How to Use the Pizza Problem for Math Intervention: T1I S1 E11

Cheri Dotterer 0:04
Music. Hello, everyone. I'm Cheri dotterer, and I'm here with jonily Zupancic, and we are here at tier one interventions, and we are so glad to have you here today. Jonily and I are gonna talk to you a little bit about this thing called a pizza problem. Absolutely.

Jonily 0:20
We have a good bit of content today that we're going to roll out to you. We're going to lay some foundation, though, and define what is tier one intervention. We want every kid, regardless of ability deficit, struggle. We want them to experience whole classroom, regular general instruction, which we're going to call tier one. Tier one is whole classroom, regular classroom, in math and writing. Tier one was not where it should be mathematically. All we need are 12 anchor problems and tasks. That's it. This is how simple it can be, tier one math intervention, every standard, from preschool through high school, every standard boils down to 12, what I call reference tasks. Reference tasks are math problems, situations, tasks, experiences, exercises that are named, that are frequently given. To students at every grade level and frequently throughout one grade level. So the 12 tasks are exactly the same no matter the grade level, no matter the age level, no matter the ability level, and they are differentiated, enough, inclusive enough, accessible, enough that any one task will meet the needs of all students in the same classroom at the same time. And as a reference task, we bring these problems up every month or every three weeks, or at a frequency level, so that kids get more interaction with the same task again and again, so that when we're teaching our content, when we're teaching our textbook, when we're teaching regular math lessons, we can refer to hence the name reference these reference tasks to make connections, and we use these reference tasks as our math intervention tool. But all students at all grade levels know and have experienced each of these 12 tasks at some point in their preschool through high school career. I can then use these reference tasks at the tier two and tier three level to provide intervention. You don't need to worry about what they are. But bottom line, mathematics comes down to these 12 tasks all preschool through high school, mathematics, and they are pizza problem, 120, chart, paper, folding, making rectangles, quick dots, locker problem, Jesse and Kay Geo, board, Candy problem, paint problem, staircase and function machine. I would use these reference tasks as intervention and extension to meet all levels of my students within the regular classroom, within tier one, and all students would be able to get the math needs that they needed through each of these tasks. We're going to do is only focus on one of these reference tasks, and that is the pizza problem. The pizza problem is a company makes square pizzas. That's it, and that's the beauty of a reference task. It can be introduced in less than like, 10 seconds. The pizza problem situation is a pizza company makes square pizzas, that's it. And what we're going to do now is we are going to show you how the pizza problem is delivered and rolled out in multiple frequencies and interactions. We know that students to achieve high need more interactions over time. With the same thing, our gifted students get kids that are truly gifted, they might need one to two interactions before they know it forever. Four that is exactly what math reference tasks do, and we're going to show you that now. So here we go, pizza problem. Let me explain interactions in the first month of school. I talk about how that's the first time I expose students to each of the reference tasks. Now let's say you're listening to this and it's February and you're like, I guess I have to wait till next year. No math in a month can happen at any time during the school year. Don't wait till the beginning of the year to have interaction one. As a matter of fact, some of us teachers will do interaction one in April or May, because testing is over, we're ready to engage kids and just keep them busy for the last month of school. Interaction one can happen at any time of the year. Don't misunderstand that interaction. One means I'm going to introduce whatever reference task it is today. It's the pizza problem. I'm going to show you how I facilitate the first interaction. Many teachers say, Look, I have this pacing guide, this textbook, I have all this curriculum I need to cover. John Lee, I don't have time for this. Great each of your interactions can be six minutes, and then you can go on to whatever you normally teach. If you don't have time. I'm asking you to make time six minutes once a week. That's it. These things can happen in a very small amount of time. Other people are like, look, my resources that I'm using, they're not working. My kids aren't learning. Can I do this for my entire class period? Absolutely. If that's the case, you might do more than one interaction at a time, but I want to caution you, as you give kids the reference task a second time or a third time or a fourth time, it is essential, based on cognitive science, that there is space between those interactions, there's time between those interactions. Cognitive science calls it spaced practice, which means repetition is essential, but we need out of context lessons that don't have to do with the pizza problem in between the frequency of the pizza problem. So between interaction one and interaction two, there might be four days that go by, there might be four weeks, there might be two months, but it's essential that we practice what cognitive science calls spaced practice. So when we introduce the pizza problem, we're only going to go so far. Then we're going to stop and move on to our lesson of the day. That is totally unrelated. These are small bursts of out of context math experiences in cognitive science, we call that interleaving. Interleaving is not my term. It's a cognitive science term, and what that means is, in order for the brain to learn and remember and create long term learning, is through interleaving out of context, bursts of content that happen in between other non related content through space practice and interleaving, reference tasks become more powerful. I had a teacher one time, and they're like, oh my gosh, I did pizza problem for six days in a row, and it was amazing. And my kids loved it. I'm like, Okay, that's great. However, that's really one interaction. You're not getting the power and the benefit of the reference task because you did the same thing for six days. There was no out of context verse, and there was no space in between, so you couldn't practice interleaving in space practice. So you've lost the opportunity to increase the memory and retention of that because really that six days in a row of the same thing is one interaction. The goal is to introduce pizza problem once in August, once in September, once in October, once in November, or once a week, or once every eight weeks, or once every other months, once every other month. You've gotta have space in between. So interaction, one a pizza company makes square pizzas. That's it. Now. What do I do with my kids? I say my favorite three words, tell me about tell me about the pizza company, and then I give kids opportunity to process. Now, Sherry and I would never talk at kids for the amount of time that we. Just been talking at you wouldn't happen in a classroom without an intervention. Rain break. At this point, with all of you, you might have been like, oh my gosh, I am totally checked out.

