Focusing on Fractions                                           3       2                                           5     ...
Joan A. Cotter, Ph.D.
Joan A. Cotter, Ph.D.  • Engineer from University of Wisconsin
Joan A. Cotter, Ph.D.  • Engineer from University of Wisconsin  • Montessori Educator
Joan A. Cotter, Ph.D.  • Engineer from University of Wisconsin  • Montessori Educator  • Math Games
Joan A. Cotter, Ph.D.  •   Engineer from University of Wisconsin  •   Montessori Educator  •   Math Games  •   Tutor
Joan A. Cotter, Ph.D.  •   Engineer from University of Wisconsin  •   Montessori Educator  •   Math Games  •   Tutor  •   ...
Joan A. Cotter, Ph.D.  •   Engineer from University of Wisconsin  •   Montessori Educator  •   Math Games  •   Tutor  •   ...
Joan A. Cotter, Ph.D.  •   Engineer from University of Wisconsin  •   Montessori Educator  •   Math Games  •   Tutor  •   ...
How are fractions                                        usually taught?© Activities for Learning, Inc. 2012
Fraction Model: “Fish Tank”© Activities for Learning, Inc. 2012
Fraction Model: “Fish Tank”                                       2© Activities for Learning, Inc. 2012
Fraction Model: “Fish Tank”                                       2                                       5© Activities fo...
Fraction Model: “Words”                                       This is fourths.© Activities for Learning, Inc. 2012
Fraction Model: “Words”                                       This is fourths.   This is thirds.© Activities for Learning,...
Fraction Model: “Words”                                       This is fourths.   This is thirds.             If this were ...
Fraction Model: “Words”                                       This is fourths.   This is thirds.             If this were ...
Fraction Model: “Rounded Corner”                                           1       1       1                              ...
Fraction Model: “Rounded Corner”                                           1       1       1                              ...
Fraction Models: Circles© Activities for Learning, Inc. 2012
Fraction Models: Circles                                                                   1               1              ...
Fraction Models: Circles                             Are we comparing angles, arcs, or area?© Activities for Learning, Inc...
Fraction Models: Circles                       Experts in visual literacy say that                       comparing quantit...
Fraction Models: Circles                       Experts in visual literacy say that                       comparing quantit...
So how should we                                        teach fractions?© Activities for Learning, Inc. 2012
Fraction Model: Linear Chart                                                                                           1  ...
Fraction Model: “Color”                                                                                              1    ...
Fraction Model: “Missing Parts”                                                                                      1    ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Definition of a Fraction© Activities for Learning, Inc. 2012
Definition of a Fraction   A fraction is part of a set or part of a whole.                                       Textbook ...
Definition of a Fraction   A fraction is part of a set or part of a whole.                                                ...
Definition of a Fraction                        An expression that indicates the                        quotient of two qu...
Definition of a Fraction                        An expression that indicates the                        quotient of two qu...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Naming© Activities for Learning, Inc. 2012
Fraction Naming© Activities for Learning, Inc. 2012
Fraction Naming                                       One divided into 2 equal parts.© Activities for Learning, Inc. 2012
Fraction Naming                                       One divided into 2 equal parts.© Activities for Learning, Inc. 2012
Fraction Naming                                       One divided into 2 equal parts.                                     ...
Fraction Naming                                       One divided into 2 equal parts.                                     ...
Fraction Naming                                       One divided into 2 equal parts.                                     ...
Fraction Naming                                       One divided into 3 equal parts.© Activities for Learning, Inc. 2012
Fraction Naming                                       One divided into 3 equal parts.                                     ...
Fraction Naming                                       One divided into 3 equal parts.                                     ...
Fraction Naming                                       One divided into 3 equal parts.                                     ...
Fraction Naming                                       One divided into 3 equal parts.                                     ...
Fraction Naming                                       One divided into 3 equal parts.                                     ...
Fraction Naming                                                        1                                       1          ...
