# Beast Belly: Fraction Game

## by prof_Ruggles, published Feb 26, 2016

Beast Belly: Fraction Game Feb 26, 2016
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# Summary

Fill the Beast's Belly with tokens to make one whole then add a feature!

Allow students to approach learning, understanding, and adding fractions with this game. Everything from the printing to the game are treated as “part of a whole” for students to practice fractions throughout the process. The game was created with Grade 3 Common Core Unit 5, Lesson 12 (5.12) in mind, but can be played by anyone!

# Print Settings

Printer Brand:

MakerBot

Printer:

MakerBot Replicator (5th Generation)

Rafts:

No

Supports:

No

Infill:

10%

Notes:

Standard quality, Layer height 0.20 mm, 2 shells

# How I Designed This

Design

Every design should start with research and the destination/implementation in mind. Knowing this, I spoke with some friends who are teachers and asked what lessons their students could use some extra help. It was clear that adding and understanding fractions were a struggle for some students.

Model + Prototype

My idea then grew as a game—playing fractional discs to fill one whole

Now that the topic was in place, I turned to Autodesk Maya to build the prototypes and create test prints. I still allowed the idea to grow as the design process continued, but the core of the idea was already established.

I began by modeling the belly and the tokens to print them as a prototype. My goal was to make sure that the printed version of the tokens were accurate in proportion to the Beast’s Belly, so that when you put 1/8, 1/8, 1/4, and 1/2 it filled the Beast’s Belly precisely. Creating prototypes, it was clear that the design worked in proportion at a smaller scale, so I began creating the Beast Belly Base with its sections for added Features.

To create the Beast Belly’s Features, I went through 2 phases. The first was to come up with ideas for shapes (cat ears, a cruly tail, etc) and the second was to make sure that when they were printed, they would fit well into the final base.

Autodesk Maya: Boolean process. One model is carved out of another model using this command

Autodesk Maya: Beast Belly Base model with wireframe overlaid and looking through

Autodesk Maya: All pieces in Maya. The blue plane shows the print area so I can see how my objects will position on the printer

# Project: Beast Belly

Objectives

**The models, game, and worksheets were created based off of Grade 3 Common Core Unit 5, Lesson 12 (5.12) and reflect objectives with that in mind. I encourage anyone to add comments on how they used/implemented/assessed using this model.

1. Identify and represent fractions equal to and between whole numbers by reasoning about their size.
2. Express whole numbers as fractions
3. Recognize fractions that are equivalent to whole numbers

Audiences

1. Grade 3 (this is the Primary Audience based on Common Core outcomes)
2. K-8—this game would also be helpful for any Primary School Students, for hands-on review or preparation for the learning outcomes

Preparation

It is not necessary, but students may have an introduction to fractions as numbers equal to and between whole numbers. Students can use this game to reinforce these learning outcomes, but any student can fill the Beast’s Belly!

Steps

**These steps are for students and teachers who are using Beast Belly as part of their approach to learning and reinforcing fractions. Teachers may opt to simply print out all the pieces and use Beast Belly as a game. To allow excitement and awareness to 3D Printing use the suggested steps below:

1. Introduce fractions as part of your regular curriculum
2. Show Beast Belly on Thingiverse and use the opportunity to talk about STEAM (Science, Technology, Engineering, Art, Math) as well as problem solving, design, creativity, and 3D Printing
3. Teachers are encouraged to place students into 5 groups and have each group “responsible” for setting up and printing one part of the game’s set.
• Please note that one “set” is outlined below. Teachers may decide to print more or less depending on the final needs of the class and the learning outcomes.
• To allow the optional worksheet to reinforce fraction knowledge best, print in the following order:

1. Two 1/2 tokens
2. Eight 1/8 tokens
3. Features: one face, two tails, two ears
4. Four 1/4 tokens
5. One Beast Belly
• Other pieces that are available (but not part of the optional worksheets) are different facial features and other tokens
4. (Optional) Distribute the worksheet (or create a similar worksheet) to reinforce that one whole can be divided in many different ways. This will also help students stay engaged while the object prints. Printing in multiple set-ups will allow printing in different colors. Having different pieces be different colors may help students quickly identify tokens representing one fraction. Different colored tokens is recommended, but not required.
• When a print is completed, have students fill in the appropriate part of the number line and color in the piece that has successfully printed.
• Reinforce that measurements of one whole can be taken in many ways. For example: The Beast Belly Base is only 1 piece (1/20) of the whole game, but it takes almost half the time and half the amount of materials needed for the whole game.
5. Once all pieces have successfully printed, play the game!

One Set Example image

Steps: Game Rules

Suggested 1-4 players.
The Beast’s Belly is empty! Can you help the Beast find its face, ears and tail by filling its belly? Be careful not to overfill the Beast’s Belly—only a perfect 1 whole will satisfy the Beast’s Belly. How many different ways can you make 1 whole?

