NationalTutoringObservatory/MathEd-PII · Datasets at Hugging Face

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	I'm doing good, let's break this question down.	11,236	2	[]
volunteer	Do you know what 35 - x represents here?	11,236	3	[]
student	Well 35 is the amount of time Sarah will use, and x how much faster Sarah can wash the car. Maybe the fractional part of the job that she completes?	11,236	4	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 30, "end": 35 }, { "pii_type": "PERSON", "surrogate": "Sarah", "start": 68, "end": 73 } ]
volunteer	Great! Not exactly, the fractional part of the job, since we are just looking at the denominator, but almost. If Sarah takes 35 minutes, and David is faster than Sarah by x minutes. Then David can do it 35 - x minutes.	11,236	5	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 115, "end": 120 }, { "pii_type": "PERSON", "surrogate": "David", "start": 143, "end": 148 }, { "pii_type": "PERSON", "surrogate": "Sarah", "start": 164, "end": 169 }, { "pii_type": "PERSON", "s...
volunteer	So Sarah can wash a car in 35 minutes, and David can in 35 - x minutes right? If you want any clarification on anything throughout this session please let me know as well!	11,236	6	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 3, "end": 8 }, { "pii_type": "PERSON", "surrogate": "David", "start": 43, "end": 48 } ]
student	Okay, thank you! Could you please expand a bit on how we know that 35-x would represent the amount of time it would take her? It is taking a bit for me to understand, sorry	11,236	7	[]
volunteer	Say you can bake a cake in 45 minutes right?	11,236	8	[]
volunteer	If I can do it 5 minutes faster, how long will it take me to bake it?	11,236	9	[]
student	40?	11,236	10	[]
volunteer	Exactly! I am 5 minutes faster than you, so you can figure out how long I will take by using the expression 45 - 5	11,236	11	[]
volunteer	Let's say now I don't know how much faster I am, but I am faster than you. It's the same exact thing right?	11,236	12	[]
student	Right!	11,236	13	[]
volunteer	You can figure out how long it takes me by doing 45 - (How much faster I am) Or 45 - x	11,236	14	[]
volunteer	So, here the denominator 35 - x represents how fast David can wash a car	11,236	15	[ { "pii_type": "PERSON", "surrogate": "David", "start": 52, "end": 57 } ]
student	That makes more sense, thank you!	11,236	16	[]
volunteer	Now, If I say it takes me and you 50 minutes to bake a cake, how can you figure out how much of it I did?	11,236	17	[]
student	I think I could start with x+y=50?	11,236	18	[]
volunteer	And what would x and y represent?	11,236	19	[]
student	x could be amount of time it took me, and y could be the amount of time it took you	11,236	20	[]
volunteer	Going back to our cake example, how long did it take you and how long did it take me?	11,236	21	[]
student	I think it took me 45 minutes, and you 40 minutes	11,236	22	[]
volunteer	Wait, I'm sorry, please scrap what I've said, I have explained this very poorly.	11,236	23	[]
volunteer	What do you think y represents here?	11,236	24	[]
volunteer	I had a slight misunderstanding about the problem earlier	11,236	25	[]
student	No worries	11,236	26	[]
volunteer	What do you think y represents here?	11,236	27	[]
student	I think it would relate to the cars, maybe how many they can wash together?	11,236	28	[]
volunteer	Not exactly, when looking at a problem like this, always try to refer to what it's asking you.	11,236	29	[]
volunteer	Here, we know 35 - x is the speed Sarah can wash a car right?	11,236	30	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 34, "end": 39 } ]
student	Yes	11,236	31	[]
volunteer	So, we are dividing something by her speed	11,236	32	[]
volunteer	So, let's say y represented the number of cars they washed together	11,236	33	[]
volunteer	We would be doing Numbers of cars / Times it takes for Sarah	11,236	34	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 56, "end": 61 } ]
volunteer	Now, that may seem very confusing, so let's plug in some random numbers. Let's say they wash 1 car and Sarah takes 30 minutes to wash one car	11,236	35	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 104, "end": 109 } ]
volunteer	So we are trying to divide 1 car by 30 minutes per car wash	11,236	36	[]
volunteer	Which doesn't really solve for anything	11,236	37	[]
volunteer	Essentially, just plug in what you think it's saying, and if it doesn't make sense, it probably isn't right.	11,236	38	[]
volunteer	Something that would make sense is doing something like Let's say I washed 3 cars in 30 minutes. I could say I did 3 cars / 30 minutes Which tells me I can do 3 cars every 30 minutes	11,236	39	[]
volunteer	In this case, I can wash one car every 10 minutes right?	11,236	40	[]
student	Right	11,236	41	[]
volunteer	So the rate at which I wash a car is 10 minutes per car. If I now tried to divide the amount of cars by the rate that I can wash cars, I would be trying to do 3 cars / 10 minutes per car	11,236	42	[]
volunteer	Which, you wouldn't divide by the rate here, you would multiply 3 times 10 instead right?	11,236	43	[]
volunteer	To backtrack the amount of time, you would do 3 X 10 right? Not 3/10 .	11,236	44	[]
student	I think so?	11,236	45	[]
volunteer	This probably is very confusing, but, essentially, it's not the total amount.	11,236	46	[]
volunteer	Just know, because you are dividing by the speed Sarah takes, the top can't the total number of cars	11,236	47	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 49, "end": 54 } ]
student	Got it	11,236	48	[]
