## Subtraction with Regrouping

22 Oct

Subtraction can be very difficult for students when they have to regroup (borrow).  I learned the algorithm as a child with no understanding of what I was doing.  We spend weeks practising and memorizing it.   It actually wasn’t until I became a teacher that I really understood what was happening when I “borrowed”.

These days we want the children to really, truly understand the concept of regrouping, adding, subtracting, multiplying and dividing.  We do more than teach algorithms.  We want the students to try to come up with ways to solve problems on their own, using what they already know.  Sometimes they come up with methods I’ve never thought of!  Students also need plenty of mental math strategies for the four operations but that’s a topic for another post.

I’m going to start with the traditional algorithm that most of us learned in school.  Here is a video using a two digit number and a single digit number.   Unfortunately I can’t figure out how to rotate the video – sorry!

Here is a video extending this method to 3 digit numbers:

There are many other ways to subtract.  The following photos show some of the ways that are possible (taken from Dr. Marion Small Big Ideas from Dr. Small):

Word problems create some problems for students as they try to figure out which operation to use.  Even is a child know how to add and subtract they need to be able to suss out what they need to do first.  Here is a chart that demonstrates the different structures of word problems:

The most difficult problems for students are the unknown parts problems in the bottom two rows.  I am going to try to use a method I’ve learned that is used in the Singapore Math program of using rods to represent problems.  I’ll keep you posted on how that goes.    This video shows one type of problem solved using rods.  I do not have this program but would draw the rods.