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Building Collaborative Groups with Broken Squares

In his book The Culture Code – The Secrets of Highly Successful Groups, Daniel Coyle refers to a competition at Stanford. In it business students in university squared off against kindergartners. The four-person teams had to beat the clock and build a tower using uncooked spaghetti, tape and string with a marshmallow on top. You would think that obviously, the group of MBA student would easily outperform a group of kindergartners. It turns out it’s good to act like a bunch of 5-year-olds. Well, at least when it comes to working in a groups. The kindergartners do better than the business school students.

Coyle further mentions a “sociometer” which can measure the energy level of an interaction, and use it to determine levels of engagement. Most important, it can combine its data with email and social media to form detailed maps that reveal the inner workings of a team, company, or classroom. There are lots of interesting insights he derives from that.

Alternatives to the Spaghetti Tower Competition

You may not wish to invest in a spaghetti tower competition or a sociometer. However, you might try the Broken Squres exercise that’s worked for me in putting teams of four to compete against each other. Or, see further below, a variant of the game of Blokus and other games reimagined.

Table of Contents

Broken Squares

Broken Squares is a fun exercise I learned on the path to my teaching credentials was Broken Squares (see various links below). You pit the groups of four against each other where each group, without speaking must complete making four squares from four envelopes of pieces give to each participant. You only win when all four squares are completed.

The sets of four envelopes are grouped such that only one holds all the pieces to make a square. The others can’t successfully complete their squares unless they get pieces from the other participants including the one who had a complete set. As you observe the competing teams, you’ll often see someone compete their square and get frustrated that his or her teammates aren’t doing their part. The team that collaborates by giving up pieces (you can give but not take and no talking) of their, possibly already completed square, to allow their teammates to all complete their squares is the one that gets all four squares.

Broken Squares

Observing the group dynamics and then talking them through can be quite insightful. You might even choose to make the envelopes with a complete set to the people that tend to be leaders to help them discover how effectively and collaboratively they lead.

In The Culture Code – The Secrets of Highly Successful Groups, Daniel Coyle goes into the various aspects of how teams function effectively. After doing a broken squares exercise, this might be a good book to suggest to your leaders.

See Also:

Blokus: Collaborative Edition – Rules for Building Together

As a former school teacher and a manager of teams at disruptive tech companies, I used to love using the Broken Squares challenge to help shift focus from competition to collaboration. It came to me that other competitive games could be shifted to teaching collaboration. The first example that came to mind was Blokus. In traditional game play, the objective is to be the first and only player to place all your pieces on the board according to placement rules. In order to win, a standard strategy is also to block other players from accessing spaces where they might place their pieces. The objective is to place as many pieces (ideally all, but that’s harder than you might imagine) pieces of all players on the board as quickly as possible. Once a piece is placed, it cannot be moved.

Download the Blokus: Collaborative Edition – Facilitator Guide

Blokus - new rules - collaborative edition

Objective

Work together as a team of four players to place as many Blokus pieces from all colors on the board as efficiently as possible.
The shared goal: fill the board with as many pieces as possible, following standard Blokus placement rules — but replacing competition with cooperation.

Setup

  • Use the standard Blokus board (20×20 for XL or the regular version).
  • Each player selects one color (blue, red, yellow, green).
  • Arrange all pieces by color beside the board.

Gameplay

  1. Starting the Game
    • The game begins as usual, with each player placing their first piece so that it touches one corner of the board.
    • Play proceeds clockwise.
  2. Turn Order
    • On each turn, a player places one piece of their color on the board.
    • The piece must follow the traditional rule:
      • It must touch another piece of the same color at one or more corners, but never along an edge.
  3. Collaboration Rule
    • Players are encouraged to discuss strategy aloud — planning together how to maximize coverage of the board.
    • The aim is not to block, but to build connections and bridges that enable everyone’s remaining pieces to fit.
  4. Helping Moves (Optional Rule)
    • Once each player has placed their piece, they suggest or assist the next player with placement ideas.
    • Alternatively, if agreed before play begins, players may take turns placing any color — symbolizing team ownership over all pieces.

