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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: is the result of a division. Quotient What 2 multiplication equations can I create from above 1. 2. 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. 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? A number is divisible by: 2 If: The last digit is even (0,2,4,6,8) Example: 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 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? A number is divisible by: 4 or 8 or If: The last 2 digits are divisible by 4 the last 2 digits divisible by 2 twice “Double Double” Example: 1312 is (12÷4=3) 7019 is not The last three digits are divisible by 8 109816 (816÷8=102) Yes number is divisible by 2 three times 216302 (302÷8=37 3/4) No “Triple Double” 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? A number is divisible by: If: 3 The sum of the digits is divisible by 3 6 The number is divisible by both 2 and 3 9 Example: 381 (3+8+1=12, and 12÷3 = 4) Yes 217 (2+1+7=10, and 10÷3 = 3 1/3)No 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 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 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? 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 Go to this site for games! http://www.studystack.com/matching-53156 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 6 Venn Diagram Divisibility by 9 Not Divisible by 9 162 3996 30 31 974 Divisible by 6 6 162 30 31 9746 Not Divisible by 6 23 517 Divisible by 9 6 39966 23 5176 79 79 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. 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 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. 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. Divisible by 2 6 Venn Diagram 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 by OR numbers you multiply together to get a product Example: 4 is a common factor of 8 & 12 1x8=8 2x4=8 HOW? 1 x 12 = 12 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 by OR numbers you multiply together to get a product Example: 3 and 9 are common factors of 18 & 27 1 x 18 = 18 2 x 9 = 18 3 x 6 = 18 HOW? 1 x 27 = 27 3 x 9 = 27 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 Factor the greatest number that both numbers are divisible by. 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? Factors of 246 Venn Diagram Factors of 326 Share your numbers with the person beside you. Do their numbers match? Assignment Page 207 # 12, 13 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. 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. Ask Yourself? ÷2 Example: 12 = 6 42 21 What are things you know that will help with the factoring? What number can I factor out of the numerator and denominator? ÷2 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…” 32 68 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…” 86 102 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.mathplayground.com/fractions_reduce.html http://www.jamit.com.au/htmlFolder/app1002.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 Equal Sections Color Fraction 2 Red 1/2 3 Blue 1/3 4 6 1/4 Green 1/6 Use the yellow shape (1 whole) to place the fractions below on in order to find your answer. Example: 1 + 1 = 2 2 or 1 + 1 + 1 3 3 3 = 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 Equal Sections Color Fraction 2 Red 1/2 3 Blue 1/3 4 6 1/4 Green 1/6 Use the yellow shape (1 whole) to place the fractions below on in order to find your answer. Example: 1 + 3 = 2 6 or 1 + 4 = 3 6 Add Fractions With Like Denominators ___ 1. 2. 3. 4. + ___ = ____ = ____ 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? Add Fractions With Like Denominators Using pattern blocks model the following equation. Write the answer 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 come up with the proper fraction. Equal Sections 2 3 4 6 Color Fraction Using Manipulatives to ADD Fractions Equal Sections Color Fraction 2 Red 1/2 3 Blue 1/3 4 6 1/4 Green 1/6 Use the yellow shape (1 whole) to place the fractions below on in order to find your answer. Example: 1 + 1 = 3 3 Try Another: 1 + 3 = 6 6 or Using Manipulatives to ADD Fractions Equal Sections Color Fraction 2 Red 1/2 3 Blue 1/3 4 6 1/4 Green 1/6 Try some more addition: 3 + 1 = 6 6 or 1 + 2 = 3 3 or Is there an “Addition Rule” for adding fractions of the same denominators? 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 the answer in lowest terms. 2 + 1 6 6 = ___ = __ 4 + 1 6 6 = ___ = __ Assignment 6.3 – Subtract Fractions with like Denominators - Handout