Transcript Document 7156920

Chapter 15
Divide by One-Digit Numbers
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15
Divide by One-Digit Numbers
Lesson 15-1
Divide Multiples of 10, 100, and
1,000
Lesson 15-2
Estimate Quotients
Lesson 15-3
Two-Digit Quotients
Lesson 15-4
Problem-Solving Strategy: Work
Backwards
Lesson 15-5
Three-Digit Quotients
Lesson 15-6
Problem-Solving Investigation:
Choose the Best Strategy
Lesson 15-7
Divide Money
15-1
Divide Multiples of 10, 100, and 1,000
Five-Minute Check (over Chapter 14)
Main Idea
California Standards
Example 1: Use Models to Divide
Example 2: Divide Multiples
Example 3: Divide Multiples
15-1
Divide Multiples of 10, 100, and 1,000
• I will learn to divide multiples of 10, 100, and
1,000.
15-1
Divide Multiples of 10, 100, and 1,000
Standard 3NS2.5 Solve division problems in
which a multi-digit number is evenly divided by
a one-digit number (135 ÷ 5 = ___ ).
15-1
Divide Multiples of 10, 100, and 1,000
Find 600 ÷ 3.
Step 1 Show 600 as 60 tens.
15-1
Divide Multiples of 10, 100, and 1,000
Step 2 Divide the 60 tens into 3 equal groups.
200
200
Answer: 600 ÷ 3 = 200
200
15-1
Divide Multiples of 10, 100, and 1,000
Find 800 ÷ 2.
A. 250
B. 400
C. 300
D. 500
15-1
Divide Multiples of 10, 100, and 1,000
The stadium has 1,800 seats divided equally into
6 sections. How many seats are in each section?
Find 1,800 ÷ 6. Use basic facts and patterns.
18 ÷ 6 = 3
18 ones ÷ 6 = 3 ones
180 ÷ 6 = 30
18 tens ÷ 6 = 3 tens
1,800 ÷ 6 = 300
18 hundreds ÷ 6 = 3 hundreds
Answer: So, there are 300 seats in each section.
15-1
Divide Multiples of 10, 100, and 1,000
A class split up into 3 teams and had a bake sale
which made $600. How much did each team earn if
the money was split evenly between the teams?
A. $200
B. $300
C. $150
D. $100
15-1
Divide Multiples of 10, 100, and 1,000
How many seats are in each section if 4,200 seats
are divided equally into 7 sections?
Find 4,200 ÷ 7.
42 ÷ 7 = 6
Use the basic fact.
420 ÷ 7 = 60
Use the pattern of zeros.
4,200 ÷ 7 = 600
Answer: So, there are 600 seats in each section.
15-1
Divide Multiples of 10, 100, and 1,000
Find 2,500 ÷ 5.
A. 350
B. 400
C. 500
D. 600
15-2
Estimate Quotients
Five-Minute Check (over Lesson 15-1)
Main Idea
California Standards
Example 1: Estimate by Rounding
Example 2: Real-World Example
15-2
Estimate Quotients
• I will estimate quotients.
15-2
Estimate Quotients
Standard 3NS2.5 Solve division problems in
which a multi-digit number is evenly divided by
a one-digit number (135 ÷ 5 = ___ ).
Standard 3MR2.1 Use estimation to verify the
reasonableness of calculated results.
15-2
Estimate Quotients
There are 238 children in the school. If there are
8 classrooms, about how many students are
there in each class?
You need to estimate 238 ÷ 8 or 8 238.
Step 1 Round 238 to the nearest ten that has a
basic fact you can use.
238 ÷ 8
240 ÷ 8
15-2
Estimate Quotients
Step 2 Write the basic fact you will use to divide.
24 ÷ 8 = 3
Step 3 Use the basic fact and patterns to divide.
24 ÷ 8 = 3
240 ÷ 8 = 30
Answer: So, 238 ÷ 8 is about 30. About 30 students
are in each class.
15-2
Estimate Quotients
A community center wants to break up its
103 members into teams of 5 for a basketball
tournament. About how many teams will the
tournament have?
