1
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Changes

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and what we started to get into on Tuesday was

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what about my actual total distance from home,
how would you

4
00:00:09,263 --> 00:00:12,446
calculate that based on all these little changes

5
00:00:12,446 --> 00:00:15,596
so let's go back to this, the next tenth of a minute

6
00:00:15,596 --> 00:00:18,910
would mean that i am at 7.1

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you guys with that tenth being point one

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k well decimal fraction sense here

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Um

10
00:00:24,649 --> 00:00:25,795
so

11
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I was three point 8 miles from home

12
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but my distance changed in that tenth
of a minute by how much

13
00:00:34,341 --> 00:00:36,792
[ten]

14
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tenth of a half

15
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so what does that mean for my
total distance from home

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go ahead say it [it will increase a tenth]

17
00:00:46,859 --> 00:00:50,072
well it will not just increase a
tenth it will increase

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[plus seven]

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It will increase by how much

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you said a tenth

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but that is how much my time

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increased was a tenth, my distance increased

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half of a half [tenth of a half]

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of a half

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Ok you guys ok with this,
my distance in that tenth

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of a minute

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increased a tenth of a half

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so this is how much my distance

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changed

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added on to where I already was

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would tell you what

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go ahead

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my total distance

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at that time

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k what about at three tenths of a minute

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so that would be if I had been on the road

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for 7.3 minutes

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this is where I started

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but how much did I change in those
next three tenths of a minute

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Not

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third of a tenth

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[Three tenths of a half]

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Three tenths of a half, not one tenth of a half

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But three tenths of a half

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K what about I talked about halfs

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now 7.5 would be elapsed time

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and in that next

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half of a minute how much would my
total distance change

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[half of a half] Half of a half

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K

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Um

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was I

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or do you know perhaps is the better
way of asking this

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do you know

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where I was

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when I started looking at my clock cause
notice look over here

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seven minutes has passed

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since I first checked my watch

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K where was I when I started my watch,
where was I when I checked my watch do you know?

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[3.8 miles away]

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No 3.8 miles is where I was 7 minutes
after I checked the clock

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but where was I right when I checked the clock,
pretty much when I said

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go

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[0]

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Was I at home?

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[You were basically at 0]

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[7 minutes before where you were]

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Ok so wherever I was seven minutes prior

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I agree with that I was wherever I was
seven minutes prior right

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but do you know where that is, was
I at home for instance?

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Well how could we figure

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Gromeck is right where I started my clock
is where I was seven minutes prior

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cause we know where I am seven minutes later

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so if only we knew where I was seven minutes

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prior

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that would tell you exactly where I was
when I started my watch

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So

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I need to

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backtrack, can we backtrack

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with constant rates of change?

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sure

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Simon did you want to say something
[Would it be 3.5 miles?]

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What would be 3.5 miles go ahead

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[How far you have traveled since you
started the clock]

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How so tell me how you figure? [Cause you are
traveling at a constant rate of
half a mile per minute]

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00:04:01,019 --> 00:04:03,296
Ok

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00:04:03,296 --> 00:04:06,883
So I am traveling at a constant rate o
f half a mile per minute

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00:04:06,883 --> 00:04:08,871
and you know I have been on the road for

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[seven minutes]

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So if I am traveling at a constant rate
of half a mile per minute

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and

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it has been seven minutes since I
past checked my watch

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how far did I go on those seven minutes,
what would be my total distance
in those seven minutes?

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[3 1/2]

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3 1/2 how are you guys both getting 3 1/2.
Go ahead Gromeck because Simon started it.

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[Cause it is half of seven]

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[For every one minute you go it is half a mile]

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K

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So Kimberly reiterate what we are talking about here.

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How is it that we know in these seven minutes

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we know my well we are trying to decide
well we think we know that I have walked 3 1/2

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miles in those seven minutes [ for every minute
you go half a mile] Right so every minute I go
half a mile so in seven minutes I should go

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3 1/2

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00:05:07,389 --> 00:05:13,461
Well if in seven minutes I should go 3 1/2
and in fact I go 3.8

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Did I start at home? [No]

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No where was I?

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I was .3 ahead wasn't I?

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So ok

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let's

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I want to do exactly you guys almost jumped ahead

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which is ok I am a fan of jumping ahead at times

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00:05:27,158 --> 00:05:32,351
but let's just get a sense of what you guys did,
let's only backtrack

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How much did I backtrack

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Half a minute

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So

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I know I was at 3.8

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But this time I am going to back up the clock
I want to look at the prior half a minute

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How should my distance from home change
in the prior half a minute

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[decrease] Gromeck

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[decrease] It will decrease

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how?

