1
00:00:00;00 --> 00:00:01;14
Getting more accurate,
getting more precise,

2
00:00:01;15 --> 00:00:04;10
That implies that it's
approaching something.

3
00:00:04;11 --> 00:00:07;06
If it's getting more accurate,
that implies that it's

4
00:00:07;07 --> 00:00:10;02
Approaching the most
accurate version possible.

5
00:00:10;03 --> 00:00:13;14
Danielle, what do you think
this accurate version is?

6
00:00:13;15 --> 00:00:15;12
[It's getting closer to zero]

7
00:00:15;13 --> 00:00:17;10
What's getting
closer to zero?

8
00:00:18;08 --> 00:00:24;03
[The number on the graph?]

9
00:00:24;04 --> 00:00:25;00
Do you want to come draw?

10
00:00:25;01 --> 00:00:28;04
I don't think I know what
you're- that's why

11
00:00:28;05 --> 00:00:30;06
[Those equations
of the numbers]

12
00:00:30;07 --> 00:00:31;12
[are approaching zero]

13
00:00:31;13 --> 00:00:33;13
Which numbers are
approaching zero?

14
00:00:33;14 --> 00:00:35;07
[Interval]

15
00:00:35;08 --> 00:00:37;12
Oh, my interval size, is
that what you mean?

16
00:00:37;13 --> 00:00:39;13
My interval size is approaching zero?

17
00:00:39;14 --> 00:00:42;07
[.1 is closer to zero]

18
00:00:42;08 --> 00:00:45;05
OK, so the interval size
is approaching zero.

19
00:00:45;06 --> 00:00:49;07
Yes, as the interval
size approaches zero,

20
00:00:49;08 --> 00:00:52;03
So if this was .1,
what about .01?

21
00:00:53;11 --> 00:00:55;08
[Extra, extra small interval]

22
00:00:55;09 --> 00:00:59;05
Extra small interval, so
extra extra accurate, right?

23
00:00:59;06 --> 00:01:02;02
But again, as it's
approaching something

24
00:01:02;03 --> 00:01:06;01
That is the epitome of
accuracy. What do you

25
00:01:06;02 --> 00:01:08;11
Think that would look like?
We have this choppy thing

26
00:01:08;12 --> 00:01:10;13
As we're stuck with the
same rate of change over

29
00:01:10;14 --> 00:01:13;12
Certain intervals. As my
interval size approaches

30
00:01:13;13 --> 00:01:18;13
Zero, like Danielle said,
what would your function

31
00:01:18;14 --> 00:01:23;10
Then approach? What is
this trying to be if it's getting

32
00:01:23;11 --> 00:01:25;14
More and more accurate
like you guys say each time

33
00:01:25;15 --> 00:01:34;05
A line. What kind of rates of
change do lines have?

34
00:01:34;06 --> 00:01:35;05
[Constant]

35
00:01:35;06 --> 00:01:38;07
Constant. Is this rate
of change constant?

36
00:01:43;04 --> 00:01:43;14
[Well, kind of]

37
00:01:45;05 --> 00:01:47;09
The graph looks linear,
but remember what

38
00:01:47;10 --> 00:01:50;04
These represent. These
are rates of changes.

39
00:01:50;05 --> 00:01:53;01
Is the rate of change
constant, meaning it stays

40
00:01:53;02 --> 00:01:54;05
The same the whole way through?

41
00:01:54;06 --> 00:01:54;13
[No]

42
00:01:54;14 --> 00:01:56;01
No. Ryan?

43
00:01:56;02 --> 00:01:57;10
[It's getting closer
to zero, so]

44
00:01:57;11 --> 00:01:59;01
[it doesn't have a
constant rate of change]

45
00:02:02;01 --> 00:02:05;03
OK, hang on. Constant
rate of change.

46
00:02:05;04 --> 00:02:07;02
What would something look
like if it had a constant rate

47
00:02:07;03 --> 00:02:08;03
Of change? Tell
me what to draw.

48
00:02:08;04 --> 00:02:09;03
[A line]

49
00:02:09;04 --> 00:02:10;01
A line, how?

50
00:02:10;02 --> 00:02:11;03
[Across]

51
00:02:12;01 --> 00:02:18;08
Across how? Draw it in
the air. Draw it in the air.

52
00:02:18;09 --> 00:02:23;11
Yeah, straight. That's a
constant rate of change.

53
00:02:23;12 --> 00:02:27;04
What's the rate of change
for the line I just drew?

54
00:02:28;04 --> 00:02:30;02
[3, no it's 2.]

55
00:02:30;03 --> 00:02:33;08
2. If this is a rate of change
graph and I just drew

56
00;02:33;09 --> 00:02:36;12
That one, that is a constant
rate of change of 2.

57
00:02:36;13 --> 00:02:39;00
No matter where you are on
the X-axis, your rate of

58
00;02:39;01 --> 00:02:41;01
Change is 2. Is this a
constant rate of change?

59
00:02:43;01 --> 00:02:44;13
[No. Linear function.]

60
00:02:43;01 --> 00:02:48;14
No. It's a linear rate of
change, or at least it's

61
00:02:48;15 --> 00:02:52;09
Approaching a linear rate of
change, but it's not constant

62
00:02:52;10 --> 00:02:55;05
By any means. The rate
of change is changing.

63
00:02:55;07 --> 00:02:57;14
What did we say again?

64
00:02:57;15 --> 00:03:02;05
From zero to 1, is it
increasing or decreasing?

65
00:03:02;06 --> 00:03:06;04
Increasing or decreasing,
wake up.

66
00:03:06;07 --> 00:03:07;00
[Increasing]

67
00:03:07;01 --> 00:03:15;14
Increasing, but how? How?
A little what each time.

68
00:03:15;15 --> 00:03:17;14
A little more each time.

69
00:03:17;15 --> 00:03:21;10
From zero to 1, it's increasing,
but whatever

70
00:03:21;11 --> 00:03:23;08
the increase is in
this first section,

71
00:03:23;09 --> 00:03:26;12
How would this compare to
what it is in the next step?

72
00:03:30;01 --> 00:03:32;12
A little bit more than this
one, yeah. What

73
00:03:32;13 --> 00:03:35;13
about in the next
step? A little bit more.

74
00:03:35;14 --> 00:03:40;06
Next step? A little bit
more, because what's

75
00:03:40;07 --> 00:03:41;06
Your rate of change doing?

76
00:03:43;01 --> 00:03:46;02
Increasing the whole way
through. It's increasing,

77
00:03:46;03 --> 00:03:48;12
Yes. Is it increasing
at a constant rate?

78
00:03:48;13 --> 0:03:51;11
No, it increases a little
bit more each time.

79
00:03:52;05 --> 00:03:57;05
So, again, how is this, who
wants a marker? I'm going

80
00;03:57;06 --> 00:04:04;04
To throw it to Samantha.
Come draw. Again, we've

81
00:04:04;05 --> 00:04:06;05
Talked about, I think
Miss Coombes, it's

82
00:04:06;06 --> 00:04:07;13
Approaching. It's getting
more accurate, it's getting

83
00:04:07;14 --> 00:04:11;00
More precise. Precise
to what, though?

84
00:04:11;01 --> 00:04:13;11
[We drew whatever we drew
on our homework.]

85
00:04:23;05 --> 00:04:26;07
That's fine, just have a seat,
we'll talk, you know us.

86
00:04:26;08 --> 00:04:28;11
If it's right, we'll discover
it's right, if it's wrong,

87
00:04:28;12 --> 00:04:29;14
We'll discover it's wrong.