1
00:00:04,234 --> 00:00:07,030
Maybe I won't do this, only because

2
00:00:07,030 --> 00:00:09,186
I'm going to need a lot of light up there today. 

3
00:00:09,795 --> 00:00:10,906
Let's see how this works. 

4
00:00:13,484 --> 00:00:14,545
Did that help? [Yeah]

5
00:00:16,655 --> 00:00:19,187
Um, So what I have on the overhead

6
00:00:19,187 --> 00:00:21,030
are what I would 

7
00:00:21,030 --> 00:00:22,858
probably say about ninety percent-ish

8
00:00:24,795 --> 00:00:26,992
of what you guys drew for me yesterday. 

9
00:00:26,992 --> 00:00:28,274
Remember your activity from yesterday?

10
00:00:28,780 --> 00:00:30,170
[Yeah] Where we did finger tool

11
00:00:30,170 --> 00:00:31,951
with Clown doin what he was doin. 

12
00:00:31,951 --> 00:00:33,609
But we tracked his distance

13
00:00:33,609 --> 00:00:36,468
from start verses total distance covered. 

14
00:00:37,140 --> 00:00:38,609
Yeah, you with me? Thinkin back 

15
00:00:38,609 --> 00:00:39,984
I know it was a whole day ago. 

16
00:00:39,984 --> 00:00:41,734
Um, and raise your hand if you 

17
00:00:41,734 --> 00:00:43,280
remember your graph looking something like this. 

18
00:00:45,140 --> 00:00:46,420
Yeah, most of us did. Like I said

19
00:00:46,420 --> 00:00:48,218
um, I think there was only a few that didn't.

20
00:00:48,218 --> 00:00:50,920
And, I even talked to Zack about it.

21
00:00:51,311 --> 00:00:52,984
We had a good little conversation about it. 

22
00:00:52,984 --> 00:00:53,832
And then, 

23
00:00:53,832 --> 00:00:55,295
I thought about it as soon as Zack left. 

24
00:00:55,295 --> 00:00:57,287
and I thought, "Well, wait let me really think about this"

25
00:00:57,287 --> 00:00:58,990
So what I want you guys to do, 

26
00:01:00,076 --> 00:01:02,011
is watch the video again. 

27
00:01:02,011 --> 00:01:03,170
and just imagine

28
00:01:03,170 --> 00:01:04,248
like you did yesterday 

29
00:01:04,248 --> 00:01:06,468
What you were in charge of graphing. 

30
00:01:06,468 --> 00:01:08,021
So, just kind of imagine what

31
00:01:08,021 --> 00:01:09,204
Clown's doing. 

32
00:01:09,204 --> 00:01:11,733
Think about, what you thought about yesterday. 

33
00:01:11,733 --> 00:01:13,686
And how this graph came about. 

34
00:01:13,686 --> 00:01:15,811
OK? I'll let it run a couple times. 

35
00:01:15,811 --> 00:01:17,640
So you can make connections if you need to. 

36
00:01:28,858 --> 00:01:30,076
OK, so are you trying to match up

37
00:01:30,076 --> 00:01:32,843
in your head, and with your eyes

38
00:01:32,843 --> 00:01:34,483
How Clown is walking?

39
00:01:34,483 --> 00:01:37,811
how the graph should model the walk?

40
00:01:48,498 --> 00:01:51,015
OK, this portion of the graph

41
00:01:51,015 --> 00:01:52,911
We'll call this portion part... 

42
00:01:52,911 --> 00:01:55,281
one, two, three, four, five.

43
00:01:55,281 --> 00:01:57,373
Okay, that very last

44
00:01:57,373 --> 00:01:58,733
portion of the graph

45
00:01:58,733 --> 00:02:01,748
Um, Why did you guys draw it

46
00:02:01,748 --> 00:02:03,515
the way that you did?

47
00:02:03,515 --> 00:02:05,484
Why did you just move that Miss. Coombs?

48
00:02:05,484 --> 00:02:07,343
You had drawn on the white board. 

49
00:02:07,343 --> 00:02:08,717
There... Um, 

50
00:02:09,186 --> 00:02:10,401
Somebody raise their hand, and just tell me

51
00:02:10,401 --> 00:02:11,824
why they drew it the way that they did. 

