Three mornings a week we meet before breakfast for an early morning run. We spend most of our time planning and reflecting on what's happening in our classrooms. This has become our favorite professional development, so we figured, why not share these moments with you? Welcome to Math Before Breakfast. This is episode 89. I'm Tracy Proffitt. I'm Ruther Kiaga. And I'm Jay Proffitt.
And before we jump into this episode, we have to let you in on a secret. So every morning before we record and we have to remember what episode number we're on, Jay tells us the number and then Ruth and I. tell him if it's prime or not so today this morning we realized that 89 is prime it is yep and ruth what did you tell us about it
It is the second to last prime number when you are studying your prime numbers to 100 because you only have 97 before you get to all 25 primes from 1 to 100. Awesome. And Jay, you were like not sure. You asked us. And my way to check was that it's not even. I checked to see if it was divisible by three by adding up the digits to get the sum. Wait, wait, do that one? Tell me how to do that. You add the digits to, and then.
If the sum is divisible by 3, then the whole number is divisible by 3. And then I just know that it's not one of the ones divisible by 7. 91 is randomly divisible by 7. Feels like it's random. It's not really random. It feels like it's random. It's not random. Yeah. So then we're going to say that. I was going to try to figure out, is there a prime test or do you just have to run it through those different oddball ones? Well, if you check.
If it's not even, then it's also not divisible by. Two, four, six, or eight. Right. Right. And then if it's dozen and five or zero. Okay. And then. So three and seven is pretty much it. Yeah. Okay. Yeah. And so then I happened to tell these friends of mine about this Twitter account that tweets prime numbers every hour. And if you want to look it up yourself, the Twitter handle is at underscore primes.
And they are the prime number that was tweeted this morning is 810,269. And we got pretty interested in the fact that the prime number before that. 800, 10,259 is only 10 away. And the one before that was only six less.
We just had this idea that they were far apart by the time they get so big, but they're not. I wonder if we're in an unusually close period right now between them. Because, you know, I was telling you that it seems it's... almost hard for me to comprehend that that big a number there's still prime numbers i know that they go on forever and ever i'm in but like the yeah the simple part of my brain has a hard time with that and i want i also think that
probably eventually get to where they're a lot further away than that but maybe not yeah the jump before that was like 14 and the jump before that was about six no 16 so Slightly, but not enough to probably count. Isn't it amazing? I just find it so cool. So another interesting fact is that there are 17,000 people following this account and only eight of them.
are ones that I follow. And I only follow people who tweet about math. So I would have expected way more than eight of my Twitter friends to... think prime numbers are as cool as i do and be following this but well this account's only been in existence for 64 000 hours how long is that september of 2013 is another way to say that Oh, right there. I see it. Did you think I just did that math? No, I knew you had found it somewhere. That's actually September 2013.
Well, maybe I was singing the song from Rhett in my head. Oh, wait, no, that's maybe when you check in a couple of weeks from now, there'll be more because people who listen to our podcast will say that sounds fun. It just kind of is a little bit comforting when I happen to pay attention to it.
twitter feed like yep prime numbers are still out there they're still going guys it hasn't ended yet yeah um yeah and they've tweeted 64.7 000 prime numbers well i'm assuming it says that's how many tweets they have Okay, so today we're going to talk for real, not about prime numbers. We're going to talk about multiplication fact fluency.
And you might be like, you talked about that before. Yes, we know. But haven't teachers like don't we come back to it every single year in every single class? So if you want to go back to hear what we've said about it before, here are some episodes you can read.
turn to um episode four is called all things multiplication and we just sort of i think we kind of talked about it from the beginning and kind of moved up sort of the little i guess this scope and sequence is that what it's called from grade to grade um episode 30 we talked about the book math fact fluency by um jennifer bay williams and crew and we um That's when we met with a group of teachers from Ruth's school and talked about what we'd learned from that book.
And then episode 40, we talked to Annalise Record, and she talked to us about math running records and from Dr. Nikki Newton. So certainly we've talked more about multiplication, but those are the ones that are really about it. You want to say anything about that, Ruth, before we? No, I think we hit it because that's kind of where we're headed today is just what.
Dr. Nikki Newton and Annalise have provided through their math running records and kind of how to implement those in your classroom. And then, well, not even how to implement them because I feel like there's so many different ways that you can.
But we both feel like it's very beneficial. And then today we're just going to brainstorm strategies of how to do that. So. I'll back up and say that a fourth grade teacher, we were having a conversation, not really even about this, and she mentioned how...
