Dataset2/D2TCSS
From Jsarmi
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: Session 3: Session 4: (L) Late
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
