This is a chart where students have a 3 digit number and they must multiply it by 1, 10, 2, 20, 3, 30, 4, 40, 5, and 50. By doing this, students will start to see the patterns when multiplying with zero in the corner. I usually start by showing them the first number times one, by ten, by 2, and by 20. By then they start to see that multiplying with the zero is not such a daunting task. I also show them how they do not need to multiply times the ones place AND the tens place and add the partial products, since one of the partial products is going to be all zeroes.
I did this with my fifth grade class as a review, since they had multiplied 3 digits times 2 digits in 4th grade. Some of my kids made remarks afterwards about how much more sense multiplying with zeroes made now.
To make it more "common core" I had them write in complete sentences on the back the pattern that they noticed, and how they would explain how to solve problems like these to a martian.