Growing Prime Factorization Trees Mrs. Shaw 6th Grade Math

Warm Up Practice your multiplication Math facts up to 12 x 12 in one of the following ways: By yourself using the My Math App on the iPad or on your iPhone By yourself using an Internet browser and going to http://www.ixl.com/math/grade- 3/multiplication-facts-to-12 QUIETLY with a partner using flashcards.

Research Prime and Composite Numbers Using a textbook or the Internet, answer the following questions in your Math journal. What is a prime number? What is a composite number?

What is a Prime Number? A whole number greater than 1 that can only be divided evenly by 1 and itself. A whole number greater than 1 that only has two whole number factors, 1 and itself.

Prime Numbers 0 1 2 3 5 7 Is 0 or 1 a prime number? NO! Prime numbers must be GREATER than 1. 0 1 How about 1.4, 2.5, or 3/2? NO! Prime numbers must be WHOLE numbers. No decimals or fractions! Examples 2 3 5 7

What is a Composite Number? A whole number greater than 1 that can be evenly divided by at least one whole number that is not 1 or itself. A whole number greater than 1 that has at least three whole number factors including 1 and itself. Composite numbers are the whole numbers greater than 1 that are not prime numbers.

Composite Numbers 0 1 Is 0 or 1 a composite number? NO! Composite numbers must be GREATER than 1. 0 1 How about 1.4, 2.5, or 3/2? NO! Composite numbers must be WHOLE numbers, too. No decimals or fractions! Examples 4 has three factors: 1, 2 and 4 6 has four factors: 1, 2, 3, and 6

Identify the Prime Numbers less than 100 On your worksheet, mark out all the numbers that are not prime numbers. Mark out 0 and 1 because 0 and 1 are not prime numbers. Remember!!! 0 and 1 are not composite either! Handout the Prime Numbers Under 100 worksheets to the students. Complete the

First, Mark Out 0 and 1 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 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

Identify the Prime Numbers less than 100 Notice that 2 is a prime number because it only has two factors: 1 and itself, 2. All even numbers greater than 2 are not prime because they have at least three factors, 1, itself, AND 2. Mark out all the even numbers greater than 2. Handout the Prime Numbers Under 100 worksheets to the students. Complete the

Next, Mark Out the Even Numbers Greater Than 2 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 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

Identify the Prime Numbers less than 100 Like 2, 3 is a prime number because it only has two factors: 1 and itself, 3. All the other multiples of 3 have at least three factors: 1, itself, AND 3. So, all other multiples of 3 are not prime. Mark out all the other multiples of 3. Handout the Prime Numbers Under 100 worksheets to the students. Complete the

Next, Mark Out the Multiples of 3 Greater Than 3 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 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

Identify the Prime Numbers less than 100 5 and 7 are prime numbers, right? Why? Because they each only have two factors: 1 and itself. Like you did for multiples of 2 and 3, mark out the other multiples of 5 and 7. Handout the Prime Numbers Under 100 worksheets to the students. Complete the

Next, Mark Out the Multiples of 5 Greater Than 5 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 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

Next, Mark Out the Multiples of 7 Greater Than 7 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 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

Because all the multiples of of the other prime numbers, 11, 13, 17, Because all the multiples of of the other prime numbers, 11, 13, 17, ... are already marked out, WE’RE DONE! 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 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

This is called PRIME FACTORIZATION. Did you notice that all Composite Numbers are multiples of Prime Numbers? You can write any composite number as the product of prime numbers by factoring and factoring, again and again, until you can factor no more. Let’s look at an example: 36 36 = 2 X 18 36 = 2 X 2 X 9 36 = 2 X 2 X 3 X 3 This is called PRIME FACTORIZATION.

Notice What It Looks Like If I Write It This Way 36 2 X 18 2 X 2 X 9 2 X 2 X 3 X 3 Writing it like this makes it look like a tree! So we call these PRIME FACTORIZATION TREES!

When I Say “Prime Factorization” You Say “Tree” Prime Factorization TREE Whenever you are asked to find the prime factors of a number, just remember you need to “grow a factor tree”.

Growing Healthy Looking Trees When factoring a composite number, always start with the lowest prime number factor so that your trees grow neatly down and towards the right, with the like factors in a neat diagonal line. 24 24 /\ /\ 2 12 2 12 2 6 6 2 /\ /\ 2 3 3 2 Using the drawing tool in Slideshow, draw a oval shape around the orange two.

Let’s Try Some Together 35 /\ 5 7 What is the lowest prime number that evenly divides into 35? Does 2? No, 35 is not an even number. Does 3? No, 35 is not evenly divisible by 3. Does 5? Yes, 5 times 7 is 35. And 7 is prime so we are done!

Let’s Try Another Together What is the lowest prime number that evenly divides into 42? Does 2? Yes, 42 is an even number. What is the lowest prime number that evenly divides into 21? Not 2, does 3? Yes, 3 times 7 is 21. And 7 is prime so we are done! 42 /\ 2 21 3 7

It’s Your Turn To Guide Me 72 /\ 2 36 2 18 2 9 3 3 56 /\ 2 28 2 14 2 7

Try some on your own 64 /\ 2 32 2 16 2 8 2 4 2 2 99 /\ 3 33 3 11

Homework You can use your calculator to help you identify the prime factors, but be sure to write down all the branches of the trees. Homework will be graded tomorrow after Warm Up. Website to explore prime numbers (Go ahead, try it!): http://www.math.com/students/calculators/source/prime-number.htm KhanAademy Websites to help you review: http://www.khanacademy.org/math/arithmetic/factors-multiples/prime_numbers/v/prime-numbers http://www.khanacademy.org/math/arithmetic/factors-multiples/prime_factorization/v/prime-factorization