Winning the Game

You win as a team when:

  • As many pieces of all colors have been successfully and according to touching rules been placed on the board before running out of legal placements, or
  • The team fills as much of the board as possible before time runs out on a timed exercise.

Note: placing all the tiles is actually quite difficult and may require quite a bit of collaboration. If you look closely, you’ll note some violations in the attempt below…

Blokus - Trying to Mazimize Tiles Places - All Colors - All Players

For example, each corner piece is not kitty-corner adjacent to a like-colored piece. However, otherwise, there’s some nice symmetry.

Scoring Options (for classrooms or workshops)

  1. Time Challenge:
    • Set a timer (e.g., 20 minutes).
    • The team that places the most total squares (sum of all colors) wins.
  2. Completion Challenge:
    • Compete to see which group can successfully place the most, ideally all pieces first. Note, without a time limit, this can take quite long as it’s not as easy to use all pieces as one might think.
  3. Reflection Round (mandatory for learning settings):
    After the game, pause to discuss:
    • What helped or hindered collaboration?
    • When did individuals sacrifice ideal moves to support others?
    • How did the conversation shift from “my color” to “our goal”?

Learning Objectives

This version transforms Blokus from a zero-sum game into a collaborative system exercise:

  • From competition to coordination: Success depends on shared spatial planning and communication.
  • From scarcity to abundance: Players learn to optimize the collective board space.
  • From self-focus to system-focus: The group experiences how generosity of space and perspective creates shared success — mirroring the insights of Broken Squares .

Variations

  1. Silent Mode: Play without speaking for the first 10 minutes — echoing the original Broken Squares rule — to highlight nonverbal collaboration.
  2. Adaptive Teams: Allow groups of 3–6 people; in larger groups, two players can share a color, practicing negotiation and joint decision-making.
  3. Reflective Remix: After the first round, switch to competitive rules to experience how behavior shifts when the goal changes.

Debrief Prompts

After each round, invite participants to reflect:

  • What changed when we played to win together instead of win alone?
  • Where did we see generosity — or frustration — arise?
  • How does this mirror collaboration challenges in real work or school teams?

See Also

Other Games That Can Shift from Competitive to Collaborative

Below are several readily available games that can be converted from competitive to collaborative play, following the same spirit and learning goals as Broken Squares and your Collaborative Blokus design. Download a simple guide to these ten games reimagined.

1. Tetris (or Tetris-style puzzles)

Traditional goal: Outlast or outscore opponents.
Collaborative twist: Two or more players work together to fill the shared grid completely, alternating turns or controlling different shapes.
Learning focus:

  • Shared strategy and pattern coordination.
  • Collective problem-solving under time pressure.
  • Recognizing when to “sacrifice” an optimal move for a partner’s future opportunity.
    Facilitation tip: Use a shared physical Tetris puzzle or an online version projected for the group to decide each move collectively.

2. Jenga

Traditional goal: Be the last player to remove a block without collapsing the tower.
Collaborative version: The group works together to build the tallest stable tower possible — measuring height at collapse or setting a height/time goal.
Learning focus:

  • Shared risk management.
  • Communication and nonverbal coordination.
  • Learning when restraint supports group success.
    Variation: “Silent Jenga” (no talking) mirrors the Broken Squares communication challenge.

3. Dominoes

Traditional goal: Be the first to play all your tiles or score the most points.
Collaborative version: Players aim to use all tiles collectively, maximizing total coverage and connections before running out of legal placements.
Learning focus:

  • Systems thinking and planning ahead.
  • Balancing individual and group optimization.
  • Pattern recognition and negotiation of shared priorities.

4. Scrabble or Bananagrams

Traditional goal: Score the most points through individual word creation.
Collaborative version: Teams work together to fill the board with interconnected words, maximizing creative vocabulary rather than point totals.
Learning focus:

  • Creative collaboration and linguistic problem-solving.
  • Building on each other’s ideas rather than competing for space.
  • Shifting from “my words” to “our language.”
    Scoring alternative: Track total tiles used or board coverage percentage instead of individual points.

5. Connect Four

Traditional goal: Be the first to connect four of your own color.
Collaborative version: The team works together to create as many four-in-a-rows as possible of either color within a set number of turns.
Learning focus:

  • Pattern recognition and joint planning.
  • Discussion of how goals shift when success is shared.
  • The experience of switching from “blocking” to “building.”