They were struggling. I think they were doing division, probably. And she was like, they're really struggling. And you know why? Because they don't know their multiplication facts. And, you know, she realized that that was the... the root problem and so I said you know I can I can help you with that I could do this running record to kind of figure out where to start with helping them learn their facts strategically. And she's like, oh, yeah, sounds great. So I asked her to not, in this case.
Because we're so close to the end of the school year, I said, let's not do every single kid. Let's do the kids that you feel like are, you know, are showing signs of needing help in this area. So she gave me a list of, I think, 11 kids. altogether out of two classes. And so I did their running records this week. And I guess I should quickly review what that looks like if people haven't listened to the first one. In a running record, in this running record that Dr. Nikki Newton has created.
It has, I think, about 12 or so math facts on a page. And they're ordered very specifically on the page. And you hand it to the kid and ask them to say. say the product going down the page and you record first off, whether they have it automatic, whether they answer it within five seconds or whether it takes them longer than five seconds to answer.
And I also tell them, and this is part of it, that if you need to work it out on paper, you can. Or if you need to use some manipulatives, and I have some base 10 blocks there, they can use just unit cubes. And or if you need to pass, you can pass. And then after we do that page of facts, then I ask them about their strategies. And I go in order in the order that kids would. Well.
I guess in order from what feels easiest to maybe hardest for them somewhat. I think it's interesting because this one, this assessment starts with zero and one as the first two facts that. they see and the first two facts or times zero and times one and the first two facts that they you ask them about but remember in the
in the Math Fact Fluency book, they said not to start with that. Do you remember why? Anybody remember why? Not to start with times zero and times one when you're teaching kids about multiplication. Oh. I don't remember how to have that conversation.
Because it's just a rule and there's no pattern? What were you going to say? Because the first one's always going to be the same. Okay. And, you know, maybe that's not something to practice right away. Yeah. I think the idea is that... like times zero and times one are kind of hard to grasp the why you know i think ruth you're kind of like head there you know it's kind of like abstract you know
So if we can get what the operation does with times 2 or times 5 or times 10, then go back and think about what does, then if we know this is what multiplication means, then what does it mean for times 0 and times 1? I think times zero and times one are confusing. Everything is zero and then times one. You didn't really do anything. Well, and it's kind of the beginning of an algorithm.
Just remember this rule. Anything times zero is zero. Yeah. Yeah, exactly. Because who really understands that? Yeah. I mean, come on. Yeah. So I assessed these little fourth grade friends. And a good, a bright point was that a lot of them, probably eight out of 11 or nine out of 11, know to double for times two.
So we've talked a lot about, Ruth and I have talked a lot about this, and then teachers at school, how oftentimes they get stuck in, if I'm going to multiply by two, I'm going to count by twos. Right. Two, four, six, eight, until I get to the right stopping point. Yesterday I was helping a student after school and she was finding the greatest common factor of 26 and 104. And so.
I was like, well, they're both even. You can divide them by two. And she's real quiet. I'm helping some other kids. And I look over and she's got 13 on her paper. Like, good. So now you have to divide 104 by two. And she's like, I don't want to count by twos to 104. Like, I don't want you to count by twos to 104 either. So at that point, we...
We're able to just talk strategy. Like, how about just half of 100 and then half of four and put those together? Yeah. And she's like, does that always work? Yeah, you don't have to count by twos. Every time you divide a number. So she could quickly tell you half of 100, right? Mm-hmm. And then half of 4. Okay. But half of 104. And maybe... Because I said what's half of 100 and said what's 100 divided by 2, she made that connection. That's good, yeah. Brilliant.
Ruth, I feel like you've had this conversation with every single kid in your sixth grade. Because you say that all the time. Every kid, every year. But it's not necessarily something that I... that I teach because I, so I just feel like there are some math strategies that should be reserved for you and me by ourselves or in a small group.
So I can make sure that you understand why. Because I'm not trying to just give you something else to remember and you to figure out when you should use it and when you shouldn't. Yeah, because then you're going to misapply it for sure. Yeah. Or, well, Missy told me to do this, and so I have to do it in her class, and then you forget it. You know, I want you to understand that it works all the time. Yeah. It's not always the most efficient way, right? Right. Yeah. Yeah.
Um, another thing that I noticed today, this, this week, as I've been doing these is that certain kids, I love this. Certain kids have certain facts that are like. ingrained in them and they use them to derive so many other things. So one kid loved six times four. And he knew if he knew what four times six, six times four is, he knew it. And then he used that to figure out all these other facts. Another for another kid, it was six times six. He used that for all kinds of things.
