1. Copy Notes into your Composition notebook
Name
Teacher and Class Period
Title
Date
Anchor Chart
Copy Notes into your Composition notebook
This is the absolute last day for completing the quiz

2. Math Quiz and SLO Early Finishers: Login In using the following:
Click on the LOCK ICON for Mastery Connect
1st SLO –
2nd SLO –
3rd SLO –
4th SLO –
6th SLO
Login In using the following:
naumstudent
green5
Early Finishers:
Raise your hand to inform me…
Choose an early finisher activity
READ A BOOK, ABSOLUTELY NO TALKING

3. Greatest Common Factors

4. Greatest Common Factor Here We Come......
6.NS.4 -
Compute fluently with multi-digit numbers and find common factors and multiples

5. 6.NS.4 - What will I do?
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express as 4 (9 + 2).
Apply and extend previous understandings of numbers to the system of rational numbers.

6. Essential Question
How do you find and use the greatest common factor of two whole numbers?

7. I Can Statements...
I can determine if a number is prime or composite and explain why.
I can find the prime factorization of a composite number.
I can find all factors of any given number, less than or equal to 100.

8. I Can Statements...
I can find the greatest common factor of any two numbers, less than or equal to 100.
I can use the distributive property to rewrite a simple addition problem when the addends have a common factor.

9. First, I must know my divisibility rules. Do you?

10. Next, I must know the difference between prime and composite. Do you?

11. Think about it…
Student A says 51 is prime because it is odd. Student B says 51 is composite. Who do you agree with and Why?

12. A prime number is a number that can only be divided by only one and itself. A composite number is a number greater than one that is not prime. Prime or composite? prime composite

13. Prime or Composite? 89
Prime
Composite
Both
Neither

14. Factors are numbers that are multiplied
8 X 8 = 64

15. What does
“Find the factors”
mean?
…find all the numbers you can multiply together to get that number as the product.

16. Always write factors from least to greatest.
What are the factors of 27
Remember, you are being asked to find all the numbers that can be multiplied together to get the answer 27.
27: 1 X 27 3 X 9
1, 3, 9, 27
HINT:
Always write factors from least to greatest.

17. Practice Find the factors:
1. 18
1, 2, 3, 6, 9, 18
2. 24
1, 2, 3, 4, 6, 8, 12, 24
3. 21
1, 3, 7, 21
4. 52
1, 2, 26, 52

18. Do Now: [In Math Binder]
HAVE HOMEWORK ON DESK
Do Now: [In Math Binder]
Prime or Composite? Explain
Composite prime Composite Composite
Find the Factors
-1, 2, 4, 13 26, , 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

19. Check Your Homework
16- 1, 2, 4, 8, 16
24- 1, 2, 3, 4, 6, 8, 12, 24
30- 1, 2, 3, 5, 6, 10, 15, 30
25- 1, 5, 25
36- 1, 2, 3, 4, 6, 9, 12, 18, 36

20. Factors that two or more numbers have in common
Common Factors
What does COMMON mean?
What does FACTORS mean?
So…..
COMMON FACTORS are:
Factors that two or more numbers have in common

21. What are the common factors of 16 and 24?
24 1 X 24 2 X 12 3 X 8 4 X 6
16 1 X 16 2 X 8 4 X 4
Hint: Once you repeat a number you’re done!!
16: 1, 2, 4, 8, 16
24: 1, 2, 3, 4, 6, 8, 12, 24
Common Factors: 1, 2, 4, 8

22. Practice
What are the common factors of:
6 & 9
24 & 48
25 & 45

23. Greatest Common Factor
The greatest factor that both numbers have in common.
GCF = Greatest Common Factor

24. Strategies to find GCF Backwards Method Prime factorization (Tree),
T-chart, List or Rainbow
Backwards Method
Venn Diagram

25. Example of List Method GCF 60 and 96
60 -1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
96 – 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

26. Rainbow Method

27. T-Chart Method List Factors for both numbers Circle common factors
The highest number in common with be the
GCF

28. Double T-Chart Method

29. Finding the GCF
What is the GCF of 15 and 30? First: Find the factors of each whole number. 1 2 3 5 1 3 30 15 15 5 30 15 10 6

