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Focusing on Fractions

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  • 1. Focusing on Fractions 3 2 5 5 Presented by Kathleen Cotter Lawer Based on the work of Joan A. Cotter, Ph.D.© Activities for Learning, Inc. 2012
  • 2. Joan A. Cotter, Ph.D.
  • 3. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin
  • 4. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator
  • 5. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator • Math Games
  • 6. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator • Math Games • Tutor
  • 7. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator • Math Games • Tutor • AL Abacus
  • 8. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator • Math Games • Tutor • AL Abacus • Middle-School Teacher
  • 9. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator • Math Games • Tutor • AL Abacus • Middle-School Teacher • Ph.D. in Math Education
  • 10. How are fractions usually taught?© Activities for Learning, Inc. 2012
  • 11. Fraction Model: “Fish Tank”© Activities for Learning, Inc. 2012
  • 12. Fraction Model: “Fish Tank” 2© Activities for Learning, Inc. 2012
  • 13. Fraction Model: “Fish Tank” 2 5© Activities for Learning, Inc. 2012
  • 14. Fraction Model: “Words” This is fourths.© Activities for Learning, Inc. 2012
  • 15. Fraction Model: “Words” This is fourths. This is thirds.© Activities for Learning, Inc. 2012
  • 16. Fraction Model: “Words” This is fourths. This is thirds. If this were chocolate…© Activities for Learning, Inc. 2012
  • 17. Fraction Model: “Words” This is fourths. This is thirds. If this were chocolate…© Activities for Learning, Inc. 2012
  • 18. Fraction Model: “Rounded Corner” 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 19. Fraction Model: “Rounded Corner” 1 1 1 3 3 3 1 1 1 1 4 4 4 4 The middle fractions are greater than the fractions at the ends!© Activities for Learning, Inc. 2012
  • 20. Fraction Models: Circles© Activities for Learning, Inc. 2012
  • 21. Fraction Models: Circles 1 1 3 3 1 1 2 2 1 3 1 1 1 1 1 1 5 5 6 6 4 4 1 1 1 1 6 6 1 1 5 5 4 4 1 1 1 6 6 5 Try to compare 4/5 and 5/6 with this model.© Activities for Learning, Inc. 2012
  • 22. Fraction Models: Circles Are we comparing angles, arcs, or area?© Activities for Learning, Inc. 2012
  • 23. Fraction Models: Circles Experts in visual literacy say that comparing quantities in pie charts is difficult because most people think linearly. It is easier to compare along a straight line than compare pie slices. askoxford.com© Activities for Learning, Inc. 2012
  • 24. Fraction Models: Circles Experts in visual literacy say that comparing quantities in pie charts is difficult because most people think linearly. It is easier to compare along a straight line than compare pie slices. askoxford.com Specialists also suggest refraining from using more than one pie chart for comparison. www.statcan.ca© Activities for Learning, Inc. 2012
  • 25. So how should we teach fractions?© Activities for Learning, Inc. 2012
  • 26. Fraction Model: Linear Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 27. Fraction Model: “Color” 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 28. Fraction Model: “Missing Parts” 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 1 1 1 1 1 1 1 1 1 1 1 1 12 12 12 12 12 12 12 12 12 12 12 12© Activities for Learning, Inc. 2012
  • 29. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 30. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Ask the children to put it together like a puzzle.© Activities for Learning, Inc. 2012
  • 31. Definition of a Fraction© Activities for Learning, Inc. 2012
  • 32. Definition of a Fraction A fraction is part of a set or part of a whole. Textbook definition© Activities for Learning, Inc. 2012
  • 33. Definition of a Fraction A fraction is part of a set or part of a whole. Textbook definition What about 3 ? 2© Activities for Learning, Inc. 2012
  • 34. Definition of a Fraction An expression that indicates the quotient of two quantities. American Heritage Dictionary© Activities for Learning, Inc. 2012
  • 35. Definition of a Fraction An expression that indicates the quotient of two quantities. American Heritage Dictionary a A number in the form bwhere b ≠ 0. Arizona Standards© Activities for Learning, Inc. 2012
  • 36. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 37. Fraction Chart 1 1 1 1÷2 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 38. Fraction Chart 1 1 1 1÷2 2 2 1 1 1 1÷3 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 39. Fraction Chart 1 1 1 1÷2 2 2 1 1 1 1÷3 3 3 3 1 1 1 1 1÷4 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 40. Fraction Naming© Activities for Learning, Inc. 2012
  • 41. Fraction Naming© Activities for Learning, Inc. 2012
  • 42. Fraction Naming One divided into 2 equal parts.© Activities for Learning, Inc. 2012
  • 43. Fraction Naming One divided into 2 equal parts.© Activities for Learning, Inc. 2012
  • 44. Fraction Naming One divided into 2 equal parts. One divided into 3 equal parts.© Activities for Learning, Inc. 2012
  • 45. Fraction Naming One divided into 2 equal parts. One divided into 3 equal parts.© Activities for Learning, Inc. 2012
  • 46. Fraction Naming One divided into 2 equal parts. One divided into 3 equal parts. One divided into 4 equal parts.© Activities for Learning, Inc. 2012