What you need is a process time the math instructional facilitation that's going to re engage and redirect you is for me to ask you right now to put in the chat your thoughts about this pizza situation that's going to re trigger the engagement and focus a pizza company makes square pizzas, that's it. Just tell me your perspective. The point of this is to reengage your mind, to redirect you, to refocus you. And for kids, it's telling them I care about what you think. I care about your perspective. I do not jump right into mathematics with solving an answer getting because solving an answer getting separates and polarizes kids. I have kids who can I have kids who can't, and everybody else is in the middle, which is why we need to have these conversations about these strategic interventions, not at the tier two or tier three level. These are things that 100% of our kids need to experience. That's it. It's as easy as that. If I'm telling them, they hear it if they're telling me, they learn it. They have to tell me. Through this, I can assess what they're thinking. So it's an assessment for me as a teacher, but it also allows students to feel like they belong, because I care about what they're thinking, and this is what Sherry and I call the Tell Me More method, if we ended this training right now and you walked away with only tell me about Tell me more, and practice that daily In your regular math classroom that, in and of itself, would increase memory, retention and motivation, focus and engagement for our students. Now, there's more to it. It's got a lot of components. This strategy right here, that doesn't take a lot of planning time is the number one strategy to do multiple things for our students, I'm asking them what they think about the pizza problem company. I could ask some additional questions. Sometimes what I'll ask in the first interaction with kids is, what are squares? Here's what's important in the first interaction of any reference tasks I'm not confirming or denying their answers, but they say to me, squares have five sides. Part of reference tasks means that I as a teacher, have to be diligent on how I respond. How do I respond to a wrong answer? And how do I respond to a correct answer? The answer to that is the same way. If a student says, squares have five sides, I'll say, tell her about that. Do you see how we're going right back to that strategy. If I tell them my opinion, they hear it, but they don't learn it. I always go back to tell me more about that. Now, in the meantime, some other students going to pipe in and be like, six don't have five sides, sides. What am I going to how am I going to respond as a teacher, tell me more about that. The best strategy we could use as a facilitation technique, not just for tier one, but for a regular classroom teacher is many times in mathematics we want to practice not confirming or denying student responses. That practice alone will increase, thinking, reasoning and sense making will increase and tap into the natural creativity that Sherry was talking about. Our ADHD students thrive on creativity, and typical traditional math classrooms hinder creativity, so by me not responding, confirming or denying student accuracies or inaccuracies, by me responding the. Same way to correct and incorrect answers or thoughts, helps the ADHD student thrive. Another question I can ask, How are squares and rectangles different? How are squares and rectangles the same? And if that's all I do on interaction one, that's it. Six minutes, 12 minutes, that's it. That's pizza problem. Interaction one, there was nothing taught. There was no teacher telling or instruction. It was just gaining student perspective, getting them excited, enriching creativity and generating curiosity. Because if I don't confirm or deny and I leave linger all of their responses and say, Okay, let's go on to our lesson of the day. Go ahead and take out your book and turn to page 384, they're going to be like lingering questions and problems are also the key of increasing memory and retention of content, because once I confirm or deny a student's thought, Everybody's thinking and reasoning stops at times, I want to leave these concepts lingering.

