## Arithmetic VS Geometric Sequences.docx - Section 3: Arithmetic VS Geometric Sequences

# Introduction to Sequences

Lesson 1 of 15

## Objective: Students will be able to make use of structure to differentiate between types of sequences and also be able to explain how a sequence can be expressed as a function with a domain consisting of the positive integers.

*42 minutes*

#### Opening Activity

*12 min*

Pre-Class Preparation:

- Have the sequences cut up and ready to go (see sequences resource)
- I usually put mine in envelopes so that I can re-use them from year to year

- Have sticky notes ready for the student’s group descriptions

Entry Procedures:

As the students enter, I have them sit in collaborative pairs. My classroom is already set up for this –they are seated in like ability groups. Next, I hand out the envelopes and roll out their mission: *Group the “lists” into piles that share a common theme. Use a sticky note to create a name for the group and detail what they all have in common.*

As the students accomplish this task, I work hard NOT to answer student questions… especially ones that ask “Is this correct?” I usually smile and answer “Well, there could be A LOT of right answers depending on what you see!”

It usually takes the students 8-10 minutes to complete this task.

Phase #2:

After everyone is finished, I have all student pairs stand up and rotate around the room. I have tried this process two different ways: structured, and free roaming. I have seen much more interactive results with students who free roam in this activity. Even if the kids gravitate to their friend’s side of the classroom, typically they are more likely to discuss similarities and differences between their piles and the piles of their classmates. Occasionally, students will try to slip through the cracks and not visit other groups. However, as a teacher who knows students, you will know exactly who to watch for. I typically invite these students to roam around with me and talk about the piles that we see. This process should take no more than 4-5 minutes. The students will have a pretty good picture of the various groupings.

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#### Work Time

*5 min*

Circulate the assignment that you desire. I typically utilize my text book; however, Kuta Software provides excellent extension problems for the students. I have provided the link below as a potential resource.

http://www.kutasoftware.com/freeia2.html

*expand content*

*This activity gave me a great idea for using it as part of a lesson on sequences and series (my students are a bit farther along). I am going to put the sequences from the activity (and added a few more with fractions, decimals, and geometric series that converge (r<1) onto cards, then sets of directions (what type is it? explicit formula? implicit formula? 20th term? sum of first 15 terms, etc) onto another set of cards. A student randomly picks one card from each pile, then everyone races to find the solution. | 3 months ago | Reply*

I used the opening activity today! It's the last day before a 5-day break, so I wanted an intro to sequences that wasn't a stand-and-deliver lesson.

The sorting went quickly. I took your advice about looking at structure rather than cosmetics, and only one group used positive/negative/bipolar (as they put it) for the categories.

My class is constantly asking for extra credit, so I extended the challenge - come up with a formula for as many as you can. Top 3 (out of 5) groups get bonus points. They know my bonus points are pretty non-consequential overall, 3 out of the 5 groups were up for the challenge and worked pretty well for about 20 minutes figuring out formulas.

I put the example "3n" on the board and showed 3, 6, 9, 12, ... so they would understand the directions. They were stuck on pretty simple expressions, so after a while I put up "4n+3": 7, 11, 15, ... and that got them thinking a bit more. Two of the groups even came up with one of the geometric sequences although I had only presented examples of arithmetic.

Thanks for a great day-before-break activity!

| one year ago | Reply##### Similar Lessons

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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!

- 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