A. about 20 teams
B. about 30 teams
C. about 15 teams
D. about 25 teams
15-2
Estimate Quotients
A theater sold 1,113 tickets for 4 shows. About
how many tickets were sold for each show?
You need to estimate 1,113 ÷ 4 or 4 1,113.
Step 1 Round 1,113 to the nearest hundred that
has a basic fact you can use.
1,113 ÷ 4
1,200 ÷ 4
15-2
Estimate Quotients
Step 2 Write the basic fact you will use to divide.
12 ÷ 4 = 3
Step 3 Use the basic fact and patterns to divide.
12 ÷ 4 = 3
1,200 ÷ 4 = 300
Answer: So, 1,113 ÷ 4 is about 300. About 300 tickets
were sold for each show.
15-2
Estimate Quotients
A fundraiser generated $1,212 from 6 local
churches. About how much money did each
church give to the fundraiser?
A. about $100
B. about $200
C. about $250
D. about $300
15-3
Two-Digit Quotients
Five-Minute Check (over Lesson 15-2)
Main Idea
California Standards
Example 1: Real-World Example
Example 2: Real-World Example
Division
15-3
Two-Digit Quotients
• I will divide a two-digit number by a one-digit
number.
15-3
Two-Digit Quotients
Standard 3NS2.5 Solve division problems in
which a multi-digit number is evenly divided
by a one-digit number (135 ÷ 5 = ___ ).
Standard 3NS2.3 Use the inverse
relationship of multiplication and division to
compute and check results.
15-3
Two-Digit Quotients
A total of 95 students signed up for basketball.
How many 5-person teams will there be?
Step 1 Model 95. Show 5 groups.
quotient
5 95
divisor
dividend
15-3
Two-Digit Quotients
Step 2 Divide the tens.
1
5 95
1 ten in each
group
5 –tens
5 used
4 4 tens left
15-3
Two-Digit Quotients
Step 3 Regroup and divide the ones.
19
5 95
9 ones in
each group
–5
4
19
Answer: So, 95 ÷ 5 = 19 or 5 95.
5
45 ones
used
– 45
00 ones left
15-3
Two-Digit Quotients
A total of 200 kids signed on for after-school
softball. If there are 10 players to a team, how
many teams will be formed?
A. 25 teams
B. 21 teams
C. 20 teams
D. 30 teams
15-3
Two-Digit Quotients
Rami wants to read an 84-page book in 6 days.
How many pages should he read per day?
Find 84 ÷ 6.
Step 1 Decide if there are enough tens to divide.
6 84
8 > 6 There are enough tens.
15-3
Two-Digit Quotients
Step 2 Divide the tens.
1
6 84
–
Divide 8 tens by 6 groups.
Write 1 in the tens place.
6 Multiply. 1 × 6 tens = 6 tens
2 Subtract 6 tens from 8 tens.
Compare. 2 < 6
15-3
Two-Digit Quotients
Step 3 Divide the ones.
14
6 84
–
24
–
Divide 24 ones by 6 groups.
Write 4 in the ones place.
6
Multiply.
4 × 6 ones = 24 ones
24
0 Subtract 24 ones from 24 ones
Compare. 0 < 6
Answer: So, Rami should read 14 pages each day.
15-3
Two-Digit Quotients
Check Multiply the quotient by the divisor.
2
14
× 6
84
quotient
divisor
dividend
The answer is correct.
15-3
Two-Digit Quotients
Shelley makes $5 a day babysitting. She wants to
buy an outfit that costs $65. How many days will
Shelley have to baby-sit to earn enough money to
buy the outfit?
A. 13 days
B. 15 days
C. 17 days
D. 12 days
15-4
Problem-Solving Strategy: Work Backwards
Five-Minute Check (over Lesson 15-3)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
15-4
Problem-Solving Strategy: Work Backwards
• I will work backward to solve problems.
15-4
Problem-Solving Strategy: Work Backwards
Standard 3MR1.2 Determine when and how to
break a problem into simpler parts.
