Ep 210: Number Hive

How can students gain fact fluency in a productive, fun way? In this episode Pam and Kim discuss Number Hive, a game that builds students multiplication fact fluency.
Talking Points:

• Product Game is great, but Number Hive is even better
• How to play Number Hive
• Who will win? Kim or Pam?
• A product approach to multiplication by considering factor pairs
• Opportunities for great classroom discussion
• Low cost of failure
• Number Hive is flexible with lots of variety and levels

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Transcript

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  00:08

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  00:17

We know that algorithms are amazing historic 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

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

Kim  00:41

Hi!

Pam  00:42

Hey, there! We're having fun. We're playing games. Let's play a game.

Kim  00:47

Yeah, yeah. We just were, huh? Susan Smith. She's a dear friend. She left us a review that said, "Best podcasts for all." And she said, "This podcast is a must for math educators and all those who want to 'math'..." She put in quotes. "...and develop their own numeracy. I walk away from each episode with new insights into my own numeracy and my own instructional practices as a math teacher. Pam and Kim can helped me become a better math teacher for my students. And best of all, the journey continues." And I have to believe that she said that because she is also one of our Journey members. 

Pam  01:23

Yeah.

Kim  01:24

She's super fantastic. Okay.

Pam  01:26

We love having her in our Journey membership. That's awesome. 

Kim  01:28

For sure. Last week, we spent some time chatting about Stick and Split, which is fantastic.

Pam  01:35

Super good game.

Kim  01:36

You know, I owned that I didn't pay attention as much as I should have. And I hope that people will chime in more about how they also love Stick and Split, send some pictures of their kids playing. Anyhoo, this week, we want to chat about another game or app that we absolutely love. And you've actually met Chris, the creator.

Pam  01:58

Chris Hogben is fun! This has been one of my favorite parts about being a math teacher educator and spreading the word that Math is Figure-Out-Able is that sometimes people will reach out to me. Chris reached out to me. I think it was on LinkedIn. And said, "Hey, let's chat. I got a thing." And he was living in... Do I tell that personal stuff? He's not there anymore. I thought he was a brit because I was contacting him in Great Britain. But he's actually from Australia. Anyway, it was super fun. I don't know that I can tell the accents apart that well yet, but I want to. I love accents. I think they're cool. We had a brilliant time chatting. He was so fun. And he said, "You know, I've got this game, and I think you might be interested in it." And I was like, "Yeah, yeah, whatever." And then...

Kim  02:40

We really have to stop that. 

Pam  02:43

I mean, there's just so much out there that's lack luster, that's just not all that helpful. So, when we find one that's good (unclear). 

Kim  02:51

It's exciting.

Pam  02:52

It's super exciting. We're all over it. And when he first showed me... Sorry, not Stick and Split. We're talking at Number Hive right now. When he first showed me Number Hive, I said, "Oh, it's kind of like the game that we've played called The Product Game. I think I first saw a version of The Product Game in Investigations in Number, Data, and Space. No. No, that's not true. I first saw it in Connected Math in CMP. I'm pretty sure that's where. And then NCTM picked it up, and they made a version of it in Illuminations. And he smiled, and he goes, "Yeah, I've done better than that." Or something. (unclear). It's just cute. He was like, "Yeah, ours is a little bit more. You know, you got to try it." Oh, he has! Like, as good as those games are. And they're good. Like, we like we liked The Product Game. He's really done a nice job to make it even better. Ya'll, last week we talked about Stick and Split, which we highly recommend. And that is really... Stick and Split really does a superb job of building multiplicative sense, and common factors, and this product approach where kids are really thinking about how to make a product multiplicatively. And Stick and Split also his practice towards fluency.

Kim  03:30

I love it. Yeah.

Pam  04:05

Today, we're going to talk about Number Hive, which really then takes from there. I think it takes off from that place from Stick and Split. And really is delightful way to practice to get more experience with fluency. And it has a lot of strategy involved. So it's very nicely differentiated. Because kids who own multiplication facts, like you and me, we have fun with the strategy of the game. And kids who don't own all of the facts yet can really just be practicing the facts and leaning into strategy a little bit. We like games that have strategy because of that nice differentiation part of it. Yeah. Cool. Alright, so, Kim, if I were to ask you to tell us about Number Hive, what's your experience. Go.

Kim  04:51

Yeah, well, you told me about it, and we were like "Yeah, we've been playing this for a little bit." So, when I first saw it... You know I don't even remember when, how it came across. Maybe it was on Twitter, or somebody said something, or... Somehow, I ran across it. And it was an game app only at that point. And when you log in, what you see is this honeycomb type pattern. It's a hive, right? It's a honeycomb type pattern, and it has a bunch of products. And then down below, there's...

