This one's for all you, parents! How can you support your children in becoming mathematicians? In this episode Pam and Kim go over their favorite ways to explore math at home in fun game-like activities.
Speak about math positively
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Hey, fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able. I'm Kim.
And I'm Pam.
And you found a place where math is not about memorizing and mimicking, waiting to be told or shown what to do. But it's about making sense of problems, noticing patterns, and reasoning using mathematical relationships. We can mentor students to think and reason like mathematicians. Not only are algorithms not particularly helpful in teaching mathematics, but rotely repeating steps actually keep students from being the mathematicians they can be.
Bam! Nice! Good job, Kim. So, it was funny. When you said, "I'm Kim", and then you laughed. I was like, "Oh that's right," because I got to say, "I'm Pam" Because I was about to say, "And I'm Kim. And that would have been silly because...
That would not be good.
We kind of have that written, obviously, people. And so, she was reading it. When you said, "I'm Kim." I'm like, "That's not what it says... Oh, right!" Because you...
Hey, I have a question? When I was saying at this time, did you do what I do when you're saying it? Because you've heard it so many times. And like say the line in your head?
Yeah, pretty much. Alright, we thought we would give that a try, everybody? Well done, Kim. That was kind of fun. Why not? Alright. Hey, let's start today with a fun comment that I got on Facebook from Nickena. Who said, "Hi, Pam, I wanted to let you know how your podcast is helping me. I don't remember exactly how I found you, but it was from other podcasts that I was listening to, specifically for elementary info. I'm not a teacher, just a parent who wants to get my math brain fired up, so I can engage my children with thought provoking games when they are developmentally ready. Ow! That is amazing. So, Nickena, that is fantastic. And I'm so glad that somehow some other podcast was saying something about our podcasts. That's wonderful. And I'll just maybe mention. Often, way too often, people will say, "Oh, yeah. Pam, you're elementary." And I'm like, "Well, yeah, but I'm not only elementary." It's actually funny that people say I'm elementary because I started secondary. Anyway, I'm super, super grateful that Nickena found us, and that she's able to use some stuff with her kids. Because we like parents.
Yeah. Well, and it's funny that she said, "I'm not a teacher, just a parent." I mean, parents are their kids first teachers.
Absolutely. And probably best teachers, right?
Yeah. Oh, for sure.
Well, speaking of parents, we want to welcome you parents. This episode is for you. We know that you love your kid, but you may or may not love math, and we can work on that. So, we have some tips and ideas for you that you can do in tiny, tiny bits of time that will make a huge difference for your students, no matter their age.
And no matter, like she said, If you love math, if you're have a shaky relationship with math. Either way, we've got some ideas that can really help you with your students do more and more math at home. I've learned a ton from Kim, things I do with my kids, my grown kids right now, that she's doing with her teenagers. Lots of fun math that we can do all the time. So, we have some tips that we'd like to start with. We're going to start with some general tips, and then we're going to do some mathy things. So, Kim, first general tip that I'm going to mention is, let's recognize, to start off, just off the bat, that adults might have some math baggage that our kids don't have, and maybe don't ever need to have. Like, I was about to say "don't have yet". And I was like, "Oh, let's not say 'yet' there." Let's say that maybe they don't have it. How is that helpful to recognize that?
So, we as adults kind of set the tone, right? And so, if we have concerns... Well, I was going to say let's not share those right away. But in general, we might have some nervousness or some worry about math that we might suggest to our kids, if we're focused on the baggage that we had.
Or if we don't focus on the fun we're having now.
Yeah. So, let's say that you did have some traumatic experiences in your past with math. Many of us did. Many people have horrific memories of time tests, or of getting something wrong in front of their peers, or being called to the board in front of people when you don't know what you're doing. Rather than saying, somehow rise above those. I wonder if we could actually just say, like those are real, but let's dive in now with our kids, and do some things in the moment now. So, like actually math with your kids now. Not rote memorize. Don't go back in that place where you're like, "Oh, I never did this well. I'm still not going to do it well. I'm going to look like a dork in front of my kid." Actually, we're going to try to give you some things to do, in the here and now, that you can math together. And as your kid goes, "Whoa, you didn't know that?" You could say, "Isn't math cool?" Instead of responding with, "No, I didn't know that you, brat." Or, "Ah, I should have known that.' You know like, in some sort of. You're just like, "Yeah, isn't it cool that we are all learning together that math is so deep and interconnected, that we can keep thinking and playing with relationships. Isn't that cool?" That could be a way to kind of respond to that? Yeah.
