Ordering at the Place Value Cafe: An Interactive model of base 10 subtraction with regrouping.
The application gives students a complete explanation of base 10 subtraction with regrouping. Students can either enter or have the application generate an arbitrary subtraction problem with up to four digits. They can then step through a fully modeled and explained solution to the problem.
The model is based on "order filling." We view the minuend (the number we're subtracting from) as a restaurant whose items are place values. It has so many ones, so many tens, and so on. The subtrahend (the number we're subtracting) is viewed as a set of orders for place values -- so many ones, so many tens, and so on. The problem then is to fill the orders.
Like any restaurant it can sometimes happen that we run out of some item and have to prepare more. For example we might have an order for 5 ones and only have 2 ones. When this happens instead of cutting up potatoes to make french fries, we cut up place values. For example, we might cut up a ten to make 10 ones or, if we don't have any tens, cut up a hundred to make 10 tens and then cut up one of the tens. This is how we model regrouping.
As can be seen from the thumbnails the explanations at each step are given in three forms. A verbal explanation is given in the color coded box at the top of screen. A visual explanation is given below that and the usual digit manipulations associated with subtraction are shown in the bottom left part of the screen. Thus the algorithm as described in terms of digit manipulation is fully integrated with the intuitive model.
This application runs on iPads, Chromebooks, Macs, PCs, Smart Boards, and any other device with a reasonably up to date browser. Though it can be run from a web site, the application is fully self-contained and so can be downloaded to a device and run without Internet access.