Download divisible

Fun and Games
Number Theory GONE WILD!
Factors “Fall” into Families
Multiples Multiply like
Rabbits!
What am I Learning Today?
Divisibility Rules
How will I show that I learned it?
Create a graphic organizer that contains the
divisibility rule, an example and an explanation.
Use divisibility rules to determine the
characteristics of numbers.
Turn to a partner and try to figure out what
the “yes” numbers have in common
YES
NO
YES
NO
2
43
10
24
64
11
65
33
128
313
225
79
16
25
610
246
Then, try to identify “What’s the rule?”
Vocabulary
Divisibility: A number’s ability to be evenly
divisible by another number. The quotient
must be a whole number with no
remainder.
The quotient is the answer to a division problem.
The divisor is the number doing the dividing.
The dividend is the number being divided.
Divisibility Rules
A number is divisible by. . .
Example
Explanation
2
if the last digit is even (0, 2, 4, 6, or 8).
3,978
8 is even
3
if the sum of the digits is divisible by 3.
315
3+1+5=9
9 is divisible by 3
4
if the last two digits form a number
divisible by 4.
8,512
12 is divisible by 4
5
if the last digit is 0 or 5.
14,975
The last digit is 5
6
if the number is divisible by both 2 and 3
48
48 is divisible by
both 2 and 3
9
if the sum of the digits is divisible by 9.
711
7+1+1=9
9 is divisible by 9
10 if the last digit is 0.
15,990
The last digit is 0
Checking Divisibility
Tell whether 462 is divisible by 2, 3, 4, and 5.
2
The last digit, 2, is even.
3
The sum of the digits is 4 + 6 + 2 = 12.
Divisible
12 is divisible by 3.
4
The last two digits form the number 62.
62 is not divisible by 4.
Not
divisible
5
The last digit is 2.
Not
divisible
So 462 is divisible by 2 and 3.
Divisible
Checking Divisibility
Tell whether 540 is divisible by 6, 9, and 10.
6
The number is divisible by both
2 and 3.
Divisible
9
The sum of the digits is 5 + 4 + 0 = 9.
9 is divisible by 9.
Divisible
The last digit is 0.
Divisible
10
So 540 is divisible by 6, 9, and 10.
Paired Discussion
Turn to a partner and discuss the
following:
How can the divisibility rules help you
identify composite numbers?
If a number is divisible by 4 and 9, by what
other numbers is it divisible? Explain.
Dynamite Divisibility
Fun and Games
Number Theory GONE WILD!
Factors “Fall” into Families
Multiples Multiply like
Rabbits!
What am I Learning Today?
Prime and Composite Numbers
How will I show that I learned it?
Compare and contrast prime and
composite numbers
Use divisibility rules to determine a
number’s characteristics
Vocabulary
Composite number: A number that is
divisible by more than two numbers.
Prime number: A number greater than one
that is only divisible by one and itself.
Sieve of Eratosthenes
How it’s done:
Step 1: Circle 2 in blue because it is prime. Now
cross out all the multiples of 2 with that
same color.
A Greek mathematician,
who made several
discoveries, including the
system of latitude and
longitude. He was the first
to calculate the
circumference of the Earth,
as well as the distance to
the sun. He invented the
Leap Day. He also
proposed a simple
algorithm for finding prime
numbers.
Step 2: Circle 3 in green because it is prime.
Now cross out every third number with
that same color.
Step 3: Circle 5 in red because it is prime. Now
cross out all the numbers that end in 0
or 5 in that same color.
Step 4: Circle 7 in yellow because it is prime.
Now cross out every seventh number
with that same color.
Step 5: Circle the remaining numbers, EXCEPT
for one, in purple because they are all
prime.
Sieve of Eratosthenes
Paired Discussion
Turn to a partner and discuss the
following:
1) How can the divisibility rules help
you identify composite numbers?
2) The Sieve of Eratosthenes didn’t
include the number ONE. Is it prime
or composite?
3) Are prime numbers mostly odd or
mostly even? Explain.
Are you up for the Challenge?
Do a little research and see if you can
answer the following questions:
What are TWIN primes?
What does the term relatively prime mean?
Where are prime numbers used today?
Credits
http://en.wikipedia.org/wiki/File:New_Animation_Sieve_of_
Eratosthenes.gif
http://my.hrw.com Selected slides from c1_ch04_01.ppt
http://www.knowledgerush.com/kr/encyclopedia/Eratosthen
es/ Picture of Eratosthenes