Ep 89: Revisiting Multiplication Fluency

Interactive Transcript

spk_0 3 mornings a week we meet before breakfast for an early morning run.

spk_0 We spend most of our time planning and reflecting on what's happening in our classrooms.

spk_0 This has become our favorite professional development, so we figured why not share these moments

spk_0 with you?

spk_0 Welcome to Math Before Breakfast.

spk_0 This is episode 89.

spk_0 I'm Tracy Prophet.

spk_0 I'm Ruth or Kiyaga.

spk_0 And I'm Jay Prophet.

spk_0 And before we jump into this episode, we have to let you in on a secret.

spk_0 So every morning before we record and we have to remember what episode number we're on,

spk_0 Jay tells us the number and then Ruth and I tell him if it's primary or not.

spk_0 So today this morning we realized that 89 is prune.

spk_0 It is.

spk_0 Yep.

spk_0 And Ruth, what did you tell us about it?

spk_0 It is the second to last prime number when you are studying your prime numbers 200 because

spk_0 you only have 97 before you get to all 25 primes from one to 100.

spk_0 Awesome.

spk_0 And Jay, you were like not sure.

spk_0 You asked us.

spk_0 And my way to check was that it's not even, I checked to see if it was divisible by three

spk_0 by adding up the digits to get the sum.

spk_0 Wait, wait.

spk_0 Do you have to tell me how to do that?

spk_0

spk_0 You add the digits to, and then if the sum is divisible by three, then the whole number

spk_0 is divisible by three.

spk_0 And then I just know that it's not one of the ones divisible by seven.

spk_0 91 is randomly divisible by seven.

spk_0 Feels like it's random.

spk_0 It's not really random.

spk_0 It feels like it's random.

spk_0 It's not random.

spk_0 Yeah.

spk_0 So then we're going to say that I was going to try to figure out is there like, is there

spk_0 a prime test or you just have to run it through those different odd ball ones?

spk_0 Well, if you check, if it's not even, then it's also not divisible by six right?

spk_0 Two or six right.

spk_0 Right.

spk_0 And then if it's doesn't it a five or zero?

spk_0 Okay.

spk_0 And then, so three and seven is pretty much it.

spk_0 Yeah.

spk_0 Okay.

spk_0 Yeah.

spk_0 And so then I happen to tell these friends of mine about this Twitter account that tweets

spk_0 prime numbers every hour.

spk_0 And if you want to look it up yourself, the Twitter handle is at underscore primes underscore.

spk_0 And they are the prime number that was tweeted this morning is 810,269.

spk_0 And we got pretty interested in the fact that the prime number before that 810,259 is only

spk_0 10 away.

spk_0 And the one before that was only six less.

spk_0 So we just had this idea that they were far apart by the time they get so big, but they're

spk_0 not.

spk_0 I wonder if we're in an unusually close period right now between them.

spk_0 Because you know, I was telling you that it seems it's almost hard for me to comprehend

spk_0 that that big number.

spk_0 There's still prime numbers.

spk_0 I know that they go on forever and ever.

spk_0 I'm in.

spk_0 But like the simple part of my brain has a hard time with that.

spk_0 And I want I also think that probably eventually get to where they're a lot further away than

spk_0 that.

spk_0 But maybe not.

spk_0 Yeah.

spk_0 The jump before that was like 14 and the jump before that was about six.

spk_0 No, 16.

spk_0 So slightly, but not enough to really probably count.

spk_0 Yeah.

spk_0 Isn't it amazing?

spk_0 I just find it so cool.

spk_0 So another interesting fact is that there are 17,000 people following this account.

spk_0 And only eight of them are ones that I follow and I only follow people who tweet about

spk_0 math.

spk_0 So I would have expected way more than eight of my Twitter friends to think prime numbers

spk_0 are as cool as I do and be following this.

spk_0 But well, this counts only been existence for 64,000 hours.

spk_0 How long is that September of 2013 is another way to say that.

spk_0 Oh, right there on the.

spk_0 I see it.

spk_0 I was like, I just did that man.

spk_0 No, I knew you had found it somewhere.

spk_0 That's actually September.

spk_0 I was singing the song from written my head.

spk_0 Oh, wait, no, that's maybe when you check in a couple of weeks from now, there'll be

spk_0 more because people who listen to our podcasts will say, that sounds fun.

spk_0 It just kind of is a little bit comforting when I happen to pay attention to it in my

spk_0 Twitter feed.

spk_0 Like, yep, prime numbers are still out there.

spk_0 They're still going.

spk_0 Guys, it hasn't ended yet.

spk_0 Yeah.

spk_0 Yeah, and they've tweeted 64,7,000 prime numbers.

spk_0 Well, I'm assuming it says that's how many tweets they have.

spk_0 Okay.

spk_0 So today we're going to talk for real, not about prime numbers.

spk_0 We're going to talk about multiplication, fact, fluency.

spk_0 And you might be like, you talked about that before.

spk_0 Yes, we know, but haven't teachers like, don't we come back to it every single year

spk_0 in every single class?

spk_0 So if you want to go back to hear what we've said about it before, here are some episodes

spk_0 you can return to.

spk_0 Episode four is called All Things Multiplication.

spk_0 And we just sort of, I think we kind of talked about it from the beginning and kind of

spk_0 moved up sort of the little, I guess, the scope and sequence that it's called from grade

spk_0 to grade.

