# Activities

• • • ##### Subject Area

• Math: PreAlgebra: Number Sense and Operations
• Math: Middle Grades Math: Number Sense

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-73 Explorer™
• ##### Other Materials
This is Activity 3 from the EXPLORATIONS Book:
Discovering Mathematics with the TI-73: Activities for Grades 7 And 8

## A Prime Investigation with 7, 11, and 13

#### Activity Overview

Students investigate the divisibility of 7, 11, and 13. They will also discover an interesting characteristic of six-digit multiples of 1001.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 25 - 29 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Choose any three-digit number, repeat the three digits in the same order to form a six-digit number
• Enter the number on the calculator and check if it is divisible by 7, 11, and 13
• Repeat the activity with other three-digit numbers
• Divide the six-digit number by the product of 7, 11, and 13
• Observe that the result of the division is the original three-digit number
• Multiply the product of 7, 11, and 13 with the three-digit number
• Observe that the result of the multiplication is the original six-digit number
• Write divisibility tests for 2, 3, and 5

• Divisibility by 7
• Take all but the last digit and form a number
• Subtract twice the units digit from the number formed
• Continue this process until the remainder is divisible by 7

• Divisibility by 11
• Take the sum of every other digit
• Take the positive difference in the two sums and see if the answer is divisible by 11
• #### After the Activity

Students will complete the Student Worksheet and analyze the results.

Review student results:

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