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Friday, August 8, 2014

Lesson #2 - The Fibonacci Breakfast

Lesson Objective: Students will use the Fibonacci Sequence to determine how many pieces of cereal are
Photo credit: Wikipedia
necessary to produce a satisfying bowl of breakfast cereal.

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

Task #1:
Use a cereal with individual pieces that are easily counted.
Good examples include choices such as Cheerios, Trix, Cocoa Puffs, Kix, Lucky Charms.
Bad examples include choices such as oatmeal, granola, Rice Krispies.

Your task is to determine, by adding pieces of cereal in increasing order of the Fibonacci Sequence, which number finally makes what you would consider to be a full bowl of cereal.

1. Place ONE  piece of cereal into your bowl.

  • Is this enough cereal to make a full bowl?
2. Next, place ONE more piece of cereal into your bowl (making a total of two pieces).
  • Is THIS enough cereal to make a full bowl?
3. This time, place TWO more pieces of cereal into your bowl (making a total of four pieces).
  • Is THIS enough cereal to make a full bowl?
4. Continue this process, each time adding the next Fibonacci number in the sequence until your bowl is filled to an acceptable level. How many numbers did it take? Was it more or less than you predicted before you began?

Task #2:
In this task your job will be to predict which exact Fibonacci number will represent the correct number of pieces of cereal necessary to make a full bowl.

For example, are 55 pieces enough? What about 89? Something more than that? This task differs from Task #1 because your answer to Task #1 will not likely be an actual Fibonacci number. For this task, you are predicting, using only the numbers in the sequence, how many pieces are necessary to fill a bowl.

Make a prediction, then count that many pieces into your bowl. If you happen to be incorrect, just change your prediction and keep trying!

Extension activity: Try changing cereal. How does changing the cereal type and/or size affect your answer to this task?

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