Using Objects to Divide: Division as
Repeated Subtraction (10 – 1)
When you divide, you subtract equal groups.
Doris has 32 strawberries. She makes box lunches by putting
4 strawberries in each box lunch. How many box lunches can
she make this way?
What you think: Doris will put 4 strawberries in each lunch box.
How many lunch boxes can she make?
What you show: Repeated subtraction
32 – 4 = 28
16 – 4 = 12
28 – 4 = 24
12 – 4 = 8
24 – 4 = 20
8–4=4
20 – 4 = 16
4–4=0
You can subtract 4 from 32 eight times.
What you write: 32 ÷ 4 = 8
32 is the dividend, the number that is being divided.
4 is the divisor, the number the dividend is being divided by.
8 is the quotient, or the answer to the division problem.
Draw pictures to solve each problem.
1. You have 15 marbles. You put 5 marbles
into each group. How many groups can
you make?
2. You have 20 ice cubes. You put
4 ice cubes into each glass.
How many glasses can you
put ice cubes into?
Division as Repeated Subtraction (10 – 2)
For City Clean-Up Day, 18 people volunteered to clean up the city
park. The volunteers worked in groups with 3 people each. How
many groups of volunteers cleaned up the city park?
Use repeated subtraction to find the number of groups.
18 – 3 = 15
15 – 3 = 12
12 – 3 = 9
9–3=6
6–3=3
3–3=0
There are 6 groups of volunteers.
Use repeated subtraction to divide. Use a number line to help.
1. Mark is placing 12 model cars into
equal groups. Each group has
4 model cars. How many groups of
model cars will he make?
2. There are 24 students in gym class.
They divided into teams of 6 for a
volleyball game. How many teams
were there?
3. Each necklace Cara makes has
5 beads. How many necklaces can
Cara make with 20 beads?
4. Amy has 12 dolls in her collection.
She places 6 dolls on each shelf.
How many shelves does she need?
5. Charlie has 16 chores to do. He
can complete 4 chores in one day.
How many days will Charlie take to
complete his chores?
6. The pet store has 9 parakeets. If
3 parakeets are in each cage, how
many cages are there?
7. Shawn needs to learn how to play
15 songs for his band’s concert. If
he learns 3 songs each week, how
many weeks will it take him to learn
all of the songs?
8. At Rosa Elementary School,
27 teachers signed up to carpool.
If 3 teachers ride together in each
car, how many cars are needed for
all of the teachers?
Using Objects to Divide:
Division as Sharing (10 – 3)
You can use models to help you solve division problems.
The models below help you find 78 ÷ 5.
Find 78 ÷ 5.
Estimate 80 ÷ 5 = 16.
First divide the
tens.
Now, change the
tens into the ones.
1
5 78
−5
28
1
5 78
−5
There is one tens block
in each group of 5
Now, divide the
ones.
Now, write the
remainder.
15
5 78
−5
28
−25
3
15R3
5 78
−5
28
−25
3
2 tens blocks and 8 ones
Each of the 5 groups has
blocks are equal to 28 ones 1 tens block and 5 ones
blocks
blocks
78 ÷ 5 = 15 R3
Use the models below to help you fill in the boxes.
1. 66 ÷
3.
=
÷7=
R2
R6
2. 97 ÷ 4 =
4. 76 ÷
R
=
R
Dividing 2-Digit by 1-Digit Numbers (10 – 4)
You can find 2-digit quotients by breaking apart the problem
and dividing tens, then ones.
Find 85 ÷ 5.
Find 55 ÷ 3.
Find 83 ÷ 7.
Estimate: 100 ÷ 5 = 20.
Estimate: 60 ÷ 3 = 20.
Estimate: 84 ÷ 7 = 12.
17
5 85
−5
35
− 35
0
18 R1
3 55
−3
25
− 24
1
11R6
7 83
−7
13
− 7
6
Check: 17 × 5 = 85.
Check: 18 × 3 = 54.
Check: 11 × 7 = 77.
The answer checks.
54 + 1 = 55
77 + 6 = 83
The answer checks.
The answer checks.
Find the missing values.
1.
3. 3 91
2.
4. 4 86
5. 2 75
Dividing 3-Digit by 1-Digit Numbers (10 – 5)
You can find 3-digit quotients by breaking apart the problem.
Find 528 ÷ 4.
