Education Technology

Magic Nines

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