spk_0 Um, episode 30, we talked about the book, Math, Fact, Fluency by Jennifer Bay Williams

spk_0 and crew.

spk_0 And we, that's when we met with a group of teachers from Ruth's school and talked about

spk_0 what we'd learned from that book.

spk_0 And then episode 40, we talked to Anilise Record and she talked to us about, um, Math

spk_0 Running Records and, and from Dr. Nikki Newton.

spk_0 So certainly we've talked more about multiplication, but those are the ones that are really about

spk_0 it.

spk_0 You know, say anything about that, Ruth, before we, no, I think we headed it because that's

spk_0 kind of where we're headed today is just what Dr. Nikki Newton and Anilise have provided

spk_0 through their Math Running Records and kind of how to implement those in your classroom

spk_0 and then won't not even how to implement them because I feel like there's so many different

spk_0 ways that you can do it.

spk_0 But we both feel like it's very beneficial.

spk_0 And then today we're just going to brainstorm strategies of how to do that.

spk_0

spk_0 So I'll back up and say that a fourth grade teacher, we were having a conversation, not

spk_0 really even about this.

spk_0 And she mentioned how they were struggling.

spk_0 I think they were dev, I think they were doing division probably.

spk_0 And she was like, they're really struggling.

spk_0 And you know why?

spk_0 Because they don't know their multiplication facts.

spk_0 And you know, she, she realized that that was the, the root problem.

spk_0 And so I said, you know, I can, I can help you with that.

spk_0 I could do this running record to kind of figure out where to start with helping them learn

spk_0 their facts strategically.

spk_0 And she's like, oh yeah, sounds great.

spk_0 So I asked her to not, in this case, because we're so close to in the school year, I said,

spk_0 let's not do every single kid.

spk_0 Let's do the kids that you feel like are, you know, are showing signs of needing help

spk_0 in this area.

spk_0 So she gave me a list of, I think, 11 kids altogether out of two classes.

spk_0 And so I did their running records this week.

spk_0 And I guess I should quickly review what that looks like if people haven't listened

spk_0 to the first one.

spk_0 In a running record, in this, in this running record that Dr. Neku Newton has created,

spk_0 it has I think about 12 or so math, math facts on a page.

spk_0 And they're ordered very specifically on the page.

spk_0 And you hand it to the kid and ask them to say, say the product going down the page.

spk_0 And you record first off whether they have it automatic, whether they answer it within

spk_0 five seconds or whether it takes them longer than five seconds to answer.

spk_0 And I also tell them you can, and this is part of it, that you can, you know, if you need

spk_0 to work it out on paper, you can, or if you need to use some manipulatives and I have some

spk_0 base 10 blocks there that can use, like, just unit cubes.

spk_0 And, or if you need to pass, you can pass.

spk_0 And then after we do that page of facts, then I ask them about their strategies.

spk_0 And I go in order, in the order that kids would, well, I guess it ordered from what feels

spk_0 easiest to maybe hardest for them somewhat.

spk_0 I think it's interesting because this one, this assessment starts with zero and one as

spk_0 the first two facts that they see and the first two facts are times zero and times one.

spk_0 And the first two facts that they, you asked them about, but remember in the, in the math

spk_0 facts, fluency book, they said, don't start with that.

spk_0 Do you remember why?

spk_0 Maybe I remember why not to start with time zero and times one when you're teaching kids

spk_0 about multiplication.

spk_0

spk_0 The first thing George is going to be the same.

spk_0 Because it's just a rule and there's no pattern.

spk_0 Where are you going to say?

spk_0 Because the first one's always going to be the same.

spk_0 Okay.

spk_0 And, you know, maybe that's not something to practice, right?

spk_0 Yeah.

spk_0 I think the, I think the idea is that like time zero and times one are kind of hard to grasp

spk_0 the why, you know, I think Ruth, you're kind of like, they're, you know, it's kind of like

spk_0 abstract, you know.

spk_0 So if we can get what the operation does with times two or times five or times 10,

spk_0 then go back and think about what does, then if we know this is what multiplication means,

spk_0 then what does it mean for time zero and times one?

spk_0 Yeah.

spk_0 It feels like I think time zero and times one are confusing.

spk_0 Yeah.

spk_0 Like time zero, everything is zero and then times one, you didn't really do anything.

spk_0 So yeah.

spk_0 Well, and it's kind of the beginning of an algorithm, like just remember this rule.

spk_0 Anything time zero, zero.

spk_0 Yeah.

spk_0 Exactly.

spk_0 Because who really understands that?

spk_0 Yeah.

spk_0 I mean, come on.

spk_0 Yeah.

spk_0 So I assessed these little fourth grade friends and a good, a bright,

spk_0 great, great, great, great, great.

spk_0

spk_0 What was that?

spk_0 That was that a lot of them, probably eight out of 11 or nine out of 11,

spk_0 know to double for times two.

spk_0 So we've talked, we've talked a lot about, Ruth and I've talked a lot about this.

spk_0 And then teachers at school, how often times they get stuck in, if I'm going to multiply

spk_0 by two, I'm going to count by two.

spk_0 Right.

spk_0 Two, four, six, eight, until I get to the right stopping point.

spk_0 Yeah.

spk_0 Yesterday, I was helping a student after school and she was finding the greatest common

spk_0 factor of 26 and 104.

spk_0 And so I was like, well, they're both even.

