##
* *Reflection: Modeling
Arithmetic Sequences - Section 2: Discussion/Notes

I used this lesson with my students to really introduce the idea of functions. We are following theUT Dana Center scope and sequence which in my interpretation starts with this unit because of the function concept. Just make sure that this is the focus of the following lessons. Instead of focusing on naked problems like some do I focused on contextual problems that emphasized understanding sequence s on a much deeper level. Here is a student sample showing that the recursive formula needs to be emphasizes. Also the excursive formula needs attention but later on in the unit students seems to grasp this concept.

# Arithmetic Sequences

Lesson 2 of 6

## Objective: SWBAT represent arithmetic sequences verbally, visually, in lists/tables, graphically, as a recursive rule/pattern, and as an explicit rule using Cornell Notes.

## Big Idea: Represent arithmetic sequences with various models using a fun cooperative sorting activity!

*80 minutes*

#### Quick Write

*10 min*

The point of this QW is to get them thinking of the vocabulary needed for the introductory unit. They will be building on preexisting knowledge developed from the previous lesson to help them understand the difference between recursive and explicit rules and use these terms throughout the lesson.

Students will enter the classroom and answer the following question in their binder or on a piece of paper (teacher choice, I have a required binder with Quick Write section they are graded on)

**"Describe the difference between recursive and explicit rules. How would you redefine them in your own words?"**

Student will have defined these terms in a previous lesson.

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#### Discussion/Notes

*30 min*

I have students take Cornell notes during this section with emphasis on understanding various models including verbal, visual, table graph and recursive rule. My video narrative explains why I choose to do this rule. I give time for questions written and a summary given at the end of the note taking section.

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#### Arithmetic Sequence Sort

*30 min*

During this section I have students work collaboratively in groups of 2-3 sorting cards to match correct models of arithmetic sequences together Prior to this time, I cut out the pieces of the Arithmetic Sequences Sort, where you can see the three completed sets. Once student think they have completed the task, I have students call me over to check their sorts. Here are some scaffolding questions I may need to give if the matches are not correct.

"What does this rule represent to you?"

"What is changing each time and by how much?"

"What are the factors involved and what which is dependent on the other?"

"Where would this data start on graph?"

"Do these pieces make sense together?"

Once correct, I have the students move on to the next activity.

#### Resources

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#### Closure/Recording

*10 min*

After completing the Arithmetic Sort activity, I have students fill out the arithmetic sequences blank template with the examples from the sort. They need to have one competed as an exit ticket, I can print off as many needed and if one group is working faster than another they can fill out multiple pages. These notes will be a model for the next lesson is arithmetic series and deriving the formula for arithmetic series.

#### Resources

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