Yeah. Because the big idea, right, is that our kids may not have that perspective. And they don't have to.
We can help them have a different path. And so, to do that, we would like to recommend that you avoid phrases like, "I can't do math," or "I was never good at math," or, you know, "Your other parent. And I struggled in math." And we want to embrace the idea that all people can math.
Absolutely. Yeah, I've been in parent-teacher conferences where parents will say in front of their kid, "We just don't do math in our family." You know, "We're not math people. We don't do math. I've never been good at math. My significant other or the parent has never been good at math." And let's avoid those. You could say things like, "Math was hard for me as a kid, but it's really interesting now." That would be okay. Maybe even, I tweaked that with like, "Fake math was hard for me. Real math is cool. I can't tell you the number of people that I talked to kids, and adults, and everybody in between that when I say, "Oh, yeah," they'll say, "Yeah, I wasn't good at math." And I'll say, "You know what, I bet you weren't good at fake math. I bet you actually could do Real Math." They just kind of light up. So, there's this idea, like it might be okay. I don't know, Kim. I guess, maybe I should ask you. Do you think it's okay to tell a kid, "Yeah, I wasn't really good at fake math. But Real Math is cool. Yeah.
Who cares about being good at something fake?
So, parents, we would invite you to come along the journey that we're kind of working on with teachers, and other parents, and ourselves to build our own numeracy. And you can engage in that in a lot of ways. But building your own numeracy alongside your students, shows them that you're open to thinking, and that it frankly it can be a lot of fun together.
Absolutely. And when we say "numeracy", we kind of use that as a global term to mean the way you think and reason about numbers. And then, beyond. You could think and reason about geometry, and the way you think and reason about algebra, and higher math. But this idea of, let's build some together. Let's build the way you think. So, when Nickena said, "Hey, I'm super glad to get some thought provoking games." I love that you can get some good thought. And we're going to do some things here, some thought provoking games. When we say "build your own numeracy", we're suggesting dive into the game yourself. So, it's not about "Oh, we're in the car. Hey, kid, go play this game." Or, you know like, "I'm the master, and I'm going to tell you the things, and you learn from this." That it really is, you know, much more game like. I think what Nickena means is, we're gonna play together. Like, these are games that we're diving in. And I'm going to be thinking. You're going to be thinking. We're going to share our thinking. That's going to work better than, "Boy, do I have a task for you now." Nah, It's like make it game-like and thinking. And, Kim, will you share with everybody. I think one of the coolest things I ever heard you say was the one day that you... I think you were in the car. I don't even know. You were going somewhere, and one of your kids asked to play a specific game that you didn't even know you guys had been playing.
Oh, yeah. Yeah, when I had my... My kids were a little bit younger, and they were both in the backseat. One of them said, "Hey, Mom." We're driving a while, and he said, "Can we play the Wonder game?" And I was like, "Wait in good gravy is the Wonder game?" I have no idea. And I said, "What are you talking about?" And he said, "You know, where we ask a couple of questions, and then we choose which one we want to think about." And it came from the fact that I would just talk out loud, and I would say things like, "Oh, we're at exit 275. I wonder how many mile markers it is till we get to number 300?" Or, "Oh, hey, the speed limit is..." whatever. And I would just wonder a lot about questions, and they would chime in with me. And then, we would choose one to continue the conversation about.
"We've been driving for 15 minutes, and it usually takes us blank to get to dad's work." If that's where you're heading, maybe.
"I wonder how long it's going to take us to get there today. I wonder how much longer?" Like, you just started. In fact, I'm going to push you a little bit. Can you remember any other things that you might wonder while you're?
How far away things were off the side of the road? How long it would take us to get to those? Yeah.