Standard 3NS2.1 Solve division problems
in which a multi-digit number is evenly divided
by a one-digit number (135 ÷ 5 = ___ ).
15-4
Problem-Solving Strategy: Work Backwards
Frannie put some money in the bank to start a
savings account. Last month she put in enough
money to double that amount. Today, she put in
more money and the total amount doubled,
again. Now she has $20. How much money did
Frannie start with?
15-4
Problem-Solving Strategy: Work Backwards
Understand
What facts do you know?
• The money doubled two times.
• The total amount at the end is $20.
What do you need to find?
• The amount of money Frannie started with.
15-4
Problem-Solving Strategy: Work Backwards
Plan
Work backward from what you know, $20, to find
the amount Frannie started with.
15-4
Problem-Solving Strategy: Work Backwards
Solve
Start with $20.
Find the number that was doubled.
Since the amount was doubled
two times, find half of $10.
$20
Half of $20 is $10
$10
Half of $10 is $5
Answer: So, the amount of
money Frannie started
with was $5.
$5
15-4
Problem-Solving Strategy: Work Backwards
Check
Look back at the problem. When you double $5, the
result is $5 × 2 or $10. When you double $10, the
result is $10 × 2 or $20.
So, the answer is correct.
15-5
Three-Digit Quotients
Five-Minute Check (over Lesson 15-4)
Main Idea
California Standards
Example 1: Real-World Example
Example 2: Real-World Example
15-5
Three-Digit Quotients
• I will divide three-digit numbers by one-digit
numbers.
15-5
Three-Digit Quotients
Standard 3NS2.5 Solve division problems in
which a multi-digit number is evenly divided
by a one-digit number (135 ÷ 5 = ___ ).
Standard 3NS2.3 Use the inverse
relationship of multiplication and division to
compute and check results.
15-5
Three-Digit Quotients
Hugan read a 572-page book in 4 weeks.
How many pages did he read each week?
Find 572 ÷ 4.
Step 1 Divide the hundreds. 5 > 4, so there are
enough hundreds.
1
Divide. 5 ÷ 4
4 572
4 Multiply. 4 × 1 = 4
–
1 Subtract. 5 – 4 = 1
Compare. 1 < 4
15-5
Three-Digit Quotients
Step 2 Regroup. Regroup the remaining 1 hundred
as 10 tens. Bring down the 7 tens.
1
4 572
4
–
7
1
15-5
Three-Digit Quotients
Step 3 Divide the tens. Regroup the remaining ten as
10 ones. Bring down the ones.
1
4
4 572
4
–
7 Divide. 17 ÷ 4
1
–
16
Multiply.
4 × 4 = 16
1
2Subtract. 17 – 16 = 1
Compare. 1 < 4
15-5
Three-Digit Quotients
Step 4 Divide the ones.
14
3
4 572
4
–
7
1
–
16
1
2Divide. 12 ÷ 4 = 3
– Multiply.
12
4 × 3 = 12
0Subtract. 12 – 12 = 0
Compare. 0 < 4
Answer: So, Hugan read 143 pages each week.
15-5
Three-Digit Quotients
A group of 500 people will be split into 4 groups.
How many people will be in each group?
A. 150 people
B. 130 people
C. 120 people
D. 125 people
15-5
Three-Digit Quotients
Akina is putting 115 books on 5 shelves. How many
books will go on each shelf?
Find 115 ÷ 5.
15-5
Three-Digit Quotients
Step 1 Divide the hundreds.
5 115
There are not enough
hundreds to divide. Regroup
the 1 hundred as 10 tens.
5 115
11 > 5 Place the first digit in
the tens place.
15-5
Three-Digit Quotients
Step 2 Divide the tens.
2
5 115
–
Divide. 11 ÷ 5 = 2
Multiply. 5 × 2 = 10
10
Subtract. 11 – 10 = 1
1 Compare. 1 < 5
15-5
Three-Digit Quotients
Step 3 Divide the ones.
23
5 115 Bring down the ones.
