Lesson plan

8. Understand that multiple functions can be described qualitatively (C)

teaches Common Core State Standards CCSS.Math.Content.8.F.B.5 http://corestandards.org/Math/Content/8/F/B/5
teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4
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Lesson objective: Extend understanding of behaviors of functions in order to compare functions.

Students bring prior knowledge of functions' behaviors from 8.F.B.5. This prior knowledge is extended to multiple functions as students describe and identify behaviors for comparison. A conceptual challenge students may encounter is differentiating between two functions presented together. 

The concept is developed through work with graphs, which provide a concrete model of the behavior of a function paired with approriate input and output labels.

This work helps students deepen their understanding of numbers because specific input-output pairs will highlight times when functions behave the same or differently.

Students engage in Mathematical Practice 2 (reason abstractly and quantitatively) as they examine multiple functions and their behaviors as they seek to compare the functions.

Key vocabulary

  • behavior
  • compare
  • constant
  • decreasing
  • function
  • greater
  • increasing
  • less