Pam  00:01

Hey, fellow mathers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam, a former mimicker turned mather.

Kim  00:09

And I'm Kim, a reasoner who now knows how to share her thinking with others. At Math is Figure-Out-Able, we are on a mission to improve math teaching. 

Pam  00:17

We know that algorithms are amazing human achievements, but they're not good teaching tools because mimicking step-by-step procedures can actually trap students into using less sophisticated reasoning than the problems are intended to develop.

Kim  00:30

In this podcast, we help you teach mathing, building relationships with your students, and grappling with mathematical relationships.

Pam  00:37

We invite you to join us to make math more figure-out-able. 

Kim  00:41

Hey, there? 

Pam  00:42

Hey, Kim! How's it going? 

Kim  00:43

Yeah, it's good. How are you? 

Pam  00:44

I'm tired, but (unclear).

Kim  00:47

It's the new year. You can't be tired already.

Pam  00:49

You know... Okay. 

Kim  00:51

Alright, so last week, we did a Problem String about...

Pam  00:55

It was fun, by the way. 

Kim  00:56

Yeah, it is fun. I'm still thinking about the orange and apple workers and... Okay, okay. Clear in the orchard. Mmhm.  Yeah. I want to know how much these people get paid. 

Pam  01:05

Okay, alright.

Kim  01:08

Alright, so last week, we did a Problem String about inverse variation, and it is a little bit of a mind twist, right? So, I want to ask you a question that I was thinking about. When students start very early in... I don't know. Third grade, fourth grade. They're working on a ratio table, hopefully, (unclear).

Pam  01:27

We suggest that. Yep.

Kim  01:28

Mmhm. Proportional relationships. And at a very early age, there's context involved, right, so that they can really make sense of doubling the number of workers, and... Well, not in this context. But doubling one thing and then doubling the other.

Pam  01:41

So, if you double the number of packs of, (unclear)...

Kim  01:44

(unclear)

Pam  01:44

...(unclear) double the number of sticks that are in each pack. Mmhm.

Kim  01:46

Right. So, last week...

Pam  01:49

Wait, I totally just said that wrong. Can I just... If you double the number of packs, then you double the number of sticks total. I said that. You don't double the number (unclear). 

Kim  01:57

Oh, I wasn't listening. I think I was talking over you.

Pam  02:00

You double the total number of sticks. Yeah. Sorry, sorry, carry on. Yes. So

Kim  02:05

(unclear). So, that is something that students we've been working with would have been comfortable doing. And then all of a sudden, they hit a ratio table or context and a story like this inverse variation. And you talked about the adults who just kind of do the thing, do the thing, do the thing, and then they... You know, you talk about the two teachers. What is... What age do you generally do the inverse variation Problem String? And do they have a similar response? Or is that typical for adults who have not spent a lot of time reasoning, but you don't see that in students who have been in classroom reasoning? Does that make sense? 

Pam  02:45

Yeah, I think so. And so just a second ago, you said, "So, when students get older and they see a ratio table with inverse inverse proportion." So, I just want to be careful a little bit that we can have paired number tables and we can have special paired number tables that we call ratio tables because the numbers are directly proportional. It's a proportional situation. The kind that we dealt with last week were inversely proportional, so I would not call that a ratio table. 

Kim  03:12

Oh, I thought you did. You said I'm drawing a ratio table.

Pam  03:17

Well, then I misspoke. 

Kim  03:18

Oh, unfortunate. Okay. It happens.

Pam  03:20

Yeah, because the ratios are not equivalent.

Kim  03:22

Right. 

Pam  03:23

Yeah, in an inversely proportional situation. Well, there you go. So... 

Kim  03:27

(unclear) I'm glad I asked.

Pam  03:28

Huh. Alright, so typo on the last podcast. Speako? How do you say that? Anyway. Yeah, so when something's inversely proportional, the situation can be... We can call it proportional.

Kim  03:42

Yeah.

Pam  03:42

But it's not a ratio table because the ratios are not equivalent. 

Kim  03:46

Yeah, that makes sense. 

Pam  03:47

Okay, cool. Alright, so your question was... Do I remember now?

Kim  03:51

Because it looks similar to the ratio table they've been working on.

