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The Birthday Challenge

Overview: The focus of this lesson is linear and exponential growth.  Students in a 1st or 2nd year Algebra course are given a scenario about two different contribution plans for a child’s college savings within non-interest bearing savings accounts.  Students will build models of each savings plan and make predictions about the growth of each account.  By comparing and contrasting the two plans, students will gain an understanding of how quickly a value can grow exponentially.

Lesson Objectives

Curriculum Context

Systems Thinking Concepts

Students will be able to:

  • increase their ability to make accurate predictions regarding linear and exponential growth
  • determine the rate of change (patterns of growth) for both linear and exponential growth
  • compare and contrast linear and exponential growth
  • build computer models that demonstrate linear and exponential growth
  • state differences between the graphs of linear and exponential growth
  • demonstrate their understanding of why exponential growth increases so rapidly
  • This lesson focuses on these curricular benchmarks:
  • Recognize, describe, create and analyze patterns.
  • Show an understanding of exponential and linear functions by identifying rates of change.
  • Use and create tables, graphs, and symbols to describe relationships and to solve problems.
  • Explain how change in one quantity results in a change in another using graphs, tables, symbols and words.
  • Reinforcing feedback
  • Accumulation

 

Materials

Length

Systems Tool(s)

  • class set of computers or a computer lab with STELLA® installed
  • handouts of “The Birthday Challenge” packet
  • projector, if desired
  • calculator
  • Two hours and 45 minutes or 3 class periods
  • Behavior-over-time graphs
  • Stock/flow diagrams
  • Computer models

 

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