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Patterns in Multiplication and Division

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.

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Patterns in Multiplication and Division

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  1. 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).

  2. 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.

  3. 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.

  4. 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?

  5. 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

  6. 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?

  7. 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”

  8. 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?

  9. 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

  10. 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?

  11. 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

  12. Divisibility Rules Assignment Page 207 - 208 # 5, 6, 18, 19, 22, Extend #25, 27 Handout – Divisibility Rules

  13. 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.

  14. 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!

  15. 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.

  16. 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?

  17. Practical Quiz #1 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

  18. Assignment Page 207 # 7, 8

  19. Factors Go to this site for showing factors http://www.harcourtschool.com/activity/elab2004/gr5/9.html

  20. 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

  21. 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

  22. 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.

  23. 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?

  24. Practical Quiz #2 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

  25. Assignment Page 207 # 12, 13 Page 208 # 24

  26. 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

  27. 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

  28. 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?

  29. 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?

  30. 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?

  31. Practical Quiz #3 • Place the fractions below into “lowest terms…” 12b) 21c) 32 16 30 40

  32. 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

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

  34. 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?

  35. 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

  36. 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?

  37. 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

  38. 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? ___ + ___ = ____ = ____

  39. 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

  40. 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

  41. 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 = ____

  42. Student Outcome: I will be able to use Manipulatives to ADD Fractions • Use the sections provided to come • up with the proper fraction.

  43. 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

  44. 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?

  45. Assignment Pages 214-215: 5ab, 6ab, 7ab, 9ab, 10ef, 12, 14 Pages 220-221: 5ab, 6ab, 8ab, 10, 11

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