30. Finding the GCF
Second: Circle all of the factors they have in common. 1 2 3 5 1 3 30 15 15 5 30 15 10 6

31. Finding the GCF
Last: Determine the greatest number that both sets of factors have in common. 1 2 3 5 1 3 30 15 15 5 30 15 10 6
GCF is 15

32. Finding the GCF
What is the GCF of 18 and 24? 1 2 3 4 1 2 3 24 18 18 9 6 24 12 8 6

33. Finding the GCF
What is the GCF of 18 and 24? 1 2 3 4 1 2 3 24 18 18 9 6 24 12 8 6
GCF is 6

34. Prime factorization OR
Write down the number they have in common only once, then write down the leftover numbers. Multiply them all together. OR
Circle all the primes the 2 numbers have in common and multiply one set of them to get your GCF.

35. Prime Factorization Example

36. Step 3: Group the Greatest Factor
24 – 1,2,3,4,6,8,12,24
36 – 1,2,3,4,6,9,12,18,36
The GCF of 24 and 36 is… 12

37. Backwards Method

38. Think Backwards…
Find Factors
Circle Common Factors
Group Greatest Factor

39. Find the GCF of 12 and 24 Step 1: Find the factors 12 – 1,2,3,4,6,12
24 – 1,2,3,4,6,8,12,24

40. Find the GCF of 12 and 24 Step 2:Circle the common factors
12 – 1,2,3,4,6,12
24 – 1,2,3,4,6,8,12,24

41. Find the GCF of 12 and 24 Step 3: Group the greatest factor
12 – 1,2,3,4,6,12
24 – 1,2,3,4,6,8,12,24
The GCF of 12 and 24 is… 12

42. Your turn! Find the Greatest Common Factor of 16 and 20.
Remember…Find Factors, Circle Common, Group Greatest!

43. The Greatest Common Factor of 16 and 20 is…4

44. Venn Diagram Method

45. Find the GCF
12 1 x 12 2 x 6 3 x 4 12: 1,2,3,4,6,12
9 1 x 9 3 x 3 9 : 1,3,9

46. Ticket out the Door Find the GCF: 12 & 26 9 & 21 Have Name on Paper
Must include All factors listed
Common Factors Circled
GCF Written

47. Independent Practice List the factors: 36 18 27
List the common factors:
18, 22
52, 36
14, 9
List the factors: 36 18 27
List the GCF:
25, 40
30, 42

48. Copy Notes into your Composition notebook
Name
Teacher/Class Period
Title
Date
Anchor Chart
Copy Notes into your Composition notebook
Interim (Progress Report) goes home Tuesday! Must be Signed and Returned

49. Math Quiz and SLO Early Finishers: Login In using the following:
Click on the LOCK ICON for Mastery Connect
1st SLO –
2nd SLO –
3rd SLO –
4th SLO –
6th SLO
Login In using the following:
naumstudent
green5
Early Finishers:
Raise your hand to inform me…
Choose an early finisher activity
READ A BOOK, ABSOLUTELY NO TALKING

50. L e a s t C o m m o n M u l t I p l e

51. LCM Least Common Multiple 6.NS.4
Compute fluently with multi-digit numbers and find common factors and multiples

52. 6.NS What will I do?
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
For example, express as 4 (9 + 2). Apply and extend previous understandings of numbers to the system of rational numbers.

53. How do you find and justify the least common multiple of two numbers?
Essential Question
How do you find and justify the least common multiple of two numbers?

54. I Can Statements…
I can create a list of multiples for any number less than or equal to 12.
I can find and justify the least common multiple of any two numbers, less than or equal to 12.

55. Poor George??? Importance of LCM
How many packages of dogs and buns would George have to buy to have a bun for every dog?

