The Box Method is used to solve a multiplication problem by putting the numbers in expanded form and then solving the problem. Students like this method because the multiplication is broken down to simple multiplication facts one through nine, and then the zeros on the numbers are added up and moved to the back of the product. Of course in class, we discuss why we "add up the zeros,"because really we are multiplying the place values of the digits as well. For example 20 times 40 is 2 times ten and 4 times ten, so we do 2 times 4 and then ten times ten, then we complete the problem be doing 8 times 100. The answer would be 800.
This is the method that would be considered the "old math". This method is still acceptable and still the end goal for solving multiplication problems. This method is much faster than some others, but students have trouble memorizing the process to solve multiplication problems
in this manner, rather than understanding the meaning behind the process. This method is often the hardest for the students. To refresh your memory, here is an example of how to multiply a two digit number by a two-digit number using standard algorithm.
This method helps students to see the connection between the box method and the standard algorithm. This method is mostly used to demonstrate one digit by multiple digit multiplication. The following image explains the partial product method for solving multiplication problems using the partial product method. It is east to see the connection between partial products, the box method, and standard algorithm.
The above image was downloaded from yenacademy. (2019), and its licensing allows re-use. See Partial Product Multiplication.
Multiplying Powers of ten is also an important concept for parents and students to understand and the following video explains how this method works. Students need to understand why the rule is not simply multiply by ten is to put a zero on the end, but why this method works. This is a concept students must understand before they can use the box method to solve multiplication problems.