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