# Ep 209: Stick and Split

June 18, 2024 Pam Harris Episode 209
Ep 209: Stick and Split
Math is Figure-Out-Able!
Math is Figure-Out-Able!
Ep 209: Stick and Split
Jun 18, 2024 Episode 209
Pam Harris

Developing multiplicative reasoning, let alone learning multiplication facts, has never been more fun. In this episode Pam and Kim discuss Stick and Split, a simple digital game your students or own kids can explore to learn multiplication in a whole new way.
Talking Points:

• We don't recommend products lightly - Stick and Split is amazing!
• Taking the product approach - How is that different?
• Noticing the commutative property
• Using common factors as tools
• What do the levels look like?

Check out our social media
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

Developing multiplicative reasoning, let alone learning multiplication facts, has never been more fun. In this episode Pam and Kim discuss Stick and Split, a simple digital game your students or own kids can explore to learn multiplication in a whole new way.
Talking Points:

• We don't recommend products lightly - Stick and Split is amazing!
• Taking the product approach - How is that different?
• Noticing the commutative property
• Using common factors as tools
• What do the levels look like?

Check out our social media
Instagram: Pam Harris_math
Facebook: Pam Harris, author, mathematics education

Pam  00:01

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 historic achievements, but they are 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  00:33

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

Pam  00:41

We invite you to join us to make math more figure-out-auble. Hey, Kim.

Kim  00:46

Hi.

Pam  00:47

Hey.

Kim  00:49

I'm loving what we have planned.

Pam  00:52

This is fun, right?

Kim  00:53

I know (unclear).

Pam  00:53

Today's going to be fun.

Kim  00:54

Pam  01:27

We like Tad. (unclear) Well, first of all, thanks, Tad for saying that about if I recommended it. And I actually tried to make that real. Like, I don't recommend stuff unless It's actually good.

Kim  02:31

Yeah.

Pam  02:32

You know, I am trying to think. I think the very first time I met David Tim, I think he poked me on Twitter. I'm not actually sure. I now we got on a Zoom. We chatted a little bit. He gave me a login. I checked it out. I was instantly interested. It was different than anything I had seen before. It wasn't like... It's just not like any other kind of app I'd ever seen.

Kim  02:58

Yeah.

Pam  02:59

Kim  09:50

Put three 2s together.

Pam  09:52

Duh. Okay, so you put a bunch of twos together. You put three 2s together a bunch of times, and you get 6. The very next level has a bunch of threes. So, how many threes would you put together to make 6?

Kim  10:05

Two.

Pam  10:06

Right. So, thank you for playing along. I have seen a little four-year-old. I was looking over his shoulder while he was playing this. And he goes, "Huh. It was three 2s made 6. And now, two 3s made 6." And then he kept playing. Like, he just like said it out loud. I don't know if he said it quite that, you know, expertly. But he like noted that. It was sort of interesting. Then the next level, there's twos and threes. There's a diamond on that level that says try to do it in whatever few is possible. Then the next level. Remember, we're still making 6. So, we're making 6. The next one says... It just has a bunch of fours, Kim. There's fours. So, I watched this kid try to put two 4s together. And if you try to stick two 4s together... I'm on that level, and I just dragged it over. The two 4s are blinking, and I hit... Oops, I meant to hit... I hit Stick, and it says, "That's more than 6." So, it won't let me put two 4s together. It just says, "That's more than 6." So, what can I do? Like, there's these fours, and I'm supposed to make 6. So, the only option available to me at this point is to take one of those fours and split it. So, if I take one of those fours and split it. That's the only option available. I think it's the only option available. And I split it, now it shows me that I can split it in half. Like the little thing comes up, and you can... And so when I click that, now I can make a bunch of twos. I didn't even realize until I was looking over this four-year-old's shoulder that I can select multiple of those fours and hit Split, and it will split them all into twos. So, I can do it really fast and split all the twos. And then I can put those twos together to make 6. Does that make sense?

Kim  11:53

Yeah. Is there... For whatever reason, I wrote down four 4s. And there...

Pam  11:58

Oh, there was a lot more fours.

Kim  11:59

Are there the number of fours that are equivalent to however many sixes you want to make? Like, is it leading in any way about? Like, you talked about it being equivalent. I can't see what you're seeing. But does it just give you a ton of fours like on the on the screen, and you just do what you want with a whole bunch of fours? Or is it across horizontally the same length as anything else?

Pam  12:23

Ooh, I'm not sure I understand what you mean. The fours right now, if I split the fours into twos, and I put three 2s together, those three 2s fit the total length of the six.

