Comparing Sequences by Form and by Pattern of Change

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Objective

SWBAT identify sequences as functions and compare arithmetic and geometric sequences. SWBAT generate explicit and recursive definitions for sequences.

Big Idea

Students explore the Fibonacci sequence and other sequences to further their understanding of functions!

Entry Ticket: Sequences as Functions

15 minutes

For the Entry Ticket: Everything In Its Right Place: Sequences as Functions students look at a set of numbers and determine the pattern or rule that describes these numbers. This entry ticket serves two main purposes.

  • First and foremost, it provides students with another opportunity to practice work with functions and mathematical relationships from previous lessons and provides the teacher with valuable assessment data.
  • Second, the short activity grounds students in work they are familiar with to activate prior knowledge that they will be able to utilize to better understand sequences as functions. 

 

Active Note-Taking: Introduction to Sequences

30 minutes

After reviewing the entry ticket, I will lead the class through a short session of explicit instruction. I will use the Class Notes: Sequences - Form and Pattern to provide students with definitions and vocabulary for our investigation. During this time, my students take Two-Column Notes. When leading direct instruction I try to provide opportunities for students to engage in different domains of receptive and expressive language (listening, reading, speaking and writing). 

 

Interactive Quiz on Sequences

30 minutes

To gain some real time data on student understanding of sequences, I will now ask students to complete an interactive sequences quiz from the online resource, Mathopolis. My plan is to project the quiz on my Smart Board and go through one question at a time. I will have students complete mini Think, Pair, Shares for each problem with a protocol of 1 minute working on the problem on their own, 1 minute to discuss with a partner, and 1 minute class discussion. By using this protocol, I give students a chance to work individually and hear the perspectives of their peers. I find that giving the quiz likes this makes it more of a learning experience for my students. 

Later, I will grade the work students write in their notebooks for the quiz. In this case, I will assess the completeness of the work, rather than the number of problems correct, so that the grade reflects their entire performance on the interactive quiz.

Exit Ticket and Homework

15 minutes

To conclude the lesson, I show the class a video on Fibonacci sequences to the tune of Everything in its Right Place by the best band ever (Radiohead). The video acts as a hook, visualization and bridge from what we talked about in class to the Exit Ticket: Everything in its Right Place: Sequences as Functions:

 

 

My rationale for closing the lesson in this way us explained in this video:

 

My homework plan for tonight is to give students a Kuta Software worksheet providing more practice on arithmetic sequences. As an alternative, I may assign a pair of Khan Academy videos and ask students to take notes as a way to learn the material taught in class today from a different perspective. 

Alternative Homework Assignment: Students watch two Khan Academy videos. The first introduces and defines the concept of a sequence and the second video goes through examples of arithmetic sequences and the third reviews the concept and examples of geometric sequences.

 

First Video: Intro to sequences

 

Second Video: Arithmetic Sequence Examples