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In half a minute

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half a minute, half a mile per minute
what is the change there

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[quarter]

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00:06:09,466 --> 00:06:12,115
How are you getting quarter just
tell me how to express it?

126
00:06:12,115 --> 00:06:15,201
[Uh a half]

127
00:06:15,201 --> 00:06:18,014
Yea it is my half of a half again, but

128
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is it the same half of a half as
it was down here

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00:06:21,341 --> 00:06:22,824
why not?

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It was still a tiny lapse of .5

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[you subtracted]

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K but it is a prior so am I increasing
my distance if I go this way up the table?

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00:06:34,742 --> 00:06:36,507
No it's

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a negative change

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00:06:38,237 --> 00:06:39,742
if I go this way

136
00:06:39,742 --> 00:06:41,812
does that make sense?

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00:06:41,812 --> 00:06:46,346
If you look at the prior half a second
compared to where I started

138
00:06:46,346 --> 00:06:47,571
I'm not

139
00:06:47,571 --> 00:06:51,377
further I am no increasing my distance
I am actually backtracking

140
00:06:51,377 --> 00:06:54,769
This is a lesser distance than the next frame

141
00:06:54,769 --> 00:06:57,978
so what about, so this what you guys started to do

142
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in your head

143
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back all the way up to when I started

144
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all those seven minutes, back all the way up

145
00:07:05,802 --> 00:07:08,487
I don't know where I started, I don't know

146
00:07:08,487 --> 00:07:12,918
if I am starting at zero, I don't know
if I am starting at one

147
00:07:12,918 --> 00:07:15,869
k but you can figure it out, back all the way up

148
00:07:19,338 --> 00:07:21,704
how much did I backtrack my clock?

149
00:07:22,630 --> 00:07:24,822
[6.57]

150
00:07:24,822 --> 00:07:26,266
All the way

151
00:07:26,266 --> 00:07:27,911
[7]

152
00:07:27,911 --> 00:07:30,314
All 7 minutes is what I want to backtrack

153
00:07:30,314 --> 00:07:34,550
Well I am traveling at half a mile per minute
so how would you calculate this change

154
00:07:50,408 --> 00:07:52,548
[Wouldn't it be half of seven]

155
00:07:52,548 --> 00:07:54,574
Gina, half of 7?

156
00:07:54,574 --> 00:07:57,107
[yea]

157
00:07:57,107 --> 00:07:59,353
Danielle half of 7?

158
00:07:59,353 --> 00:08:01,125
[would it be negative seven?]

159
00:08:01,125 --> 00:08:02,843
Half of negative 7?

160
00:08:02,843 --> 00:08:04,904
Julie, do you agree?

161
00:08:04,904 --> 00:08:07,175
Katie, half of negative 7?

162
00:08:07,175 --> 00:08:09,783
[Yea] K

163
00:08:09,783 --> 00:08:13,473
Why

164
00:08:13,473 --> 00:08:17,762
well I guess to be consistent

165
00:08:17,762 --> 00:08:19,865
this one is confusing because
they are both halves

166
00:08:19,865 --> 00:08:22,730
this is my constant rate but it is
my time that is backtracked

167
00:08:22,730 --> 00:08:25,822
Here is my constant rate but it is
my time that is backtracked

168
00:08:25,822 --> 00:08:28,288
This is different than how I write it, um

169
00:08:28,288 --> 00:08:32,722
Why negative 7? You guys are correct
but why negative 7?

170
00:08:32,722 --> 00:08:35,870
Gromeck?

171
00:08:35,870 --> 00:08:41,942
[amount of time that has gone by]

172
00:08:41,942 --> 00:08:46,802
It is the amount I have gone by but

173
00:08:46,802 --> 00:08:51,735
think changes is this a positive change
in time or a negative change in time

174
00:08:51,735 --> 00:08:54,009
[negative] It is a negative change in time

175
00:08:54,009 --> 00:08:57,282
I mean I know you guys were thinking that,
it is hard to verbalize

176
00:08:57,282 --> 00:09:01,474
It is just all about changes k
constant rates of change

177
00:09:01,474 --> 00:09:04,581
tell you how things change

178
00:09:04,581 --> 00:09:08,741
So if you want to look at the
next tenth of a second

179
00:09:08,741 --> 00:09:11,130
Then that is an increase in time

180
00:09:11,130 --> 00:09:13,418
and what you can expect with a
positive rate of change

181
00:09:13,418 --> 00:09:15,196
an increase in total distance

182
00:09:15,196 --> 00:09:18,841
if you go a negative change in time

183
00:09:18,841 --> 00:09:23,326
or backtrack you can expect a negative
change in distance

184
00:09:23,326 --> 00:09:24,988
So