Weitere ähnliche Inhalte Mehr von rightstartmath (20) Kürzlich hochgeladen (20) 1. How Visualization Enhances
Montessori Mathematics PART 2
by Joan A. Cotter, Ph.D.
JoanCotter@RightStartMath.com
Montessori Foundation
Conference
Friday, Nov 2, 2012
Sarasota, Florida
8 16 24 32 40
3 2
5 5
PowerPoint Presentation & Handout
RightStartMath.com >Resources © Joan A. Cotter, Ph.D., 2012
25. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
26. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
27. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
Tens:
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
28. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
Tens:
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
29. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
Tens: 20
+ 30
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
30. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
50 +
Tens: 20
+ 30
50
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
31. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
50 +
Tens: 20 Ones:
+ 30
50
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
32. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
50 +
Tens: 20 Ones:
+ 30
50
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
33. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
50 +
Tens: 20 Ones: 3
+ 30 ×2
50
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
34. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
50 + 6
Tens: 20 Ones: 3
+ 30 ×2
50 6
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
35. Multiplication on the AL Abacus
For facts > 5 × 5
7×8=
50 + 6 = 56
Tens: 20 Ones: 3
+ 30 ×2
50 6
This method was used in the Middle Ages,
rather than memorize the facts > 5 × 5.
© Joan A. Cotter, Ph.D., 2012
41. Multiplication on the AL Abacus
For facts > 5 × 5
9×7=
60 +
Tens: 40
+ 20
60
© Joan A. Cotter, Ph.D., 2012
42. Multiplication on the AL Abacus
For facts > 5 × 5
9×7=
60 +
Tens: 40 Ones:
+ 20
60
© Joan A. Cotter, Ph.D., 2012
43. Multiplication on the AL Abacus
For facts > 5 × 5
9×7=
60 +
Tens: 40 Ones:
+ 20
60
© Joan A. Cotter, Ph.D., 2012
44. Multiplication on the AL Abacus
For facts > 5 × 5
9×7=
60 +
Tens: 40 Ones: 1
+ 20 ×3
60
© Joan A. Cotter, Ph.D., 2012
45. Multiplication on the AL Abacus
For facts > 5 × 5
9×7=
60 + 3
Tens: 40 Ones: 1
+ 20 ×3
60 3
© Joan A. Cotter, Ph.D., 2012
46. Multiplication on the AL Abacus
For facts > 5 × 5
9×7=
60 + 3 = 63
Tens: 40 Ones: 1
+ 20 ×3
60 3
© Joan A. Cotter, Ph.D., 2012
53. Multiples Patterns
Twos
2 4 6 8 10
12 14 16 18 20
The ones repeat in the second row.
© Joan A. Cotter, Ph.D., 2012
54. Multiples Patterns
Fours
4 8 12 16 20
24 28 32 36 40
The ones repeat in the second row.
© Joan A. Cotter, Ph.D., 2012
55. Multiples Patterns
Sixes and Eights
6 12 18 24 30
36 42 48 54 60
8 16 24 32 40
48 56 64 72 80
© Joan A. Cotter, Ph.D., 2012
56. Multiples Patterns
Sixes and Eights
6 12 18 24 30
36 42 48 54 60
8 16 24 32 40
48 56 64 72 80
© Joan A. Cotter, Ph.D., 2012
57. Multiples Patterns
Sixes and Eights
6 12 18 24 30
36 42 48 54 60
8 16 24 32 40
48 56 64 72 80
© Joan A. Cotter, Ph.D., 2012
58. Multiples Patterns
Sixes and Eights
6 12 18 24 30
36 42 48 54 60
8 16 24 32 40
48 56 64 72 80
The ones in the 8s show the multiples of 2.
© Joan A. Cotter, Ph.D., 2012
59. Multiples Patterns
Sixes and Eights
6 12 18 24 30
36 42 48 54 60
8 16 24 32 40
48 56 64 72 80
The ones in the 8s show the multiples of 2.
© Joan A. Cotter, Ph.D., 2012
60. Multiples Patterns
Sixes and Eights
6 12 18 24 30
36 42 48 54 60
8 16 24 32 40
48 56 64 72 80
The ones in the 8s show the multiples of 2.
