Transcript Gr04_Ch_07 - Etiwanda E

Chapter 7
Multiply by One-Digit Numbers
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7
Multiply by One-Digit Numbers
Lesson 7-1
Multiples of 10, 100, and 1,000
Lesson 7-2
Problem-Solving Skill: Reasonable
Answers
Lesson 7-3
Use Rounding to Estimate Products
Lesson 7-4
Multiply Two-Digit Numbers
Lesson 7-5
Problem-Solving Investigation:
Choose a Strategy
Lesson 7-6
Multiply Multidigit Numbers
Lesson 7-7
Multiply Across Zeros
7-1
Multiples of 10, 100, and 1,000
Five-Minute Check (over Chapter 6)
Main Idea
California Standards
Example 1: Multiples of 100
Example 2: Multiples of 1,000
Example 3: Multiply Mentally
7-1
Multiples of 10, 100, and 1,000
• I will multiply multiples of 10, 100, and 1,000
using basic facts and patterns.
7-1
Multiples of 10, 100, and 1,000
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 relationships between them to
simplify computations and to check results.
7-1
Multiples of 10, 100, and 1,000
A leopard shark gives birth to 8 pups in 1 litter. How
many pups would be in 300 litters of that size?
You need to find 8 × 300. Use basic facts and patterns.
8 × 3 = 24
8 × 3 ones = 24 ones = 24
8 × 30 = 240
8 × 3 tens = 24 tens = 240
8 × 300 = 2,400
8 × 3 hundreds = 24 hundreds = 2,400
Answer: So, 300 litters of 8 would be 2,400 puppies.
Notice that this answer is 8 × 3 with two zeros
at the end.
7-1
Multiples of 10, 100, and 1,000
Teresa’s car payments are $200 a month. How
much will she have paid after 8 months?
A. $16
B. $160
C. $1,600
D. $16,000
7-1
Multiples of 10, 100, and 1,000
Find 8 × 7,000.
8 × 7 = 56
8 × 7 ones = 56 ones = 56
8 × 70 = 560
8 × 7 tens = 56 tens = 560
8 × 700 = 5,600
8 × 7 hundreds = 56 hundreds = 5,600
8 × 7,000 = 56,000
8 × 7 thousands = 56 thousands =
56,000
Answer: So, 8 × 7,000 is 56,000. Notice that this
answer is 8 × 7 with three zeros at the end.
7-1
Multiples of 10, 100, and 1,000
Find 4 × 0,000.
A. 36
B. 360
C. 3,600
D. 36,000
7-1
Multiples of 10, 100, and 1,000
Orca whales live in pods and can weigh up to
8,000 pounds. What is the total weight of a pod
of 6 orca whales?
To find the total weight of the pod, you need to find
6 × 8,000.
7-1
Multiples of 10, 100, and 1,000
6 × 8,000
48,000
Answer: So, the weight of the pod of orca whales is
48,000 pounds.
7-1
Multiples of 10, 100, and 1,000
A female adult elephant weighs about
4,000 kilograms. About how much would
5 adult female elephants weigh altogether?
A. 200,000 kilograms
B. 20,000 kilograms
C. 2,000 kilograms
D. 200 kilograms
7-2
Problem-Solving Skill: Reasonable Answers
Five-Minute Check (over Lesson 7-1)
Main Idea
California Standards
Example 1: Problem-Solving Skill
7-2
Problem-Solving Skill: Reasonable Answers
• I will decide whether an answer to a problem
is reasonable.
7-2
Problem-Solving Skill: Reasonable Answers
Standard 4MR3.1 Evaluate the reasonableness
of the solution in the context of the original
situation.
7-2
Problem-Solving Skill: Reasonable Answers
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 relationships between them to
simplify computations and to check results.
7-2
Problem-Solving Skill: Reasonable Answers
Odell donated 3 cases of dog
treats to a dog shelter. Each case
has 900 treats. The dogs eat
2,500 treats each month. Odell
says he has donated enough
treats for more than one month.
Is his claim reasonable?
7-2
Problem-Solving Skill: Reasonable Answers
Understand
What facts do you know?
• 3 cases of dog treats were donated.
• Each case has 900 treats.
• The animals eat 2,500 treats each month.
What do you need to find?
• Is it reasonable to say that the 3 cases of treats
will last longer than one month?
7-2
Problem-Solving Skill: Reasonable Answers
Plan
Find 3 × 900. Then determine if the amount is
reasonable.
