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Patterns in Multiplication and Division

Factors: numbers you multiply to get a product.

Example: 6 x 4 = 24

Factors Product

Product: the result of multiplication (answer).

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

1. 2.

- quotient: is the result of a division.

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.

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?

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 5 175 is 809 is not

10 The number ends in 0 220 is 221 is not

- 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?

A number is divisible by: If: Example:

4 The last 2 digits are divisible by 4 1312 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 8 109816 (816÷8=102) Yes or number is divisible by 2 three times 216302 (302÷8=37 3/4) No

“Triple Double”

- 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?

A number is divisible by: If: Example:

- The sum of the digits is divisible by 3 381 (3+8+1=12, and 12÷3 = 4) Yes
- 217 (2+1+7=10, and 10÷3 = 3 1/3)No
- 6 The number is divisible by both 2 and 3 114 (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
- 9 The sum of the digits is divisible by 9(Note: you can apply this rule to that answer again if you want) 1629 (1+6+2+9=18, and again, 1+8=9) Yes
- 2013 (2+0+1+3=6) No

- 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?

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

http://www.mathsisfun.com/divisibility-rules.html

Go to this site for games!

http://www.studystack.com/matching-53156

Assignment

Page 207 - 208 # 5, 6, 18, 19, 22,

Extend #25, 27

Handout – Divisibility Rules

Student Outcome: Use Divisibility Rules to SORT Numbers

Carroll Diagram

Venn Diagram

Divisible

by 66

Divisible

by 96

162

39966

30

31 9746

23 5176

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.

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

- Shows how numbers are the
- same and different!

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.

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 26

Divisible

By 56

Share your number with the group beside you. Do their numbers work?

Fill in the Venn diagram with these numbers:

4, 8, 12, 16, 20, 24, 30, 32, 80

Venn Diagram

Divisible

By 46

Divisible

By 86

Page 207 # 7, 8

Go to this site for showing factors

http://www.harcourtschool.com/activity/elab2004/gr5/9.html

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 & 12 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

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 = 18 1 x 27 = 27
- 2 x 9 = 18 3 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

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 & 9 2. 8 & 16 3. 36 & 12

Greatest Common Factor

the greatest number that both numbers are divisible by.

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?

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

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.

http://www.harcourtschool.com/activity/elab2004/gr5/9.html

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
- 42 21

÷ 2

÷ 2

Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms

- Place the fractions below into “lowest terms…”

24

56

Share with your neighbor. Did they do more/less/same number of factoring steps?

Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms

- Place the fractions below into “lowest terms…”

32

68

Share with your neighbor. Did they do more/less/same number of factoring steps?

Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms

- Place the fractions below into “lowest terms…”

86

102

Share with your neighbor. Did they do more/less/same number of factoring steps?

Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms

Let’s Play a game

http://www.mathplayground.com/fractions_reduce.html

http://www.jamit.com.au/htmlFolder/app1002.html

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?

Using Manipulatives to ADD Fractions

- Use the yellow shape (1 whole) to place the fractions below on in order to find your
- answer.
- Example: 1 + 1 = or 1 + 1 + 1 =
- 2 2 3 3 3

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 any combination of pattern blocks can you make one whole? How many of each does it take?

Using Manipulatives to ADD Fractions

- Use the yellow shape (1 whole) to place the fractions below on in order to find your
- answer.
- Example: 1 + 3 = or 1 + 4 =
- 2 6 3 6

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?

___ + ___ = ____ = ____

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.

2 + 1 = ___ = __

6

4 + 1 = ___ = __

6 6

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.

1 + 1 = ___ = ___

4 4

4 + 1 = ___ = ___

10

1 + 5 = ___ = ___

9 9

Student Outcome: I will learn how to add fractions with Like denominators

- Give a fraction for the…
- Red portion = ____
- Yellow Portion = ____
- Green Portion = ____
- Blue Portion = ____

Student Outcome: I will be able to use Manipulatives to ADD Fractions

- Use the sections provided to come
- up with the proper fraction.

Student Outcome: I will be able to use Manipulatives to ADD Fractions

- Use the yellow shape (1 whole) to place the fractions below on in order to find your
- answer.
- Example: 1 + 1 = Try Another: 1 + 3 = or
- 3 3 6 6

Student Outcome: I will be able to use Manipulatives to ADD Fractions

- Try some more addition:
- 3 + 1 = or 1 + 2 = or
- 6 3 3
- Is there an “Addition Rule” for adding fractions of the same denominators?

6.2 – Add Fractions with like Denominators - Handout

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.

2 + 1 = ___ = __

6

4 + 1 = ___ = __

6 6

6.3 – Subtract Fractions with like Denominators - Handout

Give handout to students to figure out activities completed during a 24 hour timer frame.

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