Unit 4: Sequences and Series
In this unit students will explore sequences and series, specifically arithmetic and geometric sequences and series. Students will learn how to write write sequences in recursive and explicit notation. They will also learn sigma notation and evaluate series in sigma notation. Students will also use Microsoft Excel to build recursive patterns.
Prerequisite Units: None
Materials needed: Computer (Microsoft Excel), Calculator
Approximately 17 Days needed
Prerequisite Units: None
Materials needed: Computer (Microsoft Excel), Calculator
Approximately 17 Days needed
4.0: Skeleton Tower Activity
In this lesson students are introduced to the patterns. Their task is to develop a formula in explicit notation for how many blocks are needed to build a skeleton tower. I got this activity from a session at an NCTM conference in 2017 and it is a perfect activity for the start of this unit (Mathematics Assessment Project (https://www.map.mathshell.org/tasks.php?unit=HE07&collection=9). Students are put into groups of 34 to work through each task. Then they create a presentation where they walk their classmates through each exercise and explain how they determined their explicit formula. I give students enough blocks to build a skeleton tower with a spine of height 6, but not more than that. Not all groups complete their final exercise in the time they are allotted. For those groups they have to explain their ideas to the class and where they are stuck as part of their presentation.
Skeleton Towers Activity Task Sheet

Mathematics Presentation Rubric



4.1: Introduction to Sequences
Smart File Lesson 4.1

PDF of Lesson 4.1

Powerpoint  Recursive Notation for Sequences
Problem Set 4.1

Problem Set 4.1 Solutions


Lesson 4.1 Video 

4.2: Arithmetic Sequences
Smart File Lesson 4.2

PDF of Lesson 4.2


Powerpoint  Arithmetic Series
POWERPOINT 
Problem Set 4.2

Problem Set 4.2 Solutions


Lesson 4.2 Video 

4.12 Review Activity
In this activity all students get a small white board and marker. A problem is flashed on the screen with a timer for 2 minutes. Students have the 2 minutes to work through the problem and earn a point from the teacher. The goal is to gather as many points throughout the class period as possible. At the end of the two minutes the teacher can move to the next slide and reveal the answer for those who didn't earn the point in the designated time. A student can earn an additional point for explaining their answer to the class.
Review Smart File

Review PDF


4.3: Sums of Arithmetic Series
Smart File Lesson 4.3

PDF of Lesson 4.3

The Story of Gauss Article (NCTM)

Problem Set 4.3

Problem Set 4.3 Solutions


Lesson 4.3 Video 

4.4: Geometric Sequences and Series
Smart File Lesson 4.4

PDF of Lesson 4.4


Powerpoint  Geometric Series
POWERPOINT 
Problem Set 4.4

Problem Set 4.4 Solutions


Lesson 4.4 Video 

4.34 Review Worksheet
Review Worksheet

Review Worksheet Solutions


4.5: Excel Tutorial  Analysis of Mom vs. Dad
Lesson 4.5 Smart File

Lesson 4.5 PDF

Lesson 4.5 Excel File (Complete)

Problem Set 4.5

Problem Set 4.5 Solutions



Lesson 4.5 Video 

Lesson 4.6: Geometric Sums
Lesson 4.6 Smart File

Lesson 4.6 PDF



Powerpoint  Finding the Golden Ratio
POWERPOINT 
Problem Set 4.6

Problem Set 4.6 Solutions


Lesson 4.6 Video 

Additional Resources
Problem Sets by Nils Abel  they are labeled Unit 6 in his materials instead of Unit 4

Problem Set Solutions
