Squares and Triangles

Photo credit: Chad Raymond

Last week I taught a combined class of students from my undergraduate globalization course and from the digital materials and fabrication (DMF) program at the IYRS School of Technology & Trades. I used an exercise based the Stars and Triangles game that Tricia Stapleton wrote about in 2013. I’m calling my version Squares and Triangles. Here is how it works:


Divide students into small teams, each team represents a different country. Each team receives scissors, ruler, pencil or pen, glue stick, a copy of Specification Sheet 1, and several sheets of colored construction paper (each team gets a different color paper). Draw a grid on the board, with countries as rows and rounds as columns. For Rounds 1, 2, and 3, create separate columns for squares and triangles. “Total world production” is the bottom row. You will also need one template each of the square and the triangle, made out of heavy card stock or plastic, and a copy of Specification Sheet 2, for later use.

Round 1 – 1700 (mercantilism)

Countries believe that they should avoid imports, so each team produces two goods for its own market – squares and triangles. Teams have four minutes to produce squares and then four minutes to produce triangles. Goods must be produced one at a time—no cutting shapes from several pieces of paper stacked on top of each other, no use of a previously-made shape as a template to trace around. Using the ruler and pencil to diagram shapes to be cut is allowed. Each team must check finished goods against Specification Sheet 1 before each four-minute session ends, anything that does not precisely meet the specifications (we used a 1 mm tolerance) must be discarded. Finished goods that pass quality assurance are put in one place and discarded goods set aside.

Ask if there are any questions before starting the clock. At the end of eight minutes, tally the number of squares and triangles each team has produced and write those numbers on the board. Tally total world production at the bottom of the table. Award a prize to the team that has produced the largest combined amount of squares and triangles (I gave a chocolate Hershey’s kiss to each member of the winning team). Clear away all manufactured squares and triangles. Distribute additional sheets of construction paper if needed.

Round 2 – 1800 (comparative advantage):

Countries no longer believe that imported goods are automatically an economic threat and international trade is starting to expand. Each country now specializes in producing just one good—either squares or rectangles—for eight minutes. Each team decides whether it wants to produce squares or triangles, but whatever the choice, each finished good has to meet specifications. Anything that doesn’t meet the specifications has to be discarded. The team that produces the most squares or triangles wins the prize for this round. Give teams a few few seconds to decide whether to produce squares or triangles.

Tally each team’s production when eight minutes have elapsed. Write grand totals in the bottom row. Award prize. Note to students whether world production is higher than before, and if so, that this demonstrates the principle of comparative advantage. Clear away squares and triangles.

Round 3 – 1900 (industrial revolution)

International trade continues to increase, but two countries (I used England and Germany) have industrialized and are using machines to produce goods (at this point dramatically give each of the industrialized countries one of the templates). As in Round 2, each country specializes in producing either squares or triangles for eight minutes, and finished goods have to meet specifications. The team that produces the most squares or triangles wins the prize for this round. Tally production for each team on the board when time has elapsed and award the prize to the winning team. Did the industrialized countries out-produce the non-industrialized countries? Is total world production higher than before? Clear away squares and triangles.

Round 4 – 2000 (globalized economy)

Trade is now a global phenomenon and the production of goods has become internationalized—goods are no longer produced from start to finish in just one country. The globalization of trade has led to increased wealth and higher incomes for hundreds of millions of people. With more money to spend, people are no longer interested in buying the squares and triangles. They want the iHexagram or the iOctagram — a 6-pointed or 8-pointed star. (Give each team a copy of Specification Sheet 2; leave the templates with the two industrialized countries.)

No single country has all the resources needed to competitively produce the iHexagram or the iOctagram entirely on its own. It must trade with at least one other country for those resources so that it can produce 6-pointed or 8-pointed stars (or both) out of paper of at least two different colors. For example, if a team has blue paper, it might want to trade with a team that has green paper. [The easiest way to make a star is to continue producing triangles (or squares) as in the previous rounds, trade to get the same shape in a different color, and glue the two triangles (or squares) together. But let students try to figure this out for themselves.]

Teams that want to engage in trade have to agree on the terms—how much paper of one color to exchange for paper of another color. Invasion and conquest is not allowed. Give teams about two minutes to engage in trade negotiations and eight minutes to produce stars. Additional trade can occur during the eight minutes. As usual each finished good has to meet specifications or is discarded. The team that produces the most iHexagrams or iOctagrams wins the prize for this round. Discuss what happened in this round, and do a general debriefing about what students’ experienced.


  • The class had a total of twenty students divided into five teams of four students each. Each team had two pairs of scissors and one ruler, but use of the ruler consumed more time than the scissors. I recommend giving each team an additional ruler. If teams have more than four people, increase the number of scissors, pencils, and rulers. If one wants to add an additional element of trade, these tools can be initially distributed to teams unevenly and teams can be allowed to trade for what they think will benefit them the most.
  • The entire game lasted about an hour, without any real discussion between rounds. The game would probably work better in a longer class.
  • I spent $57 on materials, for which I hope to be reimbursed by my university. Buy more colored construction paper than you think you will need. I was continually distributing more sheets of it during the game.
  • Two IYRS instructors who were present very helpfully acted as quality assurance engineers. For each round, they circulated around the room, randomly checking teams’ output against specifications — which caused a fair amount of finished goods to be discarded. Graduate students, or even one or two undergraduates from class, could perform this task.
  • The additional supervision helped prevent cheating. Students will try to cheat — by starting ahead of time, by tracing, and by making goods that don’t meet specifications. This behavior can be used as a subject for discussion in the debriefing.
  • Total world production increased from round to round, which demonstrated comparative advantage and real-world growth of international trade over time. However, neither England nor Germany won Round 3 despite having the templates. The team of Spain, led by an IYRS student with expertise in fabrication, outperformed the industrial powers. This led to a discussion of automation vs. the knowledge base of skilled labor during the debriefing.
  • Out of the five teams, four quickly found trading partners in Round 4. China was slow to act and was initially left out in the cold. It eventually exchanged full sheets of paper with Germany. Germany could have forced China to manufacture squares and trade them for whole sheets of paper in another color. The Germany team did not recognize that it could have imposed unequal terms of trade on China. The institutionalization of global inequality through trade could have been a subject of discussion for the debriefing, but we didn’t have enough time.
  • The game worked well; students were excited and seemed to gain a better understanding of international trade.