Fun and GamesFun and GamesNumber Theory GONE WILD!

Factors “Fall” into FamiliesMultiples Multiply like

Rabbits!

What am I Learning Today?What am I Learning Today?Divisibility Rules

How will I show that I learned it?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 Turn to a partner and try to figure out what the “yes” numbers have in commonthe “yes” numbers have in common

YES NO2

43 64 11

128 31316

25

YES NO

10 24

65 33

225 79

610 246

Then, try to identify “What’s the rule?”Then, try to identify “What’s the rule?”

VocabularyVocabularyDivisibility: 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 RulesDivisibility RulesA 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 = 99 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 = 99 is divisible by 9

10 if the last digit is 0. 15,990 The last digit is 0

Checking DivisibilityChecking DivisibilityTell whether 462 is divisible by 2, 3, 4, and 5.

2

3

4

5Not

divisible

So 462 is divisible by 2 and 3.

The last digit, 2, is even.

The sum of the digits is 4 + 6 + 2 = 12. 12 is divisible by 3.

The last two digits form the number 62. 62 is not divisible by 4.

Divisible

Divisible

Not divisible

The last digit is 2.

6

9

10

So 540 is divisible by 6, 9, and 10.

The number is divisible by both 2 and 3.

The sum of the digits is 5 + 4 + 0 = 9. 9 is divisible by 9.

The last digit is 0.

Divisible

Divisible

Divisible

Checking DivisibilityChecking DivisibilityTell whether 540 is divisible by 6, 9, and 10.

Paired DiscussionPaired DiscussionTurn 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 GamesFun and GamesNumber Theory GONE WILD!

Factors “Fall” into FamiliesMultiples Multiply like

Rabbits!

What am I Learning Today?What am I Learning Today?Prime and Composite Numbers

How will I show that I learned it?How will I show that I learned it?

Compare and contrast prime and composite numbersUse divisibility rules to determine a number’s characteristics

VocabularyVocabularyComposite 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 EratosthenesSieve of Eratosthenes

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.

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.

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 EratosthenesSieve of Eratosthenes

Paired DiscussionPaired DiscussionTurn 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?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?

CreditsCreditshttp://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/Eratosthenes/

Picture of Eratosthenes