10
–
15 Divide. 15 ÷ 5 = 3
15– Multiply. 5 × 3 = 15
0Subtract. 15 – 15 = 0
Compare. 0 < 5
Answer: So, Akina put 23 books on each shelf.
15-5
Three-Digit Quotients
Check Multiply to check.
1
23
× 5
115
quotient
divisor
dividend
The answer is correct.
15-5
Three-Digit Quotients
Tony wants to buy a mountain bike that costs $450.
If he plans to buy it in 3 months, how much money
will Tony have to save each month?
A. $175
B. $100
C. $150
D. $130
15-6
Problem-Solving Investigation: Choose the Best Strategy
Five-Minute Check (over Lesson 15-5)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
15-6
Problem-Solving Investigation: Choose the Best Strategy
• I will choose the best strategy to solve a problem.
15-6
Problem-Solving Investigation: Choose the Best Strategy
Standard 3MR1.1 Analyze problems by
identifying relationships, distinguishing
relevant from irrelevant information,
sequencing and prioritizing information,
and observing patterns.
15-6
Problem-Solving Investigation: Choose the Best Strategy
Standard 3NS2.5 Solve division problems in
which a multi-digit number is evenly divided by
a one-digit number (135 ÷ 5 = ___ ).
15-6
Problem-Solving Investigation: Choose the Best Strategy
MING: A community pool is in the
shape of a circle. It measures
80 feet across. A square fence is
going to be placed around the pool.
YOUR MISSION: Find if 340 feet of
fencing is enough to go around the
pool.
15-6
Problem-Solving Investigation: Choose the Best Strategy
Understand
What facts do you know?
• The pool is a circle.
• It measures 80 feet across.
• A square fence will be put around the pool.
• You have 340 feet of fencing.
15-6
Problem-Solving Investigation: Choose the Best Strategy
Understand
What do you need to find?
• You need to know if 340 feet of fencing is
enough.
15-6
Problem-Solving Investigation: Choose the Best Strategy
Plan
Divide 340 by 4 to find the length of each side
of the fence. Use make a drawing strategy to
compare the length of the fence to the pool.
15-6
Problem-Solving Investigation: Choose the Best Strategy
Solve
85
4 340
–
20
20–
32
0
15-6
Problem-Solving Investigation: Choose the Best Strategy
Solve
340 feet of fence is enough to make a square
that is 85 feet on each side. 80 feet is smaller
than 85 feet.
Answer: So, 340 feet of fencing is enough to go
around the pool.
15-6
Problem-Solving Investigation: Choose the Best Strategy
Check
Look back at the problem. Check the answer
by multiplying.
85 × 4 = 340
So, the answer is correct.
15-7
Divide Money
Five-Minute Check (over Lesson 15-6)
Main Idea
California Standards
Example 1: Real-World Example
Example 2: Quotients Less Than $1.00
Example 3: Find Unit Cost
15-7
Divide Money
• I will divide amounts of money.
15-7
Divide Money
Standard 3NS3.3 Solve problems involving
addition, subtraction, multiplication, and division of
money amounts in decimal notation and multiply
and divide money amounts in decimal notation
by using whole-number multipliers and divisors.
15-7
Divide Money
Standard 3NS2.7 Determine the unit cost when
given the total cost and number of units.
15-7
Divide Money
Brian and 3 friends earned $9.68 for washing cars.
How much will each boy receive after they share
the money equally?
Find $9.68 ÷ 4.
Estimate $9.68 ÷ 4
$10 ÷ 4 = $2.50
15-7
Divide Money
Step 1 Divide the dollars.
2
4 $9.68
–
8
1
Divide. 9 ÷ 4
Multiply. 4 × 2 dollars
Subtract. 9 – 8 = 1
Compare. 1 < 4
15-7
Divide Money
Step 2 Divide the dimes.
2
4
4 $9.68
–
8
1
6 Divide. 16 ÷ 4
Multiply.
–
1 6 4 × 4 dimes
0 Subtract. 16 – 16 = 0
Compare. 0 < 4
15-7
Divide Money
Step 3 Divide the pennies.
4
2Place
$2. the decimal point and
4 $9.68 dollar sign directly above.