Did you ever ask, "It's this time now. I wonder what time we left home?"
Oh, for sure. Yeah. Yeah, anything about kind of our speed or the distance we had to go. Sometimes something like on the side of a truck would give us something to wonder about. It would have a price or it would have, you know. We would wonder about the phone numbers and the digits. You know, we just were really open to talking about anything that sparked us, and it became a game really.
One of the reasons why I pushed you to kind of say a few more was the very first time I heard you talk about this, I was like, "What would you wonder about?" Because I didn't. I did not see. And there were two things happening. Part, is I've never like kind of thought about it at all, so it was a new idea to me. But also, this was early when you and I had just met, and I didn't... When it very first came up that you would ask your kids questions like this, I was like... In fact, I think we were talking about it at the grocery store. You know like, "You know, Pam. When you walk in, and you see the price. Don't you save yourself, 'I wonder how much that would...' 'How many pounds that could get for blank?' Or, ooh if I look at the oranges in the case and was like, 'I wonder how many oranges are in there.'" And you're like, "You know, how you wonder. As you're running down the road, and you look at the... Help me. That addresses. House number. The house number, and you say to yourself, "Is that prime? Is that a palindrome? Is that divisible by..." And you said, "You know, Pam, when you think like things like that." And I was like, "No. I don't ever think about things like that." So, early, early in the game. Game between you and me. Early, when we met. I had not built my own numeracy. And so, I didn't have relationships to play with. It wasn't fun for me to play with the house number because I didn't even know what questions to ask because I didn't own enough relationships to do anything. But as soon as you started saying some of the questions, and I started doing some of the routines and the games that we're about to talk about, then my brain had some relationships to hang on to, to begin to ask more questions. But if I can say one more thing about that. Even on my journey to build my numeracy, to build my math, the more questions I would ask, the more I would get ideas from whomever I was talking to. So, if it was my kids, if it was whoever else that I'm wondering about, then they would be like, "Oh, well, I'm wondering this, and wondering that, and wondering..." and then they would pop in things that. So, it's not all on you, parents. It doesn't have to be that you come up with all the magic. You can just start the conversation.
And kids are amazing wonderers. And just because you wonder it, doesn't mean that you have to know the answer or chase it down. Sometimes, just raising the things that people wonder about is rich in itself.
Oh, that's a good point. Yeah, yes. Yes. In fact, I'm super glad you said that because when I very first heard you talk about it, I thought I had to chase them all down. And I was like, "I don't know how to chase that down. Nor do I know if I want to chase that one down." Yeah, so that kind of freed me up to just wander and not have to worry about it. Okay. Kim, what are some things that parents can actively do...and teachers, but we're focusing on parents today...can actively do with their kids to build some of those relationships, so that then we can play with them?
Yeah. So, it might sound pretty simple, and it is as a routine, but you can double numbers with your students. So, you might say, "Okay, we're going to start with the number 5. What's double 5?" And they say 10. And then you say, "Okay, what's double that?" They say 20. And then you say, "What's double that?" So, getting kids to start thinking about doubling numbers, which then leads to work that they'll do with multiplication? So, literally just doubling. And then you say, "Okay, so what's... " You did 5s or some number. And then you say, "What's double 3?" 3 and 3 is 6. Double 6. Then, you can double some, you know, kind of maybe (unclear) numbers. Yeah, funkier numbers. And you say, "What's double 13.5? What's double 27?" And you can have rich conversations about which numbers were easier to double? How did you double it?
Nice. And one place I'll take that. Let's say that you had doubled 75, then you could say, "What's double 75?" Pause, pause, pause. "Is 150." You could say, "Well, what's double 750? Is that 1,500?" Does that have anything to do with that 75 and 150? 750 and 1,500? How about double 7.5? So, you can kind of have some place value relationships back and forth with that doubling. So, yeah, doubling. And why double? Mathematicians play with doubles. They recognize doubles, and they use doubles in their work. Once I knew that... Which I didn't know that for quite a while. But once I knew that, then I was like, "Oh, let's play with doubles. Let's do some more doubling." And then, doubling can be kind of cool. And then, Kim, once we've doubled with students enough that they kind of have some feel for doubles. So, you don't have to like double all the things to wait until you do this next thing, but you know double a bit, so kids kind of start playing with doubles. Then, you can begin to find halves. You can halve with students. "halve" is a funny word in the English language. Like half. Like find a half but you halve. "V" in there. Anyway.
