Pam  00:00

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

Kim  00:10

And I'm Kim Montague, 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  00:18

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  00:32

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

Pam  00:39

We invite you to join us to make math more figure-out-able! It's almost kind of boring when we get that right. Oh, well.

Kim  00:49

We'll try not to be boring today. 

Pam  00:50

There you go. 

Kim  00:51

So, speaking of not being boring, we have some exciting news to share.

Pam  00:55

Kim, we are so excited to announce that we have a brand new partnership with Hand to Mind. Hand to Mind is a cool company out there with even cooler people that work with them and for them. And we are super excited to announce that we will be doing some really cool things with Hand to Mind that we'll be announcing soon. So, today, we're just kind of announcing that we're excited about the partnership with Hand to Mind, and stay tuned to hear more about what we are doing with them. Yeah. Very exciting. Alright. So, Kim, today we thought we would talk a little bit about some cool things with games.

Kim  01:38

Yeah.

Pam  01:39

Yeah. 

Kim  01:40

I love games.

Pam  01:41

You do. In fact, I think you're better at games than I am. I like games when my kids were a little, bit not as well as you guys do.

Kim  01:49

What do you mean by “better”? Like, I play them more often with my people? Or?

Pam  01:52

That's what I mean, yeah.

Kim  01:53

Oh, okay. That's what I thought. Because I was going to say, we haven’t played a lot of games together. I don't know that I'd be better.

Pam  01:58

Oh. Ha. Yeah, no. Just like, making it happen. And, I’ll tell you, sometimes my kids have different game interests now that they're adults, so I have a harder time convincing them to play the games I want to play. But.

Kim  02:12

Yeah.

Pam  02:13

But still, it's all good. It's all good. So, there is a wonderful leader in British Columbia, Canada who did some really nice things with games. And, Kim, can you tell us about that?

Kim  02:24

Yeah, so Barb Lovich. She's one of our JourneyLEADERs. And she posted recently in our Facebook group about games. And, you know, they made some really great choices in their school. And everybody got really excited because she shared some games that they used. But one of the things that she said was when they set out to start having kids think about math, they were really focused on changing their students attitudes and beliefs about math. And I think that's a really interesting and smart entry. A lot of people want to just dive right into like, “They need better strategies. Or they need…” You know, whatever support.

Pam  03:02

Fact practice.

Kim  03:03

Yeah. Yeah. I mean, that happens. And I understand why, but they decided that they really wanted to elevate kids thinking in a different way, and so they intentionally bought games that did not involve numbers or calculations. But they were really focused on like logic, and reasoning, and spatial awareness, problem solving. All these things that we need for kids to be great at math. And so, what they did was they, the administrators, took the games from class to class, and they sat next to students when they played. And so, they were asking questions, and they had kids talk about their game strategy. What their move would be. And how they knew where to put pieces. And what they did was they started hearing that their students were developing attitudes and habits that they wanted their kids to demonstrate in math class. So, they were risk taking, and they were learning from mistakes, and they were working cooperatively, and so they were changing strategies when it wasn't working. So, all of those really important skills, and mindsets, and beliefs were emerging through these games that they had chosen. So, she shared some games with us that they had chosen, and some of them I had heard of before, but some I never had. So, that was fun for me because (unclear).

Pam  04:17

(unclear).

Kim  04:19

And we can put them in the show notes, but I'll mention a few. One was the Cubit Series and Balance Beans. Which I bought for my youngest when he was little, and it's super fun. And she mentioned Quarto, and Dimension, and Blockus, which my family loves. There are several others, but we'll put them in the show notes. But I just loved their approach to why doing games. And it felt different to me than what I've heard some people say before.

Pam  04:42

Well, and I think one of the natural outcomes of that is that the administrator and the coach then were able to develop relationships with students around those things you just mentioned.

Kim  04:53

Sure.

Pam  04:54

Strategy. What your move might be? What you're thinking about? The idea that it's logic and reasoning. And then now with that relationship, then when later these people go in and want to sit down with students and chat mathematical strategy and chat, you know, numeracy strategy, now they have this kind of what? Feeling tone already set up. And so, like, let's dive in. And hey, we're going to do the same kind of thing here. Yeah, I think that's brilliant. (unclear).