  • 47. Fraction Naming One divided into 3 equal parts.© Activities for Learning, Inc. 2012
  • 48. Fraction Naming One divided into 3 equal parts. 1 One whole© Activities for Learning, Inc. 2012
  • 49. Fraction Naming One divided into 3 equal parts. 1 One whole divided into© Activities for Learning, Inc. 2012
  • 50. Fraction Naming One divided into 3 equal parts. 1 One whole divided into 3 three equal parts© Activities for Learning, Inc. 2012
  • 51. Fraction Naming One divided into 3 equal parts. 1 One divided by 3 three© Activities for Learning, Inc. 2012
  • 52. Fraction Naming One divided into 3 equal parts. 1 Read as “one-third.” 3© Activities for Learning, Inc. 2012
  • 53. Fraction Naming 1 1 1 1 3 3 3 One divided into 3 equal parts. 1 Read as “one-third.” 3© Activities for Learning, Inc. 2012
  • 54. Fraction Naming 1 1 1 1 3 3 3 One divided into 3 equal parts. 1 Read as “one-third.” 3 In English, we use ordinal numbers to name fractions, with the exception of half.© Activities for Learning, Inc. 2012
  • 55. How should we practice what we learned?© Activities for Learning, Inc. 2012
  • 56. Games© Activities for Learning, Inc. 2012
  • 57. Games Games Math© Activities for Learning, Inc. 2012
  • 58. Games Games = Math© Activities for Learning, Inc. 2012
  • 59. Games Games Books = Math Reading© Activities for Learning, Inc. 2012
  • 60. Games Games Books = Math Reading Games provide interesting repetition needed for automaticity.© Activities for Learning, Inc. 2012
  • 61. Games Games Books = Math Reading Games provide interesting repetition needed for automaticity. Games also provide an application for new information.© Activities for Learning, Inc. 2012
  • 62. Unit Fraction War© Activities for Learning, Inc. 2012
  • 63. Unit Fraction War Purpose: Practice for naming and comparing unit fractions.© Activities for Learning, Inc. 2012
  • 64. Unit Fraction War Purpose: Practice for naming and comparing unit fractions. To help the children realize a unit fraction decreases as the denominator increases.© Activities for Learning, Inc. 2012
  • 65. Unit Fraction War Purpose: Practice for naming and comparing unit fractions. To help the children realize a unit fraction decreases as the denominator increases. Goal: To collect all, or most, of the cards by comparing unit fractions.© Activities for Learning, Inc. 2012
  • 66. Unit Fraction War© Activities for Learning, Inc. 2012
  • 67. Unit Fraction War 1 1 4 5© Activities for Learning, Inc. 2012
  • 68. Unit Fraction War 1 1 4 5© Activities for Learning, Inc. 2012
  • 69. Unit Fraction War© Activities for Learning, Inc. 2012
  • 70. Unit Fraction War 1 1 8 2© Activities for Learning, Inc. 2012
  • 71. Unit Fraction War 1 1 8 2© Activities for Learning, Inc. 2012
  • 72. Unit Fraction War© Activities for Learning, Inc. 2012
  • 73. Unit Fraction War 1 1 6 6© Activities for Learning, Inc. 2012
  • 74. Unit Fraction War 1 1 6 6© Activities for Learning, Inc. 2012
  • 75. Unit Fraction War 1 1 6 6 1 1 3 4© Activities for Learning, Inc. 2012
  • 76. Unit Fraction War© Activities for Learning, Inc. 2012
  • 77. Unit Fraction War 1 1 2 3© Activities for Learning, Inc. 2012
  • 78. More Fraction Naming© Activities for Learning, Inc. 2012
  • 79. More Fraction Naming 1 1 1 1 3 3 3© Activities for Learning, Inc. 2012
  • 80. More Fraction Naming 1 1 1 1 3 3 3 One-third taken 2 times.© Activities for Learning, Inc. 2012
  • 81. More Fraction Naming 1 1 1 1 3 3 3 One-third taken 2 times. Two 1 s 3© Activities for Learning, Inc. 2012
  • 82. More Fraction Naming 1 1 1 1 3 3 3 One-third taken 2 times. Two 1 s is 2 3 3© Activities for Learning, Inc. 2012
  • 83. More Fraction Naming 1 1 1 1 3 3 3 One-third taken 2 times. Two 1 s is 2 3 3 Read as “two-thirds.”© Activities for Learning, Inc. 2012
  • 84. More Fraction Naming 1© Activities for Learning, Inc. 2012
  • 85. More Fraction Naming 1 1© Activities for Learning, Inc. 2012
  • 86. More Fraction Naming 1 1 Two divided into 3 equal parts.© Activities for Learning, Inc. 2012
  • 87. More Fraction Naming 1 1 Two divided into 3 equal parts. 2 Two divided by 3 three© Activities for Learning, Inc. 2012
  • 88. More Fraction Naming 1 1 Two divided into 3 equal parts. 2 Two divided by 3 three© Activities for Learning, Inc. 2012
  • 89. More Fraction Naming 1 1 1 1 1 1 1 1 3 3 3 3 3 3 Two divided into 3 equal parts. 2 Two divided by 3 three© Activities for Learning, Inc. 2012
  • 90. More Fraction Naming 1 1 1 1 1 1 1 1 3 3 3 3 3 3 Two divided into 3 equal parts. 2 Two 1 3 divided by = two 3 s three© Activities for Learning, Inc. 2012
  • 91. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 92. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole?© Activities for Learning, Inc. 2012
  • 93. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole?© Activities for Learning, Inc. 2012
  • 94. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole?© Activities for Learning, Inc. 2012
  • 95. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole?© Activities for Learning, Inc. 2012
  • 96. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a whole?© Activities for Learning, Inc. 2012
  • 97. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths in a How many sixths? whole?© Activities for Learning, Inc. 2012
  • 98. Concentrating on One Game Purpose: To help the children realize that 5 fifths, 8 eighths, and so forth, make a whole.© Activities for Learning, Inc. 2012