Fraction Naming                                                        1                                       1          ...
How should we practice                                     what we learned?© Activities for Learning, Inc. 2012
Games© Activities for Learning, Inc. 2012
Games                                       Games                                        Math© Activities for Learning, In...
Games                                       Games                                               =                         ...
Games                                       Games        Books                                               =            ...
Games                                       Games             Books                                                =      ...
Games                                       Games             Books                                                =      ...
Unit Fraction War© Activities for Learning, Inc. 2012
Unit Fraction War                   Purpose: Practice for naming and                   comparing unit fractions.© Activiti...
Unit Fraction War                   Purpose: Practice for naming and                   comparing unit fractions.          ...
Unit Fraction War                   Purpose: Practice for naming and                   comparing unit fractions.          ...
Unit Fraction War© Activities for Learning, Inc. 2012
Unit Fraction War                                       1   1                                       4   5© Activities for ...
Unit Fraction War                                       1   1                                       4   5© Activities for ...
Unit Fraction War© Activities for Learning, Inc. 2012
Unit Fraction War                                       1   1                                       8   2© Activities for ...
Unit Fraction War                                       1   1                                       8   2© Activities for ...
Unit Fraction War© Activities for Learning, Inc. 2012
Unit Fraction War                                       1   1                                       6   6© Activities for ...
Unit Fraction War                                       1   1                                       6   6© Activities for ...
Unit Fraction War                                       1       1                                       6       6         ...
Unit Fraction War© Activities for Learning, Inc. 2012
Unit Fraction War                                       1   1                                       2   3© Activities for ...
More Fraction Naming© Activities for Learning, Inc. 2012
More Fraction Naming                                           1                                       1   1   1          ...
More Fraction Naming                                           1                                       1   1         1    ...
More Fraction Naming                                           1                                       1   1         1    ...
More Fraction Naming                                           1                                       1   1         1    ...
More Fraction Naming                                           1                                       1   1         1    ...
More Fraction Naming                                       1© Activities for Learning, Inc. 2012
More Fraction Naming                                       1   1© Activities for Learning, Inc. 2012
More Fraction Naming                                       1                         1                                    ...
More Fraction Naming                                       1                         1                                    ...
More Fraction Naming                                       1                         1                                    ...
More Fraction Naming                                           1                         1                                ...
More Fraction Naming                                           1                         1                                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Concentrating on One Game                   Purpose: To help the children realize that                   5 fifths, 8 eight...
Concentrating on One Game                   Purpose: To help the children realize that                   5 fifths, 8 eight...
Concentrating on One© Activities for Learning, Inc. 2012
Concentrating on One© Activities for Learning, Inc. 2012
Concentrating on One                                 3                                 5© Activities for Learning, Inc. 2012
Concentrating on One                                 3                                 5© Activities for Learning, Inc. 2012
Concentrating on One                                 3                                 5© Activities for Learning, Inc. 2012
Concentrating on One                                 3                                 5                                  ...
Concentrating on One© Activities for Learning, Inc. 2012
Concentrating on One                                       3                                       8© Activities for Learn...
Concentrating on One                                       3                                       8© Activities for Learn...
Concentrating on One                                       3                                       8© Activities for Learn...
Concentrating on One                                           7                                           8              ...
Concentrating on One© Activities for Learning, Inc. 2012
Concentrating on One                                       5                                       8© Activities for Learn...
Concentrating on One                                       5                                       8© Activities for Learn...
Concentrating on One                                       5                                       8© Activities for Learn...
Concentrating on One                                       5                                       8                      ...
Concentrating on One© Activities for Learning, Inc. 2012
Let’s begin to compare                                             fractions….© Activities for Learning, Inc. 2012
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
Fraction Stairs                              1                             10                              1              ...
Fraction Stairs                              1                             10                              1              ...
Fraction Chart                                                                                           1                ...
Fraction Chart                                                                                           1                ...