spk_0 You can divide them by two.

spk_0 And she's real quiet.

spk_0 I'm helping some other kids and I look over and she's got 13 on her paper, like good.

spk_0 So now you have to divide 104 by two.

spk_0 And she's like, I don't want to count by two's to 104.

spk_0 I don't want you to count by two's to 104 either.

spk_0 So at that point, we were able to just talk strategy.

spk_0 Like how about just half of a hundred and then half a four and put those together.

spk_0

spk_0 And she's like, did I always work?

spk_0 Yeah, you don't have to count by two's every time you divide a number.

spk_0 So she could, she could quickly tell you half of hundreds, right?

spk_0 And then half a four and then, okay.

spk_0 But half of 104 or and maybe because I said what's half of a hundred instead what's a hundred divided by two, she made that connection.

spk_0 Okay. Okay.

spk_0 That's good.

spk_0 Yeah.

spk_0 Ruth, I feel like you've had this conversation like with every single kid in your six grade because you talk, you say that like all the time.

spk_0 Every kid, every year.

spk_0 But it's not necessarily something that I that I teach because I.

spk_0 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.

spk_0 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.

spk_0 Yeah, because then you're going to supply it for sure.

spk_0 Yeah, or we'll miss you told me to do this. And so I have to do it in her class. And then you forget it.

spk_0 You know, I want you to understand that it works all the time.

spk_0 Yeah.

spk_0 It's always the most efficient way, right? Right. Yeah.

spk_0 Yeah.

spk_0 Um, another thing that I noticed today of 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.

spk_0 So one kid loved six times four and he knew if he knew what four times six times four is he knew it.

spk_0 And then he used that to figure out all these other facts.

spk_0 Another for another kid, it was six times six.

spk_0 We use that for all kinds of things.

spk_0 Um, for another kid, unfortunately, it was five times two.

spk_0 So every times two fact he was working for five times two.

spk_0 I'm like, well, at least you have the ability to derive, but let's get a better one.

spk_0 At least not starting from the beginning. Yeah.

spk_0 Um, but that was, I'd never seen that in, you know, in such repeated in such a repeated way.

spk_0 I don't know that I quite understand what you mean by that.

spk_0 Okay. So if I asked you six, this, uh, give an example of six, if I asked you what six times seven.

spk_0 Right.

spk_0 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.

spk_0 So there would go 36, 37, 38, 39, 40, 41, 42.

spk_0 I would have my brain went right to 42.

spk_0 And because it is a seven, I always second guess myself and say, I'll crap it.

spk_0 Did that wrong. And then check it real quick.

spk_0 With what do you check it with?

spk_0 I don't really know.

spk_0 Like seven, no, seven times seven. I know it was 49.

spk_0 Yeah. So maybe I backed down from that one.

spk_0 Okay.

spk_0 But anything time seven, I'm like, oh, me. Well, not anything like two times seven. I got that guys.

spk_0 Um, but you know, six times seven, nine times seven, eight times seven, five times seven.

spk_0 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.

spk_0 And you know what? Almost, I probably, if you told me seven times seven, I would go to 49 and then second guess myself.

spk_0 You know, like, um, when you say a word so many times in a row that it like doesn't have any meaning.

spk_0 Yeah.

spk_0 Like it just sounds.

spk_0 It's like the same thing with my seven. It's 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.

spk_0 And I have to, I have to like double check myself. And, and I don't know why it is. And it's nothing.

spk_0 Something dramatic happened at school today. Your teacher taught you seven.

spk_0 It could, it could be. I don't remember that.

spk_0 You're subconscious.

spk_0 It's just that.

spk_0 Yeah, it's, it's something with those mid mid seven. I don't know.

spk_0 I always say it, but I always second guess this.

spk_0 I love how when we interview Teresa Willes, she said she doesn't really have them all memorized.

spk_0 She just still derives them and just derives them quickly.

spk_0 So, you know, that's what Trace told me. Yeah, my son.

spk_0 He's a forensic science major and has always been really, really fast in math, which.

spk_0 I just assumed it was because he knew his facts and he's like, no way, mom.

spk_0 I don't know. I just know some of them and I just figure it out.

spk_0 You're the one who taught me how to do that.

spk_0 So, he's like, if you ask me, what, I forget what his example was.

spk_0 It was something like, if you ask me 11 times 12.

spk_0 Oh, if you ask me 11 times 12, then I always just use the distributive property and do 11 times 12.

spk_0 And then I always use the distributive property and do 11 times 10 and 11 times two and put them together.

spk_0 And I can do that faster than someone can remember 132.

spk_0 Cool. But without even knowing that that's like a strategy for multiplication per se.

spk_0 Like kids deriving facts. He's just like, yeah, that's what I've done my whole life.

spk_0 I don't know that I would ever expect anybody to have outside of the tens memorized.

spk_0 Yeah, they used to be a thing. I don't know.

spk_0 Yeah. So someone tweeted, I forget.

spk_0 I don't know. It was on Facebook and he had taken his daughter to like, I hop because she had passed her 12th times table test.

spk_0 I was like, that is an intense teacher.

spk_0 If you are still given 12 times table.

spk_0 I never got used to be. You have to be out 12.

spk_0 Oh, I remember as a kid. Yes. I remember.

spk_0 I still am stumped on 11 times 11 and 11 times 12.

spk_0 I know 12 times 12. But those two. I know the levens.

