Datasets:
NationalTutoringObservatory
/
MathEd-PII

Dataset card Data Studio Files
xet
 Community
1
role
stringclasses
2 values
content
stringlengths
0
2.1k
session_id
int64
10
21.7k
sequence_id
int64
0
2.38k
annotations
listlengths
0
8
volunteer
uh solve the problem.
15,082
224
[]
volunteer
Cause I mean, you know, when you look at a problem like, oh, if I can just rewrite this to be like a square hole, then I can use the square peg.
15,082
225
[]
volunteer
or something else
15,082
226
[]
student
right
15,082
227
[]
volunteer
Um, and then the following table 7.2 indicates a type of simpl fractions that are being associated.
15,082
228
[]
volunteer
associated with various kinds of rational fractions.
15,082
229
[]
volunteer
All right, so here
15,082
230
[]
volunteer
we have
15,082
231
[]
volunteer
um this first stipulation threw me off for a I I rethink about it. I don't know why, but
15,082
232
[]
volunteer
give me one sec
15,082
233
[]
student
sure
15,082
234
[]
volunteer
Right, I think I just assumed it said A cannot equal zero, and I was throwing me off.
15,082
235
[]
volunteer
Um, but this first one
15,082
236
[]
volunteer
this saying that A cannot equal zero,
15,082
237
[]
volunteer
it's kind of an important s uh stipulation.
15,082
238
[]
volunteer
because if, if A equals 0, then we'd just be left with x^2 - a^2 minus x minus x1, which is already given in the previous chapter.
15,082
239
[]
student
ohh right, we have directly formula for it
15,082
240
[]
volunteer
So they're just, yeah.
15,082
241
[]
volunteer
right now they, they're just kind of
15,082
242
[]
volunteer
stipulating that they have to be, just so that we have, we already, we already solved the other one we care about when these are the other cases of um
15,082
243
[]
volunteer
the denominator being different of the denominator being different, right? You already solved x^2 - a^2 minus a. Now we care about when it's
15,082
244
[]
volunteer
X minus A and X + X minus B. And one thing you notice, um
15,082
245
[]
volunteer
is, there is no coefficient for X, it's just 1.
15,082
246
[]
volunteer
All the everything the denominator has no eco efficient, which means that whatever form you get, you have to factor out
15,082
247
[]
volunteer
the coefficients
15,082
248
[]
student
right
15,082
249
[]
volunteer
um and pull them out of the inner grand. I mean, you don't have to pull them out of the innergra, but you do have to pull them out
15,082
250
[]
volunteer
um,
15,082
251
[]
volunteer
of the expression
15,082
252
[]
student
gotcha!
15,082
253
[]
volunteer
cause it may be useful to pull, to pull it out of the denometer and then you kind of
15,082
254
[]
volunteer
can reduce the numerator, but sometimes it won't happen, so you may just have to pull it out of the inner grand entirely.
15,082
255
[]
volunteer
So one thing that's interesting is
15,082
256
[]
volunteer
this um
15,082
257
[]
volunteer
squared term in the bottom x minus a square.
15,082
258
[]
volunteer
where it actually comes out to these two forms here.
15,082
259
[]
volunteer
the kind of X over A over X minus A and then big B over X minus B / (x-a)^2.
15,082
260
[]
volunteer
That's interesting
15,082
261
[]
student
yeah, they took it like that so that lcm can be (x-a)^a
15,082
262
[]
student
2*
15,082
263
[]
volunteer
Yeah
15,082
264
[]
volunteer
yeah
15,082
265
[]
volunteer
um
15,082
266
[]
volunteer
he's got multiple, yeah. Um
15,082
267
[]
volunteer
another thing here is that, you know, using, oh jeez, what? I don't want to talk to co-pilot. Jeez, go away.
15,082
268
[]
volunteer
Um
15,082
269
[]
volunteer
sorry, I'm just being harassed by
15,082
270
[]
volunteer
Microsoft, uh
15,082
271
[]
volunteer
and one thing, you know, using this method, you will
15,082
272
[]
volunteer
get um
15,082
273
[]
volunteer
A, B, or C, you will get fractions.
15,082
274
[]
volunteer
because you will have, because you do have to pull out the coefficients for X, you will more than likely have fractions like X minus 1/2, you know, X minus 2/3, you know, so on and so forth. So just
15,082
275
[]
volunteer
kind of be mindful of that.
15,082
276
[]
volunteer
Then
15,082
277
[]
student
yeah, right
15,082
278
[]
volunteer
here's another one
15,082
279
[]
volunteer
right.
15,082
280
[]
volunteer
LCM here.
15,082
281
[]
volunteer
and just added a separate term.
15,082
282
[]
volunteer
but this is a third-order cubic function in the bottom.
15,082
283
[]
volunteer
and same here.
15,082
284
[]
volunteer
It says we're Ax^2 + BX + C cannot be factorized further.
15,082
285
[]
volunteer
Right? Cause if you did, then you just have
15,082
286
[]
volunteer
um 3 then.
15,082
287
[]
volunteer
OK, that's the theory.
15,082
288
[]
volunteer
Now for example.
15,082
289
[]
volunteer
Um
15,082
290
[]
volunteer
I kind of want to screenshot this.
15,082
291
[]
volunteer
Do you know how to just take a pic, uh, take a screenshot of the tab
15,082
292
[]
volunteer
I forget how to do that
15,082
293
[]
student
yeah
15,082
294
[]
student
you can take snip
15,082
295
[]
volunteer
Oh yeah, snippy snip
15,082
296
[]
student
it's win + shift + s
15,082
297
[]
volunteer
When shift
15,082
298
[]
volunteer
S
15,082
299
[]
volunteer
Hm
15,082
300
[]
volunteer
Actually, you know what? I wanna take a snippy snip of the previous ones too.
15,082
301
[]
volunteer
Oh, why did they separate these? Why couldn't they just have a nice table?
15,082
302
[]
volunteer
Girl?
15,082
303
[]
volunteer
Gir.
15,082
304
[]
volunteer
Oh, wind shift S, sorry you had to be here to watch this.
15,082
305
[]
volunteer
Just some housekeeping.
15,082
306
[]
volunteer
Um.
15,082
307
[]
volunteer
not this.
15,082
308
[]
volunteer
Just snipping crazy.
15,082
309
[]
student
you can zoom out a bit, to add that one in
15,082
310
[]
volunteer
Um, I, are there any other forms?
15,082
311
[]
volunteer
Well, I guess I could have
15,082
312
[]
volunteer
Mm, lean out.
15,082
313
[]
volunteer
Hit that page divider
15,082
314
[]
volunteer
I'm sorry, hate is a strong word. I dislike it.
15,082
315
[]
volunteer
Yeah
15,082
316
[]
volunteer
Um, let's see. Are there any other forms
15,082
317
[]
volunteer
that I think it's
15,082
318
[]
volunteer
True identities
15,082
319
[]
student
you have to save this snips too, if wanna see them later
15,082
320
[]
volunteer
cause I'm too lazy
15,082
321
[]
volunteer
Oh shoot, did I not save them?
15,082
322
[]
volunteer
No, I think they're saved.
15,082
323
[]