© Joan A. Cotter, Ph.D., 2012
61. Multiples Patterns
Sixes and Eights
6 12 18 24 30
36 42 48 54 60
8 16 24 32 40
48 56 64 72 80
The ones in the 8s show the multiples of 2.
© Joan A. Cotter, Ph.D., 2012
62. Multiples Patterns
Sixes and Eights
6 12 18 24 30
36 42 48 54 60
8 16 24 32 40
48 56 64 72 80
The ones in the 8s show the multiples of 2.
© Joan A. Cotter, Ph.D., 2012
63. Multiples Patterns
Sixes and Eights
6 12 18 24 30 6× 4
36 42 48 54 60
8 16 24 32 40
48 56 64 72 80
6 × 4 is the fourth number (multiple).
© Joan A. Cotter, Ph.D., 2012
64. Multiples Patterns
Sixes and Eights
6 12 18 24 30
36 42 48 54 60
8 16 24 32 40
48 56 64 72 80 8× 7
8 × 7 is the seventh number (multiple).
© Joan A. Cotter, Ph.D., 2012
65. Multiples Patterns
Nines
9 18 27 36 45
90 81 72 63 54
The second row is written in reverse order.
Also the digits in each number add to 9.
© Joan A. Cotter, Ph.D., 2012
66. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
67. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
68. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
69. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
70. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
71. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
72. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
73. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
74. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
75. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
76. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Observe the ones.
© Joan A. Cotter, Ph.D., 2012
77. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
The tens are the same in each row.
© Joan A. Cotter, Ph.D., 2012
78. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Add the digits in the columns.
© Joan A. Cotter, Ph.D., 2012
79. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Add the digits in the columns.
© Joan A. Cotter, Ph.D., 2012
80. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Add the digits in the columns.
© Joan A. Cotter, Ph.D., 2012
81. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Add the “opposites.”
© Joan A. Cotter, Ph.D., 2012
82. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Add the “opposites.”
© Joan A. Cotter, Ph.D., 2012
83. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Add the “opposites.”
© Joan A. Cotter, Ph.D., 2012
84. Multiples Patterns
Threes
3 6 9
12 15 18
21 24 27
30
The 3s have several patterns:
Add the “opposites.”
© Joan A. Cotter, Ph.D., 2012
85. Multiples Patterns
Sevens
7 14 21
28 35 42
49 56 63
70
The 7s have the 1, 2, 3… pattern.
© Joan A. Cotter, Ph.D., 2012
86. Multiples Patterns
Sevens
7 14 21
28 35 42
49 56 63
70
The 7s have the 1, 2, 3… pattern.
© Joan A. Cotter, Ph.D., 2012
87. Multiples Patterns
Sevens
7 14 21
28 35 42
49 56 63
70
The 7s have the 1, 2, 3… pattern.
© Joan A. Cotter, Ph.D., 2012
88. Multiples Patterns
Sevens
7 14 21
28 35 42
49 56 63
70
The 7s have the 1, 2, 3… pattern.
© Joan A. Cotter, Ph.D., 2012
89. Multiples Patterns
Sevens
7 14 21
28 35 42
49 56 63
70
Look at the tens.
© Joan A. Cotter, Ph.D., 2012
90. Multiples Patterns
Sevens
7 14 21
28 35 42
49 56 63
70
Look at the tens.
© Joan A. Cotter, Ph.D., 2012
91. Multiples Patterns
Sevens
7 14 21
28 35 42
49 56 63
70
Look at the tens.
© Joan A. Cotter, Ph.D., 2012
94. Multiples Memory
Objective:
To help the players learn the
multiples patterns.
Object of the game:
To be the first player to collect all ten
cards of a multiple in order.
© Joan A. Cotter, Ph.D., 2012
95. Multiples Memory
7 14 21
28 35 42
49 56 63
70
The 7s envelope contains 10 cards,
each with one of the numbers listed.
© Joan A. Cotter, Ph.D., 2012
96. Multiples Memory
8 16 24 32 40
48 56 64 72 80
The 8s envelope contains 10 cards,
each with one of the numbers listed.
