Dataset2/D2TCSS
From Jsarmi
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p M M | p M M | ||
azemel 5/9/06 7:08:24 PM EDT: remember, 7 pm, Thursday, same room | azemel 5/9/06 7:08:24 PM EDT: remember, 7 pm, Thursday, same room | ||
| + | |||
| + | =Session II= | ||
| + | |||
| + | ===Catching up Qw=== | ||
| + | Noticed how Qw gest involved and asks a question: | ||
| + | |||
| + | Jason 5/11/06 7:18:07 PM EDT: ok, so with this aside-- i guess we should discuss our feedback from the last session | ||
| + | jsarmi 5/11/06 7:18:34 PM EDT: make sure you bring qwertyuiop up to speed | ||
| + | Jason 5/11/06 7:18:41 PM EDT: ok | ||
| + | Jason 5/11/06 7:19:35 PM EDT: for the problems last session, we came up with formulas to find the values for the columns | ||
| + | qwertyuiop 5/11/06 7:20:02 PM EDT: in the view topic thing? | ||
| + | Jason 5/11/06 7:20:03 PM EDT: You can see them to the left of this text; our formula for the total number | ||
| + | of sticks or squares for any number N is given | ||
| + | Jason 5/11/06 7:20:09 PM EDT: yes | ||
| + | qwertyuiop 5/11/06 7:20:12 PM EDT: ok | ||
| + | Jason 5/11/06 7:20:17 PM EDT: that was the problem we were given | ||
| + | Jason 5/11/06 7:20:39 PM EDT: remains of our discussion is on the whiteboard and online wiki | ||
| + | 137 5/11/06 7:21:25 PM EDT: I think David forgot today... Our teacher didn't remind us. | ||
| + | p M | ||
| + | jsarmi 5/11/06 7:22:35 PM EDT: I see... hopefully he will join you next Tuesday | ||
| + | qwertyuiop 5/11/06 7:23:35 PM EDT: n=3 is 3+2+1 squares, n=4 is 4+3+2+1 squares... how did you get n(1+n)/2 | ||
| + | Jason 5/11/06 7:23:42 PM EDT: oh | ||
| + | Jason 5/11/06 7:23:53 PM EDT: that's the formula for finding a series of consecutive numbers | ||
| + | Jason 5/11/06 7:24:08 PM EDT: 1+2+3+4+...n = ((n)(n+1))/2 | ||
| + | |||
| + | ===Recursive Function and the Feedback === | ||
| + | |||
| + | Jason 5/11/06 7:26:32 PM EDT: so apparently there's something with a recursive sequence that we should discuss | ||
| + | 137 5/11/06 7:26:55 PM EDT: What was a recursice sequence again? | ||
| + | qwertyuiop 5/11/06 7:27:03 PM EDT: recursive sequence? | ||
Revision as of 19:32, 29 November 2007
Contents |
Group Trajectory
Session 1: Session 2: Feedback attended to Session 3: Session 4:
Group composition: Stable
Session 1: js dc ot ss(L)
Session 2: js ot qw
Session 3:
Session 4:
(L) Late
(*) js knows ss: e.g. Jason 5/11/06 7:07:52 PM EDT: ssjnish says that his client is still loading
ot knows dc: e.g. 137 5/11/06 7:21:25 PM EDT: I think David forgot today... Our teacher didn't remind us.
Session I
They join within seconds:
Jason joins the room 5/9/06 6:24:03 PM EDT davidcyl joins the room 5/9/06 6:24:04 PM EDT 137 joins the room 5/9/06 6:24:15 PM EDT
We did this in class
Notice how it is 137 who ends up posting the formula
Jason 5/9/06 6:25:44 PM EDT: ooh we just did this in math class about a week ago! :-) p M M M azemel 5/9/06 6:25:54 PM EDT: if you have any questions, just ask Jason 5/9/06 6:25:55 PM EDT: well, not the exact thing, but sequences and series p M M Jason 5/9/06 6:26:03 PM EDT: anyhow p M M M M M M M Jason 5/9/06 6:26:21 PM EDT: so do we see how the number of sticks grows in a sequence? davidcyl 5/9/06 6:26:25 PM EDT: ok i've drawn n=4,5,6 Jason 5/9/06 6:26:29 PM EDT: 4(+6) = 10 Jason 5/9/06 6:26:36 PM EDT: 10(+8) = 18 p M M Jason 5/9/06 6:26:48 PM EDT: i'm guessing 18(+10) = 28 for the next one, according to this pattern davidcyl 5/9/06 6:27:32 PM EDT: the nth pattern has n more squares than the (n-1)th pattern davidcyl 5/9/06 6:27:55 PM EDT: basically it's 1+2+..+(n-1)+n for the number of squares in the nth pattern 137 5/9/06 6:28:16 PM EDT: so n(n+1)/2 davidcyl 5/9/06 6:28:24 PM EDT: and we can use the gaussian sum to determine the sum: n(1+n)/2 davidcyl 5/9/06 6:28:36 PM EDT: 137 got it
Recursive or Explicit?