6. Checkers or Chess (Collaborative Remix)

Traditional goal: Defeat your opponent.
Collaborative version:

  • Players form two teams (each side) and must agree on each move through discussion — requiring consensus and shared reasoning.
  • Alternatively, players play against the clock or a shared puzzle challenge, e.g., “Can we reach checkmate in the fewest moves possible together?”
    Learning focus:
  • Collective decision-making and strategic empathy.
  • Understanding others’ thought processes and tactical trade-offs.

7. UNO or Crazy Eights

Traditional goal: Be the first to empty your hand.
Collaborative version: Players win only when all cards from all players are gone — working together to sequence plays efficiently while managing wild cards strategically.
Learning focus:

  • Communication and coordination under constraint.
  • Managing frustration and adapting to changing conditions.
  • Turning competitive tools (like “Skip” and “Reverse”) into support mechanisms.

8. Carcassonne

Traditional goal: Build and claim territories for personal points.
Collaborative version: Teams collectively construct the landscape, focusing on completing as many cities and roads as possible before running out of tiles.
Learning focus:

  • Spatial negotiation and joint planning.
  • Thinking of territory as shared space rather than personal gain.

9. Settlers of Catan

Traditional goal: Be the first to 10 victory points through resource control.
Collaborative version:

  • Shared goal: build a thriving island where every player reaches a defined threshold (e.g., 7 points) through collective planning and trading.
  • Players may pool or redistribute resources to help the team reach “Island Prosperity.”
    Learning focus:
  • Cooperation in resource management.
  • Balancing short-term sacrifices for long-term shared gains.

10. Tic-Tac-Toe (for classrooms)

Traditional goal: Be the first to get three in a row.
Collaborative version: Students alternate X and O moves with the aim of filling the board completely without any three-in-a-row — transforming the goal from winning to balance and coordination.

Learning focus:

  • Pattern awareness and foresight.
  • The paradox of shared constraint and mutual success.

Meta-Pattern Behind the Conversions

Across all of these, the core pedagogical pattern mirrors the Broken Squares and Collaborative Blokus insight:

Competitive MechanicCollaborative Reframe
Outperform othersAchieve shared completion
Maximize personal gainMaximize collective efficiency
Block opponentsEnable teammates
Win aloneSucceed together

Appendix: Rules and Templates for Broken Circles and Squares

EXERCISES FOR COOPERATION 

This appendix contains a recommended series of skill-builders and exercises that prepare students for their first experience with working in groups at multiple learning stations with Complex Instruction materials. Students should understand that the purpose of these activities is to develop interaction skills necessaary for Complex Instruction.

LEARNING TO COOPERATE 

The most basic lesson that students must learn is to be sensitive and responsive to the needs of other members of the groOup. They must also learn that they are part of an interdependent group. What happens in the goup is important for them. There are two specific norms that express these ideas simply: 

  • PAY ATTENTION TO WHAT OTHER GROUP MEMBERS NEED. 
  • NO ONE IS DONE UNTIL EVERYONE IS DONE.

This is so different from conventional classroom behavior and so necessary for successful cooperative learning that we recommend that cach class start out with one such activity. We present two activities that can develop these norms: Advanced Broken Circles and Broken Squares. 

ADVANCED BROKEN CIRCLES 

The instructions to the participants and suggested discussion given below are those of the developers of Broken Circles, Nancy and Ted Graves (Graves & Graves,1985). Broken Circles is based on the Broken Squares game invented by DI. Alex Bavelas (1973). 

The class is divided into groups of 3-6 persons. Each person is given an envelope with different pieces of the circle. The goal is for each person to put together a complete circle. In order for this goal to be reached, there must be some exchange of pieces. Group members are not allowed to talk or to take pieces from someone else’s envelope. They are allowed only to give away their pieces (one at a time). 

Instructions to the participants 

Each of you will be given an envelope containing two or three pieces of a puzzle, but don’t open it until I say so. The object of this exercise is to put these pieces together in such a way that each member of your group ends up with a complete circle. There are a few rules to make the exercise more fun. 

