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Activity Overview

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

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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
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During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

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 digitTake the positive difference in the two sums and see if the answer is divisible by 11
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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