Algebra I
Activity:
Double Tree
Posted on Apr 17, 2008
Topic: Polynomials
Students visually model the sequence 2^n for n = 1…8 by drawing line segments that represent a tree that doubles its height every year. They then extend the sequence backward though time over negative values for n.
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Activity Key Steps:
In this problem, students model tree growth using the sequence 2^n.
They continue by graphing line segments represent 2^n.
After building the sequence by hand, students will write it with sequence notation and create it numerically on a Lists & Spreadsheet page.
Students will graph a scatter plot of the data against the top of their trees.
This will confirm that this sequence models the heights produced by .
Students return to the Lists & Spreadsheet page and extend their sequence into the negative values. Students will see that the negative and positive powers of 2 are parts of the same sequence.
At the end of this activity, students will be able to graph the first 10 terms of a sequence of the form tn = a-n and model other real world applications that follow a similar concept.