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Focusing on Fractions

  1. 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. 2. Joan A. Cotter, Ph.D.
  3. 3. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin
  4. 4. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator
  5. 5. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator • Math Games
  6. 6. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator • Math Games • Tutor
  7. 7. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator • Math Games • Tutor • AL Abacus
  8. 8. Joan A. Cotter, Ph.D. • Engineer from University of Wisconsin • Montessori Educator • Math Games • Tutor • AL Abacus • Middle-School Teacher
  9. 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. 10. How are fractions usually taught?© Activities for Learning, Inc. 2012
  11. 11. Fraction Model: “Fish Tank”© Activities for Learning, Inc. 2012
  12. 12. Fraction Model: “Fish Tank” 2© Activities for Learning, Inc. 2012
  13. 13. Fraction Model: “Fish Tank” 2 5© Activities for Learning, Inc. 2012
  14. 14. Fraction Model: “Words” This is fourths.© Activities for Learning, Inc. 2012
  15. 15. Fraction Model: “Words” This is fourths. This is thirds.© Activities for Learning, Inc. 2012
  16. 16. Fraction Model: “Words” This is fourths. This is thirds. If this were chocolate…© Activities for Learning, Inc. 2012
  17. 17. Fraction Model: “Words” This is fourths. This is thirds. If this were chocolate…© Activities for Learning, Inc. 2012
  18. 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. 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. 20. Fraction Models: Circles© Activities for Learning, Inc. 2012
  21. 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. 22. Fraction Models: Circles Are we comparing angles, arcs, or area?© Activities for Learning, Inc. 2012
  23. 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. 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. 25. So how should we teach fractions?© Activities for Learning, Inc. 2012
  26. 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. 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. 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. 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. 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. 31. Definition of a Fraction© Activities for Learning, Inc. 2012
  32. 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. 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. 34. Definition of a Fraction An expression that indicates the quotient of two quantities. American Heritage Dictionary© Activities for Learning, Inc. 2012
  35. 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. 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. 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. 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. 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. 40. Fraction Naming© Activities for Learning, Inc. 2012
  41. 41. Fraction Naming© Activities for Learning, Inc. 2012
  42. 42. Fraction Naming One divided into 2 equal parts.© Activities for Learning, Inc. 2012
  43. 43. Fraction Naming One divided into 2 equal parts.© Activities for Learning, Inc. 2012
  44. 44. Fraction Naming One divided into 2 equal parts. One divided into 3 equal parts.© Activities for Learning, Inc. 2012
  45. 45. Fraction Naming One divided into 2 equal parts. One divided into 3 equal parts.© Activities for Learning, Inc. 2012
  46. 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. 47. Fraction Naming One divided into 3 equal parts.© Activities for Learning, Inc. 2012
  48. 48. Fraction Naming One divided into 3 equal parts. 1 One whole© Activities for Learning, Inc. 2012
  49. 49. Fraction Naming One divided into 3 equal parts. 1 One whole divided into© Activities for Learning, Inc. 2012
  50. 50. Fraction Naming One divided into 3 equal parts. 1 One whole divided into 3 three equal parts© Activities for Learning, Inc. 2012
  51. 51. Fraction Naming One divided into 3 equal parts. 1 One divided by 3 three© Activities for Learning, Inc. 2012
  52. 52. Fraction Naming One divided into 3 equal parts. 1 Read as “one-third.” 3© Activities for Learning, Inc. 2012