Pam  05:27

(unclear) kind of like Tic Tac Toe except it's not a grid. It's a honeycomb. So, it's like six-sided little cells, and in each cell is a product.

Both Pam and Kim  05:34

Yeah.

Kim  05:35

Yeah. 

Pam  05:35

Mmhm.

Kim  05:35

And so, down below, there are some factors that you can multiply to create the product that's in one of the cells of the honeycomb. And so, you know, I'm glad that you mentioned that it's about practicing fluency because I think what happens is sometimes teachers are like, "Well, you know, I want to build conceptual understanding for multiplication." And so, then they do this work, and then they leave them. Right? Like, they're like, "Oh, I'm not supposed to practice facts." Which is completely untrue. We do want meaningful fluency practice.

Pam  05:43

Mmhm. To win. 

Kim  06:07

Yeah, to win the game. Yeah. 

Pam  06:07

Mmhm.

Kim  06:07

And here's a fantastic way to do it. So, this honeycomb look. There's factors down at the bottom. What's super cool about this is when you get the app, you can play with a friend. So, like you can send a code to a friend who also has the app. But you could also play online. So, you can log in at any time, and you can hit play with somebody online, and you just start playing. And the way the game works is you choose factors that make a product that you want. And so the first person goes. They choose two factors. They make the product. And then the next person has to keep one of the factors and choose a different second factor that they want to make either a block or their own separate move. And you you make several in a row to make...

Pam  06:08

So, you're sort of like trying to play Tic Tac Toe, but it's on this honeycomb looking thing. You're trying to get four in a row. And so, you might want to block the other person by getting that product. You know like, "Ooh, I better get that product. Ooh, but I can't because the two factors you've left me, there's no way that I can change only one of them." Because you only can change one.

Kim  07:15

Yeah.

Pam  07:15

You're trying to change one of them to be able to get that. "Mmm, then what can I do?" And yeah, it's super. It's pretty fun.

Kim  07:21

Which is really cool because like Stick and Split, this also has a bit about common factors that you're always considering but maybe you don't realize you're considering.

Pam  07:31

as you get into strategy because you're trying to like decide where to block, and where to go, and where not to go. And even several layers down the road. If I go there, will that allow a factor to be available that then they could go there, right? You're like. Yeah, so you want to kind of be careful of that. So, Kim, we thought we play a live game. And I'm going to take a note from Chris Hogban. He had me on a podcast once. Was it a podcast? I don't know. He interviewed me, and then he put out little bits of it and stuff. And on that live. We're on Zoom. He just surprised me. And he's like, "Hey, we want to play live?" And I was like, "Maybe." I wasn't ready to like play live. Especially

Kim  07:32

You got to think.

Pam  07:41

Yeah, I mean, because there you are on video. You know like, people are watching you. It was so much fun. 

Kim  08:17

So, you're going to do it to me?

Pam  08:18

So, I'm going to do it to you. There you go. Thanks. Thanks, Chris, for the idea. So, Kim, we're going to play the version on the app. When you get into the app, there's a couple of free versions. And then there's others that are locked, and you have to subscribe to get access to.

Kim  08:34

Okay, yep. And I haven't joined, so you ready for me to hit join? Yeah.

Pam  08:34

So, let's play the free version where we're doing 1 through 10 multiplication. Yeah. And we'll go over the other options in a minute. So, we're going to do that option. I think I've sent you the code.  I am ready. 

Kim  08:49

Okay. Alright, I'm hitting. 

Pam  08:50

So, it says, "Waiting for friends".

Kim  08:52

"Join game now." 

Pam  08:53

Okay, and so it's I'm...

Kim  08:55

Oh, Pam, "This invitation is no longer valid." 

Pam  08:58

Are you serious?

Kim  08:59

While you make another code, here's a thing friends. She just sent me the code a few minutes ago. (unclear).

Pam  09:03

Yeah, don't wait too long. Don't wait too long.

Kim  09:05

Don't wait too long. Okay, so let's

Pam  09:08

see... I'm hosting a game.  And I'm choosing the 1 through 12 multiplication.

Kim  09:10

Okay.  It's super quick to set up. 

Pam  09:14

Yep. Okay. And I put my name in. 

Kim  09:16

Yep. 

Pam  09:16

And now, Kim, it's 267387

Kim  09:19

387... And I'm joining.

Pam  09:23

Okay. Oh, we're in. Okay. 

Kim  09:24

Oh, look. Kim. I'm a bee and you're a bee. 

Pam  09:27

We're both little cute little bees. 

Kim  09:28

I got to get 4 in a row.

Pam  09:30

And I get to go first. And it starts with with a 1 highlighted and a 1 highlighted. So, I can only basically choose a 1 times something. 

Kim  09:39

Okay. 

Pam  09:39

And I'm going to go ahead and choose an 8.  So, I got the honeycomb right in the middle that says...

