Name _____ Lesson #3 - Exploring Multiples 6__ Objective: to identify multiples and common multiples and then solve problems.

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: On Thursday morning, the local radio station held a call-in contest. • Every third caller won a T-shirt. • Every seventh caller won a baseball cap. In 50 calls, which callers won a T-shirt? A baseball cap? Both prizes? Use any materials you like to solve this problem. Show how you used materials to solve this problem. Show and Share: Share your answers with another group of students. What strategies did you use to solve the problem? Discuss how using materials helped. Describe any patterns you noticed.

Name _____ Lesson #3 - Exploring Multiples 6__ BEFORE: Suppose you were the 6th caller, would you win a prize? How do you know?

Name _____ Lesson #3 - Exploring Multiples 6__ BEFORE: Suppose you were the 6th caller, would you win a prize? How do you know? Yes, I would win a t-shirt. I counted by 3’s.

Name _____ Lesson #3 - Exploring Multiples 6__ BEFORE: Suppose you were the 6th caller, would you win a prize? How do you know? Yes, I would win a t-shirt. I counted by 3’s. Would you win a prize if you were the 14th caller?

Name _____ Lesson #3 - Exploring Multiples 6__ BEFORE: Suppose you were the 6th caller, would you win a prize? How do you know? Yes, I would win a t-shirt. I counted by 3’s. Would you win a prize if you were the 14th caller? Yes, I would win a baseball cap. When I count by 7’s, the second number is 14.

Name _____ Lesson #3 - Exploring Multiples 6__ BEFORE: Suppose you were the 6th caller, would you win a prize? How do you know? Yes, I would win a t-shirt. I counted by 3’s. Would you win a prize if you were the 14th caller? Yes, I would win a baseball cap. When I count by 7’s, the second number is 14. Is it possible to win both a t-shirt AND a baseball cap? Explain.

Name _____ Lesson #3 - Exploring Multiples 6__ BEFORE: Suppose you were the 6th caller, would you win a prize? How do you know? Yes, I would win a t-shirt. I counted by 3’s. Would you win a prize if you were the 14th caller? Yes, I would win a baseball cap. When I count by 7’s, the second number is 14. Is it possible to win both a t-shirt AND a baseball cap? Explain. Yes, you could win both prizes if you are a caller whose call is both the 3rd and 7th call.

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: What strategy are you using to solve the problem?

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: What strategy are you using to solve the problem? I am writing down the “counting by 3’s” numbers and the “counting by 7’s” numbers that are less than 50.

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: What strategy are you using to solve the problem? I am writing down the “counting by 3’s” numbers and the “counting by 7’s” numbers that are less than 50. The multiples of 3 (the numbers I say when I count by 3’s) are the callers who win a t-shirt AND

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: What strategy are you using to solve the problem? I am writing down the “counting by 3’s” numbers and the “counting by 7’s” numbers that are less than 50. The multiples of 3 (the numbers I say when I count by 3’s) are the callers who win a t-shirt AND The multiples of 7 (the numbers I say when I count by 7’s) are the callers who win a baseball cap.

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: What strategy are you using to solve the problem? I am writing down the “counting by 3’s” numbers and the “counting by 7’s” numbers that are less than 50. The multiples of 3 (the numbers I say when I count by 3’s) are the callers who win a t-shirt AND The multiples of 7 (the numbers I say when I count by 7’s) are the callers who win a baseball cap. The numbers that I say in both counts are the callers who win both prizes.

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: How can you use the hundreds chart and counters to help solve the problem? 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

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: How can you use the hundreds chart and counters to help solve the problem? I can use red counters to mark the “counting by 3’s” numbers (t-shirt) AND I can use blue counter to mark the “counting by 7’s” numbers (baseball cap). The numbers that have both counters, with both prizes. That number is a “COMMON MULTIPLE” of 3 and 7.

