1. Patterns in Multiplication and Division
Factors: numbers you multiply to get a product.
Example: x 4 = 24
Factors Product
Product: the result of multiplication (answer).

2. Patterns in Multiplication and Division
Opposites: using multiplication to solve division
42 ÷ 7 = 6
Dividend Divisor Quotient
What 2 multiplication equations can I create from above
quotient: is the result of a division.

3. Introduction to Fraction Operations
Student Outcome: I will learn why a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10 and NOT 0
Divisibility: how can you determine if a number is divisible by
2,3,4,5,6,7,8,9 or 10?
Complete the chart on the next slides and circle all the numbers divisible by 2,3,4,5,6,7,8,9, and 10.
Then find a pattern with the numbers to figure out divisibility rules.
Reflect on your findings with your class.

4. Divisibility Rules for 2, 5, & 10
Student Outcome: I will learn why a number is divisible by 2, 3, 4, 5, 6, 8, 9, 10 and NOT 0
Circle the numbers in
the chart that are divisible
by 2 leaving no remainder.
Any patterns?
Can you make a rule?
Can you notice similarities in the quotients?

5. A number is divisible by: If: Example:
2 The last digit is even (0,2,4,6,8) 128 is 129 is not
5 The last digit is 0 or is 809 is not
10 The number ends in is 221 is not

6. Divisibility Rules for 4, & 8
Circle the numbers in
the chart that are divisible
by 4 leaving no remainder.
Any patterns?
Can you make a rule?
Can you notice similarities in the quotients?

7. A number is divisible by: If: Example:
4 The last 2 digits are divisible by is (12÷4=3)
 or the last 2 digits divisible by 2 twice 7019 is not
“Double Double”
8 The last three digits are divisible by (816÷8=102) Yes or number is divisible by 2 three times (302÷8=37 3/4) No
“Triple Double”

8. Divisibility Rules for 3, 6, & 9
Circle the numbers in
the chart that are divisible
by 3 leaving no remainder.
Any patterns?
Can you make a rule?
Can you notice similarities in the quotients?

9. A number is divisible by: If: Example:
The sum of the digits is divisible by (3+8+1=12, and 12÷3 = 4) Yes
217 (2+1+7=10, and 10÷3 = 3 1/3)No
The number is divisible by both 2 and (it is even, and 1+1+4=6 and 6÷3 = 2) Yes
308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No
The sum of the digits is divisible by 9(Note: you can apply this rule to that answer again if you want) ( =18, and again, 1+8=9) Yes
2013 ( =6) No

10. Divisibility Rules for 0
Circle the numbers in
the chart that are divisible
by 0 leaving no remainder.
Any patterns?
Can you make a rule?
Can you notice similarities in the quotients?

11. Divisibility Rules
Go to this site for an overall review of the divisibility rules! (or check your folder for word document)
Go to this site for games!

12. Divisibility Rules Assignment Page 207 - 208 # 3, 22, 24, 25, 26, 28

21. Student Outcome: Use Divisibility Rules to SORT Numbers
Carroll Diagram
Venn Diagram
Divisible
by 6 6
Divisible
by 9 6
Divisibility by 9
Not Divisible by 9
Divisibility by 6
162
3996 30
31 974
Not Divisible by 6
23 517 79
162
39966 30 79
Shows relationships between
groups of numbers.
Shows how numbers are the
same and different!
Discuss with you partner why each number belongs where is does.

22. Student Outcome: Use Divisibility Rules to SORT Numbers
Carroll Diagram
Create a “Carroll Diagram” that sorts the numbers below according to divisibility by 3 & 4.
12, 32, 60, 24, 3140, 99
Divisibility by
Not Divisible by
Shows how numbers are the
same and different!

23. Student Outcome: Use Divisibility Rules to SORT Numbers
Create a “Venn Diagram” that sorts the numbers below according to divisibility by 3 & 4.
12, 32, 60, 24, 3140, 99
Venn Diagram
Divisible
by 6
Divisible
by 6
Shows relationships between
groups of numbers.