For another kid, unfortunately, it was five times two. So every times two fact, he was working from five times two. I'm like, well, at least you have the ability to derive, but let's get a better one. At least we're not starting from the beginning. Yeah. But I'd never seen that in such a repeated way. I don't know that I quite understand what you mean by that.
Okay, so if I asked you six, I'll give an example. If I asked you what's six times seven, this kid who was in love with six times six said, oh, I know six times six is 36, so I'm going to add on six because I need one more group of six. So there we go, 36. 37, 38, 39, 40, 41, 42. I would have my brain went right to 42. And because it is a seven, I always second guess myself and say, oh, crap, I did that wrong. And then check it real quick in my head.
What do you check it with? I don't really know. No. Seven times seven I know is 49. Yeah. So maybe I back down from that one. Okay. But anything times seven, I'm like, oh, man. Well, not anything. Like two times seven. I got that, guys. but you know six times seven nine times seven eight times seven five times seven i don't think i it's it's those right there that but for some time for some reason i know seven times seven and you know what almost i probably
If you told me seven times seven, I would go to 49 and then second guess myself. You know, like when you say a word so many times in a row. that it like doesn't have any meaning like it just sounds it's like the same thing with my sevens like i know what they are but as soon as it comes out i'm like oh maybe i'm not maybe i'm not right and i have to i have to like double check myself and i don't know why it is and it's nothing
Something dramatic happened at school the day your teacher taught you sevens. It could be. I don't remember that. In your subconscious. It's just that. Yeah, it's something with those mid. Mid sevens. I don't know how to say it, but I always second guess this. I love how when we interviewed Teresa Wills, she said she doesn't really have them all memorized. She just still derives them and just derives them quickly. So, you know, that's what Trace told me.
Yeah. My son, he's a forensic science major and has always been really, really fast in math, which I just assumed it was because he knew his facts and he's like. No way, Mom. I don't know. I just know some of them and I just figure it out. You're the one who taught me how to do that. So it's like if you ask me – I forget what his example was. It was something like if you ask me 11 times 12. Oh, if you ask me 11 times 12, then I always just use the distributive property.
And do 11 times 10 and 11 times 2 and put them together. And I can do that faster than someone can remember 132. Cool. But without even knowing that that's like a... a strategy for multiplication per se, like kids deriving facts. He's just like, yeah, that's what I've done my whole life. I don't know that I would ever expect anybody to have Outside of the Tens memorized. Yeah, it used to be a thing. I don't know.
Yeah. So someone tweeted. I forget. I don't know. It was on Facebook and he had taken his daughter to like IHOP because she had passed her 12th times table test. I was like, that is an intense teacher if you are still given 12 times tables. I never got. It used to be you have to be out of 12. I remember as a kid, yes. I remember I still.
and stumped on 11 times 11 and 11 times 12. I know 12 times 12, but those two. I know the 11s. Well, no, no, I don't. I don't know them memorized. You're right. I don't. 11 times, yeah. Okay. I'm just quick with my strategy. Like Trace and like Teresa Wills. You must be fluent. Good job. Not a bad crew to be a member of. Yeah, that's good. Okay. So, oh, and I just, I have to share one other thing. There was a student who was struggling, who had not a lot of, you know, a lot of these guys had.
good fairly decent ways to derive them and but they just were maybe slow on at it and maybe didn't explain their ways to derive especially great but they still have them um but there was one friend who did not and However, he had the most interesting counting with his finger strategies. Have I told you about this, Ruth? Okay. So this is going to be tough to describe on.
not camera. So I'm going to try though. So when he counted, okay, let me ask you if you had to add on nine and you, I made you do it with your fingers, like, like do, um, seven plus nine and add on the nine with your fingers. Everybody do that for a second. I would start with my pointer finger and add that five with my thumb would be my fifth one.
And then I would use my pointer on this hand. Okay, so you're doing four, two hands, two different hands. Okay, what are you doing, Jay Prophet, to add on nine? I just pick my hands up and... counted up from nine until i got well where'd you start my thumb over here my left hand yeah i just held my hands up in front of me okay like i'm looking at my hands did i wash my hands
And then I went one, two, or seven, eight, nine, 10, 11, 12, 13, 14, 15, 16. And you did it. And what you left off was the thumb of your second hand. Correct. Okay. So. That's interesting, Ruth, that you start with your pointer finger because this is where my like, what is going on? I want to see how she started with the pointer finger because your pointer finger is never at the end of your hand. So that's just the one I put up.
If my hands are in front of me, I just would say, put 7 in my head, 8, 9, 10, 11, 12, and then pull my thumb out. Just like you would count when you were, I'm 1 years old, 2 years old, 3 years old, 4 years old. And then when you're five, you put your thumb. Okay. I see what you mean now. Okay. So.
