I moved up to 4th grade this year, so this is my first time teaching double-digit multiplication in quite a while. We learned several strategies (using arrays, partial products, or breaking apart the factors) before moving to the traditional algorithm. I have two students that just cannot figure out the algorithm--any ideas? The 5-8 grade math teacher expects them to be able to do it this way.
Have you tried breaking it down to a simpler skill, first? For example, start with a 2-by-1 digit multiplication problem, show them the expanded (partial products) algorithm side by side with teaching them the traditional algorithm. Have them reach mastery with that, because then, the second set of steps in a 2-by-2 digit multiplication problem is just that - another 2-by-1 digit (54 x 32 is really 54 x 2 plus 54 x 3 [tens, hence the placeholder 0]).
But make sure they know that the second time you multiply, it is by a digit in the tens place and that is why you first put a zero in the ones place of the product.
Yup. Don't have them leave an "x" there or just randomly put a 0 there without knowing why it's there! (Funny enough, I'm doing 2/3/4-digit times 1-digit right now with my fourth graders...this is always one of my favorite topics and I love helping them make the connections between the different strategies and understand why they do each step...most have just learned them as meaningless steps before).
I'm with you, mathmagic. I hate when teachers just go through procedures for multiplication and leave it at that.
For what it's worth, I'd say you should just get them to the partial product method, and if they can't go beyond that this year, they can't go beyond it. The "standard algorithm" is probably just too abstract for those kiddos now. If the 5th grade math teacher needs them to do the standard algorithm, let them get it.
Try turning lined paper sideways so you have 'columns'. Set up your problem with digits in 'place value' columns. When your kiddos move to multiplying the tens, it's more visible that they are in the next place value....and would need the 'place holder zero' to indicate that they multiplied by tens.
