Three-Act Tasks: Modeling Addition Transcript
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Sophia: One, two, three, four, five, six--
Student: I wrote the letter six and then there’s nine.
Kristen Alfonzo: The thing I enjoy most about three-act tasks is it makes them interested in something right away and makes them personally invested in thinking about math in the real world.
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Three-Act Tasks:
Modeling Addition - Kindergarten
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Kristen Alfonzo: We are gonna do a three-act task today like we have done before. And we know in three-act tasks, Satchel, that we start with watching a video. Our video today is about a birthday party.
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Kristen Alfonzo
Kindergarten Teacher
South Shore PK-8, Seattle, WA
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Kristen Alfonzo: We start off with a video or a picture, an image, something that the kids can get interested in and then we ask them what do they notice about the video, what do they wonder about the video. In kindergarten I usually try and remind them that we are thinking about math.
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Act One
The class discusses a high interest video or picture of a real-world situation.
Kristen Alfonzo: Are your eyes on the screen?
Student: Yeah!
Kristen Alfonzo: Here we go.
Children: Happy birthday to you, happy birthday, dear Abby [ph?], happy birthday to you!
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Kristen Alfonzo: Okay, give us a private thumb if you think you have something you notice, something you’re wondering about the video? I want you to quickly turn knee to knee, tell your partner what do you notice or wonder about this video.
Student: There’s so many candles. I wonder how many are candles. How many stuff are in the bag?
Kristen Alfonzo: Modeling’s important because that’s how we use math in the real world. It’s in life. They’re not gonna be able to reason with their partner at the grocery store in the future how much their budget can afford if they don’t know how to explain their thinking.
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Kristen Alfonzo: Amira, what did you notice?
Amira: I wonder how many candles.
Kristen Alfonzo: How many candles are there? If you are also wondering how many candles are there, would you do this? Say, “Me, too. I was thinking the same thing.” Solaiya, what’s your notice or wonder about the video?
Solaiya: I wonder who’s gonna blow the candle off the fire.
Kristen Alfonzo: Who will blow the candles out?
Solaiya: Yeah.
Kristen Alfonzo: Sophia, what were you noticing?
Sophia: How many napkins?
Kristen Alfonzo: How many napkins? Orelio [ph?], what were you wondering?
Orelio: How many birthday bags?
Student: There are five.
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Kristen Alfonzo: How many birthday bags. There are so many things to notice about this birthday.
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Kristen Alfonzo: The math can be anything the kids truly want to solve. So, tomorrow, if my kids say, “You know, I was really wondering how many cups there were,” we can go back and say, “Well, what information do we need? How can we find that information and solve it from there?” So it’s taking, like, a real-world scenario and helping them notice where the math is and then not only being able to find an answer, but also having to model their thinking, how they solved it.
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COMMON CORE STATE STANDARD
Math Practice 4: Modeling with Mathematics.
Students apply the mathematics they know to solve problems in contextual situations.
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Kristen Alfonzo: We are all wondering how many are there of all of those things. I was really wondering about the candles. It’s kind of hard to tell exactly how many candles there are. I see some people counting. You have some guesses? I tried counting, but it was hard for me to see.
Student: Twelve. Twelve. Twelve.
Kristen Alfonzo: How many candles do you think there were? Minyette?
Minyette: Twelve.
Kristen Alfonzo: Minyette believes there were twelve candles. Do you have a different number you want to ask? Russo [ph?], what do you think? What’s your guess?
Russo: Thirteen.
Kristen Alfonzo: Thirteen candles.
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Act Two
The class identifies the information needed to answer a mathematical question about the situation
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Kristen Alfonzo: Should we find out exactly accurately how many candles there really are?
Student: Yeah.
Kristen Alfonzo: Okay, so we have some information to help you with that. Everyone say out loud, how many blue candles are there?
Children: Six!
Kristen Alfonzo: There are six blue candles? Can we find out exactly how many candles there are now? What other information do we need to find out? How many candles all together? Rose?
Rose: Twelve-- yellow.
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Kristen Alfonzo: How many yellow candles? Do you agree with Rose? We need to know how many yellow? Solaiya agrees, Louie agrees, okay. How many yellow candles are there? Can you say it with me all together? How many yellow candles are there?
Children: Nine!
Kristen Alfonzo: Nine. Okay, we know there are six blue candles and nine yellow candles. Do you have the information to find out exactly how many candles there are on the cake now?
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COMMON CORE STATE STANDARD
Represent addition and solve word problems.
Student: Yeah.
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Kristen Alfonzo: The three-act tasks engage every single kid, not just by having a video, but also, especially I think for my English language learning students, they’re able to have a constant visual up there and something to attach it to, so they’re not trying to puzzle through the language and the words I’m giving them.
Kristen Alfonzo: Think you can find out? We have our guesses, but we have so many different numbers. We want to find out exactly how many. Are you ready to go to your tables and find out?
Children: Yes.
Kristen Alfonzo: Then they go off to their desks and solve the problem or model the math thinking that they’ve been doing. Sometimes they work on their own, sometimes they work with a partner.
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Kristen Alfonzo: So how many all together?
Student: Eleven?
Kristen Alfonzo: You don’t sound sure. How could you be sure?