Notice that Jason ASKS and david offers his opinion. See Session II
davidcyl 5/9/06 6:29:31 PM EDT: well to find the number of sticks: davidcyl 5/9/06 6:29:39 PM EDT: let's look on the board p M M M Jason 5/9/06 6:29:54 PM EDT: should we use a recursive or explicit definition for it p M M davidcyl 5/9/06 6:30:20 PM EDT: i don't think we need recursion
Horizontal and Vertical
As in Team B
(david circles horizontal lines in a pattern diagram on the whiteboard) davidcyl 5/9/06 6:32:21 PM EDT: 137: i'm separating the sticks into vertical and horizontal sticks davidcyl 5/9/06 6:30:33 PM EDT: it's simpler to express it as 1+2+...+n
Not Shared
Disoriented, then MY formula
davidcyl 5/9/06 6:32:30 PM EDT: wait what are you working on? Jason 5/9/06 6:32:32 PM EDT: wait lemme check davidcyl 5/9/06 6:32:35 PM EDT: (to 137) 137 5/9/06 6:32:46 PM EDT: Great. Confused. Jason 5/9/06 6:33:03 PM EDT: 137 are you talking about # sticks or squares 137 5/9/06 6:33:09 PM EDT: Sticks. Jason 5/9/06 6:33:18 PM EDT: ok davidcyl 5/9/06 6:33:21 PM EDT: i would think it's 2(n(1+n)/2) + n + n Jason 5/9/06 6:33:23 PM EDT: well i think my formula works Jason 5/9/06 6:33:33 PM EDT: provided that you have a value for N
but later (after an interruption)
davidcyl 5/9/06 6:35:03 PM EDT: this simplifies to n(1+n) + 2n, or n(3+n) davidcyl 5/9/06 6:35:09 PM EDT: so jason, you're right Jason 5/9/06 6:35:16 PM EDT: :-) Jason 5/9/06 6:35:36 PM EDT: so now onto a formula for the total number of squares
Ssjnish joins
ssjnish joins the room 5/9/06 6:34:25 PM EDT
Didn't we do that?
davidcyl 5/9/06 6:35:03 PM EDT: this simplifies to n(1+n) + 2n, or n(3+n) davidcyl 5/9/06 6:35:09 PM EDT: so jason, you're right Jason 5/9/06 6:35:16 PM EDT: :-) Jason 5/9/06 6:35:36 PM EDT: so now onto a formula for the total number of squares davidcyl 5/9/06 6:35:42 PM EDT: ok let's complete the table Jason 5/9/06 6:35:46 PM EDT: if you take the change in the change of the number of squares, it's constant 137 5/9/06 6:36:10 PM EDT: Didn't we do that? (points to Jason's message on 6:35:36 PM) davidcyl 5/9/06 6:36:19 PM EDT: yes Jason 5/9/06 6:36:27 PM EDT: oh, sorry i guess i must've not caught that davidcyl 5/9/06 6:36:33 PM EDT: look up (points to davidcyl 5/9/06 6:28:24 PM EDT: and we can use the gaussian sum to determine the sum: n(1+n)/2) Jason 5/9/06 6:36:33 PM EDT: could someone post it in a text box on the whiteboard davidcyl 5/9/06 6:36:38 PM EDT: sure azemel 5/9/06 6:36:40 PM EDT: be sure that SSJNISH is up to speed folks (Textbox created)
A summary for Ssjnish
Notice the diffeence between We've figured out and I divided
davidcyl 5/9/06 6:38:30 PM EDT: basically, we've figured out that the number of squares in the nth pattern is 1 + 2 + ... + n p M 137 5/9/06 6:38:33 PM EDT: It was blinding. p M M M M davidcyl 5/9/06 6:39:26 PM EDT: then, to find the number of sticks, I divided the figure into "vertical sticks" (|) and "horizontal sticks" (--) Jason 5/9/06 6:39:41 PM EDT: the formulas are on the Whiteboard azemel 5/9/06 6:39:56 PM EDT: don't forget to post your ideas to the wiki when you think it's time! davidcyl 5/9/06 6:40:15 PM EDT: the number of vertical sticks is (1 + 2 + 3 + ... + n)+ n, and the number of horizontal sticks is the same p M
Ssjnish asks for an explanation
This is interesting because it prompts a form of "bridging" in a sense
ssjnish 5/9/06 6:45:11 PM EDT: just to clarify sumthing, i am not overwhelmingly good at math as u guys seem to be,
so it may take me more time than u guys to understand sumthing..