Kim  05:23

You know, and I bet they loved it. All too often, you know, our coaches and our administrators. You know, I know they try to get in classrooms. And, you know, there's a lot of reasons why that may not be able to happen as much as they want to. But how fun is that? You know, just go sit down in classrooms and say, “Hey, let's play this game.” I bet they had a great time too.

Pam  05:42

And it would take some intentionality, right, to set aside that time, and plan, and make sure that that kind of thing happens. Yeah, that's really cool. Hey, so speaking of games. When I was in Australia, I ran into Michael Minnis, who I think, Kim, you actually might… Are you the one that sent me the first game?

Kim  06:02

No! No, you sent me a game and said, “Your boys would love this.” And so, I immediately sent it... Yeah, I don't know. You sent it to me, and I sent it to my oldest, and I said, “Hey, watch this. Learn this. Let's play it.” Yeah.

Pam  06:15

Oh, bam, nice.

Kim  06:16

Yeah. 

Pam  06:16

So, yeah. Thank you, whoever sent me the original one. I'm not sure how I ran into it. Maybe Twitter, possibly? I remember I watched the video. He has kind of funny music to his videos. It's an interesting choice. But it's fantastic because what he does is he introduces a game, but he plays it with his kids or one of his sons. And super fun. And so, I just kind of actually knew him as Nash's dad because the first one that I watched, it was him playing with his son, Nash. And so super fun. When I was in Australia, I had gotten to the Mathematical Association of Victoria, and I was doing a gig there with a wonderful group of teachers. And a gentleman walked in. He introduced himself. And he just kind of like cocked his head just enough that it was like he had done on the video. And I was like, “Huh! You're Nash's dad!” And he just laughed. He's like, “Yes…” And I was like, “No, no, no. Like, I know your YouTube channel.” And he kind of… You know, it was cute because he's like, “Really? You know who I am? Oh, well, I guess if you know Nash like you've actually watched the games.” And, yeah, it was brilliant. So, we've communicated a little bit since. And he has on his website a whole collection of games that he has videoed playing with his kids that you can watch. And, yeah, super fun. I also… When we were talking to Liesl McConchie the other day, she mentioned that she had found him during Covid because he was putting out all these videos of games, and how he just really saved her family because they were able to do these really cool games during Covid. And so, yeah, fantastic. So, Kim, we thought we'd play one of his games today. The one that I think you played with your kids, right? That you thought was pretty cool.

Kim  07:56

Yeah, we played. I played one game with Luke. Yeah.

Pam  07:59

Okay, alright. And It's called Multiple Machine. 

Kim  08:02

Yeah.

Pam  08:02

So, I'm going to be honest. I've watched him play. You've played with Luke. We're going to play together today. So, it's kind of like half brains playing together today. Okay.

Kim  08:12

We'll be okay.

Pam  08:12

Alright, so I've got the cards. You're going to kind of tell me what to do.

Kim  08:16

Okay, so what you need are 0 to 9 cards. And you're going to draw four of them, and you're going to set four of them at the top. Just kind of at the top of your table, or whatever. And those can't be a 0 or 1, so grab 4, not 0 or 1.

Pam  08:31

So, I got two 1s, so I'm putting those aside. And can they repeat? I think I remember that they can't repeat. 

Kim  08:38

Oh. Probably not, yeah. 

Pam  08:40

Okay, yeah, so I'm putting that one aside, and…

Kim  08:42

And you're going to tell me what those two are at the top. Please.

Pam  08:44

Okay, so I got another repeat. Good heavens. Okay. I have a 2, 3…

Kim  08:49

Shuffle, Pam.

Pam  08:50

..,5 and… Well, it's a brand new deck. A 2, 3, 5, and 7. 2, 3, 5, and 7.

Kim  08:54

2, 3, 5, and 7. Okay, excellent. And then, since you have the cards, you're going to deal eight for yourself and deal eight for me, and then you’re going to tell me what my eight cards are. And I'm just going to say right now I'm at a disadvantage because I can't move my cards around. I should have had cards. Oh, well.

Pam  09:10

Maybe we'll play together. Is that dumb? 

Kim  09:12

Oh, that sounds good. Yeah.

Pam  09:13

Yeah, I’m not sure we have time for both of us to play. Okay.

