GPS Pre-Calculus
(revised 06/11)
Unit Outline Title: Sequences and Series
Name of Lesson: Renaissance Festival (#1)
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 arithmetic sequences and arithmetic 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
warm-ups.
 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.

Archery Contest: This task launches the unit by reviewing students’ understanding of
arithmetic sequences and building on the knowledge to examine arithmetic series. Recursive
forms will be reviewed, as well as the explicit forms, both the connection to the slopeintercept form of a line and the common difference form.
o

Textbook: Pre-Calculus with Trigonometry: Chapter 14 (omit geometric and binomial
theorem sections)
Rock Throwing Contest: This task continues to work with students’ understanding of
arithmetic sequences and building on the knowledge to examine arithmetic series. Recursive
forms will be reviewed, as well as the explicit forms, both the connection to the slopeintercept form of a line and the common difference form. This task will introduce summing
series and summation notation. Properties of sums, including the impossibility of summing
an infinite arithmetic series, will also be addressed. (Question #3 moves beyond arithmetic
sequences and series and can be used as an extension)
o
Textbook: Pre-Calculus with Trigonometry: Chapter 14 (omit geometric and binomial
theorem sections)
Resources:

Concept Map Sample

Vocabulary Cards sample for word wall or KIM

Nspire Lessons

http://www.purplemath.com/modules/series4.htm

http://www.regentsprep.org/Regents/math/algtrig/ATP2/ArithSeq.htm

http://mathworld.wolfram.com/ArithmeticSeries.html

http://www.ucl.ac.uk/Mathematics/geomath/level2/series/ser5.html
CCSD Version Date: 06/11

http://www.columbia.edu/itc/sipa/math/summation.html
Differentiation:
 Both differentiation and extensions are provided within the tasks.
For this Lesson:
 Calculator, graph paper
Vocabulary:
 Arithmetic sequence
 Arithmetic series
 Common difference
 Expllicit formula
 Finite series
 Infinite series
CCSD Version Date: 06/11
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Limit of a sequence
Partial sum
Recursive formula
Sequence
Summation notation
Sum of finite arithmetic series
Terms of a sequence