7-2
Problem-Solving Skill: Reasonable Answers
Solve
3 × 900
2,700
Answer: Since 2,700 > 2,500, it is reasonable to say
that the three cases will last longer than one
month.
7-2
Problem-Solving Skill: Reasonable Answers
Check
You can add to see if the answer is correct.
900 + 900 + 900 = 2,700
3 × 900 = 2,700
So, the answer is correct.
7-3
Use Rounding to Estimate Products
Five-Minute Check (over Lesson 7-2)
Main Idea and Vocabulary
California Standards
Example 1: Estimate Products
Example 2: Estimate Larger Products
Example 3: Estimate Money
7-3
Use Rounding to Estimate Products
• I will estimate products by rounding.
• estimate
7-3
Use Rounding to Estimate Products
Standard 4NS3.1 Round whole numbers
through the millions to the nearest ten, hundred,
thousand, ten thousand, or hundred thousand.
7-3
Use Rounding to Estimate Products
The distance from Sydney, Australia, southwest
to Wagga Wagga, Australia is 470 kilometers.
About how many kilometers will be traveled in a
round trip?
Estimate 2 × 470. Round the larger factor to its
greatest place. Then use basic facts and patterns
to multiply.
7-3
Use Rounding to Estimate Products
2 × 470
2 × 500
Answer: So, about 1,000 km will be traveled in a
round trip to Wagga Wagga, Australia. Since
470 was rounded up, the estimated product
is greater than the actual product.
7-3
Use Rounding to Estimate Products
The distance from Terrine’s house to her aunt’s
house is 384 miles. She plans on driving back and
forth to her house to visit once in the spring and
then again in the summer. About how many miles
total will she drive in those two round trips?
A. 1,600 miles
B. 160 miles
C. 16 miles
D. 16,000 miles
7-3
Use Rounding to Estimate Products
Estimate 8 × 3,252.
First round, then multiply using basic facts and patterns.
8 × 3,252
8 × 3,000
Answer: So, 8 × 3,252 is about 24,000. Since 3,252
was rounded down, the estimated product is
less than the actual product.
7-3
Use Rounding to Estimate Products
Estimate 7 × 4,356.
A. 32,000
B. 3,200
C. 28,000
D. 2,800
7-3
Use Rounding to Estimate Products
A trip to the Grand Canyon will cost $2,804 per
person. About how much will it cost for a group
of 5 friends to travel there?
You need to estimate 5 × $2,804. First round, then
multiply.
5 × $2,804
5 × $3,000 = $15,000
Answer: So, the trip for 5 friends will cost about
$15,000.
7-3
Use Rounding to Estimate Products
If the Blackwell family saved $2,147 a year for
6 years, about how much money would they
have saved up after 6 years?
A. $1,200
B. $12,000
C. $1,800
D. $18,000
7-4
Multiply Two-Digit Numbers
Five-Minute Check (over Lesson 7-3)
Main Idea
California Standards
Example 1: Multiply with Regrouping
Multiply Two-Digit Numbers
7-4
Multiply Two-Digit Numbers
• I will multiply a two-digit number by a one-digit
number.
7-4
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
relationships between them to simplify computations
and to check results.
7-4
Multiply Two-Digit Numbers
Standard 4MR2.1 Use estimation to verify the
reasonableness of the solution in the context
of the original situation.
7-4
Multiply Two-Digit Numbers
Find 3 × 56.
Estimate
3 × 56
3 × 60 = 180
One Way: Distributive Property
3 × 56 = (3 × 50) + (3 × 6)
= 150 + 18
= 168
7-4
Multiply Two-Digit Numbers
Another Way: Partial Products
56
× 3
150
+ 18
168
3
50
6
150
18
150 + 18 = 168
Multiply Two-Digit Numbers
7-4
Another Way: Paper and Pencil
Step 1 Multiply the ones. Step 2 Multiply the tens.
1
56
× 3
8
6 × 3 = 18
Regroup 18 ones as
1 ten and 8 ones.
Answer: 3 × 56 = 168
1
56
× 3
168
3 × 5 = 15
Add the regrouped
ten, 1.
7-4
Multiply Two-Digit Numbers
Check for Reasonableness
The product, 168, is close to the estimate, 180.
7-4
Multiply Two-Digit Numbers
Find 7 × 32.
A. 204
B. 214
C. 732
D. 224
7-5
Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 7-4)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
7-5
Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.
