SlideShare a Scribd company logo

Focusing on Fractions

Download as PPTX, PDF
R
rightstartmath

The document discusses how Joan Cotter, an engineer and educator with a PhD in math education, developed innovative ways to teach fractions. It describes several fraction models she created, including linear charts, colored bars, and missing parts charts, that make fraction comparisons and concepts easier to understand compared to traditional fraction circles or "fish tank" models. The document advocates teaching fractions using these types of linear representations rather than area models like pie charts that can be more difficult for students to interpret.

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

More Related Content

PDF
Fractions and decimals made easy
santosh Mr dexter
 
PDF
Family ch22
Shirley Hills
 
PPTX
1150 day 8
Carol Defreese
 
PPTX
Scale up reisner wiltshire presentation
jrei9999
 
PDF
Unit 2 3rd grade cs 2012 2013
Isaac_Schools_5
 
PPT
SID Day 2 Mathematics Workshop
Collaborative for Teaching and Learning
 
PDF
Unit 1 intro
ackerkri
 
PPTX
Math Puzzles and Brain Teasers
rightstartmath
 
Fractions and decimals made easy
santosh Mr dexter
 
Family ch22
Shirley Hills
 
1150 day 8
Carol Defreese
 
Scale up reisner wiltshire presentation
jrei9999
 
Unit 2 3rd grade cs 2012 2013
Isaac_Schools_5
 
SID Day 2 Mathematics Workshop
Collaborative for Teaching and Learning
 
Unit 1 intro
ackerkri
 
Math Puzzles and Brain Teasers
rightstartmath
 

Similar to Focusing on Fractions (20)

PDF
[STA 2025] 5 Favourite Problems for Intermediate Mathematics.pdf
Chris Hunter
 
PPS
Fraction
mikealabacus
 
PPS
Fraction
mikealabacus
 
PPT
NCV 2 Mathematical Literacy Hands-On Training Module 4
Future Managers
 
PDF
4th grade Reference Guide for Investigations
Isaac_Schools_5
 
PDF
Unit 8 Fourth Grade 2012 2013
Isaac_Schools_5
 
PDF
2nd Grade Singapore Math Training II
Kimberly Beane
 
PPTX
Content standards math a
bgdance3
 
KEY
7-7 Equivalent Fractions
Mel Anthony Pepito
 
KEY
7-7 Equivalent Fractions
Rudy Alfonso
 
PPTX
Getting started with blackboard 9 1
Michael Payne
 
PDF
Unit 6 Fourth Grade 2012 2013
Isaac_Schools_5
 
PPT
Teaching strategies that work
Irina K
 
PDF
Unit 9 Fourth Grade 2012 2013
Isaac_Schools_5
 
PDF
Aha!Math Units Overview
Neil Stewart
 
PPTX
Assessment for Learning in an Elementary Math Classroom presentation
tbraybrook
 
PDF
Mathblogosphere
Chris Hunter
 
PDF
MAP101 Fundamentals of Singapore Mathematics Curriculum
Jimmy Keng
 
PPTX
Singapore Math Beyond the Basics Day 2
Jimmy Keng
 
PDF
Unit 7 3rd grade cs 2012 2013
Isaac_Schools_5
 
[STA 2025] 5 Favourite Problems for Intermediate Mathematics.pdf
Chris Hunter
 
Fraction
mikealabacus
 
Fraction
mikealabacus
 
NCV 2 Mathematical Literacy Hands-On Training Module 4
Future Managers
 
4th grade Reference Guide for Investigations
Isaac_Schools_5
 
Unit 8 Fourth Grade 2012 2013
Isaac_Schools_5
 
2nd Grade Singapore Math Training II
Kimberly Beane
 
Content standards math a
bgdance3
 
7-7 Equivalent Fractions
Mel Anthony Pepito
 
7-7 Equivalent Fractions
Rudy Alfonso
 
Getting started with blackboard 9 1
Michael Payne
 
Unit 6 Fourth Grade 2012 2013
Isaac_Schools_5
 
Teaching strategies that work
Irina K
 
Unit 9 Fourth Grade 2012 2013
Isaac_Schools_5
 
Aha!Math Units Overview
Neil Stewart
 
Assessment for Learning in an Elementary Math Classroom presentation
tbraybrook
 
Mathblogosphere
Chris Hunter
 
MAP101 Fundamentals of Singapore Mathematics Curriculum
Jimmy Keng
 
Singapore Math Beyond the Basics Day 2
Jimmy Keng
 
Unit 7 3rd grade cs 2012 2013
Isaac_Schools_5
 
Ad

More from rightstartmath (20)

PPTX
Fraction Mass HOPE April 2013
rightstartmath
 
PPTX
Learning Disabilities Mass HOPE April 2013
rightstartmath
 
PPTX
NCSM April 2013
rightstartmath
 
PPTX
Personalized Learning Bridges Middle School Math with a Geometric Approach
rightstartmath
 
PPTX
Mastering Math Facts with Card Games
rightstartmath
 
PPTX
A Plus 2012 The Future of Primary Math
rightstartmath
 
PPTX
2012 A Plus AL Abacus
rightstartmath
 
PPT
IMF: Visualizing and Montessori Math PART 2
rightstartmath
 
PPT
IMF: Visualizing and Montessori Math PART 1
rightstartmath
 
PDF
NDMA Presentation
rightstartmath
 
PPT
NDMA 2012
rightstartmath
 
PDF
MCTM Games
rightstartmath
 
PPT
MCTM Strategies & Games
rightstartmath
 
PPT
MCTM Future Primary Math
rightstartmath
 
PDF
Basics of AL Abacus.rsg
rightstartmath
 
PPT
NDCTM
rightstartmath
 
PPT
Geometry AMS
rightstartmath
 
PPT
NJMAC Visualization
rightstartmath
 
PDF
RightStart Geometry
rightstartmath
 
PDF
RightStart™ Mathematics Research Summary
rightstartmath
 
Fraction Mass HOPE April 2013
rightstartmath
 
Learning Disabilities Mass HOPE April 2013
rightstartmath
 
NCSM April 2013
rightstartmath
 
Personalized Learning Bridges Middle School Math with a Geometric Approach
rightstartmath
 
