Michigan League of Academic Games

~A Fish Story~ (All Levels)

One of the difficulties in teaching On-Sets to younger players is that many of them have not worked with abstract concepts or ideas much. The idea of what constitutes a set or how different sets might intersect or interact is difficult to grasp at first.

To help students along, we present the following fish story:

Imagine that all of these cards are fish. Some fish are red, some are blue, some are green, some are yellow, and most are a mixture of different colors. There's even one albino fish (the blank card). All of these fish live in a big lake, known as Lake Universe. The area outside of the lake is known as the Empty Set, and no fish live there. That's why we place the cards we don't use face down. It's easy to tell the Empty Set and Universe symbol apart, because if you try and fill the Empty Set with water, it all flows out the bottom.

Every solution that you can have in On-Sets can answer the question, "How many fish have...":

• Red union blue - "How many fish have red or blue"?
• Green intersect yellow - "How many fish have green and yellow"?
• Blue minus green - "How many fish have blue without green"?
• Yellow prime - "How many fish are not yellow"?

This story is by no means perfect, and the analogy breaks down at some more advanced points, but it does help On-Sets beginners attach concrete items to the abstract ideas involved in the game.

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