Kim  12:38

Ah, okay.

Pam  12:38

Which is taking the total width of the screen.

Kim  12:41

Yeah, that's what I was wondering. It's been so long since (unclear).

Pam  12:44

So, the total is, at least that I can see, is the length of the screen. And so you're trying to put things together to make that width. I say length and width at the same time. The total is the width of the screen, and so you're trying to put those. So, like right now, I have three 2s. And if I stick those three 2s together, the three 2s right now are are making the total width of the screen. And as soon as I stick them together. I just stuck them together. Then it's a whole 6. Now they turned into... There are a bunch of yellow twos, and they just turned into one pink 6 that was the same length of all those three 2s stuck together.  Yeah.

Kim  12:44

Yeah.

Pam  13:00

And then when you were asking how many. I can't see any more, because I've already split a bunch of them and stuff. But there were a whole bunch of fours and one 2. And I'm assuming that that one 2 was necessary to complete all of them together, so that at the end of it, I just have a bunch of sixes.

Kim  13:36

Yeah, that's exactly what I meant. If there's some sort of equivalence represented on the screen, so that you're not left with some or looking for some amount that's not there.

Pam  13:49

Yeah. So, the first time I was looking at this. I thought, "Eh, it's fine. You know, you stick these things together." And it hadn't really occurred to me the commutative property idea where you can put three 2s together and then two 3s together, and a kid can start to notice that. And I've watched kids notice that over time. It's amazing to watch them go... Like, I literally heard the kid go, "Oh! To make 12, you can do two 6s! But you can also do six 2s! Huh. It did it again!" Like, just really cool kind of commutative property thing coming out. But then I also, when I hit this level where it was try to make sixes with fours, I was like, "How do you do that?" And it literally took me as an adult a minute to go like, "What am I going to do with these fours to make a 6? You can't put fours together to make a 6? Oh, you have to split the 4 into something that then you can create a 6 out of."

Kim  14:37

Yeah.

Pam  14:38

I thought that was really cool. Anyway, so then they have these diamonds that I also think is cool. So, Kim, one of the things I wanted to mention I said a minute ago was the levels. I think you can even as an older student, step back and actually look at the levels. So, for example, the first thing that you try to do is make 4. I mean, you do that in a couple of ways. The second thing you try to do is make 6. And there are five levels to make 6. The next thing you do is make 8. When you're making 8, guess what the first thing is? First thing is a bunch of fours. Okay, so you put two 4s together to make 8. Duh. Guess what the next level is? A bunch of twos. So, again, you get that commutative property thing happening. I can stick two 4s togethe, but I can also stick four 2s together. And I start hearing kids say things like, "Huh. Did you know 8 is made up of four 2s? Did you know eight is made up of two 4s?" Like, they start thinking about... They start taking a product approach. What is 8 made up of in terms of factors? And I think that's really cool. In that 8 level, you start with fours, then twos, like I just said. Then you have twos and fours. Then the next one is sixes. So, Kim, kind of curious. If you just saw sixes, and you're going to try to make 8. I'm looking at it right now. I'll tell you there are 1, 2, 3, 4. 5... There's six 6s and one 4. You don't have to finish the level, but what would you start off with if you just had some sixes, but you have to figure out how to make 8.

Kim  14:47

I'd break up the sixes into twos, and then put four 2s together to make 8.

Pam  16:07

Bam. And that's fantastic. I think that's cool that kids think about that. The next level has twos, fours, and sixes. So, similarly, you'd break up the sixes, and then put those together. And then the last one has twos and threes.

Kim  16:24

Hmm. Okay.

Pam  16:25

Any ideas what you would do twos and threes to make 8?

Kim  16:28

I'd put some threes together to make sixes, and then break those sixes into twos.

Pam  16:34

So, you're making eight but you're also thinking about multiples of 3, and then factors of 6, to then think about...

Kim  16:46

All to get to 8.

Pam  16:47

All to get to 8.

Kim  16:48

Yeah.

Pam  16:48

So, kind of that that product approach for 8. Alright, so the levels so far have been 4, make 4, make 6, make 8. Why did we skip some? How come we didn't make 5?

Kim  17:01

Because it's a prime number.

Pam  17:03

Bam, right? So, we didn't (unclear) make 5. We didn't make 7. So, after 8, what's the next one you think we're going to make.

Kim  17:10

10.

Pam  17:11

We're actually going to make 9.

Kim  17:13

Oh. Haha. (unclear). That's awesome.