Mastering Math Facts with Card Games
rightstartmath
 
A Plus 2012 The Future of Primary Math
rightstartmath
 
2012 A Plus AL Abacus
rightstartmath
 
IMF: Visualizing and Montessori Math PART 2
rightstartmath
 
IMF: Visualizing and Montessori Math PART 1
rightstartmath
 
NDMA Presentation
rightstartmath
 
NDMA 2012
rightstartmath
 
MCTM Games
rightstartmath
 
MCTM Strategies & Games
rightstartmath
 
MCTM Future Primary Math
rightstartmath
 
Basics of AL Abacus.rsg
rightstartmath
 
NDCTM
rightstartmath
 
Geometry AMS
rightstartmath
 
NJMAC Visualization
rightstartmath
 
RightStart Geometry
rightstartmath
 
RightStart™ Mathematics Research Summary
rightstartmath
 
Ad

Recently uploaded (20)

PDF
ANTIBIOTICS.pptx.pdf………………… xxxxxxxxxxxxx
HakHe
 
PPTX
IMMUNITY IMMUNITY refers to protection against infection, and the immune syst...
shilpa939953
 
PDF
FourierSeries-QuestionsWithAnswers(Part-A).pdf
Raji Murugan
 
PDF
The Lost Whites of Pakistan by Jahanzaib Mughal.pdf
jahanzaibmughal6
 
PPTX
GDM (1) (1).pptx small presentation for students
shrawanbpkihs
 
PPTX
PPT- ENG7_QUARTER1_LESSON1_WEEK1. IMAGERY -DESCRIPTIONS pptx.pptx
KMDee
 
PPTX
Lesson notes of climatology university.
sgladness67
 
PDF
Black Hat USA 2025 - Micro ICS Summit - ICS/OT Threat Landscape
Chris Sistrunk
 
PPTX
Cell Structure & Organelles in detailed.
DHANASHREESIVAKUMAR
 
PDF
BÀI TẬP BỔ TRỢ 4 KỸ NĂNG TIẾNG ANH 9 GLOBAL SUCCESS - CẢ NĂM - BÁM SÁT FORM Đ...
Nguyen Thanh Tu Collection
 
PPTX
school management -TNTEU- B.Ed., Semester II Unit 1.pptx
NihumathunnisaH
 
PDF
Chapter 2 Heredity, Prenatal Development, and Birth.pdf
MarjorieLopezTiu
 
PPTX
Pharmacology of Heart Failure /Pharmacotherapy of CHF
Rajshri Ghogare
 
PDF
2.FourierTransform-ShortQuestionswithAnswers.pdf
Raji Murugan
 
PPTX
Cell Types and Its function , kingdom of life
ClaireMangundayao1
 
PDF
Complications of Minimal Access Surgery at WLH
mohitsuren827
 
PPTX
1st Inaugural Professorial Lecture held on 19th February 2020 (Governance and...
kawisojames10
 
PDF
Anesthesia in Laparoscopic Surgery in India
mohitsuren827
 
PDF
102 student loan defaulters named and shamed – Is someone you know on the list?
Kweku Zurek
 
PPTX
Final Presentation General Medicine 03-08-2024.pptx
ZaheerAhmad228692
 
ANTIBIOTICS.pptx.pdf………………… xxxxxxxxxxxxx
HakHe
 
IMMUNITY IMMUNITY refers to protection against infection, and the immune syst...
shilpa939953
 
FourierSeries-QuestionsWithAnswers(Part-A).pdf
Raji Murugan
 
The Lost Whites of Pakistan by Jahanzaib Mughal.pdf
jahanzaibmughal6
 
GDM (1) (1).pptx small presentation for students
shrawanbpkihs
 
PPT- ENG7_QUARTER1_LESSON1_WEEK1. IMAGERY -DESCRIPTIONS pptx.pptx
KMDee
 
Lesson notes of climatology university.
sgladness67
 
Black Hat USA 2025 - Micro ICS Summit - ICS/OT Threat Landscape
Chris Sistrunk
 
Cell Structure & Organelles in detailed.
DHANASHREESIVAKUMAR
 
BÀI TẬP BỔ TRỢ 4 KỸ NĂNG TIẾNG ANH 9 GLOBAL SUCCESS - CẢ NĂM - BÁM SÁT FORM Đ...
Nguyen Thanh Tu Collection
 
school management -TNTEU- B.Ed., Semester II Unit 1.pptx
NihumathunnisaH
 
Chapter 2 Heredity, Prenatal Development, and Birth.pdf
MarjorieLopezTiu
 
Pharmacology of Heart Failure /Pharmacotherapy of CHF
Rajshri Ghogare
 
2.FourierTransform-ShortQuestionswithAnswers.pdf
Raji Murugan
 
Cell Types and Its function , kingdom of life
ClaireMangundayao1
 
Complications of Minimal Access Surgery at WLH
mohitsuren827
 
1st Inaugural Professorial Lecture held on 19th February 2020 (Governance and...
kawisojames10
 
Anesthesia in Laparoscopic Surgery in India
mohitsuren827
 
102 student loan defaulters named and shamed – Is someone you know on the list?
Kweku Zurek
 
Final Presentation General Medicine 03-08-2024.pptx
ZaheerAhmad228692
 

Focusing on Fractions

  • 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
  • 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