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# Prime factorization

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### Prime factorization

1. 1. Exponents andPrime Factorization<br />3 x 3 x 5 x 5 x 5 = 3² x 5³<br />Mrs. Rotunno<br />5th Grade<br />2010-2011<br />
2. 2. Exponents<br />5³<br />exponent<br />base<br />An exponent shows how many times a number, called a base, is used as a factor.<br />
3. 3. How to Write an Exponent<br />Factors: 3 x 5 x 5 x 3 x 2 x 5 x 2<br />Combine like terms from smallest to largest: <br />2 x 2 x 3 x 3 x 5 x 5 x 5<br />Write down the base numbers:<br />235<br />Add exponents (shown in green):<br />2² 3² 5³<br />Add the multiplication signs:<br />2² X 3² X 5³<br />
4. 4. Match the Expression with the Exponent<br />8 x 8 5² x 7³<br />4 x 4 x 4 8²<br />7 x 5 x 5 x 7 x 7 10⁴<br />10 x 10 x 10 x 10 4³<br />
5. 5. Match the Expression with the Exponent<br />6 x 6 x 5 x 9 x 9 x 9 x 6 5³x6³x9<br />5 x 6 x 5 x 9 x 9 5²x6x9²<br />9 x 6 x 6 x 5 x 6 x 5 x 5 5²x6³x9²<br />6 x 9 x 9 x 6 x 5 x 5 x 6 5x6³x9³<br />
6. 6. Play this Game<br />http://www.studystack.com/matching-14392<br />8²<br />7³<br />7 x 7 x 7<br />8 x 8 <br />
7. 7. Do you know your exponents?<br /> Take this quiz and record your score in your math journal.<br />http://www.studystack.com/quiz-14392<br />
8. 8. Prime Factorization is . . . <br />A number written as a product of prime factors.<br />2 X 2 X 2 X 3<br />3 X 7<br />2 X 3 X 3 X 3<br />3 X 5 X 5<br />2 X 3 X 5<br />
9. 9. Prime Factorization can be solved using a Factor Tree<br />A factor tree is a model that shows prime factorization.<br />
10. 10. Example of a factor tree:<br />No matter what factors you use, you will finish with the same answer.<br /> Example 1 Example 2<br />20<br />20<br />4<br />5<br />2<br />10<br />2<br />2<br />2<br />5<br />2 X 2 X 5 = 2² X 5<br />2 X 2 X 5 = 2² X 5<br />
11. 11. Use mental math to complete the Factor Tree<br />36<br />9<br />4<br />3<br />2<br />2<br />3<br />Then click to see if you were right.<br />
12. 12. Play These Games<br />http://www.mathplayground.com/factortrees.html<br />http://nlvm.usu.edu/en/nav/frames_asid_202_g_3_t_1.html?from=category_g_3_t_1.html<br />
13. 13. Watch this video<br />Factor <br />Trees<br />http://www.youtube.com/watch?v=qGkK8xkWs6U&feature=related<br />
14. 14. Assessment<br />Click on the following link to complete an assessment on Survey Monkey. <br />http://www.surveymonkey.com/s.aspx?PREVIEW_MODE=DO_NOT_USE_THIS_LINK_FOR_COLLECTION&sm=Hyhggl7d5HcJJwK6rcftpN%2b%2fbDp3faTa2fSEgpudJtU%3d<br />We will go over the results together in class.<br />
15. 15. Definitions<br />Prime number – A number that has only two factors, 1 and itself.<br /> Examples: 2, 3, 5, 7, 11 , 13, 17, 19, 23<br />Composite number - A number that has more than two factors.<br /> Examples: 9 = factors are 1, 3, 9<br /> 24 = factors are 1, 2, 3, 4, 6, 8, 12, 24<br />Exponent – Shows how many times a number, called the base, is<br /> used as a factor. (Numbers in green are exponents.)<br /> Examples: 3² or 4³<br />Base – A number used as a factor. (Numbers in red are base numbers.)<br /> Examples: 5³ or 6²<br />
16. 16. GLCE’s<br />N.MR.05.07 Find the prime factorization of numbers from 2 through 50, express in exponential notation, e.g., 24 = 23 x 31, and understand that every whole number greater than 1 is either prime or can be expressed as a product of primes.* <br />
17. 17. References<br />Andrews, A.G., Bennett, J. M., Burton, G. M., Johnson, H.C., Luckie, L., Maletsky, E. M., … Schultz, <br /> K. A., (2002). Harcourt Math. Orlando: Harcourt School Publishers.<br />http://www.cksinfo.com/electronics/televisions/index.html<br />http://michigan.gov/documents/5th_Math-Intro_Ltrweb_149037_7.pdf<br />http://nlvm.usu.edu/en/nav/frames_asid_202_g_3_t_1.html?from=category_g_3_t_1.html<br />http://www.studystack.com/matching-14392<br />http://www.studystack.com/quiz-14392<br />http://www.surveymonkey.com/s.aspx?PREVIEW_MODE=DO_NOT_USE_THIS_LINK_FOR_COLLECTION&sm=Hyhggl7d5HcJJwK6rcftpN%2b%2fbDp3faTa2fSEgpudJtU%3d<br />http://www.youtube.com/watch?v=qGkK8xkWs6U&feature=related<br />