  • 99. Concentrating on One Game Purpose: To help the children realize that 5 fifths, 8 eighths, and so forth, make a whole. Goal: To find the pairs that make a whole.© Activities for Learning, Inc. 2012
  • 100. Concentrating on One© Activities for Learning, Inc. 2012
  • 101. Concentrating on One© Activities for Learning, Inc. 2012
  • 102. Concentrating on One 3 5© Activities for Learning, Inc. 2012
  • 103. Concentrating on One 3 5© Activities for Learning, Inc. 2012
  • 104. Concentrating on One 3 5© Activities for Learning, Inc. 2012
  • 105. Concentrating on One 3 5 2 5© Activities for Learning, Inc. 2012
  • 106. Concentrating on One© Activities for Learning, Inc. 2012
  • 107. Concentrating on One 3 8© Activities for Learning, Inc. 2012
  • 108. Concentrating on One 3 8© Activities for Learning, Inc. 2012
  • 109. Concentrating on One 3 8© Activities for Learning, Inc. 2012
  • 110. Concentrating on One 7 8 3 8© Activities for Learning, Inc. 2012
  • 111. Concentrating on One© Activities for Learning, Inc. 2012
  • 112. Concentrating on One 5 8© Activities for Learning, Inc. 2012
  • 113. Concentrating on One 5 8© Activities for Learning, Inc. 2012
  • 114. Concentrating on One 5 8© Activities for Learning, Inc. 2012
  • 115. Concentrating on One 5 8 3 8© Activities for Learning, Inc. 2012
  • 116. Concentrating on One© Activities for Learning, Inc. 2012
  • 117. Let’s begin to compare fractions….© Activities for Learning, Inc. 2012
  • 118. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 3/4 or 4/5?© Activities for Learning, Inc. 2012
  • 119. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 3/4 or 4/5?© Activities for Learning, Inc. 2012
  • 120. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 3/4 or 4/5?© Activities for Learning, Inc. 2012
  • 121. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 7/8 or 8/9?© Activities for Learning, Inc. 2012
  • 122. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 7/8 or 8/9?© Activities for Learning, Inc. 2012
  • 123. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 Which is more, 7/8 or 8/9?© Activities for Learning, Inc. 2012
  • 124. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 An interesting pattern.© Activities for Learning, Inc. 2012
  • 125. Fraction Stairs 1 10 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1© Activities for Learning, Inc. 2012
  • 126. Fraction Stairs 1 10 1 9 1 8 1 7 1 6 1 5 1 4 1 3 1 2 1© Activities for Learning, Inc. 2012
  • 127. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths equal a half?© Activities for Learning, Inc. 2012
  • 128. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths equal a half?© Activities for Learning, Inc. 2012
  • 129. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths equal a half? Eighths?© Activities for Learning, Inc. 2012
  • 130. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths equal a half? Eighths?© Activities for Learning, Inc. 2012
  • 131. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths equal a half? Eighths? Sevenths?© Activities for Learning, Inc. 2012
  • 132. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 How many fourths equal a half? Eighths? Sevenths?© Activities for Learning, Inc. 2012
  • 133. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/4 plus 1/8?© Activities for Learning, Inc. 2012
  • 134. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/4 plus 1/8?© Activities for Learning, Inc. 2012
  • 135. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/4 plus 1/8?© Activities for Learning, Inc. 2012
  • 136. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/4 plus 1/8?© Activities for Learning, Inc. 2012
  • 137. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/4 plus 1/8? [3/8]© Activities for Learning, Inc. 2012
  • 138. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 If the chance of rain is 3/4, the chance it won’t rain is .© Activities for Learning, Inc. 2012
  • 139. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 If the chance of rain is 3/4, the chance it won’t rain is .© Activities for Learning, Inc. 2012
  • 140. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 If the chance of rain is 3/4, the chance it won’t rain is 1/4 .© Activities for Learning, Inc. 2012
  • 141. Partial Chart 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8© Activities for Learning, Inc. 2012
  • 142. Partial Chart 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8© Activities for Learning, Inc. 2012
  • 143. Partial Chart© Activities for Learning, Inc. 2012
  • 144. Partial Chart 1 2 3 4 5 6© Activities for Learning, Inc. 2012
  • 145. Fraction War Purpose: To practice comparing ones, halves, fourths, and eighths in preparation for reading a ruler.© Activities for Learning, Inc. 2012
  • 146. Fraction War Purpose: To practice comparing ones, halves, fourths, and eighths in preparation for reading a ruler. Goal: To capture all the cards.© Activities for Learning, Inc. 2012
  • 147. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8© Activities for Learning, Inc. 2012
  • 148. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 8 4© Activities for Learning, Inc. 2012
  • 149. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 8 4© Activities for Learning, Inc. 2012
