Teacher Resources for Instructional Planning


Precalculus Std 9: Solve applied problems involving sequences with recurrence relations. Determining characteristics of arithmetic and geometric sequences and series, including those defined with recurrence relations, first terms, common differences or ratios, nth terms, limits, or statements of convergence or divergence Expanding binomials raised to a whole number power using the Binomial Theorem

Lesson Plans Trout Pond This investigation illustrates the use of iteration, recursion and algebra to model and analyze a changing fish population. The Devil and Daniel Webster In this lesson, students will examine the use of a recursive sequence in a game between the devil and Daniel Webster Classic Approach Traditional development of arithmetic and geometric progression is presented. Squares Inside Squares (Sequences) In this lesson, students explore another geometric pattern as they investigate the pattern determined by the areas of squares inscribed in squares formed by joining the midpoints of the sides of the previous square. The sequence generated is a simple geometric one. One special feature of this lesson is the use of the TI-92, which is used to generate the data. Students generate both the explicit and recursive forms for the sequence. The TI-92 is optional. Explicit instructions on how to use the 92 and 83 are available. Chicago Public Schools Lesson for day 171 introduces Pascal's Triangle and then provides explanation in terms of combinations. Whelk-Come to Mathematics: Using Rational Functions to Investigate the Behavior of Northwestern Crows Students will make a conjecture, conduct an experiment, analyze the data, and work to a conclusion using rational functions to investigate the behavior of Northwestern Crows. Special Limits of Special Sequences This lesson discusses the limit of a group of special and important sequences. Fibonacci and Lucas Numbers This lesson introduces the Fibonacci and Lucas sequences with some interesting problems related to each. Limits of Infinite Sequences Very colorful lesson on convergence of sequences. Chicago Public Schools This lesson for day 169 works from the formula for the sum of any finite geometric series to derive the formula for the sum of an infinite geometric series. SOS Math This develops the sum of geometric series with examples and practice.

Resources: Sum of a Geometric Series This is a geometric representation of the sum of a series. Affine Recurrence Plotter This tool is a customized spreadsheet that is preloaded so that you can numerically investigate affine recurrence relations. This site also contains plotter. Emergence of Chaos A study of iterations with another quadratic equation f(x) = kx(1-x) was a cornerstone in a related development of the science of chaos Arithmetic Chains Students construct sequences and find the equation that predicts the nth term. This site is basic, but useful. Students can incorporate Excel spreadsheets. Binomial Theorem This is an explanation of the binomial expansion with practice problems. Binomial Expansion Explanation of the binomial expansion with examples Genetics: From Genes to Genome Link between genetics and binomial theorem Pascal's Triangle Color patterns in Pascal's Triangle Golden Ratio This is the Home page for Ron Knott's Surrey University web site on the Fibonacci numbers, the Golden section and the Golden string. SOS Math Discussion of limits of sequences with interesting examples. SOS Math This page offers an interesting problem on the limit of a sequence. SOS Math This lesson discusses the convergence of some other common series. Bouncing Ball Convergence This is very good presentation of the bouncing ball problem. It includes graphics, tables, and the physics of the problem.
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