52
00:02:11,824 --> 00:02:13,717
Because most of you admit that this is how you drew it. 

53
00:02:13,717 --> 00:02:15,602
Julie? [Because he is, like]

54
00:02:15,602 --> 00:02:18,062
[walking slower and then he speeds up]

55
00:02:18,062 --> 00:02:20,889
Okay. Class?

56
00:02:20,889 --> 00:02:22,609
Is that why you drew it the way you all drew it?

57
00:02:23,248 --> 00:02:24,734
Because of that speed up at the end?

58
00:02:24,734 --> 00:02:25,576
[Yes]

59
00:02:25,576 --> 00:02:26,967
Okay. And, 

60
00:02:27,826 --> 00:02:30,962
Almost every time so far, 

61
00:02:30,962 --> 00:02:34,420
when Clown speeds up, what does your graph depict?

62
00:02:37,312 --> 00:02:40,092
How does the graph show that he sped up?

63
00:02:40,092 --> 00:02:41,826
[A steeper line?]

64
00:02:41,826 --> 00:02:43,234
A steeper thing, yeah. 

65
00:02:43,234 --> 00:02:46,187
A change in steepness of some sort. OK. 

66
00:02:48,420 --> 00:02:50,092
Let's think again about what we're tracking. 

67
00:02:50,092 --> 00:02:52,359
This graph is what versus what?

68
00:02:54,407 --> 00:02:57,092
Total distance versus, or total distance versus

69
00:02:57,092 --> 00:02:58,170
[distance from start]

70
00:02:58,170 --> 00:02:59,217
distance from start.

71
00:03:00,467 --> 00:03:01,920
Do either one of those

72
00:03:02,656 --> 00:03:03,498
incorporate speed?

73
00:03:07,920 --> 00:03:10,031
What two variables

74
00:03:10,031 --> 00:03:11,420
do you have to have

75
00:03:11,420 --> 00:03:13,514
changing to show a speed?

76
00:03:13,514 --> 00:03:15,406
On any graph or situation?

77
00:03:15,406 --> 00:03:17,359
What constitutes speed?

78
00:03:17,359 --> 00:03:18,826
Casey?

79
00:03:18,826 --> 00:03:23,123
[Distance and the amount of time it took to get to that distance]

80
00:03:23,123 --> 00:03:25,467
Okay. Well said. A certain distance

81
00:03:25,467 --> 00:03:27,498
and the time it took to cover that different

82
00:03:27,498 --> 00:03:28,530
- that distance. 

83
00:03:28,530 --> 00:03:31,248
Do we have distances going on, on this graph?

84
00:03:32,701 --> 00:03:33,280
You betcha!

85
00:03:33,280 --> 00:03:35,639
DO we have time going on, on that particular graph?

86
00:03:36,717 --> 00:03:37,326
No. 

87
00:03:38,342 --> 00:03:41,848
So, can you show an increase is speed

88
00:03:41,848 --> 00:03:43,656
if there is no unit of time to track?

89
00:03:53,670 --> 00:03:57,576
No? Well think about this. Um...

90
00:04:02,156 --> 00:04:07,389
If you were to compare this gap.

91
00:04:08,842 --> 00:04:10,406
This would be a unit of what?

92
00:04:10,406 --> 00:04:12,031
Since I'm on the horizontal axis 

93
00:04:12,031 --> 00:04:15,484
this gap would be some number of what

94
00:04:15,484 --> 00:04:17,826
Feet. Which kind of feet?

95
00:04:17,826 --> 00:04:20,624
Total feet? Or his feet that he traveled with regard to start?

96
00:04:20,624 --> 00:04:21,639
[total feet]

97
00:04:21,639 --> 00:04:22,874
His total feet. 

98
00:04:22,874 --> 00:04:26,656
So this would be some number of feet

99
00:04:26,656 --> 00:04:29,201
that he had traveled in total over that period. 

100
00:04:29,201 --> 00:04:30,656
What about 

101
00:04:32,983 --> 00:04:35,201
this, I already drew it in purple, 

102
00:04:35,201 --> 00:04:37,372
If you eyeballs weren't looking horizontal,

103
00:04:37,372 --> 00:04:38,701
but they were looking vertical

104
00:04:38,701 --> 00:04:45,733
what would that value, whatever it is, tell you?