spk_0 No, no, I don't know. I don't know I'm memorized. You're right. I don't.

spk_0 I love it. Yeah. Okay.

spk_0 I'm just quick with my, my strategy.

spk_0 Like trace and like to raise a will. You must be fluent. Good job.

spk_0 Not a bad proof of the people be a member.

spk_0 Yeah. That's good. Okay.

spk_0 So, 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.

spk_0 But they just were maybe slow on at it.

spk_0 And maybe didn't explain their ways to derive, especially great, but they still have them.

spk_0 But there was one friend you did not.

spk_0 And however, he had the most interesting counting with his fingers strategies. Have I told you about this route?

spk_0 Uh-huh. Okay. So this is going to be tough to, to describe on not camera.

spk_0 So I'm going to try though. So when he counted. Okay.

spk_0 Let me ask you if you had to add on nine and you, I made you do it with your fingers.

spk_0 Like, like do seven plus nine and add on the nine with your fingers. Or by do that for a second.

spk_0 I would start with my pointer finger and add that five with my thumb would be my fifth one.

spk_0 And then I would use my pointer on this hand.

spk_0 Okay. So you're doing four two hands, two different hands. Okay.

spk_0 When you do in J profit to add on nine.

spk_0 I just picked my hands up and counted it from nine to got.

spk_0 Well, where did you start?

spk_0 My thumb over here. My left hand. Yeah.

spk_0 I just held my hands up in front of me. Okay. Like I'm looking at my hands.

spk_0 Uh-huh. Did I wash my hands?

spk_0 And then I went one, two or seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen.

spk_0 And you didn't. And what you left off was the thumb of your second hand.

spk_0 Correct. Okay. So that's interesting.

spk_0 Ruth, that you start with your pointer finger because this is this is where my like what is going on?

spk_0 Honestly, how she started the pointer because if pointer is never at the end of your hand.

spk_0 So I that's just the one I put up. So if my hands are in front of me, I just would say put seven in my head eight nine ten eleven twelve.

spk_0 And then pull my thumb out.

spk_0 Just like you would count when you were I'm one years old, two years old, three years old, four years old.

spk_0 And then when you're five, you put your thumb. Okay. Okay. I search for me now.

spk_0 Okay. So I'm just going to step back and say I think this part is fascinating because people do it so differently.

spk_0 We are inventing we invented our own strategies to count on our fingers.

spk_0 No one taught you like you start, you know, hold your hands out and start over here and work, you know, left to right.

spk_0 No one taught you start with your pinky. You start with your pointer finger, you know.

spk_0 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 ten and start from the left.

spk_0 Okay. But but kids invent these ways to keep track of things with their fingers that no one teaches them.

spk_0 So he was had his hand has palm face down on the table tapping to count. Okay.

spk_0 And so his nine, well, his left hand was keeping track of how many nine she had.

spk_0 So we put up one every time he did another nine. He followed me with that hand. So like, he would go nine, eighteen and put up one finger for the nine, a second finger for the eighteen.

spk_0 So he could keep track of how many nine he was counting. So is he skip counting? No, he's counting on. Okay.

spk_0 So anyway, then his keeping track of not hope this isn't too confusing for people listening.

spk_0 The his keeping track of nine on the other hand, like counting by nine started with this pointer finger.

spk_0 And then middle finger and then ring finger and then pinky and then back to a thumb and then all the way to back to his pinky.

spk_0 So we kind of did his right hand twice to make nine.

spk_0 But left out his thumb the first time around.

spk_0 Ruth, did you get that? I didn't get it in my hand. So that helps.

spk_0 I can't see your hand, but I do get it. And so that was, you know, I would have started 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.

spk_0 But he was leaving his thumb off first.

spk_0 I guess I don't understand why he had to use one hand to keep track of his nines and count up on and add on by nine.

spk_0 Because he he got to he could probably say nine, eighteen and past that he couldn't he didn't know how many nine.

spk_0 So he really was trying to multiply or skip count by nine, but he wasn't skip count.

spk_0 That was how he was getting there. Okay, I he was doing different problems than us. That's why I think yes, there you go.

spk_0 So then, but then when he's counted by sevens when he was adding on seven, he's still same thing started to calm down tapping on the table, starting with his pointer finger, going to his pinky.

spk_0 So one, two, three, four back to his thumb five, six, seven, stopped it as a middle finger.

spk_0 So his seven, like the shape of it, you know, he wasn't happened to think through that his shape of his seven is naturally one, two, three, four, start over five, six, seven, where if I 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.

spk_0 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 it for you.

spk_0 How do you, how would you count on seven, Ruth?

spk_0 Like on seven for me, and I would skip, maybe I would skip my pinky if I don't know.

spk_0 I'll just spent a lot of years playing piano.

spk_0 You think that I wonder if it has something to do with with how that feels in my like if you were playing down a scale, you would start up here.

spk_0 I don't, I don't have, I'm not trying to tie that to you. I'm thinking I would do the same thing as one, two, three, four, put up my thumb for five and then six, seven.

spk_0 Well, then that's exactly what he's doing to just turn the other way, right? Right.

spk_0 Yeah.

spk_0 Yeah, because he's starting with that finger. And if he was the kid whose mom was like, how old are you? I'm one.

spk_0 Well, that's the first finger that you hold up. Right. If I'm counting like one, you know, one, two, three, I wouldn't start my pinky.

