Who does not love a quick, easy routine that gives students useful problem solving relationships? In this episode Pam and Kim revisit I Have, You Need and apply it with different target numbers.
Kim and Pam play I Have, You Need often with clocks and marathons
It's not about speed
Goal is reducing cognitive load in the midst of solving other problems
Another goal is building fluency
Other important target numbers for early elementary and even middle and high school students
Get the free I Have, You Need download! bit.ly/ihynroutine
See Episode 7 and 121 for more on I Have, You Need
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Facebook: Pam Harris, author, mathematics education
Linkedin: Pam Harris Consulting LLC
Hey, fellow mathematicians! Welcome to the podcast where Math is Figure-Out-Able! I'm Pam.
And I'm Kim.
And you found a place where math is not about memorizing and mimicking...even if you're memorizing what I'm saying, Kim, right now and repeating it in your head...waiting to be told or shown what to do. But it's about making sense of problems, noticing patterns, and reasoning using mathematical relationships. Ya'll, we can mentor students to think and reason like mathematicians. Not only are algorithms really not helpful in teaching mathematics, but rotely repeating steps actually keep students from being the mathematicians they can be.
It's the last line. Every time you get to a thing where you're like, "Not only are algorithms..."
That's when you can't say?
No, I do. It's the last line. I don't know why.
Oh, that's the one you can. Alright. That's the one you've got going in your head. That's hilarious. Hey, Kim!
So, check it out. Alright, so I decided today that I wanted to talk about something that happened in my life recently. So, listeners, you could write these down. You don't have to. You can just kind of have them in your head, but I'm going to list a series of numbers, and then ask you if you know what was happening in my life when these numbers just naturally came up. Okay? Alright, here we go. 15:36, 14:24. That's the first pair. So, pair of numbers. And I'll tell you there's a colon. So, it's 15 "colon" 36. Like, 15 minutes, 36 seconds. I don't know that might be giving too much away. 15:36 and 14:24 was the first set of numbers. 25:02, and 4:58 is the second set of numbers. And then lastly, 28:47 and 1:13. So, I threw that in our Slack communication, like our business. And I was like, "Ah, this came up!" And I said, "Hey, Kim, if that was true, your set might look like this." So, here's Kim set. If that was my set, Kim's set would look like this 6.5, 6.6 is one set. 10.2 and 2.9 is the next set. 12.9 and 0.2 is the last set. Alright, so, listeners, what do you think's going on? What's happening in my life? What's happening in Kim's life?
When you put this in Slack, I remember being so confused. Can I say? Can I say (unclear)?"
Yeah, yeah, yeah. Yes.
Okay, so when you put these in Slack, I looked at your set, and I was like, "Okay, it's combinations of 30 minutes." Like, you're doing something for 30 minutes. But when you say, "Your set might look like this..." I was like, "12.11? What is... I don't..." And I think I probably replied something snarky like, "I don't know. 12.11?"
You're like, "Pam, 30 minutes. Okay, you're counting down to 30 minutes. I can see that." And maybe we'll spend just a second there because 15:36 and 14:34. If you add those that's...
Oh, did I say that wrong? 14:24.
Those add together to 30 minutes. 25:02 and 4:58 add. But you'll notice that it sort of counting like 15. And it's like, I've done something for 15 minutes, only 14 minutes left. Done something for 25 minutes, only have 4 minutes left. And then, the last set was, done something for 28 almost and a 1/2 minutes. I only have 1 and a bit minutes left. So, then, when you were like... What number did you even say? Whatever number you said, I was like.
I said 12.11.
I was like, Kim, try again."
"Try again, idiot."
I didn't say "Idiot". I didn't say "Idiot".
You didn't say that, but that's what... In my head,, I was like. When I realized what you were doing, I was like, "Oh, ding dong!" So, the funny thing is, is when I saw your numbers, like I instantly knew what it was. But for some reason, when you put my numbers in, I was like, "12.11?" And then, when you were like, "Hey, try again."
"Add again, math girl."
And I was like, "Oh, I know what it is. 13.1."
Okay, so let's just say. So, my numbers add to 30.
And your numbers add to 12.1. So, now, let's just let listeners.