Cheri Dotterer 16:29
Teachers ask us every day how to implement these reference tasks and occupational therapists question how to integrate themselves into the regular education classroom. You have heard the science behind the tasks over the past few months, but until now, we have not implemented these tasks for you. The next segment is sponsored by disability labs, where we provide teachers and therapists with the tools to implement interactive, interdisciplinary interventions. Through our professional development programs for the general education, classroom teachers learn from OTS. OTS learn from teachers inside the community, we offer free and paid training that supports students writing and math skills so they can become adults they were meant to be. The next upcoming event is on July 12, and it will run for four consecutive Fridays. Your instructor is Theresa Rodriguez, a school based occupational therapist from Massachusetts. She's also a dysgraphia specialist using the dotterer dysgraphia method. She will be doing a book study on handwriting, brain, body, disconnect. The cost for that program is $47 go into disability labs.com under the calendar and sign up today. The next segment is called Hear me teach jonily inside her classroom, and lets you listen to her while she implements the pizza problem. This episode is in a kindergarten classroom, and please note that all appropriate releases are on file at the school. Her teaching session lasts about 30 minutes. Sit back with your cup of coffee, or listen while you're driving to and listen to hear me teach by jonily Zupancic, one to a group of kindergarten students.

Jonily 18:42
We are back here with kindergarten, and today we are not going to go back to purple x, but we will eventually. We are not going to go back to our monkeys, but we will soon. We're going to do a new task today called the pizza problem. I don't have pizza for you.

Unknown Speaker 19:06
Disappointment.

Jonily 19:08
Here's the situation. This pizza company only makes square pizzas. So we're gonna make this very mathematical. So I know you've seen pizzas that are round and then rectangle and cut different ways that. So the way that we're going to define this math task is that this company is only going to make pizzas that are square. So we're going to practice with squares today. What shape are we going to make today? Square? Somebody raise your hand and tell me about a square. Tell me about a square. Start us off. It's flat. Oh, I love it be. And we're gonna use our flat pieces. When we say flat, I'm gonna call that d2 dimensional. Say that two dimensional. Perfect, because it's going to be a certain amount it's going to be flat on your desk, and it's going to be a certain amount tall and a certain amount long. We're going to talk about how tall and how long our squares are. Tell me something else about squares. They have, oh, they have points, like the corners, and I'm gonna use a math word vertices. Say vertices. How many points do they have? Tell me on 3123, got it. I knew we were gonna do okay with that. All right. What else can you tell me about squares?

Unknown Speaker 20:36
I'm gonna have four, five,

Jonily 20:40
fantastic. Did you hear that? Say it again. What is special about the four sides that squares have? Yes, you know what? I love how he said that. Say it again. Equal sometimes some of the older kids say they're all even, but that's not the right word to use. Even means something different.

