Education Technology

From Numbers to Symbols to Graphs with a TI-92 plus

Published on 07/30/2005

Activity Overview

This activity examines students' understanding of sums, products, divisibility, and their effect on graphing polynomial functions.

Before the Activity

  • Download TI Connect™ using the TI connectivity cable
  • See the attached PDF file for detailed instructions for this activity
  • Print pages 1 - 6 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    In this activity, students will:

  • Study the divisibility tests for 6, 12, and 24
  • Understand the Divisibility by Product Theorem

  • Understand that 24 deducted from the product of four consecutive integers [none of them multiples of 5] results in a number divisible by 1000
  • Note that when 1 is added to the product, it becomes a perfect square
  • Observe that the product plus 1 is the same if the middle numbers are multiplied, lessened by 1, and then squared
  • Use factoring and discover numerical patterns for the solution
  • Examine a different approach using multiplication, make a conjecture from graphing and determine the reason for adding the extra '1'

  • Plot a graph of a function which is the product of four consecutive integers
  • Find the derivative of the function
  • Calculate its roots by equating the derivative to zero
  • Evaluate the function at critical values to find the maxima and minima

  • Examine the extensions of the problem and generalize the solution
  • After the Activity

    Review student results:

  • As a class, discuss questions that appeared to be more challenging
  • Re-teach concepts as necessary