The goal of this lesson is for students to encounter several situations where it makes sense to find the sum of a sequence, defined here as adding up the value of the terms of the sequence. At this point, the number of terms students need to sum is kept short since the summing is by hand. In a future unit students use polynomial identities to develop a formula to sum the first \(n\) terms of any geometric sequence.
The main activities in this lesson are meant to be relatively unscaffolded, giving students the opportunity to make sense of the problems using the tools they have worked with throughout this unit, such as tables, graphs, and equations (MP1).
Lesson overview
 11.1 Warmup: Math Talk: Adding Terms (5 minutes)
 11.2 Activity: Paper Trail (15 minutes)

11.3 Activity: A Threefold Design (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 11.4 Cooldown: Half the Homework (5 minutes)
Learning goals:
 Calculate the sum of a simple geometric sequence describing a situation without the use of a formula.
Learning goals (student facing):
 Let’s look at sequences and the sum of their terms.
Learning targets (student facing):
 I can determine the sum of a sequence representing a situation.
Required materials:
 Blank paper
 Scissors
Required preparation:
 Provide 1 piece of blank paper and 1 pair of scissors for every 4 students to act out the situation in the activity Paper Trail.
Standards:
 This lesson builds on the standard: CCSS.HSFLE.A.2MS.FLE.2MO.A1.LQE.A.3
 This lesson builds towards the standard: CCSS.HSASSE.B.4MS.A.SSE.4
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.