volunteer	It may not make sense now, but this will just make sense as you do more of these problems. It's much more intuitive than something you can put in words, I'm honestly genuinely sorry I just put you through that	11,236	49	[]
volunteer	Anyways	11,236	50	[]
student	That's okay	11,236	51	[]
volunteer	For a question like this, just think what can I plug into the top of the equation, to actually solve for something.	11,236	52	[]
student	Okay, I will keep that in mind. Thank you.	11,236	53	[]
volunteer	So, if y represented the total amount of time it took them to wash a car, what do you think dividing by the Sarah's speed would do?	11,236	54	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 108, "end": 113 } ]
volunteer	To put it in words, I am doing Total time / Sarah's speed	11,236	55	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 44, "end": 49 } ]
volunteer	What do you think that would tell us?	11,236	56	[]
student	I'm not too sure, because we already know Sarah's time, I don't think we are multiplying anything by Sarah's time to get the total?	11,236	57	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 42, "end": 47 }, { "pii_type": "PERSON", "surrogate": "Sarah", "start": 102, "end": 107 } ]
volunteer	Okay, let's refer back to the situation first, Sarah and David are washing this car together right?	11,236	58	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 47, "end": 52 }, { "pii_type": "PERSON", "surrogate": "David", "start": 57, "end": 62 } ]
student	Yes	11,236	59	[]
volunteer	Now, remember, you take 45 minutes to bake a cake and I take 40 minutes to bake a cake.	11,236	60	[]
volunteer	Now let's say we took 20 minutes to bake a single cake	11,236	61	[]
volunteer	If I want to find the proportion of the job that I did I would divide the time it took for us by our speed right?	11,236	62	[]
volunteer	I have a really good way to demonstrate this now.	11,236	63	[]
volunteer	Let's say it takes us some time to bake a cake together right?	11,236	64	[]
student	Right	11,236	65	[]
volunteer	You take 45 minutes	11,236	66	[]
volunteer	I take 40 minutes	11,236	67	[]
volunteer	But altogether, the amounts of the job that we did totaled to ONE cake right?	11,236	68	[]
student	Right	11,236	69	[]
volunteer	So, the fraction of work you did plus the fraction of work I did equaled the one cake	11,236	70	[]
volunteer	But, if I want to figure out what fraction of the work I did or you did, I could take our total time spent together divided by our speed right?	11,236	71	[]
volunteer	Look at the equation I have up	11,236	72	[]
volunteer	The total time we took together divided by my speed	11,236	73	[]
volunteer	Plus the total time it took together divided by the time it takes me	11,236	74	[]
volunteer	Gave us that one cake	11,236	75	[]
volunteer	Basically, the fraction of your work in the job was Total time / How long it takes you to make a cake	11,236	76	[]
volunteer	Does that part make sense?	11,236	77	[]
student	I think so, yes	11,236	78	[]
volunteer	So the fraction of work that you did is t / 45 I can do the same for the fraction of work I did which is t / 40	11,236	79	[]
volunteer	Now the work we put into the job is made us ONE cake right?	11,236	80	[]
student	Yes	11,236	81	[]
volunteer	Now, let's go back, imagine you don't know how much faster I am than you when it comes to making a cake	11,236	82	[]
volunteer	My speed in making a cake could be represented by 45 - x	11,236	83	[]
student	Okay	11,236	84	[]
volunteer	So, now my fraction of work in baking the cake is t / (45 - x)	11,236	85	[]
volunteer	So, in this situation where we are working on together and we know both our speeds, taking the total time it took us to do a job divided by how fast we normally do a job, gives us our fraction of work in the job	11,236	86	[]
student	Okay	11,236	87	[]
student	That makes sense	11,236	88	[]
volunteer	Okay, I'm honestly really sorry for this, this question is purely conceptual, I honestly think it's stupid that they ask a question like this, but I guess I just cannot seem to explain it clearly.	11,236	89	[]
volunteer	Going back to our original problem We are dividing by Sarah's speed right?	11,236	90	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 55, "end": 60 } ]
student	Yes, we are. And that's okay, I appreciate you trying your best to explain it	11,236	91	[]
volunteer	So, if we are dividing by Sarah's speed, in a situation where people are working on a job together, it would make sense to have the total time it took altogether as the numerator right?	11,236	92	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 26, "end": 31 } ]
student	Yes	11,236	93	[]
volunteer	And dividing this total time together by Sarah's speed will give us Sarah's part in the job	11,236	94	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 41, "end": 46 }, { "pii_type": "PERSON", "surrogate": "Sarah", "start": 68, "end": 73 } ]
volunteer	In this situation, how could you represent Sarah's fraction of work in the job?	11,236	95	[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 43, "end": 48 } ]
student	We could do the total amount, t over 35?	11,236	96	[]
volunteer	Exactly,	11,236	97	[]
volunteer	If we added their fractional amounts of work together, what should we get as well?	11,236	98	[]
student	The total amount of time it takes for 1 car?	11,236	99	[]
volunteer	Not exactly, we were using the total amount of time it took together to figure out how much of the job they did right?	11,236	100	[]
volunteer	By doing t / 35 t / (35-x)	11,236	101	[]

