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Lesson objective: Understand that there are two unit rates associated with quantities a and b in a proportional relationship: "a per one b" and "b per one a."
Students bring prior knowledge of unit rate from 6.RP.A.2. This prior knowledge is extended to writing a unit rate in two different ways as students use ratio tables and keep track of proper units. A conceptual challenge students may encounter is keeping track of the units properly.
The concept is developed through work with ratio tables, which helps students keep track of the original ratio, the units, and the factor to divide the components of the ratio by.
This work helps students deepen their understanding of equivalence because the two unit rates are equivalent ways of writing the same ratio.
Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they explore the truths of the four children's statements. They can recognize correct and incorrect examples of unit rate. Students also engage in Mathematical Practice 7 (Look for and make use of structure) as they step back for an overview and shift perspective to write a unit rate in two equivalent ways.
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