digit number by a two-digit
number.
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Standard 4NS3.2 Demonstrate an
understanding of, and the ability to use,
standard algorithms for multiplying a multidigit
number by a two-digit number and for dividing a
multidigit number by a one-digit number; use the
relationships between them to simplify computations
and to check results.
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Standard 4NS3.3 Solve problems involving
multiplication of multidigit numbers by two-digit
numbers.
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Antonio spends 194 minutes taking piano lesson
each month. How many minutes does he spend
taking piano lesson in a year?
Estimate 12 × 194
Step 1 Multiply 194 by 2.
194
× 12
388
10 × 200 = 2,000
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
1
Step 2 Multiply 194
by 1 ten.
194
× 12
388
1,940
1
Step 3 Add the
products.
194
× 12
388
+ 1,940
2,328
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Answer: So, Antonio spends 2,328 minutes taking
piano lessons in a year.
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Check for Reasonableness
Since 2,328 is close to the estimate, the answer
is reasonable.
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Lui spends about 321 minutes a month writing
to pen pals. How many minutes does he spend
writing letters in a year?
A. 3,210 minutes
B. 3,814 minutes
C. 3,752 minutes
D. 3,852 minutes
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Rai is paid $308 a week for her part-time job at the
city library. What is Rai’s annual salary?
Estimate $308 × 52
Step 1 Multiply $308 by 2.
1
$308
× 52
$616
300 × 50 = $15,000
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Step 2 Multiply $308 by 50.
4
1
$308
× 52
$616
$15,400
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Step 3 Add the partial products.
4
1
$308
× 52
$616
+ $15,400
$16,016
Answer: So, Rai’s annual salary is $16,016.
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Check for Reasonableness
Since $16,016 is close to the estimate, the answer
is reasonable.
8-5
Multiply Three-Digit Numbers by Two-Digit Numbers
Monique gets paid $444 a week at her job.
How much does she get paid in a year?
A. $22,088
B. $23,088
C. $21,088
D. $20,088
8-6
Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 8-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
8-6
Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
8-6
Problem-Solving Investigation: Choose a Strategy
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.
8-6
Problem-Solving Investigation: Choose a Strategy
Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.
8-6
Problem-Solving Investigation: Choose a Strategy
GREGORY: I spent 4 hours at a
carnival. I spent 45 minutes eating
and 55 minutes playing games. I
also rode 12 rides, which took
about 15 minutes each.
YOUR MISSION: Determine if Gregory
is correct in saying that he spent
4 hours at the carnival.
8-6
Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• Gregory spent 45 minutes eating.
• He spent 55 minutes playing games.
• He rode 12 rides, which lasted 15 minutes each.
What do you need to find?
• Find if Gregory is correct in saying he spent
4 hours at the carnival.
8-6
Problem-Solving Investigation: Choose a Strategy
Plan
Find the total number of minutes spent on
carnival activities and compare to 4 hours.
8-6
Problem-Solving Investigation: Choose a Strategy
Solve
Gregory gave the amount of time spent at the
carnival in hours. The amount of time spent on
each activity was given in minutes. So, change
hours to minutes. Then compare the two
amounts of time.
8-6
Problem-Solving Investigation: Choose a Strategy
Solve
60 minutes
60 minutes
60 minutes
+ 60 minutes
240 minutes
15
× 12
30
+ 150
180
45 minutes
55 minutes
+ 180 minutes
280 minutes
time Gregory said
he spent at carnival
time spent
riding rides
time spent on
carnival activities
8-6
Problem-Solving Investigation: Choose a Strategy
Solve
Answer: Since 240 minutes does not equal
280 minutes, Gregory is not correct.
8-6
Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem. Use subtraction to
check the amount of time spent on carnival
activities.
280 – 180 – 55 – 45 = 0
So, Gregory was not correct.
8-7
Multiply Greater Numbers
Five-Minute Check (over Lesson 8-6)
Main Idea
California Standards
Example 1: Real-World Example
Example 2: Real-World Example
8-7
Multiply Greater Numbers
• I will multiply four- and five-digit numbers by a
two-digit number.
8-7
Multiply Greater Numbers
Standard 4NS3.3 Solve problems involving
multiplication of multidigit numbers by two-digit
numbers.
Standard 4MR2.1 Use estimation to verify the
reasonableness of calculated results.
8-7
Multiply Greater Numbers
A science museum gets an average of 4,562 visitors
every week. How many visitors does it get in a year?
Estimate 52 × 4,562
50 × 5,000 = 250,000
Step 1 Multiply the ones. Regroup if necessary.
1 11
4,562
× 52
9,124
8-7
Multiply Greater Numbers
Step 2 Multiply the tens.
