Episode Transcript
Pam 0:00
Hey, fellow mathers! Welcome to the podcast where Math is Figure-Out-Able. I'm Pam, a former mimicker turned mather.
Kim 0:09
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 0:16
Because we know that algorithms are amazing human achievements, but they are terrible teaching tools. Mimicking step-by-step procedures, actually trap students into using less sophisticated reasoning than the problems are intended to develop and use.
Kim 0:29
In this podcast, we help you teach, mathing, building relationships with your students, and grappling with mathematical relationships.
Pam 0:36
Ya'll, thanks for joining us to make math more figure-out-able! Hey, Kim.
Kim 0:40
Hi.
Pam 0:41
Okay, let's dive right in today to this episode. Off we go.
Kim 0:45
Right in. Kristen Vollmer said one time, "I have listened to every episode of this podcast, and it has changed how I teach and think about math. I've learned so much about teaching math and doing math that I didn't know before this podcast. I tell everyone I know. Other teachers, friends with kids in elementary school, my husband, anyone who will listen about what I learn on here. I love doing the math. I can do math so much better than I could before listening to this podcast, and I've been a middle school math teacher for almost 20 years."
Pam 1:15
Whoop! Whoop!
Kim 1:15
"I was definitely a memorizer, and I'm loving actually learning the why and the flexible thinking that I should have learned all along. I have two small kids, and I'm excited for them to get older so I can do this work with them. Keep it up, Pam, and, Kim!" Aw, that is so sweet.
Kim 1:31
I know. Ooh small kids. That's the best!
Pam 1:34
I love it.
Pam 1:34
Love, love, love. Yeah, I'm already having fun with my year and a half old grandsons.
Kim 1:38
Oh, so much fun.
Pam 1:39
Somebody said the other day, "You count everything." I was like, "I know because it's fun!" Like, we go upstairs, we count the stairs. And we count their fingers. And we count the peas on their plate. And, you know like, whatever.
Kim 1:49
Yeah, yeah.
Kim 1:51
All the things.
Pam 1:52
Yeah, so fun. Alright, cool.
Kim 1:53
Yep.
Pam 1:54
So, Kim in Kristen's little thing here. Compliment? Thank you, Kristen.
Kim 2:01
Review.
Pam 2:02
Review, thank you. She said, "I can do math so much better than I could. I was a memorizer. I'm loving learning the math and the flexible thinking." So, I want to just mention sometimes people will say, "Yeah, you're more flexible now because you rote memorized all that stuff when you were little, and so now you're building on that, and that's why you're mathing the way you are now.
Kim 2:23
Oh. Oh, no, no. Okay.
Pam 2:25
So, I want to prove that wrong a little bit today.
Kim 2:25
Okay.
Pam 2:25
By... You're going to love this. So, this is a little bit of surprise for Kim.
Kim 2:25
Now, I'm nervous. What are you doing?
Pam 2:25
Kim, I'm just...
Kim 2:25
She said, "Get a review. We're going to just do the other stuff."
Pam 2:32
Get a
Pam 2:32
review, and we're going to go. We're going to dive. So, Kim, you have told me in the past of things that you would do before you were... The way you were thinking about math when you were younger.
Kim 2:51
Mmhm.
Pam 2:51
That nobody taught you, right? You weren't basing it on a bunch of rote memorized stuff.
Kim 2:55
Right.
Pam 2:55
I just want to ask you. What are some ways that you would think about things that the rest of us could go, "Huh. That's a thing?" In other words, it has been very impactful for me to listen to you just talk about your life and what you think about when you are lifeing. And I go, huh. One of the things that I said was you actually have to own some relationships in order to do what you're doing. And that spurred me on. It was a motivation to me to go, I want to do that. I want my brain to think that way. I want to be Kim when I grow up. And so, yeah. So, today just going to play a little bit. So, Kim, you're running. Ready? Go, run, run. You've been running a lot with your youngest.
Kim 3:38
Oh, yeah.
Pam 3:38
In cross country, right?
Kim 3:39
Mmhm, mmhm.
Pam 3:40
Okay, so you're running. And as you're running down the road, you see the address 1400 Blah Blah St. I don't care what the street is. Would you do anything with that number as you're running?
