# Ep 84: Single Addition Facts, Part 4

January 25, 2022 Pam Harris Episode 84
Math is Figure-Out-Able with Pam Harris
Ep 84: Single Addition Facts, Part 4

It's time for you to learn about the most important relationship your students need to know to automatize their addition facts: partners of ten. Partners of ten influence strategies for adding bigger numbers as well as strategies for other operations. In this episode Pam and Kim will discuss some of those influences and some games and routines specifically made to provide experience and build partner of ten relationships for all levels and all ages.
Talking Points:

• What are partners of ten?
• Do older students need partners of ten?
• Rich Tasks with 10
• Collect Ten
• I Have, You Need
• Establish partners of ten early in the school year
• Workshop registration is open until Feb 4!
Pam Harris:

Hey fellow mathematicians. Welcome to the podcast where Math is Figure-Out-Able. I'm Pam.

Kim Montague:

And I'm Kim.

Pam Harris:

And we make the case that mathematizing is not about mimicking steps or rote memorizing facts. But it's about thinking and reasoning about creating and using mental relationships. We take the strong stance that not only are algorithms not particularly helpful in teaching, but that mimicking algorithms actually keep students from being the mathematicians they can be. We answer the question, if not algorithms and step by step procedures, then what?

Kim Montague:

So we're knee deep into our series on addition facts, and we are finally ready to tackle our favorite and what we think is the most important relationship that everyone needs to know.

Pam Harris:

Everyone!

Kim Montague:

And that is building partners of 10. Right?

Pam Harris:

Yes, very, very important.

Kim Montague:

We say this often, right, that the 10s are super important and that we love the 10s. But why 10s? Why is that so important?

Pam Harris:

I mean, you say that, we do say that often now, but early in my career in building my own numeracy as a high school math teacher, I didn't know.

Kim Montague:

Yeah.

Pam Harris:

And now it's amazing to me, it affects so much. What's one way, Kim? What are some things you're thinking about?

Kim Montague:

So if you know about 10s, then you know how it influences Get to a Friendly Number? Because if you're at 43, then you know, you're seven away from 50, which leads to Give and Take. Right? The most important or the most sophisticated addition strategy?

Pam Harris:

Yeah, yeah. And so for example, if I'm adding something like 43, plus whatever, then I can think about, well, I know 43 plus seven gets me to that 50. And then I can sort of tack on what's leftover? And that's, either Get a Friendly Number or Give and Take. Yeah, so how far away you are from that next nice number is really, really important. That leads to understanding in rounding. So we can literally use this understanding of how far away I am from the 10 to round numbers. It leads to success in subtraction across zeros. Now if you're upper grades, teacher, I didn't know what that meant, as a high school teacher. I was like, "What? What even is that?" So that has everything to do with like 1,000 minus something. Well, if I know my partner of 10, then that can help me figure out the partner of 100, which can help me figure out the partner of 1,000. And all of a sudden I'm not doing all of that cross out the zero and carry the one and then that oh, now it's a nine and all that...

Kim Montague:

Oh my gosh.

Pam Harris:

...crazy stuff that happens when you're trying to use the subtraction algorithm when you have a bunch of zeros. No, no. You just sort of think about how far you are to that next nice number.

Kim Montague:

Yeah.

Pam Harris:

Bam, subtraction across zeros. In fact, it affects subtraction in general, we can really use this idea of how far away we are to the next nice number, as we think about using the difference or distance meaning of subtraction, that interpretation of subtraction, not just the removal, meaning of subtraction. So as I'm subtracting to a friendly number, I'm thinking about partners of 10. Also, because it impacts subtraction so much, it's going to impact strategies that we use when we are doing multiplication or division.

Kim Montague:

Yeah.

Pam Harris:

I mean, I can even give you just a simple example of if I'm doing something like how am I figuring out seven eights? Well, if I know that eight eights is 64, but I only need seven eights then I'm thinking about well I'm going to get rid of that four, and now I'm at 60. Now I got to get rid of four from 60. Ah, like, am I writing down 60 minus four and crossing out the zero? No, no, I'm thinking about the partner of 10 to play with a partner of 10 with four. Four plus what is 10 is six. Well, then, bam, I'm at fifty-six. So as I'm thinking about 60 minus four, I just use the partner of 10 to do that subtraction. And I could do that with bigger numbers, more complicated numbers. It hugely impacts the way I'm thinking about multiplication. And maybe even especially division as we're trying to think and reason using division, often I'm going to sort of multiply up to see well, how many of these fit in there? Well, I've got so many in fact, okay, now I'm wanting a, Kim, help me out with an example. I wasn't gonna give an example here but I'm dying to.

