Factors and Multiples of 12. List five multiples of 12: Decompose 12 into its factor pairs. 12: 12, 24, 36, 48, 60

Transcription

1 1 Factors and Multiples of 12 Decompose 12 into its factor pairs. List five multiples of 12: : 12, 24, 6, 48, 60 Write statements about 12 and its factors. The factors of 12 are 1, 2,, 4, 6, and 12. The factors of 12 are less than 12, except for 12 itself. The factors of 12 are mostly even, but two of them are odd. There are 6 factors of 12. Write statements about 12 and its multiples. Some multiples of 12 are 12, 24, 6, 48, and 60. The multiples of 12 are greater than 12, except for 12 itself. All the multiples of 12 are even. The multiples of 12 go on forever because you can always keep adding You Try: Factors and Multiples of 20 Decompose 20 into its factor pairs. (Arrays can be drawn on the back.) List five multiples of 20. Write at least 2 statements about 20 and its factors. Write at least 2 statements about 20 and its multiples. Page 1 of 11 MCC@WCCUSD (AUSD) 12/11/14

2 2 You can use basic facts to determine factors and multiples. We multiply factors to get a product. factor factor = product 2 6 = 12 A multiple is the product of a whole number by any other whole number. (multiple) factor factor = product 2 6 = is the product of 2 and 6, so 2 is a factor of is a factor of is a multiple of 2, and 12 is a multiple of 6. 2 You Try (a) Complete each statement using the words, factor or multiple. You can use the multiplication fact 7 = 21 to help you. 7 = 21 is a of is a of. 7 is a of is a of 7. You Try (b) Complete each statement using the words, factor or multiple. Write the multiplication fact that supports your answer. 18 is a of 9. Multiplication Fact: 6 is a of 48. Multiplication Fact: 2 is a of 16. Multiplication Fact: 40 is a of. Multiplication Fact: Page 2 of 11 MCC@WCCUSD (AUSD) 12/11/14

3 Justify whether each statement is true or false. 9 is a multiple of and a factor of 18. Is 9 a multiple of?, 6, 9, 12, 1,... and = 9 Yes! Is 9 a factor of 18? 9 2 = 18 Yes! True. 8 is a multiple of 16 and a factor of 2. Is 8 a multiple of 16? 8 2 = 16, so 8 is a factor of is not a multiple of 16. Is 8 a factor of 2? 2 4 = 8, so 8 is multiple of 2. 8 is not a factor of 2. False. You try: Justify whether each statement is true or false. 4 is a multiple of 2 and a factor of 0. 6 is a multiple of 2 and a factor of 24. Page of 11 MCC@WCCUSD (AUSD) 12/11/14

4 4 List all the factors for each number. Determine if each number is prime or composite. 17, 24, The factors are now repeating, so we don t need to go further The factors are now repeating, so we don t need to go further. 17: 1, 17 Prime 24: 1, 2,, 4, 6, 8, 12, 24 Composite 6: 1, 2, 4, 7, 8, 14, 28, 6 Composite 4 You Try: List all the factors for each number. Determine if each number is prime or composite. 27, 41, 64 Page 4 of 11 MCC@WCCUSD (AUSD) 12/11/14

5 Prime factor 12 two ways. One Way: Another Way: 12 4 Decompose 12 into 4. is prime. 4 is composite Decompose 12 into is composite. 2 is prime. 2 2 Decompose 4 into is prime. 2 Decompose 6 into 2. 2 and are prime. 12 = = 2 2 What is the same about the factor trees? They both start with 12 and end with 2 2. What is different about the factor trees? One starts with 4. One starts with 2 6. Prime factor 24 two ways. One Way: Another Way: Does it matter which basic fact you start with? Explain. Page of 11 MCC@WCCUSD (AUSD) 12/11/14

6 6 Mark has a 6 inch piece of string. He needs to cut it into equal pieces. Each piece is longer than 2 inches, but shorter than 9 inches. Describe two ways he could cut the string into equal pieces. Set Up What do we need to find out? *two ways to cut the string What do we know? *6 inches total *equal size pieces *greater than 2 in. and less than 9 in. Model:? Solve: Check: = = 6 inch pieces? 6 inches? 4 inches? 7 inches? inches? 8 inches? Decide: Find at least 2 factor pairs for 6. Conclude: He could cut the string into 21 pieces that are inches each or 9 pieces that are 7 inches each. 6 Stacy made 48 cookies for a bake sale. She wants to put an equal number of cookies in each bag. There needs to be more than 1 cookie and fewer than 7 cookies in each bag. Describe at least two ways she could put an equal number of cookies in the bags. Remember to: Set Up, Solve, Check, and Conclude. *This item is a modified version of an item from SBAC Practice Test 201 pages and 4. Page 6 of 11 MCC@WCCUSD (AUSD) 12/11/14