Pam  03:55

Yeah. I mean, this reminds me of a question that one of our Journey members had who's been doing a lot of work with proportional relationships with her students, and they've then been given tables that were still linear. There were still a constant rate of change with the data. But they weren't proportional. So, there was sort of a setup fee. So, for example, if I was going to go rent a bicycle, and I look at the bicycle fee, and for 1 hour it's $15.00, and for 2 hours it's $25.00, and for 3 hours it's $35.00, we could say, "Hey, every hour it's costing $10 an hour to rent that bike. Except the first hour, it costs $15.00. So, where's that extra $5.00 coming from? Ah, that must be like the setup fee or the down payment. Like, you've got to give us $5.00 before we let you go pick your bike out or something. And then you sort of pay us by the hour after that. So, it's important then that students have experience with those kinds of relationships, where there's still a constant rate of change, but there's kind of a starting fee or a starting... Basically a y-intercept that's not 0. Or you might be tempted to use some of the same multiplicative strategies that you use in a ratio table. You might be tempted to use that in a non-proportional, linear situation.

Kim  05:12

Right. 

Pam  05:12

So, then the same thing happens here. Again, students need experience thinking about if it takes 3 kids 1 minute to erase all blackboards in the classroom, but now it's just me and I'm going to erase the same amount of blackboards in the classroom, whiteboards, whatever.

Kim  05:28

I was going to say. Are you saying blackboards? You might as well say chalkboards. There are plenty classrooms that still have them. 

Pam  05:34

Erase the stuff. Whatever. If it took 3 students a minute to do it, but now I'm alone, is it going to take me less time to do that job or more time to do that job? And that inverse relationship is a little tricky, and we need to give kids experience kind of thinking about why that would be true. I think we also then need to give experience with the quotient meaning of fractions because that's related to the function 1 divided by x.

Kim  06:02

Yeah. 

Pam  06:02

So, it was kind of a lot of things going in. It's definitely not a one and done. 

Kim  06:06

Right. And... 

Pam  06:07

I wouldn't... Go ahead.

Kim  06:08

So, I guess what I'm hoping that you'll also acknowledge is that it's not the kind of thing that, as a teacher, you say like, "Okay, we're going to operate on this differently, so just be aware of it." Like, just like you let those teachers do, they messed with it, and they got some things incorrect, and they, you know like, got different answers, and they wondered why. And that's part of the discussion is why it doesn't end up being the same as the work that they've done on a ratio before. Like, let it be true that kids have to mess around with it, instead of saying, "Okay, well now here, we're going to do..." You know, "It's going to be inverse today, guys."

Pam  06:50

"Today, it's Tuesday, so the rule today is to do this stuff." And then on Wednesday, the kid goes, "Hey, is this the kind we did on Monday or the kind we did on Tuesday?" And you're like, "No, it's like, Wednesday." 

Kim  07:00

Don't tell to make it simple for them. 

Pam  07:01

Instead of that paradigm, yeah, we definitely recommend that kids need to experience and grapple with what does it mean to have an inversely proportional relationship? 

Kim  07:10

Yeah.

Pam  07:11

Nice. So, let's do it. Let's grapple some more. Okay. Kim, have you ever volunteered to do anything? 

Kim  07:16

Yeah. 

Pam  07:17

Yeah, our church has just gotten asked to volunteer to man these giving booths. No, they're like vending machines. 

Kim  07:26

Wait, what? 

Pam  07:27

Yeah, it's super interesting. It's a vending machine, but what you purchase is... I'm not going to do this well. But like a service. So, you pay some money, and then that goes to a charity that then provides that service for somebody. Yeah. It's kind of cool. So, they're asking for volunteers to go man the booth and kind of help people do that. What's something that you volunteered for before? 

Kim  07:51

Oh, like Meals on Wheels. And like our district has a really, really cool program where they package up food for like weekends, and holidays, and things like that. And so, they take donations, and they make like food bags for families who don't have enough for their kids over the long breaks.

Pam  08:11

Nice, nice. So, if you think about volunteers, let's say that there's a gig. There's a job. There's a thing that's happening. And we know that it's going to take 250 volunteers 3 hours to get the job done. 

Kim  08:26

Oh! Okay. 

Pam  08:27

Yeah. So, I'm not sure exactly what's happening. Though, I could kind of picture. Some friends of ours... We haven't done it yet. We might do it this year. Some friends of ours go to... There's a local restaurant that donates all the food but volunteers come and cook it and cut it up and put it in the boxes. And maybe that's something similar to what you were just talking about. And then they distribute it out. So, it takes 250 volunteers 3 hours to get that all done. 

Kim  08:50

Yep.