Kim Montague:

Alright, got my pencil.

Pam Harris:

Give me a division problem.

Kim Montague:

like a like a 63 divided by nine?

Pam Harris:

Sure. So if I'm thinking about 63 divided by nine, I might say to myself, well, I know I'm asking myself many nines are in 63. I might say, "Well, I know that there are six nines in 54. Well, how far away am I? If I know that fact, how far away am? I Oh, I'm only nine away? So it's that idea of thinking about subtraction. And if I've got partners of 10, and I can think about that subtraction easier, okay, then I've just got one more nine to get seven nines and sixty-three. I don't know if that was the best example.

Kim Montague:

Yeah.

Pam Harris:

This idea of being able to be fluent in subtraction. I need to have these partners of 10 to help me and that's going to help in multiplication and division. And you might be thinking, "I mean, Pam." You might be dropping off the podcast right now because you're like, "Okay, but you know, like I teach eighth grade." But remember Kayla in eighth grade? Remember, Kayla in eighth grade was really struggling, or not struggling, but she was counting by ones? We need kids to know their partners of 10. So that they aren't counting by ones when we need them thinking in bigger jumps of numbers, bigger chunks of numbers.

Kim Montague:

Yeah.

Pam Harris:

It's more sophisticated.

Kim Montague:

Yeah. We go to lots of places, right and hear from a lot of teachers

Pam Harris:

Hang with us. Uh-hum, yep. Not a thing, yeah. who say, you know, we share this with them. And a lot of times, there's conversation around yeah, my kids, that's not something you're automatic with. So this is not a K, one two, situation only. This is definitely for older kids who've never been exposed to the importance of partners of 10.

Kim Montague:

So we talked about this apple rich task a couple episodes ago, I think it was the first or second in the series, about just bringing understanding to ways to make 10. So I definitely feel like there's some great places to start. I'm not suggesting that you're going to do it with your eighth graders. Right?

Pam Harris:

So maybe let me just since it's been a couple episodes. So give young learners, "Hey, I've got 10 apples. I've got some green, some red, how many green apples? How many red apples?" And I specifically used the total of 10. For this very reason, because 10 is so important that we're talking about in today's episode, but back there, I could have used or, "Hey, we have a total of six apples." And the kids just could have been messing with different combinations of six. And we want teachers of younger grades to use different totals, but also really use the total of 10, a lot.

Kim Montague:

Yeah.

Pam Harris:

Like often, often use the total of 10. Because it's so, so important. Sorry for interrupting.

Kim Montague:

That's okay. So once you've given kids and experience with finding the partners of 10, then it's time to make some, that good repetition that we've been talking about with some games. And so we want to share a couple of our favorite games. The first one is Collect 10. So that looks like a numeral cards that have just the digits up there. Do they have, yeah, they wouldn't have 10. So zero through 10 on the cards, and you lay the cards out in an array. It could be like a five by five array or a six by six array. You've got partners who are going to play and they take turns and their entire game is collecting a partner of 10. So one student might say, "I found a three and a seven. And three and seven make 10." I put my cards together, I set them aside, and it's my other partner's turn. I'm going to find another pair of 10. So grab a five, grab a five, put those together, set it aside. They go back and forth until the entire game board is empty. You still have a deck of cards off to the side that you could refill in if you wanted to, to make the game a little bit longer. But that is Collect 10. A super popular game.

Pam Harris:

Yeah. Let me just talk about what if you have students who don't know their partners have 10 yet? I've literally played this with kids who don't quite have them automatized yet. A student can pick up a seven and then they can pick up a four and they can add them together and go, "Nope, that didn't work."

Kim Montague:

Yeah.

Pam Harris:

And then you can decide if you want to lose a turn or whatever. We don't usually do that. We just like, "Okay, well, then what will work?" And then you know, kind of until they find the partner of 10. And then that's their partner. So it's, you can also do it even if you don't have the facts automatized.

Kim Montague:

Well, I'm glad you mentioned that, because once you have partners of kids who do have them automatize, then that probably isn't the best game for them anymore, right? If you already have all your partners down, then you're just going through the motions of a game. That's not meeting you where you are. However, you then might do Turn Over 10, which is the concentration version. So you have that same, I would do a smaller array at this point. It's more like memory, so maybe a four by four array, or five by five array, cards go face down. They turn the first card over, you get a four. At that point, you have to think to yourself, "What would I need to get 10?" So four plus what equals 10. They flip over a card that's upside down. They say, "Oh, it's like seven too much." At that point, I would say, "How much too much? What would you be looking for?" They flip both cards back over and the game continues to be played.

