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
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
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
0 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 # 5, 6, 18, 19, 22,
Extend #25, 27
Handout – Divisibility Rules

14. 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.

15. 12, 32, 60, 24, 3140, 99 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!

16. 12, 32, 60, 24, 3140, 99 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.

17. 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?

18. Assignment
Page 207 # 7, 8

20. Factors Go to this site for showing factors

21. 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

22. 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

23. 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.

24. 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?

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

27. 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.

28. Use Divisibility Rules to Determine Factors
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

29. Use Divisibility Rules to Determine Factors
Place the fractions below into “lowest terms…” 24 56
Share with your neighbor. Did they do more/less/same number of factoring steps?

30. Use Divisibility Rules to Determine Factors
Place the fractions below into “lowest terms…” 32 68
Share with your neighbor. Did they do more/less/same number of factoring steps?

31. Use Divisibility Rules to Determine Factors
Place the fractions below into “lowest terms…” 86
102
Share with your neighbor. Did they do more/less/same number of factoring steps?

32. Use Divisibility Rules to Determine Factors
Let’s Play a game

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

35. They both Add Fractions With Like Denominators
Use Pattern Blocks & Fraction Strips to Model Fractions
They both
represent
ONE WHOLE
How many pattern blocks are in each whole above?

36. They both 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?

37. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
1/4 6
Green
1/6
Use the yellow shape (1 whole) to place the fractions below on in order to find your
answer.
Example: = or =

38. They both Add Fractions With Like 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?

39. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
1/4 6
Green
1/6
Use the yellow shape (1 whole) to place the fractions below on in order to find your
answer.
Example: = or =

40. 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?
___ ___ = ____ = ____

41. Add Fractions With Like Denominators
Using pattern blocks model the following equation. Write the
answer in lowest terms.
= ___ = __ 6
= ___ = __

42. Add Fractions With Like Denominators
Can we add fractions with other denominators other than “6”? Write the answer in lowest terms.
= ___ = ___
= ___ = ___ 10
= ___ = ___

43. Add Fractions With Like Denominators
Give a fraction for the…
Red portion = ____
Yellow Portion = ____
Green Portion = ____
Blue Portion = ____

44. Using Manipulatives to ADD Fractions
Use the sections provided to come
up with the proper fraction.
Equal Sections
Color
Fraction 2 3 4 6

45. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
1/4 6
Green
1/6
Use the yellow shape (1 whole) to place the fractions below on in order to find your
answer.
Example: = Try Another: = or

46. Using Manipulatives to ADD Fractions
Equal Sections
Color
Fraction 2
Red
1/2 3
Blue
1/3 4
1/4 6
Green
1/6
Try some more addition:
= or = or
Is there an “Addition Rule” for adding fractions of the same denominators?

47. Assignment
Pages : 5ab, 6ab, 7ab, 9ab, ef, 12, 14
Pages : 5ab, 6ab, 8ab, 10, 11

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

52. Subtract Fractions With Like Denominators
Using pattern blocks model the following equation. Write the
answer in lowest terms.
= ___ = __ 6
= ___ = __

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