spk_0 But if I get my hands down trying to keep a pattern like that, I would start, I would start on the other end of my hand.

spk_0 Okay. Point taken that we all do something different. And I love it. I just think it's, it's so cool.

spk_0 Okay.

spk_0 You didn't know you were going to get a big old lesson on counting in this episode.

spk_0 So now I met with this teacher. I shared the data with her. I, I shared it with her in like a spreadsheet for each kid for where they fought where they fell.

spk_0 The assessment kind of gives them a number zero through four on each fact.

spk_0 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.

spk_0 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.

spk_0 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.

spk_0 But she's got a whole lot left to do.

spk_0 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.

spk_0 Maybe we could work them through that at home. So that's where we are now trying to develop that idea.

spk_0 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 out your fours here, all the things that you walk through to do that.

spk_0 And now, okay, you're done with that. Now you move to eights. And here's all the things that you walk through.

spk_0 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 eights?

spk_0 Yeah, you want to talk about that now.

spk_0 I think so.

spk_0 Jay, were you going to, were you saying something?

spk_0 No.

spk_0 Okay. So the, um, 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. Nicky's, like order potentially.

spk_0 Okay.

spk_0 So that has them working zeroes and ones and then tens and then fives because I think tens are easiest.

spk_0 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.

spk_0 And then the first one is the first one that I feel like we've been needing to remediate are the two's.

spk_0 And so that strategy we want them to get is double instead of counting by two's.

spk_0 Okay.

spk_0 So then the strategy after that, why not go to three is basically is what we're saying is because the force one of the fluent one of the strategy the best strategies for four is to double the other factor and then double it again.

spk_0 So it's building directly off of the two strategy.

spk_0 And then the eighth 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 and exponent land.

spk_0 Yeah.

spk_0 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.

spk_0 Yeah.

spk_0 So then it goes so it goes two force eights then it goes to threes and the strategy that they are encouraging kids to use her threes is times two like double and then add a group.

spk_0 So if I have to do seven times three, I would do seven times two and one more group. So 14 plus a seven.

spk_0 And then six is next and you double the three amount.

spk_0 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.

spk_0 And then I all the 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 know use the finger trick over half of them yesterday, I used that, like put a finger down and see what you've got.

spk_0 But one kid definitely use the times 10 take away a group, which was really exciting.

spk_0 You know that one.

spk_0 I do.

spk_0 Okay. And then I think from there are sevens, is that all I've left off?

spk_0 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 sevens and memorize seven times seven.

spk_0 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.

spk_0 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.

spk_0 How we are, 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.

spk_0 To sevens.

spk_0 No, his square facts.

spk_0 Oh, square facts.

spk_0 Yeah.

spk_0 Did I answer your question, Ruth?

spk_0 Yeah. Okay.

spk_0 That's good.

spk_0 So let's brainstorm.

spk_0 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.

spk_0 Look like for time's fours.

spk_0 What are some components?

spk_0 We kind of talked about the math flips where you see the number double and then you see the number double again.

spk_0 Even if the first one.

spk_0 Yeah, I just think that isn't that Berkeley ever who does math flips.

spk_0 Yeah.

spk_0 He just does a really good job of animating the cards enough and

spk_0 the kids can see the pattern.

spk_0 And then once you see the pattern, you can attach those numbers to it.

spk_0 JR, are you picturing it or are you going to explain it?

spk_0 I am picturing.

spk_0 I have a few of Berkeley's animations in my head, but I don't think the ones I'm thinking about are this.

spk_0 So, but I also understand what doubling and doubling again means.

spk_0 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.

spk_0 Can you explain this to me please?

spk_0 Yes, I'd love to.

spk_0 Give us some exposition.

spk_0 Okay.

spk_0 So picture the font, what you see as a five on a die.

spk_0 Okay.

spk_0 And if that was a five 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.

spk_0 Okay, gotcha.

spk_0 So on each group is on the first side, you're like, oh, that's two groups of five.

spk_0 It's 10.

spk_0 And then wait, wait, say that again.

spk_0 That's two groups of five.

spk_0 That makes 10.

spk_0 Because I've seen them in two circles.

spk_0 Right.

spk_0 So you're, you just look at it and kind of like say what you see.

spk_0 For those people at home, she, we had the die in two different hands and then all of a sudden they both jumped to one hand.

spk_0 And it confused me.

spk_0 Okay.

spk_0 And then you flip.

spk_0 So if you're doing this on paper, you have it in a little like note card and the flip it to the back.

spk_0 If you're doing it on the Google slide, it would just be the next slide.

spk_0 And then so on the opposite side, you'd see that image just repeated right down below it.

spk_0 So now you have four groups of five showing.

spk_0 And you say, oh, that doubled is 10 instead of having to add like five, 10, 15, 20.

spk_0 You can think 10 plus 10.

spk_0 Okay.

spk_0 Yeah.

spk_0 Ruth, you look at that.

spk_0 That's not times four.

spk_0 That's only times two.

spk_0 No, it's four times five.

spk_0 Well, but you started with two times five.

spk_0 You didn't start with five.

spk_0 We're going to use two times five to help you solve four times five.

spk_0 Okay.

spk_0 Does that make sense?

spk_0 Yeah, I guess in my head, I was thinking you were going to double the five and then double the 10.

spk_0 That would be that would be times eight or something.

spk_0 No.

