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# Challenge Is Constant: The Caterpillar Game and Real-World Math

Math Educator in NYC
Transcript

## Constant Challenges Push Students to Strive for Success (Transcript)

Alicia: I need my game master to please retrieve a bin of blocks and I need my supply master to retrieve your supplies.

Constantly challenging kids in the classroom affects learning, depending on the challenge. And I think at Quest, which is something that really drew me to Quest, and what we do really well, is that in each class we challenge them in different ways. So they don't always know what to expect, which is totally different than the traditional classroom, which I've never seen any other school do, or do well.

Student: Yeah, my worthless turn.

Student: [ laughs ]

Student: You know what, you could borrow mine.

Student: No, we're done, we're done, we're done.

Student: Angus, roll one more time.

Student: Get a six, get a six!

Student: Six.

Student: No, I think I'm winning because I--

Student: Six is the bomb... Yaaww!

Alicia: Caterpillar is a board game. It uses dice and it uses colored blocks and you can play it with either two, three or four people. The goal is to create the longest caterpillar, but when you record the dice rolls, you are looking for something called the bomb. So the bomb is the most frequently rolled number and as you play, you figure out that the most frequently rolled numbers are towards the middle, so your five, six, seven and eight. And you try to build as much around it as possible, so you can get more blocks, but in the end, if that number blows, all of your caterpillar pieces go with it. So it's using skill but it's also using chance.

Student: It depends who the players are you're playing with because some are really good and some like, you know, are like me, are like beginners, because I usually don't win every round of Caterpillar that I play. I usually win like out of five, only once or twice. But yeah, it depends on the person. It doesn't depend on the game, but on the person.

Alicia: When you have problems that are just out of your reach in school or in life, you learn how to roll with the punches and figure out, "Okay, I have this skill set and I just learned this from this past challenge, and now this past challenge is solved, but I have this other challenge over here." And if it's constantly changing and you have these skill sets that are also adapting and changing with you, giving them things that are just out of their reach requires them to build that like mental muscle. It strengthens something, whether it's your mind or physically, and if we gave them challenges that just met where they are, their toolbox, their mental toolbox would never grow.

Student: It's also fun building out your caterpillar and seeing how much land you can like preserve for yourself. Like I always enjoy conquering the most land and feeling that I've really accomplished something.

Alicia: I can't speak for any other discipline but I know in math, it's allowed me to see really quickly and easily where my students are and what their weaknesses are and what their strengths are and what they're being asked to do and, a lot of times you fail at giving them the right challenge problem. And it's through that failure that you learn how to adjust and you learn what you're looking for.

Student: Without challenge, it would just be like, in a game for example, it would just be like, it doesn't really matter who wins and it won't be as fun.

Student: Caterpillar is fun to play because the game is challenging and you want to have the longest caterpillar at the end of the game, after the bomb explodes.

Student: It's always about what one number will be rolled the most and which one will be the bomb and getting away from that area and getting to an area that will also be rolled a lot, but not as much.

Alicia: The toughest part of teaching and of doing anything where you want anybody to learn, it's about knowing where your students are and knowing what their limits are at the moment, and stretching that limitation. Because I don't care what end of the spectrum you're on. I don't care if you know everything in middle school math, I can find something to challenge you. And I promise you I will, and it will be tough.

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Credits
• Director / Camera / Editor: JR Sheetz
• Associate Producer, Edutopia: Douglas Keely
• Senior Manager of Video, Edutopia: Amy Erin Borovoy
• Special Thanks: Quest to Learn, Alicia Iannuci and her students

This video was originally produced by Institute of Play, and was made possible through generous support from the Carnegie Corporation of New York and the John D. and Catherine T. MacArthur Foundation.

In my sixth grade integrated math and ELA class at Quest to Learn, students play a board game called Caterpillar to learn about probability and statistics. As a founding teacher at the NYC public school with a unique game-like learning model (currently in its fifth year), I have worked through many iterations of this game and how it affects students' mathematical experience over the years.

What makes Caterpillar particularly effective is that, as my students are introduced to the game, they are playing it through three different learning lenses:

1. The basics of the game -- rules, components, core mechanics
2. The learning goals of the game -- how to successfully win
3. The skills they develop -- how to use the game's mathematical concepts in the real world, as they apply their content knowledge to modify the existing game

Caterpillar offers a great example of how to level your students up through any game so that they master the gameplay, master the learning goals, and apply what they've learned in one seamless experience.

Two students playing the Caterpillar board game at Quest to Learn.

### Mastery of Gameplay and Rules

Caterpillar is a two- to four-player board game, played with colored blocks, two dice, and a frequency chart for recording each dice roll. The goal is to build the longest caterpillar with blocks by the end of the game. Each player begins the game by placing two blocks on any two mushroom spaces they choose. Each turn consists of a player rolling the two dice and recording the sum on the frequency chart. Any player with a block on a mushroom space touching the sum rolled receives an extra block of his or her color. Each turn also includes the opportunity to place accumulated blocks in order to build the longest caterpillar on the board.

The game ends when there are no more spaces available on the board. Players then reference their dice rolls on the frequency chart to determine the most frequently rolled number. That number is the "bird," which eats the caterpillars at the end of the game. Players must remove pieces from any space around the number that has been determined to be the bird. The player with the longest caterpillar intact at the end of this explosion is the winner!

Due to the content level, Caterpillar is most appropriate for middle school grades (6-8).

### Mastery of Learning Goals

The learning goals in Caterpillar are for all students to master the related probability and statistics content by developing strategies to win the game.