Unknown Speaker 21:07
I love that you use that

Jonily 21:09
word. Everybody say equal. Raise your hand to tell me what equal means. What's equal mean? It

Unknown Speaker 21:17
means like two sides are the art

Jonily 21:25
on the both same long, both same long. Oh my gosh, your words are beautiful. I'm gonna give you another new word today, another word for equal and the same congruent. Say that. Okay, so what are our new words for today? Our new words for today? What's congruent? What else? 2d two dimensional? What are those corners? Called

vertices? Say vertices, yes, oh yes, go ahead. All right. So what shapes are we going to make today? Okay, perfect. Okay, now here's what you're going to get. You're going to get your pieces again. You've used your pieces a lot. We use those pieces to pretend they were monkeys, and we've made rectangles with them. Before you're going to use your pieces, what shape are you going to make? Then what you're going to do is you're going to draw whatever squares you make. So you're going to look at how tall and how long, and that's how many boxes you're going to use on here. This is going to be the tricky part. You're going to build squares. It's going to be great. You're not going to trace what you build because the squares you build with are bigger than the squares on here. One square is one square. One square equals one square. So we're going to try to model, we're going to try to show on here the size of the squares that you're building. Okay, that's a lot of yakity yak for Miss Zupancic, but what we're going to do now is we're going to get you your materials and raise your hand to tell me, what are you going to do? Let's hear from your words, what are you going to do when you get your materials? What are you going to do when you get your materials? Yes, well, I already gave you the instructions. So what are you going to do first? I know, but that is such a good answer, yes, make the squares. Make the squares and what else?

Unknown Speaker 23:33
Yes,

Jonily 23:42
yeah, well, technically, yes. And then what? Yes, very, good. Okay, here we go. We're gonna get you your paper First things first, put your name on the paper when you get it. Do

put your name on this paper. Yeah,

Speaker 1 24:17
put your name on this I put your name on this.

Unknown Speaker 24:36
Put your name on this.

Jonily 24:39
Put your name on this. Friends, you're each gonna get a paper. You're gonna put your name on that. Go ahead and put your name on this paper. What

Unknown Speaker 24:51
do you think? Sure?

Jonily 24:59
I. You got you guys are great.

Oh, whatever you think you need. I love that question. Great question. You're gonna

Speaker 1 25:17
build your square first, the little square block that you have, you meal things you have, one love it. How many squares you need to create your square perfect

Jonily 25:34
and hear me in 654321,

now, now that we are situated, what I like to do is I like to give you a lot of directions at once. Then I like to give you your materials, and then I like to recap. So now that you have your materials, I want you to follow these directions, put your pieces on your desk surface and put your name on your paper. Your pieces are not going to go on top of your paper today, so push your pay your pieces off your paper, and what are you going to do with your pieces? Tell me, what are you going to do with your pieces? Tell me, what are you going to do with your pieces? What are you making? Tell me not, on top of your paper, beside your paper. So everybody make a square with your pieces. Go make a square with your pieces.

You can't make your squares on your paper. You have to make your squares over here.

Unknown Speaker 26:58
Good one of these. I remember, one of these,

Jonily 27:04
make a square. Make a square. Alrighty. How do you know this is a square? Look at this. Look at this that we think might be a square how many blocks long is it? How many blocks long is this three? How many blocks tall is it? Is three? The same as three? Yes, it is three is the same as three. So that does make a square three and three are the same number, and that's what makes a square. Oh, but let's check this one. How many blocks long is yours? How many blocks tall is it? Is four the same as four? Yes, it is. So this one has a square too

Unknown Speaker 28:06
good.

Jonily 28:09
Oh, let's check this. How many blocks long is your shape? Three? How many blocks tall is it? Count them. How many blocks tall is three the same as three? Are they equal? They sure are. That's how you know it's a square. Now you can draw your square on your paper, but it can only have the same number of pieces that the square is here. You've got a big square pizza. How many pieces long is your pizza? How many pieces tall? Five is five the same as five? Yeah, that's how we know it's a square. So on your paper, you're going to draw your square pizza, but it has to have the same number of pieces as your square. Oh, fix that. Your pencil moved it now, if I ordered a pizza and it had all these middle pieces missing, I wouldn't be very happy. So make sure your pizzas are filled in in the middle. Make sure your pizzas are filled in in the middle. Oh my gosh. I love how you modeled that. That is really fantastic. Now, make a different size pizza. Make a different size pizza. Love this one. Love this one. How many? How many pieces long as your pizza four. How many pieces tall is your pizza? Two? Oh, let's count again. Three. Three is four the same as three? Are they the same number? No, they sure are not. So it's not a square in a square, it has to be the same piece as long. In the same pieces tall.