Pam  08:50

And we know that. What if this year we're like, "Hey, let's try to get more of that. Let's try to get it done quicker." So, we're going to try to get 500 volunteers. So, if it took 250... Excuse me. 250 volunteers, 3 hours to complete the job. What if this year we get 500 volunteers? How long will it take to complete the job?

Kim  09:11

We have twice as many workers, so it is going to be faster like you said. It's going to be half as much time, so an hour and a half. 

Pam  09:18

So you think it might be an hour and a half. That's cool. So, 500 workers will take an hour and a half. What if we know... We're like planning. We're looking at the schedule and everything, and we'd really like to have the job done in 2 hours. So, we're going to go see if we can find the volunteers, so we can get it done in 2 hours. How many volunteers are we going to try to round up if we know it takes 250 volunteers three hours to do it? But we'd like to get it done in 2 hours.

Kim  09:44

I'm going to wonder about... You said 2 hours? I'm going to wonder about a half an hour. 

Pam  09:51

Okay. 

Kim  09:52

And I'm going to say that a half an hour is 3 times faster than the one we just said. 

Pam  10:00

Okay.

Kim  10:01

So, I'm going to like put that on my paper. Half an hour. And so, if it's 3 times faster, I would need 1,500 workers for that. Wow, that's a lot of workers. 

Pam  10:11

So, 1,500 workers could get that job done in a half an hour?

Kim  10:14

Mmhm. 

Pam  10:15

Yeah, okay. 

Kim  10:16

And then I'm going to...

Pam  10:17

Can I... Do you mind if I tell you what I wrote on my paper? 

Kim  10:20

Yeah. 

Pam  10:20

I went from the 500 volunteers in the one and a half hours. And I said, "From one and a half hours, I'm going to divide that by 3 to get a half an hour. Then I'm going to take the 500 workers and multiply that by 3 to get the 1,500 volunteers."

Kim  10:35

Yeah. 

Pam  10:36

Okay, cool. Alright, so now we have how many volunteers it will take for half an hour. That would be a lot of volunteers.

Kim  10:41

Lots of volunteers. And then but I really have 2 hours.

Pam  10:44

Yep. 

Kim  10:45

So, I only need a fourth of the workers, which is 375 workers.

Pam  10:51

Fourth of... A fourth of the workers from where? 

Kim  10:53

From 1,500 So...

Pam  10:55

Oh, okay, so you're going from the half hour to the 2 hours.

Kim  10:58

Yeah. 

Pam  10:58

That's like 4 times the time.

Kim  11:01

Mmhm. 

Pam  11:02

Okay. Then you only need a fourth of the workers. Okay. 

Kim  11:04

Oh, that's not 4 times as much time. 1, 2... 

Pam  11:06

Sorry?

Kim  11:07

Yeah, it is. Because there's 2 half hours in every hour, Kim.

Pam  11:13

Okay, so a half an hour times 4 is 2 hours. 

Kim  11:16

Yep, and I need a fourth as many workers. 

Pam  11:19

And what's a fourth of 1,500? 

Kim  11:21

Half is 750. And then half again is 375.

Pam  11:25

Oh, that's a nice way of finding a fourth of 1,500. Cool. So, you're saying for 2 hours, you need 375 workers.

Kim  11:32

Yep.

Pam  11:33

Cool. You're sticking by that? 

Kim  11:35

Yeah. Should I not stick by it? 

Pam  11:40

No. I mean, go... I'm sorry. I was trying to give you a non-response. 

Kim  11:45

You give me a nuetral face, but there's no nuetral face to see?

Pam  11:52

Hey, I wonder if you could think about getting from the 2 hours... So,  we didn't have the 375 workers, right? We had the 2 hours.

Kim  11:59

Mmhm. 

Pam  12:00

I wonder if there's anything else. I love how you went to the half hour. I think that was brilliant. Really nice. I'm just super curious if there were any other connections. 

Kim  12:08

Yeah, but then I just think about fractions.

Pam  12:13

Is today not a fraction day?

Kim  12:15

So, I'm kind of lazy. 

Pam  12:16

Ah, okay, okay.

Kim  12:17

Yeah, you could go from 3 to 2.

Pam  12:20

3 hours to 2 hours? 

Kim  12:21

Yeah, and if I need... I have...

Pam  12:23

How do you go multiplicatively from 3 hours to 2 hours? 

Kim  12:27

Well, 2 is two-thirds of the 3. So, I only have two-thirds of the... 