© Joan A. Cotter, Ph.D., 2012
97. Multiples Memory
7 14 21
28 35 42 8 16 24 32 40
49 56 63 48 56 64 72 80
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
© Joan A. Cotter, Ph.D., 2012
98. Multiples Memory
7 14 21
28 35 42 8 16 24 32 40
49 56 63 48 56 64 72 80
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
© Joan A. Cotter, Ph.D., 2012
99. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
© Joan A. Cotter, Ph.D., 2012
100. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63 14
70
© Joan A. Cotter, Ph.D., 2012
101. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
© Joan A. Cotter, Ph.D., 2012
102. Multiples Memory
8 16 24 32 40
48 56 64 72 80
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
© Joan A. Cotter, Ph.D., 2012
103. Multiples Memory
8 16 24 32 40
48 56 64 72 80
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
40
© Joan A. Cotter, Ph.D., 2012
104. Multiples Memory
8 16 24 32 40
48 56 64 72 80
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
© Joan A. Cotter, Ph.D., 2012
105. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
© Joan A. Cotter, Ph.D., 2012
106. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
8
© Joan A. Cotter, Ph.D., 2012
107. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
© Joan A. Cotter, Ph.D., 2012
108. Multiples Memory
8 16 24 32 40
48 56 64 72 80
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
© Joan A. Cotter, Ph.D., 2012
109. Multiples Memory
8 16 24 32 40
48 56 64 72 80
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
8
© Joan A. Cotter, Ph.D., 2012
110. Multiples Memory
8 16 24 32 40
48 56 64 72 80
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70 8
© Joan A. Cotter, Ph.D., 2012
111. Multiples Memory
8 16 24 32 40
48 56 64 72 80
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63 56
70 8
© Joan A. Cotter, Ph.D., 2012
112. Multiples Memory
8 16 24 32 40
48 56 64 72 80
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70 8
© Joan A. Cotter, Ph.D., 2012
113. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70 8
© Joan A. Cotter, Ph.D., 2012
114. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70 8
© Joan A. Cotter, Ph.D., 2012
115. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70 8
7
© Joan A. Cotter, Ph.D., 2012
116. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63 14
70 8
7
© Joan A. Cotter, Ph.D., 2012
117. Multiples Memory
7 14 21
28 35 42
49 56 63
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70 8
7 14
© Joan A. Cotter, Ph.D., 2012
118. Multiples Memory
7 14 21
28 35 42
49 56 63
70
24
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70 8
7 14
© Joan A. Cotter, Ph.D., 2012
119. Multiples Memory
7 14 21
28 35 42 8 16 24 32 40
49 56 63 48 56 64 72 80
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70 8
7 14
© Joan A. Cotter, Ph.D., 2012
120. Multiples Memory
7 14 21
28 35 42 8 16 24 32 40
49 56 63 48 56 64 72 80
70
7 14 21 8 16 24 32 40
28 35 42 48 56 64 72 80
49 56 63
70
© Joan A. Cotter, Ph.D., 2012
122. Multiplication Memory
Objective:
To help the players master the
multiplication facts.
Object of the game:
To collect the most cards by matching
the multiplier with the product.
© Joan A. Cotter, Ph.D., 2012
124. Multiplication Memory
1 2 3 4 5
6 7 8 9 10
Materials Needed:
• Ten basic cards, numbered 1 to 10
© Joan A. Cotter, Ph.D., 2012
125. Multiplication Memory
3
1 2 3 4 5
3 6 9
12 15 18
6 7 8 9 10 21 24 27
30
Materials Needed:
• Ten basic cards, numbered 1 to 10
• A set of product cards (3s used here)
© Joan A. Cotter, Ph.D., 2012
126. Multiplication Memory
3
1 2 3 4 5 3x
3 6 9
12 15 18
6 7 8 9 10 21 24 27
30
Materials Needed:
• Ten basic cards, numbered 1 to 10
• A set of product cards (3s used here)
• A stickie note with “3 x” written on it
© Joan A. Cotter, Ph.D., 2012
127. Multiplication Memory
3
1 2 3 4 5 3x
3 6 9
12 15 18
6 7 8 9 10 21 24 27
30 =
Materials Needed:
• Ten basic cards, numbered 1 to 10
• A set of product cards (3s used here)
• A stickie with “3 x” written on it
• A stickie with “=” written on it
© Joan A. Cotter, Ph.D., 2012
128. Multiplication Memory
3
1 2 3 4 5 3x
3 6 9
12 15 18
6 7 8 9 10 21 24 27
30 =
Materials Needed:
• Ten basic cards, numbered 1 to 10
• A set of product cards (3s used here)
• A stickie with “3 x” written on it
• A stickie with “=” written on it
• A manipulative with groups of five
© Joan A. Cotter, Ph.D., 2012
134. Multiplication Memory
5
3x =
3 taken 5 times
equals 15.