azemel 5/9/06 6:45:44 PM EDT: can you tell us what's puzzling you?
Jason 5/9/06 6:46:07 PM EDT: are we allowed to post images on the wiki? I could just download TeX real quick and get the
summation notation in a small graphic
ssjnish 5/9/06 6:46:12 PM EDT: the derivation of the number of squares
Jason 5/9/06 6:46:21 PM EDT: oh
Jason 5/9/06 6:46:31 PM EDT: so you see in the list a column for "N"
Jason 5/9/06 6:46:50 PM EDT: when n=1, we have 1 square; for n=2, 3; and for n=3, 6
Jason 5/9/06 6:47:00 PM EDT: we came up with a formula to find the total number of squares for any number N
Jason 5/9/06 6:47:16 PM EDT: the purpose of the formula is so that you don't have to draw out the squares and count them
ssjnish 5/9/06 6:47:39 PM EDT: um yes
ssjnish 5/9/06 6:47:41 PM EDT: i know
ssjnish 5/9/06 6:47:51 PM EDT: but how did u get that formula
Jason 5/9/06 6:48:00 PM EDT: oh
azemel 5/9/06 6:48:11 PM EDT: i believe so
Jason 5/9/06 6:48:12 PM EDT: uh, basically you try to find a pattern in the total number of squares first
Moderator's Closing
azemel 5/9/06 7:08:04 PM EDT: well, if you're done with the sticks problem as it stands,
then this might be a time to stop. there will be another problem on Thursday
p M M
azemel 5/9/06 7:08:24 PM EDT: remember, 7 pm, Thursday, same room
Session II
Catching up Qw
Noticed how Qw gest involved and asks a question:
Jason 5/11/06 7:18:07 PM EDT: ok, so with this aside-- i guess we should discuss our feedback from the last session
jsarmi 5/11/06 7:18:34 PM EDT: make sure you bring qwertyuiop up to speed
Jason 5/11/06 7:18:41 PM EDT: ok
Jason 5/11/06 7:19:35 PM EDT: for the problems last session, we came up with formulas to find the values for the columns
qwertyuiop 5/11/06 7:20:02 PM EDT: in the view topic thing?
Jason 5/11/06 7:20:03 PM EDT: You can see them to the left of this text; our formula for the total number
of sticks or squares for any number N is given
Jason 5/11/06 7:20:09 PM EDT: yes
qwertyuiop 5/11/06 7:20:12 PM EDT: ok
Jason 5/11/06 7:20:17 PM EDT: that was the problem we were given
Jason 5/11/06 7:20:39 PM EDT: remains of our discussion is on the whiteboard and online wiki
137 5/11/06 7:21:25 PM EDT: I think David forgot today... Our teacher didn't remind us.
p M
jsarmi 5/11/06 7:22:35 PM EDT: I see... hopefully he will join you next Tuesday
qwertyuiop 5/11/06 7:23:35 PM EDT: n=3 is 3+2+1 squares, n=4 is 4+3+2+1 squares... how did you get n(1+n)/2
Jason 5/11/06 7:23:42 PM EDT: oh
Jason 5/11/06 7:23:53 PM EDT: that's the formula for finding a series of consecutive numbers
Jason 5/11/06 7:24:08 PM EDT: 1+2+3+4+...n = ((n)(n+1))/2
Recursive Function and the Feedback
Jason 5/11/06 7:26:32 PM EDT: so apparently there's something with a recursive sequence that we should discuss 137 5/11/06 7:26:55 PM EDT: What was a recursice sequence again? qwertyuiop 5/11/06 7:27:03 PM EDT: recursive sequence?
