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# Comparing Sequences by Form and by Pattern of Change

Lesson 6 of 10

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

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.

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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).

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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, Share**s 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.

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#### Exit Ticket and Homework

*15 min*

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 **

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- UNIT 1: Thinking Like a Mathematician: Modeling with Functions
- UNIT 2: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable
- UNIT 3: Everything is Relative: Linear Functions
- UNIT 4: Making Informed Decisions with Systems of Equations
- UNIT 5: Exponential Functions
- UNIT 6: Operations on Polynomials
- UNIT 7: Interpret and Build Quadratic Functions and Equations
- UNIT 8: Our City Statistics: Who We Are and Where We are Going

- LESSON 1: Welcome to Algebra I!
- LESSON 2: Pre-Assessment of Skills
- LESSON 3: Visualizing the Standards for Mathematical Practice
- LESSON 4: BFFs: Domain and Range of Functions
- LESSON 5: The World's Language: Function Notation
- LESSON 6: Comparing Sequences by Form and by Pattern of Change
- LESSON 7: Which Came First the Chicken or the Egg? Inverse Functions
- LESSON 8: Functions in Everyday Situations: A MAP Project Challenge
- LESSON 9: Sorting Functions
- LESSON 10: What's Your Function?