- Students will analyze and understand the lyrics of “Bob and Bob.”
- Students will study the formation of snowflakes.
- Students will explore the question, “Are snowflakes really unique?”
- Students will understand the physical and mathematical reasons that two snowflakes are unlikely to match.
- a recording of “Bob and Bob” by Trout Fishing in America
- copies of the lyrics (download lyrics)
- access to a computer with an internet connection
- paper and scissors (optional)
- borax, salt, or sugar, string, and a beaker of water (optional)
- Listen to the song “Bob and Bob,”and read the lyrics. Discuss and make sure that the class understands the song, particularly the idea that it is a song from a pair of identical “twin” snowflakes.
- Discuss the phrase, “We’re a one of a kind two of a kind freak of nature.” Would identical snowflakes be a freak of nature? Invite the class to investigate the question, “Are all snowflakes unique?”
- Study snowflakes with these websites:
- The reason snowflakes are probably all unique is that they are crystals which grow. Each additional bit of growth can be different in so many different ways that there are millions of possibilities by the time the snowflake has finished growing and falls to earth. The mathematical concept of combinatorics shows us that a series of possibilities in combination will result in an enormous number of possible combinations. This is why, with only a few dozen notes to work with, we can come up with millions of possible tunes.
- Try it out yourself! Make a paper snowflake or a virtual paper snowflake and count the number of design decisions made. You can have everyone cut together as a class if you make paper snowflakes: “Make the first cut. Make the second cut. Make the third cut…” and so on till you’ve made 15 cuts. Compare the results: each snowflake in the class will be unique, since each one is the result of a single path through an enormous number of options.
- Try it another way: prepare a solution of borax and water, salt and water, or sugar and water in a beaker. Hang a string in the beaker and put it in a sunny windowsill. In a few days, the water will have evaporated and the string will have crystals on it. Examine the crystals with a microscope or magnifying glass to see the differences among the crystals.