Pam Harris:

Yep, yep. And now you just have that extra little concentration, nudge. And that visualizing of what the partner is, is definitely a step up. There's the memory part of it, that's like where is it? That maybe is the less important part. But there's the sort of visualizing like you said, "What do you need if you? If you popped over six, what is that partner of 10?" Yeah, totally cool.

Kim Montague:

Probably my favorite game because most kids To ten. To ten. So you have to consider, "I have a four, what do I need have experienced Go fish. So 10s Go Fish would be a version that we play instead of playing, you know, playing in a group. Instead of looking for, "Hey, do you have a four?" And you want the match for plus four. At this point, you're holding a deck of cards, a group of cards in your hand. And let's say you have a four, you're going to ask for its partner. to ask for? Ah, I need to ask for six?" I asked somebody, "Do you have a six?" They hand it to me. I say, "I have four plus six is 10." And I sit those cards down.

Pam Harris:

Now it's my turn. And then I'm looking at a nine. And so I say to you, "Do you have a one?" And you say...

Kim Montague:

Nope, go fish.

Pam Harris:

Oh, man, rude. And so then I go fish. I pull a card from the deck, and we go on. So to differentiate this game, let's say you have students who don't know their partners of 10. Yet, like at all, it's a really young, or I should say, maybe really less experienced.

Kim Montague:

Yeah.

Pam Harris:

Then you might have that student actually do the matching game first. You might, if I have a, help me, a three. I might say, "Do you have a three?" And then if you do I have a match, and if you don't, then I go fish.

Kim Montague:

Yeah.

Pam Harris:

If you have students that are just on the cusp, like you, they've done work with partners of 10. And they just need more experience to really get them automatized. This is a brilliant game. Because it's kind of fun. And you have to, you get some time to sort of think about it, and there's not a speed element involved. But you get a lot of repetition. And it's kind of self correcting. Because if I say, "I have a four, do you have a six?" and then your partner is gonna go, "Hey," Or sorry, I should have goofed. "I have a four to have a seven?" Your partner's gonna go, "Hey, it's not a seven. It's a six." And then you guys can sort of work it out and come to an agreement. So there's lots of ways that it's a really nice game for kids that are just needing that more experience. more practice.

Kim Montague:

Yeah, I've actually played Tens Go Fish with some older kids, and it feels less immature.

Pam Harris:

Like you're dumbing it down for them?

Kim Montague:

Yeah, yeah. There's other tens activities that they know. "Oh, we're working on the 10s." This one feels a little less babyish, if you will.

Pam Harris:

Yeah. So kids are more willing to play. And so then you get good practice in.

Kim Montague:

Yeah.

Pam Harris:

So y'all in this whole series as we're talking about automatizing single digit facts. We're not suggesting that once you've mentioned a relationship that, okay, now we're done. And we can just move on to do other things. And kids magically own them. No, no, they need experience. It's just the kind of experience that we want kids to have is more like these games that we're talking about. And a whole lot less speed, timed, pressure kinds of things. When we give kids speed timed pressure kinds of things, then we know now that that in many kids that can turn off their brain. They're gonna get flooded with adrenaline. And they can't think and so what we're really testing is more they're sort of metal under pressure. And that's not math. That's not mathematizing. We want to know, we want to help them develop relationships, literal connections in their brain. That's mathematizing. If you're interested in creating a kid that can take a test under time pressure, then at least admit that's what you're doing. And go do it with some other subject. Don't do it with math, because you're ruining math. You're making it equivalent to this idea that if you're good at math, then thou shalt be fast. And we just vehemently and fundamentally disagree with that Absolutely. So if you've ever heard Pam speak, pretty much at proposition. You can absolutely think deeply and carefully and purposefully about something. And that to us is more valuable than a quick answer. all, you probably have heard her mention a routine that we absolutely love called I Have, You need. It's a great routine for working with combinations of 10 which leads to combinations of 100, combinations 1000 that we can do for older kids. Pam, you want to speak to I Have, You need? Yeah, so Kim actually made it up. So she's, I'm going to give her lots of credit for I Have, You Need. It's not I Have, Who Has which is sort of instructional, it's a different routine. But I Have, You Need you specify the total. You say, "Okay, today we're working with a total of 10. And since we're talking about total of 10. Today, we're going to kind of focus on that one. Total of 10. If I have eight, what do you need to make 10?" And I can do this really early, when students are learning to count. I can hold up eight fingers and sort of flash those eight fingers and say, "How many?" And when the kid says, "Eight." Then I can say, "Well, okay, this is eight. How many do you need to make 10?" They can literally count the two fingers that are down. If you could see me I'm holding up eight fingers, two fingers are down. And my goal at that point isn't to have them automatize the partners of 10. My goal at that point is for them to learn to count, but I'm doing it with my fingers so that they start to get sort of that finger understanding. And they start to really develop the sense of 10ness. And we're dealing with sort of partners of 10, as we learned to count. So it's a brilliant, I get lots of nice outcomes. But after students are counting, and really we're trying to automatize the facts, then I can really just say, "Okay, partners of 10, here we go, ready? If I have nine? What do you need?" Kim, go ahead, just play with me real quick.