7-5
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.
Preparation for Standard 4NS3.3 Solve
problems involving multiplication of multidigit
numbers by two-digit numbers.
7-5
Problem-Solving Investigation: Choose a Strategy
ISABEL: I am making punch for a
party. One bowl of punch serves
35 guests. I am going to make four
bowls of punch.
YOUR MISSION: Find how many guests
will be served by four bowls.
7-5
Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• One bowl of punch serves 35 guests.
• Isabel is making four bowls of punch.
What do you need to find?
• Find how many guests will be served by four
bowls of punch.
7-5
Problem-Solving Investigation: Choose a Strategy
Plan
Use the four-step plan and write a number
sentence. Multiply the number of guests served
by one bowl of punch by the number of bowls
being made.
7-5
Problem-Solving Investigation: Choose a Strategy
Solve
You need to find 35 × 4 =
35
× 4
Multiply 4 × 5. 20
Multiply 4 ×+ 30.
120
Add.
140
.
120 + 20 = 140
Answer: So, four bowls of punch will serve
140 guests.
7-5
Problem-Solving Investigation: Choose a Strategy
Check
Look back at the problem. You can use repeated
addition to check your answer.
35 + 35 + 35 + 35 = 140
So, the answer is correct.
7-6
Multiply Multidigit Numbers
Five-Minute Check (over Lesson 7-5)
Main Idea
California Standards
Example 1: Partial Products
Example 2: Multiply Money
7-6
Multiply Multidigit Numbers
• I will multiply a three-digit number by a one-digit
number.
7-6
Multiply Multidigit 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
relationships between them to simplify computations
and to check results.
7-6
Multiply Multidigit Numbers
Standard 4MR2.1 Use estimation to verify the
reasonableness of calculated results.
7-6
Multiply Multidigit Numbers
Aisha’s teacher bought 5 bags of rubber bands.
If each bag has 185 bands in it, how many bands
did she buy?
Estimate
5 × 185
5 × 200 = 1,000
185
× 5
25
400
+ 500
925
Multiply 5 × 5.
Multiply 5 × 80.
Multiply 5 × 100.
Add the partial products.
7-6
Multiply Multidigit Numbers
100
5
500
+
80 + 5
400
25
500
400
+ 25
925
Answer: So, Aisha’s teacher bought 925 rubber
bands.
Check for Reasonableness
The product, 925, is close to the estimate 1,000.
7-6
Multiply Multidigit Numbers
Meredith bought 3 containers of paper clips
containing 225 in each container. How many
paper clips did she buy altogether?
A. 675 paper clips
B. 700 paper clips
C. 450 paper clips
D. 625 paper clips
7-6
Multiply Multidigit Numbers
Find 2 × $4,387.
Step 1 Multiply the ones.
1
$4,387
2
×
4
2 × 7 ones = 14 ones
Regroup 14 as 1 ten and 4 ones.
7-6
Multiply Multidigit Numbers
Step 2 Multiply the tens.
11
$4,387
2
×
74
2 × 8 tens = 16 tens
Add the regrouped tens.
16 tens + 1 ten = 17 tens
Regroup 17 tens as 1 hundred and
7 tens.
Step 3 Multiply the hundreds.
11
$4,387
2
×
774
2 × 3 hundreds = 6 hundreds
Add the regrouped hundreds.
6 hundreds + 1 hundred = 7 hundreds
7-6
Multiply Multidigit Numbers
Step 4 Multiply the thousands.
11
$4,387
2
×
$8,774
2 × 4 thousands = 8 thousands
Answer: 2 × $4,387 = $8,774
7-6
Multiply Multidigit Numbers
The area model shows that 2 × $4,387 = $8,774.
$4,000
+
$300 + $80 + $7
2
$8,000
$600
$8,000
$ 600
$ 160
+ $ 14
$8,774
$160
$14
7-6
Multiply Multidigit Numbers
Find 3 × $2,145.
A. $6,325
B. $6,435
C. $7,000
D. $7,435
7-7
Multiply Across Zeros
Five-Minute Check (over Lesson 7-6)
Main Idea
California Standards
Example 1: Multiply Across Zeros
Example 2: Multiply Across Zeros
7-7
Multiply Across Zeros
• I will multiply multidigit numbers with zeros by a
one-digit number.
7-7
Multiply Across Zeros
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
relationships between them to simplify computations
and to check results.
7-7
Multiply Across Zeros
Standard 4MR2.1 Use estimation to verify the
reasonableness of calculated results.
