Pine Tree Number Patterns

4th Grade Activity - Teacher Directions


Background

The needles of the loblolly pines found in the Pineywoods always grow in bunches of threes. Other types of pines have needles that grow in bunches of two, five, or more. Is there a pattern to the numbers found in nature? An Italian mathematician named Leonardo Fibonacci noticed these numbers in nature in the 1200s while trying to mathmatically predict the number of offspring starting from one pair of rabbits. The sequence of numbers that emerged are numbers or patterns of numbers often found in nature. Looking for patterns is fun math activity. Students try to recognize the pattern in the sequence and complete the following the following number patterns.

Skills:

Mathematics: Number patterns, Addition of two and three digit numbers

Materials

Paper
Pencil
Chalkboard or overhead


Procedure
  1. Post the following number sequences on a chalkboard or overhead.
    Number sequence Answer
    2, 3, 5, ___, 13, 21, ___               8 and 34
    1, 1, 2, 3, ___, 8, 13, 21, 34, ___ 5 and 55
    55, 89, 144, ___, 377, 610, ___ 233 and 987
  2. Have students use paper and pencil to determine the missing numbers from the sequences. (Hint: The pattern is the same for all lines of numbers. The Fibonacci numerical pattern is computed by adding the previous 2 numbers in the sequence to get the next number.)

For example:

Start with 0 and 1, 

0 + 1 = 1,

1 + 1 = 2,

1 + 2 = 3,

2 + 3 = 5,

3 + 5 = 8,

5 + 8 = 13

The Fibonacci Numerical sequence follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, . . .  and continues to infinity.

Additional Activity

Have students brainstorm things they are familiar with in nature and themselves that have these Fibonacci numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, . . .) in them, or better yet, have them go outside and start counting. For example: people have 2 eyes (which is a Fibonacci number), 5 digits on each hand, the Iris has three petals forming upward and 3 petals forming downward, etc. Fibanacci patterns are noted in spirals on pinecones and sunflowers as well. [Note: There are exceptions to Fibonacci's sequence, however the Fibonacci sequence mathmatecially describes a commonly found pattern of growth of optimial leaf placement. This activity is not presented as a governing rule in nature, but a fun observation of patterns.]

Activity developed for TPWD by Vicki Almour.


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