In this lesson, students continue to develop their ability to identify, describe, and model relationships with mathematics.
Previously, students worked mostly with descriptions of familiar relationships and were guided to reason repeatedly, which enabled them to see a general relationship between two quantities. Here, students are given tables of values and asked to generalize the relationship between pairs of quantities—by studying the values and looking for patterns (MP8), and by interpreting them in context (MP2). Some of the relationships they encounter here are novel or otherwise require perseverance and careful reasoning to pin down (MP1).
Lesson overview
 3.1 Warmup: Finding a Relationship (5 minutes)

3.2 Activity: Something about 400 (15 minutes)
 Includes "Are you Ready for More?" extension problem
 3.3 Activity: What are the Relationships? (15 minutes)
 Lesson Synthesis
 3.4 Cooldown: Labeling Books (5 minutes)
Learning goals:
 Identify and describe (orally and in writing) patterns in tables of values and in calculations.
 Use observed patterns to generalize the relationships between quantities and to write equations.
Learning goals (student facing):
 Let's use patterns to help us write equations.
Learning targets (student facing):
 I can use words and equations to describe the patterns I see in a table of values or in a set of calculations.
 When given a description of a situation, I can use representations like diagrams and tables to help make sense of the situation and write equations for it.
Standards:
 This lesson builds towards the standards: CCSS.HSACED.A.2MS.ACED.2CCSS.HSFLE.A.2MS.FLE.2MO.A1.CED.A.2MO.A1.LQE.A.3
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