105
00:04:51,124 --> 00:04:52,608
Would this number show you a speed?

106
00:04:54,045 --> 00:04:55,999
If your eyeballs looked across vertically?

107
00:04:59,093 --> 00:05:00,435
OK. It would tell you distance from start.

108
00:05:00,435 --> 00:05:01,812
Which is a number of what?

109
00:05:04,093 --> 00:05:08,139
Feet again. This is also a number of feet. 

110
00:05:09,281 --> 00:05:11,843
Only this is the number of feet with regard to...

111
00:05:11,843 --> 00:05:13,233
[Start?]

112
00:05:13,233 --> 00:05:16,437
Yeah start. With regard to start. 

113
00:05:19,201 --> 00:05:21,656
Okay, Think about this with me. 

114
00:05:23,545 --> 00:05:24,999
This portion of the graph

115
00:05:26,108 --> 00:05:29,326
Shows that he walked this many feet in total

116
00:05:29,326 --> 00:05:32,795
whatever that is, this much.

117
00:05:32,795 --> 00:05:34,687
According to how we've drawn it. 

118
00:05:34,687 --> 00:05:36,281
This is... I'm basing this off your graph. 

119
00:05:36,281 --> 00:05:38,653
According to how we've drawn it, he's walked this many 

120
00:05:38,653 --> 00:05:41,576
feet in total, and this many feet

121
00:05:41,576 --> 00:05:44,295
with regard to start. 

122
00:05:44,295 --> 00:05:46,593
Do those two values of feet, the way we've drawn it

123
00:05:46,593 --> 00:05:48,987
look like he traveled the same in total

124
00:05:48,987 --> 00:05:51,620
verses distance from start or different values

125
00:05:51,620 --> 00:05:53,468
in total verses distance from start?

126
00:05:55,406 --> 00:05:57,312
Same number of feet, or different number of feet?

127
00:05:57,312 --> 00:06:00,411
Why does this show us different number of feet?

128
00:06:00,411 --> 00:06:01,550
What is it about this graph 

129
00:06:01,550 --> 00:06:03,370
that's making you say different?

130
00:06:05,233 --> 00:06:06,586
I know you don't have specific values,

131
00:06:06,586 --> 00:06:09,297
but, what is it about that, that makes you feel like

132
00:06:09,297 --> 00:06:11,125
saying, "Oh it shows different number of feet."

133
00:06:13,264 --> 00:06:13,952
Gromick?

134
00:06:13,952 --> 00:06:19,843
[Because the gaps are different]

135
00:06:19,843 --> 00:06:23,156
Good. I mean at this point that's real-all you can look at is the gaps

136
00:06:23,156 --> 00:06:26,264
Are these gaps equivalent?

137
00:06:28,047 --> 00:06:29,172
No, one is smaller. 

138
00:06:30,093 --> 00:06:31,858
[The total] The total. 

139
00:06:31,858 --> 00:06:34,343
OK, so watch the video with me for a second. 

140
00:06:35,358 --> 00:06:37,750
In fact, he's about to do it. Ready? Watch him. 

141
00:06:39,906 --> 00:06:41,297
OK, you see that speed up?

142
00:06:41,297 --> 00:06:44,406
Watch it again. Let me see if I can get it there. 

143
00:06:44,406 --> 00:06:47,180
OK, watch him, watch the speed up. 

144
00:06:47,180 --> 00:06:48,812
And think distances!

145
00:06:48,812 --> 00:06:51,139
Watch it again. 

146
00:06:51,139 --> 00:06:54,358
Think distance. Don't think speed. Think distances. 

147
00:07:05,327 --> 00:07:09,327
Okay, so actually once for fun

148
00:07:09,327 --> 00:07:12,233
Approximately, where is he on the graph when he speeds up?

149
00:07:12,233 --> 00:07:13,745
Watch real close because he's about to do it. 

150
00:07:13,745 --> 00:07:17,093
Is it about eighteen?

151
00:07:17,093 --> 00:07:19,156
-ish? Watch it again. 

