Students compute multiples of 11, 111, 1111, 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 19 - 22 from the attached Student PDF file for the class

During the Activity

Distribute the pages to the class.

Follow the activity procedures:

Multiply single digit and two-digit numbers by 11 and record the products

Observe that the product is 10 times the number plus the number itself

Multiply other numbers with 11 and predict the result

Use the calculator to verify the prediction

Multiply two-digit numbers with 111 and note that the product is 100 times the number plus 10 times the number plus the number itself

Recognize the fact that when you multiply 111 by any two-digit number with a digit sum less than 10, the thousands digit of the product is the same as the tens digit of the given number, the hundreds and tens digits of the product are the sum of the digits of the given number, and the ones digit of the product is the same as the ones digit of the given number

Multiply two-digit numbers with 1111 and 11111 and generalize the patterns

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