5 Minute Check
Complete on a blank sheet of paper.
1. 650 ÷ 5
2. 98 ÷ 6
3. 187 ÷ 9
4. 785 ÷ 3
5 Minute Check
Complete on a blank sheet of paper.
1. 650 ÷ 5
5 Minute Check
Complete on a blank sheet of paper.
1. 650 ÷ 55
130
5) 650
-5
15
-15
0
5 Minute Check
Complete on a blank sheet of paper.
2. 98 ÷ 6
5 Minute Check
Complete on a blank sheet of paper.
2. 98 ÷ 6
16
6) 98
-6
38
-36
2
1
3
5 Minute Check
Complete on a blank sheet of paper.
3. 187 ÷ 9
5 Minute Check
Complete on a blank sheet of paper.
3. 187 ÷ 9
02079
9) 187
-0
18
-18
07
5 Minute Check
Complete on a blank sheet of paper.
4. 785 ÷ 3
5 Minute Check
Complete on a blank sheet of paper.
4. 785 ÷ 3
26123
3) 785
-6
18
-18
05
-3
2
Monday, Aug 24
Review Lesson 3
Divisibility Patterns
Divisibility Patterns
Objective: To understand divisibility
patterns.
Divisibility Patterns
Divisibility patterns or rules enable one to
determine if two whole numbers are evenly
divisible.
Divisibility Patterns
Is 4578 divisible by 2?
Divisibility Patterns
Is 4578 divisible by 2?
Divisibility Rule of 2: If the last digit is even
(0, 2, 4, 6, 8) the entire number is divisible by
2.
Divisibility Patterns
Is 4578 divisible by 2?
Divisibility Rule of 2: If the last digit is even
(0, 2, 4, 6, 8) the entire number is divisible by
2.
Multiply any number by 2 and the product will
always be an even number.
Divisibility Patterns
Is 4578 divisible by 3?
Divisibility Patterns
Is 4578 divisible by 3?
Divisibility Rule of 3: If the sum of the digits is
divisible by 3, the entire number is divisible by
3. If the sum is more than one digit, add again.
Divisibility Patterns
Is 4578 divisible by 3?
Divisibility Rule of 3: If the sum of the digits is
divisible by 3, the entire number is divisible by
3. If the sum is more than one digit, add again.
4 + 5 + 7 + 8 = 24, and 2 + 4 = 6
Since 6 is divisible by 3, then 4578 is also.
Divisibility Patterns
Is 4578 divisible by 5?
Divisibility Patterns
Is 4578 divisible by 5?
Divisibility Rule of 5: If the last digit is a 5 or 0
the entire number is divisible by 5.
Divisibility Patterns
Is 4578 divisible by 10?
Divisibility Patterns
Is 4578 divisible by 10?
Divisibility Rule of 10: If the last digit is a zero,
then the number is divisible by 10.
Divisibility Patterns
Is 4578 divisible by 10?
Divisibility Rule of 10: If the last digit is a zero,
then the number is divisible by 10.
Since 8 ≠ 0, the number is not divisible by 10.
Divisibility Patterns
Can an odd number ever be divisible by an
even number?
Divisibility Patterns
Can an odd number ever be divisible by an
even number?
NO! An odd number can never be divisible
by an even number.
Divisibility Patterns
89
Is this number divisible by 2?
Divisibility Patterns
89
Is this number divisible by 2? No
The last digit is odd.
Divisibility Patterns
89
Is this number divisible by 2? No
Is this number divisible by 3?
Divisibility Patterns
89
Is this number divisible by 2? No
Is this number divisible by 3? No
8+9=17,1+7=8
Divisibility Patterns
89
Is this number divisible by 2? No
Is this number divisible by 3? No
Is this number divisible by 5?
Divisibility Patterns
89
Is this number divisible by 2? No
Is this number divisible by 3? No
Is this number divisible by 5? No
89
Divisibility Patterns
Is this number divisible by 2? No
Is this number divisible by 3? No
Is this number divisible by 5? No
Is this number divisible by 10?
89
Divisibility Patterns
Is this number divisible by 2? No
Is this number divisible by 3? No
Is this number divisible by 5? No
Is this number divisible by 10? No
Divisibility Patterns
89
Actually, 89 is only divisible by 1 and 89.
If a number is only divisible by 1 and itself, it is
called what?
Divisibility Patterns
89
If a number is only divisible by 1 and itself, it is
called what? Prime Number
Divisibility Patterns
478
Is this number divisible by 2?
Divisibility Patterns
478
Is this number divisible by 2? Yes
The last digit is even.
Divisibility Patterns
478
Is this number divisible by 2? Yes
Is this number divisible by 3?
Divisibility Patterns
478
Is this number divisible by 2? Yes
Is this number divisible by 3? No
4 + 7 + 8 = 19, 1 + 9 = 10, 1+ 0 = 1
Divisibility Patterns
478
Is this number divisible by 2? Yes
Is this number divisible by 3? No
Is this number divisible by 5?
478
Divisibility Patterns
Is this number divisible by 2? Yes
Is this number divisible by 3? No
Is this number divisible by 5? No
The last digit is not 5.