Oh my goodness, look at this. Let's look at your square pizza. How many pieces tall is your pizza? How many pieces long is it? Is four? The same as four? Are they equal? They sure are. That's how you know it's a square pizza, so you're good. Now you want to model this. Let me ask you this question, though, how many pieces of pizza are in your square let's count all the pieces, and then on your paper, that's how many you need to box in. Let's look at yours. Oh, yep. How many pieces? How many pieces? Long? Four. Wait, it's four pieces long. How many pieces tall?

Five. Five is four the same as five? No. So we don't have a square yet, so make an adjustment and see if you can make a square all right now, how many pieces of pizza are in your square? Pizza here? How many pieces of pizza are there? Nine? Nine on your paper, you need to only show nine of these squares for that pizza. So the number of pieces in your pizza you need to show on your paper. Do you have a square here? How many pieces tall is it? How many pieces long? Is five? The same as five? It sure is. You have a square pizza. How many pieces are in your pizza? Figure that out, because you have to show me this pizza on your grid paper that you made. Let's take a look. How many pieces tall is your pizza? Three? How many pieces long? Two is three the same as two? No. So we don't yet have a square, but you are close. Don't erase this, because this is beautiful. How could you add on to this? To make a square Good? Make me a bigger square pizza and do your drawing. I love it. Here's what we're going to do. Because you are ambitious. That is a very good thing. How many pieces tall is your pizza right now? How many pieces tall?

Unknown Speaker 32:25
Six? Now, if

Jonily 32:26
you have a square, how many pieces long does it have to be if it's a square, well, is four the same as six? No, what number is the same as six? So I want you to make me a square pizza. That's a six by six. I want you to draw it here and tell me how many pieces of pizza there are. You got it? I want you to make a six by six, six, tall, six, long. Draw it here and tell me how many pieces there are. Oh, we're gonna pretend that all of these have blocks inside. Okay, because we don't want to order a pizza and have all these pieces missing. So you're gonna actually shade in all those. But let's make sure we have a square how many pieces tall is your shape?

Unknown Speaker 33:27
Seven.

Jonily 33:27
Let's try again. Ready six. How many pieces long is your square?

Count them again. So your shape is six pieces tall and six pieces long is six the same as six. Are those two numbers equal and the same? Bless you. They sure are. So you know you have a square shade those in and then write the number of pieces in your square. Write the number of pieces of pizza that you have. Hello, I love this is a great model of this beautiful let's check your shape. How many pieces of pizza long is your shape? Four? Four. How many pieces tall is it

Unknown Speaker 34:28
seven?

Jonily 34:29
It's four, the same as seven. So we don't have a square, but don't erase this. Don't erase this because this is a rectangle pizza, a four by seven, and I love it. And we could count how many pieces, but change this so that it's a square. Make me a bigger square and draw it awesome. Back with me in 531,

you all are fantastic. So let's regroup for a moment. We are discovering, well, see, I like you guys to just try to figure things out. And this is beautiful. You're making square pizzas. You're showing how many pieces in your square pizzas on your grid paper. Once you make one, then you're going to make a different size, and then you're going to make a different size, and then you're going to make a different size. But what shapes do they have to be very good. I want you to keep going, and I want you to draw as many squares as you can. Go ahead, keep working. Do you how do you know that's a square? It has four sides. How many pieces tall as your square pizza, five. How many pieces long is? It is five the same as five? It sure is. And you got it right there modeled, and I love it. How many pieces of pizza is in that five by five pizza? Figure that out and write it down. Where's your square? Build your square for me. Good. Check your check how I want you to count how many pieces there are in there. Write it down. Good. You drew that now. Make me a bigger square. Six.