Kim  09:46

Yeah, you went for a middle space. (unclear).

Pam  09:48

I did go for a middle space.  Okay. (unclear). 

Kim  09:50

You went for middle space. So, I have to keep your 8. 

Pam  09:55

Or 1. 

Kim  09:55

Or 1.  And I have to think about what's surrounding if I want to block you. Or I get to go my own path and go far away. (unclear).

Pam  10:04

Yeah, you can go somewhere else.

Kim  10:06

So, I'm going...

Pam  10:08

(unclear) all things you could talk about, right? Like, do you want to try to block me? Do you want to go far away on the other side of? Alright, so, Kim just chose the 1. She moved the 1 to a 10. So, now she has 10 times 8. And I guess I could have let you say what you did, sorry. 

Kim  10:21

No, that's okay. So, I have 80, which was the honeycomb right next to yours.

Pam  10:26

Yeah. Above my 8.

Kim  10:27

I'm going to keep next to you. 

Pam  10:29

Yeah. And so, let's see. From 8 and 10, I can think about where I want to go near you, near me probably. Let's see. Oh, thanks a lot. You didn't give me a lot of options. Around my 8 are 99, 1, 77, 132, and 4. And I don't think I get any of those with an 8 or a 10. So, now I'm going outside of those to think about where I might want to go. Hmm.

Kim  10:57

Oh, we should probably say. The factors are 1 through 12. 

Pam  11:00

Yeah. (unclear).

Kim  11:00

So, that's the numbers you have to work with.

Pam  11:02

Yep. But I can only use a 10 or an 8 right now. And thanks a lot, Kim.  Sorry. I'm going to (unclear)...

Kim  11:12

Or not sorry really, but.

Pam  11:14

Yeah.

Kim  11:14

I feel for you. 

Pam  11:16

I'm going to do that. So, I just chose a 12, so now I have 12 times 8, and I got 96. If you can see the board, my 8, it's 2 away from my 8.

Kim  11:27

Okay, so now I have... Yeah, so you look like you're going to try to make a row of four. But I have an 8 or a 12. I don't know that we're going to finish this game because you and I are going to be super strategic. But we can keep it... I wonder how long. I don't even know how long does it last on the game. Chris is yelling at us right now going, "Don't wait!"

Pam  11:45

No, I think it goes as long as you... I don't think there's a timeout until somebody quits or wins. 

Kim  11:52

Oh, goodness. Man. Okay. (unclear).

Pam  11:55

So, can you say what you're thinking out loud?

Kim  11:58

Yeah, sure. So, I'm looking at the 22. That's not. Oh, around me, I have 99, 35, 22, 81, (unclear). 

Pam  12:05

And your factors are 12 and 8. So. 

Kim  12:08

Yeah. 

Pam  12:09

None of those are...

Kim  12:09

So, I don't want 35, or 22, or 81, or 4. So, I'm going to take a cue from you. And hopefully you don't block me. And I'm going to see down below that I have a 64. So, I'm going to change the 12 to an 8, so I have 8 times 8. And now, I have something several away.

Pam  12:31

Yeah, so you're several away, but you could... It's in a line, so if you got the two in between there, then you would get four in a row.

Kim  12:37

So, what's noteworthy is that we both have something between ours, so it's it's going to be...

Pam  12:42

It's a bit of a battle to see who's going to get that 4.

Kim  12:44

And whose going to make a mistake to get the other person.

Pam  12:48

And now, we both have 8s available. So, Kim, what's fun now is as we're thinking about this, we're looking at the two factors. So, right now I have 8s available because you you chose 8 times eight and then chose 64. So, I'm looking at 8s, and I'm looking around where I am, and I'm asking myself what are the factor pairs of those numbers?  So, like, I have 132. And I'm like 8 times what is 132? Well, I know 8 times 12 is less than that, so that's not going to. That's not an option. I have 27, 8, 8. That's not an option. 45. That's not an option 14. That's not an option. So, now I'm having to look further out from me. So, part of this game that's interesting is that you're thinking about... Again, it's kind of this product approach, where you're looking at the product, and you're asking yourself, "What are the factor pairs? And do I have one of them. Right? Because you can only move one of the factors in the game to be able to choose your product. And so, this idea of being able to look at the product. In Stick and Split that we did last week, you're building up to that product, so that's why you would want to do that one first. And once you kind of have sort of a handle on some of the facts, bam, now you come here to Number Hive, and you're looking around to say, "Okay, how do I make that product based on the numbers that I have?" I'm a little tempted to talk a little bit more about what's available on the app instead of finishing the game.

Kim  13:07

Yeah. Yeah, you know what would be kind of fun is if we could... I don't think we can do this on the podcast. I probably shouldn't say it. But it would be kind of fun to share a picture. Take a screenshot. We share a picture of where (unclear)

Pam  14:23

Ooh, and ask what our next game should be (unclear). 

