Number Theory GONE WILD! 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 2 43 64 11 128 313 16 25 YES NO 10 24 65 33 225 79 610 246 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.

48 is divisible by both 2 and 3 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 3 4 5 The last digit, 2, is even. Divisible The sum of the digits is 4 + 6 + 2 = 12. 12 is divisible by 3. Divisible The last two digits form the number 62. 62 is not divisible by 4. Not divisible Not divisible The last digit is 2. So 462 is divisible by 2 and 3.

Checking Divisibility Tell whether 540 is divisible by 6, 9, and 10. 6 9 10 The number is divisible by both 2 and 3. Divisible The sum of the digits is 5 + 4 + 0 = 9. 9 is divisible by 9. Divisible The last digit is 0. Divisible So 540 is divisible by 6, 9, and 10.

Turn to a partner and discuss the following: 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

Number Theory GONE WILD! 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. 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. 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.

Sieve of Eratosthenes

Turn to a partner and discuss the following: 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/Eratosthenes/ Picture of Eratosthenes