56. The product you get when a number is multiplied by another number.
What is ?
Multiple
The product you get when a number is multiplied by another number.
Example:
Multiples of 6 – 6, 12, 18, 24, 30,...
(6 x 1) (6 x 2) (6 x 3) (6 x 4) (6 x 5)
Multiples of , 18, 27, 36, 45,...
(9 x 1) (9 x 2) (9 x 3) (9 x 4) (9 x 5)

57. LEAST COMMON MULTIPLE Smallest multiple they both have.
Let’s put
LEAST COMMON MULTIPLE
in our own words
Smallest
multiple
they both have.
Example:
LCM = 24 6
6, 12, 18, 24, 30, 36 8
8, 16, 24, 32, 40, 48

58. least common multiple (LCM): The smallest number that is a multiple of two or more numbers.
least common denominator (LCD): The smallest number that is the multiple of two or more denominators.

59. Strategies to find LCM Backwards Method, The “L”adder
Prime factorization (Tree),
T-chart, Chart or List
Backwards Method,
The “L”adder

60. Let’s Practice!! 4
4, 8, 12, 16, 20, 24
LCM = 20 10
10, 20, 30, 40, 50, 60 12
12, 24, 36, 48, 60
LCM = 36 9
9, 18, 27, 36, 45

61. What if there are 3 numbers?
Find the LCM of 4,6,and 8: 4
4, 8, 12, 16, 20, 24 6
6, 12, 18, 24, 30, 36
LCM = 24 8
8, 16, 24, 32, 40, 48

62. Write the first five multiples of each number.
1. 5
2. 6
3. 10
4. 12
5, 10, 15, 20, 25
6, 12, 18, 24, 30
10, 20, 30, 40, 50
12, 24, 36, 48, 60

63. Practice Find the first 10 multiples of 3
Is 40 a multiple of 8? Why?
Is 63 a multiple of 5? Why?

64. Common Multiple
A multiple with 2 or more numbers have in common.
Example: Find the first 3 common multiples of 3 and 6. 3 3, 6, 9,
122,
15,
18… 6 6,
12,
18,
,24,
30,
36…

65. Practice No, 9 is not 2. 3 and 6 3. 4 and 12 4. 2 and 5
1. Is 42 a common multiple of 6 and 9?
List 10 multiples of each number and circle the common multiples.
2. 3 and 6
3. 4 and 12
4. 2 and 5
No, 9 is not
3: 3, 6, 9, 12, 18, 21, 24, 27, 30
6: 6, 12, 18, 24, 30, 36, 42, 54, 60
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

66. Least Common Multiple 6 6, 12, 18, 24, 30, 36… 8, 8 16, 24, 32, 40,
The smallest multiple that 2 or more numbers have in common.
LCM = Least Common Multiple
Example: Find least common multiples of 6 and 8 6 6,
12,
18,
24,
30,
36… 8, 8
16,
24,
32,
40,
48…

67. Today, the school’s baseball and soccer teams have games
Today, the school’s baseball and soccer teams have games. The baseball team plays every 7 days. The soccer team plays every 3 days. When will the teams have games on the same day again?
3,7
7: 7, 14, 21 , 28, 35, 42,
List multiples of 3 and 7.
Find the smallest number that is in all the lists.
3: 3, 6, 9, 12, 15, 18, 21, . . .
LCM: 21. In 21 days, both teams will have game on the same day again.

68. Independent Practice List the first 5 multiples of each number. 2 4
3. Name the LCM of the following numbers:
20 and 5
4. How many common multiples less than 50 do 8 and 9 have? Name them.

69. a board, eraser, and dry erase marker from the back
Have homework on your desk turned to p11
Everyone should have: handout
a board, eraser, and dry erase marker from the back
Name
Teacher/Period
Title
Date
Write in your notes: GCF: Breaks numbers down; LCM; Multiplies (build numbers up)
Do Now: Check for Understanding
Find the least common multiple (LCM).
1. 6, , 12
3. 5, 6, , 16, 24, 36
5. Two students in Mrs. Stevens’ class are stacking blocks, one on top of the other. Cameron’s blocks are 4 cm high and Maddy’s blocks are 9 cm high. How tall will their stacks be when they are the same height for the first time? 42 36 30
144
36 cm

70. LCM Least Common Multiple 6.NS.4
Compute fluently with multi-digit numbers and find common factors and multiples

71. How do you find and justify the least common multiple of two numbers?
Essential Question
How do you find and justify the least common multiple of two numbers?

