Introduction to Vertical Addition and Subtraction

When I introduce vertical addition and subtraction (done on different days because it's too much for one day!) I do it very concretely. We actually make the problem with base ten blocks and break apart our problem by place value. When we borrow a ten for the ones place, we actually take a rod out and replace it with ten units. Or when we carry a ten from the ones, we take ten units and turn them into a rod. It doesn't take long for the kids to understand why we're doing what we're doing. Soon we move to a written version with the place value broken apart. Finally, some students will move to the standard algorithm. They only make this move when they're successful with the broken-apart method. We continue practice with the vertical method until we've reached mastery. It's important to have these concepts mastered before we begin multiplication and addition!