Kim  09:18

So, we need eight cards. And the goal of the game is to make four, two-digit numbers with those eight cards. And those need to be multiples of each of the cards that are at the top of the table. So, we're making a two digit number that's a multiple of three, and one that's a multiple of two, and five, and seven. But we have to use all eight of the cards.

Pam  09:38

We're looking to make multiples. Got it. 

Kim  09:40

Yep. So, you want to tell me what the eight cards are? 

Pam  09:42

Should I tell you them in order. Does it matter? 

Kim  09:44

It doesn't matter. 

Pam  09:44

I've already put them in order, so I'll just.

Kim  09:46

Oh, okay.

Pam  09:47

Because well, while you were…

Kim  09:47

Is that a strategy?

Pam  09:49

While you were talking, I just kind of naturally put them in order. I don’t know. Okay, so I have a 0. 

Kim  09:54

Okay.

Pam  09:55

A 3, a 3.

Kim  09:57

Okay.

Pam  09:58

4. 

Kim  09:59

Mmhm. 

Pam  10:00

6, 8, 8, 9.

Kim  10:04

Okay. So, maybe players or listeners, if you want to play at home, this would be a good time to pause. You have your four numbers at the top. You've got the eight numbers at the bottom. And you're going to make four, two-digit numbers that are multiples of those ones at the top.

Pam  10:19

Do not have enough room on my desk here, but I'm making

Kim  10:22

Yeah.

Pam  10:22

Okay, making room, making room. Okay. So, I'm thinking right now. Can I think out loud for a minute? Is that okay? 

Kim  10:28

Yeah, go for it. 

Pam  10:29

So, I need to create a two-digit number. That's a multiple of 7, and I think that might be the harder one to do, so I'm kind of…

Kim  10:36

Oh, that's so funny. That's the first one I did too.

Pam  10:38

Okay. Yeah, so I'm kind of interested to do that one maybe first. Let's see. 33, 43, 34, 36, 46, 86, 88, 98. Hmm. Umm. Uh. Mmhm. I wish I had a 2. Umm…

Kim  11:12

Do you have time or help?

Pam  11:16

Golly, I'm feeling silly. Hey, once I find the two-digit number that's a multiple of 7, those cards are out right? I can't…

Kim  11:23

Yes. Yeah, so that's the thing is you can try, but you might have to mess again when you move on. So, I also started with the 7, and I just picked a number that I knew would be a multiple of 7. And then… Do you want to know where I looked next? I won't tell you what I put, but do you want to know where I look next?

Pam  11:42

No, because I can't believe I can't find a multiple of 7 in these numbers. 

Kim  11:46

Oh. 

Pam  11:46

What is wrong with me? Oh, 49. Good heavens. I don't know if you chose that.

Kim  11:50

Kim  11:59

I didn't at first, but then I had to change, so I…

Pam  11:53

(unclear). Oh, you had something else? 

Kim  11:56

Yeah, I chose 63.

Pam  12:00

Okay, okay. But then you decided to change it because it didn't? Did you put like the 49 with the 7, so it's kind of like now those are together?

Kim  12:09

Yeah, so I wrote my number that I made underneath the number at the top.

Pam  12:13

Oh, that makes sense. Okay. 

Kim  12:14

Yeah. 

Pam  12:14

Because you're not moving cards around. Duh.

Kim  12:15

Right.

Pam  12:16

Okay, okay. So, I'm a little tempted to try to find a multiple of 5 next.

Kim  12:21

Yeah, that's what I did too. Okay.

Pam  12:23

And I have a 0, so that maybe might even be too easy, so maybe I'm not going to worry about the multiple of 5, since I have that 0. Because I can put that 0 with any of these numbers to be a multiple of 5, right? 

Kim  12:36

Yeah.

Pam  12:37

So, rather than do that, now I think I'm going to try to find a multiple of 3. And the first one that jumped out at me is 33, so I'm just going to put 33 with my 3. Now, I need an even multiple, so I'm just going to choose, I don't know, 68. Why not? And then I've got 80 to be the multiple of 5. 

Both Pam and Kim 13:04

(unclear). 

Pam  13:04

So, I was able to get all four. Did you have different? (unclear).

Kim  13:07

I did. I did, yeah. So, I did 63 for the 7. 

Pam  13:12

Okay.