Oh, good heavens. 13.1. So, let's let listeners think about that for just a second. My numbers add to 30, hers add to 13.1, which happens to be half of 26.2. There's a hint. Okay, so what I was trying to say. I was kind of curious. A, I was a little proud. I'll just say it. I was smiling that I've grown a little bit. Because that's me on my either exercise bike or elliptical. Because I've kind of gotten this 30 minute thing, where I'm like, "I'm going to go exercise for 30 minutes."
And so if I'm seeing 15:36 on the elliptical, in my head, I'm saying 14:24
So, I'm not seeing 14:24 anywhere. I'm finding part partners of 60 for the seconds, and 30 for the minutes, right? Well, 29 for the minutes.
Because I'm trying to get up to 30 minutes. I'm trying to, right? In other words, it's like, "How much do I have left?" If I'm at 25:02, and I'm trying to get to 30, well, then I get 4:58 left. And if I'm at 28:47, I'm almost done, right? I've only got 1:13 left. And it's kind of... So, listeners, if you're a longtime listener, you might have heard the episode where we were talking about combinations like this. And I had mentioned this quite a while ago. At least two years ago. When I only had 60 seconds left, that it was kind of fun for me that I was playing around with. You know like, if it said 12 seconds, then I knew I had 48 seconds left. And conversely. You know like, it would keep counting up. And I was kind of excited that I was able to play with these relationships to 60. Well, now I'm super excited because I'm not only playing with the relationships in that minute, but I'm playing with relationships up to 30. And I just love the fact that I've gained this facility of being able to like have these partners pop. Yeah. Ya'll when I'm sucking air. I mean, you know, this is after I've been given a pretty good workout. Okay, so I've kind of gone on a minute here. Because the question was, "So what are yours?" Like, 6.5, 6.6. 10.2, 2.9. 12.9 and 0.2. Why is Kim's number in the world adding up to 13.1? So, we've got listeners shouting now because Kim runs half marathons, right?
So, this is your half marathon distance. So, it's not time, now it's distance. So, here's my ignorance. Since I've never run a half marathon. Do you actually know where you are like that? Like, do you ever say, "Hey, I'm at 6.5. Man, I just have 6.6 to go."
Is that a thing?
Yes, because I run with an app, and sometimes it says numbers in my Airpods. Which is super fun because you can get it to do different things. And so, I have this weird thing where... I'm sure if there are any listeners who are also runners. I don't love to stop at like 12.64. Like, that's not going to be a thing ever. It's like on the mile, no matter what the mile is. And so, I often do this thing where like, how much more because if I'm going for a shorter run, it's like 3.64. I'm like, "Oh, I have 0.36 left to get to the next mile, so that I can (uncler)
Oh, to get to the next mile.
So, but yeah my Airpods, it will tell me like what time I'm at, how far I've gone, my pace. And so, I'm like. You know in my head, I'm just like doing all kinds of things while I'm running.
Alright, so to bring this up today, we thought we'd do an episode to recap one of our favorite routines ever that Kim made up. And we call it I Have, You Need. And I Have, You Need is a routine that you can do with your students, you can do it with yourself, you can do it with whoever you run into to help build important combinations. And so, that's a super thing that we can do. We started referring to this in Episode 7. So, if you've never heard of I Have, You Need, then you can head back to Episode 7 to hear more about it. But I Have, You Need is a routine we'll just briefly recap just here a little bit, where the teacher decides on a total. And often, it will be... Well in fact, we suggest, it's a common total, it's an important total, like 100. So, we'll say "Hey, today, the total is 100. If I have 80, you need..."
Oh, am I answering you?
Yeah. Please. If i have 80, you need?
20 to make 100. And then, I can say random numbers. Like, if I have 67, you need?
And if I have 42, you need?
And, listeners, we're not waiting very long here. We're kind of showing off a little bit how Kim owns all of her partners of 100. Now, not because she's rote memorized them, but because she's done them so often, and thought about the relationships so often, and figured those so often, that they kind of become kind of natural relationships that she can figure kind of fast. So, it's not about rote memory. It's about giving students experience figuring those relationships.
And it's not about speed. I mean, you just said "fast". It's not about speed. It's about what... Yeah, what relationships am I owning and messing with to come up with that partner?
Yeah, and maybe I'll add to that. It's not about speed. It's about cognitive load.
