# Activities

• • • ##### Subject Area

• Math: PreAlgebra: Number Sense and Operations

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-30X IIB
• TI-30X IIS
• TI-30Xa
• TI-34 II Explorer Plus™

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.

• 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