Education Technology

# Activities

• ##### Subject Area

• Math: Algebra II: Polynomials

9-12

60 Minutes

• ##### Device
• TI-92 Plus / Voyage™ 200

TI Connect™

• ##### Accessories

TI Connectivity Cable

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

#### Activity Overview

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

#### Before the Activity

• 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