The purpose of this lesson is for students to practice writing equations to define sequences given tables or visual patterns. The problems in this lesson are relatively unscaffolded compared to the work up until this point, which gives students ample opportunities to persevere in problem solving (MP1) and use appropriate tools strategically (MP5). For example, given a visual pattern students are asked to write definitions for two different sequences within the pattern, but they are not given any direct guidance on how to start. This leaves the choice to make a table or graph, or use another method to make sense of the relationship, up to the student. Students also translate between their equations and the situations to answer questions beyond the scope of the provided representations (MP2).
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
Lesson overview
 10.1 Warmup: Describing Growth (5 minutes)
 10.2 Activity: Finding Population Patterns (15 minutes)

10.3 Activity: Finding Square Patterns (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 10.4 Cooldown: Two Bacteria Populations (5 minutes)
Learning goals:
 Create equations for sequences representing situations.
Learning goals (student facing):
 Let’s decide what type of sequence we are looking at and how to represent it.
Learning targets (student facing):
 I can define a sequence using an equation.
Standards:
 This lesson builds on the standards: CCSS.HSFIF.CMS.FIFCCSS.HSFLE.A.1MS.FLE.1CCSS.HSFLE.A.1.cMS.FLE.1cMO.A1.IF.CMO.A1.LQE.A.1aMO.A1.LQE.A.1b
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