spk_0

spk_0 Double the five and double the 10.

spk_0 Because if I'm trying to, if I'm trying to learn my force.

spk_0 Okay.

spk_0 And I've got five and I'm trying to learn four times five.

spk_0 I'm going to double that five to get 10.

spk_0 And then I'm going to double again to get 20.

spk_0 I'm not going to start with 10 if I'm trying to multiply four times five.

spk_0 But I did not at the time understand that you were starting from two times five.

spk_0 Uh-huh.

spk_0 Okay.

spk_0 I was trying to get to two times five, I guess.

spk_0 Yeah.

spk_0 And what in my process?

spk_0 Got it.

spk_0 I understand now.

spk_0 Oh, almost had a fight right there.

spk_0 You were trying to tell me that that 20 was five times eight.

spk_0 I don't know what we were talking about.

spk_0 And I was going to be right.

spk_0 We got real lost.

spk_0 Okay, we'll save us.

spk_0 So I've been here.

spk_0 I think that you teach that strategy, but then you give students.

spk_0 I don't know some kind of.

spk_0 I'm going to use task card, even though those aren't my favorite thing.

spk_0 Yeah.

spk_0 To think about different ways to ask the multiplication problem.

spk_0 Like, almost like algebra, like three times something equals 12,

spk_0 but something times four equals 40.

spk_0 And they're like a click and drag and matching the missing number in the multiplication problem.

spk_0 Or a raise of 16 where they're writing the multiplication problem and circling the group of eight

spk_0 in the group of 16 like to get.

spk_0 I don't know.

spk_0 Just different ways to ask multiplication questions.

spk_0 So once you feel like you have the strategy, because let's be honest, practicing them gets you more efficient,

spk_0 as well as knowing the strategy.

spk_0 You can't just have someone tell you the strategy and not practice it.

spk_0 So how could you make little individual slides or something where each slide is a different kind of question?

spk_0 I don't know if I'm saying that right.

spk_0 Like, what if you had eight or you had four numbers, you had an eight into 32 and a 24 and they had to write the multiplication problem that goes with it?

spk_0 Ooh, 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.

spk_0 And you pick the, basically, you're picking the three that are a fact family, which is what you're saying.

spk_0 Okay, that make a fact.

spk_0 Yeah, that could be good.

spk_0 So get eight, three, 24 and 32.

spk_0 Oh, yeah, that's a good one.

spk_0 You would leave out the 32.

spk_0 Yeah.

spk_0 I like that.

spk_0 So all, yeah, all different ways to, and then that's kind of working on division.

spk_0 Some, you know, it's kind of relating it to division a little bit.

spk_0 But I think about that one that Jay just said, what about the kid who says, well, 24 plus eight equals 32.

spk_0 So that's my fact family.

spk_0 And I left out the three.

spk_0 Yeah.

spk_0 But that we have to say this, you got to make a multiplication.

spk_0 Or you say, what?

spk_0 It's like 24.

spk_0 You can do it either way you want.

spk_0 Yeah, you can use that eight times three plus one.

spk_0 Mm-hmm.

spk_0 I don't know.

spk_0 That's cool.

spk_0 Just different ways again for kids to be able to show their thinking.

spk_0 Mm-hmm.

spk_0 I like that.

spk_0 Another resource that I think we could throw in there is from the math fact fluency book, the purple one.

spk_0 Um, they've made a website that we've talked about before.

spk_0 Some Kentucky teachers have made a website where they've taken a lot, not all of them,

spk_0 but a lot of the games that are in their book and made digital versions of them.

spk_0 So I feel like we could tap into that and link to those.

spk_0 Um, on the site.

spk_0 I mean, that's kind of the point is that we typically as teachers introduce, this is what multiplication is.

spk_0 And then we may jump straight to memorize it.

spk_0 Or we may say, this is what multiplication is.

spk_0 Here's a strategy.

spk_0 Now memorize it.

spk_0 You know, um, and we don't give them.

spk_0 We don't park in the practice and derive stage, which is what they need a lot more of to get to that.

spk_0 Automaticity.

spk_0 Wow.

spk_0 What?

spk_0 And I'm glad I don't have to.

spk_0 Teach somebody the concept of multiplication from scratch.

spk_0 Yeah, I love it.

spk_0 I think it's fine.

spk_0 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.

spk_0 Okay.

spk_0 Double double.

spk_0 Sounds like a value milling McDonald's.

spk_0 I'll have the double double mill.

spk_0 Yeah.

spk_0 We talked to Ruth yesterday.

spk_0 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.

spk_0 You know, the kids should have to say it.

spk_0 So we talked about how we might have.

spk_0 Go to Berkeley, Everett site and see what he already has that demonstrates that.

spk_0 That without any words and explanation and then get them to get the kid to say it and then get the, 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.

spk_0 We want you to actually.

spk_0 Right.

spk_0 Any other ideas of what could go in there?

spk_0 Not.

spk_0 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.

spk_0 You know, you give them the guidelines of, here's a frog.

spk_0 Here's a pond.

spk_0 What kind of a story can you illustrate and tell that uses one of your strategies or one of your facts?

spk_0 So they're copying and pasting the frogs or they're making the frog jump this many times.

spk_0 You maybe think of two different things.

spk_0 Thank you.

spk_0 One was that when we did this in class last year with fifth grade class, we use the freier model, which is where you split a piece of paper into four quarters.