Pam  17:20

So, we are going to make 9. We're going to make 9 from threes. We're going to make 9 from sixes.  So, we're going to have to split the sixes up. But that's not too hard, right? But then we're also going to make 9 from twos and threes.

Kim  17:25

Yeah, mmhm.  Okay.

Pam  17:33

So what are your thoughts about making 9 from twos and threes?

Kim  17:36

Can I make twos become a 6, and then break the sixes into threes?

Pam  17:41

Right? Isn't that cool? I think it's cool. I don't know. I don't know how cool you think it is. I think it's cool. Okay, so the next one to 10. And then the next one's 12. Now, the 12 level has the most. The make 12 has the most levels in it.

Kim  17:53

Yeah. which coincides with the fact that 12 has... Do you know what I was going to say (unclear).

Pam  17:55

A lot of factor pairs. Yeah, I do. I do, yeah.

Kim  18:04

And so, then I went like, "Oh, gosh. What's the 24 level? And the 36 level? And, you know, some of those. (unclear). Ooh, nice, right? Right? Yeah. Yeah. So, 12 has a lot. 14 just has a couple. 14 has... You can make 14 from sevens. I should have had everybody guess. "Guess what you could do for 14." So, the first thing it does is make from sevens. So, it's just two 7s, right? You just put two 7s together. What's the next level then? Do you mind if I (unclear)?  After 14?

Pam  18:15

So, making 14, the first thing you do is create it from 7s.

Kim  18:19

Okay.

Pam  18:19

What would be the next way you would make 14 Just if you were (unclear)?

Kim  18:24

Twos (unclear).

Pam  18:25

Yeah, so put seven 2s together. Then you're going to make 14 from sixes.

Kim  18:33

I have to write that down. 14 from sixes. Okay. You have to get to twos to get back to fourteens.

Pam  18:50

So, because 6 you can get to 2.

Kim  18:53

Which is really brilliant for common factors.

Pam  18:57

What do you mean?

Kim  18:58

Like you're thinking about common factors from 14 and 6.

Pam  19:02

Ah.

Kim  19:03

Right? To know that 14 is 2 and 7, 2 times 7. And then 2 times 3 is 6.

Pam  19:11

Yeah, nicely said. So, a lot of teachers of older students will say kids need to have their multiplication facts.

Kim  19:17

They got to make a list. They got a circle them.

Both Pam and Kim  19:19

Yeah.

Pam  19:21

And they'll say the kids have to have their multiplication facts memorized, so that they can recognize the multiples. Or this is an example of how we can actually build the idea of thinking about common factors. And here's something else that David told me when he and I were talking in person. He's very clear that he is starting from the... Like, he started from 4. So, we're thinking about all the ways to make 4, all the ways to make 6, all ways to make 14, all the ways to make 15. Notice, how we're focusing on this product approach with small products.

Kim  19:53

Yeah.

Pam  19:54

He said if we take a factor approach, which traditionally I think almost everybody has. We're doing 2 times 9 immediately. Like, we're in the twos. You know the doubles, whatever. And we're already at 18. Boom. Or 3, we're talking about 3 times 9, 3 times 8. We're into 24 and 27. As soon as we get to 4, now we're into 38... 38. I'm trying to do too many at once. 4 times 8, 32. And we're doing 36. Like, we're instantly in these big numbers, even though we're in small factors. But his approach really gets you thinking about these small products well. Like, really breaking up 12 a lot, messing around with 12 in lots of different ways before you ever move to messing around with 14, before you ever move on to messing around with 15. So, I think that's also really intriguing that we get kids really good at these small products. And we're already thinking about some intense complex ideas, like you just said common factors, before the numbers get too big.

Kim  20:59

Yeah.

Pam  21:00

I think it's really interesting.  Yeah, nice, nice. So, one thing that I'll just mention is for every one of these makes. So, like if I look at make 24, the very first move is the largest factor pair. So, from 24, you're going to get a bunch of twelves. And then the next move, you're going to get a bunch of... Well, that's interesting. This is from 12. There's two from 12.

Kim  21:01

Well, and you know a lot of people say kids need to know their multiplication facts as they get older. And I would actually argue that one of the things they really need to know is less of the product of a multiplication facts, but they need to know... Like, they're given the product and need to know factors much more often as they get older. And there's a distinction between the two, and I think he's hitting that with this game of taking a product approach. Because, you know, when you're factoring stuff in middle school and high school, you know, they're not asking what's 7 times 8, they're asking what is 56 made of?  6 and 2?