478
Divisibility Patterns
Is this number divisible by 2? Yes
Is this number divisible by 3? No
Is this number divisible by 5? No
Is this number divisible by 10?
478
Divisibility Patterns
Is this number divisible by 2? Yes
Is this number divisible by 3? No
Is this number divisible by 5? No
Is this number divisible by 10? No
Divisibility Patterns
478
Since 478 is divisible by 2 that means it is not
a prime number. If a number has more than
two factors, it is called what?
Divisibility Patterns
478
Since 478 is divisible by 2 that means it is not
a prime number. If a number has more than
two factors, it is called what?
A Composite Number.
Divisibility Patterns
3135
Is this number divisible by 2,3,5,10?
Do this on your own.
Divisibility Patterns
3135
Is this number divisible by 2?
Divisibility Patterns
3135
Is this number divisible by 2? No
The last digit is not even.
Divisibility Patterns
3135
Is this number divisible by 2? No
Is this number divisible by 3?
Divisibility Patterns
3135
Is this number divisible by 2? No
Is this number divisible by 3? Yes
3 + 1 + 3 + 5 = 12, 1 + 2 = 3
Divisibility Patterns
3135
Is this number divisible by 2? No
Is this number divisible by 3? Yes
Is this number divisible by 5?
3135
Divisibility Patterns
Is this number divisible by 2? No
Is this number divisible by 3? Yes
Is this number divisible by 5? Yes
The last digit is a 5.
3135
Divisibility Patterns
Is this number divisible by 2? No
Is this number divisible by 3? Yes
Is this number divisible by 5? Yes
Is this number divisible by 10?
3135
Divisibility Patterns
Is this number divisible by 2? No
Is this number divisible by 3? Yes
Is this number divisible by 5? Yes
Is this number divisible by 10? No
Divisibility Patterns
3135
Is this number a prime or composite number?
Divisibility Patterns
3135
Is this number a prime or composite number?
Because it is divisible by 3 and 5, it is a
composite number.
Divisibility Patterns
14980
Is this number divisible by 2,3,5,10?
Do this on your own.
Divisibility Patterns
14980
Is this number divisible by 2,3,5,10?
14980 is divisible by 2, 5, and 10.
Divisibility Patterns
14980
Is this number a prime or composite number?
Divisibility Patterns
14980
Is this number a prime or composite number?
Because it is divisible by 2, 5, and 10, it is a
composite number.
Divisibility Patterns
26?48
What digit can be placed in the ? for the entire
number to be divisible by 3 ?
Divisibility Patterns
26?48
What digit can be placed in the ? for the entire
number to be divisible by 3 ?
2 + 6 + 4 + 8 = 20; 2 + 0 = 2
So ? can be either 1, 4, or 7
Divisibility Patterns
1?45
What digit can be placed in the ? for the entire
number to be divisible by 2 ?
Divisibility Patterns
1?45
What digit can be placed in the ? for the entire
number to be divisible by 2 ?
None, since the last digit is odd, it will never be
divisible by 2.
Divisibility Patterns
145?
What digit can be placed in the ? for the entire
number to be divisible by 5 ?
Divisibility Patterns
145?
What digit can be placed in the ? for the entire
number to be divisible by 5 ?
0 or 5
Divisibility Patterns
34?
What digit can be placed in the ? for the entire
number to be divisible by 2 ?
Divisibility Patterns
34?
What digit can be placed in the ? for the entire
number to be divisible by 2 ?
0, 2, 4, 6, or 8
Divisibility Patterns
The number of tickets needed to ride the
Ferris wheel at the county fair is three. If
Alicia has 53 tickets, can she use all of the
tickets by riding only the Ferris wheel?
Divisibility Patterns
The number of tickets needed to ride the
Ferris wheel at the county fair is three. If
Alicia has 53 tickets, can she use all of the
tickets by riding only the Ferris wheel?
5+3=8
Since 8 is not divisible by 3 the answer is no.
Divisibility Patterns
Ashley is arranging dolls on shelves at a toy
store. She has 63 dolls to arrange. She
needs to put the same number of dolls on
each shelf, and she needs to use all of the
dolls. Can Ashley use 5 shelves for the
dolls?
.
Divisibility Patterns
Ashley is arranging dolls on shelves at a toy
store. She has 63 dolls to arrange. She
needs to put the same number of dolls on
each shelf, and she needs to use all of the
dolls. Can Ashley use 5 shelves for the
dolls?
No, because the last digit is not a 5 or 0.
.
Divisibility Patterns
A company posted out 9,378 coupon
booklets. The company sent the same
number of booklets to each city. How many
cities could the coupon booklets have gone
to, either 2 or 3?
.
Divisibility Patterns
A company posted out 9,378 coupon
booklets. The company sent the same
number of booklets to each city. How many
cities could the coupon booklets have gone
to, either 2 or 3?
They could have been sent to 2 or 3 cities.
9,378 is even, which means it is divisible by 2
and 9+3+7+8 = 27; 2 + 7 = 9 and 9 is
divisible by 3.
.