Kristen Alfonzo: Use cubes.
Kristen Alfonzo: Cubes. Okay, how about if I come back. He’s showing you six. What is that from the video? What is that number six?
Orelio: Six and nine. I think I’ll need four hands.
Kristen Alfonzo: You need four hands.
Orelio: ‘Cause Minga has four hands. I mean, Minga has two and I have--
Kristen Alfonzo: So you have four hands to use. So Orelio, you said you were showing six blue. What do you need your partner to show for your idea?
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Orelio: Nine.
Kristen Alfonzo: The nine yellow. How can we find out now how many candles all together?
Orelio: One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen.
Kristen Alfonzo: So you think there are how many candles all together?
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Orelio: Fifteen.
Kristen Alfonzo: Fifteen.
Kristen Alfonzo: I noticed that because we chose numbers higher than ten they couldn’t be successful with just their fingers alone. Two students got creative and used each other’s fingers, which was an excellent strategy. But I also saw that kids went directly to direct modelling. So they either used a drawing or tally marks or cubes to show exactly how many candles there were.
Student: I put six here and I put nine right here.
Kristen Alfonzo: And how does that match the video again? Six blue candles, right? Where was the nine in the video?
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Student: Is yellow!
Kristen Alfonzo: Nine yellow candles. You have--
Student: Nine, ten, eleven, twelve, thirteen, fourteen, fifteen.
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COMMON CORE STATE STANDARD
Math Practice 1: Make sense
and persevere in solving them.
Kristen Alfonzo: Fifteen. Fifteen candles on the cake.
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Act Three
The problem is resolved and students share solutions strategies.
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Kristen Alfonzo: Right now is our time for us to be sharing out the strategies we use to find out how many candles are on the cake and it’s also time for us, Lily, to hear and listen to how other people did it. That’s how we learn new ways of doing math and new ways of thinking is by hearing other people’s strategies. So Amira offered to share her good thinking with us. Will you come on up, Amira? She’s gonna teach us how she solved the problem. Can you tell us a little but about your first drawing?
Amira: I used six blue candles.
Kristen Alfonzo: Where are those? Can you show us the six blue in your drawing?
Amira: And there’s nine yellow candles.
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Kristen Alfonzo: So how did you find out how many candles were on the whole cake?
Amira: Because I looked on the screen.
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Kristen Alfonzo: How did-- did you use your picture to help you? How did you use your picture? Did you count them all? One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve-- will you count with me? Thirteen, fourteen, fifteen. If you also came up with fifteen candles, please touch your head. But just like Amira, many of you had a different number to start with. Amira, can we share what happened with
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you? At the beginning didn’t you guess there were ten? And I see you wrote “ten” and I also saw other people do this. Did anyone else look and say, “Well, I guess there were eleven or fourteen. And so there has to be that many!”
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Kristen Alfonzo: Kids were thrown off by their estimate. We had never done an estimate in my class before. So at the beginning of the task they all said, “Oh, let’s-- when we find out how many candles there are,” they immediately, of course, started counting and then they really took ownership of that number that they really thought they saw on the screen.
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Kristen Alfonzo: So Amira drew the ten that she knew she thought there were, but then she thought, “Wait a minute. That doesn’t actually match the video.” So she revised her thinking, did a different picture and found out the number fifteen. And that’s okay. It’s okay if our first guess isn’t the correct one.
Kristen Alfonzo: So I think my next step is to talk a little bit about estimation and why it’s okay to revise thinking if our first guesses aren’t correct in math.
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Kristen Alfonzo: Satchel, would you be willing to share your strategy with us? Satchel used cubes. How did you use cubes? First you had six. How did that match the video?
Satchel: Six blue.
Kristen Alfonzo: Six blue candles. And then--?
Satchel: Nine yellow.
Kristen Alfonzo: Okay, then what?
Satchel: I counted them.
Kristen Alfonzo: How many candles did you decide were on the cake?
Satchel: Fifteen.
Kristen Alfonzo: Fifteen all together.
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Kristen Alfonzo: I love that three-act tasks are usually just difficult enough that even if kids can figure out really quickly on the carpet, they still have to go back to their tables and show us and be able to prove their thinking to us.
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Kristen Alfonzo: You worked hard today to watch a video, notice what was happening in it, think about the math you saw happening at that birthday party, and then you solved a problem. You made a model with a picture or with your fingers or with cubes to show how many candles were on the birthday cake.
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Kristen Alfonzo: They did an amazing job of solving the number story correctly, first of all, and also of showing their ways of thinking.
Kristen Alfonzo: Everybody give yourself a pat of the back. That was a lot of great thinking today.
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20 Comments
Lori Alford Feb 19, 2019 8:00pm
Where can teachers access the birthday party video?
Lee Weaver Jan 13, 2019 6:01pm
Do we access to the video you used for the birthday cake? Would love to do this with my kindergarten students.
Kathleen Bailey Aug 26, 2019 8:09pm
Did you get an answer for this? I would love the birthday cake video to utilise with my kindergarten class.
Meghan Ohumukini Mar 22, 2018 12:14pm
Bonnie Makovec Aug 10, 2017 1:25pm
Rhonda Richmond Jun 23, 2017 9:49pm