  • 150. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 8 4© Activities for Learning, Inc. 2012
  • 151. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8© Activities for Learning, Inc. 2012
  • 152. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 5 3 8 4© Activities for Learning, Inc. 2012
  • 153. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 5 3 8 4© Activities for Learning, Inc. 2012
  • 154. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 5 3 8 4© Activities for Learning, Inc. 2012
  • 155. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8© Activities for Learning, Inc. 2012
  • 156. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 3 3 4 4© Activities for Learning, Inc. 2012
  • 157. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 3 3 4 4© Activities for Learning, Inc. 2012
  • 158. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 3 3 4 4 3 1 8 4© Activities for Learning, Inc. 2012
  • 159. Fraction War 1 1 1 2 2 1 1 1 1 4 4 4 4 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8© Activities for Learning, Inc. 2012
  • 160. Advanced Fraction War© Activities for Learning, Inc. 2012
  • 161. What about fractions bigger than 1?© Activities for Learning, Inc. 2012
  • 162. Fractions > 1 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 163. Fractions > 1 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 164. Mixed to Improper Fractions© Activities for Learning, Inc. 2012
  • 165. Mixed to Improper Fractions Each row of connected rectangles represents 1.© Activities for Learning, Inc. 2012
  • 166. Mixed to Improper Fractions Each row of connected rectangles represents 1.© Activities for Learning, Inc. 2012
  • 167. Mixed to Improper Fractions Each row of connected rectangles represents 1.© Activities for Learning, Inc. 2012
  • 168. Mixed to Improper Fractions Each row of connected rectangles represents 1.© Activities for Learning, Inc. 2012
  • 169. Mixed to Improper Fractions Each row of connected rectangles represents 1.© Activities for Learning, Inc. 2012
  • 170. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and© Activities for Learning, Inc. 2012
  • 171. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction.© Activities for Learning, Inc. 2012
  • 172. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 24© Activities for Learning, Inc. 2012
  • 173. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4© Activities for Learning, Inc. 2012
  • 174. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4 two 4s© Activities for Learning, Inc. 2012
  • 175. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4 two 4s© Activities for Learning, Inc. 2012
  • 176. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4 two 4s + 3© Activities for Learning, Inc. 2012
  • 177. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4 two 4s + 3 = 11© Activities for Learning, Inc. 2012
  • 178. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4 two 4s + 3 = 11© Activities for Learning, Inc. 2012
  • 179. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4 1 two 4s + 3 = 11 43© Activities for Learning, Inc. 2012
  • 180. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4 1 13 two 4s + 3 = 11 43 = 3© Activities for Learning, Inc. 2012
  • 181. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4 1 13 two 4s + 3 = 11 43 = 3 four 3s© Activities for Learning, Inc. 2012
  • 182. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4 1 13 two 4s + 3 = 11 43 = 3 four 3s + 1© Activities for Learning, Inc. 2012
  • 183. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 24 = 4 1 13 two 4s + 3 = 11 43 = 3 four 3s + 1 = 13© Activities for Learning, Inc. 2012
  • 184. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 3 24 = 4 35 1 13 two 4s + 3 = 11 43 = 3 four 3s + 1 = 13© Activities for Learning, Inc. 2012
  • 185. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 3 18 24 = 4 35 = 5 1 13 two 4s + 3 = 11 43 = 3 four 3s + 1 = 13© Activities for Learning, Inc. 2012
  • 186. Mixed to Improper Fractions Each row of connected rectangles represents 1. Write each quantity as a mixed number and as an improper fraction. 3 11 3 18 24 = 4 35 = 5 1 13 three 5s + 3 = 18 two 4s + 3 = 11 43 = 3 four 3s + 1 = 13© Activities for Learning, Inc. 2012
  • 187. Help the student discover the algorithm.© Activities for Learning, Inc. 2012
  • 188. Improper to Mixed Fractions© Activities for Learning, Inc. 2012
  • 189. Improper to Mixed Fractions 1 1 1 1 1 1 1 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 3 3 3 3 3© Activities for Learning, Inc. 2012
  • 190. Improper to Mixed Fractions Write each quantity as an improper fraction, 1 1 1 1 1 1 1 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 3 3 3 3 3© Activities for Learning, Inc. 2012
  • 191. Improper to Mixed Fractions Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number. 1 1 1 1 1 1 1 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 3 3 3 3 3© Activities for Learning, Inc. 2012
  • 192. Improper to Mixed Fractions Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number. 1 1 1 1 1 1 1 1 1 1 1 11 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 3 3 3 3 3© Activities for Learning, Inc. 2012
  • 193. Improper to Mixed Fractions Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number. 1 1 1 1 1 1 1 1 1 1 1 11 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 3 3 3 3 3© Activities for Learning, Inc. 2012