Pam  22:00

I don't know that I've played them both. No, there's two levels from 12. So, now it's making me look. So, this one just has a bunch of twelves. Now, I got to go look. What is the second one have? Maybe I'm reading this wrong. Hold on. A second one has a different (unclear). Oh, it has a diamond. So, the first one doesn't have a... I don't know what the... I'm not sure what the difference between the two.

Kim  22:17

Is it an actual diamond or is it a rhombus parallel?

Pam  22:20

Oh, it's it's neither. It looks like a diamond ring. It's not.

Kim  22:23

Oh, that's great, that's great. I love it.

Pam  22:25

(unclear) It's a pentagon, yeah.

Kim  22:27

But it's a diamond ring. I'm all here for that.

Pam  22:29

There you go. There you go. Thank you for clarifying on that shape. Yes. So, my point is with 24, you're first going to mess around with twelves, and then the very next thing is you're going to mess around with twos. And so, that commutative property is just happening with every one of these guys. In 24, after you do twelves and twos, then you do eights, then you do threes.

Kim  22:50

Yep.

Pam  22:50

Then you do eights and threes. Then you do sixes. Then you do fours. Then you do sixes and fours. Then you do... Are you ready for this? Sixteens Oh, love it.

Kim  23:01

Yeah!

Pam  23:01

I think he's so clever. (unclear).

Kim  23:03

Does he do nines at all?

Pam  23:06

Well, after... So, let's just for everybody. Sixteens. How are you going to get from 16 to 24?

Kim  23:12

Okay, wait. I got to write it down. We're going for 24.

Pam  23:14

Mmhm.

Kim  23:15

And we have a bunch of sixteens?

Pam  23:16

Correct.

Kim  23:17

Okay, then you're going to break them into fours and put the fours together.

Pam  23:21

And put the fours together. And I was going to break them into eights and put the eights together.

Kim  23:25

Okay, will it let you break it in either.

Pam  23:27

Yes.

Kim  23:28

Okay, cool.

Pam  23:29

Yeah, you have the option. Mmhm. So, the next one is to get to 24 from eighteens.

Kim  23:35

Okay. So, sixes or threes.

Pam  23:39

Nice. Yes, yes. And then the next one is sixteens and eighteens in the same one.

Kim  23:45

Okay.

Pam  23:45

The next one is twenties. So, let's everybody think. Podcast listeners, if you have twenties, how are you going to get from twenties to 24? Okay, Kim, what are you thinking?

Kim  23:55

I'm going to break it into fours and fives, and put the fours together.

Pam  24:00

So, when you say fours and fives, you mean five 4s? Because you're not....

Kim  24:05

Oh, yeah.

Pam  24:05

One factor, right? One factor. Yeah.

Kim  24:07

I wrote 5, 4 on my paper.

Pam  24:09

There you go. There you go. Nice. Nice. And then the last level for 24 is it gives you twos, threes, fours, and fives. A minute ago you asked if nines, I think. It does not ask from nines. But (unclear).

Kim  24:21

Maybe because it's too many of them. You know? (unclear).

Pam  24:24

Yeah, maybe we only need so many twenty-fours. Yeah. Okay, cool. Okay, so...

Kim  24:28

So, what's really cool is as you go up the levels, right? I'm kind of assuming it's like you're progressing (unclear).

Pam  24:35

Yeah, yeah, yeah.

Kim  24:36

Within the 24, I had to think about the 20, so I'm reinforcing the 20 that I already did.

Pam  24:45

Mmhm.

Kim  24:46

And because I'm within 24, he's using what we've already built.

Pam  24:52

Yeah, yeah. Especially because he's using any of the factors of 24 we've already messed with.

Kim  24:59

Yeah.

Pam  25:00

Yeah, yeah. Cool. So, the next one is twenty-fives, and I wanted to actually ask you this one specifically. So, in make 25, the first level is from fives. Okay. So, you need five 5s together. The second level is from tens. I don't think that's too big of a stretch. Split the 10 into fives, and then put the fives together. The next one's from twenties. What are you thinking about from twenties? How would you get 25?

Kim  25:02

So, it's four 5s? Put some fives back together.

25:09

Put some fives back together. The last one is twos, threes, fours, and fives all in the same screen. Twos, threes, fours, and fives. Threes. That's kind of weird.

Kim  25:37

Yeah.

Pam  25:38

What are you going to do with the threes?

Kim  25:39

Do I have a bunch of threes or just a few? Like...

Pam  25:42

Let me get in there. You've got...

Kim  25:43

I can have as many as I want?

Pam  25:45

No, no.

Kim  25:46

Okay.

