Lesson plan

1. Comparing costs: extend proportionality concepts to constant rate of change (C)

teaches Common Core State Standards CCSS.Math.Content.8.EE.B.5 http://corestandards.org/Math/Content/8/EE/B/5
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7
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Lesson objective: Extend understanding of unit rate for proportional relationships to rate of change for general linear functions.

Students bring prior knowledge of unit rate from 7.RP.A.2.B. This prior knowledge is extended to rate of change as students compare a proportional linear relationship to a non-proportional linear relationship. A conceptual challenge students may encounter is not all linear relationships are proportional, yet we can still use ideas from proportional relationships. 

The concept is developed through work with a table of values, which helps students to observe changes in input values and output values side by side, and facilitates understanding that these changes are related.

This work helps students deepen their understanding of operations because, whereas calculating unit rate only required division of any output value by its corresponding input value, calculating rate of change involves dividing the differences of output values and input values.

Students engage in Mathematical Practice 7 (Look for and make use of structure) as they identify the relationship between the changes in the input and output values, and use this information to find missing values in the linear relationship.

Key vocabulary:

  • equivalent ratios
  • non-proportional
  • proportional
  • rate of change
  • unit rate