CMS Curriculum Guide 2011-2012

Advanced Functions & Modeling

Unit Title: Sequences & Series
suggested time: 10days
Enduring understanding (Big Idea):
Sequences and series can be used to predict patterns. For example, arithmetic sequences can be used to determine the number of band members in a specified row of a pyramid formation.
Essential Questions:
  • What types of patterns can be modeled mathematically?
  • How can recognizing patterns help you solve real-world problems?

Recommended
Days / Textbook Alignment / Mathematical Objectives / Connections to 2003 Standards
2 days / 10-1 Sequences, Series, and Sigma Notation /
  • Investigate several different types of sequences
  • Use sigma notation to represent and calculate sums of sequences
/ 2.05 Use recursively-defined functions to model and solve problems.
  1. Find the sum of a finite sequence.
  1. Determine whether a given series converges or diverges.
  2. Translate between recursive and explicit representations

2 days / 10-2 Arithmetic Sequences and series /
  • Find the nth terms and arithmetic means of arithmetic sequences
  • Find sums of n terms of arithmetic series
/ 2.05 Use recursively-defined functions to model and solve problems.
  1. Find the sum of a finite sequence.
  1. Determine whether a given series converges or diverges.

2 days / 10-3 Geometric Sequences and series /
  • Find the nth terms and geometric means of arithmetic geometric
  • Find sums of n terms of geometric series
  • Find the sums of infinite geometric series
/ 2.05 Use recursively-defined functions to model and solve problems.
  1. Find the sum of a finite sequence.
  2. Find the sum of an infinite sequence.
  3. Determine whether a given series converges or diverges

1 day / 10-5 The Binomial Theorem /
  • Use Pascal’s Triangle to write binomial expansions
  • Use the Binomial Theorem to write and find the coefficients of specified terms in binomial expansions
/ 1.03 Use theoretical and experimental probability to model and solve problems.
f. Apply the Binomial Theorem.

Vocabulary:

CMS Curriculum Guide 2011-2012

Advanced Functions & Modeling

sequence

term

finite sequence

infinite sequence

recursive sequence

explicit sequence

Fibonacci sequence

converge

diverge

series

finite series

nth partial sum

infinite series

sigma notation

arithmetic sequence

common difference

arithmetic means

first difference

second difference

arithmetic series

geometric sequence

common ratio

geometric means

geometric series

power series

exponential series

Euler’s formula

CMS Curriculum Guide 2011-2012

Advanced Functions & Modeling

Resources:

Glencoe McGraw-Hill (TE) Precalculus

Teacher Works Plus Precalculus

Formal Assessments:

  • Quizzes
  • Review Quiz (Practice Test)
  • Unit Test

connected.mcgraw-hill.com