Lesson plan

4. Understand that some nonlinear functions are predictable (C)

teaches Common Core State Standards CCSS.Math.Content.8.F.A.3 http://corestandards.org/Math/Content/8/F/A/3
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: Understand that even though the rate of change varies, we can make predictions about nonlinear functions.

Students bring prior knowledge of making predictions for linear equations from 8.F.A.3. This prior knowledge is extended to nonlinear functions as students explore how nonlinear functions differ from linear functions. A conceptual challenge students may encounter is understanding that nonlinear functions are sometimes, but not always, predictable. 

The concept is developed through work with a graph, which indicates nonlinearity, because of discontinuity.  The concept is also developed through analyzing tables and looking to see whether rates of change are constant.

This work helps students deepen their understanding of functions, because the operations that occur in functions define whether a function is linear or nonlinear.

Students engage in Mathematical Practice MP.4 (model with mathematics) as they use tables and graphs to solve a real-world problem about saving money.

Key vocabulary:

  • function
  • linear
  • nonlinear
  • rate of change

Special materials needed:

  • graph paper