Multiplying by 11 Exploration

Multiplying by 11 has an evident pattern for our beginning multipliers.  They love the fact that they know how to multiply by a number larger than 10! We need to be sure that they are building a conceptual understanding of what 11 times another number looks like.

In addition, we want to give our students an opportunity to identify patterns.  Why does 11 times a number less than 10 ten give a double digit number of the other factor? Help them use visual pieces to make sense of it.  I think these 10 frames +1 make it easy to see, but maybe they have another idea.

Once they can identify why 11 x 3 = 33, take them on another exploration.

Can they find the pattern when you take 11 x a 2 digit number?  Can they figure out why it happens?

11 x 12 = 132

15 x 11=165

When multiplying 11 by a 2-digit number, the tens digit is the same as the hundreds digit in the product and the ones digit in the product is the same as the ones digit in the 2-digit factor.  The tens digit in the product is the sum of the hundreds and ones digit.

Don't tell your students this pattern.  Give them the tools to uncover it, and then let them use the visuals to see if they can find an explanation.  Many 4th and 5th graders should be able to explain.    What happens when the digits in the 2 digit number have a sum greater than 10?  Looking at the groups of 11 can they figure out what is happening?
Will this pattern continue into 3 digit numbers?  What stays the same? What changes?

This is not to be taught or used as "a trick." This exploration is to help students find patterns in numbers and place value and for them to be able to see why it is happening. It is important that we give them lots of opportunities to explore and make sense of the things that they find.