(unclear) that silly word. So, then you can start with, I don't know, half 14. And, you know if they had been doubling with integers, they might have some sort of half a 14 is 7. And then you might say, "Okay, well, what's half of 16?" And they might say, "Well, half of 16. Okay, that's 8. We know those, mom. Those are easy." Well, then you might say, "Well, what's half 15?" So, if I've halved 14 to 7 and halved 16 to 8. Half 15? Is there some relationship there?" I'm almost doing a Problem String as I'm halving numbers. Now, you don't have to. You don't have to. "Halved" to. You don't have to do that. But you could then even do... So, if you've doubled 14, 16, 15, you can even double... Excuse me, halve 14.5. What's in between 14 and 15? And I got a little crazy there. But, you know, half 30, half 35, half 72, half... Often, the the numbers 36 and 72 will come up, and people will say, "How do you know those are connected?" And I'm like, "Well, I've just been doubling. I've been doubling 36 so often that it turns into 72. So, then, when I see 72, it's like half of that's 36." So, those relationships start to ping for kids, when they've played with doubles and played with halves. Do anything you want to throw in for halves?
Well, I want to say something about both Doubling and Halving. You can absolutely do these routines as you're driving in the car or driving down the road, like we just mentioned. But it also can be something that you're doing at the dinner table. You don't have to write something down. But there might be times where just keeping track on paper of what students have said might be helpful. But in all of those situations, asking them, "How did you think about that? How did you know?" is super important. So, you know, you're going back and forth saying numbers, and they're giving you numbers back. But pausing every once in a while and saying like, "How did you do that one? What were you thinking about? What pieces did you use?"
And sharing how you were thinking about?
Yeah, for sure.
Yeah, absolutely. And yeah, cool. Alright, let's do another one.
What about, in general, looking for relationships? Like, the idea of 2, 4, 8 we mentioned with doubling. Tell us a little bit about thinking about 9s.
Yeah. So, we want kids thinking about doubling. So, when they think about times 8, they're like, "Well, I could double, double, double, double to get up to that." But if I'm thinking about 9s like Kim just said, is that related to 10s? So, in a couple of ways, could I think about if I'm going to add 9, could I add 10 and backup 1? Nine is so close to 10, is there some? And often people kind of have this kind of sense that, "Yeah, 9 is like this 1 less than thing." But they really haven't ever talked about it. So, the more you can kind of talk about that thing that's kind of happening in your head with 9s for addition. But you could also... If I'm supposed to subtract 9, could you subtract 10? And then, you better give 1 back because you subtracted too much. Or, if you're going to multiply by 9, could you multiply by 10? And say, "Well, if I need 9, grab a random number, 14s, could I think about ten 14s? Ten 14s is 140, but I only be nine 14s. Oh, better get rid of a extra 14." And now, you got to think about 140 minus 14. Hey, I can think about that minus 10 that we just talked about. So, looking for relationships, like double, double, double, that gets you 8. 10s to get to 9. One other favorite relationship that we really like, is to get to 5, think about the relationship between 10 and 5. So, if I'm thinking about 5, how does that compare to 10? So, for example, that 14 we just had. If I want to find 5 times 14, I can think about ten 14s. Ten 14s is 140. So, five 14s is going to have to be half of that. Half 140? Bam! Hey, look how we're halving. Hey, Kim, halving just showed up. So, if I can think about half of 140, then I'm at 70. And indeed is 5 times 14, 70? And you can check that out if you want to. So, some relationships that are super handy and can be very useful as students are thinking are doubles 2, 4, 8, and how 9 is related to 10, and how 5 is related to 10.