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: How can you use the hundreds chart and counters to help solve the problem? 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

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: How can you use the hundreds chart and counters to help solve the problem? 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

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: How can you use the hundreds chart and counters to help solve the problem? 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

Name _____ Lesson #3 - Exploring Multiples 6__ EXPLORE: What is the first number you come across that is both a multiple of 3 and 7? (common multiple) 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

Name _____ Lesson #3 - Exploring Multiples 6__ What is the first number you come across that is both a multiple of 3 and 7? (common multiple) 21 and 42  They are both in the 3X tables AND 7X tables. 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

Name _____ Lesson #3 - Exploring Multiples 6__ CONNECT: To find the multiples of a number, start at that number and count on by the number. You can use a hundred chart to find the multiples of a number. 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

Name _____ Lesson #3 - Exploring Multiples 6__ CONNECT: The multiples of 4 are: 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

Name _____ Lesson #3 - Exploring Multiples 6__ CONNECT: The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 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

Name _____ Lesson #3 - Exploring Multiples 6__ CONNECT: The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, The multiples of 6 are: 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

Name _____ Lesson #3 - Exploring Multiples 6__ CONNECT: The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, The multiples of 6 are: 6, 12, 18, 24, 30, 36, … 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

Name _____ Lesson #3 - Exploring Multiples 6__ CONNECT: 12, 24, and 36 appear in both lists. They are multiples of 4 and of 6. They are common multiples of 4 and 6. 12 is the least common multiple of 4 and 6. 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

Wieners are sold in packages of 12 Wieners are sold in packages of 12. Hot dog buns are sold in packages of 8. Suppose you plan to sell about 75 hot dogs to raise money for charity. You do not want any wieners or buns left over How many packages of each should you buy?

Wieners are sold in packages of 12 Wieners are sold in packages of 12. Hot dog buns are sold in packages of 8. Suppose you plan to sell about 75 hot dogs to raise money for charity. You do not want any wieners or buns left over How many packages of each should you buy? Draw two number lines (showing multiples) of 12 and 8, and find a common multiple close to 75!

Wieners are sold in packages of 12 Wieners are sold in packages of 12. Hot dog buns are sold in packages of 8. Suppose you plan to sell about 75 hot dogs to raise money for charity. You do not want any wieners or buns left over How many packages of each should you buy? Draw two number lines (showing multiples) of 12 and 8, and find a common multiple close to 75! 0 12 24 36 48 60 72 84

Wieners are sold in packages of 12 Wieners are sold in packages of 12. Hot dog buns are sold in packages of 8. Suppose you plan to sell about 75 hot dogs to raise money for charity. You do not want any wieners or buns left over How many packages of each should you buy? Draw two number lines (showing multiples) of 12 and 8, and find a common multiple close to 75! 0 12 24 36 48 60 72 84 0 8 16 24 32 40 48 56 64 72 80

Wieners are sold in packages of 12 Wieners are sold in packages of 12. Hot dog buns are sold in packages of 8. Suppose you plan to sell about 75 hot dogs to raise money for charity. You do not want any wieners or buns left over How many packages of each should you buy? Draw two number lines (showing multiples) of 12 and 8, and find a common multiple close to 75! 0 12 24 36 48 60 72 84 0 8 16 24 32 40 48 56 64 72 80 Circle the common multiples: 24, 48, 72. Since 72 is close to 75, you should buy 72 wieners and 72 buns. You skip counted by eight 9 times to reach 72, so buy 9 packages of buns. You skip counted by twelve 6 times to reach 72, so buy 6 packages of wieners.

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #1, #3, and Page 57 #5, #7, and #9

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #1) List the first 10 multiples of each number. a) 2 b) 5 c) 8 d) 7

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #1) List the first 10 multiples of each number. a) 2 - 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 b) 5 c) 8 d) 7

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #1) List the first 10 multiples of each number. a) 2 - 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 b) 5 - 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 c) 8 d) 7

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #1) List the first 10 multiples of each number. a) 2 - 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 b) 5 - 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 c) 8 - 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 d) 7

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #1) List the first 10 multiples of each number. a) 2 - 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 b) 5 - 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 c) 8 - 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 d) 7 - 7, 14, 21, 28, 35, 42, 49, 56, 63, 70