72. I Can Statements…
I can create a list of multiples for any number less than or equal to 12.
I can find and justify the least common multiple of any two numbers, less than or equal to 12.

73. Let’s Practice!!

74. ASSIGNMENT! Begin Handout from the back GRADED You can do it!
Yeah! Try your best!
You can do it!

75. Do Now: Check for Understanding
Have homework on your desk
Everyone should have: handout
Name
Teacher/Period
Title
Date
Write in your notes: GCF: Breaks numbers down; LCM; Multiplies (build numbers up)
Do Now: Check for Understanding
Ms. Madison directs two singing groups. One group has 28 students and the other has 36 students. For practice, she wants to divide each group into the greatest possible equal groups with no students left over. How many students will be in each group?   
Two trains leave the train station at the same time. Train A stops every 8 minutes and Train B stops every 10 minutes. In how many minutes will they stop at the same time? 4
40 minutes

76. MAKE SURE YOU HAVE HANDOUT OUT OF THE BASKET (in the back)
Math Review
HAVE HOMEWORK ON DESK!!! (GRADED)
MAKE SURE YOU HAVE HANDOUT OUT OF THE BASKET (in the back)
GCF: Breaks numbers down; LCM: Multiplies (build numbers up)
Early Finishers:
Choose an early finisher activity
READ A BOOK, ABSOLUTELY NO TALKING

77. Do Now: Check for Understanding
Have homework on your desk
Name
Teacher/Period
Title
Date
Write in your notes: GCF: Breaks numbers down; LCM; Multiplies (build numbers up)
Do Now: Check for Understanding
Taylor is using two different colors of beads to make necklaces. She has 48 blue beads and 32 white beads. She wants to use the same number of blue and white on each necklace. What is the greatest number of necklaces she can make if she uses all of the beads?  
Allison works at a bakery. She must box 30 rolls, 24 muffins, and 48biscuits so that all of the boxes have the same number of each. What isthe greatest number of boxes she can use?  16
6 boxes

78. MAKE SURE YOU HAVE QUIZ OUT OF THE BASKET (in the back)
Login In using the following:
naumstudent
green5
Math Quiz
TURN IN HOMEWORK IMMEDIATELY (GRADED)
MAKE SURE YOU HAVE QUIZ OUT OF THE BASKET (in the back)
Everyone Should Have a handout from the basket
GCF: Breaks numbers down; LCM: Multiplies (build numbers up)
Early Finishers:
Get Computer to do Join.Quizizz.com
Enter the 6-digit game code
Choose an early finisher activity
READ A BOOK, ABSOLUTELY NO TALKING

79. ASSIGNMENT!
Finding the LCM
Yeah! Try your best!
You can do it!

80. 24 50 36 60 72
105

81. Practice Time!
Identify whether the following word problems could be solved using GCF or LCM…

82. Question #1
Mrs. Evans has 120 crayons and 30 pieces of paper to give to her students. What is the largest # of students she can have in her class so that each student gets equal # of crayons and equal # of paper.

83. GCF

84. Question #2
Rosa is making a game board that is 16 inches by 24 inches. She wants to use square tiles. What is the largest tile she can use?

85. GCF

86. Question #3
Z100 gave away a Z $100 bill for every 100th caller. Every 30th caller received free concert tickets. How many callers must get through before one of them receives both a coupon and a concert ticket?

87. LCM

88. Question #4
Two bikers are riding a circular path. The first rider completes a round in 12 minutes. The second rider completes a round in 18 minutes. If they both started at the same place and time and go in the same direction, after how many minutes will they meet again at the starting point?

89. LCM

90. Question #5
Solve the following:
Sean has 8-inch pieces of toy train track and Ruth has 18-inch pieces of train track. How many of each piece would each child need to build tracks that are equal in length?

91. LCM
72 inch train track

92. Question #6 Solve the following:
I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?

93. (5 apple trees, and 3 peach trees per row)
GCF
10 Rows
(5 apple trees, and 3 peach trees per row)

94. Question # 7 Solve the following:
Two faucets are dripping. One faucet will drip every 4 seconds and the other faucet drips every 9 seconds. If a drop of water falls from both faucets at the same, how many seconds will it be before you see the faucets drip at the same time again?