7 7 Trevor read books in the fall. He created the picture graph shown. Month Sept. Oct. Nov. Books Create another picture graph using a different key. Only use whole books in your picture graph. Select the key you will use. = books = 4 books = books = 6 books = 2 books How do we determine the key? How many books in Sept? 12 books How many books in Oct.? 4 books How many books in Nov.? 8 books = 2 books is a good key because 2 is a factor of 12, 4, and 8. What number besides 2 is a factor of 12, 4, and 8? Try : is a factor of 12. is not a factor of 4 or 8. No. Try 4: 4 is a factor of 12, 4, and 8. Yes! Try : is not a factor of 12, 4, or 8. No. Try 6: 6 is a factor of is not a factor of 4 or 8. No. New Picture Graph Month Books Sept. Oct. Nov. = 4 books This question is a modified version of SBAC Practice Test 2014 Item. You try is on the next page. Page 7 of 11 MCC@WCCUSD (AUSD) 12/11/14

8 7 You Try: Sam and his friends picked apples at his uncle s apple farm. He created the picture graph shown below. Create two other picture graphs with different keys. Only use whole apples in your picture graphs. Name Sam Adriana Juan Apples Select the key you will use. = 2 apples = 4 apples = 6 apples = 9 apples = apples Use the space to determine the new keys. New Picture Graphs Page 8 of 11 MCC@WCCUSD (AUSD) 12/11/14

9 You Try Solutions 1 You Try: Factors and Multiples of 20 Decompose 20 into its factor pairs. (1 20), (2 10), and (4 ) List five multiples of : 20, 40, 60, 80, 100 Write statements about 20 and its factors. Examples: There are 6 factors: 1, 2, 4,, 10, and 20. Most of the factors are even. Two factors are odd: 1 and. The factors are less than 20, except 20. Write statements about 20 and its multiples. Examples: The multiples of 20 go on forever because you can just keep adding 20. All the multiples have a 0 in the ones place and an even number in the tens place. Finding multiples of 20 is like counting by 2s except you are counting by 2 tens. 2 You Try (a) is a factor of is a multiple of. 7 is a factor of is a multiple of 7. You Try (b) 18 is a multiple of 9 Multiplication Fact: 9 2 = 18 6 is a factor of 48. Multiplication Fact: 6 8 = 48 2 is a factor of 16. Multiplication Fact: 2 8 = is a multiple of. Multiplication Fact: 8 = 40 You try: Justify whether each statement is true or false. 4 is a multiple of 2 and a factor of 0. 6 is a multiple of 2 and a factor of 24. Is 4 a multiple of 2? 2 2 = 4, so 4 is a multiple of 2. Yes! Is 4 a factor of 0? The factor pairs of 0 are: (1 0), (2 1), ( 10), and ( 6) No, 4 is not a factor of 0 Another Way: 4: 4, 8, 12, 16, 20, 24, 28, 2 0 is not a multiple of 4, so 4 is not a factor of 0. False Is 6 a multiple of 2? 2: 2, 4, 6 Also, 2 x = 6 Yes! Is 6 a factor of 24? 6 4 = 24 Yes! Another Way: 6: 6, 12, 18, is a multiple of 6, so 6 is a factor of 24. True. Page 9 of 11 MCC@WCCUSD (AUSD) 12/11/14

10 4 You Try: List all the factors for each number. Determine if each number is prime or composite. 27, 41, 64 27: 1,, 9, 27 Composite 41: 1, 41 Prime 64: 1, 2, 4, 8, 16, 2, 64 Composite You Try: Prime factor 24. Students show any two ways = = = Does it matter which basic fact you start with? No, it doesn t matter because you always end up with the same prime factors no matter where you start. Page 10 of 11 MCC@WCCUSD (AUSD) 12/11/14

11 6 Stacy made 48 cookies for a bake sale. She wants to put an equal number of cookies in each bag. There needs to be more than 1 cookie and fewer than 7 cookies in each bag. Describe at least two ways she could put an equal number of cookies in the bags. Ways to Set Up Solve: Check: What do we need to find out? *two ways to divide the cookies = = 48 What do we know? *48 cookies total *equal number of cookies in each bag *more than 1 cookie and fewer than 7 in each bag. Model: = = = 48? = =48 2 cookies??? 6? 4? Decide: Find at least 2 factor pairs for 48. Conclude: (Students write at least 2 possibilities.) She could put 2 cookies in 24 bags. She could put cookies in 16 bags. She could put 4 cookies in 12 bags. She could put 6 cookies in 8 bags. 7 You Try: Create two other picture graphs with different keys. Determine the New Keys Sam picked 12 apples. 4 does not work because 4 is not a factor of 18 or 6. Adriana picked 18 apples. 9 does not work because 9 is not a factor of 12, 18, or 6. Juan picked 6 apples. 2 and 6 can be used as keys. New Picture Graphs: Name Apples Name Apples Sam Sam Adriana Adriana Juan Juan = 2 apples = 6 apples Page 11 of 11 MCC@WCCUSD (AUSD) 12/11/14