  53. 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. 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. 55. How should we practice what we learned?© Activities for Learning, Inc. 2012
  56. 56. Games© Activities for Learning, Inc. 2012
  57. 57. Games Games Math© Activities for Learning, Inc. 2012
  58. 58. Games Games = Math© Activities for Learning, Inc. 2012
  59. 59. Games Games Books = Math Reading© Activities for Learning, Inc. 2012
  60. 60. Games Games Books = Math Reading Games provide interesting repetition needed for automaticity.© Activities for Learning, Inc. 2012
  61. 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. 62. Unit Fraction War© Activities for Learning, Inc. 2012
  63. 63. Unit Fraction War Purpose: Practice for naming and comparing unit fractions.© Activities for Learning, Inc. 2012
  64. 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. 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. 66. Unit Fraction War© Activities for Learning, Inc. 2012
  67. 67. Unit Fraction War 1 1 4 5© Activities for Learning, Inc. 2012
  68. 68. Unit Fraction War 1 1 4 5© Activities for Learning, Inc. 2012
  69. 69. Unit Fraction War© Activities for Learning, Inc. 2012
  70. 70. Unit Fraction War 1 1 8 2© Activities for Learning, Inc. 2012
  71. 71. Unit Fraction War 1 1 8 2© Activities for Learning, Inc. 2012
  72. 72. Unit Fraction War© Activities for Learning, Inc. 2012
  73. 73. Unit Fraction War 1 1 6 6© Activities for Learning, Inc. 2012
  74. 74. Unit Fraction War 1 1 6 6© Activities for Learning, Inc. 2012
  75. 75. Unit Fraction War 1 1 6 6 1 1 3 4© Activities for Learning, Inc. 2012
  76. 76. Unit Fraction War© Activities for Learning, Inc. 2012
  77. 77. Unit Fraction War 1 1 2 3© Activities for Learning, Inc. 2012
  78. 78. More Fraction Naming© Activities for Learning, Inc. 2012
  79. 79. More Fraction Naming 1 1 1 1 3 3 3© Activities for Learning, Inc. 2012
  80. 80. More Fraction Naming 1 1 1 1 3 3 3 One-third taken 2 times.© Activities for Learning, Inc. 2012
  81. 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. 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. 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. 84. More Fraction Naming 1© Activities for Learning, Inc. 2012
  85. 85. More Fraction Naming 1 1© Activities for Learning, Inc. 2012
  86. 86. More Fraction Naming 1 1 Two divided into 3 equal parts.© Activities for Learning, Inc. 2012
  87. 87. More Fraction Naming 1 1 Two divided into 3 equal parts. 2 Two divided by 3 three© Activities for Learning, Inc. 2012
  88. 88. More Fraction Naming 1 1 Two divided into 3 equal parts. 2 Two divided by 3 three© Activities for Learning, Inc. 2012
  89. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 100. Concentrating on One© Activities for Learning, Inc. 2012
  101. 101. Concentrating on One© Activities for Learning, Inc. 2012
  102. 102. Concentrating on One 3 5© Activities for Learning, Inc. 2012
  103. 103. Concentrating on One 3 5© Activities for Learning, Inc. 2012
  104. 104. Concentrating on One 3 5© Activities for Learning, Inc. 2012
  105. 105. Concentrating on One 3 5 2 5© Activities for Learning, Inc. 2012
  106. 106. Concentrating on One© Activities for Learning, Inc. 2012
  107. 107. Concentrating on One 3 8© Activities for Learning, Inc. 2012
  108. 108. Concentrating on One 3 8© Activities for Learning, Inc. 2012
  109. 109. Concentrating on One 3 8© Activities for Learning, Inc. 2012
  110. 110. Concentrating on One 7 8 3 8© Activities for Learning, Inc. 2012
  111. 111. Concentrating on One© Activities for Learning, Inc. 2012
  112. 112. Concentrating on One 5 8© Activities for Learning, Inc. 2012
  113. 113. Concentrating on One 5 8© Activities for Learning, Inc. 2012
  114. 114. Concentrating on One 5 8© Activities for Learning, Inc. 2012
  115. 115. Concentrating on One 5 8 3 8© Activities for Learning, Inc. 2012
  116. 116. Concentrating on One© Activities for Learning, Inc. 2012
  117. 117. Let’s begin to compare fractions….© Activities for Learning, Inc. 2012
  118. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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

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