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #3) Which numbers below are multiples of 6? What strategy did you use to find out? 36 70 66 42 54 27 120 81

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #3) Which numbers below are multiples of 6? What strategy did you use to find out? 36 - Yes, because 6 X 6 = 36 70 66 42 54 27 120 81

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #3) Which numbers below are multiples of 6? What strategy did you use to find out? 36 - Yes, because 6 X 6 = 36 70 - No, because it is not in the 6X tables. 66 42 54 27 120 81

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #3) Which numbers below are multiples of 6? What strategy did you use to find out? 36 - Yes, because 6 X 6 = 36 70 - No, because it is not in the 6X tables. 66 - Yes, because, 6 X 11 = 66 42 54 27 120 81

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #3) Which numbers below are multiples of 6? What strategy did you use to find out? 36 - Yes, because 6 X 6 = 36 70 - No, because it is not in the 6X tables. 66 - Yes, because, 6 X 11 = 66 42 - Yes, because 6 X 7 = 42 54 27 120 81

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #3) Which numbers below are multiples of 6? What strategy did you use to find out? 36 - Yes, because 6 X 6 = 36 70 - No, because it is not in the 6X tables. 66 - Yes, because, 6 X 11 = 66 42 - Yes, because 6 X 7 = 42 54 - Yes, because 6 X 9 = 54 27 120 81

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #3) Which numbers below are multiples of 6? What strategy did you use to find out? 36 - Yes, because 6 X 6 = 36 70 - No, because it is not in the 6X tables. 66 - Yes, because, 6 X 11 = 66 42 - Yes, because 6 X 7 = 42 54 - Yes, because 6 X 9 = 54 27 - No, because 27 is not in the 6X tables. 120 81

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #3) Which numbers below are multiples of 6? What strategy did you use to find out? 36 - Yes, because 6 X 6 = 36 70 - No, because it is not in the 6X tables. 66 - Yes, because, 6 X 11 = 66 42 - Yes, because 6 X 7 = 42 54 - Yes, because 6 X 9 = 54 27 - No, because 27 is not in the 6X tables. 120 - Yes, because 20 X 6 = 120 81

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 56 #3) Which numbers below are multiples of 6? What strategy did you use to find out? 36 - Yes, because 6 X 6 = 36 70 - No, because it is not in the 6X tables. 66 - Yes, because, 6 X 11 = 66 42 - Yes, because 6 X 7 = 42 54 - Yes, because 6 X 9 = 54 27 - No, because 27 is not in the 6X tables. 120 - Yes, because 20 X 6 = 120 81 - No, because 81 is not in the 6X tables.

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #5) Find the first 3 common multiples of each pair of numbers. a) 4 and 5 b) 7 and 4 c) 3 and 9 d) 10 and 15

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #5) Find the first 3 common multiples of each pair of numbers. a) 4 and 5 - 4, 8, 12, 16, 20 and 5, 10, 15, 20 b) 7 and 4 c) 3 and 9 d) 10 and 15

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #5) Find the first 3 common multiples of each pair of numbers. a) 4 and 5 - 4, 8, 12, 16, 20 and 5, 10, 15, 20 So, 20, 40, and 60 are the first 3 common multiples. b) 7 and 4 c) 3 and 9 d) 10 and 15

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #5) Find the first 3 common multiples of each pair of numbers. a) 4 and 5 - 4, 8, 12, 16, 20 and 5, 10, 15, 20 So, 20, 40, and 60 are the first 3 common multiples. b) 7 and 4 - 7, 14, 21, 28 and 4, 8, 12, 16, 20, 24, 28 c) 3 and 9 d) 10 and 15

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #5) Find the first 3 common multiples of each pair of numbers. a) 4 and 5 - 4, 8, 12, 16, 20 and 5, 10, 15, 20 So, 20, 40, and 60 are the first 3 common multiples. b) 7 and 4 - 7, 14, 21, 28 and 4, 8, 12, 16, 20, 24, 28 So, 28, 56, and 84 are the first 3 common multiples. c) 3 and 9 d) 10 and 15