  • 194. Improper to Mixed Fractions Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number. 1 1 1 1 1 1 1 1 1 1 1 11 = 2 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 3 3 3 3 3© Activities for Learning, Inc. 2012
  • 195. Improper to Mixed Fractions Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number. 1 1 1 1 1 1 1 1 1 1 1 11 = 2 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 5 3 3 3 3 3 3© Activities for Learning, Inc. 2012
  • 196. Improper to Mixed Fractions Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number. 1 1 1 1 1 1 1 1 1 1 1 11 = 2 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 5 3 3 3 3 3 3© Activities for Learning, Inc. 2012
  • 197. Improper to Mixed Fractions Write each quantity as an improper fraction, then circle the wholes and write again as a mixed number. 1 1 1 1 1 1 1 1 1 1 1 11 = 2 1 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1 1 5 = 12 3 3 3 3 3 3 3© Activities for Learning, Inc. 2012
  • 198. Remember, let the student discover the algorithm.© Activities for Learning, Inc. 2012
  • 199. Fraction of Geometric Figures© Activities for Learning, Inc. 2012
  • 200. Fraction of Geometric Figures© Activities for Learning, Inc. 2012
  • 201. Fraction of Geometric Figures Shade 1 2© Activities for Learning, Inc. 2012
  • 202. Fraction of Geometric Figures Shade 1 2© Activities for Learning, Inc. 2012
  • 203. Fraction of Geometric Figures Shade 1 2 Shade 2 3© Activities for Learning, Inc. 2012
  • 204. Fraction of Geometric Figures Shade 1 2 Shade 2 3© Activities for Learning, Inc. 2012
  • 205. Fraction of Geometric Figures Shade 1 2 Shade 2 3 Shade 1 4© Activities for Learning, Inc. 2012
  • 206. Fraction of Geometric Figures Shade 1 2 Shade 2 3 Shade 1 4© Activities for Learning, Inc. 2012
  • 207. Making the Whole© Activities for Learning, Inc. 2012
  • 208. Making the Whole 1 3 2 3© Activities for Learning, Inc. 2012
  • 209. Making the Whole Draw the whole. 1 3 2 3© Activities for Learning, Inc. 2012
  • 210. Making the Whole Draw the whole. 1 1 1 3 1 3 3 3 2 3© Activities for Learning, Inc. 2012
  • 211. Making the Whole Draw the whole. 1 1 1 3 1 3 3 3 2 2 3 3 1 3© Activities for Learning, Inc. 2012
  • 212. How about a fraction of a number?© Activities for Learning, Inc. 2012
  • 213. A Fraction of Twelve© Activities for Learning, Inc. 2012
  • 214. A Fraction of Twelve© Activities for Learning, Inc. 2012
  • 215. A Fraction of Twelve What is 1/2 of 12?© Activities for Learning, Inc. 2012
  • 216. A Fraction of Twelve What is 1/2 of 12?© Activities for Learning, Inc. 2012
  • 217. A Fraction of Twelve What is 1/2 of 12? [6]© Activities for Learning, Inc. 2012
  • 218. A Fraction of Twelve What is 1/3 of 12?© Activities for Learning, Inc. 2012
  • 219. A Fraction of Twelve What is 1/3 of 12?© Activities for Learning, Inc. 2012
  • 220. A Fraction of Twelve What is 1/3 of 12? [4]© Activities for Learning, Inc. 2012
  • 221. A Fraction of Twelve What is 1/4 of 12?© Activities for Learning, Inc. 2012
  • 222. A Fraction of Twelve What is 1/4 of 12?© Activities for Learning, Inc. 2012
  • 223. A Fraction of Twelve What is 1/4 of 12? [3]© Activities for Learning, Inc. 2012
  • 224. A Fraction of Twelve What is 1/5 of 12?© Activities for Learning, Inc. 2012
  • 225. A Fraction of Twelve What is 1/5 of 12?© Activities for Learning, Inc. 2012
  • 226. A Fraction of Twelve What is 1/5 of 12? It’s not even; there is a remainder.© Activities for Learning, Inc. 2012
  • 227. A Fraction of Twelve What is 1/6 of 12?© Activities for Learning, Inc. 2012
  • 228. A Fraction of Twelve What is 1/6 of 12?© Activities for Learning, Inc. 2012
  • 229. A Fraction of Twelve What is 1/6 of 12? [2]© Activities for Learning, Inc. 2012
  • 230. A Fraction of 100© Activities for Learning, Inc. 2012
  • 231. A Fraction of 100 100© Activities for Learning, Inc. 2012
  • 232. A Fraction of 100 100 50 50© Activities for Learning, Inc. 2012
  • 233. A Fraction of 100 100 50 50 33 1 3 33 1 3 33 1 3© Activities for Learning, Inc. 2012
  • 234. A Fraction of 100 100 50 50 33 1 3 33 1 3 33 1 3 25 25 25 25© Activities for Learning, Inc. 2012
  • 235. A Fraction of 100 100 50 50 33 1 3 33 1 3 33 1 3 25 25 25 25 20 20 20 20 20© Activities for Learning, Inc. 2012
  • 236. A Fraction of 100 100 50 50 33 1 3 33 1 3 33 1 3 25 25 25 25 20 20 20 20 20 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 2 2 2 2 2 2 2 2© Activities for Learning, Inc. 2012
  • 237. A Fraction of 100 100 50 50 33 1 3 33 1 3 33 1 3 25 25 25 25 20 20 20 20 20 12 1 12 1 12 1 12 1 12 1 12 1 12 1 12 1 2 2 2 2 2 2 2 2 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 238. Percents© Activities for Learning, Inc. 2012
  • 239. Percents Percent means a fraction of 100© Activities for Learning, Inc. 2012
  • 240. Percents Percent means a fraction of 100 or per 100.© Activities for Learning, Inc. 2012
  • 241. Percents Percent means a fraction of 100 or per 100.© Activities for Learning, Inc. 2012
  • 242. Percents Percent means a fraction of 100 or per 100.© Activities for Learning, Inc. 2012
  • 243. Percents Percent means a fraction of 100 or per 100. 1 of 100 2© Activities for Learning, Inc. 2012
  • 244. Percents Percent means a fraction of 100 or per 100. 1 of 100 = 50 2 100© Activities for Learning, Inc. 2012
  • 245. Percents Percent means a fraction of 100 or per 100. 1 of 100 = 50 = 50% 2 100© Activities for Learning, Inc. 2012