volunteer

I'm doing good, let's break this question down.

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volunteer

Do you know what 35 - x represents here?

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student

Well 35 is the amount of time Sarah will use, and x how much faster Sarah can wash the car. Maybe the fractional part of the job that she completes?

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 30, "end": 35 }, { "pii_type": "PERSON", "surrogate": "Sarah", "start": 68, "end": 73 } ]

volunteer

Great! Not exactly, the fractional part of the job, since we are just looking at the denominator, but almost. If Sarah takes 35 minutes, and David is faster than Sarah by x minutes. Then David can do it 35 - x minutes.

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 115, "end": 120 }, { "pii_type": "PERSON", "surrogate": "David", "start": 143, "end": 148 }, { "pii_type": "PERSON", "surrogate": "Sarah", "start": 164, "end": 169 }, { "pii_type": "PERSON", "s...

volunteer

So Sarah can wash a car in 35 minutes, and David can in 35 - x minutes right? If you want any clarification on anything throughout this session please let me know as well!

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 3, "end": 8 }, { "pii_type": "PERSON", "surrogate": "David", "start": 43, "end": 48 } ]

student

Okay, thank you! Could you please expand a bit on how we know that 35-x would represent the amount of time it would take her? It is taking a bit for me to understand, sorry

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volunteer

Say you can bake a cake in 45 minutes right?

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volunteer

If I can do it 5 minutes faster, how long will it take me to bake it?

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student

40?

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volunteer

Exactly! I am 5 minutes faster than you, so you can figure out how long I will take by using the expression 45 - 5

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volunteer

Let's say now I don't know how much faster I am, but I am faster than you. It's the same exact thing right?

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student

Right!

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volunteer

You can figure out how long it takes me by doing 45 - (How much faster I am) Or 45 - x

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volunteer

So, here the denominator 35 - x represents how fast David can wash a car

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[ { "pii_type": "PERSON", "surrogate": "David", "start": 52, "end": 57 } ]

student

That makes more sense, thank you!

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volunteer

Now, If I say it takes me and you 50 minutes to bake a cake, how can you figure out how much of it I did?

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student

I think I could start with x+y=50?

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volunteer

And what would x and y represent?

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student

x could be amount of time it took me, and y could be the amount of time it took you

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volunteer

Going back to our cake example, how long did it take you and how long did it take me?

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student

I think it took me 45 minutes, and you 40 minutes

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volunteer

Wait, I'm sorry, please scrap what I've said, I have explained this very poorly.

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volunteer

What do you think y represents here?

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volunteer

I had a slight misunderstanding about the problem earlier

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student

No worries

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volunteer

What do you think y represents here?

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student

I think it would relate to the cars, maybe how many they can wash together?

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volunteer

Not exactly, when looking at a problem like this, always try to refer to what it's asking you.

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volunteer

Here, we know 35 - x is the speed Sarah can wash a car right?

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 34, "end": 39 } ]

student

Yes

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volunteer

So, we are dividing something by her speed

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volunteer

So, let's say y represented the number of cars they washed together

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volunteer

We would be doing Numbers of cars / Times it takes for Sarah

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 56, "end": 61 } ]

volunteer

Now, that may seem very confusing, so let's plug in some random numbers. Let's say they wash 1 car and Sarah takes 30 minutes to wash one car

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 104, "end": 109 } ]

volunteer

So we are trying to divide 1 car by 30 minutes per car wash

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volunteer

Which doesn't really solve for anything

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[]

volunteer

Essentially, just plug in what you think it's saying, and if it doesn't make sense, it probably isn't right.

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volunteer

Something that would make sense is doing something like Let's say I washed 3 cars in 30 minutes. I could say I did 3 cars / 30 minutes Which tells me I can do 3 cars every 30 minutes

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volunteer

In this case, I can wash one car every 10 minutes right?