Pam  12:34

Hours?

Kim  12:35

Hours. I need to put labels here. Two-thirds as many hours, so I need three 1/2s or one and a third.

Pam  12:44

Uh, 1 and a 1/2?

Kim  12:44

(unclear) 1 and a 1/2 of the workers. Yeah.

Pam  12:47

So, what I've written down. I've got 250 volunteers to 3 hours. 

Kim  12:51

Yeah. 

Pam  12:51

And I went 3 hours times two-thirds...

Kim  12:55

Mmhm.

Pam  12:55

...is 2.

Kim  12:56

Mmhm. 

Pam  12:56

So, we're going to let everybody think about that. Like, if I took two-thirds of 3. I think about 3, and I cut that into thirds, and I only want two of those 1/3s.

Kim  13:04

Yep. 

Pam  13:04

That's the 2 hours.

Kim  13:05

Mmhm. 

Pam  13:06

Then, I need the reciprocal amount of volunteers. So, now I'm the 250. I need three 1/2s of the 250 volunteers. And golly, how are you thinking about that? That's... I would probably think about that as 3 times 250, which is 750.nd then divide that by 2, which is 375. 

Kim  13:27

Oh. 

Pam  13:29

No?

Kim  13:29

Yeah, yeah. I didn't... Are you asking me how I thought about it? Or are you just saying how would you? (unclear).

Pam  13:33

I mean, I asked you, and then I told you how I did. Sorry, that wasn't very nice.

Kim  13:37

That's okay. 

Pam  13:38

How would you think about three 1/2s of 250?

Kim  13:42

Well, so three 1/2s is weird for me because I guess I just think about... When I look at the 250, like I imagine the 125 and put them together. So, I guess I think about the half first and then times 3.

Pam  13:57

And you already know you have two of those halves.

Kim  13:59

Yeah. 

Pam  13:59

So, you just have to add one more half back. 

Kim  14:01

Yeah.

Pam  14:02

That's nice. And I would say that that's very... That shows that you've reasoned for a while. That took me a while to get. People would say those kinds of strategies, and I would go, "I'm sorry. What?" So, it's taken me a while to kind of be able to think that. Alright. 

Kim  14:17

So... 

Pam  14:18

Oh, yes? (unclear)

Kim  14:19

I don't know if we have time for it, but...

Pam  14:21

I don't know either. 

Kim  14:21

...it might be fun for people to wonder about going from the 1 and a 1/2. Yeah, maybe (unclear). 

Pam  14:26

1 and a 1/2 to 2. Yeah.

Kim  14:27

Yeah. 

Pam  14:27

We'll give that for homework. 

Kim  14:29

Yeah. 

Pam  14:29

So, yeah. If you only had the 500 volunteers for 1 and a 1/2 hours, how could you get from the one and a half multiplicatively to the 2 hours? And then you would do the same thing in the reciprocal from the volunteers. Cool. 

Kim  14:40

Don't tell them that! 

Pam  14:42

Oh. You're right. That was dumb. Sorry.

Kim  14:45

It's okay.

Pam  14:49

You don't want to do fractions, and I want to tell fractions today. What is up with us? Good heavens.

Kim  14:56

Oh, that's so funny.

Pam  14:57

Alright, next problem, next problem. Hey, Kim?

Kim  14:59

What?

Pam  15:00

What if you have 200 volunteers taking 3 hours to do the job, but today you've got 6 hours to do the job. 6 hours. 

Kim  15:08

Oh, good. 

Pam  15:09

How many volunteers do you need? 

Kim  15:12

I have twice as much time, so I need half as many workers. And we actually kind of explore that a little bit. It's only 125.

Pam  15:18

Yeah, totally. And so, what if I had 25 hours to do the job? 

Kim  15:24

Oh!

Pam  15:25

Lots of time.

Kim  15:26

Yeah. Oh, gosh. Okay, so I'm going to go from... 

Pam  15:32

Is that a typo? Do I mean 25 hours? 

Kim  15:35

I'm assuming you mean 24 but I could do 25 if you want. 

Pam  15:38

Well, do you want me to go... I'm going to go get it. Hang on. I got to get my book. Just a sec. 

Kim  15:41

I'm predicting 24 based on the fact that there's 3, and 1 and a 1/2, and 2, and 6. And those are all nicely connected to 24. But... Yeah, if you want me to do it (unclear).

