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