1
00:00:00,000 --> 00:00:01,645
That's one

2
00:00:03,687 --> 00:00:06,637
number of pies increases by?

3
00:00:06,637 --> 00:00:08,561
[two],two

4
00:00:12,292 --> 00:00:13,818
what about half a minute?

5
00:00:19,621 --> 00:00:21,282
half a minute elapsed

6
00:00:22,506 --> 00:00:25,289
how many more pies did he eat?

7
00:00:25,289 --> 00:00:26,794
[1]

8
00:00:26,794 --> 00:00:28,112
why only one more?

9
00:00:34,874 --> 00:00:36,225
why one more?

10
00:00:36,225 --> 00:00:38,192
I know I didn't hear of something that

11
00:00:38,192 --> 00:00:41,795
I heard mumbling, [cause it's half of
two and half of a minute]

12
00:00:44,082 --> 00:00:47,737
[with watever the rate was],
ok think constant rate again

13
00:00:47,737 --> 00:00:48,698
if

14
00:00:48,698 --> 00:00:50,384
half the time elapsed

15
00:00:52,706 --> 00:00:55,950
then what, if half the time elapses
then what do you know about the number of pies

16
00:00:58,234 --> 00:01:00,680
half of number of pies per minute
anyway it's our rate

17
00:01:00,680 --> 00:01:02,603
so in half the time half the pies

18
00:01:02,603 --> 00:01:04,769
and half of two I agree is one

19
00:01:07,078 --> 00:01:09,697
what about if two minutes elapses?

20
00:01:12,408 --> 00:01:16,096
Has that touched the cross of the two

21
00:01:16,096 --> 00:01:21,668
[yeah] ok what if two minutes elapse
then how many more pies should he have eaten? [four]

22
00:01:21,668 --> 00:01:25,602
four, why four?

23
00:01:25,602 --> 00:01:29,299
[cause it's two minutes]

24
00:01:29,299 --> 00:01:31,418
cause it's two minutes

25
00:01:31,418 --> 00:01:32,760
yes

26
00:01:32,760 --> 00:01:35,890
but we're not going one minute
which is how much?

27
00:01:35,890 --> 00:01:37,570
ok you know what?

28
00:01:39,131 --> 00:01:41,179
you come draw straight lines

29
00:01:46,442 --> 00:01:48,390
[now it's going down]

30
00:01:48,390 --> 00:01:51,578
i know but it had to go down
otherwise it could yeah

31
00:01:51,578 --> 00:01:54,676
um so if two minutes goes by

32
00:01:54,676 --> 00:01:56,787
and your eating pies at a rate of

33
00:01:56,787 --> 00:01:58,096
two pies per minute

34
00:01:59,478 --> 00:02:00,822
well two minutes is

35
00:02:03,489 --> 00:02:04,534
twice the time

36
00:02:04,534 --> 00:02:05,597
so

37
00:02:05,597 --> 00:02:07,263
[twice the pies]

38
00:02:07,263 --> 00:02:08,250
twice the pies

39
00:02:08,250 --> 00:02:09,658
so yes four

40
00:02:09,658 --> 00:02:17,604
alright, one, two, three, four

41
00:02:17,604 --> 00:02:22,235
I'm trying alright

42
00:02:22,235 --> 00:02:23,902
that works

43
00:02:23,902 --> 00:02:24,706
um

44
00:02:27,036 --> 00:02:29,425
ok now first of all I want you guys
to take notice of something

45
00:02:29,425 --> 00:02:32,237
you see how I'm dragging

46
00:02:32,237 --> 00:02:37,506
out these little, I'll go ahead and
connect this one up and I'm sure it'll
be crooked and you guys will laugh at me

47
00:02:37,506 --> 00:02:38,811
but none the less

48
00:02:38,811 --> 00:02:42,195
you see how I'm trying to draw out this elapse

49
00:02:42,195 --> 00:02:44,060
time and the number of pies

50
00:02:44,060 --> 00:02:45,282
not eaten

51
00:02:45,282 --> 00:02:46,387
um

52
00:02:46,387 --> 00:02:48,229
what do you think I'm trying to illustrate there?

53
00:02:48,229 --> 00:02:53,039
think of something we've been doing
with you guys this whole semester

54
00:02:53,039 --> 00:02:56,109
[the time elapsed]

55
00:02:56,109 --> 00:03:01,485
this part show I'm trying to show the
time elapsed yes, but why I'm I trying to show you

56
00:03:01,485 --> 00:03:07,622
both of those changes? what idea I'm I using
in my head that we've been encouraging
you guys to use in your head?

57
00:03:07,622 --> 00:03:08,346
the finger tool

58
00:03:08,346 --> 00:03:11,215
the finger tool yes

59
00:03:11,215 --> 00:03:16,650
remember how Dr. on Thursday told you
anytime you see a graph you should be thinking finger tool

60
00:03:17,877 --> 00:03:20,568
he said it do you remember? were you listening?

61
00:03:20,568 --> 00:03:25,245
he's serious, I am serious when you see graph think

62
00:03:25,245 --> 00:03:26,348
finger tool

63
00:03:26,348 --> 00:03:28,402
that's what this is showing me

64
00:03:28,402 --> 00:03:31,687
my horizontal finger my number of pies and

65
00:03:31,687 --> 00:03:33,933
elapsed half a minute

66
00:03:33,933 --> 00:03:37,147
how did number of pies change?

67
00:03:37,147 --> 00:03:39,770
my total number of minutes

68
00:03:39,770 --> 00:03:41,556
has elapsed a full minute

69
00:03:41,556 --> 00:03:44,442
how has the number of pies changed

70
00:03:44,442 --> 00:03:46,407
etc, ok finger tool it