3 6 9
12 15 18
21 24 27
30
© Joan A. Cotter, Ph.D., 2012
135. Multiplication Memory
5 21
3x =
3 taken 5 times
equals 15.
3 6 9
12 15 18
21 24 27
30
© Joan A. Cotter, Ph.D., 2012
142. Multiplication Memory
21
3x =
7
3 taken 7 times
equals 21.
3 6 9
12 15 18
21 24 27
30
© Joan A. Cotter, Ph.D., 2012
143. Multiplication Memory
3x =
3 taken 7 times
equals 21.
3 6 9
12 15 18 7 21
21 24 27
30
© Joan A. Cotter, Ph.D., 2012
147. Multiplication Memory
3x =
2
3
3 taken 3 times
equals 9.
3 6 9
12 15 18 7 21
21 24 27
30
© Joan A. Cotter, Ph.D., 2012
148. Multiplication Memory
3x =
2
3 12
3 taken 3 times
equals 9.
3 6 9
12 15 18 7 21
21 24 27
30
© Joan A. Cotter, Ph.D., 2012
153. Multiplication Memory
5
3x =
3 taken 5 times
equals 15.
3 6 9
12 15 18 7 21
21 24 27
30
© Joan A. Cotter, Ph.D., 2012
154. Multiplication Memory
5
3x =
15
3 taken 5 times
equals 15.
3 6 9
12 15 18 7 21
21 24 27
30
© Joan A. Cotter, Ph.D., 2012
155. Multiplication Memory
3x =
3 taken 5 times
equals 15.
5 15
3 6 9
12 15 18 7 21
21 24 27
30
© Joan A. Cotter, Ph.D., 2012
182. 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
© Joan A. Cotter, Ph.D., 2012
184. Fraction Chart
Stairs (Unit fractions)
1
2
1
© Joan A. Cotter, Ph.D., 2012
185. Fraction Chart
Stairs (Unit fractions)
1
3
1
2
1
© Joan A. Cotter, Ph.D., 2012
186. Fraction Chart
Stairs (Unit fractions)
1
4
1
3
1
2
1
© Joan A. Cotter, Ph.D., 2012
187. Fraction Chart
Stairs (Unit fractions)
1
5
1
4
1
3
1
2
1
© Joan A. Cotter, Ph.D., 2012
188. Fraction Chart
Stairs (Unit fractions)
1
6
1
5
1
4
1
3
1
2
1
© Joan A. Cotter, Ph.D., 2012
189. Fraction Chart
Stairs (Unit fractions)
1
7
1
6
1
5
1
4
1
3
1
2
1
© Joan A. Cotter, Ph.D., 2012
190. Fraction Chart
Stairs (Unit fractions)
1
8
1
7
1
6
1
5
1
4
1
3
1
2
1
© Joan A. Cotter, Ph.D., 2012
191. Fraction Chart
Stairs (Unit fractions)
1
9
1
8
1
7
1
6
1
5
1
4
1
3
1
2
1
© Joan A. Cotter, Ph.D., 2012
192. Fraction Chart
1 Stairs (Unit fractions)
10
1
9
1
8
1
7
1
6
1
5
1
4
1
3
1
2
1
© Joan A. Cotter, Ph.D., 2012
193. Fraction Chart
1 Stairs (Unit fractions)
10
1
9
1
8
1
7
1
6
1
5
1
4
1
3
1
2
1
© Joan A. Cotter, Ph.D., 2012
194. Fraction Chart
1 Stairs (Unit fractions)
10
1
9
1
8
1
7
1
6
1
5
1
4
1
3
1
2
1
A hyperbola.
© Joan A. Cotter, Ph.D., 2012
198. Fraction Naming
One divided into 2 equal parts.
One divided into 3 equal parts.
One divided into 4 equal parts.
© Joan A. Cotter, Ph.D., 2012
199. Fraction Naming
1
One divided into 3 equal parts.
1 One whole
© Joan A. Cotter, Ph.D., 2012
200. Fraction Naming
1
One divided into 3 equal parts.