152
00:07:20,858 --> 00:07:25,420
Yeah? So if he's about 

153
00:07:28,297 --> 00:07:31,764
What is he about right there, when he makes his speed up?

154
00:07:31,764 --> 00:07:34,531
So, if he walks from here back to home

155
00:07:34,531 --> 00:07:39,389
how much should his total distance have increased in that speed up part?

156
00:07:39,389 --> 00:07:41,406
If he sped up

157
00:07:41,406 --> 00:07:43,721
right about, I think we said here

158
00:07:43,721 --> 00:07:45,343
and he ran all the way home, 

159
00:07:45,343 --> 00:07:50,733
Okay? How much should his total distance have increased?

160
00:07:50,733 --> 00:07:54,906
Eighteen feet. Because he has to go home, which is 

161
00:07:54,906 --> 00:07:57,297
eighteen feet away. 

162
00:07:57,297 --> 00:07:59,062
What about his distance from start?

163
00:07:59,062 --> 00:08:01,687
If he's here, at the speed up

164
00:08:01,687 --> 00:08:03,827
and then he runs all the way home, 

165
00:08:03,827 --> 00:08:07,593
how did his distance from start change?

166
00:08:07,593 --> 00:08:14,500
By how many feet? [eighteen] Eighteen feet. 

167
00:08:14,500 --> 00:08:18,266
Watch it again. 

168
00:08:18,266 --> 00:08:21,766
Total distance and distance from start

169
00:08:21,766 --> 00:08:24,156
when he makes that speed up.

170
00:08:24,156 --> 00:08:29,735
There he went. Okay, it happened at around eighteen. 

171
00:08:29,735 --> 00:08:30,968
And he ran all the way home. 

172
00:08:33,890 --> 00:08:36,657
They both increased by eighteen?

173
00:08:36,657 --> 00:08:40,235
The both changed perhaps is a better way of saying that by eighteen feet?

174
00:08:42,985 --> 00:08:44,224
Is that what you're seeing? 

175
00:08:48,280 --> 00:08:49,672
Is that what this shows?

176
00:08:54,875 --> 00:08:57,735
what's going on here?

177
00:09:22,908 --> 00:09:25,250
When Clown speeds up

178
00:09:25,250 --> 00:09:30,625
his distances that he travels 

179
00:09:30,625 --> 00:09:33,875
do those distances change?

180
00:09:33,875 --> 00:09:36,407
[yes]

181
00:09:36,407 --> 00:09:39,422
How though, do they change differently or in the same way?

182
00:09:39,422 --> 00:09:44,390
Like, can one increase while the other one doesn't?

183
00:09:44,390 --> 00:09:47,203
Think of what your horizontal piece on the graph from last night. 

184
00:09:47,203 --> 00:09:50,922
Can one distance increase while the other one does something different?

185
00:09:50,922 --> 00:09:53,515
No. 

186
00:09:53,515 --> 00:09:57,703
So, can total distance increase a little bit,

187
00:09:57,703 --> 00:10:01,547
while distance from start increases a lot?

188
00:10:01,547 --> 00:10:05,672
Or do they have to change together, if you're tracking distances?

189
00:10:15,407 --> 00:10:17,485
What do you think? Forbis you look deep in thought. 

190
00:10:17,485 --> 00:10:18,782
What do you think?

191
00:10:18,782 --> 00:10:22,235
[They change differently, I guess...]

192
00:10:22,235 --> 00:10:25,827
I'm sorry? [Did you ask if they could change differently?] Yeah.

193
00:10:25,827 --> 00:10:27,937
[I don't think so]

194
00:10:27,937 --> 00:10:34,297
How come you don't think so?

195
00:10:34,297 --> 00:10:38,844
[Just cause, if you're eighteen feet from start and you go back to zero]

196
00:10:38,844 --> 00:10:41,485
[You're moving eighteen feet]

197
00:10:41,485 --> 00:10:44,047
[and in total, you're adding eighteen feet to your total]

198
00:10:44,047 --> 00:10:46,672
So they are both eighteen feet?

199
00:10:46,672 --> 00:10:49,140
[Yeah] OK, class what do you think about Forbis?

200
00:10:49,140 --> 00:10:50,379
Gromick, what do you want to add? 

