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 DividendDivisorQuotient What 2 multiplication equations can I create from above 1.2. quotient: is the result of a division.

Operations 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.

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? Divisibility Rules for 0

Circle the numbers in the chart that are divisible by 1 leaving no remainder. Any patterns? Can you make a rule? Can you notice similarities in the quotients? Divisibility Rules for 1

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? 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

A number is divisible by:If:Example: 2The last digit is even (0,2,4,6,8)128 is 129 is not 5The last digit is 0 or 5175 is 809 is not 10The number ends in 0220 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? Divisibility Rules for 4, & 8

A number is divisible by:If:Example: 4The last 2 digits are divisible by is (12÷4=3) orthe last 2 digits divisible by 2 twice7019 is not “Double Double” 8The last three digits are divisible by (816÷8=102) Yes ornumber is divisible by 2 three times (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? Divisibility Rules for 3, 6, & 9

A number is divisible by:If:Example: 3 The sum of the digits is divisible by 3381 (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 (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 ( =18, and again, 1+8=9) Yes 2013 ( =6) No

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!

Divisibility Rules Assignment Page # 3, 22, 24, 25, 26, b,5,15,17,18,23 1b, 3, 9, 11, 15, 23

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

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

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

SORT Student Outcome: 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, 13

Show Me What You Know#1 Venn Diagram Divisible By 4 6 Fill in the Venn diagram with these numbers: 4, 8, 12, 16, 20, 24, 30, 32, 80 Divisible By 8 6

Factors Go to this site for showing factors

Determine Factors Student Outcome: I will be able to use Divisibility Rules to Determine Factors Common 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 = 81 x 12 = 12 2 x 4 = 82 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

Determine Factors Student Outcome: I will be able to use Divisibility Rules to Determine Factors Common 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 = 181 x 27 = 27 2 x 9 = 183 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

Determine Factors Student Outcome: I will be able to use Divisibility Rules to Determine Factors Common 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 & & & 12 Greatest Common Factor the greatest number that both numbers are divisible by.

Determine Factors Student Outcome: I will be able to use Divisibility Rules to Determine Factors Venn Diagram Factors of 24 6 Fill in the Venn diagram with factors for 24 and 32. What factors would go in the middle area? Factors of 32 6 Share your numbers with the person beside you. Do their numbers match?

Assignment Page 207 # 12 Page 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.

Show Me What You Know#2 Venn Diagram Factors of 12 6 Fill in the Venn diagram with factors for 12 and 30. What factors would go in the middle area? Factors of 30 6

Fractions

lowest terms. Student Outcome: I will be able to use Divisibility Rules to place fractions in lowest terms. Lowest Terms Lowest Terms: when the numerator and denominator of the fraction have no common factors than 1. Example: 12 = ÷ 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?

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

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

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

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

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

GAME TIME Reach For The Stars (see handout)

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

Show Me What You Know#3 lowest terms Place the fractions below into “lowest terms…” a)12b) 21c)

SOLVE Like Student Outcome: I will learn how to add fractions with Like denominators 1.Why was this kind of difficult? 2.How could you make adding all the different shapes together easier?? What is the total amount when all the shapes are added together?

Like Student Outcome: I will learn how to add fractions with Like denominators Use PatternBlocks & 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?

ADD Using Manipulatives to ADD Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 How can you divide each whole into equal sections listed in the chart below?

ADD Using Manipulatives to ADD Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: = 2 2 = + Demo

ADD Using Manipulatives to ADD Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: = 3 3 = + Demo

ADD Using Manipulatives to ADD Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: = 4 4 = + Demo

ADD Using Manipulatives to ADD Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: = 6 6 = + Demo

ADD Using Manipulatives to ADD Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: Create you own equation with common denominators for your partner to solve = + Demo

Like Student Outcome: I will learn how to 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? ___+___=____+____ =

Like 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

Like 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 = ___ = __ = ___ = __ 4

Like 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 = ___ = ___ = ___ = ___ = ___ = ___ 9

Assignment Pages : 14 12, 16, 17,18 7,9,11,13,16 2,3,5,7,9

Assignment 6.2 – Add Fractions with like Denominators - Handout

SUBTRACT Using Manipulatives to SUBTRACT Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: = 2 2 =

SUBTRACT Using Manipulatives to SUBTRACT Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: = 3 3 =

SUBTRACT Using Manipulatives to SUBTRACT Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: = 6 6 =

SUBTRACT Using Manipulatives to SUBTRACT Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: Create you own equation with common denominators for your partner to solve =

Like 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

Like 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 = ___ = __ = ___ = __ 4

Like 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 = ___ = ___ = ___ = ___ = ___ = ___ 9

Assignment Pages ,12,13,14 3,7,8,12 3,6,8,10

Assignment 6.3 – Subtract Fractions with like Denominators - Handout

Unit Review Assignment Chapter Review Page #1-17

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

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

Different 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

Different Student Outcome: I will learn how to add fractions with Different denominators Give a fraction for the… 1.Red 1.Red portion = ____ 2.Yellow 2.Yellow Portion = ____ 3.Green 3.Green Portion = ____ = ____ 4.Blue 4.Blue Portion = ____ = ____

Different 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 1.Using any combination of pattern blocks can you make one whole? How many of each does it take?

ADD Using Manipulatives to ADD Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: = 2 6 = +

ADD Using Manipulatives to ADD Fractions Equal SectionsColorFraction 2Red1/2 3Blue1/3 4Orange1/4 6Green1/6 Example: = 3 6 = +