Lesson plan

10. Filling swimming pools: compare behaviors of functions (A)

teaches Common Core State Standards CCSS.Math.Content.8.F.A.2 http://corestandards.org/Math/Content/8/F/A/2
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
teaches Common Core State Standards CCSS.Math.Practice.MP7 http://corestandards.org/Math/Practice/MP7
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Lesson objective: Solve a real-life problem by comparing behaviors of functions.

This lesson provides an opportunity for students to apply their knowledge and understanding of function behaviors to a real-life situation. Students are asked to decide which pool fills at a faster rate, which fills first, and who pays more to fill their pool.

Key Concept students will use: 

  • Graphing inputs and outputs as ordered pairs, or looking at the graphs of functional relationships, allows us to compare the behaviors of functions qualitatively. 

Skills students will use:

  • Compare the behavior of two functions represented as graphs.
  • Create the graphs of functions based on the description of the behavior of those functions.
  • Answer questions to compare the functions.

Students engage in Mathematical Practice 2 (reason abstractly and quantitatively) and Mathematical Practice 4 (model with mathematics) as they analyze the behavior of functions and create the models of functions.

Key vocabulary: 

  • behavior
  • compare
  • constant
  • decreasing
  • function
  • increasing