2 3
1 11
4,562
× 52
9,124
228,100
8-7
Multiply Greater Numbers
Step 3 Add the partial products. Check for
reasonableness.
2 3
1 11
4,562
× 52
9,124
+ 228,100
237,224
Answer: So, the science museum gets
237,224 visitors a year.
8-7
Multiply Greater Numbers
Check for Reasonableness
Since 237,224 is close to the estimate, the answer
is reasonable.
8-7
Multiply Greater Numbers
An amusement park gets an average of
8,225 visitors every week. How many
visitors does it get in a year?
A. 427,700 visitors
B. 427,590 visitors
C. 426,790 visitors
D. 427,800 visitors
8-7
Multiply Greater Numbers
A web site gets an average of 23,149 hits each
month. How many hits does it get in 15 months?
Estimate 15 × 23,149
20 × 20,000 = 400,000
Step 1 Multiply the ones. Regroup if necessary.
1
24
23,149
×
15
115,745
8-7
Multiply Greater Numbers
Step 2 Multiply the tens.
1
24
23,149
×
15
115,745
231,490
8-7
Multiply Greater Numbers
Step 3 Add the partial products.
1
24
23,149
×
15
115,745
+ 231,490
347,235
Answer: So, the website gets 347,235 hits in
15 months.
8-7
Multiply Greater Numbers
Check for Reasonableness
Since 347,235 is close to the estimate, the answer
is reasonable.
8-7
Multiply Greater Numbers
Another web site gets an average of 19,225 hits
a day. How many hits does the website get in a
31-day month?
A. 594,975 hits
B. 595,864 hits
C. 595,975 hits
D. 594,323 hits
8
Multiply by Two-Digit Numbers
Five-Minute Checks
Math Tool Chest
Image Bank
8
Multiply by Two-Digit Numbers
To use the images that are on the
following four slides in your own
presentation:
1. Exit this presentation.
2. Open a chapter presentation using a
full installation of Microsoft® PowerPoint®
in editing mode and scroll to the Image
Bank slides.
3. Select an image, copy it, and paste it
into your presentation.
8
Multiply by Two-Digit Numbers
8
Multiply by Two-Digit Numbers
8
Multiply by Two-Digit Numbers
8
Multiply by Two-Digit Numbers
8
Multiply by Two-Digit Numbers
Lesson 8-1
(over Chapter 7)
Lesson 8-2
(over Lesson 8-1)
Lesson 8-3
(over Lesson 8-2)
Lesson 8-4
(over Lesson 8-3)
Lesson 8-5
(over Lesson 8-4)
Lesson 8-6
(over Lesson 8-5)
Lesson 8-7
(over Lesson 8-6)
8
Multiply by Two-Digit Numbers
(over Chapter 7)
Multiply. Check for reasonableness.
203
× 2
A. 426
B. 405
C. 406
D. 425
8
Multiply by Two-Digit Numbers
(over Chapter 7)
Multiply. Check for reasonableness.
506
× 7
A. 1,283
B. 3,502
C. 1,273
D. 3,542
8
Multiply by Two-Digit Numbers
(over Chapter 7)
Multiply. Check for reasonableness.
3 × 7,035
A. 21,105
B. 21,095
C. 10,368
D. 21,405
8
Multiply by Two-Digit Numbers
(over Chapter 7)
Multiply. Check for reasonableness.
8 × $4,209
A. $32,743
B. $33,672
C. $13,097
D. $33,752
8
Multiply by Two-Digit Numbers
(over Chapter 7)
Multiply. Check for reasonableness.
6 × 5,008
A. 30,042
B. 30,108
C. 30,708
D. 30,048
8
Multiply by Two-Digit Numbers
(over Lesson 8-1)
Multiply.
87
× 10
A. 807
B. 187
C. 870
D. 957
8
Multiply by Two-Digit Numbers
(over Lesson 8-1)
Multiply.
34
× 30
A. 1,020
B. 912
C. 102
D. 1,054
8
Multiply by Two-Digit Numbers
(over Lesson 8-1)
Multiply.
65
× 80
A. 5,240
B. 520
C. 5,265
D. 5,200
8
Multiply by Two-Digit Numbers
(over Lesson 8-1)
Multiply.
$23
× 50
A. $1,173
B. $115
C. $1,150
D. $1,138
8
Multiply by Two-Digit Numbers
(over Lesson 8-1)
Multiply.
$79
× 90
A. $6,480
B. $7,110
C. $711
D. $7,189
8
Multiply by Two-Digit Numbers
(over Lesson 8-1)
Multiply.