7-7
Multiply Across Zeros
The lease payment for the school’s video equipment
is $704 a month. How much can the school expect to
pay for the first 5 months of school?
Multiply the cost of each month by 5. That is, find
5 × $704.
Estimate 5 × $704
5 × $700 = $3,500
7-7
Multiply Across Zeros
The area model shows 5 × $704.
7-7
Multiply Across Zeros
One Way: Distributive Property
5 × $704 = (5 × $700) + (5 × $0) + (5 × $4)
= $3,500 + $0 + $20
= $3,520
7-7
Multiply Across Zeros
Another Way: Partial Products
$704
5
×
$ 20
$
0
+ $3,500
$3,520
Multiply 5 × $4.
Multiply 5 × $0.
Multiply 5 × $700.
Add the partial products.
Answer: So, the lease payment for 5 months
is $3,520.
7-7
Multiply Across Zeros
Check for Reasonableness
The answer, $3,520, is close to the estimate $3,500.
7-7
Multiply Across Zeros
Julie’s rent is $403 a month. If she wants to pay
4 months all at once, how much does she have
to pay?
A. $1,600
B. $1,700
C. $1,602
D. $1,612
7-7
Multiply Across Zeros
A record-breaking pumpkin weighed
1,061 pounds. What would the total weight
of 4 of these pumpkins be?
Estimate 4 × $1,061
4 × $1,000 = $4,000
Step 1 Multiply the ones.
1,061
4
×
4
4 × 1 one = 4 ones
7-7
Multiply Across Zeros
Step 2 Multiply the tens.
2
1,061
4
×
44
4 × 6 tens = 24 tens
Regroup 24 tens as 2 hundreds and
4 tens.
Step 3 Multiply the hundreds.
2
1,061
4
×
2 44
4 × 0 hundreds = 0 hundreds
Add the regrouped hundreds.
0 hundreds + 2 hundreds = 2 hundreds
7-7
Multiply Across Zeros
Step 4 Multiply the thousands.
2
1,061
4
×
4,2 44
4 × 1 thousand = 4 thousands
Answer: So, the total weight of the pumpkins
would be 4,244 pounds.
Check for Reasonableness
The answer, 4,244 is close to the estimate, 4,000.
So the answer is reasonable.
7-7
Multiply Across Zeros
Find 6 × 3,189.
A. 18,134
B. 18,684
C. 19,684
D. 19,134
7
Multiply by One-Digit Numbers
Five-Minute Checks
Math Tool Chest
Image Bank
Multiply Two-Digit Numbers
7
Multiply by One-Digit Numbers
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7
Multiply by One-Digit Numbers
7
Multiply by One-Digit Numbers
7
Multiply by One-Digit Numbers
7
Multiply by One-Digit Numbers
7
Multiply by One-Digit Numbers
Lesson 7-1
(over Chapter 6)
Lesson 7-2
(over Lesson 7-1)
Lesson 7-3
(over Lesson 7-2)
Lesson 7-4
(over Lesson 7-3)
Lesson 7-5
(over Lesson 7-4)
Lesson 7-6
(over Lesson 7-5)
Lesson 7-7
(over Lesson 7-6)
7
Multiply by One-Digit Numbers
(over Chapter 6)
Tell whether the equation is balanced.
1 dime × 3 = (1 dime + 1 nickel) × 3
A. Yes; 30¢ = 30¢
B. No; 30¢ ≠ 45¢
C. Yes; 30¢ = 45¢
D. No; 30¢ = 45¢
A.
B.
C.
D.
A
B
C
D
7
Multiply by One-Digit Numbers
(over Chapter 6)
Tell whether the equation is balanced.
2 × 6 ÷ 3 = 16 ÷ 4
A. Yes; 3 = 4
B. No; 4 ≠ 4
C. Yes; 4 = 4
D. No; 4 = 4
7
Multiply by One-Digit Numbers
(over Chapter 6)
Complete the equation to make it balanced.
(8 × 5) ÷ 4 = 2 × ( __ – 3)
A. 8
B. 5
C. 10
D. 7
7
Multiply by One-Digit Numbers
(over Lesson 7-1)
Multiply.
5 × 7; 5 × 70; 5 × 700
A. 30; 350; 3,500
B. 35; 305; 3,000
C. 35; 355; 3,555
D. 35; 350; 3,500
A.
B.
C.
D.
