GPS Pre-Calculus
(revised 06/11)
Unit Outline Title: Sequences and Series
Name of Lesson: Fascinating Fractals (#2)
Suggested Time: 180 minutes
Standards:
MM4A9. Students will use sequences and series. a.
Use and find recursive and explicit formulae for the terms of sequences. b.
Recognize and use simple arithmetic and geometric sequences. c.
Find and apply the sums of finite and, where appropriate, infinite arithmetic and geometric series. d.
Use summation notation to explore series.
Essential Question(s):
Unit: How do I add up all those numbers?
Lesson:
 What is the connection between geometric sequences and geometric series?
Assessment Description/Performance Task:
Constructed response Informal assessment
Performance task Selected response
Brief Description:
 Ongoing informal/formal assessments created by teacher such as exit cards, quizzes, and warmups.
 Use of performance tasks below provided at www.georgiastandards.org
Pre-Calculus Framework.
Instructional Methods
Design your lesson to include a combination of performance tasks and direct instruction that addresses all relevant standards. The following suggestions and information about each task can assist you in designing your lesson.
 Koch Snowflake : This task reviews students’ understanding of geometric sequences and builds on that knowledge to examine geometric series. Links are also made to summing series and horizontal asymptotes. o Textbook: Pre-Calculus with Trigonometry: Chapter 14 (omit binomial theorem section)
 Sierpinski Triangle : This task continues to work with geometric sequences and series. o Textbook: Pre-Calculus with Trigonometry: Chapter 14 (omit binomial theorem section)
 More with Geometric Sequences and Series : This task takes a look at the how the common ratio impacts the terms of a geometric sequence and its sum. o Textbook: Pre-Calculus with Trigonometry: Chapter 14 (omit binomial theorem section)
Resources:
 Worksheet: Arithmetic Series
 Worksheet: Geometric Series
 Worksheet: Snowflake Lab


Nspire Lessons http://www.purplemath.com/modules/series5.htm
-geometric series
 http://www.regentsprep.org/regents/math/algtrig/atp2/geoseq.htm
-geometric series
 http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Infinite%20Geometric%20Series.p
df practice
 http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54d_geom.htm
-lesson
Differentiation:
 Both differentiation and extensions are provided within the tasks.
CCSD Version Date: 06/11

For this Lesson:
 Calculator with statistical capabilities, normal tables (optional)
Vocabulary:

 Geometric sequence
 Sum of a finite geometric series
 Sum of an infinite geometric series

Common ratio
Convergent geometric series
 Divergent geometric series
CCSD Version Date: 06/11