Pam  15:56

Well, in my book, it says 25. Did anybody ever say anything? Whether that was a typo or not, no one knows. Hmm.

Kim  16:05

Which would you like for me to do? I bet it's 24. 

Pam  16:07

We'll go ahead and do 24, and I'm going to be thinking about 25 all day long.

Kim  16:12

Okay. Well, if it was 24... I mean, maybe that should have been asterisked by it. 24 which was be slightly nicer. Well, a lot nicer actually. Okay, I'm going to go from 6 hours to 24 hours. I have 4 times as many hours, so I need a fourth of the number of workers. Which is kind of nice to find a fourth of. Super fun. Thanks for that. A fourth of 125.

Pam  16:41

Is that sarcasm I hear there?

Kim  16:42

I'm going to go a fourth of 120 is 30. 

Pam  16:46

Oh, nice. 

Kim  16:47

And a fourth of 5 is 1.25. So, 31.25 workers. That's a little funky. 

Pam  16:59

That is a little. I don't know how you have (unclear). 

Kim  17:01

That's like 31 real workers and a little kid who's not so helpful.

Pam  17:05

Okay, there you go. 31 and a quarter volunteers. That's funny. Well, you do have me still thinking about the 25, but we're going to ignore the 25 for now. What if you had 10 volunteers? 10 volunteers?

Kim  17:20

10 volunteers. I'm going to go from the 500 volunteers.

Pam  17:27

Nice.

Kim  17:28

And it going from 500 to 10. 500 divided by 10 is 50, so that's... Oh, wait. Did you tell me it was 10 workers? Yeah, so that's divided by... I need 50 times the 1.5. 

Pam  17:44

Okay.

Kim  17:45

So, I don't know if I'm saying that out loud enough. So, when it was 500 workers to 1 and a 1/2 hours, I'm going from 500 workers to 10 workers dividing by 50. So, I'm going to multiply by 50 for the number of hours. And so, that's 75.

Pam  18:05

Cool. So, I'm a little interested to talk about that thing that we did last week that had everything to do with worker hours. In this case, it would be volunteer hours. 

Kim  18:15

Mmhm.

Pam  18:15

I'm wondering if that stayed consistent. Is there a volunteer hour thing that's happening here?

Kim  18:20

Yeah. You need 750 hours work done. 

Pam  18:25

And tell me where you where you look to see that. What told you that? 

Kim  18:31

The number of workers times how many hours they need to work, tells the total number of hours that you need worked.

Pam  18:39

Okay, cool. So, like the 250 volunteers took 3 hours, that's 250 times 3, that 750 volunteer hours. And the 500 times 1 and a 1/2, that's also 750. And so, I might, again, kind of go down the table. That 375 times 2. That's also 750. I wonder if we were to go down to where I gave you that crazy... Well, the very last one I gave you. The 10 volunteers. I liked how you figured it out. But if we'd already thought about that 750 volunteer hours, I wonder if we thought about the 750 volunteer hours, and I said 10 volunteers, does that nudge you in a different strategy for finding? 

Kim  19:19

Yeah. Well, yeah. I mean, I is that a desirable thing, I guess? I suppose it would be for kids to be like, "Hey, I just see that it's 75." Yeah, I guess it didn't occur to me. Like, I feel like you wanted me to use the relationships in there.

Pam  19:35

Sure. 

Kim  19:36

But... 

Pam  19:37

And if I was doing this with students, I would hopefully be pulling up both of those.

Kim  19:40

Yeah. But like even when you gave me 2 hours, that would have been a really nice one too to say, "Well, I have 750 hours total."

Pam  19:50

Mmm.

Kim  19:50

So, like not so much for some of the other numbers. 

Pam  19:53

So, we definitely don't want that to happen too soon. That meaning. We don't want students too soon be looking for that worker hours or volunteer hours total, and then just reasoning that way. Like, I think there's some real value in having to think about how do I go from this number of hours to a weird number of hours multiplicatively. And then I got to do the inverse thing for the number of volunteers. I think it's a real power in kids messing, grappling with that, making sense of it. Go ahead. 

Kim  20:23

It kind of reminds me of teachers who want kids to use the unit rate all the time. There are times where like finding the unit rate is like so nice. But there's other times where it's more work to find the unit rate and then scale up when you have a a related rate. Like, if you're going from to from 2 to 4, then you can double really nicely instead of finding the unit rate and then scaling up to 4. That feels like a little bit of this here where some of them were just super nice to not think about the total man hours, worker hours. But some of them. Like the last one, I should have just said, (unclear). 

Pam  20:59

I mean, or a really nice one to kind of have that go, "Oh!" Like, we want that "aha", experience for kids. Sometimes I feel like, in inquiry learning, people think, "Don't make them just go out in the field and discover math on their own. Just tell them what it is." But what if we were to craft experiences, so our students get to the point where we get to that 10 volunteers and finding number of hours, and they reason like you did, and then somebody goes, "Yeah, but it's just 750 volunteer hours." "Oh, man! And it's just 75. Ah!" Like, that experience of being able to have that "aha", you can't pay for that. Like, that's so valuable for kids to go, "Whoa!" In that moment with that emotional experience, you're going to look for that total later on, hich is why I want to delay that experience a little bit. I don't want to come too soon where then some kids who don't really work for it, then later haven't had the experience of grappling like we did. So, I want that grappling to happen. I might now say... Hey, Kim? What if I did keep that 25?

Kim  21:59

Well, do you want me to tell you because I already?

Pam  22:01

Were you already thinking about it?

Kim  22:03

Yeah. And I feel like you probably meant it to be 24. Not that it can't be done but some of the divisions funky because it lives in the land of 2, 3, 6 divisors. So, I think the nicest one would be to go from the 2 to the 25.

Pam  22:20

Okay.

Kim  22:21

So, it's times 12 and a 1/2.

Pam  22:23

Okay. Oof, and then you're going to divide 375 volunteers by 12 and a 1/2?

Kim  22:27

Yeah, but the first one I went from was the 3, so that's times 8 and a 1/3. Ugh.

Pam  22:32

So, given all that, I wonder if there's another strategy like we just saw on the 10 volunteers for 75 hours. I wonder if we might use that strategy for the 25.

Kim  22:43

Yeah. 

Pam  22:43

Hours.

Kim  22:44

Yeah. So, if you know the total man hours? 

Pam  22:46

Yeah, so if the total man hours are 750, and we know that we've got 25 hours, how many volunteers? 

Kim  22:53

Yeah.

Pam  22:54

And how are you going to do that?

Kim  22:57

If I have 25 hours, then I need 30 workers? 

Pam  23:02

Because?

Kim  23:03

Because 25 times 3 is 75 times 10 is 750.

Pam  23:09

Nice, nice. So, you sort of multiplied up to find the missing factor. Nice. 

Kim  23:13

I wonder if I would have put 25 as the last problem in the string.

Pam  23:18

Mmm. Maybe. Yeah. Yeah. Okay, fine. Fix my string. Sure. Yeah. 

Kim  23:24

If kids thought about total man hours sooner, then I was really worried about it. So (unclear).

Pam  23:30

Mmhm.

Kim  23:31

(unclear) the 25 there because I still, for some reason, am super interested in scaling up and down from the previous ones. And I'm going to challenge myself to really instead pay attention more to the total.

Pam  23:42

And I might have other students who are only paying attention to the total volunteer hours, and I want to encourage them, "Hey, but like in..." And I almost wonder, Kim, if that was my intent. 

Kim  23:51

Yeah, maybe. 

Pam  23:52

So, if I keep that 25 hours where it was and push kids to really think about the total man hours. And now they're like, "Oh, I'm going to do that every time." And then on the next one, I give them, "Well, what about 10 volunteers?"

Kim  24:04

Yeah.

Pam  24:05

I don't know.

Kim  24:06

I like it.

Pam  24:06

To scale, use the volunteers. Cool. So, just to finish it out, what if I said that I'd like to know if I had 1 volunteer, how many hours? 

Kim  24:15

750.

Pam  24:17

And if I had 750 hours, it would be 1 volunteer. And then we might just say every time it's sort of this x value, or the number of volunteers, times the y value, number of hours is 750. And we could graph that as y equals 750 divided by x. Or the number of hours equals 750 worker hours, volunteer hours, divided by the number of volunteers. And then we could look at a really nice inverse variation function. And the parent function for that is 1 divided by x. And we've scaled it by 750. What does that mean? And we can kind of look at the graph. And bam, we got kids reasoning inversely proportional. And that is a desirable thing.

Kim  24:56

It is indeed. As is volunteering in your community.

Pam  24:59

Nicely said, There you go. Alright, ya'll, thank you for tuning in, and volunteering in your community, and teaching more and more real math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com. Let's keep spreading the word that Math is Figure-Out-Able!