A
B
C
D
7
Multiply by One-Digit Numbers
(over Lesson 7-1)
Multiply.
9 × 2; 9 × 20; 9 × 200
A. 18; 189; 1,899
B. 18; 180; 1,800
C. 11; 110; 1,100
D. 18; 108; 1,800
7
Multiply by One-Digit Numbers
(over Lesson 7-1)
Multiply. Use mental math.
3 × 9,000
A. 12,333
B. 9,003
C. 27,000
D. 27,333
7
Multiply by One-Digit Numbers
(over Lesson 7-1)
Multiply. Use mental math.
2 × 500
A. 1,000
B. 722
C. 1,022
D. 700
7
Multiply by One-Digit Numbers
(over Lesson 7-2)
Decide whether the answer is reasonable. Explain
your reasoning. Kyle delivers 50 papers a day in his
neighborhood. Is it reasonable to expect that he will
deliver 320 by the end of 1 week?
A. No, 7 days in one week × 50 papers in one day
is 350 papers. He will not deliver 320 papers.
A. day
A
B. Yes, 7 days in one week × 50 papers in one
B. B
is 320 papers. He will deliver 320 papers.
C.
D.
C
D
7
Multiply by One-Digit Numbers
(over Lesson 7-2)
C. No, 5 days in one week × 50 papers in
one day is 250 papers. He will not deliver
320 papers.
D. Yes, 7 days in one week × 50 papers in
one day is 350 papers. He will deliver at
A.
least 320 papers.
B.
C.
D.
A
B
C
D
7
Multiply by One-Digit Numbers
(over Lesson 7-2)
Answer:
D.
Yes, 7 days in one week × 50 papers in
one day is 350 papers. He will deliver at
least 320 papers.
A.
B.
C.
D.
A
B
C
D
7
Multiply by One-Digit Numbers
(over Lesson 7-3)
Estimate the product.
3 × 439
A. 1,000
B. 1,200
C. 1,317
D. 1,500
A.
B.
C.
D.
A
B
C
D
7
Multiply by One-Digit Numbers
(over Lesson 7-3)
Estimate the product.
6 × 912
A. 4,500
B. 5,472
C. 6,000
D. 5,400
7
Multiply by One-Digit Numbers
(over Lesson 7-3)
Estimate the product.
7 × 291
A. 2,100
B. 2,037
C. 1,400
D. 2,000
7
Multiply by One-Digit Numbers
(over Lesson 7-3)
Estimate the product.
4 × 68
A. 272
B. 240
C. 270
D. 280
7
Multiply by One-Digit Numbers
(over Lesson 7-4)
Multiply.
2 × 44
A. 82
B. 46
C. 88
D. 98
A.
B.
C.
D.
A
B
C
D
7
Multiply by One-Digit Numbers
(over Lesson 7-4)
Multiply.
4 × 39
A. 126
B. 156
C. 43
D. 160
7
Multiply by One-Digit Numbers
(over Lesson 7-4)
Multiply.
3 × $21
A. $54
B. $24
C. $61
D. $63
7
Multiply by One-Digit Numbers
(over Lesson 7-4)
Multiply.
5 × 89
A. 445
B. 405
C. 144
D. 440
7
Multiply by One-Digit Numbers
(over Lesson 7-5)
Use any strategy to solve. Adriana went to an
amusement park on a camp trip during summer
vacation. She spent $24 on an admission ticket,
$3 on a drink, and bought 4 souvenir postcards
for $1 each. If she had $12 left, how much money
did she start with?
A. $40
B. $19
C.
D.
$43
$33
A.
B.
C.
D.
A
B
C
D
7
Multiply by One-Digit Numbers
(over Lesson 7-6)
Multiply. Check for reasonableness.
2 × 596
A. 818
B. 1,082
C. 718
D. 1,192
A.
B.
C.
D.
A
B
C
D
7
Multiply by One-Digit Numbers
(over Lesson 7-6)
Multiply. Check for reasonableness.
4 × 623
A. 1,067
B. 2,492
C. 627
D. 2,482
7
Multiply by One-Digit Numbers
(over Lesson 7-6)
Multiply. Check for reasonableness.
3 × 5,188
A. 15,564
B. 8,311
C. 15,344
D. 8,421
7
Multiply by One-Digit Numbers
(over Lesson 7-6)
Multiply. Check for reasonableness.
5 × 1,923
A. 9,505
B. 7,478
C. 9,615
D. 5,505
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