For those of you who teach grade levels involving multiplication of single or double digits, I'm both envious and sympathetic. Envious because multiplication is such a beautiful topic to cover if it's done well, and sympathetic because it's fraught with tips, tricks, and misinformation! It's very easy for us to teach our students how to solve multiplication problems using cool finger patterns or animal names, but those ways don't often allow themselves extension to greater and more complex mathematics.
Multiplication is, at its simplest, a shortcut. It is a way to conduct repeated addition very quickly and efficiently, and can be illustrated to students that way. 2 + 2 + 2 + 2 = 8, no problem. But 2 + 2 + 2 + 2 + 2 + 2 +....37 times? I think most students would welcome the chance to use a shortcut if presented with a problem like this! And single digit multiplication of numbers like two, three, and four is usually understood. It's those darn sevens, eights, and nines that give us fits.
When entering the two-digit multiplication realm, it's easy to see why our students struggle. Without a firm understanding of number sense, they consistently make mistakes that are avoidable with a place value approach to teaching two-digit multiplication. Tricks, rhymes, and finger patterns are great, but more appropriate for a time when students have already learned the concept of multiplication!