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# Modeling with Sequences and Series

Lesson 11 of 13

## Objective: SWBAT differentiate sequence from series problems and use the appropriate formula to solve sequence and series application problems.

#### Share Out

*20 min*

Posters (or videos) from the Financial Series Project are due, so we will take the first 15 minutes to hang the posters and share any videos that were created by the class. Posters go up on the bulletin board immediately and videos will be shown in class. I ask students to share a link to the video via Edmodo so that students can view it at home too. This final presentation of the problem solving process allows students to construct a viable argument for their method of solving and reflect on why it makes sense. [MP3]

*Note: Samples of student work coming soon!*

#### Resources

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#### Summary of Concepts

*30 min*

Before shifting to applications of sequences and series formulas, we make a "foldable" that summarizes all the major concepts of the unit on a single sheet. This type of summary activity is always popular with my students because it helps them understand how all of the concepts of the unit fit together.

Students begin with a blank 8.5" X 11" sheet and fold according to the instructions provided in this video and the photos, sequence series foldable outside and sequence series foldable inside. The foldable summarizes information about arithmetic patterns on the left and geometric patterns on the right. There are separate rows for connection to functions, sequences formulas and series formulas.

The final product supports the review work that students will complete in preparation for the upcoming unit test.

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#### Application of Concepts

*40 min*

Students will use their foldable as they solve the Sequence and Series Applications problems. All possible problem types are presented and students must figure out whether the scenario is best modeled as a sequence or a series and then whether the situation is an arithmetic or geometric one. They interpret their mathematical results in the context of the situation and determine whether the results make sense. If not, they must make revisions to their model. [MP4]

Students work on these problems in their table groups for the remainder of class. As they do so, I circulate and point students to their foldable when they are stuck. [MP1]

Students complete any unfinished problems for homework, and check their work with the answer key on Edmodo.

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- LESSON 1: Introduction to Sequences
- LESSON 2: Arithmetic Sequences
- LESSON 3: Geometric Sequences
- LESSON 4: Modeling with Sequences
- LESSON 5: Quiz on Sequences and Intro to Sigma Notation
- LESSON 6: Introduction to Series and Partial Sums
- LESSON 7: Arithmetic Series
- LESSON 8: Geometric Series
- LESSON 9: Financial Series Project (DAY 1)
- LESSON 10: Financial Series Project (DAY 2)
- LESSON 11: Modeling with Sequences and Series
- LESSON 12: Review of Sequences and Series
- LESSON 13: Sequence and Series Test