Divisibility Patterns
Is 5 x 5 x 5 x 5 divisible by 2?
.
Divisibility Patterns
Is 5 x 5 x 5 x 5 divisible by 2?
No.
If the factors are all odd, the product will
always be odd.
.
Divisibility Patterns
Is 4 x 6 x 2 x 8 divisible by 2?
.
Divisibility Patterns
Is 4 x 6 x 2 x 8 divisible by 2?
Yes.
If the factors are all even, the product will
always be even.
.
Divisibility Patterns
Is 4 x 5 x 2 x 8 divisible by 2?
Divisibility Patterns
Is 4 x 5 x 2 x 8 divisible by 2?
Yes.
If there are even and odd factors, the
product will always be even.
.
Divisibility Patterns
even x even = even
odd x odd = odd
even x odd = even
.
Divisibility Patterns
On homework always write first AND
last name.
And always include correct period
number.
Divisibility Patterns
Agenda Notes
Homework –
Homework Practice R.3
Due Tuesday, Aug 25
Divisibility Patterns
A red car and a blue car set off from the same point
to travel the same journey. The red car has a head
start of three minutes before the blue car takes off.
If the red car travels at
40 mph and the blue car
travels at 60 mph, how
many miles will the red
car have traveled when
the blue car catches up?
Divisibility Patterns
A red car and a blue car set off from the same point to
travel the same journey. The red car has a head start of
three minutes before the blue car takes off.
If the red car travels at 40 mph and the blue car travels at 60
mph, how many miles will the red car have traveled when the
blue car catches up?
First , we have to convert the time to the same units. We can
either convert the speed (40 mph) to miles per minutes or
convert the head start from minutes to hours. Three
minutes is what part of an hour?
Divisibility Patterns
A red car and a blue car set off from the same point to
travel the same journey. The red car has a head start of
three minutes before the blue car takes off.
If the red car travels at 40 mph and the blue car travels at 60
mph, how many miles will the red car have traveled when the
blue car catches up?
First , we have to convert the time to the same units. We can
either convert the speed (40 mph) to miles per minutes or
convert the head start from minutes to hours. Three
minutes is what part of an hour?
1 min = 1/60 of an hour; 2 min = 2/60 hour; 3 min = 3/60
hour or 1/20 hour.
Divisibility Patterns
A red car and a blue car set off from the same point to
travel the same journey. The red car has a head start of
three minutes before the blue car takes off.
If the red car travels at 40 mph and the blue car travels at 60
mph, how many miles will the red car have traveled when the
blue car catches up?
How far would the red car go in 1/20 hour?
Divisibility Patterns
A red car and a blue car set off from the same point to
travel the same journey. The red car has a head start of
three minutes before the blue car takes off.
If the red car travels at 40 mph and the blue car travels at 60
mph, how many miles will the red car have traveled when the
blue car catches up?
How far would the red car go in 1/20 hour?
At 40 mph, it would go 40 miles in 1 hour. In a half hour
(1/2) it would go half that, or 20 miles. In a fourth of an hour
(1/4) it would go one-fourth of that, or 10 miles. In 1/20 of
an hour, it would go 1/2o of 40 miles, which is 2 miles.
Divisibility Patterns
A red car and a blue car set off from the same point to
travel the same journey. The red car has a head start of
three minutes before the blue car takes off.
If the red car travels at 40 mph and the blue car travels at 60
mph, how many miles will the red car have traveled when the
blue car catches up?
3 min
2 miles
How far would the red car go in the next 1/20 hour?
Divisibility Patterns
A red car and a blue car set off from the same point to
travel the same journey. The red car has a head start of
three minutes before the blue car takes off.
If the red car travels at 40 mph and the blue car travels at 60
mph, how many miles will the red car have traveled when the
blue car catches up?
3 min
2 miles
3 min
2 miles
After sitting for the first 3 minutes, how far does the
blue car travel during the second 3 minutes?
Divisibility Patterns
A red car and a blue car set off from the same point to travel the
same journey. The red car has a head start of three minutes
before the blue car takes off.
If the red car travels at 40 mph and the blue car travels at 60
mph, how many miles will the red car have traveled when the blue
car catches up?
3 min
2 miles
3 min
3 miles
3 min
2 miles
Going 60 mph, is a mile a min, it will travel 3 miles in 3 min.
Divisibility Patterns
A red car and a blue car set off from the same point to
travel the same journey. The red car has a head start of
three minutes before the blue car takes off.
If the red car travels at 40 mph and the blue car travels at 60
mph, how many miles will the red car have traveled when the
blue car catches up?
3 min
3 min
2 miles
2 miles
3 min
3 miles
How far will each car in the next 3 minutes?
Divisibility Patterns
A red car and a blue car set off from the same point to
travel the same journey. The red car has a head start of
three minutes before the blue car takes off.
If the red car travels at 40 mph and the blue car travels at 60
mph, how many miles will the red car have traveled when the
blue car catches up?
3 min
3 min
3 min
2 miles
2 miles
2 miles
3 min
3 min
3 miles
3 miles
9 minutes after the red car leaves, both cars
will have traveled 6 miles.