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Good Morning!

Good Morning!. Please have the following on your desk Warm-Up Colored pen INB Pencil White board Whiteboard marker Complete vocabulary hand out Set up your interactive notebook for today’s lesson. 3 -1 Prime Factorization.

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Good Morning!

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  1. Good Morning! • Please have the following on your desk • Warm-Up • Colored pen • INB • Pencil • White board • Whiteboard marker • Complete vocabulary hand out • Set up your interactive notebook for today’s lesson

  2. 3-1 Prime Factorization Objective: I can find the prime factorizations of composite numbers. Now set up the left side of the page & complete: Page number: Lesson title: Prime Factorization Learning goal: (write the objective in your own words) What I know: (Write 1 or 2 sentences explaining what you already know about the lesson) Now complete the vocabulary cards for the lesson

  3. California Standards Preparation for NS2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g. to find a common denominator to add two fractions or to find the reduced form for a fraction).

  4. Vocabulary prime number composite number prime factorization factors

  5. A factor is a number that is multiplied by another number to get a product. A prime numberis a whole number greater than 1 that has exactly two positive factors, 1 and itself. Three is a prime number because its only positive factors are 1 and 3. A composite number is a whole number that has more than two positive factors. Six is a composite number because it has more than two positive factors—1, 2, 3, and 6. The number 1 has exactly one positive factor and is neither prime nor composite.

  6. Our Lonely 1 It is not prime because it does not have exactly two different factors. It is not composite because it does not have more than 2 factors. Special Note: One is not a prime nor a composite number.

  7. A composite number can be written as the product of its prime factors. This is called the prime factorization of the number. You can use a factor tree to find the prime factors of a composite number.

  8. The teacher tells students to “Stand up, put a hand up, and pair up.” • Partner A quizzes B. • Partner B answers. • Partner A praises or coaches. • Partners switch roles. • Partners trade cards and thank each other. • Repeat steps 1-6 a number of times. Vocabulary terms prime number composite number prime factorization factors

  9. Foldable for the right side of your INB • Glue the Prime Factorization Strategies at the bottom • Complete the vocabulary handouts and cut out. • Tape the edge as shown to the right to create a flip book

  10. INSIDE OF THE PRIME FACTORIZATION STRATEGIES

  11. Additional Example 1: Identifying Prime and Composite Numbers Tell whether each number is prime or composite. A. 11 B. 16 The positive factors of 11 are 1 and 11. The positive factors of 16 are 1, 2, 4, 8, and 16. 11 is prime. 16 is composite.

  12. YOUR TURN!ON YOUR WHITE BOARD Tell whether each number is prime or composite. A. 14 B. 7 The positive factors of 14 are 1, 2, 7, and 14. The positive factors of 7 are 1 and 7. 14 is composite. 7 is prime.

  13. Writing Math You can write prime factorization by using exponents. The exponent tells how many times to use the base as a factor.

  14. Additional Example 2A: Using a Factor Tree to Find Prime Factorization Write the prime factorization of the number. 24 24 Write 24 as the product of two positive factors. 8  3 4  2  3 Continue factoring until all factors are prime. 2  2  2  3 The prime factorization of 24 is 2  2  2  3 or 23 3.

  15. YOUR TURN! ON YOUR WHITE BOARD Write the prime factorization of the number. 225 Write 225 as the product of two positive factors. 225 45  5 Continue factoring until all factors are prime. 9  5  5 3  3  5  5 The prime factorization of 225 is 3  3  5  5, or 32 52.

  16. You can also use a step diagram to find the prime factorization of a number. At each step, divide by the smallest possible prime number. Continue dividing until the quotient is 1.

  17. Additional Example 3A: Using a Step Diagram to Find Prime Factorization Write the prime factorization of the number. 476 Divide 476 by 2. Write the quotient below 476. 476 2 238 2 Keep dividing by a prime number. 119 7 17 Stop when the bottom number is prime. The prime factorization of 476 is 2  2  7  17, or 22 7  17.

  18. Additional Example 3B: Using a Step Diagram to Find Prime Factorization Write the prime factorization of the number. 275 Divide 275 by 5. Write the quotient below 275. 275 5 55 5 Stop when the bottom number is prime. 11 The prime factorization of 275 is 5  5  11, or 52 11.

  19. YOUR TURN! ON YOUR WHITE BOARD Write the prime factorization of the number. 324 Divide 324 by 2. Write the quotient below 324. 324 2 162 2 Keep dividing by a prime number. 81 3 27 3 9 3 Stop when the bottom number is prime. 3 The prime factorization of 324 is 2  2  3  3  3  3, or 22 34.

  20. YOUR TURN! ON YOUR WHITE BOARD Write the prime factorization of the number. 325 Divide 325 by 5. Write the quotient below 325. 325 5 65 5 Stop when the bottom number is prime. 13 The prime factorization of 325 is 5  5  13, or 52 13.

  21. There is only one prime factorization for any given composite number. Example 2A began by dividing 476 by 2, the smallest prime factor of 476. Beginning with any prime factor of 476 gives the same result. 476 476 2 7 238 68 2 2 119 34 7 2 17 17 The prime factorizations are 2  2  7  17 and 7  2  2  17, which are the same as 17  2  2  7.

  22. Rally Coach! TB pg 130 B’s complete: #22 #30 #42 A’s complete: #21 #29 #41

  23. Left side time! What I learned: write 1-2 sentences about what you learned. Proof:Write about it. Describe how to use factor trees to find the prime factorization of a number. Reflection:Create. Invent a machine that could do prime factorization. Draw it and explain how it would work.

  24. Homework • pg 130 #27-36

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