1 One whole
divided into
© Joan A. Cotter, Ph.D., 2012
201. Fraction Naming
1
One divided into 3 equal parts.
1 One whole
divided into
3 three equal parts
© Joan A. Cotter, Ph.D., 2012
202. Fraction Naming
1
One divided into 3 equal parts.
1 One
divided by
3 three
© Joan A. Cotter, Ph.D., 2012
203. Fraction Naming
1
One divided into 3 equal parts.
1 One
divided by
3 three
In English, except for half, we use ordinal numbers
to name fractions.
© Joan A. Cotter, Ph.D., 2012
204. Fraction Naming
1
One divided into 3 equal parts.
1 Read as “one-third.”
3
© Joan A. Cotter, Ph.D., 2012
205. Fraction Naming
1
1 1 1
3 3 3
One divided into 3 equal parts.
1 Read as “one-third.”
3
© Joan A. Cotter, Ph.D., 2012
206. Unit Fraction War
Objective:
To help the children realize a unit fraction
decreases as the denominator increases.
© Joan A. Cotter, Ph.D., 2012
207. Unit Fraction War
Objective:
To help the children realize a unit fraction
decreases as the denominator increases.
Object of the game:
To collect all, or most, of the cards with
the greater unit fraction.
© Joan A. Cotter, Ph.D., 2012
223. Fraction Naming
1
1 1 1
3 3 3
Two
1s is
2
3 3
© Joan A. Cotter, Ph.D., 2012
224. Fraction Naming
1
1 1 1
3 3 3
Two
1s is
2
3 3
Read as “two-thirds.”
© Joan A. Cotter, Ph.D., 2012
225. 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?
© Joan A. Cotter, Ph.D., 2012
226. 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?
© Joan A. Cotter, Ph.D., 2012
227. 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?
© Joan A. Cotter, Ph.D., 2012
228. 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?
© Joan A. Cotter, Ph.D., 2012
229. 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?
© Joan A. Cotter, Ph.D., 2012
230. 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 eighths in a whole?
© Joan A. Cotter, Ph.D., 2012
231. Concentrating on One Game
Objective:
To help the children realize that 5 fifths, 8
eighths, and so forth, make a whole.
© Joan A. Cotter, Ph.D., 2012
232. Concentrating on One Game
Objective:
To help the children realize that 5 fifths, 8
eighths, and so forth, make a whole.
Object of the game:
To find the pairs that make a whole.
© Joan A. Cotter, Ph.D., 2012
250. 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?
© Joan A. Cotter, Ph.D., 2012
251. 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?
© Joan A. Cotter, Ph.D., 2012
252. 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?
© Joan A. Cotter, Ph.D., 2012
253. 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?
© Joan A. Cotter, Ph.D., 2012
254. 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.
© Joan A. Cotter, Ph.D., 2012
255. 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
© Joan A. Cotter, Ph.D., 2012
256. 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
© Joan A. Cotter, Ph.D., 2012
259. Fraction War
Objective:
To practice comparing ones, halves,
fourths, and eighths in preparation for
reading a ruler.
© Joan A. Cotter, Ph.D., 2012
260. Fraction War
Objective:
To practice comparing ones, halves,
fourths, and eighths in preparation for
reading a ruler.
Object of the game:
To capture all the cards.
© Joan A. Cotter, Ph.D., 2012
261. 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
© Joan A. Cotter, Ph.D., 2012
262. 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
© Joan A. Cotter, Ph.D., 2012
263. 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
© Joan A. Cotter, Ph.D., 2012
264. 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
© Joan A. Cotter, Ph.D., 2012
265. 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
© Joan A. Cotter, Ph.D., 2012
266. 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
© Joan A. Cotter, Ph.D., 2012
267. 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
© Joan A. Cotter, Ph.D., 2012
268. 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
© Joan A. Cotter, Ph.D., 2012
269. 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
© Joan A. Cotter, Ph.D., 2012
270. 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
© Joan A. Cotter, Ph.D., 2012
271. 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
© Joan A. Cotter, Ph.D., 2012
272. 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
© Joan A. Cotter, Ph.D., 2012
273. 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
© Joan A. Cotter, Ph.D., 2012
274. 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
© Joan A. Cotter, Ph.D., 2012
275. 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?
© Joan A. Cotter, Ph.D., 2012
276. 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?
© Joan A. Cotter, Ph.D., 2012