Kim 3:50
Is there just 1400?
Pam 3:52
It's like the house number on
Pam 3:54
the...
Kim 3:54
Okay, but not 14 and something.
Pam 3:56
It's 1-4-0-0.
Pam 3:58
It's... Yeah, it's what I saw.
Kim 3:59
Oh, yeah.
Pam 4:00
Would you skip that one? Would you think? Would you play with it? Would you... It's okay if you say you skip it. (unclear).
Kim 4:05
Listen,
Kim 4:05
part of it depends on how close the houses are together to be honest with you. Because if I have time to mess. Like, if I'm like there's lots of space, then I'm probably thinking about the number.
Pam 4:17
So, it's
Pam 4:18
kind of like when you're in your cap to coast run where there's nothing.
Kim 4:22
There's like nothing for so...
Pam 4:22
And you run across something that's 1400, you're going to play with it because there's nothing else.
Kim 4:23
You're like so happy to have a number.
Kim 4:23
So happy.
Pam 4:23
Okay, so pretend that's where you are and you saw 1400. What might you... You got anything?
Kim 4:32
So, I think for sure I'm always going to double a number, or halve a number, or think about factors of the number, or like how far away is it to 1,500, or how far away is it's 2,000. 1400 is kind of a boring number to be honest with you because there's... It's fine. But.
Pam 4:55
It's a multiple of 7. That's kind of nice.
Kim 4:55
Yeah, but.
Pam 4:55
Okay, alright, alright. Let me... Should I give you another one?
Kim 4:55
Sure.
Pam 4:55
Okay, so I was just at a relative's house. I'm not going to tell you who because I wouldn't want someone to actually go find these people. But the house number struck me because I was like, "Wow, it's 1-1-3-4-9.
Kim 5:07
Okay, the first thing I'm doing is adding the digits together.
Pam 5:11
Ah, so like find the digit sum. Okay, okay, okay.
Kim 5:13
Yeah.
Pam 5:15
How did you do it?
Kim 5:16
I mean, I haven't yet. I'm just telling you. That's what I would
Kim 5:18
do.
Pam 5:19
Well, can I tell you what I did?
Kim 5:21
Sure.
Pam 5:21
After you do it.
Kim 5:22
Oh, yeah. I'm adding the 1 and the 9 together for sure.
Pam 5:25
Okay, and then I added the 1 and the 4. Which was not planned. I just saw that.
Kim 5:29
That's funny. I didn't. I did the 3 and the 4. Because like I like to accumulate large, large amounts.
Pam 5:35
Large.
Kim 5:35
Like, look for nice pairings. And accumulate large. For some reason 1 and 4 isn't. It's like 5. It's not...
Pam 5:43
Okay.
Pam 5:45
Alright, so we got 18 for (unclear) sum. Would you have added the 1 in the 8 together and got 9? Just be like finish it out?
Kim 5:52
No, I don't think so. Because if I'm running, then I'm like, already holding...
Pam 5:56
A lot of number.
Kim 5:57
...stuff.
Kim 5:57
Yeah, sure enough.
Pam 5:58
Okay, okay.
Kim 5:58
Yeah.
Pam 5:59
Anything else come to mind for
Pam 6:00
that one?
Kim 6:00
I mean, I might think about how far away it is from 12,000. Part of it also depends on what else I'm doing.
Pam 6:09
651. I just had to do that. Thanks.
Kim 6:11
Yeah.
Pam 6:11
Okay.
Kim 6:12
Yeah, yeah.
Pam 6:13
Okay.
Kim 6:13
Sometimes I'll look for what is the next house and find the difference between like the first house and the next house. Especially if there's a lot of space between houses. They don't always go like the next odd number.
Pam 6:26
Yeah.
Kim 6:26
So, when I'm running, I might look for like, on this street, do they go like every odd on this side and every even on this side? And in older neighborhoods, especially, that doesn't seem to be a thing.
Pam 6:37
Okay, this is totally. You just put me in a situation I've been in a lot lately. Where the hotel room numbers don't make any sense.
Kim 6:44
Yeah.