I'm just going to step back and say, I think this part is fascinating because people do it so differently. We, we are inventing, we invented our own strategies to count on our fingers. No one taught you. Like you start, you know, hold your hands out and start over here and work, you know, left to right. No one taught you start with your pinky. You start with your pointer finger. You know, I think somebody did teach me to start left to right. Maybe not with my fingers, but that's.
That's a natural thing for me is to look at 10 and start from the left. Okay. But kids invent these ways to keep track of things with their fingers. no one teaches them so he he was had his hand his palm face down on the table tapping to count okay and so his nine well his left hand was keeping track of how many nines he had So he'd put up one every time he did another nine. You following me with that hint? So like he would go nine, 18 and put up one finger for the nine.
a second figure for the 18. So he could keep track of how many nines he was counting. So is he skip counting? No, he's counting on. Okay. So anyway, then his keeping track of not hope this isn't too confusing for people listening. His keeping track of nine, on the other hand, like counting by nine, started with his pointer finger and then middle finger and then ring finger and then pinky and then back to his thumb and then all the way to back to his pinky.
So he kind of did his right hand twice to make nine, but left out his thumb the first time around. Ruth, did you get that? I do get that. You can kind of see my hand, so that helps. I can't see your hand, but I do get it now. So that was, you know, I would have started at my thumb and gone all five of my fingers and then gone back.
And did four of my fingers and left my pinky off at the end. But he was leaving his thumb off first. I guess I don't understand why he had to use one hand to keep track of his nines and count up and add on by nine.
Because he got to, he could probably say 9, 18, and past that, he couldn't, he didn't know how many nines he had. So he really was trying to... multiply or skip count by nine but he wasn't skip count that was how he was getting there yeah okay he was doing a different problem than us that's why okay Yes, there you go. So then, but then when he counted by sevens, when he was adding on seven, he still, same thing, started palm down, tapping on the table, starting with his pointer finger.
going to his pinky. So one, two, three, four, back to his thumb, five, six, seven, stopped at his middle finger. So his seven, like the shape of it, you know, he wasn't having to think through that. His shape of his seven is naturally one, two, three, four, start over five, six, seven.
where if I was trying to keep track of sevens, I would definitely start at my thumb and do five full fingers and then two more. See, I would start with my pinky if my hand was down like that. I would start at the top. Really? Yeah, I'll do three, four. How would you count on seven, Ruth? Like on seven for me. Maybe I would skip my pinky. I don't know. I also spent a lot of years playing piano.
And I wonder if it has something to do with how that feels in my – like if you were playing down a scale, you would start up here. I don't – I'm not trying to tie that to piano. I'm thinking I would do the same thing. As one, two, three, four, put up my thumb for five and then six, seven. Well, then that's exactly what he's doing, too. Just turn the other way. Right. Right. Yeah. Well, he's starting with that finger and. If he was the kid whose mom was like, how old are you? I'm one. Well.
That's the first finger that you hold up. Right. Nobody says they're one. You know, one, two, three. I wouldn't start on my pinky. But if I get my hands down trying to keep a pattern like that, I would start on the other end of my hand. Okay. Point taken. We all do something different and I love it. I just think it's, it's so cool. Okay. You didn't know you were going to get a big old lesson on counting in this episode. So now.
I met with this teacher. I shared the data with her. I shared it with her in like a spreadsheet. For each kid, for where they fell, the assessment kind of gives them a number, zero through four.
on each fact and then I also gave her like a narrative of some of the interesting things that I saw some of what I just told you and now we're like okay now what do we do so this teacher is teaching hybrid which means she has the kids for only two days a week in class and then they're home three days and with how little time she has with them in person we were
I suggested, you know, maybe this remediation needs to happen mostly at home because it would be ideal to do it in person, but she's got a whole lot left to do. So I said, what if we could create something that would help them learn how to double or learn how to, you know, for fours, double and double again. Maybe we could work them through that at home. That's where we are now, trying to develop that idea. So of what could we...
I mean, I'm picturing kind of like a Google site that we put together and it's like you need to get fluid at your force. Here are all the things that you walk through to do that. And now, okay, you're done with that. Now you move to eights and here's all the things that you walk through. And I think it's important that we, like you discuss why they're not just going consecutively. Like why are we going to skip becoming fluid in your sixes and sevens?