How to: Through the first few game plays, your students might begin to realize the distinction between a "good" and "bad" first move, based on where they place their first two blocks on mushroom spaces. You can help students notice that these spaces correspond to the most and least frequently rolled two dice sums, which is a concept that students are introduced to in the game, as they start noticing that sevens are rolled much more frequently than twelves, and so on. Students quickly make the visual connection between the theoretical probability of rolling two six-sided dice many times and the experimental probability of the same event through rolling the dice in the game and recording them in the frequency chart. Have all classes record each dice roll on a larger frequency chart in the classroom, and a bell curve begins to appear as classes compile all the data through many rounds of gameplay. This allows students to make connections between the traditional content and the real world experience of the mathematics in games.

### Applying New Skills in Real-World Context

The ultimate goal in Caterpillar is for students to apply their mathematical knowledge by working together to develop modifications to improve the game. This challenge embodies one of my favorite phrases: "Math is a verb." Students are asked to do new things with the mathematics they're learning, and it looks different to each student.

Task your students with playing the role of game designer by making changes to the game board, rules, and/or core mechanics, and by collecting data to justify the changes they choose to make. You can do either of these:

• Ask students to make a simple modification, like filling in a blank game board with new number positions.
• Let students conduct their own inquiry into deeper modifications by:
1. Identifying the components of the original game that they enjoy and wish to keep in their modified version.
2. Brainstorming around the components that they wish to modify, delete and/or add to the original.

You can then have students draft quantitative research questions based on the parts of the game they wish to change, such as:

• What happens to the game if you use three dice instead of two?
• What if you use four-sided dice?

Groups can compile data to justify their Caterpillar mods by asking their research questions to classmates, peers, and other teachers and staff familiar with the game. Some of my students' past modifications included:

• Building and using a 3D game board
• Using three dice
• Creating a version of the game in Minecraft

This modding project allows students to stretch their understanding of the mathematical concepts in an engaging, challenging context that reflects their interests as both gamers and designers.

### Doing the Math

Having ownership of their mathematical explorations allows students to develop and sharpen their existing skillsets in order to meet (and hopefully exceed) new challenges. Through experiments with setting appropriate goals and increasing expectations for students by providing different levels of challenge in a lesson or activity, you can model the process of continuous learning, and help students learn how to keep challenging themselves. Games like Caterpillar allow students to proceed at their own pace, to fail and fix the mistakes they make, and to ultimately give real value to mathematics through experience. Math isn't something you learn -- it's something you do.

Intrigued by game-based learning, but not sure where to begin? Edutopia's new Made With Play series takes a look at game-like learning principles in action and commercial games in real classrooms -- and offers tips and tools for bringing them into your own practice. Get more resources for game-based learning here.

Videos made possible through generous support from the Carnegie Corporation of New York and the John D. and Catherine T. MacArthur Foundation.

The Made With Play series is a co-production with Institute of Play.

Made with Play: Using Games for Learning
Game-like learning principles in action, commercial games in real classrooms, and tips and tools for bringing them into your own practice
Math Educator in NYC

Hi Again Isabel,

#1- After placing their initial two blocks, players can only accumulate new blocks when the right dice rolls pop up. If I placed one of my original blocks on a mushroom space that was touching a 5, for instance, and somebody rolls a 5, then I get 1 block. and so on.

#2- If you run out of blocks, you can still get new ones, yes. But also, if the game ends and there are no available spaces, than you can't put your blocks anywhere. I'm not quite sure I understood that question.

#3- Anyway, no matter whether you have blocks or you don't have blocks, you Always roll the dice.

And yes, that sounds great that you'll have them visualize the frequencies through charting in some way. I find that one of the most interesting things in this game is that 7 is not always the most frequently rolled number, but if you chart enough games (for example, if you combined all the data from all of your classes) then there is a good chance that the chart will look more "normal", and that 7 will be the most frequent. makes students think...

Andy XU RUNYUN
From Shanghai, China. A volunteer in Walnut Valley Unified School District.

In my humble opinion, as well as letting students obtain skillful knowledge, the Caterpillar Game also cultivates them with their leadership skills with great efficiency, since it allows students learn how to lead, to collaborate, to learn the rules, and to win.

Annette

Daniel, would you have the complete version of "how to play" in one document? I read this a couple of times and your answers cleared some things up. My question is if someone else rolls your number then they give you a block. Will it be your color or their color?? Do you put one block down or two blocks? So the only caterpillar you can grow is from the two numbers you picked originally? Anytime anyone else rolls your number then you get a block, right?

Hi Annette,
To the question "if someone else rolls your number then they give you a block. Will it be your color or their color?"-- Nobody gives anybody their own blocks. There is simply a big bucket/pile of blocks (like a bank), and you get to take your color when the relevant numbers are rolled. Players don't lose blocks to each other, or blocks to other players.
So to directly answer your question then, Yes, it will be your color. Does that make sense?

When it is your turn, you may put down as many blocks as you have accumulated, though you don't have to put them all down, if you'd prefer to wait until your next turn. (rarely done, I'd say)

Yes, the only caterpillar you can grow is from your original two blocks. Connecting them up would be great, right? That's a big part of the strategy (both for you and for blocking your opponents, and vice versa).

Yes, any time anyone rolls your number then you get a block.

To the question of whether we have a complete "how to play" in one document: We are in the process of making these types of documents available, though we do not yet have one available for Caterpillar. Here's a link to the materials that are currently out. (plus, video tutorials!)
http://www.instituteofplay.org/work/projects/print-play-games-2/
http://www.instituteofplay.org/work/projects/print-play-games-2/absolute...
http://www.instituteofplay.org/work/projects/print-play-games-2/socratic...

I hope this helps. Let me know if anything is still unclear. We'd love to know how it goes if you play your own version! (and especially if students make modifications of their own :)

Annette