Someone used the search terms “multiplication breakthrough” and landed on my site the other day. I don’t even remember writing anything like that, so I went back and reread the post I composed almost three years ago. Funny, I guess we didn’t stick with it because I don’t even remember doing that. However, we have had a new breakthrough just this school year. I had tried using flashcards in the past, but they didn’t really work. I don’t know whether it had more to do with his developmental level, his lack of focus, or what. But lately, they do work. Maybe it’s because I have changed my approach. For a while, we would do two or three cards until he knew them, then we would add one at a time, mixing them up sometimes to make sure he wasn’t just memorizing the order they were in. It worked! He now knows almost the entire deck, front to back. He’s very mathematically minded, so we have made it through five years of school without ever memorizing all the facts. He could always figure them out because he came up with a system. I had him explain it to me, and this is how he did it:
Two times a number is that number plus itself.
Four times a number is two times a number plus two times a number.
Three times a number is that number plus itself twice.
Six times a number is three times a number plus three times a number.
Five times a number is half of ten times that number.
Seven times a number is three times the number subtracted from ten times the number.
Eight times a number is two times the number subtracted from ten times the number.
Nine times a number is the number subtracted from ten times the number.
It seems crazy and burdensome, but he got rather fast at it, and now he has a very good sense of how numbers interact with each other. Word problems are easy for him because he knows how math works. Distributive property is easy for him for the same reason. Now, finally, he has his facts memorized, but I believe that he is better off for having to figure them out for the last five years.