Multiplying by Eleven and Eleven Divisibility (Oct. 19 - 25)

Multiplying by 11

The skill set this reinforces is simple addition but within seconds we end up with the product of any number and 11.

First, students write down any number of any number of digits.

Second, they repeat the number below the first but move the number to the left one "place." The ones digit of the second number is directly below the tens digit of the first number.

Third, the students add the two numbers.

All they have done is added one of their original numbers to ten of their original numbers (moving the number over one place has the same result as multiplying the number by ten). Since one plus ten is eleven, they have accomplished the product of their original number and 11.

Eleven Divisibility

Once the student obtain their product, they can now check to see if their answer is right by testing for divisibility by eleven. The skill set this reinforces is adding and subtracting integers; working with negative numbers.

The students take the first digit of their answer and subtract the second digit, add the third digit, subtract the fourth, add the fifth digit and so on.  If their final result is zero, 11, -11 or some multiple like 22 or -22, then they know their number is divisible by 11.

The attached pdf has examples of both multiplying by eleven and checking for divisibility by eleven.  Also, I have worksheets for practicing although a blank sheet of paper will suffice.

Please have the children practice and bring their work to class next week.