–
8
1
6
–
16
0
8Divide. 8 ÷ 4 = 2
– 8Multiply. 4 × 2 pennies
0Subtract. 8 – 8 = 0
Compare. 0 < 4
Answer: So, each boy will receive $2.42.
15-7
Divide Money
Check for Reasonableness
$2.42 is close to the estimate of $2.50.
So, the answer is reasonable.
Since $2.42 × 4 = $9.68, the answer is correct.
15-7
Divide Money
Angie and 3 friends pay $25 for tickets to see
a movie. How much did each of them pay for a
movie ticket?
A. $6.25
B. $5.25
C. $7.25
D. $5.50
15-7
Divide Money
Divide $4.35 ÷ 5.
Estimate $4.35 ÷ 5
$4.00 ÷ 5 = $0.80
Step 1 Decide if there are enough dollars to divide.
5 $4.35
4 < 5 There are not enough.
15-7
Divide Money
Step 2 Divide the dollars as 40 dimes.
8
5 $4.35
–
3
40
5
15-7
Divide Money
Step 3 Divide the pennies.
$0.8
5 $4.35
–
–
7Add the dollar sign and
decimal point. Add a zero
to 4
show
0 0 dollars.
53
35
0
Answer: So, $4.35 ÷ 5 = $0.87.
15-7
Divide Money
Check for Reasonableness
The estimate $0.80 is close to $0.87.
So, the answer is correct.
15-7
Divide Money
Find $3.80 ÷ 4.
A. $0.87
B. $0.95
C. $0.75
D. $0.89
15-7
Divide Money
Freda paid $6.84 for 6 bags of marbles. How much
did each bag cost?
Find the unit cost. Divide $6.84 ÷ 6.
15-7
Divide Money
1
4$1.
6 $6.84
–
6
0
8
–
6
2
4
–
24
0
Check
2
$1.14
× 6
$6.84
So, the answer is correct.
Answer: So, $6.84 ÷ 6 = $1.14. Each bag
costs $1.14.
15-7
Divide Money
Chris paid $7.25 for 5 gallons of fruit punch. How
much did Chris pay for each gallon of fruit punch?
A. $1.85
B. $1.75
C. $1.55
D. $1.45
15
Divide by One-Digit Numbers
Five-Minute Checks
Math Tool Chest
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Division
15
Divide by One-Digit Numbers
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15
Divide by One-Digit Numbers
15
Divide by One-Digit Numbers
15
Divide by One-Digit Numbers
15
Divide by One-Digit Numbers
15
Divide by One-Digit Numbers
Lesson 15-1 (over Chapter 14)
Lesson 15-2 (over Lesson 15-1)
Lesson 15-3 (over Lesson 15-2)
Lesson 15-4 (over Lesson 15-3)
Lesson 15-5 (over Lesson 15-4)
Lesson 15-6 (over Lesson 15-5)
Lesson 15-7 (over Lesson 15-6)
15
Divide by One-Digit Numbers
(over Chapter 14)
Multiply.
$3.24 × 7
A. $21.68
B. $4.48
C. $6.68
D. $22.68
15
Divide by One-Digit Numbers
(over Chapter 14)
Multiply.
8 × $9.51
A. $76.08
B. $79.06
C. $74.56
D. $72.08
15
Divide by One-Digit Numbers
(over Chapter 14)
At Dora’s diner, burgers are $3.13 and drinks are
$1.29. How much are 3 burgers and 1 drink?
A. $10.24
B. $10.68
C. $8.60
D. $6.60
15
Divide by One-Digit Numbers
(over Chapter 14)
At Dora’s diner, burgers are $3.13 and drinks are
$1.29. What is the cost of 2 burgers and 2 drinks?
A. $8.84
B. $6.68
C. $4.60
D. $5.60
15
Divide by One-Digit Numbers
(over Lesson 15-1)
Divide. Use patterns.
320 ÷ 8
A. 60
B. 18
C. 32
D. 40
15
Divide by One-Digit Numbers
(over Lesson 15-1)
Divide. Use patterns.
