Introduction to Sequences

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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.

Big Idea

Are sequences just patterns? No, there is so much more!

Opening Activity

12 minutes

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.

Group Discussion - What Did You Notice?

15 minutes

Arithmetic VS Geometric Sequences

10 minutes
Arithmetic VS Geometric Sequences.docx page 1

Work Time

5 minutes

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