When I started teaching 6th grade 22 years ago (Oh my goodness that was a long time ago!) I came across this cute little trick to multiplication. It was called Lattice Multiplication. If you are unfamiliar with the trick, you can google it. Yes, I taught it to my students for a couple of years. Yes, it was nice to finally have a way for some students to always get a multiplication problem correct. But that was back when I thought that correct answers was all that mattered.
After reading research and books regarding mathematical understanding I have a different opinion about Lattice Multiplication. John Van de Walle stated in one of his books that “Correct answers do not mean understanding”.
Does Lattice Multiplication teach anything about place value? No. Does it involve place value? Of course it does; that’s what makes it work. But unfortunately very few students can explain mathematically why it works. Therefore, let’s just not show it to students.