4,500 ÷ 5
A. 220
B. 90
C. 900
D. 22
15
Divide by One-Digit Numbers
(over Lesson 15-1)
Divide. Use patterns.
720 ÷ 9
A. 80
B. 36
C. 32
D. 322
15
Divide by One-Digit Numbers
(over Lesson 15-1)
There are 6 boxes and 240 crayons. How many
crayons are in each box?
A. 40 crayons
B. 32 crayons
C. 30 crayons
D. 42 crayons
15
Divide by One-Digit Numbers
(over Lesson 15-2)
Estimate by rounding.
269 ÷ 3
A. 270 ÷ 3 = 90
B. 260 ÷ 3 = 90
C. 290 ÷ 3 = 97
D. 240 ÷ 3 = 80
15
Divide by One-Digit Numbers
(over Lesson 15-2)
Estimate by rounding.
4,179 ÷ 7
A. 4,100 ÷ 7 = 600
B. 4,200 ÷ 7 = 600
C. 4,200 ÷ 7 = 700
D. 4,900 ÷ 7 = 700
15
Divide by One-Digit Numbers
(over Lesson 15-2)
Estimate by rounding.
61 ÷ 6
A. 60 ÷ 6 = 12
B. 61 ÷ 6 = 11
C. 60 ÷ 6 = 10
D. 68 ÷ 6 = 8
15
Divide by One-Digit Numbers
(over Lesson 15-2)
Estimate by rounding.
390 ÷ 5
A. 400 ÷ 5 = 80
B. 390 ÷ 5 = 88
C. 400 ÷ 5 = 40
D. 350 ÷ 5 = 50
15
Divide by One-Digit Numbers
(over Lesson 15-3)
Divide 68 ÷ 4. Use models if needed.
Check your answer.
A. 22
B. 24
C. 12
D. 17
15
Divide by One-Digit Numbers
(over Lesson 15-3)
Divide 48 ÷ 3. Use models if needed.
Check your answer.
A. 16
B. 12
C. 14
D. 15
15
Divide by One-Digit Numbers
(over Lesson 15-3)
Divide 91 ÷ 7. Use models if needed.
Check your answer.
A. 14
B. 13
C. 10
D. 8
15
Divide by One-Digit Numbers
(over Lesson 15-3)
Jaha has 96 beads for making bracelets. She uses
6 beads for each bracelet. How many bracelets
can she make?
A. 90 bracelets
B. 14 bracelets
C. 16 bracelets
D. 88 bracelets
15
Divide by One-Digit Numbers
(over Lesson 15-4)
Use the work backward strategy to solve.
Julio is saving money for a new guitar. He doubled
his money last year by babysitting his brother.
Then he tripled that amount by working for his dad.
Now he has $90. How much did he start with?
A. $22
B. $14
C. $24
D. $15
15
Divide by One-Digit Numbers
(over Lesson 15-5)
Divide 745 ÷ 5. Check your answer.
A. 155
B. 135
C. 322
D. 149
15
Divide by One-Digit Numbers
(over Lesson 15-5)
Divide 288 ÷ 6. Check your answers.
A. 48
B. 24
C. 34
D. 84
15
Divide by One-Digit Numbers
(over Lesson 15-5)
Divide 824 ÷ 2. Check your answers.
A. 411
B. 128
C. 244
D. 412
15
Divide by One-Digit Numbers
(over Lesson 15-5)
There is a total of 784 pencils. There are 7 pencils in
each box. How many boxes of pencils are there?
A. 110 boxes
B. 144 boxes
C. 112 boxes
D. 122 boxes
15
Divide by One-Digit Numbers
(over Lesson 15-6)
Choose any strategy to solve the problem. Tia sold
9 baskets at the flea market for $138. She sold
some baskets for $12 and some for $18 each. How
many of each basket did she sell?
A. five $12 baskets and five $18 baskets
B. four $12 baskets and five $18 baskets
C. three $12 baskets and seven $18 baskets
D. four $12 baskets and four $18 baskets
This slide is intentionally blank.