Subtraction with Borrowing Done Two Ways

Many parents are scratching their heads as different methods of subtraction with borrowing are introduced in schools.  I will explain the common core method here and hopefully shed some light on the process.

Subtraction with borrowing using the traditional method goes like this:

I introduced this in my last post.  With the traditional method a 10 is borrowed from the 84 and added to the 4 to become 14.  This is the method that most parents are familiar with.

Nowadays many schools are introducing common core subtraction with borrowing which looks more like this:

This method has more to do with place value.  The first step that the student must undertake is expanding the number 625 to 600, 20 and 5.  Also, the student needs to expand the number 186 to 100, 80 and 6.  Essentially writing out the 100’s 10’s and 1’s place.  As you can see from the chart the student then borrowed a 10 from the 20 and added it to the 5 to become 15.  From there the student then borrowed 100 from the 600 and added it to the 10 to become 110.  The problem is then solvable using subtraction from there.  The final step is to add 400+30+9=439.

Many students are very used to writing numbers out in expanded form so this type of problem solving should not be much of a stretch if this is a method they are comfortable with.  I personally prefer the more traditional method of subtraction with borrowing but this could just be because this is how I was taught in elementary school.  I think it is helpful to know both methods as schools are increasingly teaching different styles of problem solving to students.

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