And go right to your aids. Yeah. Do you want me to talk about that now? I think so. Jay, were you saying something? Nope. Okay. So this particular assessment. So we just have to note that I feel like there's a, there are some differences between the math fact fluency book and Dr. Nikki's like order potentially. Okay. So that has them working. zeros and ones and then um tens and then fives because i think tens are easiest
You know, that's really easy to learn the pattern and they probably may already come with knowing it. Fives are easy because of skip counting. And then the first one is the first one that I feel like. we've been needing to remediate are the twos. And so that strategy we want them to get is double instead of counting by twos. OK, so then the strategy after that, why not go to threes, basically, is what we're saying, is because the fours, one of the best strategies for fours is to.
double the other factor and then double it again so it's building directly off of the two's strategy and then the eight's strategy is to double whatever the force was or you could call it double double double because you're taking the other factor and doubling it three times. Which is two to the third power in exponent land. Yeah. And when kids realize that there's a relationship between double, double, double.
And two to the third power. It helps solidify how an exponent is different than just a repeated addition problem. Yeah. So then it goes. So it goes two fours, eights, then it goes to threes, and the strategy that they are encouraging kids to use for threes is times two, like double, and then add a group. So if I have to do seven times three, I would do seven times two on one more group. So 14 plus a seven. And then sixes is next. And you double the.
the three amount so you think about what it was for three and then double which all of this is using having and doubling is another way to talk about it um and then i all of a sudden i'm blanking about what's next six is It's probably nines. And the nines being, I mean, let's be honest, a lot of these kids use the finger trick. Over half of them yesterday used that, like put a finger down and see what you've got.
But one kid definitely used the times 10 take away a group, which was really exciting. You know that one? I do. Okay. And then I think from there are sevens. Is that all I've left off? And that could, you know, you could use times five plus two groups. You could really just memorize the.
you know, use the other number every single time for seven said memorize seven times seven. And then the last column are the square ones. And I think the idea is that she really wants you to just have those memorized. I'll just get those automatic and then you could use them to derive other facts. And there was one kid who those were the ones he had memorized.
How weird. He's like, my dad made me memorize them all. And he said them all up. He missed seven times seven. But every single other one he had memorized. His sevens? No, his square facts. Oh, square facts. Yeah. Did I answer your question, Ruth? Yeah. Okay. That's good. So let's brainstorm. Let's start with fours because most kids are starting there. I have a couple, maybe two or three kids starting at the twos, but let's start with what would.
Something online that they could work through at home pretty much independently look like for times fours. What are some components? We kind of talked about the math flips where. You see the number double and then you see the number double again. Even if the first one. Yeah, I just think that isn't that Berkeley Everett? He does. math flips yep he just does a really good job of animating the cards enough and
the kids can see the pattern. And then once you see the pattern, you can attach those numbers to it. Jay, are you picturing it or you need me to explain it? I am picturing, I have a few of Berkeley's. animations in my head but i don't think the ones i'm thinking about are this so but i also understand what doubling and doubling again means a good example that i picture
In case there's someone, I was sort of hoping you'd say no, I don't know what you're saying. No, can you explain this to me, please? Thank you. Yes, I'd love to. Give us some exposition. Okay. So picture what you see as a five on a die. Okay. Okay. And if that was a arrangement of five dots.
beside another arrangement of five dots and there's like a circle around them to show you i have two groups of five okay gotcha so on each group is right on the first side you're like oh that's two groups of five it's ten And then... Wait, wait. Say that again? That's two groups of five. That makes ten.
Because I've seen them in two circles. Right. So you just look at it and kind of like say what you see. For those people at home, she had the die in two different hands. And then all of a sudden they both jumped to one hand. And it confused me. Okay. And then you flip. If you're doing this on paper, you have it in a little like note card and you flip it to the back. If you're doing it on the Google slide, it would just be the next slide. And then so on the.
opposite side you'd see that image just repeated right down below it so now you have four groups of five showing and you say oh that doubled is 10 instead of having to add like 5, 10, 15, 20, you can think 10 plus 10. Okay. Yeah. That's not times 4, that's only times 2. No, it's 4 times 5. Well... But you started with two times five. You didn't start with five. We're going to use two times five to help you solve four times five. Okay. Does that make sense?
Yeah, I guess in my head, I was thinking you were going to double the five and then double the ten. That would be times eight or something. Tracy, no. No. Double the five and double the ten. Because if I'm trying to learn my fours, and I've got five, and I'm trying to learn four times five, I'm going to double that five to get 10, and then I'm going to double again to get 20. I'm not going to start with 10 if I'm trying to multiply four times five.
But I did not at the time understand that you were starting from two times five. Okay. I was trying to get to two times five, I guess. Yeah. In my process. Got it. I understand now. I almost had a fight right then. You were trying to tell me that 20 was five times eight. I don't know what we were talking about. And I was going to be right. We got real lost. Okay, Ruth, save us. Jump in here. I think that you teach that strategy, but then you give students, I don't know, some kind of...
