Linear & Exponential Functions

Positioned inside the framework of linear and exponential functions, this lesson is more of an investigation into the effects of changing variables and constants inside an expression. The author takes familiar formulas, those for triangle perimeter and compound interest, and teases out how changing variable values influences overall expression results while leaving other individual parameters unchanged. Applets built around the specific examples in the lesson give some concrete meaning to the abstract questions and answers and turn this presentation into a hands-on math experiment.

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CCSS: Adaptable
Instructional Ideas

  • Consider using the compound interest applet in a lesson on budgeting and investing, allowing the class to quickly see the differences in length of investment and compounding period
  • Link presentation to class website for on-demand homework help in a traditional class or pre-class viewing in the flipped classroom model
  • Have learners develop their own problems involving geometric formulas and changing quantities similar to the first example, then trade problems to work and critique
Classroom Considerations

  • Presentation file requires the ability to open a *.pptx file
  • Embedded applets require Internet connection and updated Java player
  • Young mathematicians with a more concrete learning style might benefit from using the applets to experiment with different values before summarizing effects on the expressions given, rather than after as is ordered in the lesson
Pros

  • Embedded applets seamlessly and effectively bring technology into the lesson
  • Emphasis on trends and things that remain constant as well as things that change
  • Answers focus on what makes sense in plain English, instead of algebraic manipulations
Cons

  • No printable notes or guided practice problems provided
  • Examples are numbered 2 and 3 instead of 1 and 2
  • No discussion of inverse and direct relationships or magnitudes of increase and decrease (linear vs. exponential in particular)
Common Core