Pam 6:45
I'm like, "Okay, there's 147, so the next room should be 148. No, no.
Kim 6:50
Yep.
Pam 6:50
It's across the hall and down the way. I'm like, "What?
Pam 6:53
How? Who planned this?"
Kim 6:53
Are you staying fancy hotels? I mean sometimes.
Pam 6:56
When I'm
Pam 6:56
on the 13th floor, and you have to put your card in to get up to the 13th floor. That means you're in a dangerous city is really what that means.
Kim 7:05
Oh, that's not good.
Pam 7:05
Yeah.
Kim 7:06
Have we talked about other things that I think about with running. I know you're mentioning the...
Pam 7:10
The house numbers.
Kim 7:11
The house numbers. And that is a thing. I also look at license plates.
Pam 7:15
When you're running. Okay.
Pam 7:16
So, you run where there's cars. Okay.
Kim 7:18
Or like on the houses. Like, when I go by. Like, I'm always trying to keep myself a little busy. And because I know a lot of the songs that I listen to, and so that's not as exciting. I need better playlists. Send me songs, people!
Pam 7:31
Everybody send Kim your favorite playlist.
Kim 7:33
So, so...
Pam 7:34
Hey, you know, Vanessa Vakharia has her own rock band.
Kim 7:38
Oh, yeah, that's true.
Pam 7:39
You should check.
Kim 7:40
I need upbeat stuff.
Pam 7:41
Maybe. Okay, there
Pam 7:42
you go. It's pretty upbeat, the stuff I listen to.
Kim 7:44
I'm sure. She's
Kim 7:46
great. So, the other thing that I sometimes think about. Did you know that I... You might do this.
Kim 7:52
Do you only run...
Pam 7:53
Sorry, Vanessa Vakharia is the author of Math Therapy. I probably should (unclear).
Kim 7:56
Surely they know her (unclear).
Pam 7:57
Why I threw her name out. Okay, alright. Carry on. Okay, sorry. I didn't mean interrupt.
Pam 8:01
Go ahead.
Kim 8:02
I only run to an even, or like a whole number mile. Do you do that when you're doing exercise stuff?
Pam 8:12
Well, first of all, I don't run anymore because of my knee, so I only elliptical.
Kim 8:20
Well, I mean, you exercise.
Pam 8:14
Hey, I did run in the airport the other day, and I was super happy that I could because I just don't because they told me not to because of my knee. But we missed the flight. But I was happy because I ran. But no. I do time.
Kim 8:20
So, like a whole minute.
Pam 8:20
To the minute, yeah.
Kim 8:20
Do you ever stop... Okay, yeah. So, that's not...
Pam 8:20
No, I would never stop at like 20:05.
Kim 8:20
Yeah.
Pam 8:20
I'm going to run to 20 minutes.
Kim 8:24
Yeah.
Pam 8:24
Or, you know, elliptical. I'm an elliptical to 20 minutes. Or I'm an elliptical to 25. Never 24:36.
Kim 8:44
Yeah, so...
Pam 8:45
I'm itching right now. That makes me itch.
Kim 8:47
I know. Right. So, that means that what (unclear).
Pam 8:50
I'm not looking at the distance. So,
Pam 8:51
you're looking at distance.
Kim 8:52
Yeah. So, yeah.
Pam 8:54
Wait, wait, wait. How do you do that? What if you're already home and it was only like...
Kim 8:54
Oh, like if it was like...
Pam 8:54
5.9 miles, and you get home.
Kim 8:57
Well, I just
Pam 9:00
run past the house, and then just turn around and come back.
Pam 9:03
No way!
Kim 9:05
For sure, yes.
Pam 9:07
Ha!
Kim 9:08
So, here's the problem, though.
Pam 9:10
Clearly, I've never thought that in my lifetime. No.
Kim 9:12
So, when you're doing elliptical, then are you playing I Have, You Need? I think we've talked about this.
Pam 9:16
Oh, my gosh.
Kim 9:16
You are.
Pam 9:16
Totally.
Kim 9:17
Yeah.
Pam 9:17
Yeah,
Pam 9:17
with time, absolutely.
Kim 9:17
Okay.