95. LCM
Every 36 seconds

96. Question # 8 Solve the following:
Three pieces of timber 42 m, 49 m and 63 m long have to be divided into planks of the same length. What is the greatest possible length of each plank ?

97. GCF
7 meters

98. QUIZ Answers…
1.) GCF 2.) GCF 3.) LCM 4.) LCM 5.) LCM – 72 inch train track 6.) GCF -10 Rows (5 apple trees, and 3 peach trees per row) 7) LCM – every 36 seconds 8) GCF – 7 m

99. Identify the prime numbers in the grid below(7)X X X 7 7 39 45 22 23 23 X X X X 63 17 17 9 57 81 X X X 11 11 77 27 19 19 99 X X X 69 2 2 49 37 37 1

100. Identify the prime numbers in the grid below.(7)X X X
127
127
129
153
303
313
313 X X X X
415
199
199
213 57
187 X X X
449
449
111 93
367
367
453 X X X
666
137
137
183
919
919 1

101. GCF and LCM Learning Objectives Know what factors and multiples are
23/05/2018
Level 5
GCF and LCM
Learning Objectives
Know what factors and multiples are
Able to find the LCM of two numbers
Able to find the GCF of two numbers

102. Lowest Common Multiple (LCM)
Lowest Common Multiple – the lowest number in two or more numbers’ times tables.

103. Lowest Common Multiple (LCM)
Q. Find the LCM of 4 and 6.
Write out the first six numbers the 4 and 6 times tables
Look for the first number that appears in both lists.

104. Lowest Common Multiple (LCM)
Find the LCM of 4 and 6
 4, 8, 12, 16, 20, 24,….
 6, 12, 18, 24, 30, 36,…
We want the LOWEST common multiple, so the LCM of 4 and 6 is… 12

105. Lowest Common Multiple (LCM)
Find the LCM of 12 and 8.

106. Lowest Common Multiple (LCM)
Find the LCM of the following:
2 and 5
3 and 4
4 and 8
5 and 6 24 10
e)3 and 8
4 and 9
8 and 10
4, 5 and 12 12 36 8 40 30 60

107. Greatest Common Factor (GCF)
Greatest Common Factor (HCF) – the largest number that goes into two or more numbers exactly.
Example: Find the HCF of 32 and 56
32  1, 2, 4, 8, 16, 32
56  1, 2, 4, 7, 8, 14, 28, 56
GCF = 8

108. Greatest Common Factor (GCF)
Find the GCF of the following numbers: 4
e)32 and 80
f)60 and 10
g)36, 64, and 76
h)48, 60 and 84
a)8 and 12 b)9 and 15 c)10 and 30 d)18 and 33 16 3 12 10 4 3 12

109. Your turn…
Find the GCF of the following:
18 and 28
16 and 40
42 and 90
40 and 63
20, 64 and 108
54, 90 and 162
Find the LCM of the following:
4 and 5
8 and 12
6 and 9
12 and 15
5, 8 and 10
4, 7 and 9 2 20 24 8 18 6 60 1 40 4
252 18

110. Do NOW Find the GCF of 30 and 54 Find the LCM of 9 and 12
Write factors of 48

111. GCF and LCM Learning Objectives:
Level 5
23/05/2018
GCF and LCM
Learning Objectives:
Able to calculate the GCF and LCM of numbers using lists
Able to write a number as a product of its prime factors
Able to calculate the GCF and LCM of numbers using different strategies

112. Identify the prime numbers in the grid below. (7).X X X 7 7 39 45 22 23 23 X X X X 63 17 17 9 57 81 X X X 11 11 77 27 19 19 99 X X X 69 2 2 49 37 37 1

113. Identify the prime numbers in the grid below. (7)X X X
127
127
129
153
303
313
313 X X X X
415
199
199
213 57
187 X X X
449
449
111 93
367
367
453 X X X
666
137
137
183
919
919 1

114. Complete handout on GCF/LCM
Assignment
Complete handout on GCF/LCM