  1. This exercise must be played in complete silence. No talking. 
  2. You may not point or signal to other players with your hands in any way.
  3. Each player must put together his or her own circle. No one else may show a player how to do it or do it for him or her. 
  4. This is an exercise in giving. You may not take a piece from another player, but you may give your pieces, one at a time, to any other members of your group, and other group members may give pieces to you. You may not place a piece in another person’s puzzle; players must complete only their own puzzles. Instead, hand the piece to the other player, or place it beside the other pieces in front of him or her. 

Now you may take the pieces out of your envelope and place them in front of you, colored side up. This is a group task, and you will have 10 minutes to make your circles. Remember, the task is not finished until each of you at your table has a completed circle in front of you. When all of you have finished, raise your hands. (If one group finishes before the others, suggest that they try to discover if there are any other ways they could put the pieces together to form different circles. 

Discussion 

When all groups have completed the task or the alloted time has ended, the teacher should help the participants to idenify some of the important things that happened, analyze why they happened, and generalize to other group learning situations. The following questons can serve as a guide to the discussion: 

  • What do you think this exercise was all about? 
  • How do you feel about what happened in your group today? 
  • What things did you do in your group that helped you to be  successful in solving the problem? 
  • What things did you do that made it harder? 
  • What could the groups do better in the future? 

Help participants to be concrete about what they did also abstract about the general implications of what they did; and the lessons they learned for the future. In Advanced Broken Circles, one player may block the task for the rest of the goup by completing his or her circle satisfactorily, but refusing to share some pieces with the others. This is analagous to a member of a cooperative learning group who tries to work alone and does not help other members. 

In the discussion be sure to come back to the two key behaviors that make a group successful: Pay Attention To What Other Group Members Need. No One Is Done Till Everyone Is Done. Point out when groups report these kind of behaviors or when they decide these behaviors would help them do better in the future. 

BROKEN CIRCLES

RULES

  1. Silence – no talking! 
  2. No pointing or other hand signals. 
  3. Each player puts together his Or her own circle. 
  4. No taking, only giving: One piece at a time. 

NEW BEHAVIORS

  • PAY ATTENTION TO WHAT OTHER GROUP MEMBERS NEED 
  • NO ONE IS DONE UNTIL EVERYONE IS DONE 

Simple Broken Circles (Groups of Four) 

Broken-Squares-and-Broken-Circles-Cooperation-Exercises-Instructions-and-Templates 1
Broken-Squares-and-Broken-Circles-Cooperation-Exercises-Instructions-and-Templates 2
Broken-Squares-and-Broken-Circles-Cooperation-Exercises-Instructions-and-Templates 3
Broken-Squares-and-Broken-Circles-Cooperation-Exercises-Instructions-and-Templates 4

BROKEN SQUARES

RULES 

  1. Silence – no talking! 
  2. No pointing or other hand signals. 
  3. Each player puts together his or her own square. 
  4. No taking, only giving; 
  5. one piece at a time. 

BEHAVIORS

  • PAY ATTENTION TO WHAT OTHER GROUP MEMBERS NEED 
  • NO ONE IS DONE UNTIL EVERYONE IS DONE 

BROKEN SQUARES

This is essentially the same game as Advanced Broken Circles. There are two main differences. It is designed to be played with groups of four only. The goal is for each person to put together a complete square rather than a circle.

Use the same rules as for Advanced Broken Circles simply substitutine the word “Square” for Circle” where it occurs.

See the following pages for for patterns for Broken Squares.

Put four of five piece of the square in each person’s envelope.. You will need a complete set of shapes for each four-person group. As in Advanced Broken Circles, one member of the group can assemble a square and think he or she is finished, this preventing the rest of the group from achieving a solution.

Broken-Squares-and-Broken-Circles-Cooperation-Exercises-Instructions-and-Templates 5
Broken-Squares-and-Broken-Circles-Cooperation-Exercises-Instructions-and-Templates 6

BROKEN SQUARES II

Broken-Squares-and-Broken-Circles-Cooperation-Exercises-Instructions-and-Templates 7
Broken-Squares-and-Broken-Circles-Cooperation-Exercises-Instructions-and-Templates 8

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