201
00:10:50,379 --> 00:10:52,547
[Well no, cause like, I guess they could]

202
00:10:52,547 --> 00:10:57,265
[If, like when he turns back around,]

203
00:10:57,265 --> 00:11:02,094
['cause say, he'll be like... say the second part]

204
00:11:02,094 --> 00:11:04,344
[might be shorter.] This [That one] OK. 

205
00:11:04,344 --> 00:11:07,672
[He'd be like ten feet from start, I guess]

206
00:11:07,672 --> 00:11:12,000
[and he'd go down five, but he'd be]

207
00:11:12,000 --> 00:11:17,172
[like, five feet from start, but fifteen feet in total.]

208
00:11:17,172 --> 00:11:19,765
Uh-huh 

209
00:11:19,765 --> 00:11:22,125
Okay, I see what you're saying. So hang on. 

210
00:11:22,125 --> 00:11:25,703
What did you say, just for fun you put a value of ten here? [yes]

211
00:11:25,703 --> 00:11:27,485
And a value of five here?

212
00:11:27,485 --> 00:11:30,547
Is that what you did? Okay, So

213
00:11:30,547 --> 00:11:33,193
Let's actually build off that just a little bit, 

214
00:11:33,193 --> 00:11:35,875
If this was a change with regard to start

215
00:11:35,875 --> 00:11:37,265
from ten to five,

216
00:11:37,265 --> 00:11:39,719
how should his total distance have changed

217
00:11:39,719 --> 00:11:41,344
in that portion?

218
00:11:41,344 --> 00:11:43,312
[Five.]

219
00:11:43,312 --> 00:11:45,672
Also by five.

220
00:11:45,672 --> 00:11:49,140
If he walks from ten feet away to five feet away,

221
00:11:49,140 --> 00:11:52,610
then he also gained total distance of what?

222
00:11:52,610 --> 00:11:58,172
Five, did it match? It did. Will it always match?

223
00:11:58,172 --> 00:12:00,282
It will. 

224
00:12:00,282 --> 00:12:03,203
Is that what this shows?

225
00:12:03,203 --> 00:12:06,172
Just think about what we all drew yesterday. 

226
00:12:06,172 --> 00:12:08,469
Is that we showed?

227
00:12:08,469 --> 00:12:11,390
No. What did we show?

228
00:12:11,390 --> 00:12:14,797
We tried to show the speed. 

229
00:12:14,797 --> 00:12:18,797
And my mind wanted to do the exact same thing. 

230
00:12:18,797 --> 00:12:20,094
Didn't I Terelli

231
00:12:20,094 --> 00:12:22,125
Terelli even said, he's like,

232
00:12:22,125 --> 00:12:24,328
"I want to draw this straight down," he said

233
00:12:24,328 --> 00:12:26,532
"I fell like maybe I should go like that"

234
00:12:26,532 --> 00:12:29,937
"But then now he changed speeds so I have to show that, right?"

235
00:12:32,297 --> 00:12:35,032
You got to show that change in speed. 

236
00:12:35,032 --> 00:12:37,297
Are we tracking speed? [No.]

237
00:12:37,297 --> 00:12:39,890
No. We're tracking distances. 

238
00:12:39,890 --> 00:12:45,047
OK. So, I mean we all fell into the trap. I fell into the trap. 

239
00:12:45,047 --> 00:12:47,875
When I think speed up, I think

240
00:12:47,875 --> 00:12:51,844
I should see that. I should see steepness change somehow. 

241
00:12:51,844 --> 00:12:54,250
But Casey come back for speed with us again. 

242
00:12:54,250 --> 00:12:57,015
If we're tracking speed, what variables are involved?

243
00:12:57,015 --> 00:13:01,937
[Uh, distance and uh, however amount of time it takes to get to that distance]

244
00:13:01,937 --> 00:13:04,844
Yup. Distance traveled, time elapsed. 

245
00:13:04,844 --> 00:13:08,235
We've got distances traveled. Do we have time elapsed?

246
00:13:08,235 --> 00:13:12,532
No. So, it shouldn't have shown speeds. 

247
00:13:12,532 --> 00:13:15,500
And that's okay, it is simply not what this graph

248
00:13:15,500 --> 00:13:16,511
was doing for us.