# Arithmetic Series

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## Objective

SWBAT model arithmetic series verbally, visually, as a table, graphically, as an explicit rule and function and in summation notation.

#### Big Idea

Want your students to see connections between different models of arithmetic series and derive the arithmetic summation formula? You have come to the right place! Students will see the connection from various models using this lesson!

## Quick Write

10 minutes

The point of this Quick Write is to get students thinking about their prior knowledge coming into this section.  Place the following question on the board:

"Using your vocabulary list from the vocabulary lesson, what is the difference between sequences and series?"

I am looking for their vocabulary understanding and a few sentences using these words such as,  "a series is the summation of a sequence".  I discuss this as a class after they complete the Quick Write and also grade it during their binder checks after each unit.

## Discussion/Notes Using Previous Previous Knowledge

30 minutes

In this section I use the previous knowledge that the students have to discuss the differences between series and sequences.  I purposefully use the Louvre square pyramid problem from the arithmetic sequences lesson and develop it further into a series problem.  The students model series in various ways (MP#4) and derive the formula for summation of an arithmetic series.  Although this is not listed in the CCSS, the derivation of geometric series formula (A-SSE.B.4) is.  Deriving the formula for arithmetic series allows students the opportunity to see how to derive a formula and lends coherence when deriving the geometric series formula.

## Find Someone Who

30 minutes

During this section, students are given the attached handout and are asked to "Find Someone Who" can fill out a missing part of the 6 model representation sheet.  They can only use each person once and that person has to initial that section.  Once complete with each section, it is the students responsibility to check over the work of their peers.  If they do not agree, they need to correct an discuss with that person.  If they do agree they need to initial next to the section.  Once complete, students check their papers against a key and are responsible for fixing sections that are incorrect.

## Homework

10 minutes

The purpose of this assignment is to have the students think of the multiple representations for several application problems.  Students get to pick 2 of the 3 problems and fill out the 6 model template for the problems they selected .