FRACTIONS 20120716 www.njctl.org 1 Fractions Unit Topics Click - PDF document

6th Math Unit 3 ­ FRACTIONS Name: _____________________ 6th Grade Unit 3 FRACTIONS 2012­07­16 www.njctl.org 1 Fractions Unit Topics Click on the topic to go to that section • Greatest Common Factor • Least Common Multiple • GCF and LCM Word Problems • Distribution • Fraction Operations Review (+ ­ x) • Fraction Division • Fraction Operations Mixed Application Common Core Standards: 6.NS.1, 6.NS.4 2 Greatest Common Factor Return to Table of Contents 3 1

6th Math Unit 3 ­ FRACTIONS Interactive Website Review of factors, prime and composite numbers Play the Factor Game a few times with a partner. Be sure to take turns going first. Find moves that will help you score more points than your partner. Be sure to write down strategies or patterns you use or find. Answer the Discussion Questions . 4 Player 1 chose 24 to earn 24 points. Player 2 finds 1, 2, 3, ,4, 6, 8, 12 and earns 36 points. Player 2 chose 28 to earn 28 points. Player 1 finds 7 and 14 are the only available factors and earns 21 points. 5 Discussion Questions 1. Make a table listing all the possible first moves, proper factors, your score and your partner's score. Here's an example: First Move Proper Factors My Score Partner's Score 1 None Lose a Turn 0 2 1 2 1 3 1 3 1 4 1, 2 4 3 2. What number is the best first move? Why? 3. Choosing what number as your first move would make you lose your next turn? Why? 4. What is the worst first move other than the number you chose in Question 3? more questions 6 2

6th Math Unit 3 ­ FRACTIONS 5. On your table, circle all the first moves that only allow your partner to score one point. These numbers have a special name. What are these numbers called? Are all these numbers good first moves? Explain. 6. On your table, draw a triangle around all the first moves that allow your partner to score more than one point. These numbers also have a special name. What are these numbers called? Are these numbers good first moves? Explain. 7 Activity Party Favors! You are planning a party and want to give your guests party favors. You have 24 chocolate bars and 36 lollipops. Discussion Questions What is the greatest number of party favors you can make if each bag must have exactly the same number of chocolate bars and exactly the same number of lollipops? You do not want any candy left over. Explain. Could you make a different number of party favors so that the candy is shared equally? If so, describe each possibility. Which possibility allows you to invite the greatest number of Give each student (or group) a bag filled with items guests? Why? to be separated into party favors for their guests. Uh­oh! Your little brother ate 6 of your lollipops. Now what is the Each bag should contain 24 "chocolate bars" and 36 greatest number of party favors you can make so that the candy "lollipops". (Use counters or tiles. Numbers may be is shared equally? Note to Teacher changed.) 8 Greatest Common Factor We can use prime factorization to find the greatest common factor (GCF). 1. Factor the given numbers into primes. 2. Circle the factors that are common. 3. Multiply the common factors together to find the greatest common factor. 9 3

6th Math Unit 3 ­ FRACTIONS Use prime factorization to find the greatest common factor of 12 and 16. 1. Factor the given number into primes. 1216 2. Circle factors that are common. for steps 3. Multiply the common factors Pull Pull 3 4 4 4 together to find the greatest common factor. 3 2 2 2 2 2 2 12 = 2 x 2 x 3 16 = 2 x 2 x 2 x 2 The Greatest Common Factor is 2 x 2 = 4 10 Another way to find Prime Factorization... Use prime factorization to find the greatest common factor of 12 and 16. 1 . F a c t o r t h e g i v e n n u m b e r i n t o p r i m e s . 2 16 2 . C i r c l e f a c t o r s t h a t a r e c o m m o n . 2 12 3 . M u l t i p l y t h e c o m m o n f a c t o r s P P 8 u 2 u t o g e t h e r t o f i n d t h e g r e a t e s t c o m m o n l l l l f a c t o r . 6 2 2 4 3 3 2 2 1 1 12 = 2 x 2 x 3 16 = 2 x 2 x 2 x 2 The Greatest Common Factor is 2 x 2 = 4 11 Use prime factorization to find the greatest common factor of 36 and 90. 3690 1. Factor the given number into primes. 2. Circle factors that are common. 6 6 9 10 3. Multiply the common factors Pull Pull together to find the greatest common 2 3 2 3 3 3 2 5 factor. 36 = 2 x 2 x 3 x 390 = 2 x 3 x 3 x 5 GCF is 2 x 3 x 3 = 18 12 4