Kim  14:24

Which I have to say is exactly something I do in the classroom. Like, start a game. And I think it's very strategic move to say, "What could be a good next turn?" And have kids talk about with a partner think about it. You know like, when you use one of these kinds of apps, it doesn't have to just be one kid in their screen. Like, capitalize on the fact that there is so much discussion to be had and draw it out with the kids because A, it's going to help the kids who are just kind of multiplying two numbers and plucking different honeycombs all over the place. Which is a great place to start. But it's also taking them up a level to say, "Oh, these are the things that other kids are thinking about." Maybe (unclear) know that there could be thinking about strategy. Right now, I'm thinking about numbers I don't want you to pick because then further down the line. You know, there's there's so many different levels of entry here. And having those conversations come out, I think, is a really, really good move. So, one of the things that's been really cool about Number Hive is that it's grown so much. Lots of people have taken a hold of this game and have said like, "I love that, too." There are six different versions on the app depending on your app purchase. You had mentioned that. Like, which level you can choose. And Chris has made printable packs that you can buy to do some less tech versions. Yeah.

Pam  14:39

Yeah. And his versions have integers. So.

Kim  15:55

Yeah, so many grades. 

Pam  15:57

A lot of people ask me, you know like, what do you do with integers? Well, this would be a great way for kids, especially if they're on the app, to just like play and notice patterns, and then ask themselves like why is it happening that way? And once they kind of have a feel for integer operations to then get really nice practice with a low cost of failure. In fact, one of the things that I meant to mention in our Stick and Split episode last week is that both of these apps are excellent because they have a low cost of failure. It's one of the reasons why kids like to play video games. You know, they play, they try, whatever. Eh, they die. Okay, back up. You know like, try again. That idea of a low cost of failure being able to try, give it a shot, live again, try it again, give it another shot, give it another one. Like, that low cost of failure is super nice. And then combine that with strategy, and you've got a really nice differentiated task for kids. Because we believe in building fluency. We just want to do it in a way that's mathy. Not in a way that's about rote memorizing. Yeah, cool.

Kim  17:01

One of the other reasons that we like this game so much is that it's so flexible. Once you've taught kids how to use Number Hive, how to play with it, the content can be changed out, so it becomes a routine. You know, we talked about routines not too long ago. That what makes something really good is that you can change out the heart of the content. And it's kind of like I Have, You Need where you can find lots of different totals. You can play Number Hive for addition, subtraction, integers. He's got some really nice higher math stuff in there. And, you know, somebody might say to yourself, "Okay, well, like which one is better? Stick and Split or Number Hive?" And the answer is neither. They're both amazing. And, you know, there's a lot of variety out there. But some of it is not so useful. And kids don't want to play one thing over, and over, and over, and over again. Although, you can play these two, you know, like for the entire year. They're amazing. But there is a different approach here. And I think they complement each other well. I would absolutely have access to both of these for as many kids as possible. 

Pam  18:12

Absolutely.

Kim  18:13

Yeah. 

Pam  18:13

Hey, kim, Can I mention one other differentiating thing that I think I just forgot to mention earlier? 

Kim  18:18

Yeah. 

Pam  18:19

So, you can play like you said against a particular friend by sending them a code. You can play some random person who's out there. If they just wait until somebody else is looking for game. But you can also... It says "Practice". And when you get into practice level, you're basically playing against the computer. But you get to a point where it says, "Would you like to play mild, medium, spicy, or extreme?" And I've played those levels. And the mild, you know, basically the computer doesn't try to win in the most straightforward way. It kind of, you know like, it might choose a honeycomb slot that's over there. And then, you know, it lets you keep going. But as the levels get higher, the content changes. And the numbers change. And they get bigger and more complex. And it's like much more difficult. And so, again, now kids can sort of self differentiate what level they think that they're ready for. So, I think that's a brilliant. Both the diamond in Stick and Split and this ability here in Number Hive to choose kind of. You know, choose your challenge. I think is a super good way to build fluency and a really fun, and engaged, and enjoyable way.

Kim  19:33

Yeah, we at Math is Figure-Out-Able try to do some math with our team. And I think that this is a fantastic thing that you could do in your PLC, at a committee meeting. Just getting people involved in math in a fun and playful way but helps them think about the depth that they can do with their kids. So, we should play more, Pam.

Pam  19:55

(unclear).

Kim  19:55

Send me codes whenever.

Pam  19:56

Start your PLC. Just say, "Hey, everybody, get in there and play with a friend." 

Kim  19:59

Yeah.

Pam  20:00

That's a great idea. I love it! All right, you all thank you for tuning in, and teaching more and more real math, and getting your kids into apps that actually make a difference. 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!