Pam  25:46

Only the ones on the screen. There's a lot, so I'd have to count. Let's see. 2, 4, 6, 8, 10. There's ten 3s. You can't put them all together because that would be 30, and that's more than 25.

25:56

Yeah. So, I want something that is made of threes that's under 25.

Pam  26:01

Mmhm. That what? What are you looking for? Like, finish that sentence.

26:06

Something that's under. That's made of threes. A product under threes that is divisible by 5 also.

Pam  26:19

Nice.

Kim  26:19

So, 15.

Pam  26:21

Nice. That was well said. That took me a minute to be able to verbalize.

Kim  26:25

Yeah.

Pam  26:25

That I knew I had to do something with threes that in some way was going to get me to 25. But I had a hard time thinking about what does that mean? Oh, I need only to create a product that's divisible by 5 because I want to get fives out of it, right?

Kim  26:38

Okay, so I had to say right now. And, you know, I could wait to the end, but I'm just going to stop right now and say it. My apologies to David. I don't know if he'll ever listen to this episode. Maybe somebody can tell him. My massive apologies because... I don't know. It was like two years ago. Three years? Whenever you first saw it, and you were like, "Hey, Kim, you know like, what do you think of this game? I'm really loving it." And I, you know, looked. And to be fair, I didn't go, "Yeah, I hate it." I was like, "Yeah..." I think I might've even said to you, "Yeah, don't hate it." And I got my kids on.

Pam  27:08

Which is typically high praise, but okay.

Kim  27:13

I am judgy about techy things. I don't know why. I just feel like we spend so much time on them, and it's waste. Anyway. So, but I did. I think maybe he even gave us an account. Like, so kind. And I got my kids on it, and they played. And I was like, "Yeah. Okay, cool." But I didn't spend any time. You know like, my kids are... You know, because they're my kids, they're like not easily pleased by that kind of stuff. And you loved it. And other people have loved it. And I was like, "Yeah, great." There's so much more depth than I think I even realized.

27:19

You're realizing now.

Pam  27:19

Yeah.

Kim  27:30

Yeah.

Pam  27:38

Wow, that's (unclear).

Kim  27:40

In this conversation, I'm like, "Wow, that's..." You know, there's so many layers to it. I want his brain.

Pam  27:58

Yeah, nice.

Kim  27:59

It's really, really well done.

Pam  28:00

Hey, let me just say one more thing. So, on this 25 level, it says "Make a move for you," I'm going to click "Yes", and I'm just going to tell you that it just... Oh, see now... That's funny. It did it so fast I didn't see what it did. Ah!

Kim  28:01

Got to pay attention.

Pam  28:05

Now, I would have to sit here for to do it again. Yeah, let's not do that. So, let me just mention really quick before we're done. After 25, then 27, 28, 30 But if I'm going to go all the way up to like 35, 36, 40, 42, 44, 45, 48, and 50. In the 50, there's a level that asks how do you make 50 from 40? Which I'll just throw that out. Like, and one of them is from 45. So, just kind of be... Like, listeners, hopefully you're intrigued at this point to just go, "Whoa! Like, how would you do that?!" Ya'll, I'm scrolling. It goes all the way... Can I even get all the way to the end? It goes all the way up to make 200 is the last one. Make 144. Make 132, 121, 120 Anyway, I think it's fantastic. David, I think you're onto something. Ya'll, If it were me, I would have this on my phone. I think it's \$2.99. Stick and Split. If I was a teacher, I'd have the classroom companion thing whatever. I think this you can do unbelievably amazing things with this. I would recommend it over and over again.

Kim  28:18

Yeah.  You just recently did.

Pam  28:30

And I did actually, yes. I had just had an ultrasound the other day. Medical stuff. Whatever. And the ultrasound tech was asking me, "You know, what do you do?" Whatever. And I said... She said, "You know, what can I do to help my kid?" And I said put Stick and Split on your phone. Absolutely do it right now. Your kid will love it. It'll be fantastic. Play it with them. Talk about it. All the things." And I also suggested Number Hive, which we are going to talk about in our next episode. Yeah?

29:48

Yeah. Hey, we're in Texas, and we are either on or close to summer break in schools. And, you know, parents ask you. Teachers, it's a great time for you to check it out. There is single user app. And there's a class package available. If I were in the classroom right now, I would be writing some fantastic questions to go along with the time that my kids were spending on the app. There's so many things you can do with it. So, check it out. Let us know what you think.

Pam  30:16

Fantastic. 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 mathisfigureoutable.com And keep spreading the word that Math is Figure-Out-Able!