  • 246. Percents Percent means a fraction of 100 or per 100.© Activities for Learning, Inc. 2012
  • 247. Percents Percent means a fraction of 100 or per 100.© Activities for Learning, Inc. 2012
  • 248. Percents Percent means a fraction of 100 or per 100. 1 of 100 4© Activities for Learning, Inc. 2012
  • 249. Percents Percent means a fraction of 100 or per 100. 1 of 100 = 25 4 100© Activities for Learning, Inc. 2012
  • 250. Percents Percent means a fraction of 100 or per 100. 1 of 100 = 25 = 25% 4 100© Activities for Learning, Inc. 2012
  • 251. Percents Percent means a fraction of 100 or per 100.© Activities for Learning, Inc. 2012
  • 252. Percents Percent means a fraction of 100 or per 100.© Activities for Learning, Inc. 2012
  • 253. Percents Percent means a fraction of 100 or per 100. 1 of 100 10© Activities for Learning, Inc. 2012
  • 254. Percents Percent means a fraction of 100 or per 100. 1 of 100 = 10 10 100© Activities for Learning, Inc. 2012
  • 255. Percents Percent means a fraction of 100 or per 100. 1 of 100 = 10 = 10% 10 100© Activities for Learning, Inc. 2012
  • 256. Now let’s simplify fractions.© Activities for Learning, Inc. 2012
  • 257. Simplifying Fractions 1 2© Activities for Learning, Inc. 2012
  • 258. Simplifying Fractions 3=1 6 2© Activities for Learning, Inc. 2012
  • 259. Simplifying Fractions 4=1 8 2© Activities for Learning, Inc. 2012
  • 260. Simplifying Fractions© Activities for Learning, Inc. 2012
  • 261. Simplifying Fractions 9 12© Activities for Learning, Inc. 2012
  • 262. Simplifying Fractions 9 12 3© Activities for Learning, Inc. 2012
  • 263. Simplifying Fractions 9 12 3© Activities for Learning, Inc. 2012
  • 264. Simplifying Fractions 9 =3 12 3 4© Activities for Learning, Inc. 2012
  • 265. Simplifying Fractions© Activities for Learning, Inc. 2012
  • 266. Simplifying Fractions© Activities for Learning, Inc. 2012
  • 267. Simplifying Fractions© Activities for Learning, Inc. 2012
  • 268. Simplifying Fractions© Activities for Learning, Inc. 2012
  • 269. Simplifying Fractions 21 28© Activities for Learning, Inc. 2012
  • 270. Simplifying Fractions 21 28© Activities for Learning, Inc. 2012
  • 271. Simplifying Fractions 21 28© Activities for Learning, Inc. 2012
  • 272. Simplifying Fractions 45 72© Activities for Learning, Inc. 2012
  • 273. Simplifying Fractions 45 72© Activities for Learning, Inc. 2012
  • 274. Simplifying Fractions 45 72© Activities for Learning, Inc. 2012
  • 275. Simplifying Fractions 12 16© Activities for Learning, Inc. 2012
  • 276. Simplifying Fractions 12 16© Activities for Learning, Inc. 2012
  • 277. Simplifying Fractions 12 16© Activities for Learning, Inc. 2012
  • 278. Simplifying Fractions 12 16© Activities for Learning, Inc. 2012
  • 279. Simplifying Fractions 12 16© Activities for Learning, Inc. 2012
  • 280. Simplifying Fractions 12 16© Activities for Learning, Inc. 2012
  • 281. So how does multiplying fractions work?© Activities for Learning, Inc. 2012
  • 282. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/2 of 1/2?© Activities for Learning, Inc. 2012
  • 283. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/2 of 1/2?© Activities for Learning, Inc. 2012
  • 284. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/2 of 1/2?© Activities for Learning, Inc. 2012
  • 285. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/3 of 1/2?© Activities for Learning, Inc. 2012
  • 286. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/3 of 1/2?© Activities for Learning, Inc. 2012
  • 287. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/3 of 1/2?© Activities for Learning, Inc. 2012
  • 288. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10 What is 1/3 of 1/2? That’s multiplying fractions!© Activities for Learning, Inc. 2012
  • 289. Multiplying Fractions© Activities for Learning, Inc. 2012
  • 290. Multiplying Fractions Multiplying is not exclusively repeated addition.© Activities for Learning, Inc. 2012
  • 291. Multiplying Fractions Multiplying is not exclusively repeated addition. Area is another facet of multiplication.© Activities for Learning, Inc. 2012
  • 292. Multiplying Fractions 1x1 = 2 2© Activities for Learning, Inc. 2012
  • 293. Multiplying Fractions 1x1 = 2 2 One half of one half© Activities for Learning, Inc. 2012
  • 294. Multiplying Fractions 1x1 = 2 2 One half of one half© Activities for Learning, Inc. 2012
  • 295. Multiplying Fractions 1x1 = 2 2 One half of one half© Activities for Learning, Inc. 2012
  • 296. Multiplying Fractions 1x1 = 2 2 One half of one half© Activities for Learning, Inc. 2012
  • 297. Multiplying Fractions 1x1 = 2 2 One half of one half© Activities for Learning, Inc. 2012
  • 298. Multiplying Fractions 1x1 = 2 2 One half of one half© Activities for Learning, Inc. 2012
  • 299. Multiplying Fractions 1x1 =1 2 2 4 One half of one half© Activities for Learning, Inc. 2012
  • 300. Multiplying Fractions 1x1 =1 2 2 4 One half of one half© Activities for Learning, Inc. 2012
  • 301. Multiplying Fractions 2x3 = 3 4© Activities for Learning, Inc. 2012
  • 302. Multiplying Fractions 2x3 = 3 4 Three fourths of two thirds© Activities for Learning, Inc. 2012
  • 303. Multiplying Fractions 2x3 = 3 4 Three fourths of two thirds© Activities for Learning, Inc. 2012
  • 304. Multiplying Fractions 2x3 = 3 4 Three fourths of two thirds© Activities for Learning, Inc. 2012