So, what we don't want is for students to say... If I say one of those ones. I don't even know. 58. If I said, "I have 58, what do you need?" We don't want students going, "59, 60, 61, 62, 63..."
We don't want that. We also don't want students going, "Ugh, let's see. I've never thought about this before."
"58 to..." And it becomes this very laborious, and they have to put a lot of effort into. What we want is for them to put the effort into now, so that they get more facility with it.
They become more fluent.
So, that it's something that they've thought about a lot. And so, now in a problem when they need the difference of 48 to 100, they can just say, "Well, it's 52" because they've done it a lot. Their brain is used to doing that action. Now, it's not about rote memory, again. It's about that pathway of thought, of relationships, of connections, that they have now made that pathway strong. And let me just say, that 100 is important. Because if we use 100, and we play I Have, You Need a lot with students with a total of 100, then 100 start to show up. And they almost start blinking. A kid sees a problem like, I don't know, 200 and... No, let's do this. 1,300. 1,300 minus 48. And all of a sudden, like this partner 48 can become an important tool they can use to solve that problem, right? They can think about, "Well, if I'm doing 1, 300 or 1,300 minus 48, I can think about that 100 in between 1,200 and 300. And so, then if I know the partner of 48 is 52. Well, then bam, the answer is 1,252."
I'm really glad you said that, and you're giving some examples. Because knowing the partners of 100 or, you know, whatever other suggestions that we're going to offer, isn't the goal. It's not like, I just need to know these partners. I mean, it might be a fun party trick if people are asking you questions. I don't know. Butit's not just about like, "I have to have all these down." It's knowing those relationships, so that you can use them in the midst of other problems, that they pop for you in the midst of things that you're working on.
Yeah, totally. So, we really liked that routine. And we encourage you to use it with your students. So, Kim, let me just ask you. What are some of the totals that you think are the major relationships that would be good to do?
I think for young students working with combinations of 10 and 20 are really important. And then, 100...
Hey, can you stay... Well, so sorry. Okay. 10, 20. Go ahead, Keep going.
So, we just did 100. But you're saying total 10, partners of 10, partners or 20, partners of 100, and partners of 1,000. Those are mostly the important ones. Can you take just a second and talk about partners of 20? Because you have a twist on that?
Yeah. So, when I would have started talking about partners of 20, then first I'm working on partners of 10. And so, once my students owned partners of 10, then I would say things like, "Okay, let's work on partners of 20." And so, we made the connection. I would write the combinations of 10 on the board or on a poster. And then, as I did partners of 20, we would work together with them for a while. And then, at some point, I would pull up that poster partners of 10, and off to the side, I would call out the partners of 20 in the same order that I had them on partners of 10. So, like if I would have said 7 and 3, 4 and 6, then I would have said... I'm writing that down, so I don't forget. 7 and 3, 4 and 6. Then, when we were working on partners of 20, I would have said 17, and had them call back 3. And then, I would say 14 and have them call back 6. And then, once we made a list of some of them, I'd step back and say, "Hmm, this is interesting." Like, "Does anybody notice anything?" And so, we'd have a conversation in our class about what they noticed between the 7 and 3 and the 17 and 3, so that kids could generate conversation about "Oh, the combinations of 20 are really just that same combinations of 10, plus an additional 10. So, I would mark up that poster and circle the 7 and 3, and we'd find that combination of 10 within the combination of 20.
So, it's kind of like I literally see the equation 7 plus 3 equals 10. And next to it, I'd see 17 plus 3 equals 20.
And you'd kind of, like you said, circle. In 17 plus 3, you'd circle the 7 plus 3.
Yeah, and I might do like a 40, combinations of 40, to highlight that, that same 7 and 3 is found within each of those multiples of 10.
Like 37 plus 3.
And 34 plus 6.
And you can kind of circle that 7 plus 3 in the 37 plus 3, and the 4 plus 6 in the 34 plus 6.
Yeah. I think it takes some intentional work to help kids make the connection that if you know partners of 10, then you know that that 10 is within the other multiples of 10.
Yeah, nice, nice.
And I'm pretty sure I've heard you say that you spent most of your time on combinations of 10, and then a little bit of time on combinations of 20.