spk_0 And then in the middle, you would write in the intersection of those divisions.

spk_0 You'd write the fact and then you would require them to sort of show it for different ways.

spk_0 So the first one could just could be a model like this first box could be a model, the second box could be write the story, the third box could be make another model.

spk_0 I don't know.

spk_0 And then the last box could be the answer.

spk_0 But yeah, that multiple representations idea.

spk_0 And you could do that on Google sites.

spk_0 And then another thought I had was go so we've recently been our school purchased and.

spk_0 And so they could have to go and show three times four.

spk_0 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.

spk_0 Like do three groups of four or four groups of three.

spk_0 What else number line arrays.

spk_0 That'd be cool.

spk_0 We really cool.

spk_0 Yeah, arrays.

spk_0 Yeah.

spk_0 Girl, the relationship between arrays and area is a struggle.

spk_0 Yeah.

spk_0 Maybe that's like what teachers have left off their curriculum.

spk_0 Hmm.

spk_0 Are you going to that particular group of students?

spk_0 We had to make lots of connections because they just didn't have it.

spk_0 Yeah.

spk_0 All right, Jay probably got any other ideas.

spk_0 You're like, uh, no.

spk_0 No, no, no, no.

spk_0 Okay.

spk_0 Ruth, you have any more?

spk_0 I'm for fours.

spk_0 Okay.

spk_0 Do we want to keep going or are we, 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.

spk_0 Yeah, I kind of just repeat them.

spk_0 Yeah.

spk_0 I'm wondering how long would we give them to learn, like to work on a set of facts?

spk_0 And what kind of accountability, what would the accountability look like?

spk_0 Any thoughts about that?

spk_0 I mean, ideally your accountability would be another running record and you would see improvement.

spk_0 But yeah.

spk_0 I don't know that that's doable.

spk_0 Right.

spk_0 I was thinking about I could go back in like a month, you know, I can't, I can't do it every week, but I feel like I can go back in a month.

spk_0 And I was also thinking about not needing to redo the whole thing.

spk_0 If I got, if I saw that they were fluent all the way up to two, I should just probably start it for worse or maybe start, start it too, you know, the first one that they've prepared.

spk_0 Right.

spk_0 I don't know, I was wondering if they could do it within a week, but maybe that's too fast.

spk_0 Like, how much time would we want them to tackle the force?

spk_0 Well, and how much do they get on the computer?

spk_0 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, you know, doing what they're supposed to do.

spk_0 Right.

spk_0 I mean, potentially three days of the week.

spk_0 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.

spk_0 J. Profit says with his eyes rolling, then the back of his head is bad. It's real bad.

spk_0 Okay. We will, we also, 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.

spk_0 So 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.

spk_0 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.

spk_0 Okay. Ruth, did you want to end with your reflection about teachers and what you've been thinking about lately?

spk_0 So to be, well, to be transparent, but still very professional.

spk_0 Yeah.

spk_0 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.

spk_0 And I can go to Twitter and search Mitt Boss 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.

spk_0 Yeah.

spk_0 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.

spk_0 Now you do it.

spk_0 Yeah.

spk_0 What's the next step?

spk_0 And so I have an opportunity to influence some pre-service teachers and they are not easily influenced.

spk_0 Yeah.

spk_0 It's been a harder self than you were thinking it would be.

spk_0 Right.

spk_0 Just kind of that.

spk_0 Like this is really good.

spk_0 This is what you want to do.

spk_0 And they are, yeah, they are wanting to teach the way they were taught.

spk_0 And when you are a high school, want to be teacher, well, you were just taught that a couple years ago.

spk_0 So it's still fresh in your mind.

spk_0 And obviously that teacher did a really good job because now you want to be that kind of a teacher.

spk_0 Yeah.

spk_0 Right.

spk_0 But we've had many conversations like, listen, you were in that college calculus class when you were a junior in high school.

spk_0 So the students in your class really wanted to be there if they were excelling at that level in high school.

spk_0 And your teacher could say, I'm going to do it, you do it.

spk_0 It's done.

spk_0 But when you're signing up to teach algebra one, you don't have a classroom full of kids that want to be there.

spk_0 Yeah.

spk_0 So you got to step out and, you know, engage them.

spk_0 Right.

spk_0 So 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.

spk_0 And if it was math, 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.

spk_0 And let's do a math task together.

spk_0 Let's go what?

spk_0 Oh my gosh.

spk_0 You know, have that moment together.

spk_0 Mind blown.

spk_0 But you're, you're just sort of having to like take my word for it.

spk_0 This could happen.

spk_0 Take my word for it.

spk_0 This could happen.

spk_0 And they're not being able to see it.

spk_0 Yeah.

spk_0 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.

spk_0 Okay.

spk_0 Well, how do I do that?

spk_0 Well, you know what?

spk_0 I'm going to have to find someone.

spk_0 Yeah.

spk_0 I don't know.

spk_0 Let's see.

spk_0 Who does it?

spk_0 Yeah, I know.

spk_0 But it's a question of the way you're doing, you know, how to do it.

spk_0

spk_0 Yeah, another, another takeaway that I've heard from what you, I guess we're doing takeaways now.

spk_0 Hold on.

spk_0 Can I respond to that first?

spk_0 Yeah.

spk_0 Are you going to talk about that, too?

spk_0 I had something to say about that.

spk_0 Go ahead.