Another really important relationship is the idea of 10 more or less than a given number, or 100 more or less, or 1,000 more or less. So, for instance, if I said, "64. What's 10 more?" Students would say 74. And if I said, "What's 10 less?" They would say 54. This has huge implications for place value development that kids need. And once kids are able to tell you 10, 100, 1,000 more or less, then you can move to 9 more or less than a particular number.
Yeah. In fact, Kim, this is one of my favorite things to do with a kid that I've just met. So, somebody's like, "Hey, do math with the kid, and I'm like, "Okay, I'll just..." Off the cuff. I'll just do some math. Which is totally fun. But I'll look at the kid, and I'll like, "I don't know you. Let me get a feel for you." So, depending on the age, especially if they're like 8 or above, I'll say something like, "Hey, do you know like 46 plus 10?" And then, depending on what happens, if the kid has some sense that 46 plus 10 is 56, then I might go, "Oh, that's cool. What's 46 plus 9?" And then, I'll go back to, "Hey, what's 83 plus 10? What's 83 plus 9? What's 147 plus 10? What's 147 plus 9?" And then, depending if that goes really well, then I might say, "What's 147 plus 100? 147 plus 100, okay, if that's 247, what's 147 plus 99?" So, this idea of knowing what any number plus 10 is, any number plus 100. Let's do any number plus 1,000. If it's going well, at that point, I might go, "Okay, 792..." Well, I might... It depends on the age of the kid. I'll do this one first. "What's 792 plus 1,000?" Usually, that gets a big grin. They're like, "792 plus 1,000? That's 1,792." I'm like, "Oh, okay. Good. Good job. Good job." So, then I might say, "What's 792 plus 999?" And then, they just break out a big old grin. Now, at this point, don't make working memory work against the kid. Feel free to write that 792 down, you know?
Like, even if you just like, type it in your phone, if that's all you've got handy, or scratch it on scratch paper, something. 792 plus 1,000. They're like, "Yeah, that's 1,792." Then plus 999. Well, that's going to be 1,791, right? So, I almost wished I just written that down. I didn't. Bu like to hang on to the 792, that's not the game. The game isn't to make sure that they can...
Hold it all in their head. Yeah.
...hold it all in your head. The game is, "What can you do with the relationships?" So, yeah. Super important that you think about any number plus 10, any number plus 100, any number plus 1,000. And then, you can play with just what's a little bit more or less than that?
Yeah. And all of these ideas that we're sharing with you is all about creating flexibility, and thinking about numbers more densely, being a little bit more creative with number. It's like you said. It's not about holding it in your head, but freeing them up to be able to describe values of numbers. Instead of just writing it down and plugging out, you know, what they've always done.
Absolutely. And all those things you just described are what makes it playful, right?
That's the game-like aspect to it. Yeah. Okay. Alright, go ahead.
Okay, so our last one that we want to share today is one of our very favorite routines called I Have, You Need. Which is perfectly appropriate for very, very young students all the way up through adults. One of our favorites.
We love I Have, You Need to get the combinations of these super important numbers, like combinations of 10. What do I mean by that? What numbers combined equal 10? So, if I have 8, Kim, you need?
To make 10, right? So, if our total is 10, then you just literally call a response. So, if our total is 100, I might say, I have 85. So, Kim, you need?
To make 100. And so, it literally is just this, "Hey guys, today, the total is 20. Alright, if I have 13, what do you need to make 20?" Go ahead, Kim.
And then like, playing with those relationships. So, it's not about having the kid rote memorize those relationships. It's about having the kid figure them out, often in a game-like kind of atmosphere, so their brain does that, and they get better and better at kind of figuring it out, and then owning those things over time. (unclear).
And sharing with you how they thought about it.
Thank you. Very important. Yes. All this is conversation. You might even have them. You might say, "Okay, today, total 100. You go." So, then, your child can say, "Ha, ha, ha. I'm going to give you a really hard one. Alright, I have..." And then, whatever they say. 67. And then you're like, "Okay, that is a hard one. Let me think. 33." And then, your student might go, "How do you know that Mom? Dad? How did you know that?" You could say "Well..." and then you could describe. Like, for example, you might say, "67. Well, I thought about I need 3 to get to 70. And then, I need 30 more to get to 100. Okay, so that's 33 I needed." Or you might think about, "I needed to get 30, to add to the 60, to get up to 90. And then, I needed to fill in the rest of the 10. Since I started with 7, I need 3 more, and so..." I probably shouldn't have used one that had 33 in it. "And then, that would be 33." So, combinations of 10, combinations of 100, combinations of 1,000. Super important. So, Kim, I'll just play one really fast with you.