$57
× 60
A. $3,420
B. $3,042
C. $3,477
D. $3,480
8
Multiply by Two-Digit Numbers
(over Lesson 8-2)
Estimate. Tell whether the estimate is more or less
than the actual product.
39
× 35
A. 1,400; more
B. 1,600; less
C. 1,600; more
D. 1,200; less
8
Multiply by Two-Digit Numbers
(over Lesson 8-2)
Estimate. Tell whether the estimate is more or less
than the actual product.
63
× 44
A. 2,700; less
B. 2,400; less
C. 3,000; more
D. 2,700; more
8
Multiply by Two-Digit Numbers
(over Lesson 8-2)
Estimate. Tell whether the estimate is more or less
than the actual product.
$54
× 81
A. $4,300; less
B. $4,400; less
C. $4,800; more
D. $4,000; less
8
Multiply by Two-Digit Numbers
(over Lesson 8-2)
Estimate. Tell whether the estimate is more or less
than the actual product.
$274 × 16
A. $5,400; more
B. $3,000; less
C. $6,000; more
D. $4,125; less
8
Multiply by Two-Digit Numbers
(over Lesson 8-2)
Estimate. Tell whether the estimate is more or less
than the actual product.
719 × 94
A. 63,000; less
B. 64,800; more
C. 70,000; more
D. 64,800; less
8
Multiply by Two-Digit Numbers
(over Lesson 8-3)
Solve. Use the act it out strategy. Carlos has 8
coins in his pocket. The total value of the
coins is 73¢. What coins does Carlos have?
A. 1 quarter, 4 dimes, 1 nickel, 3 pennies
B. 2 quarters, 1 dime, 2 nickels, 3 pennies
C. 3 dimes, 2 nickels, 3 pennies
D. 2 quarters, 2 dimes, 3 pennies
8
Multiply by Two-Digit Numbers
(over Lesson 8-4)
Multiply.
17
× 11
A. 308
B. 34
C. 187
D. 200
8
Multiply by Two-Digit Numbers
(over Lesson 8-4)
Multiply.
35
× 24
A. 840
B. 210
C. 720
D. 740
8
Multiply by Two-Digit Numbers
(over Lesson 8-4)
Multiply.
59
× 46
A. 2,708
B. 590
C. 2,995
D. 2,714
8
Multiply by Two-Digit Numbers
(over Lesson 8-4)
Multiply.
$64
× 37
A. $2,248
B. $2,368
C. $640
D. $2,512
8
Multiply by Two-Digit Numbers
(over Lesson 8-4)
Multiply.
$77
× 66
A. $5,082
B. $4,242
C. $942
D. $4,642
8
Multiply by Two-Digit Numbers
(over Lesson 8-4)
Multiply.
92
× 84
A. 1,936
B. 7,628
C. 1,104
D. 7,728
8
Multiply by Two-Digit Numbers
(over Lesson 8-5)
Multiply.
124
× 13
A. 4,852
B. 1,612
C. 496
D. 1,602
8
Multiply by Two-Digit Numbers
(over Lesson 8-5)
Multiply.
206
× 32
A. 6,482
B. 1,030
C. 5,810
D. 6,592
8
Multiply by Two-Digit Numbers
(over Lesson 8-5)
Multiply.
557
× 45
A. 25,065
B. 24,865
C. 5,013
D. 22,635
8
Multiply by Two-Digit Numbers
(over Lesson 8-5)
Multiply.
648
× 74
A. 47,948
B. 7,128
C. 47,952
D. 45,322
8
Multiply by Two-Digit Numbers
(over Lesson 8-5)
Multiply.
817
× 77
A. 17,534
B. 62,469
C. 11,438
D. 62,909
8
Multiply by Two-Digit Numbers
(over Lesson 8-5)
Multiply.
993
× 86
A. 13,902
B. 85,398
C. 74,398
D. 77,688
8
Multiply by Two-Digit Numbers
(over Lesson 8-6)
Use any strategy to solve. Nitin spent 55 minutes
mowing the lawn, 48 minutes cleaning his room,
23 minutes vacuuming, and 32 minutes doing
laundry. Is it reasonable to say that Nitin spent
3 hours on completing his chores?
A. Yes, it is reasonable because he spent exactly 3
hours completing his chores.
B. No, it is not reasonable because he spent over
3 hours completing his chores.
8
Multiply by Two-Digit Numbers
(over Lesson 8-6)
C. No, it is not reasonable because he spent less
than 3 hours completing his chores.
D. Yes, it is reasonable because he spent almost
3 hours completing his chores.
8
Multiply by Two-Digit Numbers
(over Lesson 8-6)
Answer:
C. No, it is not reasonable because he spent less
than 3 hours completing his chores.
This slide is intentionally blank.