Check that it's a square, see how long, see how tall, and then draw it over here. Keep going. Make another square.

Unknown Speaker 37:00
Love it. Make me a bigger square.

Jonily 37:08
Good. How many? How many pieces long is your pizza? Two? How many pieces tall? Is it six? Is that are those numbers? The same is two, the same as seven? No. So you gotta rework this, because it has to be the same number of pieces long and the same tall. Love it. Model this right there. Good. You are going to draw this right here, however many squares is what you're going to mark over here. Good work. Did you get me a square? Okay, here we go. How many pieces tall is your pizza? Four? How many pieces long as it let's count again, is four the same as six. So it's not a square. Readjust this, and it has to be the same pieces tall and the same pieces long. Okay,

loving it.

I love this. This is really great. Did you make me a square. Make me a different size square and draw it. Make me a different size square and draw it.

Good. Now, model this one over here. How many pieces of pizza do you have in your square? Pizza?

Unknown Speaker 38:57
Three and three. Let's

Jonily 38:59
check. Let's count all of them. 1231231230, how much are three? Threes? That's a tricky one. Count all those pieces and then show that many pieces over here. Did you get a square my girl, you're close. I'm loving this. I'm loving this. Here's my question. What are all the number of pizzas that make squares? Let me ask it a different way. I want you to figure out how many pieces are in this pizza, this pizza and this pizza, there are certain numbers that always make squares. See if you can write those down. Write that down. Write Do you have one with 25 pieces? Check and see if you do. Because she does. She's got now, what are all the numbers of pieces that I can make with square pizzas? I can make a square pizza with 25 pieces. Can I make a square. Your pizza with 12 pieces. Try it. Use 12 pieces and make a square. Use 12 you are in is three and three the same, yes, yes. They are. How many pieces of pizza are in this pizza? Then,

49 nine makes it. Write that number nine because they're trying to figure out what numbers make square pizzas. So if I order square pizzas from the restaurant, I want to know how many pieces I'm going to get my pizzas. Okay, good work, kid. Now, make me a bigger one. Make a bigger one this side of the room, especially my back row here, I want you to count how many pieces of pizza are in each of your square pizzas. So I want you to count how many pieces there are. Because what we're trying to figure out is, when we make these square pizzas, how many pieces do we get in each pizza? So check your first pizza there. How many pieces are in your first pizza there. Count them for me. Show me how you count them. How many is that I want you to do the same thing. Count how many pieces of pizza are in this square pizza. So write that down. You could write it on top or beside you. Sure could.

Unknown Speaker 41:45
I'm gonna write this one down. Okay,

Unknown Speaker 41:49
write that down so you

Jonily 41:50
don't forget it. Because what we're trying to figure out over there is, when we order square pizzas, how many pieces are we gonna get? So if we order a three tall and three long pizza. How many pieces will I get? And if I order a two tall and two, oh, if I order a four tall and a four long, how many pieces will I get?

Speaker 2 42:20
I can't make a square with 12. You what? You can't make a square 12. You can't. Why not? Because there's two and three.

Jonily 42:32
Now this is interesting. She's saying that I cannot order a square pizza with 12 pieces. What do you think about that?

Speaker 2 42:45
Because there's three on one side and two on the

Jonily 42:48
top, huh? All right, friends, come on with me. In 65432,

I love how you are working today. Really love it. Here's a question I'm going to leave you with, if I,

if I call this pizza company and I order one of their square pizzas, could I ever get a pizza that has 12 pieces? Yes,

Unknown Speaker 43:36
I don't know. Hear

Jonily 43:37
me in three, two good put all your pieces in your cup, put your cup on the top of your desk, put your name on your paper, and we'll be ready in two minutes.

Unknown Speaker 43:50
Join us. Two minutes. Jonah,

Cheri Dotterer 43:53
will we do a session? Hear me teach the 120 chart? Join us in.

Transcribed by https://otter.ai