Education Technology

Magic Nines

Published on 06/09/2008

Activity Overview

Students compute multiples of 9, 99, 999, and so forth, search for patterns in the products, and write generalizations of those patterns.

Before the Activity

  • See the attached PDF file for detailed instructions for this activity
  • Print pages 11 - 13 from the attached PDF file for the class
  • During the Activity

    Distribute the pages to the class.

    Follow the activity procedures:

  • Multiply numbers 1 - 12 by nine and record the products
  • Find the sum of digits in the products and observe that it is 9
  • Multiply numbers 1 - 5 by 9 and by 79 and record the products
  • Understand that in the product, the digit in the units and tens place is the number itself; and the digits in the hundredth and thousandth place are the product of 7 and the number
  • Predict the product of 9 and 79 with other single digit numbers and check the predictions
  • Note that the sum of the digits of each product is a multiple of 9, since 9 is a factor

  • Multiply 2 digit numbers by 99 and record the product
  • Realize that the product is 100 times the number minus that number
  • Use this statement to predict products

  • Multiply a 2-digit number by 999 and recognize that each product is 1000 times the first factor minus the first factor

  • Observe that when a single digit is divided by 9, the digit repeats itself after the decimal point
  • Notice that when a 2-digit number is divided by 9, the digit repeated after the decimal point is the sum of the digits of the original number
  • Divide a single digit number by 99 and observe that the decimal has the given number repeating
  • Divide a 2-digit number by 99, and observe that the decimal has those 2 digits repeating
  • After the Activity

    Students complete the activity pages and answer questions.

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