Or some time on combinations of 20
And then, a mention of combinations of 40
Yeah, just a quick. It's like, "I wonder if it's in other 10s like this." Yeah.
Nice. I'll also note that when you first told me this, I was interested, that I tried to mimic you. And at some point I had... So, you said 7 plus 3 is 10. And then 17 plus 3 is 20. And I had 3 plus 17. And you're like, "No, no, no, no. Pam, just do the "teens" plus what's missing to 20." So, when you're working on combinations of 20, and you mentioned that combination of 40, do the... Say the 20. Do the "teens". You call out the "teen", and they tell you what's missing. When you do the combination of 40, you call out 30 something, and they tell you what's missing. So, you're always just trying to get that little partner of 10, within that bigger number. Is that right?
That's kind of hard to say. Yeah, kind of cool. So, it's not about things like combinations of 7, or combinations of 26, or like random, weird numbers. But there are some other numbers that teachers of older students could play with.
For example, combinations of 180 for angle measure, combinations of 90 for angle measure. I think we can get combinations of pi or two Pi for radian measure.
360 for degrees. Absolutely. So, there's been some other totals that participants or random people have told us that they thought were cool. We would just suggest that you start with the most important ones 10, 100, 1, 000, and then build towards the other ones as they kind of come up (unclear).
Yeah, for sure. It's really interesting to me because we've talked about this routine for a while now. I mean, in Episode 7, but even before that you shared this routine. And I love that you just said so many people have added to it because it's true. When I was doing my classroom, you know, I taught third, fourth, and fifth. And so, I was really focused on combinations of 100 and 1,000. But people have taken this kind of all over the world and have added different parts. And so, combinations of 1 and lots of other things. And so, we're always really excited to hear how people kind of make their own twist. And, in fact, somebody in the teacher Facebook group recently said, "You know, I kind of feel like I have to share this. I kind of feel like maybe I made this up." And I think it's really very cool that people were doing little pockets of great numeracy kind of all over. And as numeracy has become a bigger conversation, people are sharing things that they did kind of in isolation, and we're just getting better and better because everybody's sharing on how they want to add into some of these routines, and it just helps everybody grow.
Yeah, I think in that conversation, she actually asked "Who should I give credit for?" And you guys kind of went back and forth about like, "I don't even really know." (unclear).
Yeah, yeah, yeah.
We're kind of all generating it together and making it better.
And that's a great thing. And that Math is Figure-Out-Able Teacher Facebook group has been a great place to share, and get ideas, and help everybody kind of keep moving along. Yeah, very nice.
Let me tell you something else. I knew that we were going to talk about I Have, You Need, so I went back and re-listened to Episode 7 just to see like was there something that we would want to add to that we missed? And then, I got on Twitter. Which, you know like, I'm not super into Twitter, but I got on. And it's hilarious because Tamra Jones actually just, today, posted. "I just learned a really cool game from Pam and Kim called I Have, You Need. Such a quick and easy no prep way to get your students and yourself thinking about partner numbers! Check out this episode!" And she mentioned Episode 7.
I thought that was perfect timing.
Sweet. Thanks Tamra! Nice. Yeah. Glad you're liking it. Excellent. Yeah, cool. And so, Kim, we have... If you're like Tamra, and you're like the, I think it was Jennifer on Facebook, that are liking I Have, You Need and want to play with your students, we have a great download for you all about I Have, You Need with the rules, and how to do it, and some extensions, and things for you to think about. You can download a totally free I Have, You Need. It's a bit.ly link so bit.ly/... How do I even say this. bit.ly/ihynroutine. It's I Have, You Need. It's the first letters of I Have, You Need routine. So, ihynroutine. The word ihynroutine. We'll put that link. That's so weird right? So bit.ly/ihynroutine. I Have, You Need routine. I should say it correctly once. bit.ly/ihynroutine will get you to that download. And then, play I Have, You Need all over the place. And next time you're counting down something. Check it out. Here's my new numbers, Kim, are you ready?
My new numbers 39 "colon" 05 and 5 "colon" 55. So, 39:05 and 5:55.
Good for you! That's fantastic!
Bam! Which just means I'm finally getting some cardiovascular shrink going a little bit, a little longer on the old. Yeah. Cool. Alright, ya'll. Thanks 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!