## Opening Analysis.docx - Section 1: Opening Analysis

Investigating Infinite Geometric Series

# Investigating Infinite Geometric Series

Unit 3: Sequences and Series

Lesson 10 of 15

Lesson 10 of 15

## Objective: Students will be able to dive into a study of the uniqueness of convergence of infinite geometric series.

## Big Idea: The last several lessons have been highly practical and focused on real world application. This lesson further emphasizes mathematical questioning associated with behavior of infinite geometric series.

Standards:

Subject(s):

Math, Number Sense and Operations, Algebra, Patterns (Algebra), Algebra, master teacher project, 11th Grade

*45 minutes*

3

#### Homework Time

*15 min*

Circulate the homework sheet. This emphasizes a wide variety of problems:

1) Finding if a series has a sum

2) Finding the sum of the first several terms

3) Finding the sum of an infinite number of terms

4) Real World Application (bouncy ball problem)

- Requires the students to Reason Abstractly (**MP 2**)

5) Making use of structure to analyze infinite arithmetic series (**MP 7**)

*expand content*

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

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- LESSON 1: Introduction to Sequences
- LESSON 2: Arithmetic Sequences and Series
- LESSON 3: Geometric Sequences and Series
- LESSON 4: Sequences and Series Battleship!
- LESSON 5: A Double-Dose of Series Application
- LESSON 6: Mortgages and Geometric Series DAY #1
- LESSON 7: Mortgages and Geometric Series DAY #2
- LESSON 8: Mortgages and Geometric Series DAY #3
- LESSON 9: Mortgages Wrap-up and Additional Scaffolding
- LESSON 10: Investigating Infinite Geometric Series
- LESSON 11: Using Sequences and Series to Make Connections
- LESSON 12: The Binomial Theorem
- LESSON 13: Sequences and Series Partial Unit Review
- LESSON 14: Sequences and Series Partial Unit Review II
- LESSON 15: Unit Test: Sequences and Series

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