I'm going to use task cards, even though those aren't my favorite thing, to think about different ways to ask the multiplication problem, like almost like algebra. Three times something equals 12, but something times four equals 40. And they're like a click and drag and matching. the missing number in the multiplication problem or arrays of 16 where they're writing the multiplication problem and circling.
The group of eight and the group of 16, like to get, I don't know, just different ways to ask multiplication questions. So once you feel like you have the strategy, because let's be honest. practicing them gets you more efficient as well as knowing the strategy. You can't just have someone tell you the strategy and not practice it. So how could you make...
little individual slides or something where each slide is a different kind of question. I don't know if I'm saying that right. Like what if you had... eight or you had four numbers. You had an eight and a 32 and a 24 and they had to write the multiplication problem that goes with it. That is... There's a game just like I think just like that on Greg Tang's site where it's like a grid of four numbers and you pick the basically you're picking the three that are a fact family, which is.
what you're saying or okay that make a fact yeah that could be good so if you had 8 3 24 and 32 oh yeah that's a good one you would leave out the 32 yeah i like that So, yeah, all different ways to. And then that's kind of working on division some, you know, kind of relating it to division a little bit. But I think about the one that Jay just said.
What about the kid who says, well, 24 plus 8 equals 32. So that's my fact family. And I left out the three. But we have to say this. You've got to make a multiplication. Or you say, well, look. Or it's like 24 and you can do it either way you want. Yeah, you can use that eight times three plus one. I don't know. That's cool. Just different ways, again, for kids to be able to show their thinking. I like that.
Another resource that I think we could throw in there is from the Math Fact Fluency book, the purple one. They've made a... a website that we've talked about before some Kentucky teachers have made a website where they've taken a lot not all of them but a lot of the games that are in their book and made digital versions of them so I feel like we could tap into that and link to those
um, on the site. I mean, I mean, that's kind of the point is that we typically as teachers introduce, this is what multiplication is. And then we may jump straight to memorize it, or we may say, This is what multiplication is. Here's a strategy. Now memorize it, you know. And we don't give them, we don't park in the practice and derive stage, which is what they need a lot more of to get to that.
automaticity what and i'm glad i don't have to teach somebody the concept of multiplication from scratch yeah i love it i think we kind of talked about a video too, but if you Google learning your fours, there are lots of videos out there of teachers teaching the double-double strategy.
Okay. Double, double. Sounds like a value meal at McDonald's. I'll have the double, double meal. Yeah. We talked, Ruth, yesterday when you and I were talking about it, I was like, okay, first we have to have a video. And you're like, wait, they should. They should have to name it first. You know, the kids should have to say it. So we talked about how we might have go to Berkeley Everett's site and see what he already has that demonstrates that.
that without any words and explanation and then get them to get the kid to say it and then get you know they're probably if they're going to be working at home unfortunately there's going to have to be some amount of like hey This is the strategy. We want you to actually use it. Any other ideas of what could go in there? Not...
I mean, I feel like there's also benefit of like if you're going to do Google Slides, then maybe a student illustrates a story about it. You know, you give them the guidelines of. Here's a frog. Here's a pond. What kind of a story can you illustrate and tell that uses one of your strategies or one of your facts? They're copying and pasting the frogs or they're making the frog jump this many times. You made me think of two different things. Thank you.
One was that when we did this in class last year with fifth grade class, we used the Freyer model, which is where you split a piece of paper into four. quarters. And then in the middle, you would write in the intersection of those divisions, you'd write the fact and then you would require them to sort of show it four different ways. So the first one could just could be a model. Like this first box could be make a model. The second box could be write the story. The third box could be.
make another model I don't know and then the last box could be the answer but yeah that multiple representations idea and you could do that on google slides and then another thought I had was go so we've recently been um our school purchased and um braining camp license and so they could have to go and show three times four um
four different ways you know use four different manipulatives or something and snip them and put them in there like the number line one you know they could do groups of but do two different kinds of groups or two different like do Three groups of four or four groups of three. What else? Number nine. Arrays. That'd be cool. That'd be really cool. Yeah. Arrays. Girl, the relationship between arrays and area is a struggle. Yeah. Maybe that's like what teachers have left off their curriculum.
Are you working on that right now? But this particular group of students, we had to make lots of connections because they just didn't have it. Yeah. All right. Jay Profit, you got any other ideas? You're like, uh, no. No, no, no, no. Okay. Ruth, you have any more? Not for fours. Okay. Do we want to keep going? I mean, I was sort of picturing like once we get those things down, then we would kind of just have all the same kinds of things. Yeah, kind of just repeat them. Yeah. I'm wondering.