Pam 9:18
Especially because I do this... Not every time, but often I'll do this thing where I do intensities per minute. So, I'll do like an intensity of 6 for a minute, and then 7, and then 8, and then 9, and then I back up. 6, 7, 8, 9. 6, 7, 8, 9, 10. And then by then I'm sweating and sucking air and all the things.
Kim 9:39
Yeah.
Pam 9:39
So, when I'm at like 9 for the third time.
Kim 9:39
Mmhm.
Pam 9:39
And I'm at 46 seconds. I'm like, "I've only got..."
Kim 9:42
Yeah.
Pam 9:43
"...14 more seconds." Or 13.5 more seconds. You know? Yeah, so I'm always trying to find the difference between where I'm at and the next minute.
Kim 9:51
Sure.
Pam 9:51
Lots of combinations of 60,
Kim 9:53
Yeah.
Pam 9:54
Yeah.
Kim 9:54
Yeah. Well, yeah. So, I mean, I play I Have, You Need with the distance. And then I think depending on like how much distance is left. Like, let's say I'm at like 4.37, then I'm thinking to myself, "Okay, like, I've
Kim 10:08
got..."
Pam 10:09
Are you seeing that on your watch? Where are you seeing 4.37?
Kim 10:12
Oh,
Kim 10:12
this is lame. Listen, I'm not fancy in any way, so I don't have like a super fancy running watch or whatever. I carry my phone. And so, like I actually just hold it. People think I'm so weird. But like I hold my phone in my hand, and I just become accustomed to that over the years. And so, I have an app, and so I look down and I'm like, "Okay, it's 4.37." So, then I go like, "Okay, I have 0.62 left." Or 0.63 left. And then I'm kind of like, "Okay, how? What's the like distance? And how far? And like how many songs? And so I'm kind of just like wondering...
Pam 10:47
Ooh, how many songs. Ah.
Kim 10:49
Yeah. So, I think this is mathematical too that it's not about number.
Kim 10:52
It's like. It's like estimating time.
Kim 10:56
And wondering. And so...
Pam 10:59
(unclear). Size.
Pam 10:59
It's like size is really... Okay, that was really cool. And I'm glad to hear that. I do have one that I really want to ask you.
Kim 11:05
Okay.
Pam 11:06
So, I'm into this filtered milk lately. You guys can tell me what you think.
Kim 11:11
Filtered milk?
Pam 11:12
Yeah. So, I sat on a plane with a gal, and she said... We were talking about... You know, I have to monitor my own calcium. It's a whole thing. And she said, "Oh, you should try our filtered milk." And she works for the company. And I don't... What are they called? I know that the brand I buy at Costco is Fair Life.
Kim 11:27
Mmhm.
Pam 11:27
But they also make another version that's called Core Power.
Kim 11:32
Okay.
Pam 11:32
And they're two different. They're different. One of them has more electrolytes and one of them has more calcium. And I don't know the rest of the difference. One of them says it's like what you do.... What do you call that? After you work out. It's a recovery.
Kim 11:43
Mmhm.
Pam 11:43
And the other one's just like a protein drink.
Kim 11:46
Okay.
Pam 11:46
But it's milk. Which is I like instead of soy. I prefer milk over soy. And it's chocolate. So, hey.
Kim 11:53
You love it.
Pam 11:53
That answers that right there. Let's get some good chocolate going on. So, the Fair Life are 13... Or, sorry. $38.58. So, $38.58. At least when I looked on my app this morning. So, $38.58 for an 18 pack. Now, that might... Okay. I can get the Core Power for $32.34 for a 10 pack. So, I'm just going to tell you that much. Did you get those numbers down? $38.58 for an 18 pack or $32.34 for a 10 pack.
Kim 12:24
Mmhm.
Pam 12:24
Any gut reactions about which one I should get? What's a better buy?
Kim 12:28
Well, so the first thing I'm thinking about is like the dollar amounts are pretty close together
Kim 12:35
for 18 or 10.
Pam 12:36
Kind of, yeah, right? Yeah.
Kim 12:37
So, I think the first thing to think about is like I'm going to call it 40.
Kim 12:40
Just...
Pam 12:40
Okay. $40.00
Kim 12:42
Right of the bat. Mmhm.
