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