Lesson plan

4. Ashley's bike ride: understand and describe the behavior of functions (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.MP2 http://corestandards.org/Math/Practice/MP2
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Lesson objective: Understand the behavior of a function.

Students bring prior knowledge of interpreting unit rates from 6.EE.C.9, as well as understanding of proportional relationships and points on a graph of proportional relationships from 7.RP.A.2d. This prior knowledge is extended to the behavior of a function as students examine the graph of a function to understand how the input and output variables relate to each other. A conceptual challenge students may encounter is simply looking at the shape of the graph and not understanding the relationship of the input and output variables presented. 

The concept is developed through work with graphs of a function, which gives a concrete model of the behavior of a functional relationship.

This work helps students deepen their understanding of functions because identifying input-output number relationships (number pairs) will help students identify key behaviors of functions.

Students engage in Mathematical Practice 2 (reason abstractly and quantitatively) as they examine graphs of functions and identify input-output pairs to describe the behavior of a function.

Key vocabulary:

  • behavior
  • constant
  • decreasing
  • function
  • increasing
  • input 
  • output