Kim Montague:

One.

Pam Harris:

If I have seven, what do you need?

Kim Montague:

Three.

Pam Harris:

You need three to make 10. If I have 8, you need?

Kim Montague:

Two.

Pam Harris:

If I have six, you need?

Kim Montague:

Four.

Pam Harris:

And now you might have noticed, as I played, that I just did numbers close to 10, first. We would recommend that. As you play with students do numbers close to 10. Because if they are counting up to find the missing number, then that's going to be easier for them to do. And I usually start with 8. If I have 8, what do you need? And kids can go 9, 10. Don't start with nine, that's too easy. Don't start with six, that's too hard. Like start with eight, maybe seven, like know your content, know your kids. Know your kid well enough. I like to start with eight usually. Then once kids kind of get the hang of the game and everything. Then, I again, I said if I have eight, you need two. Then I might say well if I have two you need? Eight. So often kids go, "Oh, crud." Because then they have to like count up from the two because it's like so much farther away. But then I might notice, I might notice and go, "Oh, that's interesting. When I said eight, you said two. When I said two, you said eight. Hum." And then I might just go on and do another one, seven, three, three, seven. "Ah, that's interesting." And just notice. And I'm going to notice for a while before I make even a bigger deal of it. And then to sort of expect kids to stop counting up from three and start just using, "Oh, well I knew seven and three. So then I'm going to know three's partner is seven." But you know we're going to talk about it, we're going to make that sort of a thing. We're going to play some more, we're going to talk about it some more. Make it oh, if I know the partner then I also know this one. Kind of like your number rack flipping that we've been talking about the past couple episodes Kim. That if I know seven plus three, then I also know three plus seven. That use of the community property. So we really like I Have, You Need. It's a fabulous way to promote kids really thinking about partners of 10. And y'all, you might be thinking, "Okay, Pam, but I'm a teacher of older students. Yeah. Who don't know, their partners have 10. Really, really want me to play I Have, You Need partners of 10?"

Kim Montague:

Yeah.

Pam Harris:

Actually, maybe not. So here are a couple things that you can think about. One, you can help your student. you can, yeah, sorry, you can help your students think about partners of 10 by doing total 100, but do the decades. So you can say, "Well, if I'm trying to get to 100, if I have 70, what do you need?" Well it's like seven 10s? How many 10s do you need? And you're kind of working on the partners of 10, ostensibly working on the decades. Now you kind of have to know your kids to know if that's gonna work. But that's a thing. Now it's kind of bigger numbers. Doesn't it feel like I'm babying it or dumbing it down.

Kim Montague:

Well, and I'll tell you, Pam, that when I was teaching third grade, I absolutely played I Have, You Need with partners of 10. But it was early. Right? It was early, early, early, not at the end of the year. And it makes me think of some of my partner teachers who would say, one in particular, and I had this conversation about, it's like, middle of the year my kids don't know their partners of 10. And I remember saying, "If they came to you not knowing the partners of 10, you cannot blame the people."

Pam Harris:

Well, that's a bummer, right? If they come to you.

Kim Montague:

Right, it's December. And so what have you been doing about it? And so I start the year with a real quick, like, this is a chat kind of thing. Not a gotcha, but just like, "Hey, we're gonna do this routine." And notice who still needs to work on that combination of 10? And who I can move on with decades or partners of100?

Pam Harris:

Yeah, so y'all, if you say to yourself right now, "Oh, my students don't know their partners of ten." Okay, then, let's build them. Like let's do that. Let's develop those partners of

Kim Montague: