Exponential Functions Unit Plan

Discovery Based Learning

___________________________________________________________________________________________________________

Classroom Starter -- Crittenden

As an intro investigation, I like to talk about the fable of the inventor of chess. Apparently he was given the option of whatever prize he wanted. He wanted one grain of rice for the first square on the board, 2 for the second, 4 for the the next and so on. The grains of rice doubled for each square on the chess board.

The adjustment I make is I change it to pennies instead of rice, and offer the choice between the chess board prize or 1 billion dollars. You could even change this to 1 quadrillion dollars, and it's still not even close! Most students jump at the 1 billion dollars prize until they start playing with the numbers, and see how quickly the numbers grow.

If you keep it as a rice problem, you could talk about the plausibility of his demand. How large would a pile of this much rice be? What would this do to the Indian economy?

___________________________________________________________________________________________________________

1.  Click here for an interactive by Ron Blond to investigate the graphs of exponential functions.

___________________________________________________________________________________________________________

2.  Click here to download "Exploring What Exponential Functions Look Like" -- McInnes

___________________________________________________________________________________________________________

3.  Algebra 2: Graphing Exponentials -- Nspired Learning Math Classrom

Students will investigate the graphs of the family of exponential functions f(x) = bx. As a result, students will:

  • Infer why the conditions b > 0 and b ≠ 0 are necessary.
  • Determine how the value of b affects the increasing or decreasing behavior of the function.
  • Determine the y-intercept, domain, and range.
  • Describe the end behavior.
  • State the equation of the asymptote.

___________________________________________________________________________________________________________