6th Math Unit 3 ­ FRACTIONS Use prime factorization to find the greatest common factor of 36 and 90. 2 2 9 0 3 6 1. Factor the given number into primes. 2. Circle factors that are common. 5 1 8 3 4 3. Multiply the common factors 2 Pull Pull together to find the greatest common 9 1 5 factor. 3 3 3 3 5 5 1 1 36 = 2 x 2 x 3 x 3 90 = 2 x 3 x 3 x 5 GCF is 2 x 3 x 3 = 18 13 Use prime factorization to find the greatest common factor of 60 and 72. 6072 1. Factor the given number into primes. 2. Circle factors that are common. 6 10 6 12 3. Multiply the common factors Pull Pull together to find the greatest common factor. 2 3 2 5 2 3 3 4 2 3 2 5 2 3 3 2 2 60 = 2 x 2 x 3 x 5 72 = 2 x 2 x 2 x 3 x 3 GCF is 2 x 2 x 3 = 12 14 Use prime factorization to find the greatest common factor of 60 and 72. 2 7 2 2 6 0 1 . F a c t o r t h e g i v e n n u m b e r i n t o p r i m e s . 3 6 2 . C i r c l e f a c t o r s t h a t a r e c o m m o n . 2 3 0 2 3 . M u l t i p l y t h e c o m m o n f a c t o r s Pull Pull t o g e t h e r t o f i n d t h e g r e a t e s t c o m m o n 5 1 8 3 1 2 f a c t o r . 5 5 9 3 1 3 3 1 60 = 2 x 2 x 3 x 5 72 = 2 x 2 x 2 x 3 x 3 GCF is 2 x 2 x 3 = 12 15 5

6th Math Unit 3 ­ FRACTIONS 1 Find the GCF of 18 and 44. Pull Pull 2 16 2 Find the GCF of 28 and 70. Pull Pull 14 17 3 Find the GCF of 55 and 110. Pull Pull 55 18 6

6th Math Unit 3 ­ FRACTIONS 4 Find the GCF of 52 and 78. Pull Pull 26 19 5 Find the GCF of 72 and 75. Pull Pull 3 20 Relatively Prime: Two or more numbers are relatively prime if their greatest common factor is 1. Example: 15 and 32 are relatively prime because their GCF is 1. Name two numbers that are relatively prime. 21 7

6th Math Unit 3 ­ FRACTIONS 6 7 and 35 are not relatively prime. Pull Pull True True False 22 7 Identify at least two numbers that are relatively prime to 9. Pull Pull A 16 B 15 A and C C 28 D 36 23 8 Name a number that is relatively prime to 20. Pull Pull Answers will vary. 24 8

6th Math Unit 3 ­ FRACTIONS 9 Name a number that is relatively prime to 5 and 18. Pull Pull 25 10 Find two numbers that are relatively prime. Pull Pull A and C B and C A 7 C and D B 14 15 C D 49 26 Least Common Multiple Return to Table of Contents 27 9

6th Math Unit 3 ­ FRACTIONS Text­to­World Connection 1. Use what you know about factor pairs to evaluate George Banks' mathematical thinking? Is his thinking accurate? What mathematical relationship is he missing? Show students a real­life scenario Note to Teacher involving least common multiples. 2. How many hot dogs came in a pack? Buns? Search for the movie clip from "Father of the Bride" where George Banks is 3. How many "superfluous" buns did George Banks remove from shopping for hot dogs and buns. each package? How many packages did he do this to? George Banks identified 8 & 3 as a 4. How many buns did he want to buy? Was his thinking correct? factor pair of 24, but overlooked the Did he end up with 24 hot dog buns? factor pair 12 & 2. 5. Was there a more logical way for him to do this? What was he missing? 6. What is the significance of the number 24? 28 A multiple of a whole number is the product of the number and any nonzero whole number. A multiple that is shared by two or more numbers is a common multiple . Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ... Multiples of 14: 14, 28, 42, 56, 70, 84,... The least of the common multiples of two or more numbers is the least common multiple (LCM) . The LCM of 6 and 14 is 42. 29 There are 2 ways to find the LCM: 1. List the multiples of each number until you find the first one they have in common. 2. Write the prime factorization of each number. Multiply all factors together. Use common factors only once (in other words, use the highest exponent for a repeated factor). 30 10

6th Math Unit 3 ­ FRACTIONS EXAMPLE: 6 and 8 Multiples of 6: 6, 12, 18, 24, 30 Multiples of 8: 8, 16, 24 LCM = 24 Prime Factorization: 6 8 2 3 2 4 2 2 2 2 3 2 3 LCM: 2 3 3 = 8 3 = 24 31 Find the least common multiple of 18 and 24. Multiples of 18: 18, 36, 54, 72, ... Multiples of 24: 24, 48, 72, ... LCM: 72 Prime Factorization: 18 24 2 9 6 4 2 3 3 3 2 2 2 2 3 2 2 3 3 LCM: 2 3 3 2 = 8 9 = 72 32 11 Find the least common multiple of 10 and 14. Pull Pull C A 2 B 20 C 70 140 D 33 11

6th Math Unit 3 ­ FRACTIONS 12 Find the least common multiple Pull Pull of 6 and 14. C A 10 B 30 C 42 D 150 34 13 Find the least common multiple of 9 and 15. Pull Pull C A 3 B 30 C 45 D 135 35 14 Find the least common multiple of 6 and 9. Pull Pull A 3 C B 12 18 C D 36 36 12