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #5) Find the first 3 common multiples of each pair of numbers. a) 4 and 5 - 4, 8, 12, 16, 20 and 5, 10, 15, 20 So, 20, 40, and 60 are the first 3 common multiples. b) 7 and 4 - 7, 14, 21, 28 and 4, 8, 12, 16, 20, 24, 28 So, 28, 56, and 84 are the first 3 common multiples. c) 3 and 9 - 3, 6, 9 and 9 d) 10 and 15

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #5) Find the first 3 common multiples of each pair of numbers. a) 4 and 5 - 4, 8, 12, 16, 20 and 5, 10, 15, 20 So, 20, 40, and 60 are the first 3 common multiples. b) 7 and 4 - 7, 14, 21, 28 and 4, 8, 12, 16, 20, 24, 28 So, 28, 56, and 84 are the first 3 common multiples. c) 3 and 9 - 3, 6, 9 and 9 So, 9, 18, and 27 are the first 3 common multiples. d) 10 and 15

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #5) Find the first 3 common multiples of each pair of numbers. a) 4 and 5 - 4, 8, 12, 16, 20 and 5, 10, 15, 20 So, 20, 40, and 60 are the first 3 common multiples. b) 7 and 4 - 7, 14, 21, 28 and 4, 8, 12, 16, 20, 24, 28 So, 28, 56, and 84 are the first 3 common multiples. c) 3 and 9 - 3, 6, 9 and 9 So, 9, 18, and 27 are the first 3 common multiples. d) 10 and 15 - 10, 20, 30 and 15, 30

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #5) Find the first 3 common multiples of each pair of numbers. a) 4 and 5 - 4, 8, 12, 16, 20 and 5, 10, 15, 20 So, 20, 40, and 60 are the first 3 common multiples. b) 7 and 4 - 7, 14, 21, 28 and 4, 8, 12, 16, 20, 24, 28 So, 28, 56, and 84 are the first 3 common multiples. c) 3 and 9 - 3, 6, 9 and 9 So, 9, 18, and 27 are the first 3 common multiples. d) 10 and 15 - 10, 20, 30 and 15, 30 So, 30, 60, and 90 are the first 3 common multiples.

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #7) Find all the common multiples of 8 and 9 that are less than 100.

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #7) Find all the common multiples of 8 and 9 that are less than 100. 8 - 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104 9 -

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #7) Find all the common multiples of 8 and 9 that are less than 100. 8 - 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104 9 - 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #7) Find all the common multiples of 8 and 9 that are less than 100. 8 - 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104 9 - 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108 The only common multiple less than 100 is 72. The next one will be 144.

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #9) A spider has 8 legs. An ant has 6 legs. There are a group of spiders and a group of ants. The groups have equal numbers of legs. What is the least number of spiders and ants in each group? Show your work.

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #9) A spider has 8 legs. An ant has 6 legs. There are a group of spiders and a group of ants. The groups have equal numbers of legs. What is the least number of spiders and ants in each group? Show your work. Spider legs - 8, 16, 24, 32, 40, 48

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #9) A spider has 8 legs. An ant has 6 legs. There are a group of spiders and a group of ants. The groups have equal numbers of legs. What is the least number of spiders and ants in each group? Show your work. Spider legs - 8, 16, 24, 32, 40, 48 Ant legs - 6, 12, 18, 24, 30, 36, 42, 48

Name _____ Lesson #3 - Exploring Multiples 6__ PRACTICE: Page 57 #9) A spider has 8 legs. An ant has 6 legs. There are a group of spiders and a group of ants. The groups have equal numbers of legs. What is the least number of spiders and ants in each group? Show your work. Spider legs - 8, 16, 24, 32, 40, 48 Ant legs - 6, 12, 18, 24, 30, 36, 42, 48 The least number of spiders is 6, because 6 X 8 = 48 legs. The least number of ants is 8, because 8 X 6 = 48 legs.