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student

Right

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volunteer

So the rate at which I wash a car is 10 minutes per car. If I now tried to divide the amount of cars by the rate that I can wash cars, I would be trying to do 3 cars / 10 minutes per car

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volunteer

Which, you wouldn't divide by the rate here, you would multiply 3 times 10 instead right?

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volunteer

To backtrack the amount of time, you would do 3 X 10 right? Not 3/10 .

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student

I think so?

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volunteer

This probably is very confusing, but, essentially, it's not the total amount.

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volunteer

Just know, because you are dividing by the speed Sarah takes, the top can't the total number of cars

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 49, "end": 54 } ]

student

Got it

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volunteer

It may not make sense now, but this will just make sense as you do more of these problems. It's much more intuitive than something you can put in words, I'm honestly genuinely sorry I just put you through that

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volunteer

Anyways

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student

That's okay

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volunteer

For a question like this, just think what can I plug into the top of the equation, to actually solve for something.

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student

Okay, I will keep that in mind. Thank you.

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volunteer

So, if y represented the total amount of time it took them to wash a car, what do you think dividing by the Sarah's speed would do?

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 108, "end": 113 } ]

volunteer

To put it in words, I am doing Total time / Sarah's speed

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 44, "end": 49 } ]

volunteer

What do you think that would tell us?

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student

I'm not too sure, because we already know Sarah's time, I don't think we are multiplying anything by Sarah's time to get the total?

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 42, "end": 47 }, { "pii_type": "PERSON", "surrogate": "Sarah", "start": 102, "end": 107 } ]

volunteer

Okay, let's refer back to the situation first, Sarah and David are washing this car together right?

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 47, "end": 52 }, { "pii_type": "PERSON", "surrogate": "David", "start": 57, "end": 62 } ]

student

Yes

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volunteer

Now, remember, you take 45 minutes to bake a cake and I take 40 minutes to bake a cake.

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volunteer

Now let's say we took 20 minutes to bake a single cake

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volunteer

If I want to find the proportion of the job that I did I would divide the time it took for us by our speed right?

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volunteer

I have a really good way to demonstrate this now.

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volunteer

Let's say it takes us some time to bake a cake together right?

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student

Right

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volunteer

You take 45 minutes

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volunteer

I take 40 minutes

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volunteer

But altogether, the amounts of the job that we did totaled to ONE cake right?

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student

Right

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volunteer

So, the fraction of work you did plus the fraction of work I did equaled the one cake

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volunteer

But, if I want to figure out what fraction of the work I did or you did, I could take our total time spent together divided by our speed right?

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volunteer

Look at the equation I have up

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volunteer

The total time we took together divided by my speed

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volunteer

Plus the total time it took together divided by the time it takes me

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volunteer

Gave us that one cake

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volunteer

Basically, the fraction of your work in the job was Total time / How long it takes you to make a cake

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volunteer

Does that part make sense?

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student

I think so, yes

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volunteer

So the fraction of work that you did is t / 45 I can do the same for the fraction of work I did which is t / 40

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volunteer

Now the work we put into the job is made us ONE cake right?

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student

Yes

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volunteer

Now, let's go back, imagine you don't know how much faster I am than you when it comes to making a cake

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volunteer

My speed in making a cake could be represented by 45 - x

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student

Okay

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volunteer

So, now my fraction of work in baking the cake is t / (45 - x)

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volunteer

So, in this situation where we are working on together and we know both our speeds, taking the total time it took us to do a job divided by how fast we normally do a job, gives us our fraction of work in the job

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student

Okay

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student

That makes sense

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volunteer

Okay, I'm honestly really sorry for this, this question is purely conceptual, I honestly think it's stupid that they ask a question like this, but I guess I just cannot seem to explain it clearly.

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volunteer

Going back to our original problem We are dividing by Sarah's speed right?

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 55, "end": 60 } ]

student

Yes, we are. And that's okay, I appreciate you trying your best to explain it

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volunteer

So, if we are dividing by Sarah's speed, in a situation where people are working on a job together, it would make sense to have the total time it took altogether as the numerator right?

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 26, "end": 31 } ]

student

Yes

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volunteer

And dividing this total time together by Sarah's speed will give us Sarah's part in the job

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 41, "end": 46 }, { "pii_type": "PERSON", "surrogate": "Sarah", "start": 68, "end": 73 } ]

volunteer

In this situation, how could you represent Sarah's fraction of work in the job?

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[ { "pii_type": "PERSON", "surrogate": "Sarah", "start": 43, "end": 48 } ]

student

We could do the total amount, t over 35?

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volunteer

Exactly,

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volunteer

If we added their fractional amounts of work together, what should we get as well?

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student

The total amount of time it takes for 1 car?

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volunteer

Not exactly, we were using the total amount of time it took together to figure out how much of the job they did right?

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volunteer

By doing t / 35 t / (35-x)

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