As students practice and master math concepts that they first learned using the Montessori manipulatives, they transition to solving problems on paper alone. This is called the Passage to Abstraction. Montessori materials help children intuitively understand what they are doing when they solve arithmetic problems such as the one above, and helps them carry that understanding into their abstract work.
As Upper Elementary students complete their passage to abstraction for arithmetic operations, they review and extend these ideas by learning several ways to perform those operations. Many Upper Elementary students have been working especially hard on these methods over the past weeks, working with 3+ digit addition, subtraction and multiplication problems. Above, the same multiplication problem has been worked using four different methods, or algorithms. This work also prepares students for more advanced math topics such as decimal operations, ratios and proportions.