24. Student Outcome: Use Divisibility Rules to SORT Numbers
Fill in the Venn diagram with 7 other numbers. There must be a minimum 2 numbers in each section.
Venn Diagram
Divisible
by 2 6
Divisible
By 5 6
Share your number with the group beside you. Do their numbers work?

25. Assignment
Page 207 # 7, 8, 13

28. Practical Quiz #1 Venn Diagram
Fill in the Venn diagram with these numbers:
4, 8, 12, 16, 20, 24, 30, 32, 80
Venn Diagram
Divisible
By 4 6
Divisible
By 8 6

29. Factors Go to this site for showing factors

30. Common Factors: a number that two or more numbers are divisible by OR
Student Outcome: I will be able to use Divisibility Rules to Determine Factors
Common Factors: a number that two or more numbers are divisible by OR
numbers you multiply together to get a product
Example: 4 is a common factor of 8 & HOW?
1 x 8 = 8 1 x 12 = 12
2 x 4 = 8 2 x 6 = 12
3 x 4 = 12
What is the least common factor (LCF) for 8 and 12?
What is the greatest common factor (GCF) for 8 and 12?
How would you describe in your own words (LCF) and (GCF)? Then discuss with your partner

31. Common Factors: a number that two or more numbers are divisible by OR
Student Outcome: I will be able to use Divisibility Rules to Determine Factors
Common Factors: a number that two or more numbers are divisible by OR
numbers you multiply together to get a product
Example: 3 and 9 are common factors of 18 & 27 HOW?
1 x 18 = x 27 = 27
2 x 9 = x 9 = 27
3 x 6 = 18
What is the least common factor (LCF) for 18 and 27?
What is the greatest common factor (GCF) for 18 and 27?
How would you describe in your own words (LCF) and (GCF)? Then discuss with your partner

32. Student Outcome: I will be able to use Divisibility Rules to Determine Factors
Common Factors: a number that two or more numbers are divisible by. OR
numbers you multiply together to get a product
List the common factors for the numbers below…
6 & & & 12
Greatest Common Factor
the greatest number that both numbers are divisible by.

33. Student Outcome: I will be able to use Divisibility Rules to Determine Factors
Fill in the Venn diagram with factors for 24 and 32.
What factors would go in the middle area?
Venn Diagram
Factors of
246
Factors of
326
Share your numbers with the person beside you. Do their numbers match?

34. Assignment
Page 207 # 12, 13
Page 208 # 24

36. Factors
Factor Game
Mr. Bosch will type in a number. You must list all the factors to get a point. You are playing against your neighbor. We will play 10 rounds. Person with the most points wins. Second place person does 15 pushups.

37. Practical Quiz #2 Venn Diagram
Fill in the Venn diagram with factors for 12 and 30.
What factors would go in the middle area?
Venn Diagram
Factors of
126
Factors of
306

38. 42 21 Ask Yourself? Example: 12 = 6 Lowest Terms:
Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms.
Lowest Terms:
when the numerator and denominator of the fraction have no common factors than 1.
Ask Yourself?
What are things you know that will help with the factoring?
What number can I factor out of the numerator and denominator?
Can I use other numbers to make factoring quicker?
Example: 12 = 6
÷ 2
÷ 2

39. 6 10 Place the fractions below into “lowest terms…”
Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms
Place the fractions below into “lowest terms…” 6 10
Share with your neighbor. Did they do more/less/same number of factoring steps?

40. 24 30 Place the fractions below into “lowest terms…”
Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms
Place the fractions below into “lowest terms…” 24 30
Share with your neighbor. Did they do more/less/same number of factoring steps?

41. 9 33 Place the fractions below into “lowest terms…”
Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms
Place the fractions below into “lowest terms…” 9 33
Share with your neighbor. Did they do more/less/same number of factoring steps?

42. 15 35 Place the fractions below into “lowest terms…”
Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms
Place the fractions below into “lowest terms…” 15 35
Share with your neighbor. Did they do more/less/same number of factoring steps?

43. Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms
Let’s Play a game

44. Assignment
Page 207 # 15abc, 16abc
Section 6.3 – Extra Practice Handout

46. Place the fractions below into “lowest terms…”
Practical Quiz #3
Place the fractions below into “lowest terms…”
12 b) 21 c) 32

47. Use Pattern Blocks & Fraction Strips to Model Fractions
Student Outcome: I will learn how to add fractions with Like denominators
Use Pattern Blocks & Fraction Strips to Model Fractions
They both
represent
ONE WHOLE
Using the similar pattern blocks can you make one whole? How many does it take?

48. Using Manipulatives to ADD Fractions
How can you divide each whole into equal sections listed in the chart below?
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6

49. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: =
Demo + =

50. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: =
Demo + =

51. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: =
Demo + =

52. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: =
Demo + =

53. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: Create you own equation with common denominators for your partner to solve
Demo + =

54. Name the fractions above…
Student Outcome: I will learn how to add fractions with Like denominators
Name the fractions above…
What if I were to ADD the same fraction to the one above…how many parts would need to be colored in?
What is the name of our new fraction?
Using other pattern blocks can it be reduced to simplest form?
___ + ___ = ____ + ____ =

55. Using pattern blocks model the following equation. Write the
Student Outcome: I will learn how to add fractions with Like denominators
Using pattern blocks model the following equation. Write the
answer in lowest terms.
= ___ = __ 6
= ___ = __

56. Using pattern blocks model the following equation. Write the
Student Outcome: I will learn how to add fractions with Like denominators
Using pattern blocks model the following equation. Write the
answer in lowest terms.
= ___ = __
= ___ = __

57. Student Outcome: I will learn how to add fractions with Like denominators
Can we add fractions with other denominators other than “6”? Write the answer in lowest terms.
= ___ = ___
= ___ = ___ 10
= ___ = ___

58. Assignment
Pages : 5ab, 6ab, 7ab, 9ab, ef, 12, 14

61. Assignment
6.2 – Add Fractions with like Denominators - Handout

62. Using Manipulatives to SUBTRACT Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: = =

63. Using Manipulatives to SUBTRACT Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: = =

64. Using Manipulatives to SUBTRACT Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: = =

65. Using Manipulatives to SUBTRACT Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: Create you own equation with common denominators for your partner to solve =

66. Using pattern blocks model the following equation. Write the
Student Outcome: I will learn how to subtract fractions with Like denominators
Using pattern blocks model the following equation. Write the
answer in lowest terms.
= ___ = __ 6
= ___ = __

67. Using pattern blocks model the following equation. Write the
Student Outcome: I will learn how to add fractions with Like denominators
Using pattern blocks model the following equation. Write the
answer in lowest terms.
= ___ = __
= ___ = __

68. Student Outcome: I will learn how to add fractions with Like denominators
Can we subtract fractions with other denominators other than “6”? Write the answer in lowest terms.
= ___ = ___
= ___ = ___ 10
= ___ = ___

69. Assignment
Pages : 5ab, 6ab, 8ab, 10, 11

71. Assignment
6.3 – Subtract Fractions with like Denominators - Handout

72. Unit Review Assignment
Chapter Review
Page
#1-17

75. Wrap it Up Game
Page 226 “It’s Divisible”
See Smart File

76. Wrap it Up Assignment
Give handout to students to figure out activities completed during a 24 hour timer frame.

77. Looking towards the next unit(7)… Adding and subtracting fractions
Student Outcome: I will learn how to add fractions with Different denominators
Looking towards the next unit(7)…
Adding and subtracting fractions
with different denominators

78. Give a fraction for the… Red portion = ____ Yellow Portion = ____
Student Outcome: I will learn how to add fractions with Different denominators
Give a fraction for the…
Red portion = ____
Yellow Portion = ____
Green Portion = ____ = ____
Blue Portion = ____ = ____

79. Use Pattern Blocks & Fraction Strips to Model Fractions
Student Outcome: I will learn how to add fractions with Different denominators
Use Pattern Blocks & Fraction Strips to Model Fractions
They both
represent
ONE WHOLE
Using any combination of pattern blocks can you make one whole? How many of each does it take?

80. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: = + =

81. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
Orange
1/4 6
Green
1/6
Example: = + =