How long would we give them to learn like to work on a set of facts and what kind of accountability? What would the accountability look like? Any thoughts about that? I mean, ideally, your accountability would be another running record and you would see improvement, but I don't know that that's...
Right. I was thinking about I could go back in like a month. You know, I can't do it every week, but I feel like I could go back in a month. And I was also thinking about not needing to redo the whole thing. If I saw that they were fluent all the way up to twos, I should just probably start at four or maybe start at two, the first one that they've worked at.
I don't know. I was wondering if they could do it within a week, but maybe that's too fast. Like, how much time would we want them to tackle the force? Well, and how much do they get on the computer? I mean... Maybe they get on more because they're actually hybrid and they're doing their learning there. But I would struggle with kids being efficient and doing what they're supposed to do. Right.
potentially three days of the week. So if they go to school Tuesday and Wednesday, then Thursday, Friday, and Monday, but we know our own kids don't. necessarily make it look like that jay prophet says with his eyes um rolling in the back of his head it's bad it's real bad um okay we will um Ruth and I also talked about how we want to be careful that everything that we put on this site is something that's already shared publicly.
You know, so that we can hopefully share this out as a resource that other people can use. So, you know, it would be like links to things or things that we've made or things that are shared. like Berkeley Everett or something like that. We will be careful to not put something on there that we, you know, somebody paid for is copied out of a book, that kind of thing. Okay. Ruth, did you want to end with your reflection about?
teachers and what you've been thinking about lately so to be well to be transparent but still very professional yeah I feel like I take my Twitter family for granted because you can, I can be in my classroom and I can want to teach something that I've taught. 25 years already, but looking for a new idea. And I can go to Twitter and search MITBOSS and boom, there's something new because it feels like everybody's in the trenches with me.
Teaching the why and providing productive struggle and doing hard work. Yeah. And then I step out of Twitter into. you know, an environment where there are other teachers, and I'm constantly dumbfounded with teachers who just are completely content saying, I do it, we do it, now you do it. Yeah. What's the next step? What's the next step? What's the next step? And so I have an opportunity to influence some pre-service teachers.
They are not easily influenced. Yeah. Yeah. It's been a harder sell than you were thinking it would be. Right. Just kind of that. Like, this is really good. This is what you want to do. And they are, yeah, they are wanting to teach the way they were taught. And when you are a high school wannabe teacher, well, you were just taught that a couple years ago. So it's still fresh in your mind. And obviously that teacher did a really good job because now you want to be.
that kind of a teacher yeah right but we've had many conversations like listen you were in that college calculus class when you were a junior in high school so the students in your class really wanted to be there if they were excelling at that level in high school. And your teacher could say, I'm going to do it, you do it, it's done.
When you're signing up to teach Algebra 1, you don't have a classroom full of kids that want to be there. Yeah. So you got to step out and, you know, engage them. Right. And part of... Part of what's making it difficult for you, I feel like, is because it's all kinds of secondary teachers in the context where you're teaching. And if it was math...
If it was like all only elementary math methods, I feel like you could model what you want them to do over and over and over. Every single day you could come in and let's do a math test together. Let's go. Oh, my gosh. You know, have that moment together. Mind blown. But you're just sort of having to, like, take my word for it. You know, this could happen. Take my word for it. This could happen. And they're not being able to see it. Yeah. It's stretching me because I'm.
Trying to convince you as a high school art teacher that there can be more to your lesson than just... I do, you do, we do. Okay, well, how do I do that? Well, you know what? I'm going to have to find someone. Yeah, I don't know. Let's see. Who does it?
Another takeaway that I've heard from what you, I guess we're doing takeaways now. Hold on, can I respond to that first? Or are you going to talk about that too? I had something to say about that. Another thing that I've been hearing you say lately is how... How we as teachers talk about subjects that aren't our major, our favorite and passionate subject. And we've had a good conversation lately about.
Yeah, you can be the math teacher, but you can't be dogging on the music class or the English class. You have got to represent what it's like to be a well-rounded learner. Even if it's not what's in your gut, you know, you've got to protect what you say to each other, to the kids about other subjects. Okay. Off my soapbox. You go, Jay. That's a good one. What Ruth was talking about, you know.
She said that these students were good students. They've learned it well enough that they want to go and teach it. And working with college professors every day, I have found that... And, you know, I did not do a study on this. There's nothing coming out. No, I can't show you that the data just from my working with and what I've what I've, you know, remembered is that the.