What if I said I have 844. 844, what do you need to make 1,000?
How do you know? I know, you just own these so well. Can you even talk about your thinking?
Well, I'm not sure if you want me to share (unclear).
I just want to hear how you're thinking.
Okay, so I had 844, and I knew that I needed 100 more to... I kind of went from left to right. So, I needed 100 more to make the hundreds be 900.
And then, I had 40 in 844, so I needed 50 to make the tens column have 90.
And then, you said 844, so I knew I needed 6 in my new number, so that I would have 10 in the ones place. So, I wanted 900, and 90, and 10 to be what I was aiming for.
Because 900, plus 90, plus... Oh, sorry. I didn't mean to interrupt.
No, because all that 900, and 90, and 10 makes the 1,000.
And that's what you were looking for. So, yeah. That's a fine strategy. I'm glad you shared it with everybody. So, great. That's the kind of thinking that we want you to share with your students, and have them share what they're thinking about, as they get more practice in these important partners. These partners will come up in many important ways. Kim, if I could just give one example. Let's say that your student has to do something like, I don't know, 300 subtract 188. I'm going to say 288 just for (unclear) Alright, so 300 subtract 288. In this moment, your student could say, "Well, gee. 288 is really close to 300. And if it's super close to 300, how close is it?" Like, I'm just finding the difference between those numbers. And then they could say, "Well, golly, 80. If we're playing I Have, You Need, 88, what do I need to make 100? Well, I've done that a lot. I just need 12. Well, then, from 288 to 300, I just still need that 12." So, the answer to that cranky subtraction problem, if I use the algorithm, is just 12. And I just thought about it using partners of 100, kind of inside those other hundreds.
So, a place. It's only one. There's lots of places that they'll come in handy. But a really nice place they'll come in handy is when we do what they call subtraction across zeros because you could just find that difference up there. One more iteration that we really like with I Have, You Need is you can play total of 1. So, with a few older students... With a few older students? Why did I say "few"? With all older students, you could say, when you get to some higher math, you could say, "Hey, today we're going to play I Have, You Need total 1. What if I have 0.88 or 88/100? What do you need to make 1?" Now, some of you might smile and go, "Pam, that's just like the same as 88 to 100." Yeah, but kids don't know that at first.
So, 0.88 to make 1. Well, I'm going to need what? 0.12 or 12/100 to get to 1. You can also play total of 1. So, any decimal. Just throw out a decimal, and see what do. You can also play total of 1 with fractions. So, I could say I have four-fifths, what do I need to make 1? If I have four-fifths, what do you need to make 1? So, some nice variations. Integers, you can say the total today is 0. If I have negative 15, what do you need to get to 0?" That game doesn't play very long. But you can play it long enough to just kind of get 0 pairs kind of in there. Yeah. Ya'll, one of the most frequent questions we get from parents is, "Do you have this stuff written down in one place?"
And the answer is, yes. We have a Tips for Parents free download. Woohoo! It lists the things that we've been talking about and more, with links to learn more about many of them. And you can get that free download at mathisfigureoutable.com/parenttips. mathisfigureoutable.com/parenttips is the link to get our free parent download that will list everything that we talked about today and more. And don't worry, it's free. So, whether you're a parent who didn't like math, you're a parent who's just started talking to your kids about mathy things, or a parent who loves math and wants more tips to working with your student, download our free parents ship. It is a great help for you. You can find that at mathisfigureoutable.com/parenttips. No space. "parenttips". Two t's."parenttips". Alright, ya'll, thank you for tuning in. And, Kim, I'm pausing because I wasn't sure. You did the intro. Are you doing the outro?
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 Let's keep spreading the word that Math is Figure-Out-Able!