Pam 12:45
Okay. Mmhm.
Kim 12:46
And like right away, it's a 10 pack for $32.00. And if I double that, I've got like a 20 pack. And it's going to be like $60.00 bucks.
Pam 12:56
Yeah.
Kim 12:56
So, there's no way that that's close together.
Pam 13:00
You're like, "Pam, by the 18 pack."
Kim 13:02
Yeah, for sure.
Pam 13:02
Okay, so now let me get it a little bit more exciting.
Kim 13:02
Okay.
Pam 13:02
18 pack has only 11.5
Pam 13:03
ounces in it.
Kim 13:03
Ooh! Ooh, fun.
Kim 13:03
Okay, it's 11.5 ounces?
Pam 13:03
11.5 ounces in the 18 pack.
Kim 13:08
I can't believe I just said "fun".
Pam 13:17
Because you mean it. The ten has 14 ounces. So, the 10 pack are bigger. So, we just clearly said the 10 pack was not as good of a deal. Except they're bigger.
Kim 13:27
Yeah.
Pam 13:28
Mmhm.
Kim 13:29
So, it's like 140 ounces in the 10 pack. And like...
Pam 13:33
Okay.
Kim 13:33
100. So, I'm calling that 180, 198. I don't know about the half. I'm not going to worry about that quite yet.
Pam 13:40
Okay.
Kim 13:40
I'm calling that like 198 ounces.
Pam 13:43
For the about $40.00. Okay.
Pam 13:46
Yeah. I'm not writing stuff down. I should have. 140 ounces.
Kim 13:50
Yeah.
Pam 13:51
For $32.00. And then what you get for the $38.00? Or almost $40.00?
Kim 13:56
It's like close to 198. It's not exact. Do I need to make it exact?
Pam 14:02
I mean, not if it's clearly one way or the other with what you see here. You got anything?
Kim 14:09
So, 140 ounces for $32.00 or 198 ounces for $38.00?
Pam 14:14
Yeah. Or almost $39.00.
Kim 14:16
Yeah, yeah.
Pam 14:17
Yeah. It's close, right?
Kim 14:19
Yeah, it's closer. It's like you have to think a little bit more.
Pam 14:22
Oh, well, wait. That sounds like you... To me, I don't have a clear winner yet. Do you have a
Pam 14:28
clear winner?
Kim 14:28
No, no, no. No, I'm saying think a little bit more. So, I'm going to call it 58 ounces more for like $6.00
Kim 14:37
bucks.
Pam 14:37
Oh, that's interesting. Okay. Now, maybe don't round off the $40.00 then. Make it be the $38.00. Or $39.00 even. Because now it's $7.00 bucks, right? Like, because you were rounding to $40.00. But now.
Kim 14:59
Oh, yeah.
Pam 14:59
If you're just doing the difference, that's not...
Kim 14:59
Yeah.
Pam 14:59
That's just $7.00.
Kim 14:59
Yeah, mmhm.
Pam 14:59
So, now it's... What was it? 58 ounces for $7.00? How's that help? I mean, I kind of liked it, but now I'm not sure how it helps.
Kim 15:00
Why are you telling me $7.00 bucks?
Pam 15:00
Because that's the difference between the $39.00 and...
Kim 15:05
Oh.
Pam 15:05
...the $32.00.
Kim 15:06
So, the $39.00 is 198 ounces.
Pam 15:09
Mmhm.
Kim 15:09
And the $32.00 is 140 ounces.
Pam 15:12
Yeah.
Kim 15:13
So, I get... Oh, I see. 58 ounces for $7.00 bucks.
Pam 15:18
Yeah.
Kim 15:19
I don't think I was going to compare that way.
Pam 15:21
Oh, okay.
Pam 15:21
Sorry.
Kim 15:22
That's okay.
Pam 15:23
That's where I thought you were going, and I liked it till I went how does that help?
Kim 15:27
So, I think at this point we were talking about like what kind of play do I do?
Pam 15:32
Yeah.
Kim 15:32
And honestly, I got to be honest with you, at that point I go, "I want to play with something new." Like, to be perfectly honest with you, like I could. But I think the act of playing in that way, I find engaging until I just don't anymore.
Pam 15:46
True.
Kim 15:46
And I think that's okay.
Pam 15:49
Mmhm.
Kim 15:50
Do you want to keep playing with this one?
Pam 15:53
Well, I'm going to maybe make this point. I feel like in our last episode, we talked about word problems. So, at this point, we've got some numbers.
Kim 16:00
Mmhm.
Pam 16:00
And I like the fact that we are now at $39.00 or maybe even $38.50. At this point, I wouldn't need to round off.
Kim 16:07
Mmhm.
Pam 16:08
So, $38.50 for 198 ounces and $32.00 for 140 ounces. At this point, I have a feel that I could use technology, and I could find the price per ounce, and then I could be done. So, if I'm walking through Costco, I might not. Or I might just pull out my phone. At this point, I might just do a little division to go, "Well, then how much is it per ounce?
Kim 16:25
Yeah.
Pam 16:26
And I would just divide the... You know, it's money per ounce, so I would divide the money by the ounces. But and it has everything to do with the fact that that I've played. And I'm like, "These are pretty close."
Kim 16:36
Yeah.
Pam 16:37
So, if I really want to. I mean, maybe at this point, I'm like, "Buy the one that tastes better."
Kim 16:41
Yeah.
Pam 16:42
Or do you know what I actually did?
Kim 16:44
Hmm?
Pam 16:45
I bought both. And I do the one when I need the...
Kim 16:49
Right, right.
Pam 16:50
...when I need recovery. And I do the other one because it has more calcium. And when I need more calcium, then I get the other one.
Kim 16:55
You know what I wish was not true? And I get why grocers do it. But I wish there was not a per ounce.
Pam 17:02
Per ounce.
Kim 17:03
On everything, mmhm. Because I think it's those little things that we do that keep people from playing. So, listeners, if you're in the store and you... If it's something that you want to keep doing to work on your reasoning, don't look at the cost per ounce. What other kind of play? I'm trying to think what else.
Pam 17:27
Do you have something that right now that you're thinking, "I wish you would have asked me about."
Kim 17:33
Oh. Um.
Kim 17:34
Oh, well, we've talked about how like in the car like that's like prime play time, right? That's the time that like I'm looking at Interstate signs, and I'm looking at...
Pam 17:44
What
Pam 17:44
are you saying to yourself when you look at Interstate signs?
Kim 17:45
I'm
Kim 17:46
thinking about distances and time. Like, how far away is it? How much time will it take to get there? Yeah. I think that the overall disposition for me is when I run into something that's mathematical, almost never do I say, "Meh." Like, I always engage in some way.
Pam 18:10
In some way.
Kim 18:10
In some way. And maybe it's just like a short minute, like a quick like, "Let me go for that. Oh, I don't have time for that right now." Or maybe I engage longer. But it's the mindset of I'm going to engage in some way always. Like, if I see something on a social media, or if I see something, like or I'm in a conversation with somebody and they're like talking about something that could be mathy. Like, sometimes I like jot a little Post-it note down, and go back to it later. But it's a constant seeking of mathy type stuff.
Pam 18:42
Yeah. Ya'll, leave this episode with the idea when you own more connections, and relationships, and strategies, there's more to play with, and we can play more, and math can be more creative, and we can be more flexible. Be mathy. Ask people what they think about. Stay in the problems that feel like they would be tricky, and try some things, and ask somebody for an idea if you get stuck. Find a friend like Kim.
Kim 19:07
And Pam.
Pam 19:07
Who can motivate you to want to. And let's give some credit to Sue who on our team will often throw something into our Slack and just go, "Hey, everybody, think about this one." And then Kim, she will poke me. She's like, "I haven't seen you try it. And I'm like, "Well, I haven't been in Slack today." Yeah, no, it's super fun. Ya'll, we invite you to join us to make math more play-about-able, playful.
Kim 19:30
Playful.
Pam 19:30
As we make math more figure-out-able. Ya'll, thanks for tuning in, teaching more and more real math. To find out more about the Math is Figure-Out-Able movement, visit mathisfigureoutable.com. And keep spreading the word that Math is Figure-Out-Able!