This activity is designed to help students visualize the distributive property as it relates to fives. The goal is to use fives-facts when more challenging facts like those with factors of 6, 7, and 8. For example, 6 x 7 can be visualized as 6 x (5 + 2) which is the same as (6 x 5) + (6 x 2) = 30 + 12 = 42 . This is one way to visualize this using the smiley face array, but the fives do come in handy no matter how you see it. Try it out. This is most useful for multiplication facts greater than 5 x 5.
I have to thank my friend, Turtle, for pointing this out to me several years ago. She's one of the smartest people I know.