  • 305. Multiplying Fractions 2x3 = 3 4 Three fourths of two thirds© Activities for Learning, Inc. 2012
  • 306. Multiplying Fractions 2x3 = 3 4 Three fourths of two thirds© Activities for Learning, Inc. 2012
  • 307. Multiplying Fractions 2x3 = 3 4 Three fourths of two thirds© Activities for Learning, Inc. 2012
  • 308. Multiplying Fractions 2x3 = 6 3 4 12 Three fourths of two thirds© Activities for Learning, Inc. 2012
  • 309. Multiplying Fractions 2x3 = 6 3 4 12 Three fourths of two thirds© Activities for Learning, Inc. 2012
  • 310. Multiplying Fractions 2x3 = 6 3 4 12 Three fourths of two thirds© Activities for Learning, Inc. 2012
  • 311. Multiplying Fractions 2x3 = 6 = 1 3 4 12 2 Three fourths of two thirds© Activities for Learning, Inc. 2012
  • 312. Multiplying Fractions 2x3 = 6 3 4 12 The total number of rectangles is© Activities for Learning, Inc. 2012
  • 313. Multiplying Fractions 2x3 = 6 3 4 12 The total number of rectangles is 3 x 4.© Activities for Learning, Inc. 2012
  • 314. Multiplying Fractions 2x3 = 6 3 4 12 The total number of rectangles is 3 x 4.© Activities for Learning, Inc. 2012
  • 315. Multiplying Fractions 2x3 = 6 3 4 12 The total number of rectangles is 3 x 4. The number of double crosshatched rectangles is© Activities for Learning, Inc. 2012
  • 316. Multiplying Fractions 2x3 = 6 3 4 12 The total number of rectangles is 3 x 4. The number of double crosshatched rectangles is 2 x 3.© Activities for Learning, Inc. 2012
  • 317. Multiplying Fractions 2x3 = 6 3 4 12 The total number of rectangles is 3 x 4. The number of double crosshatched rectangles is 2 x 3.© Activities for Learning, Inc. 2012
  • 318. Multiplying Fractions 2x3 = 6 3 4 12 The total number of rectangles is 3 x 4. The number of double crosshatched rectangles is 2 x 3.© Activities for Learning, Inc. 2012
  • 319. What about dividing fractions?© Activities for Learning, Inc. 2012
  • 320. What is Division?© Activities for Learning, Inc. 2012
  • 321. What is Division? Process of separating into equal groups© Activities for Learning, Inc. 2012
  • 322. What is Division? Process of separating into equal groups  either number of groups, or© Activities for Learning, Inc. 2012
  • 323. What is Division? Process of separating into equal groups  either number of groups, or  size of the groups© Activities for Learning, Inc. 2012
  • 324. What is Division? 6 ÷ 2 = __© Activities for Learning, Inc. 2012
  • 325. What is Division? 6 ÷ 2 = __ How many 2s in 6?© Activities for Learning, Inc. 2012
  • 326. What is Division? 6 ÷ 2 = __ How many 2s in 6?© Activities for Learning, Inc. 2012
  • 327. What is Division? 6 ÷ 2 = __ How many 2s in 6? Number of groups of 2s© Activities for Learning, Inc. 2012
  • 328. What is Division? 6 ÷ 2 = __ How many 2s in 6? Number of groups of 2s© Activities for Learning, Inc. 2012
  • 329. What is Division? 6 ÷ 2 = __ How many 2s in 6? Number of groups of 2s; 3 groups© Activities for Learning, Inc. 2012
  • 330. Dividing Fractions 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 331. Dividing Fractions 1÷ 1 = 2 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 332. Dividing Fractions 1÷ 1 = 2 How many 1/2s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 333. Dividing Fractions 1÷ 1 = 2 How many 1/2s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 334. Dividing Fractions 1÷ 1 = 2 How many 1/2s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 335. Dividing Fractions 1÷ 1 = 2 How many 1/2s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 336. Dividing Fractions 1÷ 1 = 2 2 How many 1/2s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 337. Dividing Fractions 1÷ 1 = 2 2 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 338. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 = 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 339. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 = How many 1/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 340. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 = How many 1/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 341. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 = How many 1/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 342. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 = How many 1/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 343. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 = How many 1/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 344. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 How many 1/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 345. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 346. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 1÷ 2 = 3 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 347. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 1÷ 2 = 3 How many 2/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 348. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 1÷ 2 = 3 How many 2/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 349. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 1÷ 2 = 3 How many 2/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 350. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 1÷ 2 = 3 How many 2/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 351. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 1÷ 2 = 3 How many 2/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 352. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 1 ÷ 2 = 11 3 2 How many 2/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 353. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 1 ÷ 2 = 11 = 3 3 2 2 How many 2/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 354. Dividing Fractions 1÷ 1 = 2 2 1 1÷ 3 =3 1÷ 2 = 3 3 2 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 355. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 1÷ 3 =3 1÷ 2 = 3 3 2 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 356. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1÷ 3 =3 1÷ 2 = 3 3 2 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 357. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1÷ 3 =3 1÷ 2 = 3 3 2 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 358. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1÷ 3 =3 1÷ 3 = 1÷ 2 = 3 3 2 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 359. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 360. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 361. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 362. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 How many 4/3s in 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 363. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 How many 4/3s in 1? 1 1 1 2 2 1 1 1 1 3 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 364. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 How many 4/3s in 1? 1 1 1 2 2 1 1 1 1 3 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 365. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 How many 4/3s in 1? [Less than 1] 1 1 1 2 2 1 1 1 1 3 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 366. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 How many 4/3s in 1? 1 1 1 2 2 1 1 1 1 3 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 367. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 How many 4/3s in 1? 1 1 2 2 1 1 1 2 2 1 1 1 1 3 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 368. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 How many 4/3s in 1? 1 1 1 2 2 1 1 1 1 3 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 369. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 How many 4/3s in 1? 1 1 1 1 4 4 4 4 1 1 1 2 2 1 1 1 1 3 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 370. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 How many 4/3s in 1? 1 1 1 4 4 4 1 1 1 2 2 1 1 1 1 3 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 371. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 3 4 How many 4/3s in 1? 1 1 1 4 4 4 1 1 1 2 2 1 1 1 1 3 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 372. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 3 4 1 1 1 4 4 4 1 1 1 2 2 1 1 1 1 3 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 373. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 3 4 Each green pair is a reciprocal,© Activities for Learning, Inc. 2012
  • 374. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 3 4 Each green pair is a reciprocal, sometimes called a multiplicative inverse.© Activities for Learning, Inc. 2012
  • 375. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 3 4 Each green pair is a reciprocal, sometimes called a multiplicative inverse. When multiplied together, they equal 1.© Activities for Learning, Inc. 2012
  • 376. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1÷ 3 =3 1÷ 3 = 3 1÷ 2 = 3 3 2 1÷ 4= 3 3 4 Sometimes textbooks put a 1 under a whole number to make it look like a fraction,© Activities for Learning, Inc. 2012
  • 377. Dividing Fractions 1÷ 1 = 2 2 1÷ 2 = 1 2 1 1 1 1 1÷ 3 =3 1÷ 3 = 3 1 1 1÷ 2 = 3 3 2 1÷ 4= 3 3 4 Sometimes textbooks put a 1 under a whole number to make it look like a fraction, but it is not necessary.© Activities for Learning, Inc. 2012
  • 378. Dividing Fractions 2 3 3 ÷4 = 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 379. Dividing Fractions 2 3 3 ÷4 = Is the answer more or less than 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 380. Dividing Fractions 2 3 3 ÷4 = Is the answer more or less than 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 381. Dividing Fractions 2 3 3 ÷4 = Is the answer more or less than 1? 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 382. Dividing Fractions 2 3 8 3 ÷4 = 9 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4© Activities for Learning, Inc. 2012
  • 383. Fraction Chart 1 1 1 2 2 1 1 1 3 3 3 1 1 1 1 4 4 4 4 1 1 1 1 1 5 5 5 5 5 1 1 1 1 1 1 6 6 6 6 6 6 1 1 1 1 1 1 1 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 8 8 8 8 8 8 8 8 1 1 1 1 1 1 1 1 1 9 9 9 9 9 9 9 9 9 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10© Activities for Learning, Inc. 2012
  • 384. Fraction Chart Allow the student to explore the whole picture© Activities for Learning, Inc. 2012
  • 385. Fraction Chart Allow the student to explore the whole picture and relationships within the whole© Activities for Learning, Inc. 2012
  • 386. Fraction Chart Allow the student to explore the whole picture and relationships within the whole using the linear perspective.© Activities for Learning, Inc. 2012
  • 387. Focusing on Fractions 3 2 5 5 Presented by Kathleen Cotter Lawer Based on the work of Joan A. Cotter, Ph.D.© Activities for Learning, Inc. 2012

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