1. The teacher mixes all tokens in a mixing container and randomly distributes 4 tokens to each player. The left over tokens go back into the mixing container.
2. The teacher decides who will go first
3. The first player plays one token into the Beast Belly
4. Go clockwise to the next player. The next player plays a token.
a. If a student cannot play because their tokens will overfill the Beast Belly, their turn is skipped. (The teacher may opt to allow students who cannot play a token to pick another piece from the mixing container, but not play a token that turn)
b. If a student runs out of tokens, they are given 4 new random tokens from the mixing container
5. This repeats until the Beast Belly is full. The Beast Belly may not overfill.
6. The student who places the last token into the Beast Belly to fill one whole empties the Beast Belly and chooses a feature (face, tail, ear) to position on the Beast Belly Base.
a. Note: the ear and tail are the same size, so if a student is feeling silly—place the tail in the ear! The face is also square, so it may be places sideways, up-side down or right side up.
7. All students help place the tokens that filled the Beast’s Belly from smallest to largest in front of the student who placed the feature
8. The student who placed the feature describes how the Beast Belly was filled. Example: “Beast Belly is full because one whole equals 1/8 plus 1/8 plus 1/4 plus 1/2.”
9. All tokens that were used to fill the Beast Belly go back into the mixing container.
a. Students who still have tokens keep their tokens in front of them
b. Students who have no tokens immediately get 4 new random tokens from the mixing container
10. The turn order continues from where the play stopped
11. Fill the Beast Belly again, turn by turn
12. When 3 features have been placed, the student who places the last token for the last time, places the last feature. All student help to order the tokens from smallest to largest in front of the student who placed the feature. The student who placed the feature describes the tokens that filled the Beast Belly: “Beast Belly is full because one whole equals 1/2 plus 1/2.” After the one whole is described, the Beast Belly is fully featured so all students yell “BEAST BELLY!!” The game is over.

**NOTES:

1. If the 2-whole Beast Belly is used in play, the 2-whole Beast Belly should only get a feature when both bellies are full. The same procedure is followed, except now students describe what it takes to fill 2 wholes instead of one whole.
2. Consider having multiple Bellies in play or mixing in some more complicated fraction tokens for more advanced students—Keep printing and expanding!

Optional Worksheets attached as PDF in files tab

Results + Assessment

1. Students learn how to set up a print based off of their assigned portion of the game
2. Students will be able to play the game at the conclusion of the printing
3. If the optional worksheets are used, teachers may consider grading/assessing the successful completion of the worksheets

Quick Reference for printing time and printing material needed for each piece or common sets

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While I recognize this is an educational game for 3rd graders, I can't help but notice that there are some areas of improvement to make this a truly enjoyable game, while still retaining the cooperative aspect. Here's a few thoughts:

Drawing from a bag makes it hard to be truly random with manipulatables, since they could feel for the 1/2 every time. Hence the reason that an impartial 3rd party needs to intervied. You say "teacher", I say "DM". What if instead the pieces were dumped on the table and arranged in a triangle, like bowling pins. Players would be able to draw from the bottoms of the triangles, provided that piece isn't blocked by any pieces lower than it. Kind of like drawing cars in tri peaks or Mojang solitaire. And at the top of the triangle is a hero that your monster needs to be strong enough to defeat. Your monster fights by rolling a dice associated with the parts on them. So if they have a green arm, a blue arm, and a green face they can roll a green dice, a blue dice, and another green dice. The heros on the other hand always roll 3 of the same colored dice. The dice have a sort of "rock/paper/scissors" icons on them but are weighted so that each dice has a higher chance of beating another certain color. To win more of your dice have to turn up favorably against the heroes dice. So you can weight your monster to beating a green hero by loading up the red parts, but then it'll be weak against the orange hero. This entourages variety or in the case of team play, cooperating to loading up multiple monsters to prep them to defeat a certain hero.

Also, add 1/6 and 1/3 counters to the pile. Now it may become possible to lock up your monster, so they'll be encouraged to think ahead. You've got a 1/3 in there, you'd better hold of on those halfs and quarters.

This is a really cool concept. I printed the whole thing at 1.25 scale to make everything a little bigger. If I do it again I might go to 1.5 as the slots are still a bit small for even little fingers. If you are ever up for refining it I'd love to see a "1" piece added along with more monster parts and a more monster shaped body. I'm new to 3d printing so this was a great build for my kids and I. My daughter is designing a game box right now.

Thank you! I have modeled a 1 whole piece and am working on more ears, tails, and faces as well as slight fixes to enhance the print time of the body and other pieces. You'll see that in the next edition.

Feel free to suggest pieces you'd like to see!

The thought comes that the face can be in 3 segments, mouth, nose, eyes, with different sculpted parts and that students can mix and match face parts for more of the funny.

Thank you for making this model available. Your model was shared in my 3D Printing in the Math Classroom presentation at the Virginia Council of Teachers of Mathematics conference. The full presentation and resources links are available at http://designmaketeach.com/3dmath/

I've also created a collection of useful classroom models. http://www.thingiverse.com/DesignMakeTeach/collections/3d-printing-in-the-math-classroom. Please feel free to share any suggestions or resources that support 3D printing in the math classroom.
-Josh

Thank you for sharing - love seeing ways 3D printing can be educational and not just fun toys. :)

I ran into an issue with printing from BeastBody_oneWholeSet.stl. After printing, the face won't fit in the body. Measuring the dimensions using NettFabb the face is 36.05mm wide and 36.16mm tall. The face opening on the body is only 35.61mm wide. So, one or the other needs to be resized in that file. Thanks and have a great day. -Josh

You're probably overextruding. One of the foibles of FFF printing is that minor differences in filament diameter means significant differences in the ability for models to fit together accurately. These parts could probably be made loose without consequence, but if you need a tight fit this can be a pain, especially since it means re slicing the models with different settings for every different roll of filament you use.

Josh,
Thank you for the comment regarding the face feature. I have resized the feature and it should fit now--please see the "v2" files. I suggest downloading and opening the .thing file with the features, this will allow you to select the pieces you do not want and delete them while keeping only the face(s) you wish to print.
Thanks again

I would like permission to share a link to this project and physical examples at my 3D Printing in the Math Classroom presentation at the Virginia Council of Teachers of Mathematics conference. Thank you. -Josh

Josh-
I appreciate your post. I would be thrilled to be a part of the 3D Printing in the Math Classroom presentation at the Virginia Council of Teachers of Mathematics. If you are able, please share pictures of Beast Belly in VA!
Thank you Josh.

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