\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016a.00420}
\itemau{Davis, Marsha}
\itemti{Modeling with sequences.}
\itemso{Consortium 108, 17 p., pull-out section (2015).}
\itemab
From the text: In Activity 1, students use two types of sequences to model population growth over time. The assumption that population grows by a constant amount each year leads to an arithmetic-sequence. A more realistic assumption that population grows by a constant annual percentage leads to a geometric sequence. The context in Activity 2 is credit-card debt. In the first scenario, no interest is charged and the \$ 200 payments lead to debt balances that form an arithmetic sequence. In the second scenario, interest is charged on the balance. In this case, the debt balances form a mixed sequence (a combination of arithmetic and geometric sequences). In Activity 3, students work with sequences that describe the rows of Pascal's triangle. A search for efficient formulas to calculate various terms in Pascal's triangle leads to several of Pascal's identities, which appear in his ``Treatise on the Arithmetical Triangle". Finally, the connection is made between the terms in the $n$th row of Pascal's triangle and combinations ``$n$ choose $k$" for $k=0$,\dots $n$. Then, students use the rows of Pascal's triangle to construct probability models for the number of heads in $n$ flips of a coin.
\itemrv{~}
\itemcc{D80 I30 K20 M10}
\itemut{sequences; student activities; teaching units; arithmetic sequences; geometric sequences; recursion; mathematical model building; real-life mathematics; mathematical applications; population growth; spreadsheets; graphing calculators; mixed sequences; Pascal's triangle; probability; teaching guides; worksheets}
\itemli{}
\end