Kim  13:12

And then I went to the 5. And I actually did choose a number, and I went for something that I had a lot of digits, so I put 30 right away because I had two 3s.

Pam  13:24

Mmhm. 

Kim  13:24

Then I went to the 3 because I thought 2 would be easy. I went to the three. And at that point, I don't remember what I had left, but I was like, “Oh, you know what? I'm going to go back to the 7 and change it to 49, and I'm going to move to 63 to the 3. 

Oh, nice. (unclear)

Kim  13:40

(unclear).

Pam  13:42

(unclear) were like. That 63 is both…

Kim  13:44

Yeah.

Pam  13:45

..so, you can move it around. That's nice. And then what did you have left?

Kim  13:47

And then I had 88 left.

Pam  13:49

Okay. Alright, cool. 

Kim  13:51

Yeah. 

Pam  13:51

So, great game because you're sort of looking for multiples. And I thought it was interesting where both of us were like, “Ooh, let's do the 7 first because it's going to be the hardest one to find.”

Kim  14:02

Yeah.

Pam  14:02

And…

Kim  14:02

I’ll tell you what? 

Pam  14:04

Yeah? 

Kim  14:04

Sorry, to interrupt.

Pam  14:04

Can I say the 2? And then, both of us are like, “Leave the two to the end. Like, dude, that's going to be…” But I also, once I realized I had that 0, leave the 5 to the end. Because if we have the 0, I mean, that would take the 0. But yeah, what were you going to say?

Kim  14:19

Well, I was going to say that I felt like this particular draw was pretty smooth. The one that Luke and I had, I mean, I…

Pam  14:28

Much harder? 

Kim  14:30

Yeah, I was like, “Are you kidding me, right now, Luke? Why can't I figure it out?” And I found three of them, and I could not get the fourth one. You know, I messed a little bit. And he would not let me leave. He was like, “No.” And I don't remember if he had found four already or if we were doing it the first time. I can't remember. It's been a little while. But he was like, “No.”

Pam  14:55

“Keep going. Keep going.” Yeah. And I was like, “Okay, good.”

Kim  14:55

Yeah. And I was like, “Okay, good for you. Yeah.” Like, and I persevered. And I found four. And I felt really proud of myself. Nicely

Pam  15:03

Nicely done. And I think I remember when I watched the video that Michael said, usually, if you play three rounds, usually someone can't get all four, and so there's kind of like a winner. If that's important. You and I are pretty competitive, so we kind of like to play.

Kim  15:19

Yeah.

Pam  15:20

But, yeah, love it, love it, love it. So, Multiple Machine. Oh, yeah, go ahead.

Kim  15:24

Let's talk about the math for just a second because…

Pam  15:26

Okay

Kim  15:24

It's called Multiple Machine, so obviously we're talking about multiples, but what I also loved was that we're thinking about maybe which numbers, which factors maybe have more options, so save those for the end. Like, when you said, “Save 2.” Well, yeah, because lots of things could be 2. And, you know, I don't know why we both navigated towards the 7. Maybe we're less familiar. 

Pam  15:50

I mean, like, half, right? 

Kim  15:51

I don't know, yeah.

Pam  15:51

Can I stay on the half? Lots of numbers are 2. Like half. Like half are multiples of 2. Okay, just had to say that out loud.

Kim  15:57

So, and so like, the constant. You know, people ask all the time, like, “Fact practice?” Hello? Like, you're constantly rearranging in a fun way that's not just “Hold the card, hold the card, hold the card. Do you know it? Do you know it? Do you know it?” So, I think this is a brilliant game, and you were so right that we were going to love it. And I love that you shared it. I would play this in third grade math any day.

Pam  16:22

Yeah. Nice, nice. And so, if you would like to find more games for Michael Minnis and his kids, you can go to lovemaths.me/games. lovemaths.me/games. We'll put that link in the show notes. Notice, it's “Love Maths” because he's in Australia. We like the “S” on the end of math there. Yeah, super cool. And thanks for doing that, Michael, thanks for putting those out there. And, ya’ll, have fun playing some games. And thank you for tuning in and teaching more and more real math. To find out more about the Math is Figure-Out-Able movement, visit mathisfiguratable.com. And keep spreading the word that Math is Figure-Out-Able!