49
Fibonacci
High school
• • • • • • • • • • • • • • • • • • • • • Objective • • • • • • • • • • • • • • • • • • • • •
Appreciate the use of letters to represent variables.
Explore number patterns arising from a variety of situations.
Interpret, generalize and use simple relationships, and generate rules for number sequences.
Express simple functions symbolically.
• • • • • • • • • • • • • • • Explanation of the activity • • • • • • • • • • • • • •
Use the calculator to generate the Fibonacci sequence.
While working on this activity, students will be developing skills of generalization and refin-
ing their methods of expressing mathematical rules.
• • • • • • • • • • • • • • • • • Using the calculator • • • • • • • • • • • • • • • • •
Calculator functions used: Addition, subtraction, multiplication, division,
last answer memory, Multi-line Playback
The Italian mathematician Fibonacci discovered this sequence:
1
,
1
, 2, 3, 5, 8,
1
3, 2
1
, 34, 55, 89,
1
44...
To generate a similar sequence, begin with two numbers and add them to get the next.
Continue adding the last two numbers to get the next term.
Let’s try making a regular series similar to the Fibonacci series above. First, select two
suitable integers.
Press the following buttons and then start operation.
Example:
Let’s try making our own similar sequence,
starting with 2 and 6.
[2, 6, ?…]
Adding the two starting numbers yields the third value
in the series.
2
6
[2, 6, 8, ?…]
The next value is the sum of the two terms preceding it.
Thus…
6
8
[2, 6, 8,
1
4, ?…]
Similarly, find subsequent terms in the series by adding
the preceding term and the one before it.
8
14
2+6=
DEG
6+8
DEG
8+14
DEG
Summary of Contents for EL-531RH
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