1. Understand the proportional relationship between quantities (C)
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Lesson Objective: Understand that an equation showing the proportional relationship between two quantities includes two variables and a constant.
Students will choose an equation that represents the relationship between and independent and dependent variable related by a unit rate. This task requires students to select the correct equation to relate the number of coaches and players in a soccer league as well as create a table of values to defend their thinking. Students often reverse this relationship, interpreting "Each coach works with 20 players as c=20p.”
Students bring prior knowledge of writing equations to represent relationships. This prior knowledge is extended to writing equations using two variables as students describe two quantities that vary together in a constant multiplicative way. A conceptual challenge students may encounter is writing a literal translation of “1 coach for every 15 players” as c=15p. This is a very common and persistent reversal.
This work helps students deepen their understanding of operations in general, and the inverse relationship between multiplication and division in particular.
Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they explain their findings during Inclass practice. They also look for structure in the equations they develop, interpreting the meaning of each component and of its position relative to the other components.
Key vocabulary:

equation

variable