patterns in multiplication and division factors: numbers you multiply to get a product. example: 6 x...

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 above1. 2.

quotient: is the result of a division.

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.

Circle the numbers inthe chart that are divisibleby 2 leaving no remainder.

Any patterns?Can you make a rule?Can you notice similarities in the quotients?

Divisibility Rules for 2, 5, & 10

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

0 The number ends in 0 220 is 221 is not

Circle the numbers inthe chart that are divisible

by 4 leaving no remainder.

Any patterns?Can you make a rule?Can you notice similarities in the quotients?

Divisibility Rules for 4, & 8

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 inthe chart that are divisible

by 3 leaving no remainder.

Any patterns?Can you make a rule?Can you notice similarities in the quotients?

Divisibility Rules for 3, 6, & 9

A number is divisible by: If: Example:

3 The sum of the digits is divisible by 3 381 (3+8+1=12, and 12÷3 = 4) Yes217 (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) Yes2013 (2+0+1+3=6) No

Circle the numbers inthe chart that are divisible

by 0 leaving no remainder.

Any patterns?Can you make a rule?Can you notice similarities in the quotients?

Divisibility Rules for 0

Divisibility Rules

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

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

Go to this site for games!

Divisibility Rules

Assignment

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

Extend #25, 27

Handout – Divisibility Rules

Use Divisibility Rules to SORT Numbers

Carroll Diagram

Divisibility by 9

Not Divisible

by 9

Divisibility by 6

1623996

3031 974

Not Divisible

by 623 517 79

Venn Diagram

Divisible by 6 6

Divisible by 9 6

30

31 9746

162

39966 23 5176

Shows how numbers are thesame and different!

Shows relationships betweengroups of numbers.

Discuss with you partner why each number belongs where is does.

79

Use Divisibility Rules to SORT Numbers

Carroll Diagram

Divisibility by

Not Divisible

by

Divisibility by

Not Divisible

by

Shows how numbers are thesame and different!

Create a “Carroll Diagram” that sorts the numbers below according to divisibility by 3 & 4.

12, 32, 60, 24, 3140, 99

Use Divisibility Rules to SORT Numbers

Venn Diagram

Divisible by 6

Divisible by 6

Shows relationships betweengroups of numbers.

Create a “Venn Diagram” that sorts the numbers below according to divisibility by 3 & 4.

12, 32, 60, 24, 3140, 99

Use Divisibility Rules to SORT Numbers

Venn Diagram

Divisible by 2 6

Fill in the Venn diagram with 7 other numbers. There must be a minimum 2 numbers in each section.

Divisible By 5 6

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

Assignment

Page 207 # 7, 8

Factors

Go to this site for showing factors

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

Use Divisibility Rules to Determine Factors

Common Factors: a number that two or more numbers are divisible byOR

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 = 122 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

Use Divisibility Rules to Determine Factors

Common Factors: a number that two or more numbers are divisible byOR

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 = 272 x 9 = 18 3 x 9 = 273 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

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…

1. 6 & 9 2. 8 & 16 3. 36 & 12

Greatest Common Factorthe greatest number that both numbers are divisible by.

Use Divisibility Rules to Determine Factors

Venn Diagram

Factors of 246

Fill in the Venn diagram with factors for 24 and 32.What factors would go in the middle area?

Factors of326

Share your numbers with the person beside you. Do their numbers match?

Assignment

Page 207 # 12, 13Page 208 # 24

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.

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

Use Divisibility Rules to Determine Factors

Lowest Terms: when the numerator and denominator of the fraction have no common factors than 1.

Example: 12 = 6 42 21

÷ 2

÷ 2

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?

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?

Use Divisibility Rules to Determine Factors

Place the fractions below into “lowest terms…”

3268

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

Use Divisibility Rules to Determine Factors

Place the fractions below into “lowest terms…”

86102

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

Use Divisibility Rules to Determine Factors

Let’s Play a game

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

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

Assignment

Page 207 # 15abc, 16abc

Section 6.3 – Extra Practice Handout

Add Fractions With Like Denominators

Use Pattern Blocks & Fraction Strips to Model Fractions

They both

represent

ONE WHOLE

1. How many pattern blocks are in each whole above?

Add Fractions With Like Denominators

Use Pattern Blocks & Fraction Strips to Model Fractions

They both

represent

ONE WHOLE

1. 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 youranswer.

Example: 1 + 1 = or 1 + 1 + 1 = 2 2 3 3 3

Equal Sections Color Fraction

2 Red 1/2

3 Blue 1/3

4 1/4

6 Green 1/6

Add Fractions With Like Denominators

Use Pattern Blocks & Fraction Strips to Model Fractions

They both

represent

ONE WHOLE

1. 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 youranswer.

Example: 1 + 3 = or 1 + 4 = 2 6 3 6

Equal Sections Color Fraction

2 Red 1/2

3 Blue 1/3

4 1/4

6 Green 1/6

Add Fractions With Like Denominators

1. Name the fractions above…2. What if I were to ADD the same fraction to the one above…how

many parts would need to be colored in?3. What is the name of our new fraction?4. Using other pattern blocks can it be reduced to simplest form?

___ + ___ = ____ = ____

Add Fractions With Like Denominators

Using pattern blocks model the following equation. Write theanswer in lowest terms.

2 + 1 = ___ = __6 6

4 + 1 = ___ = __6 6

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 10

1 + 5 = ___ = ___9 9

Add Fractions With Like Denominators

Give a fraction for the…

1. Red portion = ____

2. Yellow Portion = ____

3. Green Portion = ____

4. Blue Portion = ____

Using Manipulatives to ADD Fractions

Use the sections provided to comeup with the proper fraction.

Equal Sections Color Fraction

2

3

4

6

Using Manipulatives to ADD Fractions

Use the yellow shape (1 whole) to place the fractions below on in order to find youranswer.

Example: 1 + 1 = Try Another: 1 + 3 = or 3 3 6 6

Equal Sections Color Fraction

2 Red 1/2

3 Blue 1/3

4 1/4

6 Green 1/6

Using Manipulatives to ADD Fractions

Try some more addition:

3 + 1 = or 1 + 2 = or 6 6 3 3

Is there an “Addition Rule” for adding fractions of the same denominators?

Equal Sections Color Fraction

2 Red 1/2

3 Blue 1/3

4 1/4

6 Green 1/6

Assignment

Pages 214-215: 5ab, 6ab, 7ab, 9ab, 10ef, 12, 14

Pages 220-221: 5ab, 6ab, 8ab, 10, 11

Assignment

6.2 – Add Fractions with like Denominators - Handout

Subtract Fractions With Like Denominators

Using pattern blocks model the following equation. Write theanswer in lowest terms.

2 + 1 = ___ = __6 6

4 + 1 = ___ = __6 6

Assignment

6.3 – Subtract Fractions with like Denominators - Handout