spk_0 Another thing that I've been hearing you say lately is how, how we as teachers talk about subjects that aren't our majors are favorite and passionate subject.

spk_0 And we've had a good conversation lately about, yeah, you can be the master but you can't be dogging on the music class or the English class.

spk_0 You've, you have got to represent what it's like to be a well-rounded learner, even if it's not what's in your cut, you know, you've got to protect what you say to each other to the kids about other subjects.

spk_0 Okay.

spk_0 Off my soap box.

spk_0 You go, Jay.

spk_0 What Ruth was talking about, you know, you should, you should said that these students were good students or that's, you know, they've learned it well enough that they want to go and teach it and working with college professors every day.

spk_0 I have found that, you know, I've did not do a study on this.

spk_0 There's nothing coming out.

spk_0 No, 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 faculty that I worked with, the professors that say,

spk_0 they were not good students and then they struggled are the ones that are quicker to look for different ways of teaching.

spk_0 The professors that were good students love this thing from day one and, you know, it's all they've everyone do is be a professor.

spk_0 And I'm not saying they're inflexible, but they're the ones that are most comfortable with this is how it was taught a traditional way of that's how I learned it.

spk_0 This is how I'm going to teach it.

spk_0 We're just going to, we're going to keep this line going forever and ever.

spk_0 And there's a couple of people that I've worked with lately that, you know, I have worked with them in one facet and they are and they are very innovative.

spk_0 We're going to do it this way.

spk_0 We're going to bring this so 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.

spk_0 And those are the people that are, again, not going to say this is always a case, but in my experience, those are the people that are most likely to find those different ways of doing it or try something different.

spk_0 That's cool. I bet that's a true correlation.

spk_0 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.

spk_0 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.

spk_0 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.

spk_0 And I always got seas. I worked hard, but I always got seas. 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.

spk_0 I still remember in second grade the little mouse that came out of the ones place and walked over to the tens place to get 10 pieces of cheese to come back.

spk_0 I just was so so confused and frustrated.

spk_0 I will have to say that half of that sentence I thought you were still talking about a mouse.

spk_0 There's a mouse that walked out.

spk_0 No, just the whole.

spk_0 Because I'm a math teacher that, you know, that analogy is not readily available in my brain.

spk_0 Yeah.

spk_0 My take will go hard. Well, I was going to I was going to bring us to take away as we've talked about prime numbers. We talked about multiplication assessment and remediation.

spk_0 We've talked about counting strategies. We 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?

spk_0 My takeaway is not math related.

spk_0 Okay.

spk_0 Earlier I talked about my sevens, seven of application facts and always saying them and thinking I'm wrong and compared it to saying a word so often.

spk_0 Saying a word so many times that it loses its meaning and just becomes sounds and that process or that phenomenon is called semantic cessation.

spk_0 Whoa.

spk_0 And 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 a collection of sounds and it's like it becomes almost unfamiliar again.

spk_0 So I wonder if there's numeric cessation.

spk_0 I don't know.

spk_0 Without the words of satiate.

spk_0 What is semantic cessation?

spk_0 Cool.

spk_0 What in the world did you Google to figure that out?

spk_0 Saying a word until it sounds weird.

spk_0 Okay.

spk_0 Perfect.

spk_0 Well done with your searching skills.

spk_0 Well done. Well done.

spk_0 Google.

spk_0 I understand that sense.

spk_0 Ruth, what's your takeaway?

spk_0 Well, if I have an opportunity to have takeaways with prime numbers, I absolutely have to do it.

spk_0 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.

spk_0 Because we were doing this activity in every single class period, every single kid had to have five post-it notes.

spk_0 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?

spk_0 I'm like, no, I'm counting two, three, five, seven, eleven.

spk_0 And it's awesome.

spk_0 Not very many kids like even got that like, what is that?

spk_0 And then someone's like, oh, that's the first five prime numbers.

spk_0 So, and my other favorite thing to do is to.

spk_0 Yeah.

spk_0 Oh my word.

spk_0 Yeah.

spk_0 And walk away.

spk_0 It's to tell people on their birthday, like I'm always taking people's birthdays and making math equations and finding prime numbers.

spk_0 And the other day of a colleague's child turned nine.

spk_0 And 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.

spk_0 And you won't be a perfect square for seven more years.

spk_0 And that number is prime.

spk_0 And his mom was like, we were starting to get a matching.

spk_0 Yeah.

spk_0 That's awesome.

spk_0 So, prime numbers rock.

spk_0 Yes.

spk_0 My take away 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.

spk_0 Like I'm really, I'm really thinking about the two, three numbers or what's the missing number or, you know, doesn't always have to be this time.

spk_0 This is what there can be.

spk_0 I should be a little more creative than that.

spk_0 So, I'm going to be looking for other ways.

spk_0 I like that.

spk_0 That was good.

spk_0 All right.

spk_0 We'll report back in.

spk_0 I don't know.

spk_0 It's probably going to take us a month to get this together.

spk_0 But we'll report back in.

spk_0 Let you know how it's going.

spk_0 It could be month for the next episode.

spk_0 It comes out here.

spk_0 You know, let's be honest.

spk_0 All right, Ruth.

spk_0 It's the weekend.

spk_0 So, I'll see you on Monday for a run, right?

spk_0 All right.

spk_0 Sounds good.

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Ep 89: Revisiting Multiplication Fluency

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