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# Focusing on Fractions

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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