Estimate 500 ÷ 4 = 125.
4
−
−
−
Find 575 ÷ 5.
Estimate 600 ÷ 5 = 120.
115
5 575
− 5
132
528
4
12
12
8
8
0
241R2
3 725
− 6
7
−5
12
− 12
25
− 25
0
Check 132 × 4 = 528
The answer checks.
−
Check 115 × 5 = 575
The answer checks.
Find the missing values.
1.
3. 3 462
2.
4. 5 640
Find 725 ÷ 3.
Estimate 750 ÷ 3 = 250.
5. 9 919
5
3
2
Check 241 × 3 = 723
723 + 2 = 725
The answer checks.
Deciding Where to Start Dividing (10 – 6)
Sometimes there are not enough hundreds to divide by.
Sometimes you have to break up the hundreds into 10 tens.
Find 325 ÷ 5.
Estimate 300 ÷ 5 = 60.
Try to divide the
hundreds.
Divide the tens.
Now divide the ones.
6
5 325
− 30
2
5 325
65
5 325
− 30
25
−
5 does not divide into 3.
The 3 hundreds now have
to be changed to 30 tens.
25
0
With 32 tens, 6 tens
can go into each one
of the 5 groups.
Each of the five groups
has 6 tens and 5 ones.
Find the missing values in the problems below.
1.
2.
3. 5 125
4. 8 418
Dividing 4-Digit by 1-Digit Numbers (10 – 7)
An estimate will help you decide where to place the first digit
of the quotient. It will also help you check your answer.
Divide 5,493 ÷ 6.
Estimate first. You can use
compatible numbers to divide
mentally.
Divide to find the actual quotient.
Compare: Is the estimate close
to the quotient?
estimate:
54 is a multiple of 6.
quotient:
5,400 is close to 5,493 and 5,400
÷ 6 will be easy to divide.
If it is, then your answer
is reasonable.
5,400 ÷ 6 =
Estimate. Then find each quotient. Use your estimate to check if
your quotient is reasonable.
1. Divide 4,318 ÷ 7.
2. Divide 4,826 ÷ 5.
Estimate:
Estimate:
÷
=
÷
=
4,318 ÷ 7 =
4,826 ÷ 5 =
Is your answer reasonable?
Is your answer reasonable?
3. Divide 4,377 ÷ 8.
4. Divide 7,192 ÷ 9.
Estimate:
Estimate:
÷
=
÷
=
4,377 ÷ 8 =
7,192 ÷ 9 =
Is your answer reasonable?
Is your answer reasonable?
Problem Solving:
Multiple-Step Problems (10 – 8)
Solve Problems Step-by-Step
Scott and Gina want to go see a movie after they eat dinner. They
have brought $35 with them. Scott’s meal costs $9 and Gina’s
meal costs $8. Movie tickets are $9 each. Will they have enough
money left over after dinner to pay for 2 movie tickets?
First Step
Write down what you know:
• They have $35 to spend.
• They are spending $9 and $8 on dinner.
Second Step
Write down what you need to know:
• How much money is left over?
• Is it enough for 2 movie tickets?
Third Step
Develop a problem-solving strategy:
• Subtract $9 and $8 from $35.
(Tip: Instead of subtracting these from
$35 one at a time, combine them and
then subtract from $35.)
$9
$35
+ $ 8 then,
−$17
$17.00
$18
Fourth Step
Finish the problem:
• Is $18 enough for 2 movie tickets that cost
$9 each?
$9 × 2 = $18
They have $18 left. Yes, they have enough
for 2 movie tickets.
Solve the problems below using the step-by-step process.
1. Nick and his friends are working on a project.
They need to write 29 pages altogether. If his friend
Kara writes 14 pages, and his friend Jared writes
12 pages, how many pages are left for Nick to write?
2. Ashlyn and Brooke went to the arcade with $18.
They bought 4 bottles of water, which cost
$2 each. They each bought a sticker book for
$3 each. Ashlyn put $1 in a fundraiser jar.
A game of pool cost $3 per game. Did they have
enough money left to play?
3. Reasoning Cyndi and Jewel went shopping for school
supplies. They had $14 to spend. They spent $4 on pencils,
$3 on pens, and $6 on notebook paper. Cyndi thought she
had enough money left over to buy a $2 pencil sharpener.
Was she correct?