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Chapter 1 Lesson 1

Chapter 1 Lesson 1. Prime Factorization Pages 7-8 2-12 even Created By: Cindy Smith, OMSD. 3 Column Notes – Chap. 1 Lesson 1. Main Ideas/Cues: Prime number Composite number. Details: A whole number greater than 1 whose only whole number factors are 1 and itself.

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Chapter 1 Lesson 1

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  1. Chapter 1 Lesson 1 Prime Factorization Pages 7-8 2-12 even Created By: Cindy Smith, OMSD

  2. 3 Column Notes – Chap. 1 Lesson 1 Main Ideas/Cues: Prime number Composite number Details: A whole number greater than 1 whose only whole number factors are 1 and itself. A whole number greater than 1 that is not prime. Picture/Example: 5 is a prime number because its only number factors are 1 and 5. 6 is a composite number because its factors are 1, 2, 3, and 6.

  3. 3 Column Notes – Chap. 1 Lesson 1 Main Ideas/Cues: Prime factorization Factor tree Details: Expressing a whole number as a product of prime numbers. A diagram that can be used to write the prime factorization of a number. Picture/Example: The prime factorization of 54 is 54=2 x 3 x 3 x 3 = 2 x 33 54 6 x 9 2 x 3 x 3 x 3

  4. 3 Column Notes – Chap. 1 Lesson 1 Details: 1. Write the numbers from 1 – 50. Cross out 1 since 1 is not a prime number. 2. Circle 2 and cross out all multiples of 2, other than 2. 3. Circle the next number that is not crossed out. Then cross out its multiples. Repeat until all numbers are either crossed out or circled. Picture/Example: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 Main Ideas/ Cues: Steps to determine which numbers are prime using the Sieve of Eratosthenes

  5. 3 Column Notes – Chap. 1 Lesson 1 Details: 1. Write each pair of multiples for a number, starting with 1. 2. Stop when the factors repeat. Picture/Example: Factors: 1, 2, 3, 5, 6, 10, 15, and 30 Main Ideas/ Cues: Writing Factors of a Number

  6. 3 Column Notes – Chap. 1 Lesson 1 Details: Using either the Sieve of Eratosthenes or by listing the Factors of a number, determine if a number is prime or composite. Picture/Example: 56 56 = 1 x 56 = 2 x 28 = 56 isn’t divisible by 3. = 4 x 14 = 56 isn’t divisible by 5. = 56 isn’t divisible by 6. = 7 x 8 = at 8 we repeat STOP. Factors: 1, 2, 4, 7, 8, 14, 28, and 56 11 The only factors of 11 are 1 and 11. So, 11 is prime. Main Ideas/ Cues: Identifying Prime and Composite Numbers

  7. 3 Column Notes – Chap. 1 Lesson 1 Details: When a prime factor appears more than once in the prime factorization, use an exponent. An exponent shows how many times the base is used as a factor in the product. Picture/Example: Main Ideas/ Cues: Writing the Prime Factorization using a factor tree.

  8. Problem #2 Directions: Write all the factors of the number First Step: Write the Problem 2. 32

  9. Problem #2 Second Step: Write all the factors of the number. 2. 32 = 1 x 32 = 2 x 16 = 4 x 8

  10. Problem #2 Final Step: List all the factors of the number, from least to greatest. 2. 32 = 1 x 32 = 2 x 16 = 4 x 8 1, 2, 4, 8, 16, and 32

  11. Problem #4 Directions: Write all the factors of the number First Step: Write the Problem 4. 23

  12. Problem #4 Second Step: Write all the factors of the number. 4. 23 = 1 x 23

  13. Problem #4 Final Step: List all the factors of the number, from least to greatest. 4. 23 = 1 x 23 1 and 23

  14. Problem #6 Directions: Tell whether the number is prime or composite First Step: Write the Problem 6. 81

  15. Problem #6 Second Step: Write all the factors of the number. 6. 81 = 1 x 81 = 3 x 27 = 9 x 9

  16. Problem #6 Final Step: Tell whether the number is prime or composite. 6. 81 = 1 x 81 = 3 x 27 = 9 x 9 Composite

  17. Problem #8 Directions: Tell whether the number is prime or composite First Step: Write the Problem 8. 79

  18. Problem #8 Second Step: Write all the factors of the number. 8. 79 = 1 x 79

  19. Problem #8 Final Step: Tell whether the number is prime or composite. 8. 79 = 1 x 79 Prime

  20. Problem #10 Directions: Use a factor tree to write the prime factorization of the number. First Step: Write the Problem 10. 48

  21. Problem #10 Second Step: Create the factor tree 10. 48 2 x 24 2 x 12 2 x 6 2 x 3

  22. Problem #10 Final Step: Write the prime factorization (remember to use exponents) 10. 48 = 2 x 2 x 2 x 2 x 3 = 24 x 3

  23. Problem #12 Directions: Use a factor tree to write the prime factorization of the number. First Step: Write the Problem 12. 75

  24. Problem #12 Second Step: Create the factor tree 10. 75 3 x 25 5 x 5

  25. Problem #12 Final Step: Write the prime factorization (remember to use exponents) 12. 75 = 3 x 5 x 5 = 3 x 52

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