The faculty that I worked with, the professors that say they were not good students and then they struggled are the ones that are quicker to look for different ways of teaching. The professors that were good students. love this thing from day one. And, you know, it's all they've ever wanted to do is be a professor. And I'm not saying they're inflexible, but they're the ones that are most comfortable with. This is how I was taught.
a traditional way of that's how I learned it. This is how I'm going to teach it. We're just going to, we're going to keep this line going forever and ever. Yeah. And there's a couple of people that I've worked with lately that. I have worked with them in one facet, and they are very innovative. We're going to do it this way, or we're going to bring this, or we're going to try this. And then you come later to find out.
they were bad students. Like they barely made it out of high school and somehow through experiences between then and now decided to get into academia and be a professor. And, and those are the people that are. Again, I'm not going to say this is always the case, but in my experience, those are people that are most likely to find those different ways of doing it or try something different. That's cool.
I like that. I bet that's a true correlation in most cases. So just this week I was talking to the algebra teacher in my building because I was trying to have him... teach me about something so I could take it back to one of my students. And the conversation ended with, you know, Ruth, you have always been the most out-of-the-box thinker, teacher that I have ever met.
And Jay, I would say that that is because I struggled through math. I didn't make it to calculus. Like algebra two was how far you had to go to graduate high school. And I made it to algebra two. And I always got C's. I worked hard, but I always got C's. And so when a student is sitting in my class and looking at me, like silently shaking their head or making their eyes big, like I don't get this, I totally feel them. Like I remember.
feeling like that. I still remember in second grade, the little mouse that came out of the one's place and walked over to the 10's place to get 10 pieces of cheese to come back. I just was so... So confused and frustrated. I will have to say that halfway through that sentence, I thought you were still talking about a mouse. It's like, there's a mouse that walked out of the room? No. Because I'm not a math teacher, that analogy is not readily available in my brain.
Well, I was going to bring us to takeaways. We've talked about prime numbers. We've talked about multiplication assessment and remediation. We've talked about counting strategies. We've talked about... getting convincing pre-service teachers to break the cycle so we talk about a lot of things so what's your takeaway today my takeaway is not math related okay uh earlier i talked about um
my sevens, my seven multiplication facts and always saying them and thinking I'm wrong and compared it to saying a word so often, saying a word so many times that it loses its meaning and just becomes sounds. And that process or that. that phenomenon is called semantic satiation. Whoa. And it's a, it's a real thing in which the saying a word over and over so many times makes it lose meaning. And it's just this collection of sounds and it's like, it becomes almost.
unfamiliar again. So I wonder if there's numeric satiation. I don't know. Is that the word? What is it? Semantic satiation. Oh, cool. What in the world did you Google to figure that out? Saying a word until it sounds weird. Okay, perfect. Well done with your searching skills. Well done Google for understanding that sentence. Ruth, what's your takeaway?
Well, if I have an opportunity to have takeaways with prime numbers, I absolutely have to. Do it. So I, yeah, I'm just, I count by prime numbers all the time. And I told. Tracy and Jay that I was counting out five post-it notes because we were doing this activity and every single class period every single kid had to have five post-it notes and so I said to my students does anybody know what I'm doing when I'm
giving you their notes and they're like, you're counting one, two, three, four, five. I'm like, no, I'm counting two, three, five, seven, 11. That's awesome. Not very many kids like even got that. What is that? And then someone's like, oh, that's the first five prime numbers. And my other favorite thing to do is to— Did somebody then shake their head and go, oh, my word, and walk away? Is to tell people on their birthday, like—
I'm always taking people's birthdays and making math equations and finding prime numbers. And the other day, a colleague's child turned nine. I wrote on his Facebook page or on his mom's Facebook page, I'm like, well, it's not a prime year, but it's a square year. And you won't be a perfect square for seven more years. And that number is prime. And his mom was like, we were so confused. Imagine. Imagine. That's awesome. So prime numbers rock. Yes. My takeaway is what Ruth said about thinking of.
interesting but related ways to ask multiplication questions. as part of what we create for them to do at home. Like I'm really, I'm really thinking about the choose three numbers or what's the missing number or, you know, doesn't always have to be this times this is what there can be. I should be a little more creative than that. So I'm going to be looking for other ways. I like that. That was good.
All right, we'll report back in, I don't know, it's probably going to take us a month to get this together, but we'll report back and let you know how it's going. It could be a month for the next episode comes out, who knows? You know, let's be honest. All right, Ruth. It's the weekend, so I'll see you on Monday for a run, right? All right. Sounds good. All right. Bye. Bye.