# Arithmetic & Geometric Sequences: Putting It All Together

## Objective

SWBAT fluently use a variety of representations for arithmetic and geometric sequences. SWBAT to write recursive and explicit equations, construct graphs and tables, and identify common differences and common ratios.

#### Big Idea

Putting the pieces of the puzzle together. Students work in small groups to show what they have learned about geometric and arithmetic sequences.

## Opening

10 minutes

Today's class gives students the opportunity to demonstrate what they have learned about arithmetic and geometric sequences.  They will be working in groups of 4 and putting together posters that show all the ways they can represent sequences given one piece of information about the sequence.

I start class today by asking students: What are some things we can know about an arithmetic or geometric sequence?

I am looking for students to share out things like: a recursive equation, an explicit equation, a graph, a table, etc.  (All representations that we have been working on throughout the unit).  Next, I introduce today's task to students letting them know that they will look at a variety of sequences but will be given one piece of information about each one. From that one piece of information, they will work in small groups to include as many of the representations that they can from the list above.

## Investigation

40 minutes

We read through I Know, What Do You Know? together.  I break students into groups of 4 and let them know that they will be responsible for different representations on different sequences. For example, for the first sequence it might be one student's job to come up with the table, but on the second sequence, that same student might be responsible for the graph.   For this lesson, I use a customizable spinner app to determine which students will be responsible for which representation for each problem.  Once they are ready to start a new sequence, each student will spin the wheel to be assigned the representation they will complete for that sequence.  The options on the spinner are: a table with 5 terms of the sequence, a graph of the sequence, an explicit formula, a recursive formula, common ratio or difference and type of sequence.  Of course, the options for students will depend on what part of the sequence was given. For example, if the recursive formula was given, that will not be an option for that particular problem.

Students will put their representations on chart paper so everything they know about a sequence will be visible below the given information.  Depending on the size of the class, I might assign different groups to work on different problems.

## Discussion + Closing

10 minutes

I anticipate that this task will take most of the class for my students to complete. I will leave some time at the end of class for us to take a look at the posters and see where students disagree or got stuck.

At this point in the unit, I also want students to reflect on what representations are most challenging for them to come up with in regards to sequences. I'll pose the following prompt to students and ask them to write a written reflection: Which representation (table, graph, recursive, etc) is most challenging for you to figure out? Why? Which representation do you feel most comfortable with? Why?

## Citations

1. I Know What Do You Know? is licensed by © 2012 Mathematics Vision Project | MVP In partnership with the Utah State Office of Education Licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported license.

http://www.mathematicsvisionproject.org/secondary-1-mathematics.html